THE DEEP2 GALAXY REDSHIFT SURVEY: DESIGN, OBSERVATIONS, DATA REDUCTION, AND REDSHIFTS^*

Spectroscopic redshift surveys have been a major gateway to understanding galaxy evolution. By locating each galaxy in both space and time, they provide the raw material for compiling a census of galaxy properties as a function of cosmic epoch and position in the cosmic web. Clustering measures derived from redshift surveys of sufficiently large volume—such as the correlation function, ξ(r_p, Π) diagram, and measures of the local overdensity of galaxies—probe the gravitational growth of structure. Pair counts contain information on merger rates, while satellite motions probe dark-halo masses and dynamics. When the galaxy sampling is sufficiently dense, groups of galaxies become well defined and allow the estimation of the number density of groups (constraining cosmology), as well as the determination of the environments in which individual galaxies are found. The spectra themselves can reveal a wealth of detail on emission-line strengths, stellar populations, star-formation rates, active galactic nucleus (AGN) activity, gas and stellar metallicities, internal motions, and dynamical masses. Finally, spectroscopic redshifts provide the fundamental data needed for calibrating photometric redshifts, which are the only way to estimate distances for the hundreds of thousands of fainter galaxies that are beyond the reach of current redshift surveys.

Pioneering low-redshift surveys out to z ∼ 0.2, such as the Sloan Digital Sky Survey (SDSS; York et al. 2000; Abazajian et al. 2003) and the Two Degree Field Survey (2dF; Colless et al. 2001) have demonstrated the value of mammoth samples of galaxies containing hundreds of thousands of objects. Huge samples enable finer slicing in redshift and galaxy-parameter space, reveal rare phases of galactic evolution, and provide sufficient weight to measure statistical scatter about the various galactic scaling laws.

Redshift surveys of more distant galaxies at z ∼ 1 progressed more slowly, primarily as they have targeted galaxies more than 100 times fainter than SDSS or 2dF. The first substantial surveys were conducted in the 1990s, measuring redshifts of several hundred objects at intermediate redshift; e.g., the LDSS survey (Colless et al. 1990), the ESO-Sculptor Survey (Bellanger et al. 1995; Arnouts et al. 1997), the CNOC and CNOC2 surveys (Yee et al. 1996, 2000), and the Hawaii Deep Fields Survey (Cowie et al. 1996).

Surveys of even more distant galaxies began taking shape at roughly the same time. The pioneering Canada–France Redshift Survey (CFRS; Lilly et al. 1995) garnered ∼600 redshifts and was the first to provide a dense, statistical sample of galaxies out to z ∼ 1. Though conducted with only a 3.6 m diameter telescope, it had a fairly deep magnitude limit of I_AB = 22.5 and yielded a median redshift of z = 0.56. Augmented by Hubble imaging, it established landmark norms for the luminosities and sizes of galaxies and the star-formation history of the universe to z ∼ 1.

The LRIS multi-object spectrograph on the Keck telescopes enabled a variety of even deeper surveys. Cowie and collaborators (Cowie et al. 1996) used roughly 400 redshifts down to I ∼ 23 in the Hawaii Deep Fields to elucidate the phenomenon of "downsizing," that the peak of star formation occurred first in the most massive galaxies and swept down later to smaller galaxies. This concept has since become central to understanding galaxy evolution. Later surveys by the same group have probed the nature of distant X-ray sources (e.g., Barger et al. 2005, 2008).

The Caltech Faint Galaxy Redshift Survey (Cohen et al. 2000) exploited the Keck 10 m telescope and went roughly 1 mag fainter than CFRS (R = 23–24), assembling several hundred redshifts with median z = 0.70 in two fields (one of them containing the Hubble Deep Field-N, HDF-N). Notable discoveries included the extreme amount of clustering found even at z ∼ 1, the relatively normal morphologies of most field galaxies observed (i.e., the rarity of true peculiars and mergers), the measurement of the shape of the luminosity function to deeper magnitudes, and the exploration of the nature of distant mid-IR and radio sources (van den Bergh et al. 2000; Hogg et al. 2000; Cohen 2002).

The largest of this first generation of deep redshift surveys was DEEP1. This survey used the LRIS instrument on the Keck I telescope to obtain spectroscopy to a magnitude limit of R ∼ 24 in and around the HDF-N and the Groth Survey Strip, a 127 arcmin² region observed with WFPC2 on Hubble Space Telescope (HST) in both I and V (Groth et al. 1994; Vogt et al. 2005). DEEP1 was conceived and executed as a pilot survey for the DEEP2 Galaxy Redshift Survey described in this paper. Over 720 redshifts were measured in total (Phillips et al. 1997; Weiner et al. 2005) having a median value of ∼0.65, and bulge and disk parameters were fitted to the Groth Strip HST images (Simard et al. 2002). Scientific highlights include an early sub-survey that helped to establish the nature of Lyman-break galaxies (Lowenthal et al. 1997), the detection of a strong color bimodality out to z ∼ 1 (Im et al. 2002; Weiner et al. 2005), the measurement of fundamental plane evolution for distant field spheroidal galaxies (Gebhardt et al. 2003), the detection of "downsizing" in the star formation rate of compact galaxies (Guzmán et al. 1997), measurements of interstellar medium (ISM) metallicity evolution to z ∼ 1 (Kobulnicky et al. 2003), an extensive analysis of selection effects on disk–galaxy radii and surface brightnesses (SBs; Simard et al. 2002), and the discovery of the prevelance of already-red bulges in typical disk galaxies at z ∼ 1 (Koo et al. 2005; Weiner et al. 2005). A distinguishing feature of DEEP1 was the use of relatively high spectral resolution (R ∼ 3000, FWHM = 3–4 Å), which resolved redshift ambiguities by splitting the [O ii] λ3727 doublet and also yielded linewidths and rotation curves. These were used to extend the Tully–Fisher (TF) relation to z ∼ 1 (Vogt et al. 1996, 1997), a strategy that was later used in the Team Keck Redshift Survey (TKRS, GOODS-N; Wirth et al. 2004) to yield an even larger sample of linewidths (Weiner et al. 2006a, 2006b).

DEEP1 was a valuable learning experience. In addition to proving the scientific value of the high spectral resolution made possible by LRIS, it confirmed that faint spectral features could be more easily seen in the dark stretches of spectrum between the OH lines. On the other hand, achieving photon-limited sky subtraction under the newly concentrated OH lines places even higher requirements on flat-fielding accuracy, wavelength calibration, and night-sky spectral modeling. Furthermore, pushing beyond the de facto redshift limit that then existed near z ∼ 1 (the so-called redshift desert) would require pursuing [O ii] λ3727 to well beyond 8000 Å. A new spectrograph on one of the largest optical telescopes would be necessary to achieve these goals.

The present paper describes the design and execution of the DEEP2 Galaxy Redshift Survey (commonly referred to as DEEP2 in the remainder of this paper), which was conducted by a collaboration of observers primarily based at UC Berkeley and UC Santa Cruz, together with astronomers from the University of Hawaii and other institutions. The survey was executed with the DEIMOS multi-object spectrograph (Faber et al. 2003) on Keck 2; aspects of the survey have previously been described in Davis et al. (2003, 2005), Coil et al. (2004b), and Willmer et al. (2006). The survey obtained roughly 53,000 spectra, coming close to the target of ∼60,000 galaxies in the original survey design.

The DEIMOS spectrograph was designed primarily to enable the DEEP2 survey, building on the lessons learned from the surveys conducted with the LRIS instrument at Keck. It differs from LRIS primarily in utilizing a larger detector array, covering a larger field of view (FOV), offering wider spectral coverage at fixed resolution, enabling better sky-subtraction due to an active flexure compensation system (FCS), and permitting the simultaneous observation of 3–4× as many objects.

DEEP2 was conceived as a legacy survey for the astronomical community, and all data are now public. The present paper is intended as a handbook for users to understand and utilize the data products in Data Release 4 (hereafter DR4), which is available at http://deep.berkeley.edu/DR4/. Brief descriptions of the data and methods are given there, but the present account is more complete and presents new details on the final data reduction techniques, redshift measurement procedures, the current generation of redshifts, and summary data tables. Additional measurements that were not part of previous DEEP2 data products are also included. All data in this paper are available in the form of FITS BINTABLE files at the DR4 Web site.

The outline of this paper is as follows. Section 2 sets forth the overarching goals and tradeoffs that determined the design of the DEEP2 survey. Section 3 summarizes some of the major scientific results so far, giving examples of how various aspects of the design have translated into specific science gains. Section 4 gives the basic DEEP2 survey parameters and field properties and describes the extensive existing ancillary data that are available in the DEEP2 fields. DEEP2 is put into context in Section 5, which compares DEEP2 to other leading z ∼ 1 surveys (VVDS-deep, VVDS-wide, zCOSMOS, and PRIMUS) using several different measures of survey size and information content.

Section 6 describes the parent galaxy photometric catalogs and selection cuts that were used to determine potential targets for DEEP2 spectroscopy. The slitmask design process is covered in Section 7, which describes the DEIMOS detector and slitmask geometry, as well as the algorithms used to place objects on masks. Section 8 is an exhaustive discussion of all known selection effects resulting from the slitmask design process, caused either by loss of objects from the initial target pool or by systematics in the rate at which we select pool objects of given properties for masks.

Sections 9 and 10 describe the spectroscopic exposures and their reduction, including detailed information on the spec2d pipeline that produces the reduced one-dimensional (1D) and two-dimensional (2D) spectra. This pipeline has been employed by many DEIMOS users; this paper provides its definitive description. The features of the DEIMOS spectrograph and spec2d pipeline that enable photon-limited sky subtraction accuracy even under the OH lines are described in the Appendix. The range in quality of DEEP2 data is discussed in Section 10, where examples of typical data, bad data, and interesting spectra are given.

Section 11 describes the redshift measurement process, including the automated spec1d redshift pipeline that produces a menu of redshift possibilities and the subsequent visual inspection process to select among them via the interactive user GUI zspec. Final results on redshift success, quality codes, completeness, biases, and redshift accuracy are also given there. Section 12 investigates the impact of multiple galaxies masquerading as single galaxies in the ground-based pcat photometry. Section 13 is a guide to DR4 and the two main data tables in this paper, which summarize the mask data and final redshifts and quality codes.

Section 14 is provided to enable correlation function measurements with DR4 data and to aid theorists who wish to make mock DEEP2 catalogs from model galaxy data. It describes a set of files being distributed along with DR4 that describe the selection and redshift success probability for a DEEP2 target as a function of location on the sky. Finally, Section 15 illustrates the properties of the DEEP2 data set via plots of numbers, colors, magnitudes, etc., as a function of redshift.

Depending on their interests, readers may wish to focus on certain sections of this paper. For instance:

• 1.  
  Users of DEEP2 Data Release 4 data. Key sections are Section 4 (survey parameters), Section 8 (assessment of biases in targeting), Section 10.3 (presenting sample spectra), Sections 11.3 and 11.4 (redshift results and completeness), Section 13 (describing the released data tables), Section 14 (describing the released 2D selection functions), and Section 15 (describing trends in the sample with z).
• 2.  
  Individuals interested in the design of DEEP2 and comparison to other deep surveys. Key sections are Section 2 (design goals), Section 3 (science results), Section 4 (survey parameters), Section 5 (comparison to other surveys), Section 8 (assessment of biases in targeting), Section 12 (evaluating how frequently spectroscopic targets consisted of multiple unresolved galaxies), and Section 15 (describing trends in the sample with z).
• 3.  
  Users of the DEEP2/DEIMOS data reduction pipelines. Key sections are Section 10 (on the 2D data reduction pipeline and spectral extractions) and Section 11 (on the redshift determination pipeline).
• 4.  
  Individuals interested in details of DEEP2 target selection and techniques. Key sections are Section 6 (describing the target selection criteria), Section 7 (slitmask design algorithms), and Section 9 (observational strategy).

Throughout this paper, unless specified otherwise we utilize magnitudes on the AB system and assume a ΛCDM concordance cosmology with Ω_m = 0.3, Ω_Λ = 0.7, and H₀ = 100 h km s⁻¹ Mpc⁻¹. The DR4 data tables also use these quantities.

DEEP2 was originally envisioned as a tool for simultaneously studying galaxy evolution and the growth of large-scale structure since z ∼ 1. However, while the survey was being designed it was realized that such data could also be used to constrain the nature of dark energy (i.e., its equation of state) by counting the abundance of groups and clusters as a function of velocity dispersion and redshift (Newman et al. 2002; Newman & Davis 2000, 2002; Gerke et al. 2005). This was one of the first methods proposed for studying dark energy by counting massive objects (see also Haiman et al. 2001). The distribution of clusters in velocity and redshift depends on both the growth rate of large-scale structure and on the volume element (i.e., the amount of volume per redshift interval per angular area), which are each related to fundamental cosmological parameters in predictable ways. Counting the abundance of intermediate-mass groups to high accuracy therefore became a third major goal guiding the design of DEEP2.

It was clear from the start that one of the most important DEEP2 data products would be precision counts, to be compared with various types of model predictions. Obtaining high-precision counts requires:

• 1.  
  many galaxies,
• 2.  
  an accurately known and simple selection function—DEEP2 is basically magnitude-limited with nearly uniform sampling on the sky and in redshift space at z > 0.75—and,
• 3.  
  low sample (commonly referred to as "cosmic") variance.

These aims—large numbers, simple selection function, and low cosmic variance—were the central guiding principles for DEEP2. They had to be achieved, however, while using as little total telescope time as possible.

Optimizing the measurement of environment and clustering statistics played a major role in setting the sizes and shapes of the DEEP2 survey fields. Galaxy properties vary systematically with environment, and the length-scale of this influence can shed important light on the physical mechanisms causing these effects: for example, differentiating between processes associated with the parent dark matter halo of a galaxy from those that act on larger scales. Since the typical comoving radius of galaxy groups and clusters is of order ∼1 h⁻¹ Mpc, measuring the local overdensity of other galaxies around a given object (the most common measure of environment used today) requires counting neighbors to a separation at least this large, corresponding to 15 at z ∼ 1. As a result, even when corrections for lost area are applied, neighbor counts become inaccurate for galaxies that are too near to survey boundaries (cf. Cooper et al. 2005); minimizing the number of lost objects in environment studies requires:

•   
  Fields that are at least 10 times wider in each direction than the radius within which environments are measured, corresponding to a minimum dimension of ∼15' on the sky for a survey at z ∼ 1.

This restriction also ensures that fields will be well-sized for characterizing groups and clusters, in support of our third science goal.

The measurement of correlation functions drives the choice of a minimum field dimension in similar ways, as the dominant error terms on large scales increase rapidly for pair separations larger than half the minimum field dimension (e.g., Bernstein 1994). It is also necessary to survey a large volume to minimize the effects of cosmic variance on correlation function estimates. Typical values of the scale length of galaxy clustering, r₀, for galaxy populations of interest are generally ≲ 5 h⁻¹ co-moving Mpc at z ∼ 1 (Coil et al. 2004a, 2008), corresponding to an angular separation of 74. Measuring correlation functions well therefore requires:

•   
  Contiguous volumes spanning several times r₀ in one dimension, with the other two dimensions spanning many times r₀.

A field size of 05 × 2° was accordingly selected for three out of the four DEEP2 fields, corresponding to 4 r₀ by 16 r₀ at z = 1. Rectangular fields rather than square fields were chosen to increase the statistical power of the sample: the opposite ends of a strip will be more statistically independent than regions closer to each other, reducing cosmic variance (Newman & Davis 2002).

Since environment measures involve the pairwise counting of objects, the statistical weight of such data increases as the square of the volume density of galaxies sampled, all other things being equal.²⁷ Essentially all environmental studies in the Poisson-dominated regime should benefit from this scaling, including those which employ a wide variety of galaxy environment estimators, the measurement of correlation functions and cross-correlations for dilute samples or at small scales, pair counts, comparisons of group and field populations, and studies incorporating the dynamical masses of groups. The DEEP2 targeting strategy is therefore designed to obtain:

•   
  A high number density of galaxies (or equivalently, number of objects per unit area and redshift) down to the faintest feasible magnitude limit.

However, under the constraint of finite telescope time, the need for large, densely sampled fields to enable accurate correlation function and environment measurements conflicts with the desirability of covering many independent regions on the sky to minimize (and allow assessment of) cosmic variance. The sample variance in a single large field, whose subregions are correlated due to large-scale modes of the power spectrum, will always be greater than in a larger number of widely separated fields on the sky covering the same total area. Our preferences for large field sizes but small cosmic variance are most efficiently reconciled by choosing:

•   
  Several widely separated areas on the sky, each one of which exceeds the minimum width and length needed for correlation and environment studies.

The final choice to survey four fields was driven by cosmic variance calculations utilizing the QUICKCV code of Newman & Davis (2002)²⁸ and by the instability of standard deviation measurements with fewer samples. Surveying multiple fields spaced well apart in R.A. also makes telescope scheduling easier.

Obtaining a dense sample of galaxies can be achieved by selecting down to a very faint magnitude limit; but that would require prohibitive observation time. Instead, it is desirable to go as faint as one must to obtain enough targets to fill slitmasks, but no fainter. Since the DEIMOS spectrograph generally has 10 slots available for user slitmasks, observation times of order 1 hr per mask are optimal. In order to obtain redshifts for a majority of objects in an hour's observation time, we desire:

•   
  A target population brighter than R_AB ∼ 24.

In order to include a large enough sample to optimize the filling of slitmasks, the final DEEP2 sample extends down to R_AB = 24.1.

A single DEIMOS slitmask covers an area on the sky of roughly 53 × 167 (cf. Section 7), of which more than 30% is unsuitable for galaxy target slitlets due to vignetting, chip gaps, or variation in wavelength coverage. DEIMOS masks can generally include ∼130–150 objects, corresponding to a surface density of 2.2–2.6 galaxies per square arcminute, comparable to the number counts of galaxies down to R_AB ∼ 21.4. However, targeting just those objects would result in a relatively bright and quite dilute sample of galaxies, weighted toward more luminous galaxies and lower redshifts than were of interest for DEEP2. Furthermore, many objects of interest would be lost as we are unable to observe multiple objects at the same displacement in the spatial direction on a slitmask, lest spectra overlap, reducing our sampling of overdense regions. Given our desire to maximize the number density of high-redshift galaxies, we therefore require:

•   
  Rejection of lower-redshift (z < 0.7) galaxies, as well as coverage of each point on the sky by at least two slitmasks.

In the Extended Groth Strip (EGS, DEEP2 Field 1), however, we do not reject low-z galaxies, both to test our selection methods and to take advantage of the rich multiwavelength data in that field; as a consequence, in that field we require coverage of each point on the sky by at least four slitmasks to compensate. To keep the number of slitmasks per field roughly constant, the width of the area covered is half as large in the EGS as for the remaining fields (i.e., the survey area goal in this field was 025 × 2°, rather than 05 × 2° as in the other DEEP2 fields).

The field area of 05 × 2° is roughly 60 times the area covered by a single DEIMOS slitmask; double coverage thus requires 120 slitmasks per field. Assuming an average of 135 targets per slitmask thus leads to a survey goal of ∼65,000 spectra.

With the field geometry and sample sizes determined, the main parameters remaining are spectral dispersion and spectral coverage. These also involve tradeoffs. For a fixed detector size, low dispersion captures more spectral features and thereby enhances spectral information and (potentially) redshift completeness. However, as noted above, high dispersion yields more information per angstrom by resolving internal galaxy motions and yielding more accurate redshifts. It also splits the [O ii] λ3727 doublet, converting that feature into a unique, robust redshift indicator even when it is the only feature visible. At high resolution, the OH sky lines are each concentrated into a few pixels, leaving the remainder of the pixels dark and thereby shortening required exposure times (see Section 10.2). High dispersion also reduces flat-fielding errors due to "fringing" (see Appendix A.2). In conventional grating spectrographs, it increases anamorphic demagnification, which narrows slitwidth images still further and reduces the displacement of spectra along the spectral direction due to variations in slitlet position, maximizing the spectral region common to all objects. Finally, high dispersion allows the use of wider slits for the same net spectral resolution, thereby capturing more galaxy light.

Evidently, we would like to have both high dispersion and broad spectral coverage. The DEIMOS CCD detector/camera system was designed to do this by providing a full 8192 pixels along the spectral direction, with minimal chip gap. Our ideal choice balancing resolution and coverage would have used an 830 line mm⁻¹ grating, which covers 3900 Å of spectrum with DEIMOS. However, this grating suffers significant ghosting, which we feared would interfere with accurate sky subtraction. We therefore conservatively chose the 1200 line mm⁻¹ grating, which captures 2600 Å of spectrum over 2000 separate resolution elements. When centered at 7800 Å, this spectral range yields at least one strong spectral feature for essentially all galaxies from z = 0 to z = 1.4. Redshift ambiguities are rare and, if present, can largely be resolved in the future by using photometric redshifts (Kirby et al. 2007). We therefore selected:

•   
  DEIMOS' highest-resolution grating, 1200 line mm⁻¹, typically covering 6500 Å–9100 Å and yielding a spectral resolution R ≡ λ/Δλ ∼ 6000 with a 1'' wide slit.²⁹

Practical considerations influenced many of the final design decisions for DEEP2. The detailed layout of slitmasks on the sky was governed by the DEIMOS slitmask geometry (cf. Section 7). The final fields were chosen to have low Galactic reddening utilizing the Schlegel et al. (1998) dust map and to be well spaced in R.A. to permit good-weather observing at Keck. Field 1 (the EGS) was specially selected for its excellent multiwavelength supplemental data (as described in Section 4).

Finally, detailed attention was paid to ensuring good sky-subtraction accuracy even under the bright OH lines. These lines would occupy only a small portion of the spectrum (due to the use of high dispersion), but any sky-subtraction errors would spread to other wavelengths whenever spectra were smoothed. Requirements for excellent sky subtraction include (1) a highly accurate and stable calibration of the wavelength corresponding to every pixel on the detector; (2) a constant point-spread function (PSF) for OH lines along each slitlet; and (3) highly reproducible CCD flat-fielding, which was to be attained by maintaining exactly the same wavelength on each pixel between the afternoon flat-field calibration and the night-time observation. These requirements in turn require a very stable spectrograph, uniform image quality over the FOV, careful calibration and observing techniques, and high-precision data reduction methods. Further details are provided in the Appendix, which discusses CCD fringing, sky subtraction, the DEIMOS FCS, image stability, and wavelength calibration methods.

