PREDICTING FUTURE SPACE NEAR-IR GRISM SURVEYS USING THE WFC3 INFRARED SPECTROSCOPIC PARALLELS SURVEY

Virtually all surveys suffer incompleteness from objects lost as the strength of their signals approaches the level of the noise. A slitless grism survey, like WISP, also suffers significant incompleteness due to confusion from nearby bright sources. In addition to those two fundamental sources of incompleteness, emission lines can also be lost as part of the extraction methodology. These sorts of failures include objects missed by the automatic line-finding routine, objects removed due to redshift confusion, and objects incorrectly rejected by visual inspection. In order to derive final completeness corrections to account for all the forms of incompleteness that affect the grism data, we must simulate the entire line extraction process from beginning to end.

We start with the generation of a set of emission-line galaxy models, covering the full range of redshifts (z = 0.3–2), brightnesses (19–26 F110W mag), spatial extent (0.2''–1'' radius), and EWs (20–2000 Å) found in our WISP data set of emission-line galaxies. We have used two different spectral templates extracted from the Kinney–Calzetti Atlas in the STSDAS/SYNPHOT library. The spectra are from real starburst galaxies observed over the whole UV and optical range up to 1 μm. We have chosen two spectra with relatively flat continuum in f_ν and different line ratios of Hα/[O iii] ∼ 4.3 and 0.75. The sizes of the galaxies were then simulated using random values of the minor and major axis defined as the FWHM of the light profile in the SExtractor catalog. Throughout this paper any reference to galaxy size or galaxy radius always refers to the size of the direct (F110W) image and not to the spatial extent of the emission lines seen in the grism spectra. We place each model galaxy randomly into one of our actual pairs of WISP G102 and G141 grism images using the aXeSIM software (Kuemmel et al. 2007), before extracting it using the same methodology and pipeline as used for extracting all the real emission-line galaxies. This means that first we identify the lines using the automated software and then two separate team members visually examine each spectrum to ensure that it contains a real emission line. During the visual inspection we mix 15 model galaxies along with another 15 randomly chosen galaxies, such that the reviewer could not assume that each spectrum must contain a visible emission line. Overall we insert 923 model galaxies (74 fields each with typically 10–15 model galaxies) and, including the random galaxies, extract twice that number.

We find that the primary determinants of completeness for the emission-line galaxy sample are the observed EW and the line flux of the emission line. In practice, the latter translates to the S/N of the emission-line flux measurement, as the background noise varied from field to field by a factor of four. We also find that completeness had some dependency on the radius (here defined as the major and minor axis determined by SExtractor averaged in quadrature) of the source galaxy, but that this is of secondary importance due to the relatively small number of large (>075) radius galaxies in the observed sample, approximately 0.5% (see Section 4.2 for further discussion of the size of emission-line galaxies).

In Figure 1, we plot completeness as a function of these three parameters (line flux S/N, EW, and size), where each bin is a combination of recovery rates for the model galaxies. We weight all the model galaxy recovery rates for each single parameter by the frequency in which galaxies with the other two parameters appear in our full sample of actual emission-line galaxies. We acknowledge that these observed frequencies of the different galaxy parameters are not the absolute true frequencies. However, the implied differential numbers of "missing" emission-line galaxies due to incompleteness are not large enough to make a significant impact on the final derived incompletenesses, so we weight by the observed parameter frequencies in the interest of simplicity. For instance, if the full sample has twice as many small EW objects as large EW objects, model galaxies with small EWs will be given twice the weight when deriving completeness for S/N or size.

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One immediate result from this simulation is that the recovery rate drops rapidly from 60% to <20% as the observed EW (Å) of the emission line becomes less than 40 Å (log EW = 1.6; see Figure 1). In the rest frame of our z ∼ 1 galaxies, this EW limit corresponds to 20 Å, roughly two-thirds that of the average Hα EW for spiral galaxies in the Local Volume (Lee et al. 2007) and approximately equivalent to the average Hα EW for the most massive z = 0.8–1.5 galaxies (11 < log M_☉ < 11.5) identified by 3DHST (Fumagalli et al. 2012). In the interest of not introducing extremely large (>5) and uncertain completeness corrections to the number counts, we apply a cut of EW > 40 Å to all of our analysis. After combining this EW cut with our requirement that all detected emission lines have an S/N >5, the total number of model galaxies is 553. Of those model galaxies, we recovered 380, yielding an approximate recovery rate of 69%. We note that for this combination of EW and S/N, there are effectively no galaxies fainter than 25 mag (as measured at F110W band, although the simulated galaxies are flat in F_ν) in the final sample we use for our analysis.

In Figure 2, we present emission-line EW as a function of S/N for both observed and model emission-line galaxies. One can see that the model galaxies span the same parameter range as the real galaxies, extending farther to brighter lines with large EWs and fainter lines with smaller EWs in order to test how our sample completeness acts at these extremes. One complication is that over a significant portion of the redshift range (z = 0.7–1.5), there are actually two strong emission lines, [O iii] and Hα. In some cases [O iii] is the more powerful line, particularly as we go to fainter line fluxes (see Section 4.2 below). We therefore used both model templates where Hα is more powerful and ones where [O iii] is the stronger emission line (Hα/[O iii] = 0.75–4.3). We plot the redshift distributions for the detected Hα and [O ii] emitters in Figure 3. The gap in the Hα distribution around z = 0.8 is a result of the low S/N wavelength range edges of the G102 and G141 grisms where they overlap at 1.1–1.2 μm.

