HST Grism-derived Forecasts for Future Galaxy Redshift Surveys

The WISP Survey (PI: M. Malkan; Atek et al. 2010) is an HST pure-parallel program, obtaining WFC3 observations of nearby fields while other HST instruments are in use. In particular, WISP observations are taken in parallel when either the Cosmic Origins Spectrograph (Froning & Green 2009) or the Space Telescope Imager and Spectrograph (Kimble et al. 1998) are used as the primary instrument, as programs with these two instruments typically involve long integrations of a single pointing. The WISP parallel field is offset by ∼5' from the primary target. Since the selection of parallel opportunities depends on the integration time rather than the position of the primary target, WISP fields are independent and uncorrelated. In this paper, we include emission-line measurements from 419 WISP fields collectively covering ∼1520 arcmin².

The WISP observing strategy depends on the details of each parallel opportunity and therefore varies from field to field. In short opportunities consisting of one to three continuous orbits, the G141 grism is typically used along with one imaging filter (F140W or F160W) to aid in spectral extraction and to mark the zero-point for wavelength calibration. The G102 grism and the F110W imaging filter are added to longer opportunities consisting of four or more continuous orbits. For these deeper fields, the integration times in the two grisms are tuned to achieve approximately uniform sensitivity for an emission line of a given flux across the full wavelength range. As the visit lengths depend on the specifics of the primary observations, we do not reach a uniform depth in all WISP fields. Additionally, the sky background in each field is affected to varying degrees by, for example, zodiacal light and Earth limb brightening. The median 5σ detection limit for emission lines in both grisms is ∼5 × 10⁻¹⁷ erg s⁻¹ cm⁻², yet the detection limit in a given field can differ from this median by more than a factor of 2. As a consequence, while all WISP fields are deeper than the Euclid Wide Survey, only ∼75% of fields reach the expected depth of the Euclid Deep Survey.

All WISP data are reduced with the WFC3 pipeline CALWF3 in combination with custom scripts that account for the specific challenges of undithered, pure-parallel observations. The foundation of the WISP reduction pipeline is described in Atek et al. (2010), and crucial updates implemented for the current version will be presented in I. Baronchelli et al. (2020, in preparation). We use the AstroDrizzle software (Gonzaga 2012) to combine the individual exposures, correcting for astrometric distortions and any potential alignment issues. The IR direct images are drizzled onto a 008 pixel⁻¹ scale. Object detection in the IR direct images (F110W, F140W, and F160W) is performed with Source Extractor (version 2.5; Bertin & Arnouts 1996). For fields with imaging in two filters, we create a combined detection image and supplement the catalog with sources detected individually in only one of the filters. We use the aXe software package (Kümmel et al. 2009) to extract and calibrate the spectra. The aXe software drizzles all extracted spectral stamps from individual exposures to a combined spectral image with a constant dispersion and cross-dispersion pixel scale, thus removing geometric distortions. The individual drizzled spectral stamps are on the 013 pixel⁻¹ scale. For each source identified in the direct imaging, the spatial width of the extraction window is a factor of 4× the projected size of the source (either semimajor or semiminor axis depending on the source orientation) onto the extraction direction.¹² We then use aXe's optimal weighting method with Gaussian weights (with widths based on the size of the sources in the direct image) to extract 1D spectra from the 2D spectral stamps. The emission-line-finding process described in the next section is performed on the 1D spectra.

2.1.1. WISP Emission-line Catalog

The 3D-HST Survey (PI: P. van Dokkum; Brammer et al. 2012; Skelton et al. 2014; Momcheva et al. 2016) and the AGHAST Survey (PI: B. Weiner; Weiner 2009) together obtained spectroscopic observations of the CANDELS (Grogin et al. 2011; Koekemoer et al. 2011) fields. In ∼150 pointings, the 3D-HST+AGHAST Survey covered each field to a uniform two-orbit depth, including G141 observations and direct imaging in the F140W filter. We add the 3D-HST+AGHAST pointings from the AEGIS, COSMOS, GOODS-North (GOODS-N), and GOODS-South (GOODS-S) fields, ∼507 arcmin² in total, to the WISP fields. Including these fields in our analysis has several benefits in addition to the increase in area coverage. With the extensive multiwavelength catalogs available for the well-studied CANDELS fields, we can identify regions in color space indicative of misidentified single emission lines (see Section 4.6).

The 3D-HST+AGHAST team has released a catalog with emission-line measurements for all galaxies detected in imaging (Momcheva et al. 2016). Their method involves combining the CANDELS photometry with the grism spectroscopy to determine augmented photometric redshifts, which are then used as a prior for detecting and measuring emission lines in the grism data. The Euclid Wide survey observations will, at a minimum, include imaging in the Y, J, and H filters of the NISP instrument, as well as the very broad VIS filter covering ∼5500–9000 Å. While additional ground-based imaging in the g, r, i, and z bands will be obtained, the spectral energy distributions (SEDs) of sources will not be as fully sampled as in the CANDELS fields. The amount of information Euclid obtains for each source will be closer to the level obtained in WISP observations. We therefore reprocess all 3D-HST+AGHAST data in a consistent manner with the WISP fields (Rutkowski et al. 2016). We note, however, that timescales and effort required to run even the improved WISP emission-line procedure on all 15,000 deg² of the Euclid Wide survey will be impossibly unrealistic. Alternative emission-line detection algorithms will be needed, such as the citizen science pilot program described in Dickinson et al. (2018) or the integration of machine learning and human classification such as that of Beck et al. (2018).

Rutkowski et al. (2016) describe the reduction of the 3D-HST+AGHAST data using the WISP pipeline with minor modifications to account for the dithered observations, as well as the creation of the 3D-HST+AGHAST emission-line catalog. Emission-line detection and measurement are performed using the first version of the WISP line-finding procedure, which is presented in Colbert et al. (2013) and discussed in Appendix A.2. Briefly, emission-line candidates are identified as groups of contiguous pixels above the continuum. In contrast to the WISP catalog (Section 2.1.1), we fit each 3D-HST+AGHAST emission-line individually, therefore measuring the redshift, flux, FWHM, and EW separately for each line. Single, symmetric emission lines are again assumed to be Hα. The 3D-HST+AGHAST catalog includes ∼5700 emission-line objects and is combined with the WISP catalog in Section 2.4.

Grism surveys such as WISP, 3D-HST+AGHAST, and Euclid can suffer from incompleteness for a variety of reasons. Sources may be lost amid the noise in images if their fluxes are close to the detection limit. Some sources may not be detected, or their emission lines missed in their spectra, because they overlap or are blended with nearby bright objects. The completeness of a survey depends on the specific selection function used to detect sources. In the case of the WISP and 3D-HST+AGHAST emission-line catalogs, the selection function includes the detection of the sources in the direct images, the identification of emission-line candidates via the detection algorithm, and the acceptance during visual inspection.

The completeness corrections applied to the WISP and 3D-HST+AGHAST emission-line catalogs were derived in a manner consistent with each of the emission-line detection procedures. These derivations are similar but not identical for the two catalogs, reflecting the differences in the line-finding algorithms, visual inspection, and emission-line fitting. Specifically, the completeness corrections from Colbert et al. (2013) are adopted for the 3D-HST+AGHAST catalog, while a new set of simulations is used to determine the completeness of the updated line-finding procedure that created the WISP catalog. Each method is described in more detail in the Appendix.

Finally, in the sample selection presented in the following section, we have adopted additional selection criteria: line EW_obs > 40 Å and S/N > 5. We discuss the motivation behind these two additional criteria in the Appendix. We note, however, that while these two criteria are applicable to the emission-line detection processes used for both the WISP and 3D-HST+AGHAST data sets in this paper, they will not necessarily be appropriate for Euclid or other future grism surveys.

The Euclid mission will be composed of two surveys. The Wide Survey aims to obtain redshift measurements for ∼25 million galaxies over 15,000 deg² (e.g., Vavrek et al. 2016), using the Euclid Red grism (1.25–1.85 μm, R ∼ 380) and achieving a 3.5σ line flux sensitivity of 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² for a source with a diameter¹⁴ of 05. The Deep Survey will cover 40 deg² in three separate pointings, reaching a depth of 6 × 10⁻¹⁷ erg s⁻¹ cm⁻². In addition to the Red grism, the Deep Survey may make use of a Blue grism (0.92–1.3 μm, with a tentative R ∼ 250). In this paper, we focus on observational constraints relevant for the Wide Survey but note that HST grism observations are valuable for Deep Survey predictions as well.

