LATIS: The Lyα Tomography IMACS Survey

In the D1 and D4 fields, the basis of our photometric catalogs is the final release (T0007) of the CFHTLS.⁹ We use the catalogs produced from $u* {griyz}$ stacks that are sigma-clipped means of the 85% best-seeing images. The depth in r is 25.6 AB mag (85% completeness for point sources), which is 0.8 mag fainter than our flux-limited selection described below. We use fluxes measured within 22 diameter apertures, corrected for Galactic extinction and for the light outside of the aperture as estimated using bright point sources.

In the D2/COSMOS field, we instead use the Ilbert et al. (2009) catalog of I < 25 sources covering 2 deg² with 30 band photometry. Using this catalog enables a potential future extension of the survey beyond the central 1 deg² covered by the CFHTLS. Because the Lyα forest is most easily observed in rest-UV-bright galaxies, we preferred the optical selection in this catalog to the near-infrared selection used in the more recent Laigle et al. (2016) catalog.

We cross-matched these catalogs to publicly available databases of spectroscopic redshifts, including VVDS (Le Fèvre et al. 2013a), VUDS DR1 (Le Fèvre et al. 2015; Tasca et al. 2017), MOSDEF (Kriek et al. 2015), DEIMOS 10K (Hasinger et al. 2018), 3D-HST (Brammer et al. 2012; Momcheva et al. 2016), ZFIRE (Nanayakkara et al. 2016), FMOS-COSMOS (Silverman et al. 2015), CLAMATO (Lee et al. 2018), MilliQuas (Flesch 2015), VIPERS (Scodeggio et al. 2018), and the G10/COSMOS catalog (Davies et al. 2015), which includes the zCOSMOS-Bright (Lilly et al. 2009) and PRIMUS surveys (Cool et al. 2013).¹⁰

Obtaining a high density of sightlines requires an efficient color-based selection of galaxies in the desired redshift range. Two approaches are widely used to select Lyman-break galaxies (LBGs): ugr colors and photometric redshifts. (We refer to UV-bright, high-redshift galaxies as LBGs generically, irrespective of their exact redshift.)

The quality of photometric redshifts is highly dependent on the number of filters used and their wavelength sampling, which is not uniform over the LATIS fields. A particular problem is that near-infrared photometry only partly covers the D1 and D4 fields. With only optical photometry, there is a significant degeneracy in the photometric redshifts for high-z sources due to ambiguity between the Balmer and Lyman breaks. In order to maintain a consistent selection function within each field, we decided to adopt a ugr selection in all fields and to supplement this with a photometric redshift selection within the COSMOS field, which contains the best-tested and most highly constrained photometric redshifts.

3.2.1. Color Selections and Completeness

Our goal is to devise an efficient color selection for galaxies in the redshift range z = 2.2–3.2. The lower limit is driven by the limited sensitivity of IMACS at λ < 390 nm, i.e., ${z}_{\mathrm{Ly}\alpha }\lt 2.2$. (Although a galaxy must have z > 2.28 in order to observe absorption at ${z}_{\mathrm{Ly}\alpha }=2.2$ in a usable region of its spectrum, we also want to include galaxies at z = 2.2–2.28 in order to study their positions and properties within the IGM map.) Beyond the upper limit of z = 3.2, the utility of sightlines diminishes as less than about half of the Lyα forest lies within the intended tomographic volume from z = 2.2–2.8. The sample selection is much less sensitive to the high-z cutoff, as there are few sufficiently bright galaxies at z ≳ 3.

A ugr color selection has been widely and effectively used to identify z ≈ 2–3 sources, and the color limits can be tuned to select redshifts of interest (e.g., Adelberger et al. 2004). Ideally, the bounds of the color selection are derived from a flux-limited sample of galaxies with spectroscopic redshifts. Fortunately, the VVDS-UltraDeep survey falls within the CFHTLS D1 field and contains a flux-limited sample with i = 23–24.75 and sufficiently deep exposures to achieve a spectroscopic success rate of ≳80% for z ≈ 2–3 sources (Le Fèvre et al. 2013a). The left panel of Figure 2 shows the distribution of VVDS-UltraDeep sources in ugr space, with the galaxies in our target range z_spec = 2.2–3.2 colored. Based on this color distribution, we defined the selection box outlined in black: $0.5\lt u-g\lt 2.2$ and $-0.1\lt g-r\lt 1.0$ and $u-g\,\gt 0.50+2.3(g-r-0.35)$.

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The upper limit of u − g sets the upper redshift limit; as mentioned before, the sample is not very sensitive to this limit as the density of available targets is low. The lower limit of u − g sets the lower redshift limit. Toward bluer u − g colors, the number of z < 2.2 interlopers increases rapidly, so there is a trade-off between completeness and purity, particularly for the z = 2.2–2.3 sources highlighted in blue in Figure 2. The u − g > 0.5 limit was chosen as it selects about half of z ∼ 2.2 sources. The notch in the upper-right corner of the selection box helps to avoid part of the stellar locus when the color selection is applied at brighter magnitudes.

The right panel of Figure 2 shows the completeness of this ugr selection relative to the VVDS-UltraDeep sample. The color selection identifies 64% of galaxies within our target redshift range of z = 2.2–3.2. The main contaminants are galaxies slightly below z = 2.2 and low-z interlopers with z ≲ 0.3.

Our target selection differs in the COSMOS field in two respects. First, the Ilbert et al. (2009) catalog contains photometry with different filters from the CFHTLS catalogs, particularly the u band. In order to use the ugr selection that we calibrated in the D1 field, we apply a conversion to the Ilbert et al. (2009) u − g and g − r colors. The conversion was derived by comparing the colors of galaxies in the two catalogs that lie in the color selection box in Figure 2: ${\rm{\Delta }}(u-g)\,=0.09$, ${\rm{\Delta }}(g-r)=0.10$ $(g-r{)}_{\mathrm{COSMOS}}^{2}-0.31$ ${(g-r)}_{\mathrm{COSMOS}}$ + 0.03, and ${\rm{\Delta }}r=-0.04$, where Δ is CFHTLS-COSMOS.

Second, we supplement the ugr color selection in the COSMOS field by adding galaxies with $2.2\lt {z}_{\mathrm{phot}}\lt 3.2$. We take z_phot from the COSMOS2015 catalog (Laigle et al. 2016). For any objects not present in this NIR-selected catalog, we use the Ilbert et al. (2009) z_phot instead. Although we cannot assess the completeness of this z_phot selection against the VVDS, we find that among sources selected by either the ugr or the z_phot selection, only 15% are not ugr-selected in the magnitude range $23.5\lt r\lt 24.8$ motivated below. Thus, the z_phot selection does not add many targets, but as we will see in Section 6.2, the z_phot selection has a significantly higher purity, especially at brighter fluxes, and so is useful for prioritizing targets.

3.2.2. Flux Limits

Ultimately, QSOs contribute only 2% of the sightlines in our tomographic reconstructions. Although their inclusion is not likely to make a major improvement in the map quality, they are worth observing in LATIS because they provide high-fidelity probes of H i and metals along sightlines that may pierce regions of particular interest (e.g., a protocluster). However, given their low numbers, our QSO selection must maintain an acceptable level of purity. Selecting QSOs in our target redshift range z = 2.2–3.2 based on their colors alone is difficult. The left panel of Figure 3 shows the distribution of point sources in the CFHTLS D2 catalog in ugr space. Colored circles identify known broad-line QSOs from the MilliQuas catalog, and red circles indicate those at z = 2.2–3.2. These overlap the stellar locus considerably, which would introduce an unacceptable contamination rate if not mitigated.