The design resulting from the above considerations has enabled a wide variety of scientific investigations; more than 130 refereed papers to date have utilized DEEP2 data. An early summary appeared in the 2007 May 1 special issue of the Astrophysical Journal Letters (Vol. 660) devoted to the AEGIS (the All-wavelength Extended Groth Strip International Survey) collaboration which is described in Section 4; Table 1 of this paper presents an updated list of selected highlights. Among our major findings are:

• 1.  
  DEEP2 confirmed and buttressed the conclusion of Bell et al. (2004) that the number of red-and-dead, quenched galaxies has at least doubled since z ∼ 1, implying that some galaxies arrived on the red sequence relatively recently (Willmer et al. 2006; Faber et al. 2007). Stellar populations confirm late quenching (Schiavon et al. 2006), and the mean restframe U − V color of galaxies evolves slowly due to these late arrivals (Harker et al. 2006).
• 2.  
  Star-formation rates have been measured as a function of stellar mass using both 24 μm fluxes and Galaxy Evolution Explorer (GALEX) photometry (Noeske et al. 2007b; Salim et al. 2009). In star-forming galaxies, the star formation rate follows stellar mass closely at all epochs out to z ∼ 1, displaying a "star-forming main sequence" that can be modeled by assuming that larger galaxies start to form stars earlier and shut down sooner (Noeske et al. 2007a). The rms scatter about this relation is ∼0.3 dex. Most star formation at z ≲ 1 is taking place in normal galaxies, not in merger-triggered starbursts (Noeske et al. 2007a; Harker 2008). Red spheroidal galaxies are truly quenched, and the strong [O ii] emission in some is due to AGN and/or LINER activity, not star formation (Yan et al. 2006; Konidaris 2008).
• 3.  
  The fraction of quenched galaxies is larger in high-density environments (Cooper et al. 2006) and is higher in groups versus the field (Gerke et al. 2007a). However, the decline in global star formation rate since z ∼ 1 is strong in all environments and is not driven by environmental effects (Cooper et al. 2008). The fraction of quenched galaxies in high-density environments decreases with lookback time and essentially vanishes at z ≳ 1.3, implying that massive galaxies started shutting down in bulk near z ≳ 2. Environment correlates much more strongly with galaxy color than luminosity; a color–density relation persists to z > 1 (Cooper et al. 2006, 2007, 2010). Many massive, blue star-forming galaxies were still found in high-density regions at z ∼ 1 but have no analogs today; they must have quenched in the interim time (Cooper et al. 2006, 2008). Post-starburst galaxies are found in similar environments as quenched galaxies at z ∼ 0.8, but similar to star-forming galaxies at z ∼ 0.1; given the overall movement of galaxies toward denser environments at lower z, the absolute (as opposed to relative) overdensity around quenching galaxies may not have evolved with redshift (Yan et al. 2009). Finally, massive early-type galaxies in high-density regions are ≳ 25% larger in size relative to their counterparts in low-density environs at z ∼ 1, strongly suggesting that minor mergers may be important in the size evolution of massive ellipticals (Cooper et al. 2012a).
• 4.  
  The roots of the TF relation are visible out to z ∼ 1 (Kassin et al. 2007). Disturbed and merging galaxies have low rotation velocities but high line-widths that will place them on the TF relation after settling (Covington et al. 2009). The zero point of the stellar-mass TF relation has evolved very little since z ∼ 1, in agreement with LCDM based models (Dutton et al. 2011), and the Faber–Jackson relation for spheroids likely arose from the TF relation via mergers and quenching. Clear evidence of disk settling is seen via a decline of random (as opposed to ordered/rotational) motions over time, and this settling occurs faster in larger galaxies (Kassin et al. 2012).
• 5.  
  The number of disky galaxies has declined and the number of bulge-dominated galaxies has increased since z ∼ 1 (Lotz et al. 2008). However, X-ray-detected AGNs are not preferentially found in major mergers, and the fraction of merging galaxies is not appreciably higher at z ∼ 1 than now (Pierce et al. 2007; Lin et al. 2004, 2008; Lotz et al. 2008). Many distant galaxies previously classed as peculiar or merging are more likely normal disk galaxies in the process of settling.
• 6.  
  The clustering properties of a wide variety of galaxy and AGN samples have been measured. The auto-correlation function of typical DEEP2 galaxies implies halo masses near 10¹²M_☉. The clustering amplitude is a stronger function of color (Coil et al. 2008) than luminosity (Coil et al. 2006b), matching the results from environment studies. Red galaxies cluster more strongly than blue ones, with intermediate-color "green valley" galaxies preferentially found on the outskirts of the same massive halos that host red galaxies (Coil et al. 2008). The halo mass associated with star formation quenching has been estimated both from the correlation function (Coil et al. 2008) and via the motions of satellite galaxies (Conroy et al. 2007). Coil et al. (2006a) use the clustering of galaxies with group centers to separate out the "one-halo" and "two-halo" contributions to the correlation function. Using the cross-correlation of AGN and DEEP2 galaxies, Coil et al. (2007) find that quasars cluster like blue, star-forming galaxies at z = 1, while lower-accretion X-ray detected AGN cluster similarly to red, quiescent galaxies and are more likely to reside in galaxy groups (Coil et al. 2009). Comparison between X-ray and optically-selected AGNs indicates that the fractions of obscured AGNs and Compton-thick AGNs at z ∼ 0.6 are at least as large as those fractions in the local universe (Yan et al. 2011).
• 7.  
  Ubiquitous outflowing winds have been detected in normal star-forming galaxies for the first time, at z ∼ 1.3 using [Mg ii] absorption (Weiner et al. 2009). Outflow speeds are higher in more massive galaxies and are comparable to the escape velocity at all masses. At z = 0.1–0.5, outflows are detected in both blue and red galaxies but are more frequent in galaxies with high IR luminosity or recently truncated star formation (Sato et al. 2009). Overall, these results suggest that stellar feedback is an important process in regulating the gas content and star formation rates of star-forming galaxies and that galactic-scale outflows play an important role in the quenching and migration of blue-cloud galaxies to the red sequence.
• 8.  
  The cause of AGN activity and the role of AGNs in galaxy quenching remain major puzzles. X-ray AGNs are found in massive galaxies at the top of the blue cloud, on the red sequence, and in the green valley (Nandra et al. 2007), as expected if AGN activity is associated with black-hole growth and bulge-building. However, X-ray AGNs are not especially associated with mergers (Pierce et al. 2007) or with high star formation rates (Georgakakis et al. 2008). A surprise is the large number of luminous, hard, obscured X-ray sources in morphologically normal red spheroidals and post-starburst galaxies (Georgakakis et al. 2008), well after star formation should nominally have stopped. If AGN feedback causes galaxy quenching, these persistent hard AGNs imply that considerable nuclear gas and dust must remain in the central regions, where it continues to feed the black hole.

To summarize these findings: the roots of most present-day galaxy properties are visible far back in time to the edge of DEEP2 (z = 1.4, more than eight billion years in the past); galaxy evolution over this time has on balance been a fairly regular and predictable process; and a good predictor of a galaxy's properties at any era is its stellar mass. An overarching hypothesis that may unite all of these findings is that the most important physical driver controlling a galaxy's evolution at z < 1.4 is the growth of its dark halo mass versus time. On the other hand, several of the above findings point to close couplings between AGNs, starbursts, quenching, and galactic winds, and the causal connections among these seems more complex than the simple halo-driven model would predict. These issues are the great frontier for future work.

In addition, the DEEP2 data set has also enabled a variety of scientific anaylses originating from outside of the DEEP2 survey team, totaling more than 75 published papers to date. For example, Zahid et al. (2011, 2012) employed the Keck/DEIMOS spectra to probe the mass–metallicity relation at z ∼ 1 with greater statistical significance than previous studies (see also Yuan et al. 2013); this work concluded that outflows are a ubiquitous process in normal star-forming galaxies, though such ejective feedback cannot account for the total baryon content found in the intergalactic medium. By similarly utilizing emission-line measurements derived from the DEEP2 spectra, Zhu et al. (2009) measured the [O ii] luminosity function to higher precision than previous efforts, thereby constraining the star-formation-rate space density at z ∼ 1.

In conjunction with the SDSS, DEEP2 has also facilitated the scientific community in extending studies of galaxy evolution over more than half the age of the universe (e.g., Chen et al. 2009; Prescott et al. 2009; and Matsuoka & Kawara 2010). As an example, Blanton (2006) employed the color–magnitude distributions from the two spectroscopic surveys to place limits on the fading of the massive red galaxy population as well as the importance of mergers in driving blue galaxies onto the red sequence at z < 1. In addition, Data Release 4, along with its predecessors (DR1, DR2, and DR3), has provided an invaluable repository for testing and calibrating photometric redshift codes (e.g., Brammer et al. 2008; Mandelbaum et al. 2008; Banerji et al. 2008; Coupon et al. 2009; Freeman et al. 2009; Gerdes et al. 2010; Bielby et al. 2012; Matute et al. 2012).

The present data in DR4 do not exhaust the information from DEEP2. Many additional quantities have been derived from survey data, and have either been published separately (see Table 1), or may be obtained by contacting the individual scientists involved. These include measurements of emission-line equivalent widths (from B. Weiner, R. Yan, N. Konidaris, and J. Harker); improved velocity widths for emission and absorption lines (from B. Weiner and S. Kassin); local environmental densities (from M. Cooper); group identifications and group memberships (from B. Gerke); stellar masses (from K. Bundy and C. N. A. Willmer); ISM metallicities (from A. Phillips); D4000 and Balmer-line absorption strengths (from J. Harker and R. Yan); optical AGN IDs (from R. Yan) and morphologies (from J. Lotz); pair catalogs (from L. Lin) satellite kinematics (from C. Conroy); star-formation rates (from K. Noeske and S. Salim); and indicators for poststarburst galaxies (from R. Yan).

In Section 2, we presented the goals which were used to fix the basic properties of the DEEP2 survey. In the remainder of this paper, we describe the design and execution of the project and the resulting data sets in more detail. This first section serves as a basic introduction to the DEEP2 survey.

To first order, DEEP2 is a magnitude-limited spectroscopic galaxy redshift survey with limiting magnitude of R_AB = 24.1.³⁰ Instrument and exposure parameters are summarized in Table 2. The survey was designed to be executed in four separate 05 (or 025 in the case of the EGS) × 2° rectangular fields widely spaced in right ascension, with an average of 120 DEIMOS slitmasks per field. The spectral setup used the 1200 line mm⁻¹ high-resolution DEIMOS grating with a spectral resolution of R ∼ 6000 and a central wavelength of 7800 Å; the typical exposure time is 1 hr per mask. The survey is primarily sensitive to galaxies below a redshift of z ∼ 1.45, past which the [O ii] 3727 Å doublet moves beyond the red limit of our typical spectral coverage. The total number of spectra obtained is 52,989, and the total number of objects with secure (classes with >95% repeatability) redshifts is 38,348. Due to the total allocation of telescope time being somewhat smaller than originally envisioned, the total area of sky covered by the final survey sample is roughly 3.0 deg² (rather than 3.5), and 411 (rather than 480) slitmasks were observed.

Table 2. Instrument and Exposure Parameters

Parameter	Value
Slitmask parameters
Total slit length	167
Usable slit length	163
Maximum mask width	53
Typical number of slitlets per mask	140
Slit width	10
Slitlet tilts	Up to 30°
FWHM along slit for point source	05–12 (best/worst seeing)
Spectral parameters
Grating	1200 line mm−1, gold-coated, 7500 Å blaze
Typical spectral range	6500–9300 Å
Dispersion	0.33 Å pixel−1
FWHM of sky line in spectral direction	1.29–1.39 Å; center best, worse at detector edges
Spectrograph image quality, point source	2.1 pixels (field center), 2.7 pixels (corners) (FWHM)
Spectral resolutiona	R ≡ λ/Δλ = 5900 at 7800 Å
Equivalent velocity σ	24 km s−1
Order blocking filter	GG495
Peak throughput, telescope+spectrograph	29% with fresh coatings
rms image stabilityb	0.3 pixels along spectrum, 0.5 pixels perpendicular
Detector parameters
Detector mosaic	Eight 2K × 4K CCDs in 2 × 4 array
Pixel size	15 μ
Total array size	8192 pixels × 8192 pixels; 12.6 cm × 12.6 cm
Blue-red gap in spectral direction	7 pixels
Gap between CCDs, spatial direction	Approx. 8''
Detector scale	01185 pixel−1
Gain	1.25 e− per DN
Read noise	2.55 e−
Exposure parameters
Nominal exposure	3 × 20 minutes
Typical sky level between OH lines	13 photons pixel−1 in 20 minutes near 8000 Å
Brightest OH sky line	∼2000 photons pixel−1 in 20 minutes

Notes. ^aΔλ is the FWHM of an OH night-sky line. ^bDaily, spanning evening observations and matching afternoon calibrations.

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Objects are pre-selected in DEEP2 Fields 2–4 using broad-band Canada–France–Hawaii Telescope (CFHT) 12K BRI photometry to remove foreground galaxies below z ∼ 0.7 (cf. Section 6.3); this selection is essentially complete for galaxies at z > 0.75. This preselection removes 55% of galaxies brighter than R_AB = 24.1, thus multiplying the efficiency of the survey for studying galaxies at z ∼ 1 by a factor of 2.2. Field 1 is the EGS (Groth et al. 1994) and is treated differently owing to the wealth of ancillary data there. In that field, we do not reject low-redshift galaxies on the basis of their colors, though faint, nearby galaxies are given lower weight for selection (cf. Section 7.2).

To select objects, we first define a target pool of candidate galaxies in each field, consisting of all objects between R_AB = 18.5 and R_AB = 24.1 except those with exceptionally low SB or large (>80%) Bayesian probability of being a star.³¹ The photometric catalogs ("pcat"s) used for this selection are described in Section 6.1. We then apply a color pre-selection to this pool to remove z < 0.7 objects (in Fields 2–4). The remaining galaxies are used to design the masks; in a typical field, roughly 60% of potential targets receive slitlets.

The chosen depth of R_AB = 24.1 is suitable for several reasons. At this depth, DEEP2 probes down to L* in the luminosity function at z ∼ 1.2. The surface density of 20,000 objects/□° (after high-z preselection) is large enough to pack slitmasks efficiently while leaving a modest excess for flexibility. Finally, the majority of galaxies at this magnitude limit still yield secure redshifts in 1 hr of observation time.

Information on the four DEEP2 fields is given in Table 3, including coordinates, average reddening, field sizes, number of slitmasks planned and observed, and number of target galaxies and redshifts. By ranging in R.A. from 14^h20^m to 2^h30^m, with spacings of 3–7 hr between fields, the four DEEP2 fields are well suited for observing in what is historically a good-weather period at Keck, ranging from March through October. Masks were designed over 05 wide by 2° long regions in Fields 2–4, but not all of these masks were ultimately observed. As noted, Field 1 (EGS) is special: it hosts a wide variety of deep multiwavelength data from X-rays to radio. It is also one of the darkest and most dust-free regions of the sky. Since no z > 0.7 preselection was done in Field 1, the surface density of targets on the sky there is roughly twice that in the other DEEP2 fields; in order to sample high-redshift objects at the same number density as in other fields, only half as much area could be covered using the same number of slitmasks. As a result, the spectroscopy in EGS covers an area that is only ∼16' wide (but still 2° long). All masks in EGS were observed.

The field layouts and final slitmask coverage in Fields 2–4 are shown in Figure 1. The boundary of each individual CFHT 12K BRI pcat photometric pointing is shown by dashed lines; individual fields are labeled by their field and pointing number (e.g., pointing 12 is the second CFHT pointing in Field 1). The chevron pattern permits slitlets to be aligned with atmospheric dispersion both east and west of the meridian (the odd pattern in Field 2 was a result of this requirement, combined with the high priority assigned to observations in Field 1); see Section 7 for details. The gray scale at each point represents the probability that a galaxy in that mask meeting the DEEP2 sample selection criteria was targeted for spectroscopy and that a secure (Q = 3 or Q = 4, cf. Section 11) redshift was measured. This spatial selection function can be downloaded from the DEEP2 data release Web site by users who wish to perform clustering measurements or make theoretical models of the survey (see Section 14). Certain areas were redesigned following the first semester of survey operations, which caused a few regions to be observed twice with different masks (darker stripes). All DEEP2 masks, including these regions of double coverage, are included in DR4. The density of masks is especially high where CFHT 12K pointings overlap in Field 4. This duplication of coverage occurred because slitmasks were designed separately pointing by pointing in Fields 2–4 (but not EGS). Although photometry was obtained for three CFHT pointings in each of Fields 2–4, due to limited time for spectroscopic observations, Field 23 (which had inferior photometry) and most of Field 43 were not observed with DEIMOS. The photometric (pcat) catalogs for these fields are still included in the data release accompanying this paper.

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A similar plot of combined selection and redshift success probability is given for Field 1 (the EGS) in Figure 2. The layout of this field is long and narrow, both to allow dense coverage and in order to follow the geometry of preexisting space-based data. The strip is divided into eight blocks, each containing 15 masks. Within each block, eight masks run perpendicular to the strip and seven run parallel to it. Unlike Fields 2–4, a single pcat was created by merging the photometry from all four pointings before the masks were defined. There are thus no regions where separately designed masks overlap, unlike in Field 4.

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A summary of the existing data in all DEEP2 fields is given in Table 4, and skymaps of the major multiwavelength EGS surveys are shown in Figures 3 and 4. The data in EGS are particularly deep and rich. EGS is one of only two deep-wide Spitzer MIPS and IRAC regions (Fazio et al. 2004; Papovich et al. 2004; Dickinson et al. 2007 [FIDEL survey]) and is receiving ultra-deep imaging at 3.6 μm and 4.8 μm in the Warm Spitzer Extragalactic Deep Survey (SEDS), a Warm Spitzer mission. It has one of only two large two-color HST Advanced Camera for Surveys (ACS) mosaics (Davis et al. 2007; Lotz et al. 2008), the other being GEMS in ECDFS (Rix et al. 2004). It has the deepest GALEX imaging on the sky and the deepest wide-area Chandra mosaic (800 ks, Laird et al. 2009). It is a CFHT Legacy Deep Survey field, is slated for deep Herschel imaging, and many other deep optical, IR, submillimeter, and radio data have been taken or planned. This includes the follow-on DEEP3 survey (Cooper et al. 2011, 2012a), which has acquired ∼8000 new spectra down to R_AB = 25.5 and will double the redshift sampling density over the area covered by the HST ACS mosaic (see Table 4). Most recently, EGS has become one of five fields targeted by the CANDELS (Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey) Multi-Cycle Treasury program on HST (Grogin et al. 2011; Koekemoer et al. 2011); it is being imaged deeply with both the ACS and WFC3 instruments as part of this project.

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Table 4. Existing and Planned Data in DEEP2 Field 1 (Extended Groth Strip)^a

Data	Wavelength	Depthb	Areac	Contact
Keck DEIMOS (DEEP2)	6500–9100 Å	R = 24.1	16' × 125'	M. Cooper
z = 0–1.4
Keck DEIMOS (DEEP3)d	4800–9600 Å	R = 25.5	16' × 60'	M. Cooper
z = 0–1.4
MMT Hectospec	4500–9000 Å	R = 22.5	17' × 120'	C. Willmer, A. Coil
GTC-EMIR GOYA	1–2.5 μ	K = 24.5	∼0.3 deg2	R. Guzmán
Chandra ACIS	1–10 keV	200 ks	17' × 120'	P. Nandra
Chandra ACIS (AEGIS-X)	1–10 keV	800 ks	17' × 40'	P. Nandra
XMM EPIC	0.1–15 keV	70–82 ks	30' diam	⋅⋅⋅
GALEX UDeep imaging	FUV, NUV	154, 270 ks	125 diam	S. Salim
GALEX grism	FUV, NUV	291, 291 ks	125 diam	C. Martin
Hubble ACS	F606W, F814W	28.7, 28.1	10' × 67'	A. Koekemoer, J. Lotz
Hubble ACS (CANDELS)	F606W, F814W	28.9, 28.8	7' × 26'	A. Koekemoer
Hubble NICMOS	JH	25.0, 24.8	0.013 deg2 e	S. Kassin
Hubble WFC3 (CANDELS)	F125W, F160W	27.2, 27.3	7' × 26'	A. Koekemoer
CFHT 8K × 12K (pcat)	BRI	24.5, 24.5, 23.5f	4 × 28' × 42'	J. Newman, A. Coil
CFHT Megacam (CFHTLS)g	ugriz	ugri ∼ 27, z ∼ 25.5	1 deg2	S. Gwyn
MMT Megacam	u'g'i'z'	26.2, 27.2, 26.0, 26.0	1 deg2	M. Ashby
LBT	UY	∼25, 23.9	17' × 110'	B. Weiner
Subaru	R	27.0	1 deg2	M. Ashby
KPNO 4 m NDWFSh	BWRI	27.1, 26.2, 25.8	1.4 deg2	A. Dey
Palomar 5 m (POWIR)i	JKs	23.9, 21.7–22.5	0.2, 0.7 deg2	K. Bundy
CFHT WIRCAM	YJHK	∼25	20' × 20'	R. Pello
CFHT WIRCAM (WIRDS)j	JHK	24.8, 24.6, 24.5	3 × 20' × 20'	C. Willott
Subaru	K	24.5	7' × 40'	T. Yamada
KPNO 4 m NEWFIRM	JK	24.4, 23.9	1.4 deg2	M. Dickinson
KPNO 4 m NEWFIRM (NMBS)k	JH(med.)j	K = 23.4	28' × 28'	P. van Dokkum
Spitzer IRAC GTO	3.6, 4.5, 5.8, 8.0	0.9, 0.9, 6.3, 5.8 μJy	10' × 120'	P. Barmby
Spitzer IRAC GTO (broader "handle")	3.6, 4.5, 5.8, 8.0	1.0, 1.5, 9.3, 12.0 μJy	60' × 25'	J. Huang
Spitzer IRAC (SEDS)l	3.6, 4.5	25.7, 25.7 μJy	12' × 75'	G. Fazio
AKARIm	15 μ	115–150 μJy	10' × 70'	M. Im
Spitzer MIPS GTO	24, 70 μ	77 μJy, 10.3 mJy	10' × 120'	J. Huang, R. Hickox
Spitzer MIPS FIDELn	24, 70, 160 μ	30 μJy, 3 mJy, 20 mJy	10' × 90'	M. Dickinson
Herschel PACS (HERMES)o	110, 170 μ	5.2, 7.4 mJy	10' × 67'	D. Lutz
Herschel SPIRE (HERMES)o	250, 350, 450 μ	11.1, 15.2, 12.9 mJy	10' × 67'	S. Oliver
Scuba2 Legacy Deep	850 μ	3.5 mJy	1 deg2	R. Ivison
VLA	6 cm	0.6 mJyp	30' × 80'	S. Willner
VLA	20 cm	100 μJy	30' × 80'	R. Ivison
GMRT	50 cm	75 mJy	10' × 90'	A. Biggs

Notes. ^aPlanned or in progress are in italics. For a general overview, see http://aegis.ucolick.org/astronomers.html. ^bAll magnitudes are AB mags. Limiting magnitudes are 5σ unless otherwise stated; where none are available we list total integration time instead. ^cAreas are approximate. ^dDEEP3 has acquired ∼8000 new spectra and doubled the redshift sampling density in the Hubble ACS mosaic region. ^eNICMOS: 63 pointings. ^fCFHT pcat: 8σ. ^gCFHTLS: CFHT Legacy Survey (http://www.cfht.hawaii.edu/Science/CFHTLS). ^hNDWFS: NOAO Wide-Deep Field survey; EGS is an extension of the main NDWFS. ⁱPOWIR: Palomar Observatory Wide Infrared Survey (Conselice et al. 2008). ^jWIRDS: WIRCAM Infrared Deep Survey (http://terapix.iap.fr/rubrique.php?id_rubrique=256). ^kNMBS: Newfirm Medium Band Survey; five medium-band filters from J through H (van Dokkum et al. 2009). ^lSEDS: Spitzer Extragalactic Deep Survey (G. Fazio 2010, private communication). ^mAKARI: 50% of the field is at the two quoted depths (5σ; M. Im 2010, private communication). ⁿFIDEL: Far-Infrared Deep Extragalactic Legacy Survey (http://irsa.ipac.caltech.edu/DATA/SPITZER/FIDEL). ^oHERMES: Herschel Multi-Tiered Extragalactic Survey (http://astronomy.sussex.ac.uk/~sjo/Hermes). ^pVLA, 6 cm: 10σ (S. Willner 2007, private communication).

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To exploit the great richness of data in EGS, a broader research collaboration has been formed called AEGIS. This collaboration is combining efforts from more than a dozen teams who have obtained data in this field ranging from X-ray to radio wavelengths. More information on AEGIS may be found at the AEGIS Web site (http://aegis.ucolick.org) and in the 2007 May 1 special issue of the Astrophysical Journal Letters.