From the full WISP+3D-HST catalog, we create a WS (i.e., Wide Sample) of ELGs selected to match the planned Euclid Wide Survey. We leave the construction of a "Deep Sample" (DS) for future work, but we capitalize on the depth of the WISP+3D-HST catalog to discuss contamination and redshift misidentification in Section 4.6. We begin by considering only sources with secure redshifts, where either both reviewers agree on the assigned redshift or multiple, high-S/N lines are detected in the source's spectrum. Next, we impose a selection in emission-line S/N and observed EW to match the completeness limits of the full WISP+3D-HST catalog: S/N > 5 and EW_obs ≥ 40 Å (see the Appendix, as well as Colbert et al. 2013). For galaxies at z ∼ 1–1.5, EW_obs > 40 Å corresponds to a rest EW of ∼16–20 Å. The remaining selection criteria depend on emission-line flux and observed wavelength. For the WS, we select sources with at least one emission line with flux f ≥ 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² and λ_obs ≥ 1.25 μm. The DS will include additional sources down to f ≥ 6 × 10⁻¹⁷ erg s⁻¹ cm⁻² and, in fields observed with the Blue grism, λ_obs ≥ 0.92 μm. Given the drop in the sensitivity of the G141 grism at wavelengths longer than ∼1.7 μm, this wavelength selection results in Hα ([O iii]) coverage from 0.9 ≤ z ≤ 1.6 (1.5 ≤ z ≤ 2.4) for the WS and 0.4 ≤ z ≤ 1.6 (0.8 ≤ z ≤ 2.4) for the DS, respectively. See Table 1 for a summary of the selection criteria.

We note that given the spectral resolution of the planned missions, Hα+[N ii] will be blended for most sources in Euclid (and some sources in Roman) spectra. These two emission lines are also blended in observations obtained with the WFC3 grisms. For the purpose of predicting the number, size, and EW distributions of the Hα emitters that will be detected by the galaxy redshift surveys, we do not correct the observed Hα fluxes for the contribution by [N ii]. All measurements presented here of Hα flux, EW, and size refer to Hα+[N ii].

Similarly, the [O iii] λλ4959, 5007 doublet is partially blended at the resolution of the WFC3 grisms. The [O iii] fluxes are obtained by fitting two blended Gaussians of the same FWHM to the doublet line profile using amplitudes fixed in a 1:3 ratio, following the theoretical calculations of Storey & Zeippen (2000). Since the [O iii] doublet will be resolved by Euclid and Roman, we correct the observed [O iii] λ5007 flux for the contribution from the λ4959 line using the same flux ratio. All measurements presented here of [O iii] flux therefore refer to [O iii] λ5007 only.

The WS consists of 1277 ELGs (2270 deg⁻²), the majority of which are Hα+[N ii] emitters below redshift z ≲ 1.5 (85%; see Figure 2). There are 73 galaxies in the redshift range 1.5 ≲ z ≲ 1.6, where both Hα and [O iii] are accessible to the Euclid Red grism. Of these, only nine (16 deg⁻²) have both Hα+[N ii] and [O iii] λ5007 bright enough for the Euclid WS selection. The median Hα+[N ii]/[O iii] λ5007 of these nine galaxies is 1.45 ± 0.30, though the strength of this ratio increases with Hα+[N ii] line flux, as can be seen in Colbert et al. (2013) and Mehta et al. (2015). The Euclid NISP instrument will reach a 5σ sensitivity of 24th magnitude in all three of its imaging filters. Fainter sources will be in the photometric catalogs, but the current observing strategy calls for spectral extraction only for sources brighter than this 5σ limit. We note that the 28 real ELGs (50 deg⁻², ∼2% of the WS) with H > 24 in the bottom panel of Figure 2, all with emission lines brighter than the Euclid flux limit, would be missed by this extraction strategy. Extracting spectra for sources detected at lower S/N (e.g., 3σ–3.5σ) or down to fainter magnitudes (H < 24.5) would allow for the recovery of these high-EW sources. Yet this strategy would also result in significantly more spectra to process and search for emission lines. For example, 10% of sources in the full WISP+3D-HST catalog have continuum magnitudes in the range 24 < H < 24.5, amounting to ∼2500 more extracted spectra per square degree.

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We construct an empirical PSF using the imaging and spectral stamps of ∼3000 stars in the WISP fields included in the WS. The stars are selected by H-band magnitude and half-light radius as described in S. Bruton et al. (2020, in preparation). We consider stars in the magnitude range 22 ≥ H ≥ 18.3, where the faint limit is imposed to avoid selecting compact galaxies, and the upper limit conservatively removes stars that may be saturated or approaching the nonlinearity regime of the detector, where the Source Extractor  centroids are unreliable. We do not explicitly select isolated sources, which are ideal for minimizing imaging and spectral overlap with nearby sources, but instead depend on the median profile to provide an accurate representation of the observed PSF.

We begin by describing the creation of the imaging PSF. For each star in the Source Extractor  imaging catalog, we create 10'' × 10'' stamps in all available IR filters. We then construct a radial profile of each star by calculating the azimuthally averaged flux in circular annuli of increasing radii. The median radial profile for F160W is shown in Figure 3 as an example. The half-width at half-maximum (HWHM) is indicated by the circle and dashed lines and corresponds to an FWHM = 018, larger than the FWHM reported in the WFC3 Instrument Handbook¹⁵ for Cycle 26: 0145 for F160W. As we have measured the radial profile of each star individually, rather than from a stacked image, we conclude that the discrepancy is not caused by problems centering the stars in the imaging stamps. There are not enough stars in all fields containing ELGs to measure a field-dependent PSF. Additionally, the HST PSF is undersampled. The FWHM of an undersampled PSF is typically measured by sampling the PSF with multiple stars and therefore multiple subpixel centroid positions. We therefore take the median profile as the effective PSF and adopt this FWHM for all ELGs, including those in 3D-HST+AGHAST fields. We note that the values reported in the handbook are listed before pixelation and are therefore expected to be smaller than the measurements of the pixelated PSF we perform here, though slight variations in the telescope focus during these observations can also contribute to the discrepancy. Here we aim to deconvolve the PSF from galaxy emission size measurements, and so we adopt the larger, empirically measured FWHMs to ensure that the galaxy emission and PSF are measured consistently from the same data.

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The grism PSFs are measured on median-combined spectral stamps in order to achieve a high S/N. As aXe drizzles together the individual exposures using the positions of the sources in the corresponding individual imaging exposures, the spatial centroid and the wavelength solution are consistent enough in each spectral stamp to allow stacking. The combined stellar spectrum in G141 is displayed in the top panel of Figure 4. We measure the FWHM of the combined spectrum along the spatial axis (vertically in Figure 4) by fitting a Gaussian to the flux profile at each wavelength in a moving average window 5 pixels wide. The FWHM measured in this manner is plotted as a function of wavelength in the bottom panel of Figure 4 (black curve). We smooth the wavelength-dependent FWHM using a Savitzky–Golay filter (Savitzky & Golay 1964) with a window 11 pixels wide (red curve). Finally, we calculate the integrated FWHM over the passband of each imaging filter and confirm that the FWHMs measured in the grisms are consistent with those measured in imaging. This comparison is also displayed in Figure 4 for G141, F140W, and F160W. Table 2 provides the measured FWHM in each filter, as well as the number of stars that were included in the measurement.

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We measure the sizes of each ELG in both the continuum and the Hα+[N ii] emission. The continuum sizes are measured on 9'' × 9'' stamps created from the H-band direct images in either the F140W or F160W filters. The emission-line sizes are measured on stamps created from the two-dimensional spectra extracted from the full grism images (see Section 2.1 for a description of this spectral extraction). We create stamps for each emission line from the 2D spectra as follows. The stamps extend 35 pixels in the wavelength direction (∼850 Å in G102, ∼1600 Å in G141) on either side of the center of the emission line. We fit the continuum row by row in the stamp by fitting a line to the fluxes in the pixels on either side of the line excluding 8 pixels (370 Å) centered at the wavelength of the emission line. We subtract each linear fit from the corresponding full row and are left with a continuum-subtracted map of each galaxy in the given emission line. An example of an Hα+[N ii] emission-line map is shown in the bottom left panel of Figure 5.

