THE Hα LUMINOSITY FUNCTION AND STAR FORMATION RATE VOLUME DENSITY AT z = 0.8 FROM THE NEWFIRM Hα SURVEY

The NewHα Survey is an ongoing campaign designed to extend deep, wide searches for emission-line galaxies into the intermediate redshift universe. The survey takes advantage of the 276 × 276 field of view of the NEWFIRM, which achieved first light on the KPNO 4 m telescope in 2007 February, and became available for general observing in 2007 November.

NewHα uses narrowband observations to identify emission-line galaxy candidates. Imaging is taken through 1% filters that are designed to sample low OH airglow windows in the near-infrared, and objects are selected by detection of a photometric excess in a narrowband, relative to continuum measurements in a broadband. Bandpasses are centered at 1.18 μm and 2.09 μm, which capture Hα emission at redshifts of 0.80 and 2.19, respectively. The continuum flux is constrained with J and K_s imaging. A combination of techniques, including dedicated follow-up spectroscopy and empirical broadband color classification, is used to identify the emission line(s) responsible for the narrowband excess, as discussed in more detail below. A full description of the overall survey is provided in J. C. Lee et al. (2011, in preparation). Here, we give a summary of the 1.18 μm imaging observations, data reduction, and selection technique used to construct a robust sample of Hα emitters at z = 0.80.

The analysis presented in this paper is based upon NEWFIRM J band⁹ and 1.18 μm narrowband (hereafter NB118)¹⁰ observations of areas in the Subaru-XMM Deep Survey (SXDS; Furusawa et al. 2008) and Cosmic Evolution Survey (COSMOS; Scoville et al. 2007) extragalactic deep fields. The observations were carried out in 2007 December, 2008 September, and 2008 October at the KPNO 4 m telescope. Data were acquired for three regions in the SXDS and one region in COSMOS, each spanning the ∼750 arcmin² subtended by the detector array of the camera. In total, these observations cover 0.82 deg² for a comoving volume of 9.12 × 10⁴ h⁻³₇₀ Mpc³ at z = 0.8.

We follow standard near-infrared observing procedures to obtain the data. Integration times of 240 s and 30 s are used for the individual NB118 and J exposures, respectively. The NB118 exposures are read out with eight Fowler samples. In 2008, on board co-adding was enabled in the camera, and was used for our J-band observations, with every two J exposures being summed. A combination of nine-, six-, and four-point dither patterns is used to cover a 75'' square grid with 61 positions. The dithers serve to smooth over cosmetic defects, bridge the 35'' gaps between NEWFIRM's four 2048 × 2048 InSb arrays, and enable the rejection of pixels affected by persistent afterimages caused by the latency properties of the detectors. The pattern, with small offsets from the initial position, is repeated as necessary to achieve a minimum 3σ depth of 23.5 AB (NB118) and 23.7 AB (J), in apertures containing at least ∼80% of the flux of a point source, given the seeing conditions during the observations (see Section 3.1). Cumulative integration times range between 8.2 and 12.7 hr in NB118 and 2.3 and 4.0 hr in J. The median seeing during our observations was ∼12, and varied between 10 and 19, hence point sources are adequately sampled with 04 pixels. Sky conditions were mostly photometric, but some data were taken through thin cirrus. A summary of the observations is given in Table 1.

Data reduction is performed with our own automated PyRAF-based pipeline, which builds upon routines from the IRAF/nfextern package and is optimized for the processing of NewHα observations. Our procedures follow standard, iterative, near-infrared reduction techniques to produce flat-fields, subtract the sky background, and reject artifacts, particularly those due to persistent afterimages from bright sources.

The NewHα pipeline processes the data in two passes. One of the purposes of the initial pass is to create a deep object mask that is used to construct flat-fields and sky frames from the science images themselves. The pipeline first subtracts the dark current, masks for bad pixels, corrects for the nonlinear response of the detector, and performs a preliminary sky-subtraction using a median of the temporally closest five exposures. The geometric distortion is rectified, and the astrometry is calibrated relative to the Two Micron All Sky Survey (2MASS) catalog. The dithered science images are then projected onto a common pixel grid and stacked. A deep object mask is made from this initial stack, and applied to the individual science exposures on the original pixel grid.

The first pass sky-subtracted frames are also used to identify artifacts due to persistent afterimages. Object masks are created for each individual frame, and pixels in a given image are compared to corresponding pixels from previous frames. Pixels containing object flux in consecutive frames are masked. Non-science images, such as short exposures used to check and adjust the telescope pointing, are also included in this process. This method flags roughly 95% of visually apparent persistent artifacts. The remaining 5% are faint and decay quickly enough in subsequent frames that they are not detectable in the final mosaics after the stacking of the entire data set.

Flat-fields for each night are made by combining J-band science images, which have been masked for both real objects and persistent sources. The flats are used to normalize the response within each detector in both the J and NB118 images. Corrections that account for sensitivity variation between detectors are also applied.

In the second pass, all the data are flat-fielded, and the sky subtraction is again performed, but with stacks of temporally neighboring frames which have now been masked of all sources. Any problematic frames (e.g., due to read-out problems or jumps in the telescope pointing) are rejected. The flat-fielded, sky-subtracted, persistence-masked frames are then combined to produce the final mosaic. The astrometry of the mosaics is tested against 2MASS sources, as well as against sources in the COSMOS optical catalog, and is found to be accurate to within 015–020 with negligible systematic offsets.

Photometric calibration of the mosaics is performed using 150–300 unsaturated 2MASS (Skrutskie et al. 2006) sources in each field. We check for systematic errors as a function of both J/NB118 magnitude and radius from the mosaic center, and find no significant offsets. The resultant zero points are accurate to within 0.05 mag. Absolute flux calibration for the 2MASS catalog is based on Vega (Kurucz 1979), hence we convert to AB magnitudes by convolving the filter bandpasses with the Vega spectrum, and find that m(AB) − m(Vega) = 0.87 (NB118) and 0.95 (J).