With Field 1 designated to be the EGS, Fields 2–4 were selected by finding regions free of bright stars, with low reddenings based on the IRAS dust map (Schlegel et al. 1998), spaced roughly 4 hr apart in R.A., and weighted toward higher R.A. where Keck weather is better. Their distribution also avoids the prime Galactic observing season and balances the number of nights required in each semester in order to ease telescope scheduling. The chosen fields all have declinations such that they are observable for more than 6 hr with an airmass less than 1.5, to ensure that differential refraction across a slitmask is below 02 (DEIMOS does not have an atmospheric dispersion compensator). Fields 3 and 4 are also in the multiply observed Equatorial Strip (Stripe 82) of the SDSS (York et al. 2000; Adelman-McCarthy et al. 2007; Ivezic et al. 2007) and are visible from both northern and southern hemispheres. The recently released deep SDSS photometry in this stripe should yield useful photometric redshifts down to DEEP2-like depths. A summary of complementary data available in these fields is given in Table 5.

The original design of the DEEP2 survey consisted of 480 slitmasks. The expected number of 135 slitlets per mask would then target ∼65,000 galaxies, of which 52,000 were expected to yield secure redshifts assuming an 80% success rate. One can therefore crudely think of DEEP2 as having roughly twice the number of objects and three times the volume of the Las Campanas Redshift survey (Shectman et al. 1996), but at z ∼ 1 rather than at z ∼ 0.1. The design volume of 9 × 10⁶ h⁻³ Mpc³ would be expected to contain only a handful of rich clusters but is large enough to count both galaxies and groups of galaxies to good accuracy. At 1 hr per mask and eight masks per night, such a survey would take 60 clear nights of Keck time. Ninety nights were allocated via a Keck Large Multi-Year Approved Project proposal with Marc Davis as PI, which left a cushion of 50% for bad weather and equipment malfunction.

The above plan was followed closely, but the yield of reliable redshifts per galaxy targeted was only 71%, not 80%, owing to the fact that more galaxies than expected were beyond the effective redshift limit of z ∼ 1.4 (Section 11). Weather also did not fully cooperate, with the result that only 411 out of the 480 original slitmasks were observed, yielding a total of ∼53,000 spectra. The final area and numbers of slitmasks and targets observed in each field are given in Table 3, and sky maps of the regions covered are shown in Figures 1 and 2. The final survey observed 86% of the proposed number of slitmasks and 88% of the proposed number of galaxies.

In this section and Table 6, we compare the properties of DEEP2 (considering both Fields 2–4 and EGS separately) to other large z ∼ 1 surveys in a variety of ways. The other projects considered include the TKRS in GOODS-North Wirth et al. 2004), the VVDS-deep survey in CDFS and in one other field (Le Fevre et al. 2005), the VVDS-wide survey in four fields (Garilli et al. 2008), zCOSMOS-bright in the COSMOS field (Lilly et al. 2007), and PRIMUS, which covers seven fields including several of the above (Coil et al. 2011).³² The first five are conventional spectroscopic surveys, but PRIMUS is a low-resolution prism survey yielding less precise redshifts but targeting many more galaxies. DEEP2 and TKRS have released all data, but the properties of the others have been deduced from stated plans and/or the available published data. Details of the data and sources used for these comparisons are given in the footnotes to Table 6.

Given the significant redshift failure rate in all distant galaxy surveys, it is important to have a consistent definition of "redshift success." "Reliable," "secure," or "robust" redshifts are defined in this paper to be those with ⩾95% probability of being correct based on the identification of multiple features, according to their authors (for all surveys described, this means quality codes 3 and 4 (or equivalent, e.g., including codes 13, 14, 23, and 24 for VVDS), but not 1 or 2). In comparing surveys we use the sizes of the presently published data sets for all surveys except zCOSMOS, for which we use the design values.

We now proceed to compare the power of the various z ∼ 1 surveys using a variety of metrics. Numerical results are summarized in Table 6.

• 1.  
  Redshift efficiency. A useful concept is "redshift efficiency," for which we offer two definitions. The first is the overall redshift efficiency, z_effic1, which is defined as the fraction of all slitlets (including stars) that eventually yield reliable galaxy (or QSO) redshifts. Values of z_effic1 are shown for the various surveys in Table 6. Apart from the two VVDS surveys, there is considerable degree of homogeneity in this quantity, with efficiencies hovering between 56% and 72%. With this definition, the efficiencies of VVDS-deep and VVDS-wide are only 28%–40%, partly because these surveys do not exclude stars, which hence take up a larger fraction of the slitlets than in other surveys, but mostly because of our high standard for redshift reliability, ⩾95% repeatability, which excludes many VVDS redshifts.The second definition of efficiency is the galaxy-only efficiency, z_effic2, which is defined as the fraction of galaxy-only slitlets that yield reliable galaxy redshifts.³³ The percentages rise by 3%–4%, to 59%–76%, for the non-VVDS surveys and are now 42%–43% for the two VVDS surveys. The efficiency of VVDS-wide rises the most due to the high fraction of stars among its targets.
• 2.  
  Volume sampled versus number of objects. Figure 5 compares the number of reliable redshifts versus volume sampled for both high- and low-redshift surveys. The volume used is computed from the areas in Table 6, bounded by the redshifts corresponding to the 2.5 percentile and 97.5 percentile point within a given survey (or by z = 0.2 and z = 1.2, the redshift range the team uses for science, in the case of PRIMUS). For surveys other than DEEP2 and TKRS (where the actual percentiles are used), these redshift limits are computed from analytic redshift distributions of the form $n(z) \propto z^2 e^{-z/z_0}$, using fits to z₀ as a function of limiting magnitude determined as described in Coil et al. (2004b), but using the full DEEP2 data set for calibration. This results in values of z₀ of 0.26 for DEEP2 and TKRS, 0.224 for VVDS-wide and zCOSMOS-bright, and 0.283 for VVDS-deep. Among the contemporaneous distant spectroscopic surveys (i.e., excluding PRIMUS), DEEP2 has the best combination of total number and volume sampled, with 2.5 times as many redshifts as the next competitor, zCOSMOS-bright, and roughly twice its effective volume. PRIMUS surpasses DEEP2 and all other high redshift surveys in this space, targeting a larger number of galaxies over a larger volume (but with lower spectral resolution).
• 3.  
  Number density. Figure 6 uses the same data used to produce Figure 5 to compute cosmology-independent sample densities, expressed as the number of galaxies with secure redshifts per square degree per unit redshift interval; we also include the corresponding curve for the SDSS (for which we take $n(z)\propto z^2 e^{(-z/0.075)^{1.5}}$ based upon empirical fits to the data set) for comparison. Figure 7 converts this to the co-moving number density of objects, assuming our standard cosmology. The diamonds mark the median redshifts of the various surveys. The sample density is important since the statistical weight of a survey for environmental and small-scale clustering measurements increases as the square of this density if sky area is held constant (see below). Figure 7 shows that DEEP2/EGS is ∼4 times denser than zCOSMOS-bright and VVDS-deep in the redshift range z = 0.6–1.0 and ∼20 times denser than VVDS-wide. Both the higher secure-redshift rate and denser targeting of DEEP2 contribute to this difference. We omit PRIMUS from these figures and the environment figure of merit calculation (below) as the ability to determine local environment for individual objects in the PRIMUS sample is limited by redshift errors (σ_z/(1 + z) ≳ 0.005 ≳ 15 h⁻¹ Mpc comoving) rather than sample number density; its number density is intermediate between that of zCOSMOS-bright or VVDS-deep and that of DEEP2.
• 4.  
  Statistical weight for environment measures. A useful figure of merit that describes a survey's total statistical weight for environmental purposes (i.e., determining the average overdensity of the regions in which a given galaxy population is found) scales as N²/A, where N is the number of reliable redshifts and A is the area covered (assuming matching redshift distributions).³⁴ This metric is given for the various surveys in Table 6 ("Env. metric"). The combined environmental weight of DEEP2+EGS will be four times that of zCOSMOS-bright when that survey is fully completed, and is 14–35 times the weight of VVDS-deep and VVDS-wide in their present states.
• 5.  
  Spectral information. Other measures of survey power include spectral resolution and the total number of independent spectral resolution elements sampled. With a spectral resolution that is 10 or 26 times higher than zCOSMOS-bright or VVDS, respectively, DEEP2 is the only large deep survey that can measure the internal kinematics of galaxies, satellite motions, and small group velocity dispersions. Each DEEP2/DEIMOS spectrum has ∼2000 independent spectral resolution elements, as opposed to ∼320 for zCOSMOS-bright, ∼120 for VVDS-wide and VVDS-deep, and ∼20 for PRIMUS. Multiplying by the number of design targets (excluding stars) gives the total number of spectral elements present in galaxy spectra. By this metric, DEEP2+EGS has 16 times more information than zCOSMOS-bright, 10 and 33 times more information than VVDS-wide and VVDS-deep, and 185 times more information than PRIMUS. These figures are generous, as we have here assumed design numbers for total survey size and that all spectra in all surveys are equally likely to yield reliable redshifts once stars are excluded.
• 6.  
  Galaxy counts. A final metric of survey power is the accuracy of galaxy counts. Two sources of noise contribute: Poisson statistics in the number of galaxies counted, and sample (or "cosmic") variance, which is determined by the number of fields, their areas, and geometries. Using the publicly available QUICKCV code of Newman & Davis (2002), we find that the cosmic variance in the count of a population of galaxies with r₀ = 4 h⁻¹ Mpc (comoving) and γ = 1.8 at z = 0.75–0.95 will be 7.6% for DEEP2, as opposed to 30% for TKRS, 14% for the completed area of VVDS-deep, 6.6% for VVDS-wide, 12% for the full zCOSMOS-bright area, and 5.1% for PRIMUS (here we assume square field geometry and equal area per field for all surveys but DEEP2; this will underestimate variance for VVDS-wide, as most redshifts are concentrated in a single field in that case). As a result, the noise in DEEP2 galaxy counts (e.g., measurements of the abundance of any particular population) will be smaller than in other distant z ∼ 1 grating spectroscopic surveys (though not than in PRIMUS); the larger sample size yields smaller Poisson errors, while the relatively long, narrow field geometry of DEEP2 gives smaller cosmic variance than would nearly square fields of the same area (Newman & Davis 2002).

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To conclude, by all of these measures, DEEP2+EGS is more powerful than any contemporaneous high-resolution spectroscopic survey at z ∼ 1; in many cases, by a factor of 4–30×. This power enables a wide variety of unique scientific investigations. Of course, different figures of merit may be relevant for other types of studies than those considered here, but these areas of comparative advantage have led directly to much key DEEP2 science.

We have excluded PRIMUS in many of these comparisons; it has largely followed DEEP2 in time, and operates in a very different domain. Due to the very low resolution of its spectroscopy, redshift uncertainties are relatively large, ∼1800–3300 km s⁻¹ (depending on redshift, due to the wavelength dependence of resolution in prism spectroscopy). This makes it infeasible to measure environment on ∼Mpc scales for individual objects (see Cooper et al. 2005), making our usual environmental figure of merit irrelevant. However, with nearly 80,000 redshifts over seven different fields, it has, by a significant factor, the lowest cosmic variance of any of these surveys and will be able to count rare objects and measure mass and luminosity functions for bright objects with unparalleled accuracy. It will also be effective at measuring clustering extending to relatively large scales; this allows measurement of the average overdensity of a population, an important measure of environment complementary to the measurement of overdensities for individual objects.

6.1. Photometric Catalog and p_gal Probabilities

The photometric catalogs used for selecting DEEP2 targets (the pcat catalogs, described in detail in Coil et al. 2004b) are derived from CFHT images taken with the 12K × 8K mosaic camera (Cuillandre et al. 2001) in the B, R, and I bands. These images were taken as part of a major weak-lensing survey by Nick Kaiser and Gerry Luppino, and we were very fortunate to piggyback on their efforts. The FOV of the camera is 28' × 42', as illustrated by the pointing boundaries in Figures 1 and 2.

The R-band images have the highest signal-to-noise ratio (S/N) and are used to define the object catalog, which is complete to R_AB > 24.15 in all pointings. Objects were identified using the imcat software package written by N. Kaiser and described in Kaiser et al. (1995). This package was also used to calculate other image parameters used in object selection, such as object sizes and photometry. In Fields 2–4, the calibrated pcat catalogs for separate pointings are only utilized separately, and slitmasks in these fields were designed independently (though pointings overlap in Field 4, which means that one object can appear in two pcat's). In Field 1 (EGS), the pcat's were merged to make a single catalog for the whole area before the masks were designed (retaining the higher-quality photometry in overlap regions), so that each galaxy can appear only once. Each object is assigned an eight-digit object number; the first digit of the object number indicates the field the object was found in, the second digit indicates the CFHT pointing number, and the remaining digits provide a unique identifier, counting upward from zero. As an example, object 32001226 is the 1227th object in the pcat catalog for Field 3, pointing 2.

Objects with a high probability of being a star (i.e., a low probability of being a galaxy, p_gal, as described in Coil et al. 2004b) were excluded when defining the pool of objects from which DEEP2 targets are selected. Figure 8 plots object radius r_g versus apparent R_AB magnitude, where r_g is the 1σ radius in pixels of a circular Gaussian fitted to the CFHT photometry. The plot shown is for Field 3, pointing 2 (also referred to as pointing 32), which has seeing matching the overall median for the CFHT/DEEP2 data (084 FWHM); however, apparent object sizes are analyzed separately for each CFHT pointing. Stars are identifiable as the relatively tight, horizontal locus of points below and to the left of galaxies. Stellar radii increase at bright magnitudes due to saturation; the vertical line marks the point at which saturation becomes detectable in this particular pointing. Saturation sets in at R_AB ∼ 16.7–18.0 depending upon pointing, establishing the bright magnitude limit for DEEP2 targets, R_AB > 18.5.

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Information from the size–magnitude diagram in Figure 8 is used in conjunction with the B − R versus R − I color–color diagram to compute p_gal; we summarize the classifications here, and refer the reader to Coil et al. (2004b) for details. First, objects with bad pixel or saturation flags set for their central pixel are assigned p_gal = −2, and objects without a complete set of BRI magnitude measurements are given p_gal = −1. Next, objects that have colors unlike any other stars or bright galaxies in the sample are given p_gal = 2 (regardless of their size and magnitude, so long as p_gal has not yet been set); this classification will not be overridden by that below. After those objects are excluded, the upper horizontal dashed line denotes the 95% upper radius range for stars (determined separately for each CFHT pointing), and all unclassified sources above this line are considered extended and assigned p_gal = 3. However, stars have sizes indistinguishable from galaxies at dim magnitudes, particularly below R_AB ∼ 23. In this regime, we can use the fact that stars tend to be brighter than and occupy a different locus in color–color space from compact galaxies to differentiate the two classes. The differences in colors are illustrated in Figure 9, which shows the BRI color–color diagrams for stars and extended galaxies in one DEEP2 pcat. For all objects having sizes consistent with the stars in a given pointing, the value of p_gal indicates the net Bayesian probability that an object is a galaxy (as opposed to a star) based on both color information and brightness; it is therefore a value between 0 and 1. The red points in Figure 8 are the objects identified as likely stars, which we define as those having p_gal < 0.2.

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To summarize: negative p_gal values indicate objects with problematic photometry. p_gal = 3 indicates an extended source, all of which are included for target selection. Objects with peculiar colors have p_gal = 2; these are also all taken as candidates (the vast majority have turned out to be objects with large photometric errors). Finally, values of p_gal from 0 to 1 are used for compact objects with a size consistent with stars. More details are provided in Coil et al. (2004b). All objects with p_gal > 0.2 are included as candidate targets for DEEP2, with selection weight proportional to p_gal (to a maximum weight of 1). Further details on sample selection are given in Section 6.2, and possible biases are described in Section 8.

Note that the trajectory of stellar colors in Figure 9 is approximately described by two straight lines with a "knee" separating the two. Demanding that this knee be identical in all fields allows us to place all CFHT 12K pointings on a common color system, with an overall zero point determined via comparison to stars in the SDSS. From a variety of tests, we have found that pointing-to-pointing variations in the average photometric zero points are at the <0.01 mag level, while variations within pointings and absolute zero point uncertainties are ∼0.02–0.04 mag (Coil et al. 2004b).

6.2. Target Pool Selection Procedure

With p_gal determined, a pool of potentially acceptable DEEP2 target galaxies can be defined. The final slitmasks are designed by selecting objects from this pool and placing them on slitlets. All galaxies selected as targets must fulfill three separate selection criteria that apply in all four DEEP2 fields.

First, the object must be classified as a potential galaxy by our probabilistic star–galaxy separation procedure. All extended objects and objects with peculiar colors are automatically included (p_gal = 2 or 3). Objects whose sizes are consistent with stars are taken as eligible targets if they have p_gal > 0.2, i.e., the probability of being a galaxy is greater than 20%. The distribution of p_gal is extremely bimodal, with values piling up around zero or one (Coil et al. 2004b); as a result, varying the cut level between 0.2 and 0.8 makes very little difference to the sample.

The next cut is on apparent R-band magnitude: to be considered for DEEP2 targeting, an object must lie in the range 18.5 < R_AB < 24.1.³⁵ For science purposes, it would have been more ideal to use a redder band like I to set the survey magnitude limit, but the CFHT I photometry obtained was less uniform in depth, necessitating the adoption of R.³⁶

Finally, the object must have a SB above a fixed limit (indicated by the slanting line in Figure 8). This SB requirement is defined by the equation:

$$\begin{equation} {\rm SB} = R_{\rm AB} + 2.5 \log _{10}{[\pi (3r_g)^2]} \le 26.5, \end{equation} \tag{ 1 }$$

where r_g is the Gaussian profile radius for that object, here given in arcseconds. The minimum r_g is set to 033, so that objects with 3r_g < 1'' are presumed to have an effective 3σ radius of 1'' minimizing the effect of noise in measuring the sizes of compact objects on this cut. Visual inspection of the low-SB objects which are excluded by this cut indicates that nearly all are double or multiple sources in the BRI images that were incorrectly identified as single objects in the pcat due to blending. Their SBs are low because their radii are falsely inflated. Since the data for multiple objects are ambiguous, they are not good targets for DEEP2, and this cut properly excludes many of them.

The problematic deblending of these objects would affect counts of pairs within DEEP2 at separations corresponding to the distance between the two components. Almost all objects excluded by the SB cut have estimated Gaussian radii r_g < 125, which generally roughly corresponds to the distance between the brighter and fainter component of the blend. We therefore can conclude that counts of pairs with separations ≲ 125 would be substantially negatively affected by the deblending algorithms used. This separation corresponds to a comoving separation of 14 h⁻¹ kpc at z = 1 (or 7 h⁻¹ kpc physical). For comparison, papers which have investigated DEEP2 pair counts exclude separations below 10 h⁻¹ kpc physical from consideration, while DEEP2 clustering studies have excluded pairs with separations below 50 h⁻¹ kpc comoving. We thus do not expect these deblending issues to have any significant effect on published science results, but advise users of the DEEP2 catalog to be cautious about conducting analyses which rely on counting pairs of objects with separations ${\lesssim } 2^{\prime \prime }\;\hbox{--}3^{\prime \prime }\;$. Further discussion of blended multiple objects may be found in Section 12.

6.3. Color Pre-selection in Fields 2–4

In Fields 2–4, the target pool is further refined to remove galaxies with redshifts likely to be below z ∼ 0.75. All but the bluest galaxies exhibit a significant break in their spectra at λ ∼ 4000 Å. This break causes a strong separation in color–color space between objects where the break falls in the B band or on the blue side of R, versus those where it occurs at redder wavelengths. We therefore use galaxies' B − R and R − I colors to identify the low-z interlopers. Since the bluest, flattest-spectrum objects exhibit minimal breaks (having colors near 0 at all redshifts), we always include those objects within our selection region in order to ensure that our sample is complete for galaxies at z > 0.75.

Figures 10–12 show color–color plots of galaxies in different redshift regimes in the EGS, where we obtained spectroscopy of galaxies at all redshifts (i.e., galaxies were not excluded based on this color cut). The lines show the nominal color boundary used to screen out low-redshift galaxies—essentially, only objects to the right and below this line are chosen in Fields 2–4, while objects of all colors are observed in EGS.

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The boundary used is not perfectly sharp, but rather the weight given an object for selection falls off (from 1) as a 2D Gaussian with σ = 0.05 mag in both coordinates; we call the resulting weight the "color-weighting factor" for Fields 2–4 in the discussion below. This "pre-whitening" is done to reduce the impact of possible systematic color errors within a single CFHT 12K pointing, which are of order 0.02–0.04 mag (Coil et al. 2004b). The lines shown are not the nominal (i.e., sharp) boundary but rather depict the locus of points where the color-weighting factor equals 0.1 (i.e., 10%), the minimum for objects that will be selected for DEEP2 spectroscopy (for R − I < 0.2, the plotted lines are only approximately correct). Although this weight is used in target selection, selection probability is a slow function of the weight.³⁷ The boundary in these figures corresponds to selection criteria for DEEP2 targets of

• 1.  
  (B − R) < 0.5; and/or
• 2.  
  (R − I) > 1.1; and/or
• 3.  
  (B − R) < 2.45 × (R − I) − 0.2976.

The selection weight is 100% for objects with (B − R) < 0.389; (R − I) > 1.211; and/or (B − R) < 2.45 × (R − I) − 0.311.

Figure 13 demonstrates why we would expect such a color pre-selection to be effective. This figure shows the tracks of redshifted galaxy spectral energy distributions (SEDs) from Coleman et al. (1980, augmented by starburst galaxies from Kinney et al. 1996) in color–color space. Galaxies move across the color–color boundary rapidly as their Balmer and 4000 Å breaks move first through B − R and then through R − I near z = 0.7. The resulting valley in the colors can be used to sort galaxies into two groups below and above z ∼ 0.75.

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The CWW (Coleman, Weedman, and Wu) models are illustrative only—the actual boundary was tuned using DEEP1 data and early redshifts in Field 1 (EGS), where all galaxies are eligible targets regardless of their color. Figure 14 shows the final redshift histograms of objects passing and failing the color cut in EGS. The vertical dashed line is the desired redshift cut at z = 0.75, and the 50%–50% crossover point is at z = 0.714. The crossover has been placed significantly below the target cut in order to enhance sample completeness at z > 0.75 (at the expense of somewhat decreased efficiency for targeting only high-z objects). Figure 15 shows the targeted fraction at all redshifts, which indicates the completeness of our color cut at a particular z. For the bin centered at z = 0.75, the pre-selection color cut correctly captures 91% of all objects and incorrectly rejects 9%. For bins above z = 0.8, these fractions are approximately constant at 97.5% and 2.5%, respectively. Figures 10 and 12 show that the loss of high-z galaxies and the creeping in of low-z galaxies are primarily due to blue objects in the lower-left corner of the color–color diagrams, whose colors tend to blur together at low and high redshift, as well as to objects with catastrophic photometric errors.

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The net effect of the color pre-selection in Fields 2–4 is to remove ∼55% of R < 24.1 objects from the target list—almost all unwanted foreground galaxies—with very minimal loss of the desired distant galaxies, and thus to increase the survey's efficiency for studying objects at the target redshift of z ∼ 1 by a factor of ∼2.2 at the cost of a ∼3% loss of desirable targets.

7.1. DEIMOS Detector and Slitmask Geometry

Having described the factors which determine whether an object is targeted by DEEP2, as well as the factors which contribute to their selection weight, we now turn to the methods used to design individual slitmasks from this target pool.