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Next, we model the shapes of the continuum and Hα+[N ii] emission for the Euclid WS sources using Sérsic profiles. The Sérsic profile describes the intensity of the source as a function of radius (Sérsic 1963, 1968). The functional form is given by

$$\begin{eqnarray}&&I(R)={I}_{e}\ \exp \ \left\{-{b}_{n}\left[{\left(\displaystyle \frac{r}{{r}_{e}}\right)}^{1/n}-1\right]\right\},\end{eqnarray} \tag{ 1 }$$

where r_e is an effective or scale radius and I_e is the profile intensity at r_e. The Sérsic index, n, determines the shape of the light profile, with larger values corresponding to more centrally concentrated sources. A value of n = 1 results in an exponential profile that is a good approximation of disk galaxies, while n = 4 gives the de Vaucouleurs (1948) profile approximating elliptical galaxies. The constant b_n is coupled to n such that r_e is the half-light radius—or the radius that encircles half of the light emitted by the source—and is therefore not a free parameter.

For each image stamp and emission-line map, we determine the best-fit Sérsic models using the two-dimensional image fitting software Galfit¹⁶ (v3.0; Peng et al. 2010). In fitting, Galfit convolves the Sérsic profiles with a Gaussian kernel to emulate the PSF, such that the best-fit model parameters will be those of the PSF-corrected emission shapes and sizes. For the continuum emission measured in the imaging stamps, the FWHM of either the F140W or F160W filter is used. The FWHM for each emission-line map is taken from the smoothed function described in Section 3.1 at the wavelength of the line. We use relatively large stamp sizes (9'' in the continuum) so that a sufficient number of sky pixels are available for the Galfit fitting algorithm. However, we ensure that close neighboring sources do not interfere with the fitting of the target source by constraining all models to have centroids within ±3 pixels of the stamp centers. The stamps, models, and residuals for one of the WISP sources are shown in Figure 5 as an example of the model fitting.

We perform the same size measurement on the simulated data discussed in Section 2.3 and Appendix A.1. Recall that the simulated sources are the same size and shape in both the continuum and emission lines. The effective radii should therefore be tightly correlated, and we can use the scatter as an estimate of the statistical error of our model fitting. As the synthetic sources were simulated as two-dimensional Gaussians, we similarly fit the simulated data with elliptical Gaussian models rather than the Sérsic profiles used for the real sources.

The R_eff for the simulated data are shown in Figure 6, where R_eff refers to a circularized radius constructed from the standard deviation of the Gaussian model along each axis, R_eff = $\sqrt{{\sigma }_{x}{\sigma }_{y}}$. The median Hα+[N ii]R_eff in bins of continuum R_eff are plotted as squares with 1σ error bars. The standard deviation of the relation between the continuum and emission line R_eff is ∼005–015. The continuum and Hα+[N ii] emission sizes are correlated down to small radii, R_eff ∼ 007, below which the R_eff are smaller than 1 pixel in the grism spectra and therefore unreliable. We present the relationship between continuum and Hα+[N ii] R_eff for the observed WS sources in Section 4.2.2.

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We begin by considering the number of ELGs that meet the selection criteria for the Euclid WS. Galaxies emitting Hα+[N ii] are the main target for the dark energy science, as they will be used to trace the large-scale structure at z ∼ 1–2. There are 1939 ± 21 Hα+[N ii] emitters deg⁻² in the WS from 0.9 ≤ z ≤ 1.6 and an additional 288 ± 9 [O iii] λ5007 emitters deg⁻² up to z ∼ 2.3. Correcting these observed counts for the incompleteness of the WFC3 grism data, there are 3266 (Hα+[N ii]) and 445 ([O iii] λ5007) deg⁻², respectively. In addition to the WS sources with Hα+[N ii] and [O iii] λ5007 emission, there are a handful of sources at lower redshift (z ∼ 0.4) that were selected due to the strength of the [S iii] and He i emission. The number counts with and without completeness corrections of all selected emission lines are presented in Table 3.

Table 3.  WS Number Counts for Lines with 1.25 μm ≤ λ_obs ≲ 1.7 μm

	Flux	Nobs	Nobs/deg2	Ncorr/deg2
Hα+[N ii]	≥4	${269}_{-7.0}^{+6.2}$	${478.1}_{-12.4}^{+10.9}$	${704.5}_{-18.0}^{+19.7}$
(0.9 ≤ z ≲ 1.6)	≥3	516 ± 10.0	917.2 ± 17.8	${1421.0}_{-35.0}^{+42.0}$
	≥2	1091 ± 12.0	1939.2 ± 21.3	${3266.0}_{-174.8}^{+157.7}$
	≥1	${2378}_{-19.7}^{+17.8}$	${4226.7}_{-34.9}^{+31.7}$	${7887.3}_{-166.0}^{+148.5}$
[O iii] λ5007	≥4	${20}_{-2.0}^{+1.0}$	${35.5}_{-3.6}^{+1.8}$	${46.0}_{-2.0}^{+2.2}$
(1.5 ≤ z ≲ 2.4)	≥3	${46}_{-2.2}^{+2.0}$	${81.8}_{-3.8}^{+3.6}$	${112.2}_{-2.5}^{+3.8}$
	≥2	162 ± 5.0	287.9 ± 8.9	${444.6}_{-10.6}^{+15.5}$
	≥1	${517}_{-9.0}^{+8.3}$	${918.9}_{-16.0}^{+14.8}$	${1608.5}_{-11.9}^{+14.6}$
[S iii] λ9069	≥4	6 ± 1.0	10.7 ± 1.8	14.6 ± 1.3
(0.38 ≤ z ≲ 0.87)	≥3	6 ± 1.0	10.7 ± 1.8	14.6 ± 1.3
	≥2	${6}_{-2.0}^{+1.0}$	${10.7}_{-3.6}^{+1.8}$	14.6 ± 1.3
	≥1	6 ± 2.0	10.7 ± 3.6	14.6 ± 1.3
[S iii] λ9532	≥4	4 ± 1.0	7.1 ± 1.8	${11.2}_{-1.2}^{+1.6}$
(0.31 ≤ z ≲ 0.78)	≥3	${6}_{-2.0}^{+1.0}$	${10.7}_{-3.6}^{+1.8}$	${15.7}_{-1.4}^{+1.5}$
	≥2	${10}_{-2.0}^{+3.0}$	${17.8}_{-3.6}^{+5.3}$	${25.1}_{-1.3}^{+1.9}$
	≥1	20 ± 3.0	35.5 ± 5.3	${52.6}_{-1.5}^{+1.7}$
He i λ10830	≥4	3 ± 1.0	5.3 ± 1.8	${7.9}_{-1.4}^{+1.8}$
(0.15 ≤ z ≲ 0.57)	≥3	${6}_{-1.0}^{+2.0}$	${10.7}_{-1.8}^{+3.6}$	${18.8}_{-2.3}^{+3.9}$
	≥2	${8}_{-1.2}^{+2.0}$	${14.2}_{-2.1}^{+3.6}$	${28.9}_{-4.0}^{+7.2}$
	≥1	10 ± 2.0	17.8 ± 3.6	${35.6}_{-6.4}^{+5.1}$

Note. Observed (N_obs) and completeness-corrected (N_corr) cumulative number counts. Numbers presented here are for unique sources, i.e., ELGs with both Hα+[N ii] and [O iii] λ5007 are counted only for Hα+[N ii]. The redshift ranges associated with each emission line are given for observed wavelengths 12500 Å ≤ λ_obs ≲ 17000 Å, where the approximate upper limit is set by the decreasing sensitivity of the HST G141 grism. The line fluxes indicated in the first column are ×10⁻¹⁶ erg s⁻¹ cm⁻².