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One would expect a source with multiple lines to have a higher completeness than a single line source with the same line flux and EW. Therefore, to determine the likelihood of identification, we measure the combined S/N of both lines, add them quadratically, and use that total S/N for calculating our completeness. For the combined EW we use a simple sum of the two emission lines. We plot these combined values of S/N and EW as blue stars in Figure 2, along with the single-line cases of Hα (red triangles) and [O iii] (green squares). In most cases one line is clearly stronger, so the final S/N used for the completeness correction can usually be approximated as the S/N of just the brightest emission line. We do not use the other, weaker emission lines ([O ii], [S ii], Hβ, etc.) for determining completeness, as these lines are never alone and their relative fluxes are almost always small compared to Hα and [O iii].

We find that for even the highest S/N lines (S/N > 100), we reach only 90%–95% completeness. The main reason for this is contamination, from either overlapping spectra or large, bright objects in the direct images used to identify the galaxy counterparts. Either the line is lost under an extremely bright spectrum (most fields have three to five moderately bright H < 19 objects), the object lies in a complicated region where we are unable to determine which of the nearby, overlapping objects to associate with the emission line, or the contamination from overlapping sources has caused the automatic line finder to fail, i.e., SExtractor fails to find the source or the continuum fit fails badly. Altogether contamination from nearby sources explains about 75% of line extraction failures. Most nearby source contamination issues would be resolved if data could be taken at two or more roll angles, such that the spectra do not overlap, but that is not an option for parallel programs. Another reason a strong line will fall out of our sample is if the two emission-line reviewers cannot come to consensus on the redshift of the object (10% of the bright extraction failures), which most commonly occurs where it is unclear whether the line is Hα or [O iii]. For instance, when a source is spatially extended, the grism wavelength resolution is effectively lowered, making it difficult to distinguish between the [O iii] doublet and a single emission line. This sort of confusion almost never occurs in G102 (R ∼ 210), suggesting that data taken with a higher spectral resolution would largely solve this problem as well. The remaining ∼15% of bright emission line failures are mostly miscellaneous extraction errors by the visual line inspectors.

In Figure 4, we plot the final completeness corrections used for all of our analysis, derived as a function of both the EW and the S/N of the line flux. While the object size also has an effect on whether an emission-line galaxy will be recovered, we found that accounting for galaxy size has little effect on the overall completeness corrections, as the largest galaxies make up only a tiny percentage of the sample, <2%, even after accounting for their higher incompleteness. Or to put it another way, galaxy size is not very important to the overall completeness correction, because size completeness corrections grow larger as the actual number of galaxies is decreasing, unlike EW or line flux, where the number of objects tends to grow just as their completeness corrections are significantly increasing. A three-parameter completeness correction is also not practical for the required double visual inspection of each suspected emission line. Each added parameter increases the human workload geometrically. Instead, for each bin of EW and line flux S/N, we weight the input model galaxies by the frequency that each galaxy size appears in our observed sample list of emission-line galaxies.

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3.1.1. [O iii] Completeness

Using the simulations, we can also get an estimate of the redshift accuracy that is possible with grism spectroscopy of this wavelength resolution. Each emission-line source is placed at a random position in the field, which introduces the same uncertainties on the wavelength solution as seen in real data, including unknown absolute positions and inexact object sizes. While this is not a measurement of the absolute wavelength accuracy—the model spectra are put in and taken out with the same software (aXe) and the same assumed wavelength solution—it is a reasonable test of the accuracy one can expect with this pixel sampling, extraction method, and S/N.

We removed the emission lines flagged because the reviewers could not agree on a redshift and then applied our S/N cut of 5 and EW cut of 40 Å. We found that going to even higher S/N and larger EW made almost no difference in the redshift accuracies we derived. For this analysis we are not interested in the catastrophic errors, which represent contamination of false lines in our samples rather than a real reflection of redshift accuracy, so we removed any objects with errors in 1 + z > 0.5%. We discuss issues of contamination of false sources in Section 3.3. We further note that there is an error in the aXe process of inserting and removing user-generated spectra that incorrectly shifts the output wavelength calibration by a single pixel, corresponding to 24 Å in G102 and 46 Å in G141, which we have removed from all further analysis.

In Figure 5, the histogram of (z_observed − z_input)/(1 + z_input) shows that the results are strongly peaked around zero. The median offset is −0.0002 with a standard deviation of 0.0017, or roughly 0.2% accuracy in redshift. Modeling of BAOs suggests that the redshift accuracies required for such an experiment are more like 0.1% (Wang et al. 2010), which is also the requirement for both the Euclid and WFIRST missions. However, it is important to recall that the WISP redshifts are a combination of two different near-infrared grisms (G102 and G141) with two different resolutions (R ∼ 210 and R ∼ 130). If we split the redshift accuracy histograms by the grism from which it came, we find that the higher resolution grism reaches accuracies of 0.13% (as opposed to 0.19% in G141), demonstrating that 0.1% redshift accuracy is possible if the wavelength resolution R > 200.

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It is important to note that the lack of sub-pixel dithering of the parallel observations prevents any meaningful resampling of pixels along the direction of the wavelength dispersion. Such resampling would provide a small improvement in the overall wavelength resolution and would therefore also potentially increase the redshift accuracies that are possible.