Our slitmask design algorithms intimately intertwined with the geometry of the DEIMOS detector array and slitmasks, which are illustrated in Figure 16. Related instrument parameters are given in Table 2. The telescope focal plane and slitmask geometry are shown as they are imaged onto the CCD detector array. For simplicity, we adopt the same coordinate system convention used for DEIMOS pipeline software outputs: "columns" run horizontally in the figure—i.e., parallel to the slitlet direction—while "rows" run vertically in the figure, parallel to the spectral direction. A typical extracted spectrum will therefore have 8192 columns but considerably fewer rows.³⁸

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The CCD detector is composed of eight 2K × 4K MIT Lincoln CCDs with 15 μ pixels, for a total size of 8192 × 8192 pixels and total physical dimensions 126 mm × 126 mm. The CCD thickness is greater than normal (40 μ rather than 15 μ), which renders fringing negligible at wavelengths below 8000 Å and still yields low fringe amplitudes at longer wavelengths (e.g., only ±2% at 9000 Å). This thickness also boosts total system quantum efficiency at far-red wavelengths, e.g., to 16% at 9000 Å.³⁹ The spacing between CCDs in the spectral direction is only seven pixels wide, while the gap between the long sides of the chips is roughly 1 mm, or $8^{\prime \prime }\;$. A single spectrum in general falls on only two CCDs.

The slitmasks are flexible, flat aluminum sheets that are 23.6 cm wide, 75.7 cm long, and 0.50 mm thick. The total length of the mask on the sky is 167, while the maximum usable slit length (subtracting the CCD gaps) is 163. The masks are milled flat on a computer-controlled milling machine and spring-loaded onto a cylindrically curved mandrel in the spectrograph that approximates the spherically curved telescope focal surface. Eleven slitmasks can be held in a jukebox-like cassette at one time.

7.2. Mask Design Algorithm

The widest part of a DEIMOS slitmask projects to 52 across on the sky, but we place slitlets only within the inner 4' because the outline on one side is irregular. The wavelength range of the portion of the spectrum from a given slitlet which actually falls on the DEIMOS CCDs will vary according to slitlet placement. To maximize the wavelength range that is common to all objects (given anamorphic shifts in central wavelength with position on the sky), we select targets for spectroscopy only within a strip which is curved slightly "backward" on the sky, with edges corresponding to lines of constant wavelength on the detector.

To ensure good sky subtraction, we require that slitlets generally be at least ∼3'' long, implemented by requiring that successive targets be at least 3'' apart in the long direction of a DEIMOS slitmask (i.e., along a "row"). Objects are not placed within 03 of the end of a slitlet in order to ensure uniform slit width along each object, enabling accurate sky subtraction. We also require 06 of dead space in the slitmask's long direction between slitlet ends to limit cross-contamination between light from adjacent spectra (this is part of, rather than adding to, the minimum spacing between objects). The average slitlet length resulting from this procedure is 7''.

In Fields 2–4, the pattern of slitmasks on the sky is chevron-shaped, as shown in Figure 1. The two arms of the chevron are observed either east or west of the meridian to better align the slitlets with the atmospheric dispersion direction. Masks are designed separately for each of these two sets of masks; where they overlap at the point of the "V," some objects are observed multiple times, allowing tests of the repeatability of DEEP2 measurements. The slanting pattern also keeps the masks within the boundaries of the 28' wide CFHT 12K pointings, despite the masks being >14' long. Mask centers are separated along the long direction of a DEEP2 field by 2' on average, which gives each object roughly two chances to be included on a slitmask. The actual step size is modulated by an adaptive tiling scheme (see below).

The algorithm to place objects on masks in Fields 2–4 assigns each object a weight W between 0 and 1 that is the product of four factors. The first factor, W_SG, comes from the star–galaxy separation probability p_gal; it is unity if p_gal = 2 or 3 but equals p_gal if p_gal is in the range 0 to 1 (i.e., for small galaxies or stars); only objects with p_gal > 0.2 are considered for targeting. The second factor, W_c, which we will refer to as the "color-weight" is a measure of each object's consistency with the DEEP2 color–color cut. As explained in Section 6.3, this factor runs between 0 and 1 and is the result of smoothing a sharp-edged step function in the color–color diagram by a 2D Gaussian of width σ = 0.05 mag in each coordinate. Only objects with color weight >0.1 are considered for targeting.

The third factor, W_R, is a function only of R magnitude and is designed to reduce gradients in the distribution of objects in redshift and magnitude. In Fields 2–4, this weight is given by the smaller of the two numbers (0.75 × 10^{−0.4*(R − 24.1)}) and 1, which yields a weight that rolls off smoothly from 1.0 to 0.75 in the last 0.31 mag, de-weighting the faintest galaxies moderately. The final factor, applied only for DEEP2 objects observed in 2003 or later, is designed to reduce the number of high-redshift galaxies beyond z = 1.4 that are targeted, as they often fail to yield redshifts in DEEP2 spectroscopy. The target selection weights for these "blue corner" objects (those with B − R < 0.5 and R − I < 0.45) are multiplied by a factor W_bc that rises linearly from 0.1 for objects with R − I ⩽ 0.045 to 1 for objects with R − I ⩾ 0.45. Hence, in Fields 2–4, W = W_SG × W_c × W_R × W_bc.

In the EGS, p_gal is still used for weighting, but no color pre-selection or blue-corner deweighting are applied, eliminating the second and fourth weighting factors. However, ignoring color information entirely yields a sample which is dominated by faint foreground galaxies. Therefore, a somewhat different form is used for the R-magnitude-based weight (W_R) in this field.

Specifically, for EGS we calculate this weight factor differently according to which of two possible different scenarios applies:

• 1.  
  If R < 21.5 or the galaxy passes the color cut to be at high redshift,⁴⁰ W_R takes the same value as it would in Fields 2–4, falling from 1 at R ⩽ 23.8 to 0.75 at R = 24.1.
• 2.  
  If R ⩾ 21.5 and the galaxy fails the color cut (i.e., it is both faint and at low redshift), the weight is the lesser of the numbers 0.1 × 10^{−0.4(R − 24.1)} and 1. This yields a weight that rolls off smoothly from 1.0 at R = 21.6 to 0.1 at R = 24.1, thereby decreasing the sampling rate for faint low-z galaxies.

As a result, distant EGS galaxies are weighted very like those in Fields 2–4 (except for small differences in the color boundary), while rare, intrinsically-bright low-redshift galaxies are given extra priority in target selection. In EGS, W = W_SG × W_R; but unlike in Fields 2–4, W_R here depends indirectly on BRI color. We will summarize the effects of the two weighting schemes on the resulting sample at the end of this section, after describing the actual mask design process.⁴¹

In Fields 2–4, objects are allocated among the slitmasks in a two-stage process.⁴² The first pass places slitlets only in a central strip that is 2' wide on average (though this width can vary due to adaptive tiling, q.v. below). This central, curved strip is favored in order to maximize the wavelength region common to all spectra (with our chosen grating, the wavelength shift across 2' is ∼200 Å).

Cosmic variance in the number of targets within a 16' × 2' region is high, so that some masks will have fewer slitlets than others if masks are evenly spaced. To minimize this variation, we iteratively adjust the positions (and correspondingly the widths of the central regions) of masks in Fields 2–4 such that the number of targets selected in the first pass is held roughly constant from mask to mask (see Figure 17, which reflects these variations). This "adaptive tiling" strategy helps to ensure that a uniform fraction of target galaxies is sampled over the survey region.

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At the beginning of the first pass, the list of targets is temporarily trimmed by generating a random number between 0 and 1 and retaining only objects for which this random number is less than their weight. Thus, low-W objects (e.g., likely stars and galaxies just outside the nominal color cut) are only rarely placed on slits in this first pass. The trimmed list is then searched for cases where we can place two of the selected objects (separated by less than 3'' in the long direction) on a single slitlet that has a position angle (P.A.) relative to the long axis of the mask of less than 30°. Slitlets are allocated first to all such cases, boosting our ability to study close pairs of galaxies.

A random priority uniformly distributed between 0 and 1, P₁, is then generated for each of the remaining objects in the trimmed list. Slit allocation then begins at one end of the mask (along its long axis) and proceeds to the opposite limit. Each object that can be observed without precluding the observation of any other is selected for observation; in cases of conflicts, the object with greatest P₁ is taken. A new object will be allocated a slitlet only if it is more than a minimum distance along the long axis of the mask away from any object already targeted. This minimum buffer distance is the greater of 3'' or (03 + twice the radius of the new object projected along the slit, r_{g, proj}), where the latter is computed from the new object's Gaussian radius r_g, axis ratio, and P.A. New objects that are large must therefore be farther from existing objects and will be allocated longer slitlets as a result.

This procedure (initial selection according to W followed by nearly random selection among the surviving targets) yields a sample where the probability of selection is almost perfectly proportional to an object's weight, making the best possible use of the central portion of each mask. In Fields 2–4, 77%–80% of slitlets are allocated in the first pass.

After the first pass through all masks is completed, the remaining galaxies that overlap a given mask (over the full 16' × 4' area) are given new weight values W₂ according to their initial selection weights, with W₂ = (W/1–0.55W). This new weight accounts for the fact that the probability a given object is selected in pass 1 is very close to 0.55W, so the probability it is not selected is 1–0.55W. A new random number uniformly distributed between 0 and 1, P₂, is then generated for each object; all potential second-pass targets are then ranked in descending order of W₂/P₂, providing a priority to each one. If all objects in pass 2 were subject to conflicts (i.e., have to compete with other objects for slitlets), this priority would ensure that the final probability an object is selected after passes 1 and 2 is proportional to its initial weight, W. The probability an object is selected in pass 1 is obviously proportional to W. To be selected in pass 2, an object had to not be selected in pass 1 (with probability (1–0.55W)); by ranking in W₂/P₂, objects are selected in pass 2 with a probability that is proportional to W₂ = (W/1–0.55W). Thus, the net probability of being selected in pass 2 must be proportional to (1–0.55W)(W/1–0.55W)∝W as well.

Objects are then allocated slitlets in descending order of their priority, subject to the requirement that they do not conflict with any slitlet that has already been added to the mask (e.g., as an alignment star, in pass 1, or as an object with higher priority in pass 2). In the end, any target that can be placed on the mask without causing a conflict is included; as a result, in the second pass, low-weight objects will frequently be selected if they are cost-free. This causes the final selection probability of an object not to be simply proportional to W; in Fields 2–4, the probability is instead closely approximated by p_selection = 0.27976 + 0.44717W − 0.09137W². Hence, an object with a weight of 0.1 will be selected for observation 32% of the time, while one with W = 1 will be selected 64% of the time. Since most eligible targets have a weight near 1, the overall selection rate is close to the latter value. The second pass proceeds from west to east, assigning targets to all the masks in a row (i.e., all the masks with similar P.A.) in order.

The set of targets selected in the EGS differs in two respects from those in Fields 2–4. First, as noted above, there is no pre-selection based on color, and the R-magnitude-based weighting factor employed is different in order to suppress the number of faint foreground galaxies. The tile pattern in EGS is also different owing to the narrower width of the region, 16' rather than 30'. Masks are divided into eight groups with 15 masks per group, with each group approximately square in size (see Figure 2). In each square, eight masks have their long dimensions perpendicular to the long axis of the strip, and seven masks have their long axes parallel to the strip; masks parallel to the strip (within a given pointing) are given larger mask numbers.

In order to maximize the number of galaxies having measured rotation curves, we first divide all extended, clearly elliptical objects (those with eccentricity > 0.081 (corresponding to axis ratio b/a < 0.85) and size 3r_g > 1 arcsec) into two sets, one consisting of objects with their major axis within 45° of the long axis of the strip and the other including the remainder. The two-pass maskmaking algorithm described previously is then run on the set of objects in the second category, combined with those which are too small or round to have a well-defined P.A., to assign objects to masks that have their long direction perpendicular to the strip. Then, any galaxies not yet assigned to a mask, as well as the extended objects with their long axis aligned along the strip, are used to design the masks which have their long dimension parallel to the strip, again using our standard slit assignment algorithm. The crossed orientations again permit observations both east and west of the meridian and enable an expanded set of rotation curve measurements. However, in EGS the step size between masks is only 1' to allow for the greater density of targets on the sky; unlike in the other fields, the step size is not varied adaptively.

In EGS, 74% of objects on slitmasks are selected in the first pass, which again places targets only in the central 2' width of a mask. The second pass is similar to the second pass in Fields 2–4; again, galaxies are selected over the full 4' active width. By limiting the first pass selection to a field of only 2', the spectral coverage of the dispersed light for the galaxies is made more uniform. In the EGS, the probability an object is selected for observation depends on the weight W (which here is the product of W_SG and the magnitude-dependent weight W_R) as p_selection = 0.33398 + 0.42687W; so an object with W = 0.1 is selected 38% of the time, while 76% of objects with W = 1 are targeted.

Once all objects are chosen, the final step is to set the lengths of the slitlets. Since no account was taken of the sizes of previously selected objects when new ones were added, it may happen that two projected buffer distances, each of size 2r_{g, proj} + 03, overlap for two neighboring objects. In this case, the available space is evenly allocated between the objects, regardless of which one is larger. Much more commonly, when the separation is larger than the two buffer distances, the available slit lengths are allocated in proportion to their values of r_{g, proj}. In both cases, half the dead space of 06 between slitlets is subtracted from the extent of each slitlet in the direction of overlap.

Once slitlets have been placed on targets, the design of all DEEP2 masks are adjusted to include ∼8 sky-only slitlets placed in open spaces on the masks. Their positions along the long axis of the mask are chosen to fall in-between the objects with largest separations, while their positions along the short axis are chosen to lie in empty regions (i.e., positions with no significant deviation from the background flux level within a 1'' radius) in the CFHT 12K images. The sky slitlets are used to perform fallback, "non-local" sky subtraction, which proved useful in dealing with some rare instrumental anomalies and, occasionally, for very short slitlets. These sky slitlets are only 07 wide; to produce a non-local sky model, the spectrum from a sky slitlet is convolved with a kernel that varies with wavelength, which is determined by a fit to each individual slitlet's estimated sky spectrum. In practice, this method proved inferior to local sky subtraction using the object's own sky spectrum, even for short slitlets, and it has therefore seen only limited use. However, non-local-sky-subtracted versions of both 1D and 2D spectra are included in the pipeline-produced data files for completeness.

As a final step, in order to preserve rotation curve information, the long axis of each slitlet is oriented as closely as possible along the major axis of its galaxy (as measured from the CFHT photometry), provided the following conditions are met: (1) the major axis of the object is within ±60° of the long axis of the mask, (2) the galaxy has r_g ⩾ 1'', (3) the slitlet has not already been tilted to observe another object, and (4) the galaxy is measurably ellipsoidal, with CFHT axis ratio less than 0.85. As slitlet tilts, θ, can be up to 30° away from the long axis of the mask but no more, the mismatch between slitlet and galaxy P.A. can be up to 30° (except in cases where slits were tilted to cover multiple objects or for objects without measurable P.A.). We note that P.A.s measured from high-resolution ACS images can differ considerably from those determined from ground-based images, as found by Wirth et al. (2004).

In the central portions of a slitmask, slitlets are still tilted by ±5° compared to the mask direction for objects which do not fulfill these requirements. These small tilts ensure better wavelength sampling of the night-sky spectrum, improving sky subtraction (optical distortions provide the necessary sampling for untilted slits at the ends of a mask, so those slitlets are designed with P.A. = 0 relative to the mask's long axis). The crosswise widths of tilted slitlets are reduced by cos(θ) in order to maintain a fixed projected slitwidth along the dispersion direction.

Figure 17 shows a blowup of a region covered by several slitmasks in Field 3, with the central first-pass regions, eligible targets, selected targets, and slitlets with their final lengths and orientations all plotted. The overlap of slitmasks at the "V" of the chevron pattern provides a sample of multiply observed objects for statistical and reliability assessment purposes; we make use of this information in Section 11.3.1, below.

In the end, 61% of eligible targets are assigned slitlets in Fields 2–4. More precisely, this is the fraction selected out of targets that have 18.5 < R < 24.1 and p_gal > 0.2; pass the SB cut; and have probability >0.1 of meeting the color–color cut. Slitmasks in these fields contain ∼110–140 target slitlets (mean 121) that are typically 7'' long but span the range 3''–15+''.

In EGS, the average number of slitlets per mask is 148. In pointings 11–13 of EGS (the southern three-fourths of the field), R-band de-weighting of low-redshift galaxies boosts the relative number of high-z galaxies, with the result that, of those targets that would have been eligible for selection in Fields 2–4 (as described above), roughly 73% are selected in EGS.⁴³ In contrast, due to the deweighting of faint objects that fail the color cut, only 53% of low-z galaxies are selected. Without this deweighting, only 55% of the galaxies in a Field 2–4 equivalent sample would have been selected, which would have made the sample sparser in number density at high redshifts than the other DEEP2 fields.

The final DEEP2 target sample suffers from a variety of known selection effects. These effects should in general be taken into account and/or corrected for when utilizing the DEEP2 data set. A variety of methods for doing so have been implemented in DEEP2 science papers; see Section 3 and Table 1 for examples.

• 1.  
  Galaxy color bias due to the R magnitude limit. Selection according to a fixed apparent R-band magnitude limit causes the resulting sample to reach different depths (in terms of absolute magnitude) for galaxies of different intrinsic colors at the same redshift. At z ∼ 0.5, the R-band filter corresponds closely to restframe B, so objects are selected down to the same B-band absolute magnitude independent of color. Below that redshift, R-band selection favors redder galaxies, while above this, it favors bluer galaxies. The effect was first illustrated in Willmer et al. (2006) and is discussed in more detail in Section 15. Though fundamental, this bias is well understood and can readily be applied to mock catalogs and other statistical predictions. The same type of bias will inevitably affect any magnitude-limited sample which spans a range of redshifts, due to the broad span of intrinsic galaxy colors.
• 2.  
  Loss of bright star-like objects. The use of p_gal discriminates against point sources (i.e., objects with apparent size consistent with stars; cf. Figure 8), and thus potentially discriminates against bright Type I AGNs, i.e., QSOs. AGNs will be lost only if they are both point-like and lie on or near the stellar locus in the color–color diagram. As a result, Type I AGNs will be included in the DEEP2 sample at some redshifts, but excluded at others.
• 3.  
  Misclassification of faint stars as galaxies. Although the differential number counts of objects classified as stars (p_gal < 0.2) in the DEEP2 pcat's rise approximately linearly at bright magnitudes, they flatten out at R_AB ∼ 22.5; it is likely not coincidental that this is where large numbers of galaxies begin to populate the stellar regime in Figure 8. It appears that the p_gal values overestimate the probability that faint objects are galaxies rather than stars; we therefore tend to include more stars than expected within the DEEP2 target list. This is conservative from the standpoint of galaxy selection, as the contaminant objects are trivial to weed out once spectra are obtained.⁴⁴ However, as a result of this misclassification, a list of photometric stars selected purely via their p_gal values will be incomplete at the faint end and would be of limited use for stellar studies.
• 4.  
  Loss of objects due to missing B or I photometry. The definition of p_gal and the DEEP2 color pre-selection both depend on having measured B − R and R − I colors.⁴⁵ Though the R-band photometry is complete to the R_AB = 24.1 magnitude limit in all fields (Coil et al. 2004b), very red or blue objects may not be detectable in either the B or I imaging. However, in the three EGS pcat pointings with accurate B and I photometry (11–13), which contain 59,594 objects brighter than R_AB = 24.1, only 153 galaxies are missing B. They tend to be faint and red and constitute only 4% of distant (red-sequence) galaxies with R_AB > 23 and R − I > 1.0. Their loss is not significant. Similarly, 71 galaxies with R_AB < 24.1 are not detected in I; they are predominantly very blue. We expect similar rates of loss in other DEEP2 pointings.
• 5.  
  Loss of small, distant, faint red galaxies. Our Bayesian method for discriminating faint stars from galaxies depends on the contrast between stars and galaxies in a color–color plot (Figure 9), as well as on the fitting functions used for the magnitude distributions of each class. The blue stellar locus is quite narrow, so the loss of blue galaxies misclassified as stars is fractionally small. The situation changes where B − R > 1.5 and R − I > 0.6, where the surface density of stars becomes more comparable to that of galaxies. As shown by Figure 13, this region of the color–color plot is populated by intrinsically red galaxies beyond z ∼ 0.7. Loss of such galaxies was estimated by Willmer et al. (2006) using the higher-resolution HST ACS images in EGS and partial redshift data. We redo that calculation using final EGS redshifts and a larger database.Figure 18 plots the color–color diagram for EGS but restricts to objects in the ACS mosaic fainter than R = 23.0, where misclassification is most likely (cf. Figure 8). DEEP2 stellar candidates (p_gal < 0.2) that are confirmed as stars in EGS ACS images are plotted in blue; those shown instead to be galaxies are red. The latter are missed by DEEP2 and are thus a concern. Galaxies are lost in a narrow band in B − R, which corresponds to certain combinations of intrinsic red-sequence color and redshift (cf. Figure 13).The central rectangle in Figure 18 delineates the region in which galaxies are lost. Setting true stars aside (the blue points) leaves a total of 99 galaxies in the rectangle, of which 27 were misclassified as stars by p_gal (red points). However, only about half of all R > 23 red-sequence galaxies at z = 0.75–1.1 lie in the rectangle—the others lie in the rectangles above or below—and this fraction is found to be virtually constant at all redshifts above z = 0.75. Since galaxies outside the central rectangle are not lost, the net result is that ∼0.27 × 0.50 ∼0.13=13% of red-sequence galaxies in the dimmest magnitude bin are lost, and this loss is uniform beyond z = 0.75. This matches the estimate of Willmer et al. (2006). A loss of this size is not generally important for analyses of total counts along the red sequence but might be important (effects as large as 27%) for studies in individual restframe color bins within the red sequence that have apparent B − R near 2.25.
• 6.  
  Loss of objects at small separations. Because spectra of galaxies on the same mask cannot be allowed to overlap, the number of slitlets that can be put down in a small area is limited for objects that would have similar positions on a mask (along its long axis); this affects the sampling rate in dense regions. This effect is illustrated in Figure 19, expanded from Gerke et al. (2005), which shows that the sampling rate in the very densest regions (in terms of nearest neighbor distance on the sky) is reduced by almost a factor of two from nominal, but that the fraction of sampled galaxies that yield reliable redshifts is unaffected. The upturn of the sampling rate at small separations is due to the placement of close pairs on a single slitlet.It should be noted that this effect is much weaker as a function of three-dimensional density: unlike in nearby galaxy surveys like SDSS, most conflicting objects (and most sets of nearest-neighbors on the sky) are actually at very different redshifts from each other (a consequence both of L_* brightening with z and the comparatively small contrast in luminosity distance between z ∼ 0.7 and z ∼ 1.4). The effect is already substantially smaller in impact than fiber collisions in nearby-galaxy surveys, since in DEEP2 objects can conflict with each other along only one dimension, and even then only at scales not much larger than an individual galaxy (1'' spans ∼10 h⁻¹ kpc comoving at z = 1, while the minimum separation between objects along the mask direction—i.e., the separation within which they conflict with each other—is 3'').Nonetheless, the diminished sampling rate in dense regions is a large enough effect that it needs to be taken into account for certain statistics. For example, Coil et al. (2001) investigated the impact of prototype DEEP2 target selection algorithms on the ξ(r_p, π) diagram; they found that it introduces moderate distortion into the two-point redshift-space autocorrelation function at small projected separations, reducing the elongation of contours along the "finger of God" by about 20%. The data shown in Figure 19 can be used for modeling purposes. In all DEEP2 clustering analyses (e.g., Coil et al. 2006a, 2008) this effect is quantified and corrected using mock catalogs that have been passed through the DEEP2 target selection code.
• 7.  
  Multiple galaxies masquerading as single galaxies. The final known bias in the DEEP2 target sample is due to the finite resolution of the CFHT BRI ground-based images, in which separate galaxies may appear blended. This blending can distort the magnitudes and colors of DEEP2 galaxies, and it can also elevate galaxies that would otherwise be too faint to meet the R_AB = 24.1 magnitude limit above that threshold. Investigating these composite objects requires redshift information, and so this topic is deferred to Section 12 after DEEP2 spectroscopy, data processing, and redshift measurements have been discussed.