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We obtained the errors presented on the number counts in Table 3 through a Monte Carlo process by creating 200 realizations of the full WISP+3D-HST emission-line catalog, rerunning the WS selection, and measuring the resulting distribution of number counts. For the observed number counts (N_obs), each catalog realization is generated with redshifts and emission-line fluxes (and therefore EWs) pulled randomly from Gaussian distributions centered at the measured values and with standard deviations equal to the uncertainties on these measurements in the catalog. The number of sources recovered by the selection criteria varies from realization to realization. For the completeness-corrected number counts (N_corr), we leave the line fluxes and redshifts untouched and pull the completeness corrections from Gaussian distributions with standard deviations equal to the uncertainties on the completeness corrections. In this case, the number of recovered sources stays the same, while the completeness-corrected number varies. In both cases, we report the 16th and 84th percentiles as the lower and upper errors in Table 3, respectively.

The cumulative number counts of both Hα+[N ii]-emitters and [O iii] λ5007 emitters are shown in Figure 7. The observed counts are shown as fainter points, with Poisson uncertainties determined by the number of sources in each bin. The completeness-corrected counts are calculated as

$$\begin{eqnarray}&&{N}_{\mathrm{corr}}=\sum _{i}\displaystyle \frac{1}{{C}_{i}},\end{eqnarray} \tag{ 2 }$$

where C_i is the completeness for each source in the bin. The error bars are obtained by varying the completeness corrections maximally within the uncertainties, i.e., C_i + ${\sigma }_{{C}_{i}}$ and ${C}_{i}-{\sigma }_{{C}_{i}}$. These error bars therefore represent the range of possible number densities given the uncertainties on the completeness corrections. The number counts are separated into two redshift bins in the left column to highlight the evolution in the number density with redshift due to the increasing luminosity limit. There is a factor of more than 1.5 times more Hα+[N ii] emitters at 0.9 ≤ z < 1.2 than at 1.2 ≤ z ≤ 1.6. The observed number counts are in good agreement with the predictions from Mehta et al. (2015), calculated using a subset of WISP fields from the earlier data reduction and original line-finding procedure. The top right panel includes the cumulative number counts for the full redshift ranges available to the HST grism: 0.9 ≤ z_{Hα +[N ii]} ≲ 1.6 and 1.9 ≤ z_{[O iii]λ 5007} ≲ 2.3. Finally, the redshift distributions of Hα+[N ii] and [O iii] λ5007-emitting galaxies (dN/dz) in bins of Δz = 0.1 are shown in the bottom right panel.

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In the right column of Figure 7, we compare the observed Hα+[N ii] number counts with the empirical models of Pozzetti et al. (2016) in purple. The three models represent different parameterizations of the Hα luminosity function and its redshift evolution. For the purposes of comparison, we have converted the Hα counts of all three models to Hα+[N ii] counts using a fixed [N ii]/Hα line ratio: Hα = 0.71 (Hα+[N ii]), the same conversion used in Section 5 of Pozzetti et al. (2016) while comparing the model counts to observations. The observed Hα+[N ii] number counts in the top right panel of Figure 7 agree most closely with Model 3, which is the result of a fit to observations presented by Sobral et al. (2013, HiZELS), Colbert et al. (2013, WISP), Yan et al. (1999), and Shim et al. (2009). Model 3 is also one of the models against which the Euclid Flagship mock catalog has been calibrated. While the cumulative counts agree with Model 3 at almost all fluxes across the full redshift range, the distribution of Hα+[N ii] emitters with redshift falls off at z ∼ 1.5. For Hα+[N ii], this redshift corresponds approximately to the wavelengths at which the sensitivity in the G141 grism begins to decrease.

We also show the predictions from Valentino et al. (2017) in orange in the right panels of Figure 7. Valentino et al. (2017) use the large photometric samples in the COSMOS and GOODS-S fields to predict the number counts of ELGs that will be accessible to future galaxy redshift surveys. They derive Hα fluxes from the star formation rates obtained via SED fitting and use Hα emitters at z = 1.55 observed with the FMOS-COSMOS survey (Silverman et al. 2015) to calibrate the star formation rate to Hα conversion. The Hα+[N ii] predictions for galaxies on the star-forming main sequence in the range 0.9 ≤ z ≤ 1.6 are shown in orange in Figure 7. The counts have been corrected for the Eddington bias, which is a bias introduced by measurement uncertainties that can enhance the observed number of bright galaxies compared to fainter galaxies (Eddington 1913). The orange shaded bands indicate the 68% Poissonian confidence intervals, where the authors report the maximum of the upper and lower Poisson uncertainties. The uncertainties due to the Eddington bias correction are not included here but are available in Table 3 of Valentino et al. (2017). The cumulative flux counts, particularly in the GOODS-S field, are consistent with the HST grism measurements at all fluxes and are in good agreement with the predictions of Mehta et al. (2015) and Pozzetti et al. (2016). The redshift distributions of galaxies in both fields are consistent up to z ∼ 1.5, where the differential counts from Valentino et al. (2017) follow a shallower evolution than those from the other predictive works.

We note that the different [N ii] corrections adopted by each team can introduce some systematic uncertainties and contribute to this disagreement in the blended counts. Specifically, while we have used a single correction for all number counts from Pozzetti et al. (2016), Valentino et al. (2017) employ a complex correction as a function of mass that is smaller on average than that used for the models from Pozzetti et al. (2016). As a result, the Hα-only counts (i.e., not including the [N ii] correction) from Valentino et al. (2017) lie between Models 1 and 3 of Pozzetti et al. (2016), yet their Hα+[N ii] counts are generally lower and agree most closely with Model 3 (see Figure 12 from Valentino et al. 2017 compared with the top right panel of Figure 7). The median log₁₀ ([N ii]/Hα) of the sample in Valentino et al. (2017) is ∼−0.45 for galaxies with an Hα flux of 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² (see their Figure 9), while the correction applied here to Models 1, 2, and 3 corresponds to log₁₀ ([N ii]/Hα) = −0.39. The arrows in the top right panel of Figure 7 indicate the extent to which the number counts of Valentino et al. (2017) would change if the Hα+[N ii] fluxes were boosted by an additional factor (corresponding to Δlog₁₀([N ii]/Hα) = 0.06) to match the [N ii]/Hα ratio adopted by Pozzetti et al. (2016). These arrows can be interpreted as the approximate uncertainty in number counts due to the [N ii] correction. As the [N ii]/Hα line ratio remains uncertain at these redshifts and observations at the resolution of the HST grism cannot provide adequate constraints, these uncertainties are an important consideration when comparing Hα and Hα+[N ii] number counts from different models and observations.

We finally compare the observations with predictions from Merson et al. (2018), who use the Galacticus galaxy formation model (Benson 2012) and the dust attenuation methods from Ferrara et al. (1999), Calzetti et al. (2000), and Charlot & Fall (2000) to predict Hα+[N ii] number counts in the redshift range 0.9 ≤ z ≤ 1.55, matching that available to the HST grism. Merson et al. (2018) use Hα+[N ii] blended fluxes where the [N ii]/Hα ratios are determined by cross-matching the stellar mass and specific star formation rate of each Galacticus galaxy to the Sloan Digital Sky Survey sample from Masters et al. (2016). For each dust model, the red curve and shaded region in Figure 7 is the mean and standard deviation of 1000 Monte Carlo realizations sampling the model's optical depth parameters. The likelihoods for the sampling were constructed as ${ \mathcal L }\propto \exp (-{\chi }^{2}/2)$, where the χ² values were obtained by stepping through the dust parameter space and comparing Galacticus counts to the WISP counts from Mehta et al. (2015) for 0.7 ≤ z ≤ 1.5 (see Merson et al. 2018, for more information). While the HST grism Hα+[N ii] number counts presented in this paper (blue circles in Figure 7) are lower than all three predictions from Merson et al. (2018) for the brightest galaxies, the predictions and observations are consistent at the depth of the Euclid Wide Survey.