Sources that show a significant J− NB118 color excess are selected as emission-line object candidates. Our selection procedure follows general techniques commonly used in narrowband surveys (e.g., Fujita et al. 2003; Ly et al. 2007; Shioya et al. 2008; Villar et al. 2008; Sobral et al. 2009).

To construct our sample, we first use SExtractor (version 2.5.0; Bertin & Arnouts 1996) in dual-image mode to generate source catalogs for each field. That is, sources are identified on the NB118 image, and fluxes are measured on both J and NB118 images in matched apertures at the position of every 3σ NB118 detection. Detection in the J band is not required for inclusion in the candidate list.

In each field, photometry is performed in two sets of apertures. The sizes of the apertures for each pair of J and NB118 images are chosen to contain at least 80% and 99% of light from a point source, given the size of the point-spread function (Table 1) and assuming a Gaussian profile. In the SXDS-N and SXDS-W fields, the seeing during our observations was between 11 and 12, and thus 2'' and 3'' diameter apertures are used. The aperture sizes are increased to 25 and 4'' for the SXDS-S and COSMOS fields, where the seeing was worse and varied from 125 to 16. One of the purposes of using two aperture sizes is to allow the selection to be sensitive to galaxies with concentrated star formation as well as those with more extended nebular emission. In order to derive global quantities, however, the Hα luminosities and EWs for all selected sources are calculated from fluxes measured in the larger aperture.

Sources are considered to have a significant narrowband excess if:

• 1.  
  They have a color above a minimum threshold given by

  $$\begin{equation} \Delta (J-{\rm NB118}) \ge 0.2\; \mbox{mag,} \end{equation} \tag{ 1 }$$

  where Δ(J − NB118) is defined below, and 0.2 mag roughly corresponds to the 5σ scatter in Δ(J − NB118) for bright point sources with 18 < NB118< 20 mag. It is imposed to help exclude bright foreground sources with blue continua from the candidate list.
• 2.  
  The color is significant at the 3σ level

  $$\begin{equation} \Delta (J-{\rm NB118}) \ge 3 \sqrt{\sigma _{J}^2+\sigma _{\rm NB118}^2}\;. \end{equation} \tag{ 2 }$$

  Other recent near-infrared narrowband surveys have adopted a lower threshold of 2.5σ (Villar et al. 2008; Sobral et al. 2009, hereafter V08 and S09, respectively). We also extract a secondary sample with this relaxed significance criterion to facilitate comparisons with these studies (Section 7).

Two issues critical to the robust application of these criteria for the selection of line emitters are the determination of Δ(J − NB118), and the calculation of accurate photometric errors. We discuss each of these in turn.

Flux excess in the NB118 filter cannot be directly calculated from the J − NB118 color since the NB118 filter does not fall at the center of the J bandpass, but rather was designed to sample the low-OH airglow window toward the blue edge. This not only results in a non-zero mean color for pure continuum sources 〈J − NB118〉_c, but also leads to variation about the mean color as a function of continuum slope. This systematic is illustrated in the left panel of Figure 1, which shows a standard color–magnitude selection diagram for one of our fields. The points in the diagram are color coded to correspond to different ranges in the z' − J color, which provides a measure of the continuum slope. Sources with red continua have lower values of 〈J − NB118〉_c compared with those with blue continua, as expected. Here, the J photometry is from our NEWFIRM observations, while the z' measurements are from Subaru/Suprime-Cam (see Furusawa et al. 2008 for SXDS and Taniguchi et al. 2007 for COSMOS).

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To account for this systematic, we define

$$\begin{equation} \Delta (J-{\rm NB118})=(J-{\rm NB118})-\langle J-{\rm NB118} \rangle _c \end{equation} \tag{ 3 }$$

where

$$\begin{equation} \langle J-{\rm NB118} \rangle _c=f(z^\prime -J). \end{equation} \tag{ 4 }$$

A linear fit is performed for sources with J − NB118 within ±0.25 mag of the overall mean value. We find that 〈J − NB118〉_c = −0.15(z' − J) + const. for z' − J < 0.5. For z' − J > 0.5, there is no apparent slope so a constant value is assumed for redder sources. Accordingly, we compute corrections and apply them relative to the value of 〈J − NB118〉_c for sources with an intermediate z' − J of 0.25 mag. The right panel of Figure 1 shows the color–magnitude diagram after this correction is applied and demonstrates the removal of the systematic.

Photometric uncertainties are calculated by combining the errors generated by SExtractor with measurements of the background noise taken through a large number of apertures randomly placed on the images. This hybrid scheme ensures that our uncertainties account for (1) correlated (non-Poissonian) noise arising from pixel interpolation during astrometric reprojection in the image reduction (captured in the random aperture measurements) and (2) local variations in the noise, for example, due to non-uniformity in the exposure map (captured by the SExtractor errors). A detailed discussion of these issues is given in Gawiser et al. (2006).

The global, average uncertainty due to the background can be robustly measured using a large number of apertures (identical in size to the apertures used for the photometry) that randomly sample the sky in the images. We perform this exercise separately for different quadrants in the image to account for quantum efficiency differences between the NEWFIRM detectors.¹¹ The distribution of measurements is well fitted by a Gaussian function, and the standard deviation given by the fit provides the 1σ uncertainty. The average depths of our observations determined in this way are given in Table 1.

To incorporate information on local variations in the noise that is included in the SExtractor errors, the SExtractor estimates are compared with those computed from the random apertures. We find that SExtractor yields lower uncertainties, which is expected since the program assumes that the noise is purely Poissonian and simply computes the error from the global pixel-to-pixel rms. To account for the contribution of non-Poissonian noise components, we scale the median SExtractor error (as a function of the object flux and on a per-quadrant basis) to match the average uncertainty determined from the random apertures. The errors from SExtractor are increased by 2%–51%, depending upon the aperture size used. These scaled SExtractor errors are adopted to evaluate the significance of the color excess detected in our observations.