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Instrument and exposure parameters for the DEEP2 survey are summarized in Table 2. Each mask is observed for at least three 20 minute exposures with the DEIMOS 1200 lines mm⁻¹ gold-coated grating centered at 7800 Å. No dithering is performed between exposures because sky subtraction is natively almost photon-limited (see Section 10.2), and dithering would waste roughly half of the detector real estate.

The DEIMOS guider camera is rigidly mounted in the slitmask coordinate frame with known orientation and offset (Figure 16). Locating a guide star at a precomputed pixel location while the mask is at the proper P.A. therefore succeeds in placing all alignment stars within their 4'' square slitlets. In a direct image of the night sky through the mask, the locations of alignment stars and of all slitlets, including the alignment boxes, are visible (the latter are illuminated by the sky and hence much brighter than the interslit background).

We obtain the necessary direct alignment images efficiently by tilting the grating to zeroth order, rather than swapping the grating for a mirror; the images obtained are then analyzed using custom-designed software using a graphical interface. The pointing of the telescope and the P.A. of DEIMOS are then adjusted to center all alignment stars within their boxes, which in general centers all galaxies in their slitlets to within 01 (modulo astrometric errors). Slitmask alignment generally converges after two direct images and takes roughly five minutes. It is generally checked once using the same procedure after the first of the three spectroscopic exposures (see below).

The fraction of wavelengths common to all spectra is shown in Figure 20; 50% coverage limits are 6500 Å–9100 Å. The 10 slitwidth used for all targets yields OH skylines with an FWHM of ∼1.3 Å, which produces a spectral resolution R ≡ Δλ/λ = 5900 at 7800 Å. A custom data verification program called quicklook⁴⁶ is run during observing. This program performs a coarse reduction of 10% of the slitlets on each exposure and computes the cumulative S/N for an R = 23.5 source obtained by combining all exposures so far. We continue obtaining exposures until a minimum S/N threshold is met, which enables productive observing even under clouds or poor seeing. The quicklook software also checks for missing lamps in arcs, the occasional slitmask buckling, FCS misalignments, guiding errors along the slit, and bad or degrading seeing (based on the FWHM of the alignment star spectra). Run on a Sun workstation from circa 2002, it is able to evaluate a single DEIMOS frame in roughly 10 minutes (compared to our 20 minute exposure time).

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All slitmasks are observed at airmass below 1.5. Under optimal conditions, eight masks can be observed per night, yielding 1000–1200 spectra.

10.1. The spec2d Data Reduction Pipeline

The DEIMOS spec2d pipeline (Cooper et al. 2012b) is an IDL-based code that is modeled on and borrows significant code from the SDSS spectral pipeline of David Schlegel and Scott Burles (Schlegel & Burles 2012). Most of it was written by Douglas Finkbeiner, Marc Davis, Jeffrey Newman, and Michael Cooper, with important contributions from Brian Gerke regarding non-local sky subtraction (see below). The pipeline operates in five separate stages, each of which produces its own output files. The code operates without supervision and usually does an excellent job of wavelength fitting, sky subtraction, and object fitting.⁴⁷

The first step in data reduction is creation of a "planfile" (a plain-text file with extension.plan) which may be generated automatically after a night's observing and defines the locations of all files needed to reduce a given mask's data. The planfile may optionally control various parameters of the reduction such as the chips to be reduced, the arc line list to be used, etc. The planfile is used by a controlling IDL program, DOMASK, which calls separate routines which perform a series of reduction steps.

Step I. The first stage of data reduction is to produce calibSlit files (i.e., a set of FITS BINTABLE format files whose filename begins with "calibSlit") from the flatfield and arc frames taken through a given mask. This processing is controlled by the IDL procedure DEIMOS_MASK_CALIBRATE. Each of the eight DEIMOS CCDs is analyzed completely independently through all stages of the 2D reductions, allowing trivial parallelization; in general, every spectrum will span two of these eight CCDs, which we will generally refer to as "blue" and "red"; hence for each object's spectrum there are two separate calibSlit, spSlit, and slit files (q.v. below). The calibSlit files indicate where the slitlets fall on the CCD array for each mask and contain flatfield information and a 2D wavelength solution for each slitlet.

To produce the calibSlit files, first the multiple flats are read in, corrected for pixel-to-pixel response variations, and processed to reject cosmic-rays. To identify every slitlet, edges that are detected in the flats using an unsharp mask are compared to a table in the DEIMOS header data that describes where each slitlet should appear; a smooth polynomial is fitted to the edges of each curved spectrum to define its upper and lower limits. Each chip's combined flat frame is then mapped into rectangular arrays for each slitlet, which greatly simplifies further processing, by shifting its edges to be parallel, using interpolation (over the spatial direction) to accommodate subpixel shifts. Hence, we turn the entire flatfield image into a set of individual rectangular flatfields for each slitlet. Each slitlet's flatfield is first used to measure the "slit function," i.e., the relative throughput (maximum 1) of each slitlet as a function of position (i.e., row number) along it.⁴⁸ After normalizing by the slit function and any large-scale variation in light intensity with wavelength and position along a given slitlet, the flats are smoothed on small scales to generate a 2D fringing-correction map with mean 1.

Step II. The next step, also controlled by DEIMOS_MASK_CALIBRATE, is to solve for the wavelength of each pixel in the 2D data array. First, the entire arc (or arcs, if multiple ones are available⁴⁹) is read in and corrected for pixel-to-pixel response variations. Next, a single shift in the spatial direction between a given chip's arc data and the original flatfield, dx, is determined by finding the lag which maximizes the cross-correlation between the intensity summed over the central (in the wavelength direction) region of the arc frame with the light profile predicted from the slit edges found in Step I (only whole-pixel shifts are considered). Then, individual slitlet arc spectra are extracted and rectified in the spatial direction using the same algorithms applied for the flatfield, but using slit edges shifted from the flat by dx; the individual spectra are then corrected for the slit function and fringing using the results of Step I.

Starting with the DEIMOS optical model (produced by Drew Phillips), which gives a rough initial guess, we fit for the relationship between wavelength and pixel in a spectrum in multiple stages, obtaining a wavelength solution that is typically accurate at the 0.007 Å (∼0.02 pixel) rms level or better over the entire 2D spectrum; 0.003 Å rms is commonly achieved. The fits used are linear regressions for the coefficients of Legendre polynomials of up to fifth order (for wavelength as a function of pixel number along the central row of the slitlet) or second order (for specifying the local tilt of the constant-λ locus as function of central pixel number). The mean residual about the fit in each row of the slitlet is also stored and incorporated into the wavelength solution (i.e., we apply a row-by-row shift from the smooth polynomial-based solution, which can account for defects or dust along the slit which shift the mean wavelength of a row). The requirements that accurate OH-line subtraction places on sky subtraction are discussed in Section 10.2 and in the Appendix. We generally require errors below ∼0.01 Å rms for good sky subtraction; to be useful in attaining wavelength solutions, individual arclines must contain ∼10,000 photons in each row. The result of Steps I and II is a single calibSlit file containing all necessary calibration information per slitlet per chip (i.e., each spectrum is split into blue and red files).

Step III. The third stage of the reductions, controlled by the procedures DEIMOS_2DREDUCE and DEIMOS_SPSLIT, uses the calibSlit files produced in Steps I and II to flatfield and rectify the on-sky ("science") data for each slitlet. Response correction, slitlet extraction/rectification, and flatfielding are all done using the same procedures as for the arc files. All CCDs are again treated separately. An inverse-variance image is also produced based on the photon and read noise (with compensations for all multiplicative corrections applied), as well as maps of bad pixels (which will have zero inverse variance; this map provides flag information on why a given pixel is bad) and questionable ones (e.g., those which may be affected by imperfect vignetting corrections or cosmic rays, which will not have their inverse variance set to zero; again, this map provides flag information for each pixel).

The most important operation in this step is computing the proper sky background level (including bright OH lines) at every location in a 2D science spectrum as a function of both wavelength and position along the slitlet. First, a constant wavelength shift (relative to the arc wavelength solution) for each frame is determined using cross-correlation against a high-resolution night-sky spectrum. Then, a B-spline model for sky intensity as a function of wavelength is fitted to the sky regions of the slitlet (i.e., regions where, based on their location and size, both contamination from DEEP2 targets and slitlet edge effects are expected to be minimal). A key stratagem is tilting all slitlets by at least 5° with respect to the detector array so that each night sky line is substantially oversampled, making the B-spline fit more accurate; see Appendix A.4. The result of Step III is one spSlit file per slitlet per chip, which contains the reduced 2D spectra (with associated wavelength, inverse variance, and mask arrays) from each science frame for that slitlet and that frame's B-spline fit in alternating HDUs.

Step IV. The fourth stage, controlled by SPSLIT_COMBINE and SLITEXAM, combines the separate science exposures for each slitlet into one inverse-variance-weighted mean, sky-subtracted, cosmic ray-cleaned 2D spectrum (which we will generally refer to below as a "combined" or slit file). First, the B-spline model sky for each slitlet is subtracted from its flux. Next, the (generally) three 20 minute exposures are combined, weighting them according to the inverse variance maps from the previous stage. Cosmic ray rejection is also done at this time based on the time variability of a given pixel. The result of this process is one slit file for each slitlet for each chip, containing the processed, combined 2D spectrum, inverse variance, and wavelength solution, along with various diagnostic information (e.g., bad pixel masks). Each row of each spectrum has its own wavelength solution; a 2D map of wavelength as a function of position in an image may be obtained with the IDL function LAMBDA_EVAL.

Step V. In the fifth and final stage, 1D spectra are extracted from the combined 2D spectrum using the routine EXTRACT1D (controlled by the procedure DO_EXTRACT). Extraction is done using both "optimal" and boxcar (i.e., fixed-width sum) extraction techniques (see below), as usual processing the blue and red chips separately. As a first step in both approaches, each 2D spectrum is rectified in the wavelength direction by using whole-pixel shifts (as opposed to interpolation), making the wavelength scale in each row match the central row of the object.

The optimal extraction (or "horne" as it is labeled in the FITS headers) loosely follows the algorithm of Horne et al. (1986). However, due to the lower S/N of some DEEP2 data, instead of using the light profile evaluated at a single location along the slit to weight pixels, a Gaussian model is used for weighting. First, we measure the light profile along each slit by performing an inverse-variance weighted average of the flux along each row of the slit, excluding regions around bright night sky emission lines. Next, an overall offset between the positions of objects along each slit predicted from the mask design and their actual observed positions is determined by fitting a Gaussian to each peak in the individual slits' light profiles and comparing their locations to the prediction. We also determine the quantity that must be added to or subtracted from (in quadrature) the sizes of objects in the CFHT photometry (r_g values) to match the observed widths of each Gaussian peak, allowing compensation of sizes for differences in seeing. The center of the extraction window is determined from either the peak of the spatial profile of the object along the slit or (in low-flux cases where the peak differs by at least 5 pixels from the prediction) using the predicted position with the just-determined shift in the spatial direction applied. The extraction center is determined independently on the red and the blue sides, ameliorating the small shifts between them expected due to differential refraction.

The weighting kernel P used for optimal extraction is then a Gaussian with peak at the center of the extraction window and σ derived from a Gaussian fit to the light profile in the 2D spectrum in high-S/N cases, or the expected seeing-corrected size as derived from the photometry in the event of low S/N. In our reductions the extracted flux f at a particular wavelength is

$$\begin{equation} f ={ {\Sigma _i f_i P_i S_i} \over {\Sigma _i P_i^2 S_i}}, \end{equation} \tag{ 2 }$$

where f_i is the flux, P_i is the model profile, and S_i is the inverse variance at a particular row (at fixed wavelength). Including the inverse variance in the weight in this way yielded slightly improved results over using the Gaussian profile alone.

In the boxcar approach, bad pixels are masked (rather than interpolated over as in the optimal extraction) and the fraction of flux missed within these pixels is determined using the Gaussian model spatial profile along the slit determined for the optimal extraction. The flux from all pixels at a given wavelength is then summed, and that sum is divided by the fraction of flux which should have come from the included rows. Hence, this algorithm differs only in the case of bad pixels from a generic boxcar or tophat weighting. For this reason, the extraction is called a "boxsprof" extraction in the headers of the spec1d FITS files. The half-width of the extraction window used is a multiple of the light-profile model Gaussian width: 1.75σ (in the optimal case) or 1.3σ (in the boxcar case).

The extractions are saved in a spec1d FITS file, which contains the blue and red portions of each object's spectrum for each type of extraction, each in its own header data unit (i.e., four HDUs total). Note that in cases where multiple DEEP2 targets are placed on the same slitlet, there will be only one set of calibSlit/spSlit/slit files, but separate spec1d files for each object.

There is no step in the pipeline data reduction process that explicitly flux-calibrates the data using standard star spectra. However, DEIMOS is a fairly stable instrument, and a relative flux calibration accurate to roughly ±10% over the whole spectral range has been determined, based on tests with standard stars and the coadded spectra of galaxies on each chip (R. Yan et al., in preparation). This error does not include variations in absolute throughput due to clouds, seeing, and long-term drifts in optics reflectivity (the latter at the 30% level); in applications requiring flux calibration, we tie our observed spectra to the CFHT photometry. Standard star observations are taken on a regular basis, but these data are not part of the regular reduction process. Throughput plots (for freshly recoated optics) are available online.⁵⁰

10.2. Final Data Quality

Sample raw and reduced spectroscopic images are shown in Figures 21 and 22. Figure 21 shows a blowup of a portion of a single 20 minute sub-exposure (cosmic rays are clearly visible), while Figure 22 shows the fully reduced, CR-cleaned, sky-subtracted, and coadded ensemble of three 20 minute exposures. This particular region represents a typical reduction, with sky subtraction that is photon-noise-limited as signaled by the random noise pattern under the OH lines (although some aliasing is visible in the sky subtraction for slits which were not tilted significantly compared to the detector; this mask was one of the first observed, and we required a 5 deg minimum slit tilt only afterward).

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Poor sky subtraction happens occasionally, and some examples will be shown below. However, quantitative analysis indicates that the sky subtraction accuracy is close to photon-noise-limited even under bright sky lines and under most conditions. This is illustrated in Figures 23 and 24, which show distributions of the quantity δ/σ for sky pixels, where δ is the difference between the actual and predicted pixel intensity and σ is the read noise combined with the photon noise in that pixel based on the measured sky level at that location (inferred from a local median filtering of the inverse-variance map). If sky subtraction is noise-limited, this distribution should follow a Gaussian with rms width unity. Significant numbers of pixels with bad sky subtraction will depress the middle and enhance the tails.

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We consider first Figure 23, which treats pixels between the bright sky lines. Two sets of 800 spectra were analyzed, one set for which visual inspection confirmed good sky subtraction over the whole spectrum ("normal"), and one set for which visual inspection indicated significant systematic sky-subtraction errors over at least part of the range (see "bsky" comment code in Section 13). The horizontal axis is the ratio of the actual flux deviation at that pixel divided by the predicted noise due to read noise and photon sky noise at that pixel. If the noise is random and is properly predicted, the observed curves should be Gaussian with rms σ = 1. Both sets of spectra do indeed populate the same Gaussian, but with rms width 0.86, not 1.0, indicating that if anything the errors have been overestimated, It is reassuring to see that the tails of the distribution are not significantly overpopulated.

Figure 24 repeats this test under more difficult conditions, using the same spectra but now with pixels under bright OH lines. Small errors in the wavelength scale or in flat-fielding will cause the residuals to be large and populate the tails of the distribution. The normal, well-subtracted spectra again closely follow the same Gaussian curve with σ = 0.86; our pipeline error model appears to be modestly overconservative. The "bsky" spectra look slightly worse but are still remarkably similar to the normal spectra here as well as in the benign sky regions in Figure 24. The two figures collectively demonstrate that our sky subtraction accuracy is very close to being photon-limited both on and off the OH lines, even in spectra that the eye sees as having imperfect sky subtraction.

Figure 25 shows the major speed gain that has been obtained by deciding to use high spectral resolution for the DEEP2 survey. This figure shows the ratio of exposure times needed to obtain the same S/N at each wavelength using a spectral resolution of R = 600, which is typical of distant redshift surveys, versus DEEP2's resolution of R ∼ 6000. The red curve is the raw ratio at each pixel, while the blue curve is the red curve smoothed by a 7 Å boxcar. The speed gain varies rapidly with wavelength depending on whether one is on a sky line or not, but the median (unsmoothed) gain from 7600 to 8800 Å is 1.58. This factor is the savings in exposure time. The gain occurs because high resolution confines OH photons to a small fraction of the pixels, leaving most of the pixels much darker than they otherwise would be.

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Figure 26 illustrates various data reduction problems and their associated comment codes. For example, spectra (a) and (b) show regions with poor sky subtraction in the OH lines along the slitlets, recognizable by the systematic patches of bright and dark sky values under the OH lines. Variable wavelength errors sometimes cause these residuals to wrap along the slitlet, yielding a "barberpole" pattern. Appendix A.2 derives an allowed image-motion criterion of 0.6 pixels (rms) in the wavelength direction in order to keep flat-field fringing-induced errors in sky subtraction to tolerable levels. DEIMOS's actual image motion is two times smaller than this. Thus, the sky-subtraction errors seen in spectra (a) and (b) should not be due to fringing errors but rather to tiny residual sky-line modeling errors, due either to wrong sky-line profile shapes or to small wavelength calibration errors. Errors in the latter case of only 0.015 pixels are sufficient to shift the model sky lines enough during "de-tilting" to produce noticeable subtraction errors. Less than 1% of the total pixel area in the DEEP2 spectra is noticeably affected by such problems.

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10.3. Sample Spectra

Typical 1D spectra for eight galaxies are shown in Figure 27, arranged by R-band magnitude and color. The spectra have been smoothed with a 15 pixel boxcar. The selected galaxies lie near z = 0.8 and are sorted into two color bins, four from the blue cloud and four from the red sequence. Notable features in the 4000 Å region are visible, including [O ii] λ3727, the 4000 Å break, Ca H and K, two CN bands near 3800 Å and 4100 Å, and the higher-order Balmer lines. The lowest four panels illustrate galaxies near the survey magnitude limit (R_AB = 24.1). Emission-line redshifts are still quite easy at this level for galaxies in the blue cloud (right side), but continuum S/N is becoming marginal for red-sequence galaxies, as noted in Section 11. Velocity broadening is detectable in most spectra; 66% of all galaxies with redshifts have emission linewidths at least 3σ larger than the instrumental signature (while 79% of these galaxies have at least one line detectable at >3σ).

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Figure 28 summarizes the mean counts and S/N of the combined one-hour 1D spectra as a function of R-band magnitude. Panel (a) shows the median continuum number of photons per pixel for a range of galaxy brightnesses near z ∼ 0.8. The median value is 14 photons pixel⁻¹ near R_AB = 24.1 and scales slightly more slowly than the linear relation (shown by the dashed line) because brighter galaxies tend to overfill the slit. Much of the scatter is due to size variations—larger galaxies at fixed magnitude have lower counts per pixel. Panel (b) shows the median inverse variance per pixel for the same spectra, which is nearly flat with brightness, being dominated by sky noise (see below). Panel (c) plots the median continuum S/N per pixel, which is panel (a) divided by the square root of panel (b). The upper, dot-dashed line shows the shape of the trend expected if noise is dominated by photon statistics from the object, while the lower dashed line shows the shape expected if noise is dominated by sky. The actual data are bounded by these extremes.

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This figure is useful for predicting the S/N available from single and stacked DEEP2 spectra. For example, it says that summing together roughly 50 spectra at R ∼ 22.0 will yield S/N = 25 Å⁻¹, which is the recommended minimum for absorption-line velocity dispersion and stellar-population work (e.g., Schiavon et al. 2006).

More information about sky counts is given in Table 2. Comparing the sky continuum level between the OH lines with the read noise tells whether an individual 20 minute exposure is sky-limited or read-noise limited. The typical continuum sky count in the range 7700–8300 Å is 13 photons per 2D pixel in 20 minutes, while the variance of the read noise is only 2.55² = 6.5 e⁻ pixel⁻¹. Thus, read noise is less than sky noise but is not negligible. This suggests that some gain in continuum S/N could be obtained by using a 600 line grating instead of the 1200 line grating. Having explored several tens of thousands of galaxies at very high resolution for DEEP2, we have indeed chosen DEIMOS' 600 line grating for the DEEP3 survey in EGS, which will capture galaxies over a wider redshift range, sample more spectral features, and yield somewhat higher continuum S/N, with the tradeoff of greater difficulty in measuring linewidths and in identifying [O ii] amidst sky lines.

Figure 29 illustrates various types of information that are available from the 2D spectra. Spectra (a)–(f) illustrate a range of galaxy internal motions, from highly ordered and resolved rotation curves, as in spectrum (a), to unresolved but broadened lines, as in spectrum (f). The quantity $S_{0.5} \equiv \sqrt{0.5V_{\rm rot}^2 + \sigma ^2}$, where V_rot is rotation speed and σ is linewidth, combines both systematic and random motions into a single line-width broadening parameter (Weiner et al. 2006a, 2006b) and proves to be a remarkably useful and robust internal velocity indicator that places the internal speeds of both highly regular and highly disturbed galaxies on the same scale (Kassin et al. 2007, 2012).

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Spectra (g)–(j) show four candidate dual AGNs (Gerke et al. 2007b; Comerford et al. 2009). The first two exhibit spatially separated AGNs, while the third shows a large velocity offset between [O iii] and the stellar absorption lines, as would be expected for an in-spiralling black hole following a galaxy merger. Several dozen such offset cases have been found (Comerford et al. 2009). Panels (j)–(l) show examples of close pairs that are suitable for measuring satellite galaxy motions. Also measurable from the resolved spectra but not shown are equivalent widths and line-ratio gradients.

11.1. The spec1d Redshift Pipeline

11.2. Visual Redshift Inspection Process: The zspec Tool

To allow us to check and fit for redshifts interactively, we have developed an IDL widget-based program called zspec. This program allows the user to examine interactively each of the candidate redshifts proposed by the spec1d pipeline, or to provide an alternative redshift solution. Using this program, all redshifts from spec1d have been checked by eye, a process typically requiring 1–2 minutes per spectrum.

The three computer display screens for the zspec IDL widget are shown in Figure 30. When a candidate redshift is selected, the zspec control panel (top) displays both 1D and 2D spectra of small regions around any of the six most common absorption or emission features seen in DEEP2 spectra. The middle panel shows the full 2D spectrum, which is displayed using the ATV tool developed by Aaron Barth (Barth 2001; middle panel). The final window, shown at bottom, displays the full extracted 1D spectrum using the SPLOT tool developed by David Schlegel; the user can smooth the 1D spectrum by varying amounts if so desired. The predicted locations of more than 20 common absorption and emission features are marked in each of these windows. The spec1d pipeline template that is fitted for a given choice of redshift is plotted both in the full view and subwindows, and the variance is also plotted in the 1D spectrum view to aid the user in identifying false features associated with sky-subtraction residuals or Poisson noise. Optionally, a smoothed version of the 1D spectrum may be plotted instead of the raw measurements, and plot ranges may be adjusted arbitrarily to help the user check redshifts.

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In many cases, obvious, resolved multiple emission (e.g., the [O ii] doublet or Hβ and [O iii]) and/or absorption (e.g., Ca H and K) features will appear in the upper inspection windows at the proper positions (compared to the template) for some choice of redshift, providing immediate confirmation. In other cases, the full spectrum in either the 2D or 1D windows must be examined in order to find rarer emission features or to confirm a redshift using the ensemble of absorption lines in the spectrum of an early-type or post-starburst galaxy.