Identifying emission lines in grism spectroscopy fields without dithering or field rotation is a challenging task. Even the well-behaved WFC3 near-infrared arrays still have cosmic rays, hot pixels, and other phenomena that can mimic real emission lines. Therefore, as we approach the detection threshold there is a real chance of contamination of our Hα line sample by false emission lines. To investigate this further, we look again to the simulation data. For the completeness calculation, we track whether an emission-line galaxy is detected and placed into our final emission-line list. There is no requirement that input and output redshifts must match. A mismatched redshift indicates contamination. While an emission line was found, it is clearly not identical to the emission line that was input. We label all extracted simulated spectra with a difference between input and output (1 + z) of more than 1% as contamination.

Of the 364¹² simulated Hα emission lines that meet all extraction criteria (S/N > 5, EW > 40 Å), 312 are good emission lines found at the input redshift, a successful extraction rate of 85.7%. An additional 21 emission lines are at the correct input redshift if we assign them to be [O iii] rather than Hα, for a contamination of Hα emission lines by [O iii] of 5.8%. For the remaining lines there are no alternative emission lines with which they could be associated, so they are contamination of non-emission lines to the sample. That gives us two contamination rates for our sample: 8.5% contamination by false emission lines and 14.3% total contamination rate of Hα emission lines by the combination of [O iii] and false emission lines. These contamination rates are similar to the 15%–30% contamination rates found for narrowband Hα searches (Ly et al. 2011; Sobral et al. 2013), although we note that additional information (e.g., galaxy colors, photometric redshifts, and especially the use of a second narrowband filter) can reduce the narrowband contamination rate down to 5% (Lee et al. 2012; Sobral et al. 2013).

This false emission line contamination rate decreases slightly as we increase the cut-offs of either EW or S/N of the line fluxes, but contamination rate never improves to much less than 10%. For instance, whether we raise the EW cut-off from 40 Å to 200 Å or raise the S/N line flux cut-off from 5 to 20, the false emission line contamination rate drops by only 3.5%, to 10.8% total contamination.

We note that one other potential contaminant is [O ii] λ3727. [O ii] emission is generally faint, with fluxes around 40% those of [O iii] λλ5007 + 4959. For redshifts where [O ii] and [O iii] both fall into the detectable near-infrared wavelength range (1.3 < z < 2.3), if we detect [O ii], we always detect [O iii] as well. There are some rare cases where [O ii] λ3727 can be as much as 30% brighter than [O iii], but that [O ii]/[O iii] ratio is not large enough to make any significant number of [O iii] emitters undetectable. Therefore, we do not expect any contamination from [O ii] λ3727 below a redshift of z < 2.3. However, the assumption that all single emission lines are Hα could potentially lead us to miss a population of very high redshift (z > 2.3) [O ii] emitters. These high-redshift [O ii] emitters would have to be very luminous, i.e., more than five times the L_⋆ found for O ii at z = 1.47 (Ly et al. 2007), and should therefore be quite rare. By z = 2, the number density of [O ii] emitters detectable by the WISP survey has dropped below 2 × 10⁻⁴ Mpc⁻³. If we allow for a simple luminosity evolution from z = 1.5–2.5 that is consistent with the observed z = 2 [O ii] number density (a 0.2 mag increase in L*), then we would not expect more than a dozen z > 2.3 [O ii] emitters hidden in our Hα sample.

We do not make any separate corrections for these false emission line contamination rates in our analysis. The completeness corrections we apply are based on all the extracted emission lines from the simulations, including the contaminating lines. While the contaminating lines artificially inflate the number of model emission-line galaxies recovered, which reduces the derived completeness corrections, we expect the same contamination rates in the actual data. If we used completeness corrections that did not include contaminating lines, we would incorrectly produce final number counts that were too large. By leaving the contaminating lines in our completeness derivation, we produce completeness corrections that simultaneously account for the effects of both incompleteness and contaminating lines. To put it another way, the completeness corrections we use are ∼15% smaller than they would otherwise be because of the extra emission lines we added due to contamination.

To derive the number density of the Hα emission lines in our survey, we employed the V_MAX method (Felten 1977), in which we derive the maximum distance for which an emission line of that absolute luminosity could be detected, depending on the flux limits of each field, and then translate that to a volume, V_MAX. This can be translated into a density:

$$\begin{equation} \delta _{{\rm gal}} = \frac{4\pi }{\Omega }{\sum}C({\rm S/N,EW}) \frac{1}{V_{{\rm MAX}}}, \end{equation} \tag{ 1 }$$

where C(S/N, EW) is the completeness correction for each detected emission-line galaxy, as a function of S/N and equivalent width. We scale the volume of the entire sphere of the sky by the angular area observed, 4π/Ω, to reach the volume density for each object, δ_gal. Then we add up all the δ_gal to get the total volume densities, which we then use for derivation of the luminosity functions (see Section 4.3).

Similarly, we also calculate area number densities, deriving an A_MAX for each source. A_MAX is the total angular area from the survey for which the emission-line flux is greater than that of the 5σ line limit of the field. For the brighter emission lines, A_MAX will simply equal the angular area of the entire survey (29 fields in this case). Similar to the V_MAX method, once the A_MAX values are determined, we add up all the 1/A_MAX values to determine the area number density. For calculation of both V_MAX and A_MAX, the detector area used is roughly 85% of the total area of the WFC3 IR chip (4.5 arcmin²), as objects are lost to the edges where either the first-order spectrum falls off the chip (right side) or there are no direct images of galaxies available (left side).