The selection criteria are illustrated in Figure 2, which shows the color–magnitude diagrams for one of our fields, where the photometry has been measured in the larger choice of aperture. Horizontal lines indicating the minimum accepted color excess are plotted, along with curves representing the average values of the color excess at 3.0σ, 2.5σ, and 2.0σ significance (as determined using random apertures). Objects selected at 3σ (red circles) and 2.5σ (black diamonds) are both shown. Hereafter, quantities related to the 2.5σ samples are quoted in brackets unless otherwise noted.

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The selection is performed separately for the photometry determined through the two sets of apertures, as well as for the individual quadrants in each field. The use of a second, larger detection aperture results in a ∼10% increase of the number of narrowband excess candidates. In total, we find 150–300 [250–450] candidates per field. All candidates are inspected by visual examination of the NEWFIRM J and NB118 data, alongside publicly available deep z' imaging. The inspection process leads to the removal of four sources from the sample (two are artifacts and two are significantly blended with adjacent candidates). The overall process yields a total sample of 818 [1218] NB118 excess emitters in the combined survey area of 0.82 deg². A summary of the number of sources identified in each field is given in Table 2. A catalog of NB118 excess emitters, including emission-line fluxes and EWs, will be provided in a forthcoming paper (J. C. Lee et al. 2011, in preparation).

An excess in the narrowband can arise from various emission lines that are redshifted into the bandpass of the filter. The main emission lines detected in our NB118 observations are as follows:

• 1.  
  [S iii] λλ9052,9532 at z = 0.31 and 0.24,
• 2.  
  [S ii] λλ6717,6731 at z = 0.76,
• 3.  
  Hα at z = 0.80,
• 4.  
  [O iii] λλ4959,5007 at z = 1.39 and 1.36,
• 5.  
  Hβ at z = 1.44, and
• 6.  
  [O ii] λ3727 at z = 2.2.

To isolate the Hα emitters in our sample, we use a combination of techniques. For 62% [46%] of the 3σ [2.5σ] selected objects, spectroscopic data are available from our own targeted follow-up of NewHα narrowband excess sources (see below) with a small contribution from public spectroscopic data sets. For the remainder of the sample, a classification scheme based on optical broadband colors is used. The classification is empirically calibrated with a combination of (1) the subset of NB118 excess emitters for which spectroscopy and optical broadband photometry are available, and (2) galaxies in the COSMOS spectroscopic catalog whose redshifts would cause an emission line to appear in the NB118 bandpass.

Overall, we find that 48% of our 3σ narrowband excess sample (394/818) can be identified as Hα emitters. The fraction is slightly lower (43% or 522/1218) for the 2.5σ sample. Among our four fields, the fraction ranges from 35% to 65%. This observed field-to-field variation is discussed in the context of predictions for cosmic variance in Section 6.1. A summary of these statistics is given in Table 2.

3.2.1. Spectroscopy of NewHα Narrowband Excess Sources

We carried out spectroscopy of NewHα narrowband excess sources between 2008–2009 with the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) at the 6.5 m Magellan I telescope. IMACS enables multi-object spectroscopy with slit masks over a 274 diameter area (an excellent match to the field of view of NEWFIRM), and has good sensitivity to ∼9500 Å. These two characteristics make IMACS an ideal instrument for optical spectroscopic follow-up of NewHα NB118 excess sources, and in particular, Hα emitters at z = 0.80. Our observational setup yields spectral coverage from 6300 Å to 9600 Å with 9 Å resolution, and captures the complete ensemble of strong rest-frame optical emission lines blueward of Hα at z = 0.80, from [O ii] λ3737 at 6720 Å to [O iii] λ5007 at 9030 Å. The spectra have a median integration time of ∼3.5 hr on average, reaching 5σ sensitivities of ∼2 × 10⁻¹⁷ erg s⁻¹ cm⁻². IMACS spectroscopy has been obtained for 56% [42%] of our candidates, and the data are currently being used to probe the attenuation and metallicity properties of the sample (I. Momcheva et al. 2011, in preparation). A more complete description of the NewHα IMACS follow-up campaign is provided in J. C. Lee et al. (2011, in preparation) and I. Momcheva et al. (2011, in preparation).

Additional spectroscopy is available from observations carried out by the SXDS (M. Akiyama 2008, private communication) and zCOSMOS (DR2; Lilly et al. 2007) survey teams. The sample sizes of the spectroscopic catalogs are 11,975 for COSMOS and 4231 for SXDS, and among these, 2690 and 2386 fall in our survey regions. The zCOSMOS survey uses the VIMOS spectrograph on the Very Large Telescope 8 m, and targets I < 22.5 mag sources, as well as galaxies that are color-selected to have 1.4 < z < 3.0. The existing SXDS spectroscopic catalog is formed from the composite of data from a number of individual observing programs targeting a range of SXDS subsamples, using various instruments, and achieving different depths. The mean and 1σ dispersion of the magnitude distribution for the available SXDS z_spec catalog are R_C = 21.7 and 2.0 mag, respectively. Both of the resultant SXDS and zCOSMOS spectroscopic catalogs are dominated by objects that are bright relative to our NB118 excess emitters, and hence the overlap with our sample is small (5% or 58/1218).

In total, 504 [566] sources in our NB118 excess sample have spectroscopic redshifts. The redshift distribution for these galaxies is shown in Figure 3. There are 253 [272] galaxies with redshifts between 0.790 and 0.817, which places Hα in the NB118 bandpass, and thus confirms them as Hα emitters.

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3.2.2. Empirical Optical Color Classification

For the remaining 38% [54%] of the NB118 excess sources that do not have spectroscopic redshifts, a classification scheme based on publicly available Suprime-Cam broadband photometry is developed to separate Hα emitters from other sources in the sample. Our classification uses R_C i' z' in the SXDS fields, and r' i' z' in the COSMOS field. These sets of bandpasses are chosen because at z = 0.8, the Balmer and 4000 Å breaks occur at ∼6500 Å (in the R band), so NB118 Hα emitters will appear much redder in R − i' for a given i' − z' than other narrowband excess sources (Figure 4).

