<table><caption>**Table 10.** Description of WISP emission-line catalogue.</caption><thead><tr><th>Title</th><th>Description</th></tr></thead><tbody><tr><td>PAR</td><td>WISP field ID number</td></tr><tr><td>OBJ</td><td>Object ID number</td></tr><tr><td>RA</td><td>Decimal RA from HST images (deg)</td></tr><tr><td>DEC</td><td>Decimal Dec. from HST images (deg)</td></tr><tr><td>JMAG</td><td>J-band magnitude; S<sub>EXTRACTOR</sub> MAG_AUTO_F110W from WISP photometric catalogue (mag)</td></tr><tr><td>HMAG</td><td>H-band magnitude; S<sub>EXTRACTOR</sub> MAG_AUTO_[F140W or F160W] from WISP photometric catalogue (mag)</td></tr><tr><td>A_IMAGE</td><td>S<sub>EXTRACTOR</sub> profile RMS along major axis measured on 0.08 arcsec pixel<sup>-1</sup> HST images (pixels)</td></tr><tr><td>B_IMAGE</td><td>S<sub>EXTRACTOR</sub> profile RMS along minor axis measured on 0.08 arcsec pixel<sup>-1</sup> HST images (pixels)</td></tr><tr><td>FILTER_FLAG</td><td>Flag identifying filter coverage for field (10 bit flags; see Appendix E)</td></tr><tr><td>GRISM_FLAG</td><td>Integer flag identifying grism coverage for field; (1=G102, 2=G141, and 3 = G102 + G141)</td></tr><tr><td>[GRISM_FILTER].FLAG<sup>a</sup></td><td>Flags identifying any problems with the grism data for this field (5 bit flags; see Appendix E)</td></tr><tr><td>EDGE_FLAG</td><td>Flag identifying objects close to edges of direct image (5 bit flags; see Appendix E)</td></tr><tr><td>NNEIGHBORS</td><td>Number of sources in WISP photometric catalogue within 1 arcsec of object</td></tr><tr><td>NLINES</td><td>Number of lines detected at >2σ for object</td></tr><tr><td>REDSHIFT</td><td>Redshift from simultaneous fit to all lines in spectrum</td></tr><tr><td>REDSHIFT_ERR</td><td>Redshift 1σ uncertainty</td></tr><tr><td>dz_OIII</td><td>Shift in redshift of the [O III] profile fit compared with reported REDSHIFT for object</td></tr><tr><td>dz_OII</td><td>Shift in redshift of the [O II] profile fit compared with reported REDSHIFT for object</td></tr><tr><td>dz_SIII_HE1</td><td>Shift in redshift of the [S II] and He I profile fit compared with reported REDSHIFT for object</td></tr><tr><td>DELTA_REDSHIFT</td><td>Difference in redshift fits of the two reviewers</td></tr><tr><td>REDSHIFT_FLAG</td><td>Flag identifying quality of redshift fit (6 bit flags; see Appendix E)</td></tr><tr><td>FWHM_OBS</td><td>FWHM used for all emission-line profile fits; observed frame using the 46.5 Å pixel<sup>-1</sup> dispersion in G141 grism (Å)</td></tr><tr><td>FWHM_OBS_ERR</td><td>FWHM 1σ uncertainty (Å)</td></tr><tr><td>FWHM_FLAG</td><td>Flag identifying quality of reported FWHM (5 bit flags; see Appendix E)</td></tr><tr><td>COMPLETENESS</td><td>Source completeness reflecting the selection function of the full line-finding procedure (see Section 5.4)</td></tr><tr><td>[LINE].NREVS<sup>b</sup></td><td>Number of reviewers who measured emission line</td></tr><tr><td>[LINE].FLUX<sup>b</sup></td><td>Emission-line flux from profile fit (erg s<sup>-1</sup> cm<sup>-2</sup>)</td></tr><tr><td>[LINE].FLUX_ERR<sup>b</sup></td><td>Emission-line flux 1σ uncertainty (erg s<sup>-1</sup> cm<sup>-2</sup>)</td></tr><tr><td>[LINE].DELTA FLUX<sup>b</sup></td><td>Difference in emission-line fluxes of the two reviewers (erg s<sup>-1</sup> cm<sup>-2</sup>)</td></tr><tr><td>[LINE].EW.OBS<sup>b</sup></td><td>Emission-line EW reported in observed frame; -1 for undetected lines (Å)</td></tr><tr><td>[LINE].DELTA_EW<sup>b</sup></td><td>Difference in emission-line EWs of the two reviewers (Å)</td></tr><tr><td>[LINE].FLAG<sup>b</sup></td><td>Flag identifying quality of emission-line measurements (6 bit flags; see Appendix E)</td></tr><tr><td>[LINE].CONTAM<sup>b</sup></td><td>Flag identifying the contamination noted by each reviewer ('a' and 'b'); String has form 'a.b' (4 bit flags; see Appendix E)</td></tr><tr><td>[LINE].WAVEOBS<sup>b</sup></td><td>Observed wavelength of emission line (Å)</td></tr><tr><td>[LINE].EDGE FLAG<sup>b</sup></td><td>Flag identifying emission lines close to edges of grism where sensitivity decreases (4 bit flags; see Appendix E)</td></tr></tbody></table>

Notes.<sup>a</sup> [GRISM_FILTER] is one of: G102 or G141. <sup>b</sup> [LINE] is one of: O II, Hg, Hb, O III, HN II, S II, S III_9069, S III_9532, or HeI_10830.