The primary surveys of the future near-infrared grism space missions, Euclid (Laureijs et al. 2012) and WFIRST (Green et al. 2012; Dressler et al. 2012), will both cover thousands of square degrees to depths significantly shallower than the WISP program. The Euclid wide spectroscopic survey will cover 15,000 deg² over a wavelength range of 1.1–2 μm, with a resolution of R = 250 and a 3.5σ line flux depth of 3 × 10⁻¹⁶ erg s⁻¹ cm⁻². At time of publication, the WFIRST mission is still considering several competing designs, but the primary spectroscopic mission will likely cover at least 2000 deg² at a resolution of R = 600, down to a 7σ line flux depth of 1 × 10⁻¹⁶ erg s⁻¹ cm⁻². The wavelength range for WFIRST will likely start between 1.3 and 1.5 μm and end somewhere between 2 and 2.4 μm. While this paper focuses on comparisons and predictions for the future shallow wide surveys of Euclid and WFIRST, it should be noted that both missions will certainly contain deeper surveys done over less area. For instance, the Euclid mission plan contains at least two 20 deg² deep fields with planned depths very similar to the observations for the WISP program, with line flux limits around 5 × 10⁻¹⁷ erg s⁻¹ cm⁻².

In Figure 8, we plot cumulative number counts versus limiting flux for the WISP survey, covering the primary range of interest ((1–10) × 10⁻¹⁶ erg s⁻¹ cm⁻²) of these future surveys. Completeness corrections have been applied to all points, and the plotted errors include those derived from our simulations of the completeness rates (see Figure 4) combined with the Poissonian error. There are no corrections to the fluxes for extinction or the contribution from [N ii], which is completely blended with Hα for WISP. We present three cumulative number measurements: total Hα emitters (red squares), 0.7 < z < 1.5 Hα emitters (blue circles), and 0.7 < z < 1.5 Hα emitters for which [O iii] is also detected (green triangles). At the bright flux end (10⁻¹⁵ erg s⁻¹ cm⁻²) we find a factor of 1.5 times more Hα emission lines at 0.3 < z < 0.7 than at 0.7 < z < 1.5. As we approach fainter fluxes, the percentage of high-redshift objects increases, with the number of 0.7 < z < 1.5 sources exceeding those at 0.3 < z < 0.7 around 2 × 10⁻¹⁶ erg s⁻¹ cm⁻².

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The WISP survey reaches shorter wavelengths (0.85 μm) than currently planned for these future space missions. The Euclid short wavelength limit, 1.1 μm, translates into an Hα redshift of z = 0.7, so we use the 0.7 < z < 1.5 cumulative number counts to predict what these future space missions will find, noting that the WFIRST number counts will be somewhat lower depending on the exact low wavelength cut-off used. The 1.65 μm WISP cut-off is a shorter long-wavelength cut-off than the 2 μm or better planned for these future missions, but that only means the WISP survey is not sensitive to the highest redshift Hα emitters. Because of the steep fall-off in number counts with redshift for the flux limits being planned, it is unlikely that the cumulative Hα number counts presented will be much different even with longer wavelength sensitivity.

We find approximately 2500 (18,500) Hα emitters deg⁻² in the redshift range 0.7 < z < 1.5 down to 3 (1) × 10⁻¹⁶ erg s⁻¹ cm⁻². For comparison, we plot the 0.75 < z < 1.9 number counts predicted by the study of Geach et al. (2010), which is mostly based on HST NICMOS grism and near-IR narrowband number counts (Shim et al. 2009; Geach et al. 2008; Sobral et al. 2009). We have decreased the result from the published article by a factor of ln(10) to account for an error in the published values of Φ_⋆ used, a result of improper conversion of Φ(log L) luminosity functions to the more standard Φ(L) luminosity functions. We have also shifted the Geach et al. (2010) predicted counts to brighter fluxes by a factor of 1.4 to account for the [N ii] contamination that is included in the WISP counts but has been removed from the counts of Geach et al. (2010). Once we account for these offsets, we find that the NICMOS-derived cumulative distribution and the WISP distribution approach each other at the faint end, but that there is an increasingly large disagreement toward the brighter fluxes, reaching a factor of six difference by 10⁻¹⁵ erg s⁻¹ cm⁻². This large disparity at the bright flux end is likely a result of the NICMOS luminosity functions (Yan et al. 1999; Shim et al. 2009) used to normalize the Geach et al. (2010) number count models. The NICMOS luminosity functions contain significantly more high-luminosity (>3 × 10⁴² erg s⁻¹) Hα line emitters than we see for WISP (see Section 4.3).

We are in better agreement with the emission-line galaxy count predictions of Wang et al. (2013), who also find a number density of roughly 1000 deg⁻² down to an Hα flux of 4 × 10⁻¹⁶ erg s⁻¹ cm⁻². Note that this flux limit is higher than the approximately 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² flux limit given in Wang et al. (2013), but to properly compare the two we had to add the [N ii] contribution back into their Hα fluxes. The Wang et al. (2013) predictions are based on the Hα luminosity functions from the narrowband survey of Sobral et al. (2013), with which we also largely agree (see Section 4.3 below). The general agreement between these two different emission line detection methodologies (near-infrared grism and narrowband filters) suggests that the counts presented here are a robust measurement of the number of Hα-emitting galaxies.