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In the SXDS fields, we examine the distribution of NB118 excess sources that have spectroscopy from our follow-up IMACS observations (Figure 4, left panel), and identify Hα emitters as those sources with

$$\begin{eqnarray} &&R_{\rm C}- i\mbox{$^\prime $}\ge 0.25, \;\;\; \mbox{if} \; i\mbox{$^\prime $}- z\mbox{$^\prime $}\le 0.35 \; \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} &&R_{\rm C}- i\mbox{$^\prime $}\ge 0.846(i\mbox{$^\prime $}- z\mbox{$^\prime $}) + 0.204, \;\;\; \mbox{if} \; i\mbox{$^\prime $}- z\mbox{$^\prime $}> 0.35. \; \end{eqnarray} \tag{ 6 }$$

In the COSMOS field, our IMACS spectroscopic data set sparsely samples the color–color diagram. Thus, to improve coverage of the diagram, we also include galaxies in the zCOSMOS spectroscopic catalog which lie outside the area of our imaging, but whose redshifts would cause an emission line to appear in the NB118 bandpass (open triangles in Figure 4, right panel). Similar color criteria are adopted:

$$\begin{eqnarray} &&R_{\rm C}- i\mbox{$^\prime $}\ge 0.39, \;\;\; \mbox{if} \; i\mbox{$^\prime $}- z\mbox{$^\prime $}\le 0.30 \; \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &&R_{\rm C}- i\mbox{$^\prime $}\ge 1.08(i\mbox{$^\prime $}- z\mbox{$^\prime $}) + 0.162, \;\;\; \mbox{if} \; i\mbox{$^\prime $}- z\mbox{$^\prime $}> 0.30. \; \end{eqnarray} \tag{ 8 }$$

An additional 141 [250] NB118 excess sources lacking spectroscopic redshifts are identified as Hα candidates with these criteria in both fields.

Of course, this color method is a blunt selection tool compared with the use of spectroscopic redshifts—it leads to the inclusion of some interlopers, while missing true Hα emitters that do not lie within the color selection region, as evident from Figure 4. In particular, the color criteria cannot distinguish between Hα and [S ii] emitters because the wavelengths of the emission lines are separated by ∼100 Å.

Fortunately, we can estimate the contamination and miss rates by examining the color classification of the NB118 excess sources with spectroscopic redshifts. In the SXDS fields, 15% of the excess sources with available spectroscopy that lie in the Hα selection region are incorrectly classified as Hα emitters, and 5% are confirmed Hα emitters that fall outside the color selection region. The corresponding numbers for the COSMOS field are 29% and 8%. Applying these rates to the number of Hα emitters that are added to the Hα sample via the color method, we find that 25 [45] sources are potential interlopers and 8 [15] Hα emitters could be missed. However, the overall contamination and miss rates are far more limited with a high level of spectroscopic completeness of the sample: the estimated number of interlopers and missed Hα emitters are only 6% [2%] and 9% [3%] of the total Hα sample.

Emission-line fluxes and EWs for the z = 0.8 Hα galaxy sample are calculated as follows. Flux densities (erg s⁻¹ cm⁻² Å⁻¹) may be written as f_NB = f_C + F_L/ΔNB and f_J = f_C + F_L/ΔJ, where f_C is the continuum flux density, F_L is the emission-line flux (erg s⁻¹ cm⁻²), and ΔNB and ΔJ are the full width at half maximum of the NB118 (110 Å) and J (1786 Å) filters. Therefore, the emission-line flux and the continuum flux density are computed as

$$\begin{eqnarray} F_{L} = &\Delta {\rm NB} \frac{f_{\rm NB} - f_{J}}{1-(\Delta {\rm NB}/\Delta J)}, {\rm and} \end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray} f_C = &\frac{f_{J} - f_{\rm NB}(\Delta {\rm NB}/\Delta J)}{1-(\Delta {\rm NB}/\Delta J)}.\quad\ \ \end{eqnarray} \tag{ 10 }$$

By definition, the observed EW, which is a factor of 1 + z larger than the rest-frame EW, is the ratio of the emission-line flux to the continuum flux density, and thus

$$\begin{equation} {\rm EW}_{\rm obs} \equiv \frac{F_L}{f_C} = \Delta {\rm NB}\frac{f_{\rm NB} - f_{J}}{f_{J} - f_{\rm NB}(\Delta {\rm NB}/\Delta J)}. \end{equation} \tag{ 11 }$$

With this equation, the minimum Δ(J − NB118) = 0.2 mag excess corresponds to an observed EW of 40 Å. To compute luminosities, we adopt a distance of 5041 h⁻¹₇₀ Mpc, which corresponds to z = 0.803, the median redshift of our spectroscopically confirmed Hα emitters. Distributions of the observed emission-line fluxes and EWs for our sample of Hα emitters are shown in Figure 5.

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To determine the intrinsic Hα luminosity from the observed line luminosity, corrections must be applied for contamination of the flux by the adjacent [N ii] lines, and for attenuation by dust internal to the galaxy. The corrections that we adopt are based on standard, empirically calibrated relationships, which describe average corrections for ensemble populations. They should yield luminosities appropriate for computing averaged/integrated quantities such as the SFR volume density. However, it should be noted that the corrections will not be accurate for individual galaxies, since the scatter in the relationships is large, as described below.

N ii contamination. The NB118 bandpass is wide enough to include flux from the [N ii] λλ6548,6583¹² emission lines for narrowband excess selected Hα emitters.