The number of galaxies observed by WISP+3D-HST are a lower limit to those that will be observed by Euclid. We remind the reader that the upper wavelength of the Euclid Red grism is ∼18500 Å, 1500 Å redder than the WFC3 G141 grism. The Euclid Hα+[N ii] and [O iii] λ5007 observations will therefore extend out to z ∼ 1.8 and z ∼ 2.7, respectively. Euclid will detect more sources per square degree than those reported here. However, as can be seen in Figure 2, at the depth of the Euclid Wide Survey, the number of detected ELGs drops quickly with redshift. The majority of the ELGs that Euclid detects will be Hα+[N ii] at z ≲ 1.5, a population that is fully sampled by the HST grism observations presented here.

With these HST grism observations, we show that Euclid will meet the goal of measuring redshifts for ∼25 million galaxy redshifts over 15,000 deg². Extrapolating the completeness-corrected number densities to the full Euclid Wide Survey area provides a rough estimate of ∼48 million Hα+[N ii] emitters and ∼6 million [O iii] λ5007 emitters down to f ≥ 2 × 10⁻¹⁶ erg s⁻¹ cm⁻². Even the observed, uncorrected counts, which provide an estimate in case the Euclid galaxy redshift survey and these HST grism observations suffer from the same level of incompleteness,¹⁷ are larger than the planned number of galaxy redshifts. These HST observations therefore contribute a valuable resource to the effort to calibrate and verify the performance of the planned Euclid survey. Finally, we note that at the resolution of the Red grism, Euclid will be able to resolve the Hα and [N ii] λλ6548, 6584 doublet for compact galaxies. However, the contribution from [N ii] for compact, low-mass (<10¹⁰ M_⊙) galaxies is ≲10% (e.g., Erb et al. 2006; Masters et al. 2016; Faisst et al. 2018). Therefore, even for the galaxies for which Euclid will resolve the two lines, we do not expect an [N ii] correction to the Hα+[N ii] fluxes to significantly affect our results.

The location and size of the window used for spectral extraction from grism images depend on the detection of the galaxy in a direct image. This process relies on a few assumptions, including (1) that the full extent of the source has been detected in the direct image and (2) that the emission-line size is correlated with the source size in the direct image. We briefly explore both assumptions below.

4.2.1. Flux Loss from Spectral Extraction

The first case is analogous to slit or fiber losses in spectroscopic observations obtained with apertures smaller than the source. In this case, flux loss depends partially on the color and morphology of the galaxies (e.g., Brinchmann et al. 2004) and therefore is not a simple systematic flux offset. We can test the extent of the flux lost in WFC3 slitless grism data with the simulations described in Section 2.1. The aXeSIM software generates the synthetic spectrum of a source by convolving an imaging template with a template spectrum. We use two-dimensional Gaussians to model the sources, but in principle any image of the source can be used. Regardless, the shape and size of the emission at each wavelength in the synthetic spectrum are assumed to be the same as in the direct image. The one-dimensional spectrum is then produced by collapsing the extracted spectral stamp along the spatial axis. If the extraction window is too small in the spatial direction, the flux in the one-dimensional spectrum will underestimate the total. We can therefore determine what fraction of flux is lost in the emission lines by comparing the input values with those recovered and measured by the full analysis process. The ratio of the measured to input flux is shown in Figure 8 as a function of input line flux and input semimajor axis, where we find that the fluxes are consistent for the primary lines Hα and [O iii] λ5007 down to the flux limit of the Euclid Deep survey. Additionally, there is no clear dependence on source size (bottom panel), indicating that the extraction windows are adequate even for the largest sources, i.e., those most likely to have a surface brightness that drops below our detection threshold. However, we note that, due to incompleteness, there are very few sources with semimajor axis a > 07.

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4.2.2. Hα+[N ii] Emission Size Measurements

As discussed in Section 3.2, we fit Sérsic models to the continuum images and emission-line maps. We show the size distributions as a function of redshift, Hα+[N ii] flux, and H magnitude in Figure 9, where R_eff refers to the half-light radius of the Sérsic profile. We have removed from this figure and analysis six sources¹⁸ for which the models could not be successfully fit (<1% of the sample). The R_eff measured in the Hα+[N ii] emission-line maps are shown as black points, while the continuum R_eff are represented by the shaded, two-dimensional histogram calculated using a Gaussian kernel density estimation. The continuum and Hα+[N ii] size distributions are shown in the rightmost panel, along with the median and quartiles in blue dotted and black dashed lines, respectively. The median continuum R_eff is 037 (∼2.9–3.1 kpc for redshifts 0.9–1.5) with an interquartile range of 02 (=048–028). The Hα+[N ii] size distribution is slightly wider with a median of 039 (∼3.0–3.3 kpc) and an interquartile range of 027 (=055–028).

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These R_eff values are on the low end of what is presented for continuum emission by van der Wel et al. (2014) and for Hα and continuum emission by Nelson et al. (2016). For example, Nelson et al. (2016) find r_{1/2, Hα} = 2.91 and 3.10 kpc for galaxies in the mass ranges 9.5 < log(M_*) < 10.0 and 10.0 < log(M_*) < 10.5, respectively, whereas we expect some if not all of the bright (H ≲ 24) galaxies in the WS to be in a higher stellar mass bin. The discrepancy between our measurements and those of these other works is most likely due to the lower surface brightness limits these authors reach by stacking images and spectral stamps (e.g., ∼1 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² by Nelson et al. 2016), enabling them to recover more of the flux in the wings of each source. In this paper, we measured R_eff on individual stamps to reflect the role the continuum and emission-line sizes have on the selection function of slitless spectroscopic surveys, but we note that stacking would be required to statistically recover and measure the sizes of such sources.

These half-light radii have been deconvolved with the empirical WFC3 PSF and therefore represent the intrinsic sizes measured to the depth of the HST grism observations. The median R_eff measured in both the continuum and Hα+[N ii] emission is <01 larger than the size of 1 pixel on the NISP instrument (03). Approximately 20% (40%) of the WS presented here has half-light radii smaller than the NISP pixel in both (either) the continuum and (or) Hα+[N ii]. As more flux will be concentrated in each source's central pixel on the NISP detector, sources will be more undersampled in Euclid observations than they are when observed by HST. However, the planned multiple dithers will help compensate for the larger pixel scale.

We next compare the R_eff measured in the continuum to that of the Hα+[N ii] emission in Figure 10. The two sizes are correlated, but with significant scatter. The standard deviation of the relation between the continuum and emission-line sizes is ∼02–035, compared to the 005–015 measured for the simulated sources. As the observed and simulated data have been fit with different models, we also fit the observations with Gaussian models to test whether this increase in scatter is due to model choice. However, the Gaussian R_eff of the observed galaxies is very similar to what is shown in Figure 10, and so the observed scatter must be due in part to other causes.

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Many of the sources above the one-to-one correlation in the left panel of Figure 10, where the measured Hα+[N ii] R_eff is larger than that of the continuum, have broad Hα+[N ii] line profiles along the dispersion direction. The extent of the emission in these cases is not spatial, and these sources are erroneously fit with elongated profiles. For others, the Hα+[N ii] emission is more extended than the continuum as discussed by, e.g., Nelson et al. (2016). For some of the sources with Hα+[N ii] R_eff smaller than the continuum, we may be measuring small knots of emission concentrated within a smaller radius than the full galaxy. In these cases, we may be detecting Hα from star-forming clumps (e.g., Bournaud et al. 2014; Zanella et al. 2015; Mandelker et al. 2017), while any more extended line emission has a surface brightness below our detection sensitivity. We note that such sources may have increased noise in the extracted, one-dimensional spectra, as the extraction windows and extraction weights are determined by the size of sources in the direct imaging (see Section 2.1). The scatter in the Hα+[N ii]-continuum R_eff relation in Figure 10 can therefore reveal important information about the optimization of the spectral extraction process and the resulting S/N measured for emission lines.

Part of the scatter may be due to the fact that Sérsic models are simplified representations of galactic light profiles. For example, approximately 25% of the WS has either continuum or line emission characterized by clumps or other structure that may indicate merging or interacting systems. In these cases, the single-component fits are too simple to properly model the emission. However, much of this substructure will be unresolved when observed with the larger NISP pixel, and single-component models may provide better fits to source continuum and line emission. On the other hand, most disk galaxies have a bulge component that is best fit with larger n. More realistic models may be achieved by allowing for a two-component model fit consisting of both disk-like and bulge-like profiles. The resulting measurements could then be compared with the distributions of bulge and disk lengths and axis ratios in the Euclid Flagship mock catalog.