Confirmation of multiple features (where a resolved [O ii] doublet counts as two features) is required to assign a redshift to a given object with a reliable redshift quality code (Q = 3 or Q = 4; see Section 11.3). The 1D extracted spectrum and the 2D spectrum are both checked to ensure that the features are real and not a consequence of perverse Poisson noise under a sky line or due to much of the spectrum being obscured by a bad column, for instance. Other redshift quality codes which the user may assign indicate that an object's spectrum is completely masked by instrumental artifacts so that the object was effectively never observed (Q = −2), is a star (Q = −1), yields no useful redshift information (Q = 1), or may potentially yield redshift information but needs more analysis or re-reduction (Q = 2); many, but not all, Q = 2 cases may be resolved with more inspection. Section 13 below provides a more extensive description of the DEEP2 redshift quality codes.

During the zspec process, the user may also fill in one or more comment codes that signify additional information about the data; the standard codes are also described in Section 13. These codes are useful, but their application has varied over time and among various zspec users, so they are the least homogeneous aspect of the DEEP2 database. Additional descriptions can be found in Section 13.

In a small minority of cases, none of the 10 χ²-minimum redshifts from the spec1d pipeline are correct for a given galaxy, but the true redshift is still measurable with human intervention; these constitute fewer than 1% of the reliable redshifts in the DEEP2 sample. In those cases, the person inspecting the redshifts can use the zspec widget to fit for a redshift using the same algorithms used by spec1d (described in Section 11.1) but searching only a limited range in redshift around a user-specified value and optionally using only a limited set of templates and/or spectral features.

The result of the zspec process for a given mask is a FITS BINTABLE "zspec" file, recording the properties of the best redshift choice identified by the user (template fit, velocity dispersion, etc.), the assigned redshift quality code Q, and the user's comment codes, if any. These are compiled into a catalog with one entry for each spectrum that has been checked.

The combined results of the zspec process are compiled into a single master redshift catalog, labeled the "zcat." To make this catalog, for each mask, we use the zspec results from the most experienced zspec user who has examined it. The redshifts (z), redshift quality codes (ZQUALITY, or Q for short), and comments provided by this user, together with all derived parameters determined by the spec1d pipeline (e.g., the coefficients for each template, the measured linewidth, etc.) and selected photometric information from the pcat files are combined in this catalog.⁵³ There is one entry in the catalog for each observation of an object (e.g., if an object was observed on two different slitmasks, it is listed in the catalog twice); for convenience, we also distribute a version of the zcat in which only the single best redshift estimate per object is included.⁵⁴

The redshifts stored in a zspec file are first compared to those provided in the corresponding mask's zresult file (i.e., the original output from the spec1d redshift pipeline), which contains information on 10 candidate redshifts, selected based on reduced χ², for each object. For all objects to which the zspec user assigned redshift quality code Q = 3 or 4 (i.e., obtained a secure redshift measurement), we compare the redshift identified by the zspec user to the χ² minima compiled in the zresult file. If there is a χ² minimum within Δz = 0.01 of the user's selected z, then we use the redshift stored in the zresult file, rather than the zspec result. This is done to accommodate objects which went through the zspec inspection process before the spec1d and spec2d code was finalized; in such cases, redshifts may change slightly between software versions, and we wish to use the best possible estimates of object attributes.

For those objects which were assigned Q = 3 or 4 but for which Δz > 0.01 for all minima in the zresult file, we attempt to re-fit for the redshift, again using the spec1d redshift-fitting code, but restricting the redshift range considered to a limited window (half-width = 0.03 in z) centered about the redshift chosen in the zspec process. If the re-fit redshift agrees within Δz = 0.01 of the zspec result, then the properties corresponding to that χ² minimum (its redshift, template coefficients, velocity dispersion, etc.) are assigned to that object in the zcat. However, if there is no χ² minimum within Δz = 0.01, the object is assigned redshift quality Q = 2, as we are unable to provide standard pipeline quantities (such as velocity dispersion) in the same way as for a redshift with well-defined minimum. There are 138 objects assigned Q = 2 for that reason.

Next, we read in a set of ASCII-format tables that provide a list of all redshift corrections that have been compiled outside of the usual zspec process (q.v. below); in these cases, we override the zspec results. In cases where the object is reassigned a redshift with a quality code of Q = −2, −1, 1, or 2, we simply update the redshift, redshift quality, and comment according to the override information. For those assigned a secure redshift (Q = 3 or 4), we again utilize the spec1d redshift-fitting code and search for a χ² minimum in a Δz = ±0.03 redshift window centered about the corrected redshift given in the override file. If this fit fails (again a Δz = 0.01 criterion is applied), which occurs for 105 objects, we update the redshift and comment, but we set the redshift quality to Q = 2. When the fit succeeds, we update the zcat with the full set of corrected parameters from spec1d, as well as the override-provided redshift quality and comment.

The measurement of DEEP2 redshifts for difficult cases is still a work in progress; in particular, objects with Q = 2 may still be possible to obtain redshifts for. A good example are the superimposed serendips (supser's; 377 objects); i.e., cases where the spectra of two separate galaxies are superimposed in the same spectrum (cf. Section 13). These have not yet been disentangled (and indeed, it is ambiguous which redshift should be assigned in such cases). Another class is spectra that exhibit only one reliable feature (sngls's; 1161 objects). Many such cases can be resolved using BRI photometry alone (Kirby et al. 2007), and many more will eventually yield to high-accuracy photometric redshifts that are being prepared using multi-band data from u to 8 μm (Huang et al. 2013). These revised redshifts are not included in DR4.

11.2.1. Redshift Re-inspections

A few of the objects for which redshift overrides are provided resulted from scattered anomalies discovered by the DEEP2 team in the course of performing survey science. A greater number resulted from two focused efforts: an investigation of all objects in the EGS with multiple zspec inspections or secure redshift codes, conducted before DEEP2 Data Release 3 (DR3); and a reinspection of all Q = 2 objects by experienced zspec users in order to recover additional redshifts.

In preparation for the previous major data release (DR3), we undertook a detailed review of the data quality in Field 1, in order to provide the community with the most dependable redshift catalog in the EGS region, as well as to ascertain the rates of error in our full redshift catalog. This quality review was carried out in two stages: (1) a comparison and resolution of differences between zspec efforts from different reviewers, and (2) a review of all Q ⩾ 3 redshifts in EGS.

By the middle of 2007 (the time of the review), most masks observed in Field 1 had gone through multiple zspec checks. The zspec results from all reviewers were combined together into a database with 14,509 independent entries, where an entry corresponded to a single observation of a single target; i.e., multiple observations (on different slitmasks or at very different times) of the same target were treated as separate entries in the database. Out of all entries in the database, 10,763 entries (75%) had gone through the zspec process more than once. Several criteria were applied to flag cases of possibly erroneous redshifts or redshift quality among the multiply-checked targets in the EGS. The selected objects (1102 in total) were:

• 1.  
  Targets with redshift quality Q ⩾ 3 in all reviews, but with differences in assigned redshift greater than 0.001. There were 63 such cases, most of which had complex spectra that were misidentified by novice reviewers;
• 2.  
  Targets assigned Q ⩾ 3 by one or more reviewers and Q < 3 by at least one reviewer, the bulk of the sample; or
• 3.  
  Targets classified as a "supser" (cf. Section 13) by any reviewer. In certain cases, rare and complex spectra, e.g., from AGNs, were assigned this quality class in error. There were roughly 100 such objects.

Using zspec, the flagged targets were subsequently reviewed again carefully by expert team members and a final judgment was made on their best-fitting redshift and redshift quality. From a total of 1102 flagged targets (10.2% of multiply-checked spectra), 544 were verified to have good redshifts (Q ⩾ 3 or spectroscopically confirmed stars), 523 were assigned Q = 2 and 30 were assigned Q = 1. The objects assigned Q = 2 were primarily either supser's (which are assigned Q = 2 due to their ambiguous redshifts) or objects to which zspec users with limited experience had assigned inappropriately high redshift confidence.

As a result of this process, we developed a procedure to visually examine the spectra of all Q ⩾ 3 objects in Field 1 in a rapid manner, to ensure that egregious redshift errors would be caught. Using custom-purpose software to display multiple spectra simultaneously on a common rest-frame wavelength scale, we examined approximately 10,000 spectra, 2600 of which had only had a single zspec review at the time. This was done in two passes. In the first pass, sections of the 2D spectra were examined in regions around major emission lines to verify emission line redshifts and catch mismatches. Objects which lacked strong emission lines were then further reexamined in a second pass using their 1D spectra. At the end of both passes, objects for which the redshift could not be verified by this quick-inspection procedure, 739 in total, were subjected to another round of full zspec review by a set of expert team members. This guaranteed that every putatively secure redshift in Field 1 was reviewed at least twice by a human eye.

As a result of this process, ∼250 objects (out of the 10,000 inspected) were downgraded to Q = 2, and 8 were downgraded to Q = 1. As a check on the quality of the redshift catalogs we distribute, we compared the results of our review with the redshift catalog from which DEEP2 Data Release 2 was constructed; it contained the results from 14,175 spectra in the EGS. We found that out of those objects, 31 galaxies had incorrect redshifts (0.3% of all Q ⩾ 3 redshifts), while 249 new, secure redshifts had been obtained for objects that previously had Q < 3 (largely due to reobservations of masks with problematic S/N), while there were 493 galaxies with Q ⩾ 3 that we downgraded to Q < 3 during reinspection (i.e., in 3% of cases, the original zspec user was judged to be overoptimistic on whether the assigned redshift was secure). The results of these redshift reinspections were included in the DEEP2 DR3 catalog, yielding a uniform, internally consistent, high quality catalog for objects in the EGS.

As a result of this inspection process, we have now required that all DEEP2 masks were inspected by at least one expert zspec user, and use their results in the current (Data Release 4) redshift catalog. Additionally, we have reinspected all objects assigned redshift quality Q = 2, searching for reliable redshifts that might have been missed in more cursory examinations. This was done by first having a single expert user (Marc Davis) examine all spectra assigned Q = 2 and search for an improved redshift estimate. Then, a second expert user examined each spectrum assigned a new redshift and judged whether they concurred with the result. In cases where both experts agreed that a redshift had been recovered, a new redshift, quality code, etc., were assigned and the results incorporated into the zcat. As a result of this process, more than 1000 Q ⩾ 3 redshifts were recovered out of more than 5000 spectra inspected.

11.3. Redshift Results

Redshift results are summarized in Table 7, which gives the number of galaxies assigned each quality code in a set of bins of apparent magnitude. These are totals over all spectra in the zcat redshift catalog; hence, a galaxy observed on multiple slitmasks will be counted multiple times, once per observation. A total of 52,989 spectra were obtained. One percent are so severely compromised by instrumental issues that the object was effectively never observed (Q = −2); 1.8% are stars (Q = −1); 16.8% are of such poor quality/S/N that they will likely never yield useful redshifts (Q = 1; many of these are faint blue galaxies beyond our redshift range); 9.8% contain information that could be used to determine a redshift but no definitive determination was made (or no single redshift could be assigned; Q = 2); 11.7% yield a redshift estimated by the zspec user to be reliable at the 95% level (Q = 3); and 58.8% have redshifts estimated to be reliable at the 99.5% level (Q = 4). These reliability estimates appear to be accurate (see below). This information is also shown in Figures 31 and 32, which show the fraction of spectra with different quality codes versus R magnitude in Fields 2–4 and in Field 1 (EGS). The trends are as expected: in Fields 2–4, while the fraction with Q = 4 falls off near the magnitude limit, the fraction with Q = 1 rises greatly (owing mainly to the onset of the faint blue galaxies), while the fraction with Q = 3 is low among the brightest objects but remains fairly constant fainter than R_AB = 21. The fraction of potentially recoverable redshifts (Q = 2) is rather constant at about 15 at all magnitudes, while the number of stars (Q = −1) and catastrophic instrumental failures (Q = −2) is generally very small. The behavior in Field 1 is similar except for the much larger fraction of stars at the brightest magnitudes (where there are few total targets), which is likely due to differences in target selection strategy in that field.

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Table 7. Redshift Quality Codes Assigned to All Targets

RAB mag Range	Color a	Q = −2b	Q = −1c	Q = 1d	Q = 2e	Q = 3f	Q = 4g	Total
<20.0	Blue	0	11	2	13	6	168	200
	Red	2	29	0	10	8	215	264
	Total	2	40	2	23	14	383	464
20.0–21.0	Blue	6	16	5	63	23	401	514
	Red	3	48	5	45	34	416	551
	Total	9	64	10	108	57	817	1065
21.0–22.0	Blue	9	9	29	104	64	1020	1235
	Red	14	89	30	122	213	1658	2126
	Total	23	98	59	226	277	2678	3361
22.0–23.0	Blue	29	12	346	396	217	2203	3203
	Red	70	211	306	571	954	6158	8270
	Total	99	223	652	967	1171	8361	11473
>23.0	Blue 184	17	5871	2050	1071	6033	15226
	Red	217	504	2327	1812	3634	12906	21400
	Total 401	521	8198	3862	4705	18939	36626
Full sample	Blue 228	65	6253	2626	1381	9825	20378
	Red 306	881	2668	2560	4843	21353	32611
	Total	534	946	8921	5186	6224	31178	52989

Notes. ^aColor: blue = R − I < 0.5, red = R − I > 0.5. ^bQ = −2: data so poor that object was effectively never observed. ^cQ = −1: star. ^dQ = 1: probable galaxy but very low S/N; data not likely to yield redshift. Many of these are distant galaxies beyond the nominal redshift limit of z = 1.4. ^eQ = 2: low S/N or data are somehow compromised for reliable redshift; reason given in comments. ^fQ = 3: reliable redshift with probability of accuracy ⩾95%. ^gQ = 4: reliable redshift with probability of accuracy ⩾99%.

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11.3.1. Reliability of DEEP2 Redshifts

The accuracy of the redshifts and estimated errors can be assessed by comparing multiple observations of the same object. Duplicate data come from the overlapping areas between the top and bottom rows of masks in the chevron pattern used for Fields 2–4, from the several overlapping pointings in Field 4, and from a few other scattered regions which have been covered repeatedly (see Figure 1). Due to the relatively large fraction of DEEP2 objects observed twice (roughly 2.5%), the reliability of our redshift measurements can be tested robustly.

We first consider whether the claimed reliability rates for quality codes 3 (95%) and 4 (99.5%) are borne out by real data (using only observations outside the EGS, as in that field discrepant redshifts were investigated and reconciled). Since the claimed error rate for Q = 4 is 0.5%, if we compare two independent observations of the same galaxy both of which were assigned Q = 4, they should agree (to within, say, 500 km s⁻¹) 99.0% of the time and disagree 1.0% of the time. In fact, two Q = 4 redshifts disagree only 0.29% of the time (the 95% upper limit on the mismatch rate is 0.60%), considerably better than the claimed quality.⁵⁵ Similarly, the mismatch rate for Q = 3 versus Q = 4 pairs is only 0.68% (upper limit 1.60%), compared to a predicted rate of 5.5%, and the mismatch rate for Q = 3 versus Q = 3 pairs is 1.5% (upper limit 4.4%), compared to a predicted rate of 9.7%. We conclude that the actual catastrophic error rates in zcat redshifts are roughly half as large as claimed; i.e., the claimed rates are very conservative.

To assess the accuracy of our redshift error estimates, we consider the set of all objects that have been observed exactly twice and for which Q ⩾ 3 for both observations.⁵⁶ Figure 33 shows histograms of actual velocity differences for pairs of objects with Q = 3 versus Q = 3, Q = 3 versus Q = 4, and Q = 4 versus Q = 4. The observed rms difference when comparing two redshifts both assigned Q = 3 is 62 km s⁻¹ (with outliers removed), compared to a mean predicted rms difference of 21.5 km s⁻¹ based on the pipeline errors of the same duplicates, or 21 km s⁻¹ based on the mean pipeline Q = 3 error for the sample as a whole. The observed rms difference for cases where one spectrum was assigned Q = 3 while the other received Q = 4 is 51 km s⁻¹, versus 16 km s⁻¹ expected based on the pipeline errors of the same duplicates, or 17 km s⁻¹ based on the mean pipeline errors for Q = 3 and Q = 4 spectra. Finally, the observed rms difference for cases where both objects received Q = 4 is 22 km s⁻¹, compared to a mean predicted rms difference of 10 km s⁻¹ based on either the objects' or the full-sample mean pipeline error. Though small number statistics may distort these histograms, it is true in general that the observed errors are larger than either set of pipeline-predicted errors, and the latter need to be corrected upward. From this test, we find that the pipeline Q = 4 rms errors can be made to match the observed Q = 4 rms errors if 14 km s⁻¹ is added in quadrature to each error estimate, while the pipeline Q = 3 rms errors can be made to match the observed Q = 3 rms errors if 41 km s⁻¹ is added in quadrature.

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Figure 34 sheds more light by plotting the individual measured velocity differences for each of the above duplicate galaxy pairs versus the predicted velocity differences based on the pipeline errors of the two galaxies. The predicted pipeline error is $\sqrt{(}(\sigma _{z,1})^2+(\sigma _{z,2})^2)/(1+z)$, where σ_{z, 1} is the pipeline redshift error of the first observation, σ_{z, 2} is the pipeline redshift error of the second observation, and z is the mean of the two redshift estimates. Points are color-coded by quality code (blue for Q = 4 versus Q = 4 pairs and red for Q = 4 versus Q = 3). We again find that the pipeline-estimated errors are too small; i.e., the measured differences for galaxies with small pipeline errors are larger than would have been predicted. As before, this can be cured by adding an extra error in quadrature to the pipeline values. The blue lines correspond to the predicted 3σ limits if an extra error of 14 km s⁻¹ is added in quadrature to the pipeline errors for each individual galaxy, while the red lines have 43 km s⁻¹ (=$\sqrt{14^2 + 41^2}$) total added in quadrature; these values are based on the Q = 3/Q = 4 excess errors determined above. These additions make the lines fit the observed 3σ excursions of the two populations fairly well.

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A similar test is shown in Figure 35, which compares errors for red and blue galaxies rather than dividing up objects according to their quality codes (though blue, emission-line galaxies predominantly yield Q = 4 redshifts, with a greater Q = 3 fraction for red galaxies). By adding an extra 17 km s⁻¹ error in quadrature for blue galaxies, or 32 km s⁻¹ for red galaxies, we can match the observed results reasonably well. These tests suggest that an effective method for correcting DEEP2 pipeline redshift uncertainties to match empirical errors is to make the replacement $\sigma _v = \sqrt{\vphantom{A^A}\smash{\hbox{${\sigma _{v_{{\rm pipeline}}}^2 + \sigma _Q^2}$}}}$, where σ_v is the predicted empirical error, $\sigma _{v_{{\rm pipeline}}}$ is the error in v predicted by the pipeline, and σ_Q = 25 km s⁻¹ if Q = 3, or 11 km s⁻¹ if Q = 4. We note that the fact that the pipeline underestimates observed errors is not necessarily a failing of the spec2d or spec1d error model; it could instead reflect miscentering of objects in slits or the relative rotational velocities of the dominant star-forming regions in target galaxies.

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The final way in which we can assess the accuracy of information in the zcat is by checking the consistency with which the various quality codes have been applied. Table 8 shows agreement among quality codes for duplicate pairs. Star identification (Q = −1) seems highly reliable; ∼90% of objects assigned Q = −1 in one observation received the same quality code in the other. The assignment of Q = 4 codes is also quite repeatable: galaxies receiving Q = 4 in one observation received it again 68% of the time and Q = 3 another 19% of the time, and hence received a "reliable" rating 87% of the time. The Q = 1 quality code, too, is a fairly consistent indicator of poor quality, being paired with itself or Q = 2 78% of the time.

Table 8. Quality Codes for Duplicate Observations

Q	−1	1	2	3	4
−1	43
1	4	264
2	2	186	52
3	0	48	54	68
4	0	82	114	295	1038

Note. Entries represent the number of duplicate pairs with the indicated combination of quality codes.

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The Q = 2 codes are more highly scattered, being paired frequently with other codes either worse or better, as we might expect for this marginal category. Nearly half of the Q = 2 objects observed twice were assigned Q = 4 on the second observation; this could happen because a bad-data problem such as bad sky-subtraction or inconsistent continuum levels (bsky or bcont, cf. Section 13) was not present in the Q = 4 observation. Q = 3 codes also seem to repeat relatively rarely; the second observation of a Q = 3 object is classified with Q = 4 some 66% of the time.

A final way to look at these issues is to group all Q = 1 and Q = 2 together to form the "unreliable" class, and all Q = 3 and Q = 4 together as the "reliable" class. Problematic pairs are those that have one member in each class. According to Table 8, this happens 14% of the time. Of the discrepant cases, roughly half are due to technical problems in one observation but not the other: i.e., these are galaxies that would normally yield reliable redshifts if the data were good. The remainder appear to be dominated by objects which received Q = 1 or Q = 2 in one observation due to poor S/N or a single visible emission line.

11.4. Target Selection and Redshift Success as a Function of Color and Magnitude

We conclude this section by showing two series of diagrams that illustrate the density of objects in the original pcat galaxy candidate catalog in color or color–magnitude space; then the fraction that received slitlets; then the fraction that yielded either Q = 3 or Q = 4 redshifts (summed); and finally the fraction of Q = 4 redshifts alone. The first series plots the density of galaxies in the apparent R − I versus R_AB plane. Figure 36 demonstrates that relatively blue galaxies dominate a pure R < 24.1 sample at faint magnitudes. However, only half of them are targeted in EGS, as may be seen in Figure 37, due to the fact that we de-weight faint nearby galaxies (most of which are very blue) in target selection. The same plot for Fields 2–4 (Figure 38) is much more uniform, reflecting the mild 25% roll-off of weights over the faintest 0.3 mag in these fields.

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Figure 39 shows the fraction of targeted galaxies (combining data from all fields) that yield either Q = 3 or Q = 4 redshifts as a function of color and magnitude (i.e., over the same plane as Figures 36–38). The steep loss for faint blue galaxies is due to the fact that many are beyond our z ∼ 1.4 redshift limit. There is also a slight loss in the last 0.3 mag for red galaxies, reflecting the difficulty of measuring z's for objects with weak or featureless continua and negligible emission. Finally, Figure 40 repeats this figure but including Q = 4 redshifts only. There is relatively little change in the faint blue corner but a large change for faint red galaxies, showing that the latter tend to have Q = 3 redshifts, in keeping with the difficulty of measuring their redshifts.

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The second series of plots is similar to the first, but now plots objects in apparent B − R versus R − I color–color space. Figure 41 plots the density of the full target sample in this diagram, while Figure 42 shows the target sampling density in Field 1 (EGS). Several factors are evident here. First, the de-weighting of nearby faint galaxies reduces the sampling rate for low-redshift blue galaxies, which may be found in the lower-left corner of the z < 0.7 region (above the color cut line). Second, the de-weighting of all nearby galaxies in EGS reduces the sampling rate of objects to the upper left of the color pre-selection boundary compared to those below and to the right. Third, the high sampling rate at the outer edges of the distribution reflects the high priority given to objects with peculiar colors, which are outliers in this diagram.

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Figure 43 repeats this diagram for Fields 2–4 (combined). The main features evident are the strong color pre-selection, the slow roll-off in the selection function near this boundary due to "pre-whitening," and, again, the strong preference given to objects with peculiar colors in the outer parts of the distribution. Redshift success rates are plotted in Figures 44 and 45. When considering quality codes Q > 3, the redshift success rate is a relatively flat function for galaxies of all types save in the bluest corner of color–color space, where z > 1.4 galaxies may be found. It is worth noting that even in the most favorable regions of color space the redshift success rate is approximately 90%, not 100%, however. Since Q = 4 redshifts are predominantly assigned to blue galaxies, it is little surprise that the objects assigned Q = 4 are more localized in color space; regions dominated by intrinsically red galaxies will generally yield a lower rate of Q = 4 redshifts.