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Photometric variability provides one way to distinguish QSOs from stars. The CFHTLS fields were observed regularly over a decade, providing a time baseline for monitoring. Time series photometry for point sources in the CFHTLS-Deep fields with 17.5 < g < 24 have been constructed by Gwyn (2012).¹¹ The left panel of Figure 4 shows the rms g-band magnitude variations for point sources in the D2 field, with known QSOs from the MilliQuas catalog identified as red circles. It is immediately apparent that virtually all of the QSOs are variable with fluctuations of tenths of magnitudes. We select variable sources as those lying above the blue curve in the left panel of Figure 4, which delineates the region where the rms exceeds the mode by 4σ. At g = 23–24, many of the known QSOs are not present in the time series catalog because they are not point-like, so we confine our subsequent variability analysis and QSO selection to g < 23 sources.

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This variability selection reduces contamination but still includes variable stars. We follow (Palanque-Delabrouille et al. 2011; see also DESI Collaboration et al. 2016) and compute the structure function of the variable sources. We fit a power law $A{({\rm{\Delta }}t)}^{\gamma }$ to the magnitude difference Δm as a function of the time lag Δt in years. The right panel of Figure 4 shows that QSOs are clearly distinct from the bulk of the variable sources in their distribution of γ, reflecting the fact that their magnitude differences tend to increase with the time separation.

Based on this analysis, we make an initial identification of QSO candidates as variable g = 17.5–23 point sources with 0.1 < γ < 1. The middle and right panels of Figure 3 show that this selection dramatically reduces contamination by stars while rejecting only a small fraction of QSOs. To further reduce the residual contamination by variable stars, we exclude sources along a narrow strip (enclosed by green lines in Figure 4, middle panel) aligned with the peak density of the stellar locus.

We now must further restrict the QSO candidates to those likely to lie in the target redshift range z = 2.2–3.2. Figure 5 shows the relationship between u − g color and redshift for the known QSOs in the CFHTLS-Deep fields. To select QSOs in the target range while minimizing contamination from lower redshifts, we require $0.35\lt u-g\lt 1.5$.¹² This cut should remove most QSOs at z ≈ 1–2, but we expect some contamination from z ≲ 1 QSOs.

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Of the 112 QSOs at z = 2.2–3.2 in the MilliQuas catalog and CFHTLS-Deep fields, 101 are variable, 94 also pass the γ cut, and 57 also pass the color criteria, for a completeness of 51%. Most of the missed targets are at the front of the volume, with z < 2.4, and must be excluded as their u − g colors are indistinguishable from the bulk of the QSO sample at z ≈ 1–2. Among the z > 2.4 QSOs in the sample, which are the most useful for tomography, this method selects 78%. In the D2/COSMOS field, 83% of the QSO photometric candidates have a literature spectroscopic redshift. However, in the D1 and D4 fields the fraction is only 48% and 3%, respectively, so our variability selection method takes on greater importance.

To increase multiplexing, we conduct observations through a custom bandpass filter. The blue cutoff was motivated by the 390 nm design limit of the IMACS f/2 camera (Dressler et al. 2011). The red cutoff was motivated by our desire to observe the strongest interstellar lines, including C iv λλ 1549,1551, in the spectra of galaxies out to z ≃ 2.75, which we anticipated as roughly the useful limit of the tomographic map. This motivates a red cutoff near 589 nm, which additionally serves to isolate the darkest part of the night-sky spectrum. The filter was fabricated by Asahi Spectra on Ohara PBL25Y glass. The measured half-power points are 383 nm and 591 nm; the transmission is >95% (average 97%) over the range 387–586 nm.

To improve the sensitivity of IMACS at blue wavelengths, we moved the more blue-sensitive detector mosaic to the f/2 focus in 2017 December. We also designed and purchased a new grism. Based on the spectral resolution considerations outlined in Section 2, we selected from the Richardson Grating Lab (RGL) catalog a grating with 400 grooves mm⁻¹ and a nominal first-order blaze wavelength of 460 nm. The grating was replicated by RGL onto a BK7 prism that has an antireflection coating on the input side. In the mean seeing of 07, the typical image size is 11 (the galaxies are semiresolved and IMACS contributes some broadening). For such objects, the grism provides an average resolution of R = 880 in the Lyα forest, ranging from R = 830–920 over ${z}_{\mathrm{Ly}\alpha }=2.2\mbox{--}2.8$. The absolute first-order diffraction efficiency, as measured by RGL, is shown by the green line in Figure 6. Due to a manufacturing error, the grating dispersion is not precisely aligned with the symmetry plane of the prism. The effect of this is to shift the spectra orthogonally to the dispersion, which results in a minor loss of 5% of targets that are shifted off the detector mosaic.

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Figure 6 (black curve) shows the throughput of the instrument and telescope measured in 2019 April. The throughput increases from 9% to 24% over the range 390–460 nm, i.e., ${z}_{\mathrm{Ly}\alpha }\approx 2.2\mbox{--}2.8$.

Targets are selected from three sources: LBG candidates based on the criteria in Section 3.2, QSO candidates based on the criteria in Section 3.3, and LBGs or QSOs with prior spectroscopic redshifts from the literature. Masks were designed using the maskgen software, which accounts for our filter bandpass and allows multiple ranks of slits. We used a slit width of 12. Slits are 6'' long by default, but we extended the boundaries when necessary to ensure that a length of at least 35 is free of sources and useful for sky subtraction. maskgen can resolve slit conflicts using user-provided numerical priorities, or alternatively, it can attempt to maximize the number of slits. Although these modes may suffice for general galaxy surveys, for tomography, the distribution of sightlines is also important. We therefore used a custom procedure, described below, in which we run maskgen in several stages to prioritize targets while also evening out the sightline distribution. Because this is most easily accomplished among targets with similar priority, we introduce targets with progressively lower priorities in subsequent stages.

The highest priorities are assigned to known QSOs and QSO candidates. We then add LBG candidates in stages. We first consider z_phot-selected or z_spec-selected targets in the magnitude range r = 23.0–24.4 (Section 3.2.2). The z_phot-selected sources are considered before the ugr-selected sources because, as we will show in Section 6.2, they have a higher purity. Among sources with z_phot = 2.2–3.2, we attempt to concentrate the redshift distribution slightly to maximize the Lyα forest path length within the tomography volume from z = 2.2–2.8. We do this by drawing a random subset of the LBG photometric candidates with a probability W(z_phot) that is unity over z_phot = 2.3–3.0 and ramps linearly to zero over z_phot = 2.2–2.3 and 3.0–3.2.

Using this initial subset of highest-priority targets, we generate a target list for maskgen and produce a mask. We then attempt to redistribute the targets more uniformly throughout the IMACS footprint using a simple Monte Carlo procedure. Targets are initially prioritized randomly. We first randomly select a target for which the local density of assigned slits is particularly low. We swap its priority with a second target in the same region of the mask that has a higher local density of slits. We run maskgen and measure the rms separation between a random point in the field and the nearest slit. If the priority swap has decreased this metric, we consider the spatial distribution to have improved and keep the swap. Iterating the procedure produces a somewhat more uniform target distribution.