In the local universe, integrated spectroscopic surveys have found that the Hα/[N ii] flux ratio is 2.3 for typical L_⋆ galaxies (Kennicutt 1992; Gallego et al. 1997), and past narrowband surveys have often adopted a fixed correction of 2.3 for all selected Hα emitters. The flux ratio, however, has been shown to increase with larger emission-line EWs (see, e.g., V08) and with decreasing B-band luminosities (Kennicutt et al. 2008; Lee et al. 2009). Such correlations are likely a consequence of the mass–metallicity relationship (e.g., Lee et al. 2004; Tremonti et al. 2004). In a recent deep optical narrowband survey with Subaru Suprime-Cam, Ly et al. (2007) adopted 4.66 based on optical spectroscopic follow-up of their emitters. The sample of Ly et al. (2007) consists of galaxies with fainter luminosities, and hence are more metal-poor and would have a higher Hα/[N ii] flux ratio on average.

For this study, we follow V08 and S09 in adopting an EW-dependent Hα/[N ii] flux ratio to facilitate comparisons of results. The EW-dependent correction was constructed from thousands of z ∼ 0.1 star-forming galaxies from the Sloan Digital Sky Survey fourth data release with which V08 determined the mean relationship between the rest-frame EW of Hα + [N ii] λ6583 and the Hα/[N ii] flux ratio. The correlation exhibits a scatter of ∼0.2 dex, which implies that estimates of the Hα/[N ii] ratio for individual sources will only be accurate to ∼50%. Such errors will average out in the calculation of integrated quantities however, and are adequate for our purposes here.

Also, our correction assumes that the Hα/[N ii] relation does not evolve with redshift. This is a valid assumption since the evolution of metallicity between z = 0.07 and z = 0.7 has been found to be no more than 0.1 dex (see, e.g., Mannucci et al. 2009 and references therein). Near-infrared multi-object spectroscopy will be needed to examine the Hα/[N ii] ratio for NB selected galaxies on a case-by-case basis. Assuming the V08 [N ii] correction, the Hα/[N ii] ratio varies from 1.85 to 10.0 with a median (average) of 2.50 (2.81) for our population of Hα emitting galaxies.

Dust attenuation. To correct for dust attenuation, we adopt a luminosity-dependent extinction relation following Hopkins et al. (2001):

$$\begin{eqnarray} &&\log {\left[{\rm SFR}_{{\rm obs}}({\rm H}\alpha)\right]}=\log {\left[{\rm SFR}_{\rm int}({\rm H}\alpha)\right]}-2.360\nonumber\\ &&\quad\times \log {\left[\frac{0.797\log {\left[{\rm SFR}_{\rm int}({\rm H}\alpha)\right]}+3.786}{2.86}\right]}. \end{eqnarray} \tag{ 12 }$$

Hopkins et al. (2001) showed that attenuations computed from this equation show a 0.2 dex scatter relative to those based on Balmer decrement measurements for individual galaxies. Much like the [N ii] correction, these dust extinction corrections are more reliable when considering multiple sources of a given luminosity/SFR. The Hopkins et al. (2001) relation was also adopted in other studies (e.g., Ly et al. 2007; V08; Dale et al. 2010). For our sample, this correction (A[Hα]) ranges from 0.66 to 1.87 mag with a median and average of 1.19 and 1.21 mag, respectively.

One piece of evidence that supports the Hopkins et al. (2001) relation is the work of Garn et al. (2010), which has looked at the UV, Hα, and mid-infrared fluxes for a sample of narrowband selected Hα emitters to determine dust attenuation. They find a correlation between the observed Hα luminosity and dust attenuation that is similar to Hopkins et al. (2001). This multi-wavelength comparison will be conducted for our sample of Hα emitters. We will also investigate dust attenuation determined from Balmer decrements, which are obtained from the combination of our NB118 measurements and our IMACS follow-up spectroscopy (I. Momcheva et al. 2011, in preparation). Preliminary results do indicate that the attenuations based on Balmer decrements for the NB118-selected Hα emitters are consistent with the Hopkins et al. (2001) correction.

Motivation. To account for the detection limits and photometric selection of the NewHα survey, we need to estimate the completeness fraction as a function of luminosity, κ(L). The greatest uncertainty for such a task is the intrinsic EW distribution, that is, the inherent distribution of the population that we are able to seek. Since the narrowband and broadband imaging sensitivities of the survey are known, the completeness is determined for a source of a given brightness with a J − NB118 excess color (i.e., an EW). However, sources of a given emission-line luminosity can be faint with large EWs or bright with low EWs. Thus, the adopted EW distribution affects the estimated completeness for individual emission-line luminosity bins. For this reason, we conduct Monte Carlo realizations of our data, and follow a "maximum likelihood" approach to determine the completeness of NewHα.

Technique/approach. The methodology intends to simultaneously reproduce the shape of the observed¹³ Hα+[N ii] EW distribution and the observed Hα LF. We begin with a grid of models that adopt certain EW distributions. With these distributions, we generate artificial emission-line galaxies. We add noise to these galaxies, and use their measured magnitudes and colors to determine if these mock galaxies satisfy the NB118 excess selection. We construct the observed EW distribution and Hα LF from the sample of mock NB118 excess emitters to compare to the respective distributions from NewHα. We determine a best model and define the completeness, κ(L), as the ratio of the number of mock NB118 excess emitters to the total number of generated artificial galaxies:

$$\begin{equation} \kappa (L) = {\rm N}(L)_{\rm obs} / {\rm N}(L)_{\rm tot}. \end{equation} \tag{ 13 }$$

Assumptions. For the prior distributions, we make two assumptions. First, for the Hα LF, a proper normalization of bright-to-faint sources is necessary, otherwise we will generate relatively too many bright sources, and a decline in the simulated LF will not be seen and cannot be compare to the observed Hα LF. To constrain the ratio of bright-to-faint sources, we examine the galaxy number counts (N[J]) in the NewHα fields and find that log [N(J)] ∝ 0.344 × J. This relation implies that the number of galaxies at magnitude J' + 1 is a factor of 2.2 more numerous than those at J'.