Regardless, the distribution of emission sizes measured in slitless data, the relation between the continuum and line emission, and the observed scatter in this relation are important quantities for evaluating the effects of the selection function of future grism-based galaxy redshift surveys.

The emission-line EW, a measure of the strength of the emission, is a very important property of ELGs that must be correctly included in forecasts for emission-line studies. Hydrogen recombination lines such as Hα and Hβ are produced by the ionizing radiation from young, massive stars, while the strength of the stellar continuum reflects the buildup of emission from the older, less massive population. The EW of Hα is therefore an estimate of the ratio between the average star formation from current and past events. It is a measure of a galaxy's specific star formation rate, or the star formation rate per unit stellar mass. Given an assumed star formation history, the specific star formation rate can be converted to an age for the galaxy. The addition of [N ii] complicates this picture, as the [N ii] contribution to the Hα+[N ii] line flux depends on factors such as mass, metallicity, star formation rate, ionization parameter, and AGN activity and also varies with redshift (e.g., Baldwin et al. 1981; Erb et al. 2006; Kewley et al. 2013; Masters et al. 2016; Kashino et al. 2017; Faisst et al. 2018). It is crucial that the simulations created to evaluate the survey design of missions such as Euclid reproduce the physical properties, and not just the number counts, of the selected population that will be observed. As discussed in Section 4.1, Hα and [N ii] will be blended at the resolution of the Euclid Red grism for all but the most compact sources, and so the observed joint Hα+[N ii] EW distribution should also be reproduced in the simulations.

In Figure 11, we present both the observed and completeness-corrected Hα+[N ii] EW distributions of the Euclid WS. The median observed Hα+[N ii] EW is 250 Å, which corresponds to 100–125 Å for galaxies at z ∼ 1–1.5. The interquartile range of the observed EW is 160.2–397.5 Å. The EW distribution ranges from 40 Å (the EW completeness limit for the WISP emission-line detection algorithm) to ≳4000 Å. The WISP completeness limit represents the EW below which the detection algorithm does not reliably detect emission peaks in the grism spectra (see Section 2.1) and is therefore applicable to all grism observations run through this software. The Euclid Wide survey will have an approximate upper EW limit of ∼2370 Å, calculated for the 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² flux limit and an H = 24 (for λ_pivot = 18000 Å). While there are ∼32 sources deg⁻² in the WS above this approximate limit, only ∼4 deg⁻² are also fainter than H = 24. The WISP completeness limit and approximate Euclid Wide Survey limit are indicated in Figure 11 by dashed and dotted–dashed lines, respectively.

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As described in Section 2.1.1, we assume that single emission lines in the grism spectra are Hα unless the line has noticeable asymmetry indicative of the [O iii]+Hβ line profile. We now briefly consider whether this assumption leads us to selectively identify [O iii] lines with asymmetric profiles.

We compare the [O iii] line profiles of sources with multiple lines, and therefore secure redshifts, with the profiles of single-line emitters that have been identified as [O iii]. The question is whether a sample of sources with multiple lines have, on average, a more symmetric profile because the characteristic asymmetry is not needed for line identification. We create two subsets of [O iii] emitters randomly sampled from the WISP emission-line catalog. All sources have [O iii] fluxes with S/N ≥ 5. The Hα+[N ii] fluxes in the first subset also have an S/N ≥ 5, making this a sample of confirmed [O iii] emitters. The second subset is taken at z ≥ 1.6, where Hα+[N ii] has redshifted out of G141, and excludes any sources with an [O ii] S/N ≥ 2. We restrict both selections to z ≥ 1.24 so that all emission lines are measured in G141 with the same resolution and dispersion. There are ∼120 sources in each sample. The individual one-dimensional spectra are represented by faint dots in Figure 12, and the median spectrum is shown as the black curve. We also median-combine 20% of the two-dimensional spectra for each sample, displayed below the one-dimensional spectra. All spectra (one- and two-dimensional) are shifted to the rest frame and normalized by the integrated [O iii] line flux.

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The [O iii] line profiles for each sample are indicated in blue (confirmed) and red (unconfirmed). As can be seen in the inset in the bottom panel, the median profile of confirmed [O iii] emitters is indeed more symmetric than that of the unconfirmed ones. To quantify the level of asymmetry, we fit both line profiles with a Gaussian function and measure the residuals. Within ±20 Å of the [O iii] λ4959 line, the residuals of the fit to the red profile in Figure 12 are a factor of >5 times larger than that of the fit to the blue profile. The median 5σ depth in the WISP spectra at the wavelengths of the [O iii] lines is 6 × 10⁻¹⁷ erg s⁻¹ cm⁻². This bias could be even more pronounced for shallower data such as those of the Euclid Wide survey, where the [O iii] λ4959 line will fall below the detection limit more often than in deeper spectra. The resulting [O iii] λ5007 line profiles may appear symmetric and be more likely to be identified as Hα under visual inspection. However, the Euclid Red grism will have a higher spectral resolution (R ∼ 380 compared with R ∼ 130 for G141), and galaxies will appear more compact on the larger pixel scale (03 vs. 013). Additionally, as discussed in Section 2.2, unaided human classification will not be a feasible method for line identification in the Euclid data.

The measurement of the BAO signal in galaxy clustering requires accurate distance measurements to a large sample of galaxies. It has been shown through simulations that the redshift accuracy for a survey such as Euclid must be σ_z/(1 + z) ≤ 0.1% (Wang et al. 2010; Laureijs et al. 2011). As shown by Colbert et al. (2013) with simulated sources added to real WISP fields, the required redshift accuracy is achievable with R > 200 grism spectroscopy (see their Figure 5). Here we provide empirical confirmation of the redshift accuracy that can be expected from slitless spectroscopy.

We perform an empirical measurement of the redshift accuracy using fits to the grism spectra of WISP sources that were observed more than once. Over the six cycles of parallel observations, there are 36 WISP fields that overlap to some degree with another field. There are therefore ∼140 sources that have been observed multiple times, often with very different exposure times, field depths, and roll angles. In order to increase the sample size, we consider all possible permutations of pairs of observations of a given source. We randomize the order in which we calculate the delta redshift to avoid systematic shifts that may be introduced if a subset of these WISP fields have problems. Such problems could include issues with the wavelength calibration or noisy grism data, which would increase the uncertainty in the measured emission-line centers. In Figure 13, we show this empirical measurement of the redshift accuracy (σ_z/(1 + z) = 0.00136), as well as a similar measurement of the accuracy of the Hα+[N ii] fluxes of these sources. Note that the redshift accuracy presented here of ∼0.14% is the result of a fit to the difference in two redshift measurements and therefore has twice the variance of either measurement alone.

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In both the simulated data (Colbert et al. 2013) and the empirical measurement presented here, the redshift accuracy measured from the WFC3 slitless data is on the order of 0.1%, indicating the level achievable for future grism-based galaxy redshift surveys. However, such surveys will also have to contend with redshift contamination from misidentified emission lines. We quantify the expected fraction of contamination as a function of survey flux limit in the following section.

For proper forecasts of dark energy experiments, a critical parameter is the purity of the measured redshifts of galaxies, which can be quantified by the fraction of targets with incorrectly identified emission lines. There are two possible sources of contamination: spurious sources such as noise peaks incorrectly identified as emission features, and real lines that have been misidentified and are therefore assumed to be at the wrong redshift. The first case depends on the method used for line identification. For example, Colbert et al. (2013) find that ∼8.5% of emission lines in the first version of the WISP emission-line catalog are in fact hot pixels, cosmic rays, or other artifacts. Though we have not quantified this fraction in the new catalog, the updated procedure using a continuous wavelet transform should improve on this false detection rate (see Section 2.1.1).