To predict the number of multiple emission line (Hα + [O iii]) sources a future near-infrared slitless spectroscopy space mission could expect to find per square degree, one must first choose a flux limit down to which [O iii] will also be detectable. This detection limit will vary depending on survey depth and secondary line reliability requirements. We can start with the currently planned Euclid mission 3.5σ detection limit of 3 × 10⁻¹⁶ erg s⁻¹ cm⁻². If we make the further assumption that one could reach a lower significance limit of 2σ for a secondary line if one already had a higher confidence line in hand, then one could detect [O iii] flux down to 1.7 × 10⁻¹⁶ erg s⁻¹ cm⁻². We apply this [O iii] flux limit to the green cumulative count line in Figure 8, producing a prediction for Euclid for the number density of emission-line galaxies where both Hα and [O iii] will be detected. Down to an Hα flux of 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² we find that roughly 24% of the 0.7 < z < 1.5 Hα emitters are also detected in [O iii], or 600 Hα + [O iii] emitters per square degree. A higher limit on the [O iii] flux will obviously exclude more multiple emission line objects from the final counts. For instance, if we require the [O iii] and Hα line fluxes to both be greater than 3 × 10⁻¹⁶ erg s⁻¹ cm⁻², then the density of Hα + [O iii] emitters drops by half, down to around 280 deg⁻².

With 314 detected (before completeness correction) Hα emission lines at z > 0.7 with fluxes above 10⁻¹⁶ erg s⁻¹ cm⁻², we have enough emission lines to break down the cumulative number counts into even smaller redshift bins in Figure 9. This more detailed redshift breakdown allows us to examine the evolution of the number counts that will be available to these future near-infrared slitless spectrographs in space. At a flux of 10⁻¹⁵ erg s⁻¹ cm⁻² the 0.7 < z < 1.5 Hα emission line galaxies are split roughly equally between 0.7 < z < 0.95 and 0.95 < z < 1.2. However, by 6 × 10⁻¹⁶ erg s⁻¹ cm⁻², the emitters from the 0.95 < z < 1.2 redshift range outnumber those from 0.7 < z < 0.95 by a factor of 1.5–2 and remain more numerous down to fainter fluxes. Our highest redshift bin, 1.2 < z < 1.5, has no emission lines as bright as 10⁻¹⁵ erg s⁻¹ cm⁻² and is not a significant percentage of the emission-line sample until fluxes less than ∼3 × 10⁻¹⁶ erg s⁻¹ cm⁻².

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We can also look at the number densities of the [O iii] emission lines on their own in Figure 10. Over the same range of line fluxes, the number counts of [O iii] emitters initially rise much more slowly than the numbers of Hα emitters, before rising quickly for fluxes fainter than 3 × 10⁻¹⁶ erg s⁻¹ cm⁻². At 10⁻¹⁵ erg s⁻¹ cm⁻², there are three times more Hα than [O iii] emission lines, but by 6 × 10⁻¹⁶ erg s⁻¹ cm⁻² that number density difference has increased to a factor of seven. Then, thanks to the steep rise of the fainter [O iii] emitters, this number density disparity rapidly shrinks and returns to a factor of three for line fluxes of 10⁻¹⁶ erg s⁻¹ cm⁻². This steep rise in the relative [O iii] number density can also be seen in the decreasing Hα/[O iii] ratio we measure for fainter line fluxes (see Section 4.2 below).

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We find roughly 1.5 times as many 0.7 < z < 1.5 [O iii] emitters, where Hα can also be identified in the WISP data, as [O iii] emitters found at the higher 1.5 < z < 2.3 redshifts. This is after accounting for the extra incompleteness [O iii] suffers at the higher redshift (see Section 3.1.1). In the actual raw counts we find three times as many 0.7 < z < 1.5 [O iii] emitters. This number difference between redshifts remains fairly constant over the (1–5) × 10⁻¹⁶ erg s⁻¹ cm⁻² flux range. In the data we see an unexpected crossover toward the brightest end, with the highest redshift emitters becoming the most populous. However, the number statistics here are quite poor, with only nine total [O iii] emitters covering the (5–10) × 10⁻¹⁶ erg s⁻¹ cm⁻² flux range, split into the two redshift bins. Within the error bars, we find that the number counts are consistent with no significant change in the number ratio between the high- and low-redshift [O iii] emitters over the entire flux range. This relatively steady number count ratio across a wide range of redshifts suggests that the luminosity of the typical [O iii] emitter (L_⋆) is increasing strongly with redshift, something we examine further when we look at the [O iii] luminosity function in Section 4.3. All the cumulative count number predictions from Figures 8–10 are also listed in Table 2.

Over the near-infrared wavelength range probed by the WISP survey, 0.85–1.65 μm, the vast majority of the emission lines observed are either Hα or [O iii]. When other emission lines are identified, they are always found at the same time as one of those two lines, largely because these two emission lines are almost always significantly stronger than the other available lines. Besides the possibility of a rare [O ii] emitter (see Section 3.3 above), our simulations suggest that the assumption that all single-line emitters are Hα mainly results in the misidentification of [O iii] emission. While these failed identifications only affect 6% of Hα lines, it has a large effect on the high-redshift (z > 1.5) [O iii] emitters, where we lose nearly 50% from our final sample.

The future near-infrared grism space missions are likely to suffer similar single emission line misidentification issues. Increased wavelength resolution will certainly aid in identification, as a resolved [O iii] λλ5007 + 4959 doublet will not be confused with Hα. However, for grism spectroscopy wavelength resolution is not the only limiting factor. If the emitting region is large in spatial extent, it will smear out the doublet, effectively lowering the available wavelength resolution. The median effective radius (the radius within which one-half of the total flux is contained, measured using the F110W filter) of our sample is only 03. Using a similar set of HST near-infrared filters and grisms, van Dokkum et al. (2013) also found effective half-light radii of ∼035 (3 kpc) across their sample of z = 0.5–2 galaxies. However, future wide-area grism missions will reach shallower flux depths and therefore should find larger objects, as there is a strong correlation between line flux and galaxy size, at least for Hα.