In the second stage, we fix the slits already assigned, and we add ugr-selected targets in the magnitude range r = 23.5–24.4. (Note that the bright limit is fainter for ugr-selected sources because, as we will see, their purity declines rapidly at r < 23.5.) We again selected a subsample of these targets following a priority W(u − g) that is unity over $u-g=0.8\mbox{--}1.5$ and linearly ramps to zero over $u-g=0.5\mbox{--}0.8$ and 1.5–2.2. As for the z_phot-selected galaxies, this is an attempt to slightly taper the ends of the redshift distribution. We again attempt to even out the sightline distribution as described above.

In the third stage, we revisit all z_phot-selected targets (without any subsampling) and consider the full magnitude range r = 23.0–24.8. Slits already assigned are fixed, and additional slits are allocated according to a priority based on the sum of W(z_phot), W(r), and W(n_slit). Here, W(r) is unity over the range r = 23–24.4 and declines linearly to zero over r = 24.4–24.8 to deprioritize faint sources. The W(n_slit) term prioritizes galaxies in sparsely populated regions of the mask.

In the fourth stage, we consider all ugr-selected sources over the full magnitude range. The procedure is the same as for the z_phot-selected sources, except that the W(r) term ramps from 0 to 1 over the range r = 23.0–23.5, rather than remaining at unity, due to the lower purity of bright ugr-selected galaxies (Section 6.2). At the end of the fourth stage, 280–310 slits are assigned on the final mask. Typically 8% of these slits are not observable, usually because the spectrum falls into a gap between detectors or is shifted off the mosaic by the grism defect described in Section 4.1, which leaves 270 usable slits on average. Masks for the CFHTLS D1 and D4 fields are constructed similarly, but the above procedure is simplified as there is no z_phot selection.

These slits comprise the first of two "target sets" for the footprint. Masks for the second target set are constructed similarly, with two main differences. First, in order to enable studies of the inner circumgalactic medium with LATIS, we prioritize a small number (typically ∼3–10) of candidates within 6'' of a galaxy with a redshift z = 2.2–3.2 determined from the first target set observations or a literature source. Second, sources from the first target set are repeated only where no other targets are available.

Although the two target sets largely correspond with two masks in each footprint, this is not true in detail. We attempt to improve purity by initially observing a slitmask for ≃1/3 of the total exposure time. We can then identify ∼10%–20% of targets as being outside the range z = 2.2–2.8, and we generate a new mask by deleting these slits and repeating the third and fourth stages described above to add new targets. The remainder of the exposure is then spent on this improved mask.

In addition to the main survey masks described in the previous subsection, we also constructed masks consisting of brighter LBG candidates in the magnitude range r = 22–23.5. Although few of these are genuine high-redshift galaxies, they can be observed when the conditions are not suitable for the main masks, and they allow us to place the very brightest LBGs and active galactic nuclei (AGNs) within the tomographic maps. We construct the bright target masks in two tiers by feeding maskgen a prioritized list. In the first stage, we include the z_phot-selected targets in COSMOS, while in the second stage, we add the ugr-selected targets. In both tiers, we prioritize fainter candidates given their much lower rate of contamination.

Figure 1 shows a fiducial layout of footprints for the survey. Currently we have obtained full or partial observations in the D1M3, D1M4, D2M4, D2M5, D2M8 (full), D1M1, D1M2, and D4M3 (partial) footprints. The overall positioning of the footprints is designed to maximize overlap with the external surveys shown in the figure. We also chose footprints that are a subset of a complete tiling of each field, in order to allow for the possibility of future observations over a larger area. (This also accounts for the nonsequential numbering of the footprints shown.) Small shifts from a uniformly spaced tiling are needed to allow the guide probes to reach suitable guiding and Shack–Hartmann stars.

Fields are separated by 24' in R.A. because at field radii R > 12', IMACS suffers from some vignetting and degraded image quality. Our tiling scheme ensures that much of the R > 12' region is covered by two footprints, which allows targets in the vignetted overlap region to have twice the exposure time. Accounting for our wavelength coverage constraints, the addressable field of view is a circle with R = 15' truncated by two lines of constant declination separated by 21', and also lines of constant right ascension located 141 west and 123 east of center. The east–west truncations reflect the detector mosaic boundary, and they are asymmetric because of the lateral shift of the spectral traces described in Section 4.1. Each footprint covers 0.15 deg².

Over 28.5 operable nights from 2017 December to 2019 April, we conducted LATIS observations in all of the footprints listed in Section 4.4. At least one target set has received the full planned exposure in the D1M3, D1M4, D2M4, D2M5, and D2M8 footprints (outlined in bold in Figure 1), and the remainder of the paper will focus on these data, although we have partial observations in other footprints. We have fully observed both of the main target sets in all of these fields except D1M4, where only one is complete. In addition, we have observed bright target masks in D1M4 and D2M4.

The total exposure time that a galaxy receives varies according to several factors, e.g., weather conditions, duplication on multiple target sets or footprints, or removal from a target set following identification as an interloper. The median exposure time is 12.2 hr, or 14.2 hr for those galaxies we will ultimately use for tomography. This exposure time was intended to produce a typical signal-to-noise ratio of roughly ∼2 Å⁻¹ in the Lyα forest. This limit was in turn motivated by McQuinn & White (2011), who showed that gains in measuring the flux correlation function using a quasar survey begin to diminish at higher signal-to-noise ratios, as the noise in the spectra becomes smaller than the amplitude of IGM fluctuations for a wide range of scales ≳2 cMpc.

In order to minimize the effect of read noise, we operate IMACS in 1 × 2 binning, i.e., with 02 pixels and a dispersion of 1.8 Å (04) per pixel, and use the slow read mode coupled with exposures of 45 minutes. Wavelength calibration is obtained using helium and mercury lamps that illuminate the flat-field screen at the telescope pupil. To obtain adequate counts at blue wavelengths, we use exposures of the twilight sky for flat fielding. The Magellan Baade telescope is equipped with an atmospheric dispersion corrector, which removes chromatic differential atmospheric refraction (DAR). Due to the wide field of view, achromatic DAR (i.e., a gradient in scale) can be appreciable. We calculate the typical hour angle for a planned observing sequence and design the mask using the DAR capability of maskgen. For observations of a mask over its full arc, we design two masks for use east and west of the meridian. This strategy should reduce the DAR-induced offsets between images and slits to ≲02.

The data were reduced using a series of Python scripts designed to process IMACS observations in a highly automated way. For a given mask, a fiducial mapping from the focal plane to the detector is first refined using direct images of the slitmask. Lines are then identified in the arc lamp spectra, and a two-dimensional polynomial is fit to the global wavelength solution on each of the eight detectors. Twilight flats are reduced by modeling and dividing out the sky spectrum. The slit functions, which encode the variation in throughput along a slit, are factored from the pixel-to-pixel variations in the flat. We generally take twilight flats at a series of gravity angles and then reduce each science frame with the closest matching flat. For each science exposure, we subtract the bias using the overscan region before using cross-correlations to estimate the small residual flexure between the flat and science exposure. These shifts are applied to the slit functions, which are then divided from the science frame along with the pixel flat. Sky subtraction is performed in two phases using b-spline techniques (Kelson 2003). The first pass is used to roughly remove the sky emission and locate the targets. The portion of the slit within 07 of the target position is then masked, thereby isolating the sky flux for the second pass. For each galaxy on a given mask, the spectra are then rectified, normalized to a common flux level, and averaged using inverse-variance weighting with outlier rejection. A one-dimensional spectrum is then optimally extracted (Horne 1986). Noise spectra based on standard CCD statistics are propagated throughout.