Second, each plausible model assumes a log-normal EW distribution described by a mean 〈log(EW₀/Å)〉 and a sigma σ[log(EW/Å)]. We adopt such a distribution, since it is fairly similar to the observed NewHα distributions and the distributions seen locally (Lee et al. 2007). Our models span 〈log(EW₀/Å)〉 = 1.15–1.55 and σ[log(EW/Å)] = 0.15–0.40 both in increments of 0.05 dex for a total of 54 EW distributions. Here, 〈log(EW₀/Å)〉 is the logarithm of the rest-frame EW, and we later include a factor of 1+z for the "observed" magnitudes, colors, fluxes, and EWs.

Implementation. For each of the 54 models, we generate ∼40,000 mock galaxies with J-band (continuum) magnitudes chosen to follow the above relation between log [N(J)] and J. We assume that these galaxies are spatially unresolved and follow the FWHM of seeing for each mosaic. For the EWs, we randomly draw from a log-normal distribution given by 〈log(EW₀/Å)〉 and σ[log(EW/Å)]. With these two information, we "fill" the color–magnitude diagram (Δ(J − NB118) versus NB118; see Figure 6).

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We add observational uncertainties to the J and NB118 magnitudes as follows. For each mock galaxy, we have a randomly chosen position in the mosaics, and generate 200 realizations based on the sensitivity at that position. The sensitivity is governed by the exposure maps for both the NB118 and J-band mosaics, thus accounting for detector and pixel-to-pixel variations. We compute the NB118 or J-band 3σ limiting magnitudes, m_lim(x, y), signal-to-noise ratios, S/N(x, y), and 1σ uncertainties, Δm(x, y), as

$$\begin{eqnarray} m_{\rm lim}(x,y) = & \langle m_{\rm lim}\rangle + 2.5\log {(\sqrt{t(x,y)/t_0})}, \end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray} {\rm S/N}(x,y) = & 3 \times 10^{-0.4[m - m_{\rm lim}(x,y)]}, {\rm and} \end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray} \Delta m(x,y) = & 2.5 \log {\left[1+\frac{1}{{\rm S/N}(x,y)}\right]}, \end{eqnarray} \tag{ 16 }$$

where 〈m_lim〉 and t₀ are the individual detector's median limiting magnitudes and exposure times (see Table 1), respectively, and m is the NB118 or J magnitude. For the Δ(J − NB118) colors, the errors are added in quadrature: $\sqrt{\Delta m_{\rm NB118}(x,y)^2+\Delta m_J(x,y)^2}$. The magnitudes for the 200 realizations follow a Gaussian distribution with a mean of m and 1σ of Δm(x, y).

We identify mock galaxies that are NB118 excess emitters using the same methods described in Section 3.1. For the smaller apertures (2'' or 25), we assume that the flux enclosed is between 81% and 86% of the total flux within the larger apertures (3'' or 4''). We determine these values by considering a Gaussian distribution with an FWHM equal to the seeing size for each NEWFIRM pointing. Note that we adopt limiting magnitudes appropriate for the size of the measurement aperture.

Comparisons with observations. For each model, we construct the observed EW distribution and Hα LF from the mock NB118 excess emitters. Since we generate many mock galaxies, we normalize each distribution to best match the observed NewHα distributions. We illustrate an example of these model–observation comparisons in Figure 7 for the SXDS-W field. We find the best fit by minimizing χ² through a comparison of the mock and the NewHα EW distributions and Hα LFs. We show in Figure 7 that the best-fit model is able to reproduce both the EW distribution and the Hα LF. We find that observed EW distribution provides a better constraint on the best-fit model (versus the Hα LF). That is, multiple EW models can sufficiently explain the Hα LF. We find the model with 〈log(EW₀/Å)〉 = 1.35 and σ[log(EW/Å)] = 0.40 best matches the observed distributions.

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We calculate the completeness as the ratio of the number of mock galaxies that meets the NB118 excess selection criteria to all mock galaxies (N ≈ 200 × 40, 000) as a function of L(Hα). We illustrate in Figure 8 how the completeness differs by adopting different 〈log(EW₀/Å)〉 values. This comparison shows that we miss bright galaxies with low EWs, which is not surprising given the minimum observed EW of 40 Å. This figure also reveals that the completeness can vary between 60% and 90% for observed fluxes of 5 × 10⁻¹⁷–6 × 10⁻¹⁶ erg s⁻¹ cm⁻² or roughly 0.1–1 L_⋆ (see Section 6.1), and emphasizes that proper choice in the prior EW distribution is necessary for an accurate determination of the LF. We also show the completeness as a function of Hα luminosity and observed EW for each of the fields assuming the best-fitting model with 〈log(EW₀/Å)〉 = 1.35 and σ[log(EW/Å)] = 0.40 in Figure 9.

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Discussion of simplifying assumptions. In the above calculations, we made a couple of simplifications to allow the Monte Carlo simulations to be significantly less computationally intensive. First, we assume that the galaxies are unresolved sources. Second, instead of detecting sources on the images, we estimate the measured magnitudes and fluxes where the photometric uncertainties are based on pixel-to-pixel and detector-dependent sensitivity. Third, it is important to note that our current simulations assume that the EW distribution is the same at all continuum magnitudes. It would be more correct to allow the EW distribution to vary as a function of continuum magnitude, since it has been shown that more luminous star-forming galaxies tend to have lower emission-line EWs than those at lower luminosity (e.g., Lee et al. 2007). However, this adds another degree of freedom to our models, and significantly increases the computational time required to complete the simulations. Future work will include greater complexity in the modeling of the EW distribution, and will examine the impact of the current assumptions on the resultant completeness corrections. These simplifications allow for a few orders of magnitude faster production of completeness results rather than the approach of adding sources directly to the images, and is able to reproduce the distributions of scatter in Figures 1 and 2 (e.g., see Figure 6).