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The net result of all of these selection and success functions multiplied together is summarized in Figure 19, which illustrates the fraction of galaxies that meet the DEEP2 selection criteria that receive slitlets and the total fraction that yield Q ⩾ 3 redshifts, as a function of distance to the third-nearest neighbor. Overall, 61% of qualifying targets in Fields 2–4 are placed on slitlets (59% in Field 1, EGS); and 43% out of all qualifying targets are in fact observed and yield Q ⩾ 3 redshifts (43% in Field 1, EGS).

As noted in Section 8, blending in the CFHT ground-based BRI imaging can cause biases in the DEEP2 target sample. Such blends have two possible negative effects. First, galaxies that have ostensibly reliably determined redshifts may in fact consist of two superposed but separate galaxies, in which case the photometry, as well as derived properties dependent on continuum strength such as equivalent width, will reflect the properties of the blend rather than the particular galaxy providing a redshift. Second, it may happen that the combination of two galaxies, each of which is just below the R_AB = 24.1 magnitude limit, is bright enough that their combined light brings them above that limit. These pairs may or may not contaminate the "reliable" (Q > 2) redshift sample, as they may be identified as supsers in the zspec process; however, even if they do not, their presence still falsely enlarges the target sample and could distort its statistical properties.

In contrast, the presence of multiple subclumps within a single galaxy is not a significant problem from either of these standpoints. Similarly, in cases where the light from a pair of galaxies with sufficiently high brightness ratio (e.g., 5:1) is combined, one galaxy dominates and few conclusions would be altered. In this section, we attempt to investigate the degree to which unresolved combinations of unrelated galaxies may affect the DEEP2 sample.

We estimate the number of superpositions (hereafter called "multiple galaxies") by comparing the low-resolution ground-based DEEP2 pcat catalog to a high-resolution Sextractor catalog based on the HST ACS mosaic in EGS by Lotz et al. (2008). This latter catalog consists of all objects detected in either the V or I ACS images. Four percent of DEEP2 candidate objects with R_AB < 24.1 prove to have multiple Sextractor matches within a 075 radius, and 10% have multiple matches within a 10 radius. Inspection by eye confirms that objects within either of these separations frequently look single in the ground-based CFHT imaging, depending on seeing.

To understand the superpositions in more detail, we start with the quarter that were targeted for spectroscopy and yielded reliable redshifts (Q ⩾ 3). Note that this fraction is only half as large as the 50% targeting + redshift rate obtained for pcat objects overall in Figure 19; we will return to that point later. The fraction of multiples as a percent of all galaxies with redshifts is plotted as a function of z in Figure 46.

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The number of objects found in the larger aperture versus the smaller remains constant at about 2.5 at all redshifts. This number is larger than the ratio of the areas of the two apertures (1.8). One possible explanation is that pairs with separations below ∼05 are treated as single objects by Sextractor, so the ratio of the two numbers is really the ratio of the areas of two annuli, the inner one relatively narrow. Alternatively, to the degree to which close pairs are likely to be associated with each other, it could represent the impact of physical processes: 1'' corresponds to 11 h⁻¹ kpc comoving, or 5.6 h⁻¹ kpc physical, at z = 1. Closer pairs could have merged, preventing us from seeing them; alternatively, the background galaxy in a pair might be hidden from view by dust in the foreground object.

Figure 46 shows a clear increase in the rate of multiple galaxies near z ∼ 1, apparent with either aperture size. To explore this, we have inspected all HST images of the multiple galaxies with redshifts by eye to see if Sextractor is reliably identifying the same kind of galaxies at all redshifts. It appears that this is not the case. At low redshifts (where the multiplicity fractions are low), we find that only 40% of the multiple galaxies consist of well-separated, distinct galaxies of comparable brightness—the remainder are either subclumps within the same galaxy, pairs with high brightness ratios, or regions with bad ACS data.

Since these latter cases are not a problem for DEEP2 data, we can multiply the fractions of multiples below z ∼ 1 in Figure 46 by 0.4 to find the true numbers of problematic galaxies. We find that ∼1% of DEEP2 galaxies at z < 1 have a contaminating galaxy within 075, while ∼2% have a potential contaminant within 1''. These numbers are quite close to those expected if the companion objects consist of R  <   ∼ 25_AB mag galaxies (i.e., roughly those down to the brightness limit of the Sextractor catalog) distributed randomly on the sky. We therefore estimate that at redshifts z < 1, 1%–2% of DEEP2 galaxies are seriously contaminated by unrelated superimposed foreground or background galaxies; we further conclude that most of these superpositions are not caused by neighboring galaxies, but rather by physically unassociated objects at widely separated distances along the line of sight.

The situation changes above z ∼ 1, where the fraction of multiples in Figure 46 increases. We would not expect the number of random superpositions within a fixed angular separation to depend on redshift. As a consequence, the analysis we have done for z < 1 galaxies demonstrates that randomly superimposed galaxies can make up at most a small fraction of the multiple companions at z ⩾ 1. Based on our inspection of ACS postage stamp images, the fraction of multiples which are in fact single objects with several subclumps doubles near z ∼ 1; this is reasonable, since more distant galaxies tend to look clumpier (both because we are observing them at shorter rest-frame wavelengths and due to their intrinsic properties; cf. Papovich et al. 2003). However, this increase cannot account for the full rise, and we are forced to conclude that the number of physically close but distinct companions also rises beyond z = 1.

These trends can be followed to even greater z by using the location of multiple galaxies in the color–color diagram as a crude redshift guide. Figure 47 plots the distribution of the fraction of pcat objects which have multiple components within 075 in the HST imaging over color–color space. The highest peaks in multiplicity rate lie away from the bulk of the galaxy color distribution; they tend to be regions containing only one or two galaxies. Inspection suggests that the apertures used to measure CFHT 12K photometry for those objects were suboptimal due to the multiple components, so that magnitudes and colors were compromised, yielding peculiar colors. Setting aside these outliers, most multiples cluster in the lower-left part of the diagram, where z ≳ 1.5 blue galaxies may be found (cf. Figure 13). Evidently most multiples are quite distant, beyond the z ∼ 1.4 limit where [O ii] passes beyond our spectral coverage. This explains why relatively few multiples were both targeted for spectroscopy and yielded reliable redshifts (which was required for the sample plotted in Figure 46).

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The increase in multiplicity rate at higher redshifts inferred from Figure 47 agrees with the trend found previously in Figure 46, which showed a large increase setting in around z ∼ 1. Inspection of the HST images of the bluest and presumably most distant multiples in Figure 47 shows a similar mix as at z ∼ 1: a small subset of pairs with large brightness ratios, a moderate number of galaxies consisting of multiple subclumps, and a large fraction of apparently well separated, distinct galaxies which are blended in ground-based photometry.

To sum up, the fraction of DEEP2 galaxies down to R_AB = 24.1 whose ground-based CFHT photometry is blended due to purely random superposition of physically unrelated objects along the line of sight is of order 1%–2%. This random-overlap rate should not depend on redshift; these objects dominate the population of significantly blended galaxies below z ∼ 1. At higher redshifts, the fraction of single galaxies which are incorrectly broken up into multiple clumps in the HST data by Sextractor goes up; but at the same time, the occurrence of physically associated pairs of galaxies that are well-separated in HST images (but not from the ground) also increases. This population appears to extend to higher redshift (z ∼ 2). We might speculate that we are viewing a different phase of galaxy evolution at these higher redshifts, in which a larger fraction of the mass accretion occurred in major mergers rather than in minor mergers or smooth flows. Indeed, in LCDM models we would expect that merger rates were higher at z ∼ 2 than today, so this finding should not be surprising. Overall, we find that ground-based photometry of blue galaxies beyond z ∼ 1 is significantly contaminated by companions or overlapping objects as much as 5%–10% of the time.

This investigation into multiplicity is qualitative and has barely touched the surface of this subject. It does, however, give some rough indications for the number of contaminating blends expected in ground-based data and their likely effects. These issues are likely to be important for deep weak lensing studies, as close pairs may preferentially align along filamentary large-scale structure and their photometric redshift estimates will be contaminated; photometric redshift calibration requirements for next-generation projects such as LSST are extremely tight (Ma et al. 2006). Future work will benefit from comprehensive spectroscopic redshift surveys extending beyond z = 1.4, better photometric redshifts for distant galaxies, and near-IR HST images, which will establish whether the separate-appearing blue clumps in the HST optical images are in fact distinct galaxies or merely blue star-forming clumps within larger potential wells. Samples of galaxies with spectroscopic redshifts z > 1.4 and HST imaging from the Gemini Deep Deep Survey (cf. Abraham et al. 2007) or objects from the zCOSMOS-deep survey (Lilly et al. 2007) might provide fruitful sources for follow-up work. Thanks to its high-resolution restframe-optical imaging the new CANDELS survey, which includes the EGS among its fields, will provide an ideal testbed for these studies (Grogin et al. 2011; Koekemoer et al. 2011).

The two tables in this section contain the main data from DEEP2 DR4, which is the first release of the complete set of spectra from the DEEP2 survey. Future data releases are planned as redshifts are further improved and additional spectral quantities (e.g., EWs, velocity widths) are added. Only the first few lines of each table are presented here; the complete tables are available electronically at http://deep.berkeley.edu/DR4/. In addition to the tables summarized herein, DR4 includes a variety of other survey data products, such as the design parameters for each DEIMOS slitmask, sky-subtracted 1D and 2D DEIMOS spectra, and the CFHT 12K BRI photometric catalogs from which the targets were selected. Below, we provide a brief list of the primary DEEP2 DR4 data products along with the relevant URLs:

DEEP2 redshift catalog (Table 10).

   http://deep.berkeley.edu/DR4/zcatalog.html

Summary of slitmask observations (Table 9).

   http://deep.berkeley.edu/DR4/masktable.html

Slitmask design parameters.

   http://deep.berkeley.edu/DR4/maskdesign.html

1D and 2D DEIMOS spectra.

   http://deep.berkeley.edu/DR4/spectra.html

2D completeness maps (Figures 1 and 2).

   http://deep.berkeley.edu/DR4/completeness.html

CFHT 12K BRI photometric catalogs.

   http://deep.berkeley.edu/DR4/photo.html

Table 9 lists data on the individual slitmasks, one line per observation. In some cases, multiple masks with the same mask number but covering different objects were observed due to the mask centers being adjusted early in the survey; each mask/date combination in the table corresponds to a unique slitmask. For each mask, this table records the four-digit mask ID number; the observation date; a nominal R.A. and decl. near the center of the mask; the P.A. of the long axis of this mask; the number of objects from this mask in the DR4 zcat data release (and hence the number in Table 10 below); the estimated S/N per pixel for an R = 23.5 galaxy spectrum on the mask; the estimated seeing; the redshift completeness obtained on this mask for all galaxies targeted; and the redshift completeness obtained for red galaxies only (R − I > 0.5).

Table 10. Galaxy Data (Sample)

ID	R.A.	Decl.	B	R	I	σB	σR	σI	rg	e2	P.A.	pgal	E(B − V)	MB	U − B
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
11001673	213.86870	51.95644	23.49	23.14	22.58	0.026	0.022	0.029	1.370	0.046	−46.95	1.000	0.011	−999	−999
11001699	213.81047	51.94232	22.07	20.03	19.55	0.009	0.001	0.002	1.957	0.026	−0.40	3.000	0.011	−19.23	1.130
11001770	213.84843	51.94888	24.14	24.10	24.02	0.068	0.077	0.152	2.184	0.332	−9.43	3.000	0.011	−999	−999
11001800	213.83176	51.95255	25.34	23.51	23.08	0.169	0.033	0.050	1.796	0.069	−2.61	0.510	0.011	−999	−999
11001860	213.83255	51.95417	24.38	23.40	22.57	0.079	0.034	0.035	2.023	0.048	−12.92	3.000	0.011	−20.08	0.752
11001861	213.81732	51.95325	23.25	22.82	22.21	0.035	0.028	0.035	2.823	0.114	−38.11	3.000	0.011	−20.22	0.532
11001878	213.81459	51.93851	23.97	23.42	23.13	0.056	0.032	0.053	1.844	0.077	62.49	0.663	0.011	−17.67	0.395
11001898	213.81851	51.96013	24.18	23.14	22.60	0.090	0.040	0.054	3.049	0.359	−81.78	3.000	0.011	−18.75	0.646
11001909	213.82000	51.94717	23.10	21.18	20.52	0.025	0.004	0.005	2.059	0.037	−24.73	3.000	0.011	−21.02	0.813
11001922	213.82240	51.93072	22.01	21.26	21.06	0.014	0.008	0.016	2.415	0.089	21.47	3.000	0.011	−14.92	0.563
11001927	213.82467	51.96038	25.29	22.05	20.96	0.208	0.012	0.010	2.547	0.145	−28.47	3.000	0.011	−20.43	1.253
11001934	213.82196	51.95469	22.89	22.14	21.83	0.022	0.013	0.021	2.430	0.108	43.00	3.000	0.011	−19.66	0.417
11001950	213.83030	51.94160	23.60	22.41	22.12	0.052	0.017	0.028	2.445	0.295	−75.92	3.000	0.011	−999	−999
11001974	213.80832	51.94306	23.05	22.47	21.92	0.019	0.012	0.016	0.799	0.053	−2.44	0.999	0.011	−20.59	0.464
11001978	213.78782	51.95398	24.46	23.85	23.55	0.064	0.042	0.070	1.339	0.096	36.55	0.769	0.011	−999	−999
11002016	213.79909	51.95631	24.10	23.91	23.44	0.046	0.044	0.064	1.664	0.042	78.09	1.000	0.011	−19.49	0.460
11002019	213.78484	51.94730	23.99	22.75	22.26	0.052	0.018	0.025	1.909	0.197	−43.56	0.429	0.011	−19.15	0.639
11002024	213.75619	51.93770	24.12	23.60	23.07	0.069	0.040	0.053	1.979	0.395	−19.89	3.000	0.012	−18.69	0.516
11002039	213.78086	51.95369	25.60	24.09	23.36	0.183	0.058	0.059	1.644	0.042	72.13	0.980	0.011	−999	−999
11002051	213.77227	51.94480	24.61	23.20	22.40	0.110	0.032	0.033	2.262	0.192	87.64	3.000	0.011	−999	−999
11002064	213.73228	51.93605	24.63	23.52	23.22	0.131	0.048	0.077	2.336	0.437	−23.33	3.000	0.012	−999	−999
11002085	213.76673	51.95897	23.55	23.33	23.05	0.032	0.030	0.051	1.898	0.062	61.91	0.941	0.011	−999	−999
ID	Mask	Slit	Date	MJD	Slit R.A.		Slit Decl.	Slit Length	Slit P.A.	z	$z_{{\rm best}}^{{\rm hel}}$	σz	Q	Comment
(17)	(18)	(19)	(20)	(21)	(22)		(23)	(24)	(25)	(26)	(27)	(28)	(29)	(30)
11001673	1101	0	2003-05-06	52765.46	213.86906		51.95637	4.86	−48.86	−1	−1	999.9	2	bcol; bext
11001699	1100	7	2003-05-03	52762.44	213.81044		51.94244	4.20	−48.86	0.29064	0.29061	4.26e−05	4
11001770	1101	3	2003-05-06	52765.46	213.84874		51.94867	10.27	−18.86	−1	−1	−5	1
11001800	1100	4	2003-05-03	52762.44	213.83186		51.95259	3.77	−48.86	−1	−1	−5	1
11001860	1101	10	2003-05-06	52765.46	213.83284		51.95412	4.98	−48.86	0.95771	0.95767	9.87e−05	4
11001861	1101	14	2003-05-06	52765.46	213.81763		51.95319	6.33	−48.86	0.90908	0.90904	2.95e−05	4
11001878	1100	3	2003-05-03	52762.44	213.81496		51.93842	4.57	−48.86	0.50301	0.50297	5.04e−06	4	bsky; iffy
11001898	1101	17	2003-05-06	52765.46	213.81873		51.96013	5.01	−78.86	0.64987	0.64984	5.21e−05	3
11001909	1101	11	2003-05-06	52765.46	213.82013		51.94721	4.64	−48.86	0.67948	0.67944	6.97e−05	3	ZREVISED
11001922	1100	0	2003-05-03	52762.44	213.82199		51.93105	10.01	−48.86	0.07411	0.07408	1.01e−05	4	fix; bext; ZREVISED
11001927	1146	15	2003-05-06	52765.30	213.82497		51.96045	7.18	41.14	0.68392	0.68388	6.57e−05	4
11001934	1100	9	2003-05-03	52762.44	213.82227		51.95463	3.56	−48.86	0.65117	0.65114	1.21e−05	4
11001950	1101	5	2003-05-06	52765.46	213.83038		51.94163	4.89	−75.92	−1	−1	2.54e−05	2	sngl; ZREVISED
11001974	1100	8	2003-05-03	52762.44	213.80847		51.94308	3.05	−48.86	0.93205	0.93201	1.34e−05	4
11001978	1146	3	2003-05-06	52765.30	213.78787		51.95391	7.38	41.14	−1	−1	1.42e−04	1	offser
11002016	1146	7	2003-05-06	52765.30	213.79964		51.95657	5.57	41.14	1.05800	1.05796	2.03e−05	4
11002019	1100	18	2003-05-03	52762.44	213.78477		51.94747	3.80	−43.56	0.64948	0.64945	2.48e−05	4
11002024	1100	23	2003-05-03	52762.44	213.75636		51.93768	4.02	−19.89	0.74553	0.74550	3.40e−05	4
11002039	1100	22	2003-05-03	52762.44	213.78119		51.95361	4.63	−48.86	−1	−1	−5	1
11002051	1100	21	2003-05-03	52762.44	213.77234		51.94483	6.49	−78.86	−1	−1	7.34e−05	2	bcont; disc; ZREVISED
11002064	1100	30	2003-05-03	52762.44	213.73241		51.93608	4.74	−23.33	−1	−1	−1	1
11002085	1100	29	2003-05-03	52762.44	213.76717		51.95884	5.37	−48.86	−1	−1	−5	1

Notes. See Section 13 for details. Columns: (1) unique DEEP2 object ID from pcat; (2) and (3) object R.A. and decl. (2000.00); (4)–(9) total BRI magnitudes and errors from pcat; (10)–(12) Gaussian radius, ellipticity and P.A. from proprietary team pcat; (13) probability of being a galaxy determined from photometry; (14) Galactic E(B − V) from Schlegel et al. (1998); (15) and (16) absolute B magnitude (M_B − 5 · log₁₀ h) and rest-frame (U − B) from Willmer et al. (2006) K-corrections (sometimes labeled (U − B)₀ in DEEP2 papers). Stars and objects without robust redshifts are assigned the value −999 for derived quantities such as these; (17) unique DEEP2 object ID from pcat; (18) slitmask number; (19) slitlet number on mask; (20) UT date of observation; (21) modified Julian date of observation; (22) and (23) R.A. and decl. of slitlet center; (24) and (25) slitlet length in arcsecond and P.A.; (26) redshift from this observation in geocentric reference frame; (27) best redshift from all observations (heliocentric reference frame); (28) pipeline-estimated error in this redshift observation (negative values indicate χ² minima whose widths, and hence the resulting redshift errors, were not well determined); (29) redshift quality code: Q = −2 (data so poor that object was effectively never observed); Q = −1 (star); 1 (very low S/N; data are not likely to yield a redshift); Q = 2 (redshift information present, but definitive redshift not obtained); Q = 3 (reliable redshift with probability of accuracy ⩾95%); Q = 4 (reliable redshift with probability of accuracy ⩾99%); (30) comment codes: see explanations in Section 13. Values of −1 for z, and z_best are used for non-robust redshift estimates; σ_z values of −1, −5, and 999.9 are also used by the pipeline to flag poor redshift estimates in some cases.

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The first two digits of the mask ID number indicate the CFHT pointing, using the same numbering scheme as in Figures 1(a) and (b), while the last two digits are a position code within each pointing.⁵⁷ Completenesses are based on reliable redshifts only, which are defined as having quality code Q = 3 or 4, and seeing is the FWHM measured from spectra of stars in the slitmask alignment boxes. The S/N estimate used is the continuum S/N per 1D pixel in the extracted spectrum, computed from skyline-free regions near 6900 Å with 3σ outliers rejected. The value reported is based on a median-median line fit (Brown & Mood 1951) to the S/N versus magnitude for objects with 23.1 < R_AB < 24.1, evaluated at R = 23.5.

Both redshift completeness fractions are useful indicators of mask quality and are plotted along with seeing and S/N in Figure 48. We report both as, for galaxies bluer than (R − I) = 0.5, the redshift completeness obtained does not correlate with S/N or seeing; instead, it likely reflects only cosmic variance in the number of bright z > 1.4 galaxies in a given mask region. The trends are as expected, with the fractions of reliable redshifts increasing strongly with both S/N and seeing, which are closely correlated. Probably the single most useful mask-quality indicator is the seeing FWHM, which ranges between 04 and 15 with a median value of 076.

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Table 10 is the master data table for DEEP2, presenting redshifts and associated data for each individual candidate galaxy targeted for spectroscopy. Each line corresponds to a single observed slitlet spectrum. multiply observed objects have multiple entries, though a z_best for each object is provided based on information from all spectra (see below). Data are given for targeted objects only; many serendipitous objects are visible on the 2D spectra, but they have not been uniformly analyzed. Their presence is signaled by the comment code offser ("offset serendip") in the comment field of the targeted galaxy (see below). Serendip spectra may be obtained by downloading the slitlet spectra from http://deep.berkeley.edu/DR4.

Table 10 is similar to the DEEP2 zcat table at http://deep.berkeley.edu/DR4/, but certain confusing or rarely-used quantities have been omitted (we describe those quantities in Section 13.1), while some other quantities derived from mask design files have been added (the dropped quantities continue to be available in the zcat available online). Table 10 is thus a melding of data in the DEEP2 DR4 spectral database, the previously released pcat photometry catalogs (Coil et al. 2004b),⁵⁸ and data from the slitmask design files, collected together for easy reference.

Objects in Table 10 are ordered by their object number in the DEEP2 pcat catalogs. The variable names in caps are defined here or, if pre-existing, agree with published catalogs and Web site. Sources of all entries are given in footnotes to the table. The columns are as follows.

Column 1. OBJNO: a unique eight-digit DEEP2 object number drawn from the pcat photometric catalogs. The object number format is XXyyyyyy, where XX indicates the CFHT field/pointing used to derive the photometry (e.g., "23" for DEEP2 Field 2/pointing 3) and yyyyyy is a unique identifier within the pointing. The fields and pointings are shown in Figures 1 and 2.

Column 2. R.A.: right ascension of the object, in decimal degrees.

Column 3. Decl.: declination of the object, in decimal degrees.

Column 4. MAGB: B-band apparent AB magnitude m_B from the pcat CFHT photometry. This is defined as $m_B = m_R + (B-R)_{1^{\prime \prime }\;}$, where $(B-R)_{1^{\prime \prime }\;}$ is the apparent color measured through a 1''-radius aperture and m_R is the apparent R magnitude (next column). Using a small fixed aperture for the color yielded the most robust colors and total magnitude corrections from R to B and I (Coil et al. 2004b).

Column 5. MAGR: R-band apparent AB magnitude m_R from the pcat photometry. This is measured through a circular aperture whose radius is three times the Gaussian radius, r_g, defined in Column 10. If 3r_g < 1'', the magnitude is measured through a 1''-radius aperture (Coil et al. 2004b). All magnitudes provided have been corrected for Galactic extinction.

Column 6. MAGI: I-band apparent AB magnitude m_I, defined as $m_I = m_R - (R-I)_{1^{\prime \prime }\;}$, where $(R-I)_{1^{\prime \prime }\;}$ is measured through a 1''-radius aperture. See Column 4.

Columns 7–9. MAGBERR/MAGRERR/MAGIERR: rms B-band/R-band/I-band magnitude error (σ_B/σ_R/σ_I). These error estimates include sky and photon noise only. Based on the analyses presented in Coil et al. (2004b), there may be additional systematic zeropoint errors internal to each pointing of order 0.04 mag in B and 0.02 mag in R and I, but mean zeropoints should differ from pointing to pointing by <0.01 mag.