Galaxies are usually observed on multiple masks. For each galaxy in the survey, we then optimally combine all of the extracted spectra. Flux calibration to f_ν is performed based on twilight observations of white dwarfs in the X-Shooter standards library (Moehler et al. 2014). Spectra can be contaminated in several ways, most commonly by overlapping the zeroth order spectra of other slits. We use automated methods to identify many of these contaminated regions, which are also flagged during our visual inspection of the spectra (Section 6.1).

We developed an interactive GUI to examine the 1D and 2D spectra of every target. For each target, we attempted to identify the spectrum and measure an approximate initial redshift by comparing to the Shapley et al. (2003) LBG composite spectrum and a set of SDSS templates that include low-redshift galaxies, stars, and QSOs.¹³ These initial redshifts serve only as starting points for the refined versions based on an expanded template library that we will describe in Section 7. We assigned a redshift quality zqual as follows:

• 1.  
  zqual = 0: no redshift could be assigned (12.3% of spectra).
• 2.  
  zqual = 1: only a single emission line was identified and assumed to be Lyα (1.2%).
• 3.  
  zqual = 2: low-confidence guess, not suitable for most analyses (9.0%).
• 4.  
  zqual = 3: high-confidence redshift, multiple lines, and a well-modeled spectrum (19.8%).
• 5.  
  zqual = 4: certain redshift, high signal-to-noise spectrum with numerous lines identified (57.8%).

Throughout the remainder of the paper, we consider reliable redshifts as those with zqual = 3 or 4, which comprise 78% of the spectra. Because our exposure times are driven by requirements in the Lyα forest, the region of the spectrum redward of Lyα achieves a rather high signal-to-noise ratio of 3.3 pixel⁻¹ on average, which accounts for the high fraction of high-confidence redshifts. The interactive tool also allows us to flag QSOs and AGNs.

The distribution of redshifts is shown in Figure 7. It is clear that the sources are indeed concentrated in the target range z = 2.2–3.2 (dotted lines), as we will quantify below. The main identifiable contaminant is a population of low-mass galaxies primarily at z ≲ 0.4. Some galaxies at z ≈ 0.5–1.5 are probably also present, but their redshifts would be hard to identify given the bandpass of our filter. Table 1 shows the numbers of galaxies observed to date and extrapolated to the full LATIS survey. We note that 97% of the z = 2.2–3.2 targets are LBGs while only 3% are QSOs.

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Figure 8 gives an idea of the data quality by displaying a set of example spectra spanning the 10th–90th percentiles of the signal-to-noise distribution. All of these galaxies have high-confidence redshifts z > 2.2 and show clear evidence of multiple interstellar transitions indicated in the top panel. Figure 9 graphically presents the full set of 1360 LBG spectra with high-confidence redshifts in the targeted range z = 2.2–3.2. The Lyα forest region is colored blue. For completeness, in Figure 10 we show representative spectra with zqual = 0 (no redshift), 1 (single emission line), and 2 (low confidence). Although redshifts with zqual = 1 or 2 are likely to be correct in most cases, we do not use them for the analyses in this paper.

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We compared the redshifts of galaxies in common with the full VUDS (Le Fèvre et al. 2015, 2019), zCOSMOS-Bright (Lilly et al. 2009), and zCOSMOS-Deep (Lilly, S. J., et al. 2020, in preparation) surveys, which were not used to inform targeting. Galaxies were matched to the nearest source in our photometric catalogs within 1''. Throughout this paper, we only consider VUDS and zCOSMOS redshifts with quality flags of 3 or 4, corresponding to the most secure redshifts. There are 333 galaxies with high-confidence redshifts in both LATIS and one of these surveys. Among these, we identify twelve 5σ outliers. One is a QSO with an uncertain velocity, and two are blended systems where the target is uncertain. After reviewing the LATIS spectra of the remaining nine, we find that three support the LATIS redshift, two support the literature redshift, and four cases are ambiguous. We conclude that this external comparison supports our redshift identifications, with ≲2% of the high-confidence LATIS redshifts called into question, all of which were graded with zqual = 3.

Figure 11 shows the rate at which candidate LBGs and QSOs were targeted as a function of r-band magnitude. For this figure, we consider only those footprints in which both main target sets have been fully observed (D1M3, D2M4, D2M5, D2M8). In COSMOS, ≃46% of candidates have been observed near r ≃ 24, the highest-priority magnitudes, while in D1 the fraction is 64%. The higher target sampling rate (TSR) in D1 is due to a lower number of candidates in the D1M3 footprint, which in turn seems to arise from cosmic variance; the higher TSR will likely not apply to the D1 field as a whole. Thus, overall, LATIS targets around half of the $\gtrsim {L}^{* }$ LBG candidates.

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In both fields, there is a sharp decline in TSR at r > 24.4 reflecting the lower prioritization of these faint sources. In D1 there is also a decline at r < 23.5, since bright ugr-selected targets have lower priority, whereas in COSMOS this decline is more gradual as z_phot-selected targets with r = 23–23.5 are not deprioritized (Section 4.2). The colors and photometric redshifts of candidate and observed targets are compared in Figure 12. The distributions are quite similar; galaxies at the edges of the z_phot range and those with the bluest u − g colors are only slightly underrepresented in the observed targets, reflecting the prioritization scheme discussed in Section 4.2.

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The overall purity of our targeting is illustrated in Figure 13, which breaks down the targets according to their redshift and confidence. Overall, 55% of sources in our main target sets have confident redshifts in the desired range z = 2.2–3.2, which we define as the purity. A further 7% have redshifts in this range at lower confidence. The purity is similar between the COSMOS and D1 fields. Although Figure 13 shows that the purity is higher for z_phot-selected galaxies in COSMOS than for ugr-selected galaxies, which are the only type available in D1, this does not translate to a large difference in the overall sample purity (compare the second and fifth rows). The reason is that the surface density of z_phot-selected sources only permits two-thirds of the slits to be filled, and a similar proportion (61%) of the more abundant ugr-selected sources are also z_phot-selected anyway. We note that 14% of targets had a prior z_spec in the literature; excluding these would lower the purities discussed here at the 5% level.

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While Figure 13 encapsulates the overall statistics of our target selection, the purity is a strong function of magnitude. Figure 14 shows the fraction of targets for which we measured z = 2.2–3.2 (at any zqual). Here we consider only the LBG candidates without a prior z_spec and include targets from both our main and bright target sets. For candidates with r ≳ 23.7, the purity of the z_phot and ugr selections is actually fairly similar. But for brighter galaxies, the ugr selection is significantly less pure. This motivates our decision to deprioritize ugr-selected galaxies with r = 23–23.5 in our main target sets, and to reserve r < 23 targets for the backup bright target masks.

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In addition to the LBGs, we have observed 53 QSO candidates. The majority of these (44) were known as QSOs with spectroscopic redshifts in the literature. Among the additional nine photometric candidates, two were confirmed as QSOs (1 at z = 2.2–3.2) with most of the rest being stars. The low success rate among new candidates is likely due to the fact that two-thirds of the current data are in COSMOS, where the quasar population has already been well observed (Section 3.3).