Prior to these MC simulations (for this discussion, we refer to the above approach as "Method II"), we generated a simulation where artificial extended sources were directly added to the mosaics and detected. In this simulation (referred to as "Method I"), we adopted a log-normal Gaussian EW distribution with 〈log(EW₀/Å)〉 = 1.52 and σ[log(EW/Å)] = 0.16, motivated by the results in Lee et al. (2007). We performed Method I by adding 1000 artificial galaxies to each NEWFIRM mosaic, and compared the number of artificial NB118 excess emitting galaxies to the number detected. We created the galaxies using IRAF/mkobjects with physical parameters similar to those found in local galaxies. The parameters include luminosities, Hα EWs, semimajor to semiminor axial ratios (between 0.15 and 1.0), and the Hα disk scale length (3.6 kpc; Dale et al. 1999). After extracting sources in the same manner described in Section 3, we calculated the completeness. We repeated each simulation 30 times using different seed numbers to increase the statistical accuracy of the results (N ∼ 30, 000 per NEWFIRM pointing). The similarities in the shape of the completeness curves in Methods I and II suggest that the simplifications we made do not have a significant effect on the estimated completeness. There are certain differences such that the comparison is not completely "apples-to-apples;" however, good agreement suggests that proceeding with Method II is satisfactory. The greatest benefit of this simulation is the determination of a model that best matches two different sets of measurements.

Finally, we assume a power-law distribution for N(J) to normalize the number of bright and faint sources. Ideally, the distribution should be constructed from galaxies at z ∼ 0.8. An investigation with the COSMOS photo-z sample (after the simulation was completed) finds that the faint-end slope of the number counts is approximately 0.25, which is to be compared to the adopted 0.34. Also, an exponential decline exists at bright continuum luminosities. This will impact our completeness estimates for the brightest emitters. Future work will address and examine the impact that these differences have on the completeness reported here.

The volume that the survey is capable of probing is determined by the shape and width of the NB filter. The ideal filter will have a perfect top-hat profile, and will survey the same co-moving volume at all emission-line fluxes. However, with real filters a weak emission line can either result from the line falling in the wings of the NB filter profile or from an intrinsically weak line located near the filter center. The net result is that a weak emission line is more likely to be detected near filter center, so a non-square filter reduces the effective volume at the faint end (Ly et al. 2007).

We can quantify how much the filter profile deviates from being a perfect top-hat by comparing the area underneath the profile with that of a rectangle with width equal to the FWHM, and height equal to the maximum transmission of the actual filter. The area enclosed by the profile is just 9% smaller, so the shape of the bandpass is close to ideal.

To determine the effective volume as a function of emission-line flux, we calculate the range in wavelengths such that an emission line is considered detectable within the NB filter. This emission line has an intrinsic S/N. We then place it at different wavelengths to determine what the degradation in the S/N will be due to lower throughput. We define an emission line to be undetected below 2.5σ, and this criterion yields the minimum and maximum NB118 wavelengths (hence redshift) that is observable for a particular S/N. The effective comoving volume per unit steradian would then be

$$\begin{eqnarray} \frac{V}{d\Omega } & = & \int _{z_1}^{z_2} dz\frac{dV}{dz d\Omega },\; {\rm where} \end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray} \frac{dV}{dz d\Omega } & = & \frac{c}{H_0}\frac{D_M^2}{E(z)}, \end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray} E(z) & \equiv & \sqrt{\Omega _M(1+z)^3 + \Omega _{\Lambda }},\; {\rm and} \end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray} D_M & = & \frac{c}{H_0}\int _0^z \frac{dz\mbox{$^\prime $}}{E(z\mbox{$^\prime $})}. \end{eqnarray} \tag{ 20 }$$

Here, z₁ and z₂ refer to the minimum and maximum redshifts that the emission line is detectable. Note that these equations assume a flat universe. The maximum surveyed volume (V_eff/Ω = 1.11 × 10⁵ Mpc³ deg⁻² or Δλ = 110 Å) is observable for S/N ⩾ 5.1 and decreases to V_eff/Ω = 5.54 × 10⁴ Mpc³ deg⁻² (Δλ = 55 Å) at S/N = 2.57. This is illustrated in Figure 10.

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Figure 11 presents the (observed) Hα LF for this survey with and without completeness corrections. Applying the necessary completeness corrections and adopting the Hopkins et al. (2001) extinction correction, we have the Hα LF shown in Figure 12. Both raw, and extinction- and completeness-corrected number densities as a function of luminosity are listed in Table 3. The binned LF can be summed together to obtain a model-free, lower-limit Hα luminosity density of $\mathcal {L} = 10^{40.01\pm 0.04}$ erg s⁻¹ Mpc⁻³ [$\mathcal {L} = 10^{40.08\pm 0.03}$ erg s⁻¹ Mpc⁻³].

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The median variation of the number density relative to the average of all four fields is ∼50%, and we illustrate in Figure 13 the fluctuation of the four different pointings relative to the average. Using predictions from Somerville et al. (2004; hereafter S04), we find that the expected fluctuation per NEWFIRM pointing (shaded region in Figure 13) is consistent with what is observed. The hourglass-like shape of the expected amount of field-to-field fluctuations is due to (1) the stronger clustering of luminous galaxies, (2) the decrease of cosmic variance with number density, and (3) the small volume surveyed at low luminosities due to the weakness of emission lines. Thus, the minimum of field-to-field variations is around an extinction-corrected Hα luminosity of 1 × 10⁴² erg s⁻¹.

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It is common to model the Hα LF by fitting the LF with the Schechter (1976) function:

$$\begin{equation} \Phi (L)dL = \phi _{\star }\left(\frac{L}{L_{\star }}\right)^{\alpha }\exp {\left(-\frac{L}{L_{\star }}\right)}\frac{\it dL}{L_{\star }}. \end{equation} \tag{ 21 }$$

This function was derived from the Press & Schechter (1974) formalism, which describes the halo mass function, and was adapted to explain the distribution of galaxy continuum luminosities. An explanation for why the Schechter function can describe the continuum LF is that a connection exists between the luminosities of galaxies and their stellar masses and/or halo masses. However, such a link may be much weaker with the Hα luminosity and SFR; thus, one might question whether the Schechter function is a good model for the Hα LF. For the current analysis we simply assume that the Schechter function can be used to adequately model the distribution of Hα luminosities and SFR since it appears to provide a good fit to our data. This also facilitates comparisons with previous work. However, this assumption should be explored further when more accurate LFs from future studies show evidence that a Schechter function is not the best model to explain the Hα LF.