Column 10. RG: Gaussian radius r_g of a circular 2D Gaussian fit to the R-band image, expressed in units of CFHT pixels (one pixel is 0207).

Columns 11 and 12. EL/P.A.: ellipticity e₂ (EL) and P.A. of the object's CFHT R-band image, derived from an analysis of image moments. The ellipticity parameter e₂ is defined as e₂ = (1 − b/a) = 2/(1 + ), where is the conventional eccentricity, and P.A. is relative to north. Note that P.A.s determined from ground-based images do not necessarily match those from high-resolution Hubble images; e.g., see Wirth et al. (2004).

Column 13. PGAL: probability of being a galaxy p_gal, based on the R-band image. A value p_gal = 2 indicates a source with unusual BRI colors; p_gal = 3 indicates an extended source. All sources with p_gal = 2 or 3 are treated as galaxies in target selection. A value of p_gal in the range 0.0–1.0 is the Bayesian probability of a compact object's being a galaxy (not a star). Objects with p_gal < 0.2 are treated as stars and excluded from selection for spectroscopy; objects with p_gal between 0.2 and 1.0 are included with a selection weight proportional to their value of p_gal; and those with p_gal > 1 are given the same weight as an object with p_gal = 1. For further explanation see Section 6.2 and Coil et al. (2004b).

Column 14. SFD_EBV: Galactic reddening E(B − V) from Schlegel et al. (1998). This value was used to correct the photometry for a given object for Galactic extinction.

Columns 15 and 16. M_B/UB_0: absolute CFHT 12K B-band magnitude, M_B, and restframe U − B color, U − B₀, both computed from the BRI photometry after corrections for Galactic reddening, as described in Willmer et al. (2006). We use the subscript 0 here to indicate that the calculations are done with z = 0 passbands; no correction for dust internal to DEEP2 galaxies has been applied. M_B is calculated assuming an LCDM cosmology with h = 1; i.e., the listed value is M_B − 5log₁₀ h.

Column 17. OBJNO: repeated from Column 1.

Column 18. MASK: slitmask number on which the object was observed, from Table 9.

Column 19. SLIT: slitlet number on which the object was placed. Slitlets are numbered in order of position along the long axis of the mask, starting with Slitlet 0 lying to the far left on Figure 16.

Column 20. DATE: UT date of observation in YYYY-MM-DD format.

Column 21. MJD: Modified Julian date of observation.

Column 22. SLITRA: R.A. of slitlet center.

Column 23. SLITDEC: declination of slitlet center.

Column 24. SLITLEN: slitlet length in arcseconds.

Column 25. SLITPA: slitlet P.A. relative to north.

Column 26. Z: observed best-fitting redshift z from this spectrum, in the geocentric reference frame. This is the value obtained from the zspec process.

Column 27. ZBEST: best heliocentric-reference-frame redshift combining information from all spectra obtained for an object, $z_{{\rm best}}^{{\rm hel}}$. Uses the highest-Q value or, when there are multiple choices of equivalent quality, uses the first value observed. A value of $z_{{\rm best}}^{{\rm hel}}$ is given only if there is at least one redshift with Q ⩾ 3.

Column 28. ZERR: redshift error σ_z derived by the spec1d pipeline for this observation, as described in Section 11.

Column 29. ZQUALITY: redshift quality code Q for this observation. Codes are as follows: Q = −2 (data so poor that object was effectively never observed; tracked for statistical purposes); Q = −1 (star); Q = 1 (probable galaxy but very low S/N; data are not likely ever to yield a redshift); Q = 2 (objects with low S/N and/or for which data are in some way compromised, but for which a redshift may be obtainable with extra effort. The reason for assigning Q = 2 is generally listed in the COMMENT column (below)—all supser's and sngls's automatically get Q = 2); Q = 3 (reliable redshift with probability of accuracy ⩾95%); Q = 4 (reliable redshift with probability of accuracy ⩾99%). Further details are given in Section 11, while the relevant comment codes are explained below.

Column 30. COMMENT: a comment provided in the course of the zspec and catalog compilation process. The comment can be used to identify interesting features of a given spectrum, as well as a variety of problems or issues with the data (see also http://deep.berkeley.edu/DR3/comments.html). In total, more than 16,000 objects in the DEEP2 catalog have comments provided, of which 5113 (less than 10% of the DEEP2 sample) indicate some problem with a spectrum, as described below. As noted in Section 11, their application has varied, and they should be used with caution; many are a matter of judgment and may have been applied differently by different zspec users. See further remarks below.

There are two separate categories of problems that are given comments, those that have a high probability of impairing redshift quality and those that may or may not do so. All Q = 2 redshifts should have at least one comment from the first category; where none is assigned, the marg keyword (marginal S/N) may be assumed. The first category consists of:

bsky: bad sky subtraction. This comment highlights badly subtracted sky continuum or sky lines or both. An incorrect sky spectrum shape results in incorrectly subtracted sky, and consequent errors in the extracted object spectrum. Examples are shown in Figure 26.

bcol: bad column(s). One or more bad CCD columns spoil a significant part of the extracted spectrum and/or the neighboring sky region. Note that "columns" here run parallel to the dispersion direction; i.e., the name of the comment code refers to columns on the detector rather than columns within the extracted 2D spectrum. This is the opposite convention from Figure 16, where they run parallel to the slitlet direction. The pipeline interpolates across bad columns and manages to repair a single bad column fairly well, but three or more adjoining columns seriously degrade data quality. bcont (and bsky) may also be assigned when a piece of spectrum that is curved due to optical distortion falls onto a vignetted region or onto a gap between CCDs. An example is shown in Figure 26.

bcont: bad continuum shape. This is a catchall phrase expressing the fact that the continuum shape does not look right. It is often associated with bsky or bcol.

bext: bad extraction window. The extraction window used by the pipeline for the spectrum is displaced from the actual object, or is too wide or too narrow, or is contaminated by a companion.

edge: edge. The object is too near the end of the slitlet and consequently has poor sky subtraction and/or extraction.

In the case of these problems (bcol, bcont, bext, bs and edge), whether an object is assigned Q = 2 (redshift possibly measurable), Q = 1 (redshift not measurable due to the object properties) or Q = −2 (object was effectively not observed) will sometimes involve judgment calls, which may differ from one zspec user to another.

disc: discontinuity. There is an unphysical jump in the continuum level between the blue and red-side spectra. This is typically caused by mismatched extraction windows on the red and blue sides or by bad sky subtraction on one side. An example is shown in Figure 26.

marg: marginal. The S/N is low and the spectrum barely meets standards for its assigned quality code.

sngl: single. Only one feature is visible (we count a resolved [O ii] doublet as two features). All sngl's automatically get Q = 2.

supser: superimposed serendipitous object ("serendip"). There are two redshifts measurable from the spectrum, and hence it is ambiguous what redshift should be assigned to the target. If one or both spectra have only one line, supser sngl is used. Either z can be entered into the zspec file, and the second z is not necessarily recorded. All supser's get Q = 2. We note that supser's are among the most difficult phenomena to spot, and many have probably been missed.

The second category of comments represents conditions that can often be present without impairing redshift quality:

fix: fix. Some element of the reductions went wrong and should be redone. The redshift is not necessarily affected.

iffy: iffy. The extracted 1D spectrum may be adequate for determining a redshift (as indicated by the Q code), but there is something wrong that makes the observation unreliable as an integrated spectrum of the galaxy, and therefore unsuitable for other analyses such as measurement of equivalent widths, rotation curves, linewidths, or SEDs. Examples include: (1) a bad extraction window that gets only part of a galaxy or is contaminated by a companion, (2) emission extending beyond the extraction window and therefore under-summed in the 1D spectrum (this may also result in oversubtracted sky, as shown in Figure 26), (3) a severe flux discontinuity across the blue/red CCD boundary disc. With rare exceptions, iffy was used only for objects assigned Q = 3 or Q = 4. It may be further qualified by adding bsky, bcont, bcol, disc, bext, or edge to explain the nature of the problem.

offser: offset serendip. A second spectrum is present in the slitlet but is well enough separated or dim enough that the extraction window and sky-subtraction of the target object are not seriously affected. If only one line is visible, offser sngl is used. The redshift of the serendip is not necessarily recorded. Serendip spectra may be obtained by downloading the 2D slitlet spectra at http://deep.berkeley.edu/DR4/. Offser's are easier to spot than supser's but, again, some have probably been missed.

fill-gap failed: identifies those instances where a redshift could not be measured because the spec2d data reduction pipeline failed to construct a robust 1D spectrum for the object. In the vast majority of cases, this resulted from an exceptionally poor wavelength solution, due to which the blue and red halves of the object spectrum (see Sections 7 and 10.1) overlapped in wavelength space rather than being separated by ∼5 Å corresponding to the gap between the two DEIMOS CCDs. These spectra are assigned the bad-data quality code, Q = −2.

ZREVISED: identifies those objects for which the redshift was changed based on information obtained outside the first zspec analysis of the mask. This includes objects whose redshifts were assigned following the Q = 2 rechecking process; for more details see Section 11.

ZREVISED: zfix failed: identifies those cases where a redshift revision was attempted (see ZREVISED) but failed. This failure generally resulted from the inability of the spec1d redshift pipeline to find a suitable fit (i.e., chi-squared minimum) that matched the revised redshift value to within Δz = 0.01. These objects are assigned Q = 2.

ZMATCH-FAIL: identifies those cases where a redshift that was previously identified as having Q = 3 or 4 failed to yield a good fit that matched the previous redshift value (within Δz = 0.01) when spectra were run through the newest version of the spec1d redshift pipeline. In some cases, a revised redshift (indicated by the ZREVISED keyword) was successful where the original pipeline redshift was not; otherwise, ZMATCH-FAIL objects receive Q = 2.

13.1. Additional Parameters in Online DR4 Catalogs

As part of DEEP2 Data Release 4, we are releasing a set of files describing the 2D selection function of the DEEP2 Galaxy Redshift Survey: i.e., the probability (as a function of position on the sky) that an object meeting the DEEP2 target criteria (magnitude limit and color cut, as applicable) is selected for observation and successfully yielded a redshift. The calculation of these selection function (or, as they are sometimes called,"window function") maps has been described in Coil et al. (2008), and references therein; we review the methods used here.

The 2D selection function maps take into account the actual placement and geometry of the overlapping slit masks used for DEEP2, as well as vignetting in the DEIMOS camera and the locations of gaps between the DEIMOS CCDs. In producing these maps, we account for the multipass nature of DEEP2 targeting and the fact that some overlapping DEEP2 slitmasks were designed simultaneously and some were not (as the mask design code will not place an object on multiple masks designed at the same time and in the same row of masks; cf. Section 7) in computing selection probabilities. The redshift completeness for red (R − I > 0.5) galaxies is used to determine the probability a targeted object yields a redshift; the redshift success rate for bluer objects is both low and not correlated with observing statistics such as seeing (rather it primarily reflects the density of z ∼ 2 galaxies at a given location on the sky), so the red galaxy completeness provides the best estimate of the probability that a targeted galaxy at a redshift where DEEP2 can obtain a z will actually yield a reliable redshift measurement.

In these maps, we also mask out all regions where the photometric data are affected by either saturated stars or CCD defects and hence no galaxies were targeted. The region where these maps are nonzero provides a geometrical outline of the regions of sky targeted by DEEP2, while the actual value at a given position represents the probability that we both targeted a galaxy (which depends on how many masks overlap a given area, whether the object is in the first or second-pass region of those masks, and whether they were designed simultaneously) and then successfully measured its redshift. Note that the provided files do not include pointing 14 in the northernmost region of the EGS. Due to poorer photometry, the mask design differed in that pointing from the rest of the survey, such that the spatial selection is not uniform between it and the rest of DEEP2. No DEEP2 clustering measurements use data from that pointing. In a recent paper (Matthews et al. 2013) we have provided improved photometry for this region based on imaging obtained as part of the CFHT Legacy Survey (Gwyn 2012).

The selection function maps are distributed at the DEEP2 DR4 Web site in the form of FITS-format images, with World Coordinate System headers describing the mapping from right ascension and declination to pixel, and the value at a given pixel (ranging from 0 to 1) being the combined selection and redshift success probability for a DEEP2 target galaxy at that position. Outside of the EGS, where the mask making was done independently for each CFHT pointing, we provide one file per pointing. For the EGS, we provide one file describing the selection function over the entire field. In order to produce random catalogs for calculating correlation functions, one should use the value of the selection function at a given position as the probability of keeping an object (between 0 and 1) at that location within the catalog. We note that for some measurements, it may also be necessary to correct for the dependence of selection probability on source density at small scales (cf. Section 8); in DEEP2 science papers, this has been done with mock galaxy catalogs (e.g., Yan et al. 2004).

We conclude this overview of the DEEP2 survey by illustrating certain major trends in the data as a function of redshift, summarizing properties of the DEEP2 data set.

Figure 49 shows redshift histograms for each of the four fields, using only objects with reliable (Q = 3 and Q = 4) redshifts. These figures illustrate graphically that, fractionally, the contribution of Q = 3 (>95% reliable) redshifts is rather small; the great majority (83%) of secure redshifts have Q = 4 (>99% reliable). Field 1 (EGS) is well sampled at all redshifts, whereas our BRI color pre-selection has efficiently eliminated foreground galaxies in Fields 2–4. As expected, strong peaks due to large-scale structure are evident, which differ in detail from field to field, demonstrating the need for statistically independent samples to beat down cosmic variance.

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Figure 49 also sheds light on whether a significant number of redshifts are lost when important spectral features fall on atmospheric absorption bands (e.g., the A band of O₂ at 7620 Å). The [O ii] λ3727 emission line should fall on the A band for objects at z = 1.045. There is no depression in the diagrams at that redshift, indicating that any loss is small.

Figure 50 plots apparent magnitudes and colors versus redshift. The top row is for Field 1 (EGS); the bottom row combines all objects in Fields 2–4. The most striking feature of these diagrams is the clear bimodality visible in the color plots. The lower, densely populated sequence consists of blue-cloud galaxies, while the more thinly populated upper trace is the red sequence. The latter fades out near z ∼ 1, due partly to a real reduction in numbers there (Bell et al. 2004; Willmer et al. 2006; Faber et al. 2007) and partly because the survey begins to lose red galaxies rapidly at that redshift. This is a combined effect of such objects having difficulty meeting the DEEP2 magnitude limit (as the 4000 Å break moves redward of the CFHT R band at z > 1) and poorer redshift success for faint red objects without emission lines (cf. the discussion of color–magnitude diagrams below).

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Also notable are the two small islands of very blue, z ∼ 0.15 galaxies visible in Fields 2–4. These reside in the blue corner of the BRI color–color diagram where the colors of low-redshift, high star-formation rate galaxies overlap those of more distant blue galaxies (cf. Figure 13); as a result, a BRI color pre-selection cannot reject them cleanly without also rejecting real high-redshift galaxies. Some of these are exceedingly low in luminosity, with M_B as low as −14 (see below), and likely present an interesting population of objects for follow-up studies.

The vertical striping visible in these figures (especially for Field 1) is a consequence of cosmic variance: redshifts where the density in our fields are higher than average will have more objects of all colors and magnitudes, and those with low density will have few. The stripes correspond directly to the features visible in the redshift histograms in Figure 49. In Fields 2–4, the impact of large-scale structure is much reduced, as we are effectively averaging the properties of three statistically independent regions of the universe. A significant dearth of galaxies near z = 1.15 is nevertheless still visible, despite combining roughly 22,000 galaxies in three widely separated fields, illustrating how difficult it is to reduce cosmic variance to a small error at every redshift (at z = 1.15, [O ii] λ3727 overlaps with one of the cleanest regions in the night sky spectrum, eliminating sky subtraction errors as a possible culprit). The impact of cosmic variance increases the smaller the redshift bins (δz) considered. As a result, we find no detectable correlation between the DEEP2 redshift histogram and the DEIMOS-measured night sky spectrum (evaluated either at the central wavelength of [O ii] or at the wavelength of either doublet component). Variations in the DEEP2 redshift success rate on the scale of the width of a night skyline, if they exist at all, are completely swamped by the large cosmic variance on those scales.

Figure 51 plots absolute B magnitude and restframe (U − B)₀ color versus redshift. These are calculated from the CFHT 12K BRI photometry using the methods of Willmer et al. (2006); we use the subscript 0 to indicate that restframe passbands are used (no correction for dust internal to DEEP2 galaxies has been applied). The color bimodality and the low-redshift blue galaxies are again evident. The most interesting aspect of this figure is the curved locus in (U − B)₀ versus z traced out by blue-cloud galaxies. The solid line shows the median color of blue cloud galaxies (defined as having ((U − B)₀ < 1.0)) as a function of z, while the dotted and dashed lines show quintiles of the distribution. Figure 52 suggests that this curvature is not due to errors in the K-correction procedure for restframe (U − B)₀ but is instead caused by the interaction of the fixed R_AB = 24.1 magnitude limit with the color–magnitude distribution of galaxies in the blue cloud (see below), combined with the impact of any color evolution (Blanton 2006).

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Figure 52 plots restframe color–magnitude diagrams binned by redshift. The well-known color trends within both the red sequence and blue cloud are clearly evident, with brighter galaxies being redder in both cases. Straight lines approximate the boundaries imposed by the fixed R_AB = 24.1 survey limit at different redshifts. In each panel, the heavy solid line shows this limit for the far side of the indicated redshift bin while the dashed line is the corresponding limit for the near side of that bin. Light dotted lines repeat the lines from all other bins to guide the eye.

The aggregate trends of (U − B)₀ with z seen in Figure 51 can be explained by what is seen here. At the highest redshifts, the survey tends to include bluer galaxies but lose redder ones (at fixed M_B), as the limit lines become highly slanted in restframe color-absolute magnitude space. The mean color of the most distant detected galaxies is therefore by necessity bluer than for lower-distance samples. At lower z, the R = 24.1 limit line is more vertical, permitting redder blue-cloud galaxies to enter the survey across a wider range in M_B. At even lower redshifts, the survey is able to pick up abundant, very faint blue galaxies, which causes the median color of blue-cloud galaxies selected to fall again. We have not modeled these effects quantitatively, but it is clear that the most obvious trends in color plots like Figure 51 need careful interpretation.

This paper has presented DEEP2 Data Release 4, the first spectroscopic database resulting from a complete DEEP2 Galaxy Redshift Survey sample, containing 52,989 spectra and 38,348 reliable redshift measurements for objects as faint as R_AB = 24.1. The information in this paper is intended as a handbook for users of the survey, as well as for those using the DEEP2 data reduction pipelines to reduce DEIMOS data. Both raw and reduced spectra, photometry, and all redshifts are available for download from the Data Release 4 Web site (http://deep.berkeley.edu/DR4/) as well as other Web sites listed in Section 10. We do not expect this to be the final data release from the DEEP2 survey. Future releases may include improved photometry, revised redshift estimates (e.g., from incorporating photometric redshift information for Q = 2 objects), improved data reductions and extractions, and/or additional derived parameter measurements not included here.

The discoveries from DEEP2 have led to the development of the DEEP3 Galaxy Redshift Survey (Cooper et al. 2011, 2012a). This project has obtained more than 8000 spectra, primarily of objects in the EGS. The primary goals of DEEP3 were to obtain redshifts for three different samples.

• 1.  
  Objects of interest identified through AEGIS multiwavelength observations.
• 2.  
  R_AB < 24.1 galaxies that were not previously targeted by DEEP2 to avoid slit overlaps, enhancing the sample of objects which can be used to trace galaxy environments in the EGS, and providing an enlarged DEEP2-like sample of galaxies that have deep multiwavelength imaging.
• 3.  
  Faint, highly star-forming galaxies down to R_AB = 25.5, allowing us to test whether they continue to follow the same scaling relations as brighter galaxies.

In order to maximize complementarity to DEEP2 data, DEEP3 observations were conducted with a 600 line mm⁻¹ (R ∼ 3000) grating on DEIMOS, with spectra typically covering the wavelength range from 4600 Å to 9800 Å. Hence, DEEP3 provides worse kinematic information than DEEP2 but covers more spectral lines in a given galaxy. We expect the first data release from DEEP3 to occur in the next year, and that the legacy of DEEP2 will continue into the future.

Thanks are due to the many institutions and individuals who have made the DEEP2 survey possible. First thanks go to the W. M. Keck Foundation, the University of California, and NASA for providing funds to construct and operate the Keck telescopes. Second, we wish to thank the technical teams in the UCO/Lick Shops and at Keck Observatory for their role in building and commissioning the DEIMOS spectrograph and for their superb support during many observing runs. Funds for the spectrograph were provided by instrumentation grant ARI 92-14621 from the National Science Foundation and instrument funds from the California Association for Research in Astronomy (Keck Observatory) and from the University of California/Lick Observatory.

The DEIMOS data-reduction pipeline is based in part on code from the Princeton Sloan Digital Sky Survey spectrograph pipeline, and we thank Scott Burles and David Schlegel for their help in adapting this software for DEIMOS. Particularly vital components were the SDSS code developed for slitlet extractions, B-spline sky subtraction, and redshift determination. Patrik Jonsson's study of fringing in the LRIS spectrograph led to the basic understanding of fringing needed to establish image-stability specifications for DEIMOS. The ATV image display tool created by Aaron Barth, SPLOT created by David Schlegel, the IDL Astronomy User's Library supported by the Goddard Space Flight Center, and the idlutils package were all instrumental in this work. The submit_prepare perl script by Marshall Perrin was of great assistance in the submission of this paper.

We benefitted greatly from advice and input from Jeremy Mould, Charles Steidel, Mark Metzger, Richard Ellis, Chris Conselice, Harlan Epps, Edward Groth, Garth Illingworth, Richard Kron, Alex Szalay, Roc Cutri, Charles Beichman, Peter Eisenhardt, Giovanni Fazio, and Kevin Bundy in conceiving, designing, and executing the survey. We wish to thank the anonymous referee for their detailed reading and helpful comments on this paper, and for helping to raise awareness of our unconscious boreal-centrism. We also wish to thank the entire DEEP1 team for their pioneering efforts which helped greatly in designing DEEP2.

The DEEP2 survey was initiated under the auspices of the NSF Center for Particle Astrophysics. Major grant support was provided by National Science Foundation grants AST 95-29098, 00-711098, 05-07483, and 08-08133 to UCSC, AST 00-71048, 05-07428, and 08-07630 to UCB, and 08-06732 to the University of Pittsburgh. Computing hardware used to analyze DEEP2 data was provided by Sun Microsystems. The HST ACS imaging mosaic in EGS was constructed by Anton Koekemoer and Jennifer Lotz and was funded by grant HST-AR-01947 from NASA. NASA imaging of the original Groth Strip was planned and executed by Ed Groth and Jason Rhodes with support from NAS5-1661 and NAG5-6279 to the WFPC1 IDT. Support for this work was provided by NASA through Hubble Fellowship grants 51256.01 and 51269.01 awarded to E.N.K. and M.C.C., respectively, by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. Sandra Faber thank CARA for a generous research grant and the Miller Institute at UC Berkeley for a Visiting Miller Professorship, during which much of this paper was written. Jeffrey Newman and Alison Coil acknowledge support from Hubble Fellowships during their DEEP2 work, and Michael Cooper acknowledges support from both Hubble and Spitzer Fellowships.

Marc Davis acknowledges support from the entire DEEP2 team who filled in while he was recovering from a stroke.

Finally, we recognize and acknowledge the highly significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community; it has been a privilege to be given the opportunity to conduct observations from this mountain.

A.1. Sky Subtraction

A.2. Fringing Physics and Image Motion Tolerance

A.3. The DEIMOS Flexure Compensation System

A.4. Pipeline Sky Subtraction