The sample statistics for the bright target masks (Section 4.3) are quite different. These masks consist of ugr- and z_phot-selected targets with r = 22–23.5, which are usually not high-redshift galaxies, as Figure 14 shows. Furthermore, the masks are observed in substandard conditions. Among the 243 targets with r < 23.5 that were observed only on the two bright target masks, 10% were confirmed to be z = 2.2–3.2 galaxies with any zqual. Most are stars or low-redshift galaxies. The yield is much higher (42%) among the z_phot-selected targets, but there are only 12 of these. These backup masks therefore do not contribute appreciable to the sightline density, but they do allow poorer conditions to be productively used to map the locations of very luminous galaxies up to ≃(4–5) L*.

Although the Lyα forest is relatively flat in LBG spectra, it is not a featureless continuum. Furthermore, as we will show, the strength of the absorption features in the forest is correlated with the interstellar absorption features redward of Lyα. Therefore, in order to make the best estimate of an LBG's intrinsic spectrum in the Lyα forest, it is best to model the entire spectrum.

We do this by constructing a set of galaxy spectral templates from the LATIS data set. The templates and model fits were constructed iteratively. We divided the observed LBGs with high-confidence redshifts z > 2.28 (ensuring that part of the Lyα forest is included) into five bins of Lyα equivalent width (EW). We initially shifted these into the rest frame using the redshifts determined from manual inspection and in comparison to the Shapley et al. (2003) composite spectrum (Section 6.1). For each spectrum, we divided out the mean transmission F(z) of the Lyα forest, as measured by Faucher-Giguère et al. (2008). We then fit a power law to the spectrum redward of 1250 Å, masking the strong interstellar absorption lines, and divided it from the entire spectrum to remove the continuum slope. All such spectra in a given bin of Lyα EW were then averaged, excluding a small fraction of sources with spectroscopic evidence of an AGN.

The templates were then offset in velocity to v_stars = 0 using the C iii 1175.7 Å line. (Consistent results are obtained using other photospheric lines, but this line is the strongest and the most robustly detected in all of the templates.) We then modeled each LBG as a nonnegative linear combination T(λ; z) of these five templates, redshifted and multiplied by $\langle F\rangle ({z}_{\mathrm{Ly}\alpha })$ (where $1+{z}_{\mathrm{Ly}\alpha }(\lambda )=\lambda /1215.67$ Å) and a power-law continuum C(λ). We included the Lyα forest in the fit so that it can contribute to the determination of the continuum slope. The product $T\times \langle F\rangle \times C$ was fit to the observed spectrum using a standard nonlinear least-squares method. The resulting redshifts should be more accurate than those based on the Shapley et al. (2003) composite spectrum, as the templates are better matched to the spectral properties of each galaxy. Because the initial templates were constructed by stacking spectra with approximate redshifts, we then constructed an improved set by shifting each galaxy into its rest frame, now using our refined redshifts, and generating the templates again as just described. This procedure was then iterated a second time; by this point, changes in the redshifts and templates were quite minimal, indicating we had reached convergence.

Figure 15 shows the five resulting template spectra, which span a wide range in Lyα emission and absorption and in the strength of the interstellar lines. Figure 16 compares the templates in the Lyα forest region, which we define to be 1040–1187 Å in order to exclude the Lyβ forest and to provide adequate separation from Lyα and Si ii λλ 1190, 1193 absorption. In our Lyα forest analysis, we exclude data in the four shaded regions, selected to include the two strongest lines and the two that show the largest variation among the templates (1084, 1135, 1144, and 1176 Å). We mask a ±2 Å window in the rest-frame around each line (±3 Å for 1176 Å), amounting to 6% of the forest length. Although the exact choice of mask is somewhat arbitrary, we found that adding the next two strongest lines (1063 and 1123 Å) ultimately had a negligible effect on the tomographic maps.

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This procedure generally does a good job at matching the continuum shape and the main absorption lines in the individual spectra, which Figure 8 demonstrates. The median reduced χ² is 1.13 redward of Lyα (to exclude IGM fluctuations), indicating the models are generally sufficient and that our noise spectra are realistic. However, in order to ensure that the continuum is adequately modeled in the Lyα forest region, we employ the mean flux regularization (MFR) technique introduced by Lee et al. (2012). In this method, the Lyα forest region of a galaxy spectrum is multiplied by a low-order polynomial that best matches the spectrum to the mean flux $\langle F\rangle (z)$ determined from quasar measurements (Faucher-Giguère et al. 2008). This suppresses power on very large scales Δz ≃ 0.2 (∼170 ${h}^{-1}$ cMpc) while mitigating continuum errors that could adversely affect the smaller scales of interest. We set the order of the polynomial by the length of the Lyα forest contained in the spectrum. When ${\rm{\Delta }}{z}_{\mathrm{Ly}\alpha }\lt 0.15$, we do not perform MFR. When $0.15\lt {\rm{\Delta }}{z}_{\mathrm{Ly}\alpha }\lt 0.3$, we fit and divide by a constant. When ${\rm{\Delta }}{z}_{\mathrm{Ly}\alpha }\gt 0.3$, we fit and divide by a line. MFR typically makes only modest continuum adjustments by a factor of 0.99 ± 0.12 (median and rms; see Figure 8).

As discussed in Section 6.1, we matched our redshifts to the full zCOSMOS and VUDS data sets, finding a small fraction of catastrophic outliers. Among z > 2 galaxies with high-confidence redshifts in LATIS and one of these surveys, we find a median offset of $c({z}_{\mathrm{LATIS}}-{z}_{\mathrm{zCOSMOS}})/(1+z)\,=118$ km s${}^{-1}$ and $c({z}_{\mathrm{LATIS}}-{z}_{\mathrm{VUDS}})/(1+z)=187$ km s⁻¹, or about half of our instrumental resolution. Given the range of velocities that different features in the UV spectrum present, it is understandable that different measurement procedures could lead to systematically different redshifts. When we combine LATIS with the zCOSMOS and VUDS redshifts to plot the locations of galaxies in our tomographic maps (Section 9), for consistency we adjust the zCOSMOS and VUDS redshifts onto the LATIS system using these offsets.

Our LBG spectral modeling is designed to produce redshifts that are, on average, the systemic redshift z_sys, as the templates are shifted to v_stars = 0. We assessed this by comparing LATIS redshifts to nebular redshifts from the MOSDEF survey. For 24 galaxies with high-confidence redshifts (excluding AGNs), we find a median offset $c({z}_{\mathrm{LATIS}}-{z}_{\mathrm{MOSDEF}})/(1+z)\,=-92$ km s⁻¹, with a standard deviation of 100 km s⁻¹. This scatter is equal to that obtained when an optimal combination of Lyα and interstellar line redshifts is used to estimate z_sys (Steidel et al. 2018), which indicates that the precision of the LATIS redshifts is good. The origin of the −92 km s⁻¹ offset is unclear. We apply a global shift to the LATIS redshifts, as well as the adjusted zCOSMOS and VUDS redshifts, to place them on the MOSDEF system when we compute the positions of galaxies in our tomographic maps. However, this amounts to a small correction of 0.9 h⁻¹ cMpc, well below the map resolution.