To evaluate the contamination from misidentified redshifts, we use the CANDELS multiwavelength observations available for the 3D-HST fields and the full wavelength coverage of the G102+G141 WISP observations to evaluate the purity of spectroscopic redshifts measured with grism data. Figure 1 shows the redshift ranges for which multiple lines will be identified in Euclid spectra. For many redshifts only one line will be available. In addition, depending on the intrinsic Hα+[N ii]/[O iii] λ5007 ratio and the amount of dust extinction, it is likely that Hα+[N ii] will still be the only line detected, even in the redshift range where both [O iii] λ5007 and Hα+[N ii] are present. Indeed, only about 10% of the WS sources in the proper redshift range have both Hα+[N ii] and [O iii] λ5007. When only individual lines are detected, these are operationally identified as Hα unless other information such as the emission-line shape or galaxy color is available. However, it is possible that a substantial fraction of these single lines are in fact [O iii] at ${z}_{[{\rm{O}}{\rm{III}}]}+1=({z}_{{\rm{H}}\alpha }+1){\lambda }_{{\rm{H}}\alpha }/{\lambda }_{[{\rm{O}}{\rm{III}}]}$. We aim to constrain the purity of slitless-selected samples with two complementary approaches: (1) a comparison with spectroscopically confirmed and photometrically determined redshifts, and (2) an analysis of the additional secure redshifts made possible by increasing the survey wavelength range.

First, we use the redshifts compiled in version 4.1.5 of the 3D-HST catalog¹⁹ to determine the fraction of 3D-HST grism redshifts assigned through the WISP emission-line detection procedure that have been misidentified. In Figure 14, we explore this redshift misidentification as a function of line flux using the best available redshift for each source ("z_best") from the 3D-HST catalog. Sources where "z_best" is a spectroscopic redshift from Skelton et al. (2014) are shown as blue circles. All other redshifts are determined either from grism measurements (black squares) or from SED fitting using the full suite of available CANDELS photometry (black triangles). Note that here the grism redshifts are those from the 3D-HST data release, which include the CANDELS photometric redshifts as a prior, rather than the measurements performed using the WISP emission-line detection described in Section 2.2. We consider all Hα+[N ii] emitters in the 3D-HST catalog where the redshift is based on a single line. We select galaxies with a "z_best" ≥ 0.9 to match the WS selection.

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The prevalence of misidentified single emission lines depends on the survey depth. At the depth of the Euclid Wide Survey ∼14% of the single-line emitters with spectroscopic redshifts (blue circles) assumed to be Hα+[N ii] are in fact a different emission line. This percentage increases to ∼40% at the depth of the Euclid Deep Survey, below which the sample size of sources confirmed spectroscopically decreases. As it is prohibitively difficult to follow-up every grism detection of an ELG from the ground, we also show the misidentification percentage for the sources with no slit-based spectroscopic redshift, where ∼25% to ∼60% of sources with single emission lines are misidentified. For the majority of the Euclid Wide Survey, photometry—and efforts to calibrate photometric redshifts (e.g., Masters et al. 2015)—will be critical for correctly identifying single emission lines in the grism spectra and improving the sample purity attained in the Wide Survey.

Measuring the BAO signal from galaxy clustering measurements requires a full understanding of the sample redshift contamination, as galaxies with misidentified redshifts will reduce the strength of the clustering signal. The Euclid Deep Survey will therefore provide a redshift calibration sample, which will be used to quantify the contamination fraction present in the Wide Survey. For this calibration effort, the Deep Survey will aim to achieve a purity of p > 99% over the 40 deg² region, where p is the number of sources with correctly identified redshifts divided by the total number measured (Laureijs et al. 2011), p = N_correct/N_measured. We use the WISP emission-line catalog to estimate the purity of the emission-line sample observed in the Euclid Deep Survey. From the full WISP emission-line catalog (Section 2.1.1), we only consider fields with spectral coverage in both the G102 and the G141 grisms. Additionally, we include in the following analysis only ELGs with secure redshifts (i.e., measured with at least two emission lines). Having observations in both grisms ensures a spectral coverage between 0.85 μm ≤ λ ≤ 1.65 μm. Given the emission lines considered in the redshift determination ([O ii], Hγ, Hβ, [O iii], Hα+[N ii], [S ii], [S iii] λ9069, [S iii] λ9532, and He i λ10830), the catalog derived for the fields with both grisms spans the redshift range between z ∼ 0.25 and z ∼ 2.3. The approximate 5σ depth of the selected WISP fields is 5 × 10⁻¹⁷ erg s⁻¹ cm⁻², consistent with the expected line flux limit in the Euclid Deep Survey observations with the Red grism.

From this two-grism WISP catalog, we apply the same selection criteria described in Section 2.4 to create a sample analogous to that which will be selected using the NISP Red Euclid grism. We call this sample the Euclid Shallow (ES) sample, and it is the same as the WS of Section 2.4 but only includes WISP sources from fields observed with both grisms. The redshift distribution of the ES sample is shown in Figure 15 (blue histogram). In the WISP catalog, sources with redshift in the range of 0.4 < z < 1.6 are mostly selected via their Hα emission line. At redshifts z ≳ 1.6, galaxies are selected via the [O iii] emission lines, while at redshifts z ≲ 0.4, galaxies are identified because of the [S iii] and He i lines. We stress that the WISP sample considered in this analysis only includes secure redshifts measured with two or more emission lines.

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Multiple emission lines are required in order to be able to perform an unambiguous redshift identification. Thus, we look at the fraction of galaxies in the ES sample that would show additional lines in the wavelength range of the Euclid Red grism, with f_line^add > 2σ (where σ = 1.4 × 10⁻¹⁷ erg s⁻¹ cm⁻² is the required spectroscopic depth of the Euclid deep survey). We find that 77% of the ES sample has multiple emission lines in the wavelength range of the Euclid Red grism and at the depth of the Deep Survey. The redshift distribution for this population is shown in Figure 15 (orange histogram). The red histogram in Figure 15 shows the redshift distribution of the remaining 23% of galaxies in the ES sample that would be single-line emitters in the Euclid Red grism even at the depth of the Deep Survey.

For single-line emitters the simplest assumption is that the line is Hα. The red histogram, however, clearly shows that this assumption would get the redshift wrong for single-line emitters at z < 0.9 and z > 1.8. Here we are assuming that Euclid would detect Hα for the [O iii]-selected WISP sources in the 1.6 < z < 1.8 redshift range. We find that 6% of all ES galaxies would have incorrect redshift measurements in a Deep Survey observed with only the Euclid Red grism, corresponding to a sample purity of 94%. These incorrect redshifts would make quantifying the redshift contamination and purity of the Euclid Wide Survey more challenging.

Given the wavelength range of the G102 grism, we can quantify the extent to which the addition of the Euclid Blue grism would improve the sample purity. The Euclid Blue grism extends the survey wavelength coverage down to 0.92 μm. Encouragingly, almost all of the 6% of objects with misidentified redshifts have additional detectable emission lines in this extended blue wavelength coverage. Specifically, 85% of the misidentified redshifts would be removed, bringing the purity of the ES sample up to 99.1%. The Blue grism would be a valuable addition to the Euclid Deep Survey and would allow for a better understanding of the fraction of single-line emitters with incorrect redshifts in the Wide Survey.

In order to assess the completeness of the WISP Survey and the line-finding procedure, we create a simulated catalog of 10,000 synthetic sources and their spectra. The parameters for each source—redshift, source size and shape, Hα line flux, Hα EW, and Hα/[O iii] λ5007 line ratio—are pulled randomly from uniform distributions chosen to bracket the observed values in the emission-line catalog. The one exception is the Hα/[O iii] λ5007 line ratio, which is pulled from a Gaussian distribution centered at the measured ratio for real sources but with a standard deviation two times larger. We create synthetic direct and grism images of each source using aXeSIM (Kümmel et al. 2007). The source images are elliptical Gaussians, which aXeSIM convolves with input template spectra to create the dispersed grism stamps. The simulated sources therefore have the same size and shape at all wavelengths. We insert the simulated sources into real WISP images from 20 fields, chosen to cover the ranges of exposure times, depths, and filter coverage that exist in a survey composed of parallel opportunities of varied length. We produce 20 realizations of each field, with 25 simulated sources per realization. We then process all fields through the full WISP reduction pipeline and emission-line detection software.