In Figure 11 we plot line flux versus effective radius for both Hα and [O iii] emission line galaxies. The large squares (triangles) with error bars are the mean effective radii for each Hα ([O iii]) flux bin, where each input emission-line galaxy has been weighted by the inverse of the completeness determined for size from Figure 1. Effective radius for Hα emitters shows a clear trend with line flux, r_eff = 3.6(±1.5) + 0.2(±0.1) × log F, where the units of r_eff are arcseconds and log F is measured in erg s⁻¹ cm⁻². However, there is virtually no trend for [O iii] emitters at all, with our best fit being r_eff = −0.1(± 1.1) − 0.025(± 0.07) × log F, essentially consistent with a constant effective radius over this range of [O iii] emission line fluxes.

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Down to 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² and limiting our analysis to redshifts of z > 1.2 (where Hα/[O iii] confusion becomes an issue at 1.1 μm), we find that the radius of the median object increases 33% to 04. While the sample of objects with both high fluxes and high redshifts is small, 13% (2 of 15) have radii larger than 06. Fortunately, the pixel scale for the Euclid mission will be 03 pixel⁻¹, more than twice that of the IR WFC3, which should greatly mitigate the degradation of wavelength resolution caused by extended sources. While the exact pixel scale for WFIRST detectors remains uncertain, it will likely be close to that of the WFC3 IR channel, 013 pixel⁻¹. However, the proposed WFIRST wavelength resolution (R = 600) is large enough that the wavelength smearing should not prevent identification of the [O iii] λλ5007 + 4959 doublet in most cases.

To investigate the likelihood of single emission line confusion further, we plot the ratio of Hα/[O iii] as a function of Hα flux in Figure 12. We limit our redshift range to that for which both Hα and [O iii] can be detected. Upper limits are 2σ, assuming that the FWHM of the line for which a limit is being derived is the same as for the measured emission line. We find only two cases where [O iii] is detected without Hα. We are able to identify these two emission lines as [O iii] without secondary emission lines because they are compact and high enough S/N that the distinctive [O iii] doublet line profile is visible.

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The upper left part of Figure 12, where the Hα/[O iii] ratio is large and Hα fluxes are small, is empty of sources because that is where the flux limits of the survey prevent sampling. If the high Hα/[O iii] ratios we see at brighter fluxes continue down to fainter fluxes, then presumably we would find many of the lower limits moving into that region if we were sensitive enough to detect such faint [O iii] fluxes. The lower right portion of Figure 12, where Hα/[O iii] ratio is small and the Hα fluxes are bright, is similarly devoid of objects, but that region is not excluded by our sensitivity limits. There is a real scarcity of low Hα/[O iii] sources at the bright flux limits. Excluding three lower limits, we find that none of the 58 galaxies with Hα fluxes greater than 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² have ratios of Hα/[O iii] < 0.95.

While the WISP survey does not cover the same wavelength range as the future space near-infrared grism missions (WISP goes to shorter wavelengths while the future missions will go longer), it does give us a rough estimate of the percentage of single line emitters those missions are likely to find. The exact percentage of single line emitters will depend on their final flux limits and criteria for establishing the reality of an emission line. For this example we again choose the currently planned detection limit for Euclid (3.5σ limit of 3 × 10⁻¹⁶ erg s⁻¹ cm⁻²) and assume that a secondary line only needs to be detected at a 2σ significance (1.7 × 10⁻¹⁶ erg s⁻¹ cm⁻²). The shaded orange region in Figure 12 shows the region for which only single line emitters would be expected for these sets of limits. We find that at least 60% (35/58) of sources with emission lines brighter than 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² will be single line emitters in future surveys. This single-line discovery rate could potentially be as high as 80% if all the lower limits presented actually lie within the single-line discovery region.

We can also look at a sample where the redshift is z > 1.2, as that would better reflect the range over which [O iii] would be detectable if the lower wavelength cut-off is the 1.1 μm cut-off of Euclid rather than the 0.85 μm of the WISP survey. The number of bright emitters is much smaller (12), but the percentage of expected single line emitters, 67%–83%, is virtually the same as when we included the lower redshifts emitters.

Our analysis assumes that all the single emission lines are Hα, which we know to be incorrect roughly 10% of the time. Therefore, it is possible that approximately 3 of the 31 single line emitters in that flux range could be low Hα/[O iii] sources, although if their true redshifts are greater than z = 1.5, then their Hα fluxes and Hα/[O iii] ratios are not constrained. It is important to emphasize that of the 25 sources with bright fluxes where we detect both Hα and [O iii], none of them have Hα/[O iii] < 1. There is no obvious reason why we would be missing all the galaxies with low Hα/[O iii] from 0.7 < z < 1.5, unless the ratio is so low that we lose the ability to detect Hα. However, that would require an unlikely large gap in the Hα/[O iii] ratio, making all galaxies either strong Hα or strong [O iii] emitters, with none in between.

Regardless of the exact quantity of contamination from single-line [O iii] emission, clearly Hα/[O iii] < 1 sources are much rarer at the bright fluxes that future near-infrared grism missions will probe than in our fainter sample. Therefore, the assumption that all single-line emitters are Hα should produce very few contaminating interlopers for these space missions, although further data are required to better establish exactly what the [O iii] contamination rate is.