Although free of narrow absorption features, the QSO continuum in the Lyα forest is complicated by the broad wings of the Lyα and Lyβ emission lines and the presence of metal emission lines. We obtain a first estimate of the intrinsic QSO spectrum (absent foreground absorption) using the suite of principal components determined by Suzuki et al. (2005). We use the first 10 eigenspectra, following the recommendation of Suzuki et al., and perform a least-squares fit to the spectrum redward of Lyα. Metal lines from foreground absorbers are then identified and masked, and the fit is repeated. In a few cases, the model flux density became negative within the observed wavelength range; we then decrease the number of eigenspectra used in the fit until the model is everywhere positive. This procedure produces a predicted QSO continuum in the Lyα forest, in which the emission lines are predicted via their correlations with the emission lines redward of Lyα.

The model for one quasar is shown by the blue curve in Figure 17. As noted by Suzuki et al. (2005), the slope of the Lyα forest continuum is not always accurately predicted from the red part of the spectrum. Therefore, as for the LBGs, we use MFR to correct the forest continuum shape. Due to the more complex QSO continuum, we use polynomials of order 1 or 2 when the observed length of forest is Δz = 0.15–0.3 or Δz > 0.3, respectively. The blue curve in Figure 17 shows that this procedure produces an accurate continuum model, both in terms of the continuum slope (due to MFR) and the higher frequency features (due to the principal components analysis).

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Our current data set contains 47 broad-line QSOs at z = 2.2–3.2. Of the 44 sources targeted on the basis of a literature classification, the redshifts are almost always confirmed, but 8 turned out to be unsuitable for the Suzuki et al. templates to model. Among the 47 broad-line QSOs in LATIS, 16 were excluded from the Lyα forest analysis either because they have broad absorption lines (3 QSOs); the length of the forest contained in our spectrum was too short to permit MFR (Δz_Lyα < 0.15), which in contrast to the LBGs seems to be necessary in most cases (7 QSOs); or visual inspection of the spectrum showed that it was otherwise not accurately modeled using the Suzuki et al. templates (6 QSOs).

Errors in the continuum placement directly propagate to the transmitted flux F = S/C, where S and C are the spectrum and continuum model, respectively. To estimate the continuum uncertainties, we measured the dispersion in $\langle F\rangle$ averaged over 3 pMpc (Δz ≈ 0.01) segments of the Lyα forest. (We note that this scale is much smaller than the Δz ≳ 0.1 scales that are suppressed by the MFR.) Faucher-Giguère et al. (2008) measured the rms dispersion to be 0.11 at z = 2.4 based on high-resolution quasar spectra and found no large redshift dependence over the range relevant for LATIS. We first consider the LBGs and split these Lyα forest segments into bins of continuum-to-noise ratio, CNR = C/σ_noise, where σ_noise is the random noise. In each bin, we compute the rms σ_obs of $\langle F\rangle$ among the segments. We consider this dispersion to be composed of three components: ${\sigma }_{\mathrm{obs}}^{2}={\sigma }_{\mathrm{noise}}^{2}+{\sigma }_{\mathrm{IGM}}^{2}+{\sigma }_{\mathrm{cont}}^{2}$, where σ_IGM = 0.11 represents the intrinsic IGM fluctuations and σ_cont incorporates any additional scatter. We think that continuum errors are likely the dominant contributor to σ_cont, but this term also includes any additional noise beyond that propagated during the data reduction.

The excess noise σ_cont relative to the continuum is shown in Figure 18. The solid line shows a simple fit $0.24\times {\mathrm{CNR}}^{-0.86}$. We conservatively place a lower limit of 0.05. Repeating this procedure for the QSOs yields consistent but less precise estimates of the continuum errors, so we adopt the same continuum errors for LBGs and QSOs. The dashed line in Figure 18, 1/CNR, demonstrates that the random noise dominates when CNR < 20, i.e., virtually always. We will incorporate this estimate of the continuum uncertainty when calculating uncertainties in the Lyα forest fluctuations (Section 8.2) and when simulating LATIS (Section 8.3). Our estimates of the LBG continuum uncertainty are compatible with those of the CLAMATO survey (Lee et al. 2016), and our QSO continuum uncertainties at high CNR are similar to the 4%–7% estimated by other authors using different techniques (e.g., Lee et al. 2012; Eilers et al. 2017).

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We repeated this analysis for the subset of LBGs where the continuum is not adjusted using MFR because of the short length of the Lyα forest that is observed (${\rm{\Delta }}{z}_{\mathrm{Ly}\alpha }\lt 0.15$). The excess noise in these spectra is very similar to that in the full sample, giving us confidence that these spectra can be used for tomography. In contrast, QSO models produced without MFR were generally not usable.

Damping wings from high-column-density systems produce absorption over a wide wavelength range. When this range significantly exceeds our spectral resolution, it violates the mapping between wavelength and velocity that underlies tomographic reconstruction. We therefore use an automated procedure to mask these lines. An absorber with a column density of ${N}_{{\rm{H}}{\rm{I}}}\gtrsim {10}^{19.7}$ cm⁻² and an equivalent width W₀ = 5 Å absorbs approximately half of the flux in the adjacent resolution elements of our spectra. We mask absorption lines that are detected at >5σ and have an equivalent width >5 Å in the absorber frame. We find a total of 102 such absorbers over a total path length of Δz = 384. Roughly interpolating between prior measurements of the number density of sub-DLA (Zafar et al. 2013) and DLA (Péroux et al. 2003) systems at z ≈ 2.5 indicates dn/dz ≈ 0.3, so the expected ∼115 absorbers is in good agreement with the number we find, particularly because some damped systems may be present at a detection significance below our threshold.

Our tomographic reconstruction incorporates all sightlines contained within the four footprints listed above whose Lyα forest overlaps the range ${z}_{\mathrm{Ly}\alpha }=2.2\mbox{--}2.8$, that have high-confidence redshifts, and that were not manually excluded due to reduction defects. These total 1071 sightlines (98% LBGs, 2% QSOs) with an areal density of 1850 deg⁻². Figure 19 shows the positions of these sightlines on the sky (red circles). Although the targeted galaxies (red circles and gray crosses) are reasonably uniformly distributed, there are some areas with few or no sightlines usable for tomography. This is expected given the clustered nature of luminous galaxies. The consequences of a variable sightline density for map quality will be assessed using simulated mock surveys (Section 8.3).

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The sightline density and the continuum-to-noise ratio are key metrics determining the quality of a tomographic reconstruction. The left panel of Figure 20 shows the areal density n of sightlines piercing a given z_Lyα, averaged over each footprint, and the corresponding mean transverse sightline separation at z = 2.5, $\langle {d}_{\perp }\rangle =70.6\,{n}^{-1/2}\,{h}^{-1}$ cMpc. In most fields, the sightline density is relatively constant at $\langle {d}_{\perp }\rangle \simeq 2.5$ ${h}^{-1}$ cMpc over z = 2.2–2.6, meeting the design goal of the survey. At z > 2.6, the sightline density declines. We limit the tomographic reconstruction to z < 2.8, where the sightline separation falls to $\langle {d}_{\perp }\rangle \approx 4$ ${h}^{-1}$ cMpc, which we take as the maximum useful value based on the simulations by Stark et al. (2015b). The distribution of CNR is shown in the right panel of Figure 20. The median CNR varies with redshift due to the wavelength-dependent sensitivity of IMACS (Figure 6), ranging from 1.7–2.7 per pixel. These values are roughly consistent with the target CNR = 2 that set our exposure times.

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Interesting, in the D2M4 footprint, we achieved a far higher sightline density than typical. Because targeting procedures and the depth of the spectra were not different, we conclude that an overdensity of galaxies allows us to reach n = 1300 deg⁻², the highest density yet employed for Lyα tomography.