The completeness is calculated in bins of emission-line EW and "scaled flux," or the line flux scaled by the grism sensitivity in that particular field at the wavelength of the line. This scaled flux is a tracer for line S/N but also reflects the effect of the varying depths reached in each field of a parallel survey such as WISP. The bin edges are determined by the distribution of sources in the real WISP emission-line catalog such that there are an approximately equal number of real sources in each bin. The one exception is the bin of lowest EW, which we add in order to probe an area of the parameter space with low completeness (EW_obs < 40 Å; see Colbert et al. 2013). We note that source size and shape can strongly affect the completeness of both the imaging and emission-line catalogs, as extended, low surface brightness sources may fall below the adopted Source Extractor  detection thresholds and their low emission-line EWs may be missed by the line detection algorithm. However, the large sources that suffer from the highest levels of incompleteness (with semimajor axis a ≥ 07) constitute less than 1% of either the imaging or the emission-line catalogs. We therefore weight the distribution of input sources by the distribution of observed sizes in the emission-line catalog, allowing us to account for the effect of source size while considering a two-parameter completeness correction. We use a radial basis function to interpolate the recovery fractions across all bins, smoothing over sharp jumps in the completeness at bin edges. Uncertainties on the completeness corrections are taken as $1/\sqrt{{N}_{\mathrm{rec}}}$, where N_rec is the number of recovered sources in each bin of EW and scaled flux. Completeness corrections are calculated using the line with the highest "scaled flux" in each spectrum as a proxy for the "primary" lines identified by the detection software. Accordingly, these completeness corrections are applied to each source in the emission-line catalog—given the flux and EW of its strongest line—rather than to individual emission lines.

In the top row of Figure A1, we compare the completeness corrections from this new line-finding method and that of Colbert et al. (2013). The completeness corrections for sources identified with the new method (WISP catalog) are shown on the left, and those for the 3D-HST+AGHAST catalog using the method described by Colbert et al. (2013) are displayed on the right. In both cases we plot the corrections as a function of line S/N and observed EW to allow for a direct comparison.

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Finally, this analysis identified two thresholds below which the completeness corrections are highly uncertain: line EW_obs < 40 Å and S/N < 5, identified in Figure A1 by dashed and dotted–dashed lines, respectively. In the bottom left panel of Figure A1, we show the fraction of simulated sources that were recovered by the automatic detection algorithm binned by observed EW. The fraction drops rapidly for EW_obs < 40 Å, indicating that 40 Å is an effective limiting EW for which the automatic algorithm can detect a significant peak above the continuum in the WISP spectra. Overall, fewer than 10% of input emission lines with EW_obs < 40 Å were recovered by the automatic detection algorithm, while this fraction increases to 28% for 40 Å < EW_obs < 60 Å.

In the bottom right panel of Figure A1, we show the distribution of emission-line S/N as measured in both the simulated (gray distribution) and real (purple distribution) WISP emission-line catalogs. There is a decrease in the number of sources in both catalogs where the strongest emission line present in the spectrum is detected with S/N < 5. We have included in the simulated catalog emission lines with fluxes pulled from a uniform distribution reaching well below the flux limit of the survey. The bottom right panel of Figure A1 therefore demonstrates that we are not complete to sources with emission lines below this cutoff. Additionally, during visual inspection, reviewers are less consistent in their treatment of S/N < 5 emission lines. The fraction of lines accepted by only one reviewer, i.e., when the reviewers do not agree that the emission-line candidate is real, doubles for lines with S/N < 5. We note that these same EW and S/N thresholds were adopted by Colbert et al. (2013) in their completeness analysis that is used for the 3D-HST+AGHAST emission-line catalog described in Section 2.2, where the motivation is similar. We therefore include these thresholds in our sample selection criteria described in Section 2.4.

Colbert et al. (2013) derive completeness corrections for the earlier version of the WISP emission-line detection process following a similar procedure, by adding simulated sources to WISP images and processing them all the way through the visual inspection stage. We briefly summarize the steps here and refer the reader to Colbert et al. (2013) for more details.

A total of 923 model ELGs are generated pulling parameters such as redshift, source size, emission-line flux, and EW randomly from distributions informed by real measurements in WISP data. These are added to 74 realizations of WISP fields, with 10–20 simulated sources per field. The automatic line detection algorithm identifies sets of 3 or more contiguous pixels above the continuum that each have an S/N $\gt \sqrt{3}$ (or 2 contiguous pixels that are each at an S/N $\gt \sqrt{5}$ to account for unresolved objects). Each emission-line candidate is then inspected by two reviewers, where the criteria for accepting or rejecting a candidate are the same as in the updated line-finding procedure. The reviewers identify each emission line, thereby assigning a redshift, and measure line properties by fitting Gaussians to the line profiles. The completeness corrections of Colbert et al. (2013) are calculated in bins of line S/N and observed EW, with input distributions weighted by source size as described in Appendix A.1. These corrections are applied to the 3D-HST+AGHAST catalog in the top right panel of Figure A1.

The completeness analysis of Colbert et al. (2013) differs in three ways from the analysis described in Appendix A.1. First, the automatic line detection identifies candidate emission lines through the detection of contiguous pixels above the measured continuum. Many hot pixels and noise spikes were detected in this way and needed to be rejected during the visual inspection phase. In the updated procedure, this step is supplemented by the continuous wavelet transform that selects for emission-line shape, as well as strength above the continuum. This addition, more than any other, serves to remove the majority of spurious detections that were identified by the original algorithm. The new procedure also implements additional quality checks, including a cut on very low EW emission lines designed to remove noise spikes and a higher S/N threshold of S/N > 2.31 pixel^–1 (compared with the $\sqrt{3}=1.73$). The algorithm automatically rejects any emission-line candidates detected within 5 pixels of the edge of each spectrum, a region where the grism sensitivity decreases rapidly and in which many spurious lines were identified by the first version. Finally, the continuum is estimated on a median-filtered spectrum rather than with a spline fit as was used in the first version. This approach produces a better fit, especially in regions where the continuum changes rapidly. Detecting lines as pixels with excess flux above the continuum requires a properly fit continuum.

Second, in the original procedure, the reviewers identified and fit emission lines individually for each source. Once they selected an emission feature for fitting—thus assigning a redshift to the source—they would step through the spectrum fitting Gaussians at the wavelengths expected for other lines given the assumed redshift. The widths and central wavelengths of these Gaussians were not constrained and so could vary from line to line in the same spectrum. The new procedure fits each spectrum simultaneously, including the continuum and all emission lines, and each line is constrained to have the same FWHM. Additionally, the reviewer has the option of refitting the global continuum during the spectral fitting process, an option that can provide better emission-line fits and more accurate EW measurements.

The two differences discussed so far refer to the line-finding and line-fitting procedure, while the third difference relates specifically to the completeness analysis from Colbert et al. (2013). During the visual inspection used to calculate the completeness, the reviewers inspected a random collection of spectra from real and simulated sources. The goal was to avoid the bias that can be introduced when reviewers expect all spectra to have emission lines. This step allowed Colbert et al. (2013) to calculate a contamination rate of 8.5% due to false emission lines. While we have not calculated this for the new line-finding procedure, we emphasize that the criteria for accepting or rejecting emission-line candidates, as well as the data products included in the inspection (direct images, 2D spectral stamps, S/N spectra, and 1D spectra), are the same for both procedures.

We have explored the results of the two emission-line detection methods using 20 WISP fields that have been processed with both versions. In Figure A2, we show the number of accepted and rejected sources as a function of emission-line flux. In the left panel, the dashed and dotted–dashed lines show the number of sources identified by the two algorithms that were later rejected by reviewers. For a given emission-line flux, the first version of the line-finding algorithm identified >2× more sources, the majority of which were rejected during inspection. Yet the distributions of algorithm-identified and reviewer-accepted sources are similar down to the flux limit of the Euclid Wide Survey, which is indicated by the gray shaded region. This similarity is even greater in the right panel, where we show the same comparison after applying quality cuts to the samples that select sources with secure redshifts. We emphasize here that the y-axes of both panels show the number of sources and not a fraction or normalized distribution. As we apply the same quality cuts to the WISP and 3D-HST+AGHAST catalogs during the creation of the WS in Section 2.4, the distributions in the right panel are indicative of the performance of the two algorithms in our full analysis.

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