The trend of increasing Hα/[O iii] ratio with Hα flux is a result of the known correlation between the Hα/[O iii] ratio and Hα luminosity previously reported by WISP (Domínguez et al. 2013). Their analysis also indicates that dust extinction increases with Hα luminosity, meaning that dust extinction is suppressing [O iii] emission more at the bright luminosity end. However, the trend of stronger relative [O iii] with fainter Hα luminosity is far stronger than their measured effects of extinction. The dominant determinant of the Hα/[O iii] ratio is most likely the metallicity, as the [O iii] λ5007/Hβ ratio strongly correlates with metallicity in the local universe (i.e., Liang et al. 2006). Metallicity is known to correlate with mass and luminosity (Tremonti et al. 2004; Kobulnicky & Kewley 2004), so it is not surprising that the brightest Hα emitters, which tend to be the most luminous in the continuum as well, would also have higher Hα/[O iii] ratios.

Another possible reason for the enhancement of [O iii] could be the presence of an active galactic nucleus (AGN), although its effect on the Hα/[O iii] ratio would be at least somewhat mitigated by the similar enhancement of [N ii], which cannot be disentangled from Hα at the WISP wavelength resolution. However, line ratios from WISP stacked spectra are more consistent with the low-metallicity tail of a star-forming region than that of an AGN (Domínguez et al. 2013). This agrees with Garn et al. (2010), who found that z = 0.84 Hα-selected samples contain only 5%–11% AGNs. Sobral et al. (2013) suggest the AGN fraction does increase with redshift, but remains only 15% of the Hα emitters above z > 1, with the biggest increases in AGN contribution at the brightest luminosities. While it is likely that some of the galaxies with the smallest Hα/[O iii] ratios are AGNs, they do not appear to make up enough of the total population of Hα emitters to have a significant effect on the overall trend of increasing Hα/[O iii] ratio with Hα flux.

Using the total volume densities derived for each luminosity bin (see Section 4.1), we are able to plot Hα luminosity functions in Figure 13 and Table 3. We have split the Hα emission line luminosity function into two redshift ranges, 0.3 < z < 0.9 and 0.9 < z < 1.5. We chose to split the sample at z = 0.9 as that divides the detected Hα emission lines by the grism with which they were detected (the dividing line between G102 and G141 is ∼1.2 μm), which also has the added benefit of producing roughly even sample sizes (436 0.3 < z < 0.9 versus 517 0.9 < z < 1.5). We make no correction for dust extinction, but there is a correction factor of 0.71 applied to the luminosities to account for [N ii] contamination. Please note that before directly comparing these luminosity functions to the cumulative counts from Section 4.1, the [N ii] contamination correction must be removed. Our best-fit Schechter parameters are presented in Table 4.

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Generally we find that the 0.9 < z < 1.5 luminosity function is comparable at the faint luminosity end to luminosity functions measured by the previous NICMOS grism studies (Yan et al. 1999; Shim et al. 2009). However, the WISP number densities drop more quickly as the Hα luminosities become brighter, dropping well below the bright luminosity number counts from previous NICMOS surveys by log L = 42.5. While many of the earlier NICMOS surveys are too small in area for accurate counts at the bright end of the luminosity function (Yan et al. 1999; Hopkins et al. 2000), the Shim et al. (2009) luminosity function plotted here is derived from an area roughly comparable (104 arcmin²) to the WISP data presented in this work. With more than 139 different fields spread across the sky, the expected cosmological variance for Shim et al. (2009) is also low (<2%; Trenti & Stiavelli 2008), so it cannot explain the observed difference either. Finally, the redshift sampling difference (0.7 < z < 1.4 with NICMOS versus 0.9 < z < 1.5 with WFC3) is not sufficiently different to effect the luminosity function comparison. The majority of deviation between the two luminosity functions comes down to a single bin at log L = 42.7, so the observed luminosity function difference may simply be a result of an unfortunate 2σ–3σ deviation at that single point.

We also find our 0.9 < z < 1.5 number densities to be consistent with the z = 1.47 number densities derived from the narrowband Hα surveys (Sobral et al. 2013). However, the redshifts sampled by Sobral et al. (2013) (at z = 0.84 and 1.47) straddle the sampled range of our high-redshift sample (median redshift of z = 1.15), so if all the luminosity functions were consistent, then the WISP luminosity function ought to lie between the two Sobral et al. (2013) distributions. That the number densities at z = 1.47 and our median z = 1.15 instead overlap suggests that the WISP grism survey may be finding slightly more line emitters than the narrowband survey, although the absolute differences are very small. Alternatively, the evolution in the luminosity function between z = 0.8 and z = 1.5 could be occurring mostly at the low end of that redshift range, as suggested by Geach et al. (2010). The HiZELS data sample down to very similar EWs (25 Å), so that is not a likely source of the difference. Neither data sample has made any attempt to remove AGNs, so that cannot be a source of difference either. There is some difference in the extraction apertures used. HiZELs uses a fixed 2'' aperture at z = 1.47, while WISP uses a varying aperture of twice the object size in the direction perpendicular to the wavelength dispersion (there is effectively no limit to the size of line emission detectable along the dispersion axis). However, the majority of objects are compact enough that it seems unlikely that either extraction methodology could be missing much flux.

Our lower redshift 0.3 < z < 0.9 sample (median z = 0.58), on the other hand, does fall below the Sobral et al. (2013) narrowband z = 0.84 number counts, as well as the z = 0.8 narrowband counts (not plotted) from the NEWFIRM Hα Survey (Ly et al. 2011), although the difference at the bright end of the luminosity function is within the errors. The more consistent low-redshift luminosity densities suggest that the WISP survey is not generally finding line emitters at a higher rate than narrowband surveys, but only for its higher redshift bin. A single minor inconsistency such as this could be partially explained by cosmological variance, which is expected to be on the order of 15% (Trenti & Stiavelli 2008) for the z = 1.47 Sobral et al. (2013) narrowband sample.