We are now ready to transform the LATIS spectra into 3D maps of the IGM opacity. We reconstruct the transmitted flux F, rather than attempting to recover the underlying density field (Pichon et al. 2001; Gallerani et al. 2011; Horowitz et al. 2019). We use Wiener filtering, a method that has widely been used in the mapping of large-scale structure, to invert the sightline data. The Wiener filter incorporates noise weighting and regularizes the output map, as described below. Its utility for IGM tomography was investigated theoretically by Pichon et al. (2001) and Caucci et al. (2008), and more recently by Stark et al. (2015a, 2015b) in the context of the CLAMATO survey, which also employs a Wiener filter (Lee et al. 2014b, 2018). For LATIS, we specifically use the efficient dachshund code developed by Stark et al. (2015b).

The input data consist of measurements of flux contrasts δ_F and associated uncertainties σ_δ at a series of positions (x, y, z) within the volume to be reconstructed. Each such measurement is one pixel in the Lyα forest of a background source. The flux contrasts are defined as fractional variations around the mean, the fundamental metric in which the spectra and the maps are expressed:

$$\begin{eqnarray}&&{\delta }_{F}=\displaystyle \frac{F}{\langle F(z)\rangle }-1,\end{eqnarray} \tag{ 1 }$$

where F = S/C is the continuum-normalized spectrum and $\langle F(z)\rangle$ is the mean flux transmission derived from quasar observations (Faucher-Giguère et al. 2008). The uncertainty σ_δ includes both random noise and the continuum uncertainty (Section 7.4) added in quadrature. We have carefully assessed the accuracy of these noise estimates using multiple techniques, as described in the Appendix. To avoid placing excess weight on a few quasar sightlines with very high signal-to-noise ratios, we impose a floor of σ_δ > 0.2. The coordinates (x, y, z) are expressed in h⁻¹ cMpc and are aligned with the R.A., decl., and redshift axes, respectively. We convert sky coordinates and redshifts to (x, y, z) coordinates using redshift-dependent radial and transverse comoving distances. Although we express the line-of-sight coordinate as a distance, our method does not attempt to correct for peculiar velocities, so the maps are made in velocity space. This is all that is needed to compare to the galaxy distribution, our main concern in this paper.

The 173,185 data points are used to reconstruct the IGM opacity in two volumes with dimensions 64 × 51 × 483 h⁻³ cMpc³ in D2/COSMOS and 33 × 27 × 483 h⁻³ cMpc³ in the D1 field. One quadrant of the COSMOS volume has no sightlines yet (see Figure 19); we exclude this region with x < 30 ${h}^{-1}$ cMpc and y < 24 ${h}^{-1}$ cMpc from our analysis. This leaves a total volume of 1.7 × 10⁶ h⁻³ cMpc³ in the maps.¹⁴ Each voxel in the maps occupies (1 h⁻¹ cMpc)³.

Wiener filtering interpolates between the sightlines to estimate the δ_F in each voxel. When the underlying field and the noise are Gaussian, Wiener filtering is the optimal linear operator and can be shown to correspond to the maximum a posteriori estimate in certain Bayesian approaches (Pichon et al. 2001). Interpolation requires a statistical description of the underlying field. Specifically, Wiener filtering requires the covariance matrix between input data and map voxels, C_MD, as well as the covariance among the input data points, C_DD + N. We assume independent Gaussian measurement errors, so that N is a diagonal matrix, and we follow the usual ad hoc assumption that ${C}_{\mathrm{DD}}={C}_{\mathrm{MD}}=C({{\boldsymbol{r}}}_{1},{{\boldsymbol{r}}}_{2})$ is Gaussian:

$$\begin{eqnarray}&&C({{\boldsymbol{r}}}_{1},{{\boldsymbol{r}}}_{2})={\sigma }_{F}^{2}\exp \left[-\displaystyle \frac{{\rm{\Delta }}{r}_{\parallel }^{2}}{2{\sigma }_{\parallel }^{2}}-\displaystyle \frac{{\rm{\Delta }}{r}_{\perp }^{2}}{2{\sigma }_{\perp }^{2}}\right],\end{eqnarray} \tag{ 2 }$$

where Δr_∥ and Δr_⊥ are the components of ${{\boldsymbol{r}}}_{1}-{{\boldsymbol{r}}}_{2}$ along and perpendicular to the line of sight, respectively (see, e.g., Lee et al. 2018, Equation (3); Caucci et al. 2008, Equation (10)). As discussed by Caucci et al. (2008), choosing ${\sigma }_{\parallel }\sim {\sigma }_{\perp }\sim \langle {d}_{\perp }\rangle$ regularizes the output map by suppressing structure on scales smaller than the mean sightline separation. The amplitude ${\sigma }_{F}^{2}$ represents the a priori expected variance in a volume of order ${\sigma }_{\perp }^{2}{\sigma }_{\parallel }$. Where observational errors are much larger than this, Wiener filtering suppresses the signal in favor of the prior δ_F = 0.

Because one of our goals is to compare the LATIS and CLAMATO maps where they overlap, and the surveys' sightline separations are comparable, we choose ${\sigma }_{\perp }=2.5$ ${h}^{-1}$ cMpc and ${\sigma }_{F}^{2}=0.05$ following Lee et al. (2018), who in turn relied on simulations by Stark et al. (2015a) that showed these parameters to be nearly optimal. To account for the smoothing of the spectra along the line of sight, we take ${\sigma }_{\parallel }^{2}={\sigma }_{\perp }^{2}-{\sigma }_{\mathrm{inst}}^{2}$, where ${\sigma }_{\mathrm{inst}}=1.4$ ${h}^{-1}$ cMpc is the instrumental resolution expressed in line-of-sight distance at z = 2.5.

For most applications, we then smooth the Wiener-filtered maps using an isotropic Gaussian kernel. Smoothing reduces noise at the expense of resolution, and it must be tailored to the requirements of each application. For display purposes, we use σ_kern = 2 ${h}^{-1}$ cMpc, while for some of the quantitative applications described in the rest of the paper, we will we use a broader kernel with σ_kern = 4 ${h}^{-1}$ cMpc. Finally the maps are multiplied by a calibration factor described in the next section.

Figure 21 shows that although the individual Lyα forest spectra are noisy and are, as an ensemble, consistent with Gaussian random noise at the level of individual pixels (top panel), the maps do contain significant structure. This can be demonstrated by comparing the fluctuations δ_F in the actual maps (bottom panel, solid line) with those in maps that are constructed from pure noise realizations (dashed line), i.e., from spectra composed of independent Gaussian random deviates with an rms of σ_δ. The range of δ_F in the actual maps is considerably broader, indicating that LATIS recovers spatially and spectrally coherent fluctuations from spectra that individually are noisy.

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Before we display the LATIS maps, we first would like to estimate their uncertainties and assess the fidelity of a LATIS-like survey for mapping the underlying flux field. We do this by performing 90 mock LATIS surveys in a large N-body simulation.