In order to obtain the best-fitting Schechter parameters, a Monte Carlo simulation was performed to consider the full range of scatter in the extinction- and completeness-corrected Hα LF. We ignored luminosities below our 50% completeness limit (1.0 × 10⁴¹ erg s⁻¹ observed; 3.0 × 10⁴¹ erg s⁻¹ extinction-corrected). Each data point was randomly perturbed 1 × 10⁵ times following a Gaussian distribution with 1σ in Φ(L) given by Poisson statistics. Each iteration is then fitted to obtain the Schechter parameters. The best-fitting Schechter parameters are then determined from the averages of these fits. The confidence contours for the best fit are shown in Figure 14. A summary of the best fits and the corresponding integrated Hα luminosity density ($\mathcal {L} = \int L\Phi (L) dL$) and SFR density (see below) is provided in Table 4. We find a relatively steep faint-end slope for the Hα LF (α = −1.6) at z ∼ 0.81, indicating that galaxies below 0.2 and 1L_⋆ contribute 61% and 89% to the total Hα luminosity/SFR density, respectively. Often, past studies have opted to fix the faint-end slope since they were unable to reliably constrain it. Following this methodology, we also report the results of our fits when α is set to −1.6 in Table 4.

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Table 4. Schechter Fits, Hα Luminosity Densities, and SFR Densities

Survey	log L⋆	log Φ⋆	α	$\log {\mathcal {L}} (0)$	$\log {\mathcal {L}} (L_{\rm lim})$	log ρSFR(0)	log ρSFR(0)a	log ρSFR(Llim)a
NewHα	43.00 ± 0.52	−3.20 ± 0.54	−1.6 ± 0.19	40.15 ± 0.18	40.01 ± 0.08	−0.96 ± 0.18	−1.00 ± 0.18	−1.10 ± 0.08
NewHα	43.03 ± 0.17	−3.20 ± 0.13	−1.6	40.17 ± 0.05	40.04 ± 0.05	−0.93 ± 0.05	−0.98 ± 0.05	−1.06 ± 0.05
V08	42.97 ± 0.27	−2.76 ± 0.32	−1.34 ± 0.18	40.35	...	−0.76	−0.80	...
S09	42.33+0.16−0.12	−2.51+0.17−0.16	−1.64 ± 0.21	40.21	...	−0.89	−0.96	...

Notes. L_⋆ and Φ_⋆ are in units of erg s⁻¹ and Mpc⁻³, respectively. Luminosity ($\mathcal {L}$) and SFR densities (ρ_SFR) are provided for L ⩾ 0 and L ⩾ L_lim. All LFs adopt Hopkins et al. (2001) dust attenuation. Note that S09 incorrectly reported the normalization (Φ_⋆) for their Hα LF and was off by a factor of ∼0.43. D. Sobral provided a new preliminary fit, which adopts the Hopkins et al. (2001) extinction and the proper LF normalization. ^aCorrections for AGN contamination applied.

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The extinction-corrected Hα luminosity density can be converted into an SFR density by using the recipe given in Kennicutt (1998): SFR(Hα) = 7.9 × 10⁻⁴²L(Hα), where the SFR is given in M_☉ yr⁻¹ and the Hα luminosity is given in erg s⁻¹. This conversion assumes a Salpeter IMF with minimum and maximum masses of 0.1 M_☉ and 100 M_☉ and solar metallicity. We determined that the Hα SFR density is ρ_SFR = 10^{−0.96±0.18±0.04} M_☉ yr⁻¹ Mpc⁻³ down to L = 0, where the second set of errors account for cosmic variance estimated from S04. Compared to measurements at z ≲ 0.1 (Gallego et al. 1995; Pérez-González et al. 2003; Brinchmann et al. 2004; Nakamura et al. 2004; Hanish et al. 2006; Ly et al. 2007; Westra et al. 2010), our Hα SFR density at z ∼ 0.8 is higher by a factor of 3.8 to 16.6 with a median of 8.1.

It is thought that the Hα luminosity density is dominated by emission from star formation and not active galactic nuclei (AGNs). However, to accurately compute the SFR volume density, we statistically account for the fraction of the Hα luminosity volume density originating from AGNs. While estimating the AGN fraction is an observational challenge because deep x-ray data and/or spectroscopic information are needed, previous studies have typically found that 10%–15% of galaxies have AGNs. For example, Brinchmann et al. (2004) estimate that 11% of the Hα luminosity density is due to AGNs at z ≲ 0.1. Gallego et al. (1995) found 15% AGN contamination to the Hα SFR density at z ∼ 0. V08 used X-ray data for a small (∼50) sample of Hα emitters at z ∼ 0.8 and found 10% ± 3%. S09 looked at the [O iii]/Hβ and [O ii]/Hβ flux ratios (Rola et al. 1997), for a subset of 28 z ∼ 0.8 Hα emitters with optical spectroscopy and reported 15% ± 8%. Our preliminary analysis of the rest-frame optical emission-line flux ratios from our IMACS spectroscopy (see Section 3.2.1) finds similar results. Based on the [O iii]/Hβ and [O ii]/Hβ flux ratios, 5 (10) of 141 Hα emitters are AGNs (LINERs). Thus, we correct the above Hα SFR density by 11% to account for AGN and LINER contamination. This reduces our total Hα SFR density to ρ_SFR = 10^{−1.00±0.18±0.04} M_☉ yr⁻¹ Mpc⁻³.