A significant strength of the WISP survey compared to narrowband studies is the relatively small contribution of cosmological variance to the overall error budget. First, the large difference in redshift depth (Δz = 1.2 for WISP versus Δz = 0.02 for a typical narrow band) means that despite covering a much smaller area of sky (e.g., 130 arcmin² versus 1–2 deg²), the WISP survey actually covers a comparable amount of volume. For instance, a single WISP pointing covers roughly 10⁴ Mpc³ (z = 0.3–1.5), while the z = 0.84 and z = 1.47 narrowband samples of Sobral et al. (2013) cover 10⁴ Mpc³ over 210 and 100 arcmin², respectively. The 29 fields used in this paper survey a volume of nearly 3 × 10⁵ Mpc³, roughly equivalent to 1 deg² of the z = 1.47 narrow band of Sobral et al. (2013).

Secondly, pencil-beam studies like WISP, which cover a small area over a large redshift range, have significantly lower cosmological variance than a similar cubical or spherical volume, as the long, narrow window must pass through many different environments while a regularly shaped cube could potentially lie right on top of an extreme overdensity (Trenti & Stiavelli 2008). For objects with a density of 10⁻³ Mpc⁻³, the cosmic variance is only ∼12% for a single WISP pencil beam, while it is nearly 60% for z = 0.85 and z = 1.47 narrow beam samples covering the same volume (Trenti & Stiavelli 2008). Of course, the total areas covered by the Sobral et al. (2013) narrowband surveys are 6–20 times larger (1–2 deg²) from two separate fields, reducing their associated cosmological variance to 15%–20%. However, as the WISP fields are widely separated on the sky, the cosmological variance from field to field is uncorrelated, reducing the cosmological variance of the total sample by the square root of the number of fields. For our example of 10⁻³ objects per Mpc³, the contribution of cosmological variance to the WISP sample presented in this paper is only 2%. We have included cosmological variance in our calculations of total errors for the luminosity functions, although its contribution is essentially negligible compared to the Poissonian uncertainty and completeness correction errors.

We note that while a deep pencil-beam study like WISP has the advantage of very little cosmological variance because of the large redshift range observed, it does so by sacrificing the ability to sample the behavior of galaxies at more discrete redshifts. In effect, it blurs all the evolutionary effects that take place within each redshift bin. This averaging of galaxy evolution is not a significant issue if the evolution over the sampled redshift range is taking place at a steady, predictable pace, but could be misleading if the galaxy behavior changed particularly rapidly or became strongly non-linear. Of course, if the evolution becomes too rapid or unpredictable, narrowband surveys risk completely missing significant behavior that happens to fall between their sampled redshifts. Because of this, deep pencil-beam grism and narrowband surveys are actually complementary, each a check on the potential weaknesses of the other.

Regardless of how our sample selection may differ from other surveys, we can robustly compare how the luminosity function evolves within the WISP survey as we use the same methodology for selection and completeness corrections. It appears that most of the evolution from z = 0.3–1.5 takes place at the bright end of the luminosity function. Within the errors, the luminosity functions are converging below log L = 41. However, with only two low-luminosity bins for the high-redshift sample, this low-luminosity convergence is not definitive. Generally it appears that most of the evolution in Hα from z = 0.3–1.5 is taking place in L_⋆, which is consistent with previous findings (Sobral et al. 2013). Further discussion of the Hα luminosity functions, their implied star formation rates, and the evolution of the star formation density will be presented in a separate paper (A. Bunker et al., in preparation).

We also present the [O iii] luminosity functions in Figure 14 and Table 5 along with their accompanying best-fit Schechter parameters in Table 4. For [O iii] we split luminosity functions into two redshift ranges, 0.7 < z < 1.5 and 1.5 < z < 2.3, which are the highest redshifts for which the [O iii] luminosity function has been determined to date. The lower redshift bins cover the range over which the Hα line can also be found within the grism spectra. For z > 1.5, Hα is redshifted beyond 1.65 μm, leaving [O iii] as the most powerful detectable line in the grism spectrum. The total sample sizes are 192 [O iii] emitters at 0.7 < z < 1.5 versus 58 at 1.5 < z < 2.3.

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As remarked in Section 3.1.1, the [O iii] number densities require higher completeness corrections than for Hα. Even after application of these additional larger corrections, we still find that the lowest luminosity bin for each redshift range appears low, indicating that there is some incompleteness for which we are not accounting. One possibility is that the number of misidentified single-line [O iii] emitters is even larger at the faintest ends than our simulations indicate. For instance, our simulations assume Hα/[O iii] ratios similar to the emission-line sources that we find and can measure. Therefore, if a population of faint, low Hα/[O iii] sources exists, we would be underestimating the number of single-line misidentifications at the lower redshifts (at higher redshifts the Hα/[O iii] ratio does not matter as we cannot see Hα at all). Regardless of the reason for the low faintest bin, we exclude them from the Schechter fits and further analysis.

Comparing our [O iii] luminosity functions to those derived at lower redshift (Pirzkal et al. 2013; Ly et al. 2007), we see a strong increase in L_⋆ with redshift along with a decrease in Φ_⋆. However, our measured luminosity bins do not constrain α well. If we require the 0.7 < z < 1.5 α to be the same as seen at low redshift (α = −1.5), we find only minor changes in Φ_⋆, with all the evolution in [O iii] from z = 0.7–2.3 taking place in L_⋆.