Briefly, we use the particle data from the MultiDark Planck 2 (MDPL2) simulation (Klypin et al. 2016) recorded at z = 2.535, near the midpoint of the LATIS redshift range. The density field in a grid with 0.25 ${h}^{-1}$ cMpc cubic voxels is estimated using cloud-in-cell interpolation. We then use the fluctuating Gunn & Peterson (1965) approximation (FGPA; e.g., Weinberg et al. 1998) to estimate the Lyα flux field. This method assumes that the gas density follows the dark matter density and that there is a one-to-one mapping between density and temperature; we use the relation measured by Rudie et al. (2012). It therefore ignores astrophysical sources of scatter and breaks down on small scales where the gas is pressure supported. However, when the FGPA is applied to N-body simulations with a similar interparticle spacing to MDPL2, it does produce estimates of the flux field that are fairly accurate on the large scales relevant to LATIS (Sorini et al. 2016). Confirming this, the simulated one-dimensional flux power spectrum matches BOSS measurements (Palanque-Delabrouille et al. 2013) well on velocity scales larger than k⁻¹ ∼ 50 km s⁻¹, which is smaller than our instrumental resolution by a factor of 3 and so more than adequate for our purposes.

In each of 90 nonoverlapping subvolumes, we impose a Hubble flow to convert coordinates along one dimension into velocities. We construct mock spectra with the same relative (x, y, z) coordinates as the LATIS data, i.e., matching the exact sightline distribution. The spectra are smoothed and sampled like the observations, and Gaussian random noise is added to match each sightline's noise properties. We also simulate continuum errors. For each sightline, we take the median CNR in the forest, determine the corresponding continuum uncertainty from Figure 18, draw a Gaussian random deviate with this dispersion, and modify the mock observed spectrum accordingly (see Krolewski et al. 2018, Equation (5)). We then feed these mock data to dachshund to reconstruct the flux field using the same parameters applied to the real data.

The relationships between the true ${\delta }_{F}^{\mathrm{true}}$ and recovered ${\delta }_{F}^{\mathrm{rec}}$ flux fields, smoothed on several scales, are shown in Figure 22. The mock surveys are clearly able to recover fluctuations with a meaningful precision relative to the range present in the simulated volumes. For larger smoothing kernels, this relationship tightens, as expected. We fit lines to the relations in Figure 22 and determine slopes of 0.69, 0.77, and 0.85 for kernels with σ = 2, 3, and 4 ${h}^{-1}$ cMpc, respectively.¹⁵ The slopes are shallower than unity primarily because of reconstruction errors that scatter ${\delta }_{F}^{\mathrm{rec}}$ away from the peak of the distribution at ${\delta }_{F}^{\mathrm{true}}\approx 0$. A fitting method that attempts to measure the relation between ${\delta }_{F}^{\mathrm{rec}}$ and ${\delta }_{F}^{\mathrm{true}}$ in the absence of noise would likely yield a steeper slope. However, our main purpose is to minimize the squared error $\mathrm{Var}({\delta }_{F}^{\mathrm{rec}}-{\delta }_{F}^{\mathrm{true}})$ for a given value of ${\delta }_{F}^{\mathrm{rec}}$ in the maps, which we will use when calculating the map signal-to-noise ratio below. To a first approximation, this is achieved by multiplying the maps by a calibration factor equal to the ordinary least-squares slope. Ultimately, this is relevant only for the signal-to-noise ratio, as for other applications we will normalize each map by its standard deviation, which we denote σ_map,¹⁶ and any global calibration factor thus cancels out.

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The distribution of fluctuations in the LATIS maps is compared to the mock surveys in Figure 23. (Throughout this section, we exclude voxels within 4 ${h}^{-1}$ cMpc of the map edge where boundary effects are strong.) The broad curves show the raw Wiener filter output, while the narrow curves show maps after smoothing by σ_kern = 2 ${h}^{-1}$ cMpc. Although there is a slight deficit of voxels with high δ_F (matter underdensities) in the real maps relative to the simulations, overall the agreement is strikingly good. We do not expect a perfect agreement for several reasons, including our approximate treatment of the IGM and the fact that the simulated maps are fixed at z = 2.5. Nonetheless, this comparison confirms that at the level of the one-point statistic, the LATIS maps are compatible with expectations for ΛCDM in the Planck cosmology.

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The mock surveys also allow us to estimate the noise in the maps. We follow Lee et al. (2014b, 2018) and use the metric

$$\begin{eqnarray}&&{\rm{S}}{/{\rm{N}}}_{\epsilon }^{2}=\displaystyle \frac{\mathrm{Var}({\delta }_{F}^{\mathrm{true}})}{\mathrm{Var}({\delta }_{F}^{\mathrm{true}}-{\delta }_{F}^{\mathrm{rec}})},\end{eqnarray} \tag{ 3 }$$

where ${\delta }_{F}^{\mathrm{true}}$ and ${\delta }_{F}^{\mathrm{rec}}$ are the true and recovered flux fields, both smoothed by σ = 4 ${h}^{-1}$ cMpc. We evaluate the denominator at each voxel in the map, measuring the variance over the 90 mock surveys, which allows us to measure the variation in S/N throughout the volume. The left panel of Figure 24 shows the mean S/N as a function of redshift, which is fairly constant at S/N ≃ 1.8 over the range z = 2.2–2.6 and then declines toward the back of the volume, due to the falling sightline density. In other words, the noise in the reconstruction is about half of the intrinsic IGM fluctuations on 4 ${h}^{-1}$ cMpc scales.

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Lee et al. (2014b) considered a good map construction to have S/N ≈ 2–2.5. LATIS falls slightly short of this range, but only by 10%. We also show S/N for the CLAMATO first data release (Lee et al. 2018), which we have calculated using the same methods as applied to LATIS. Note that we have adjusted the noise properties of the CLAMATO spectra based on a close analysis discussed in the Appendix, which was also applied to the LATIS data, and this lowers S/N by ≃20% from the value quoted by Lee et al. (2018). Compared to CLAMATO, the current LATIS map has a ≃10% lower S/N on average, but covers a 4.4× larger volume.

Nearly the entire footprint of the CLAMATO first data release (Lee et al. 2018) is already contained within LATIS. The two surveys overlap in the redshift range z = 2.2–2.55. Using the criteria described above, we identify four overdensities in either map that fall within the region of overlap. (We exclude peaks close to the CLAMATO map boundary, because edge effects are likely significant.) The LATIS and CLAMATO maps around these peaks are compared in the left panel of Figure 29. In the first, second, and fourth rows, there is a reasonably good agreement in the positions and morphologies of the overdensities in the two maps. The agreement is less good in the third row, where a strong LATIS peak is weaker and less extended in the CLAMATO map. Examining the LATIS sightlines near this position, we find that all show some absorption, but the strength of the map feature is enhanced by one sightline that is nearly opaque. There are also four underdensities identified in either map within their common volume, which are shown in the right panel of Figure 29. The first three rows show LATIS-detected voids; among these, the first two are seen in the CLAMATO maps, although at reduced significance. The third is not evident in CLAMATO, but it falls within just 5 ${h}^{-1}$ cMpc of the back of the CLAMATO volume, where edge effects and the declining sightline density (Figure 24) might explain the difference. The fourth row shows a CLAMATO-detected void that is not present in the LATIS map. Because the S/N_e is not particularly low at this location in our map, the reason for this discrepancy is not clear.

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This is a first comparison of megaparsec-resolution tomographic maps produced by independent groups using different data sets, and we conclude that the strong overdensities discussed in this Section usually have similar morphologies. The reproducibility of matter underdensities may be somewhat worse, but a larger sample of structures that are common to two surveys is needed to confirm this possibility and better understand its origins.