2020, 2021), we urge caution in using sources with only a single emission line (NLINES ≤ 1; 3350 sources in catalogue). It is also important to consider the redshift quality flags (REDSHIFT_FLAG; see Appendix E) that indicate potential disagreements between emission-line reviewers.

For sources with multiple detected emission lines (i.e. NLINES > 1; 4842 sources in catalogue), the reliability of the redshifts is expected to higher, however this is difficult to quantify without independent metrics or follow-up higher resolution spectroscopy. We refer readers to Baronchelli et al. (2020, 2021) for a detailed discussion on the issues pertaining to contamination and purity in a grism spectroscopic sample. Masters et al. (2014) presented a subset of 26 emission-line galaxies (from 23 WISP fields) where follow-up observations with Magellan/FIRE (R ~ 6000; 0.8–2.5 µm) were made on sources with S/N ≥ 10 (from grism) in [O III] and/or Hα. They found very good agreement in line identification (close to 100 per cent) for these sources, although these cases have higher S/N than most of the WISP sources. A larger sample with follow-up observations from VLT/FORS2 (Very Large Telescope/Focal Reducer and low dispersion Spectrograph; R ~ 1200; 0.51–0.85 µm) will be presented in Boyett et al. (in preparation), which we briefly highlight here. This program observed 85 emission-line galaxies out of 138 potential emission sources in the

four targeted WISP fields. Emission lines were detected in the FORS2 data for 38/85 cases, with agreement in the line identification between the grism and FORS2 data seen for 36 of those galaxies (suggesting 95 per cent accuracy of line identification). Of the 38 galaxies with detected lines, 17 are cases where the grism redshift is based on a single line. All cases where lines were not detected with FORS2 are either cases where no lines were predicted to lie in the FORS2 window (15/85) or the grism redshift is based on a single line (32/85). In summary, these findings add further support that selecting sources with multiple emission lines is necessary to ensure robust redshift estimates.

The precision of the redshifts (relating to REDSHIFT_ERR) are a separate metric from accuracy, with the former mainly driven by the spectral resolution of the grism data. For reference, the WFC3/IR detector using the G141 grism has a sampling of 46.5 Å pixel<sup>-1</sup> and a FWHM ~ 110 Å. We characterize the precision as σ<sub>σ</sub>/(1 + z) (i.e. REDSHIFT_ERR/(1 + REDSHIFT)), which has a median value of 0.00088 (~0.09 per cent) and the 16th and 84th percentiles are 0.00045 and 0.00154, respectively. Bagley et al. (2020) performed an independent test of the precision using the 36 WISP fields that overlap to some degree with each other. These fields result in ~140 sources that were observed multiple times, often with very different exposure times (field depths) and roll angles. This comparison
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Demonstration of the wavelength coverage of WISP stacked spectra for different redshift windows. Multiple emission lines are simultaneously available for several windows in the redshift range from *z* = 0.3 to 2.3. The sample size indicated corresponds to sources that satisfy the criteria for our science results (criterion 1–8; see Section 7.1).</figcaption></figure>

showed an empirical precision of $\sigma_z/(1+z) = 0.00136$, which is in close agreement with the median value in the catalogue when accounting for the fact that the test combines the uncertainty of two line measurements.

(iv) grism coverage from [O II] to [S II] ($1.27 < z < 1.45$; maximum $\lambda$-coverage).

## 7 RESULTS

We demonstrate the utility of combining the WISP photometric and emission-line catalogues to study galaxy evolution by dividing the sample into four grism windows (redshift regimes) where different sets of emission lines are available in G102 and/or G141 (i.e. do not always require both) to constrain properties of the interstellar medium (ISM):

(i) grism coverage of H$\alpha$ + [N II], [S II], and [S III] doublet (0.30 < *z* < 0.73),

(ii) grism coverage of H$\alpha$ + [N II] and [S II] (0.30 < *z* < 1.45),

(iii) grism coverage of H$\beta$ and [O III] (0.74 < *z* < 2.31),

We do not examine the window where H$\beta$, [O III], and H$\alpha$ + [N II] are simultaneously covered to constrain the Balmer decrement (H$\alpha$/H$\beta$; 0.74 < *z* < 1.51), which is a subset of sources in the third window above, because this was the focus of Battisti et al. (2022). Similarly, we do not examine the window where [O II], H$\beta$, and [O III] are covered ($1.27 < z < 2.31$; wider redshift than fourth window above) to constrain the metallicity via the $R_{23} \equiv ([\text{O II}]\lambda\lambda3726, 3729 + [\text{O III}]\lambda\lambda4959, 5007)/H\beta$ diagnostic because this was the focus of Henry et al. (2021). Both of those studies also supplement their samples with other HST grism surveys such that they have larger sample sizes than are available from WISP alone. A visual demonstration of the spectral coverage from WISP for these windows is shown in Fig. 13, together with the sample size satisfying the criteria for our science results (Section 7.1).
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Demonstration of the wavelength coverage of WISP stacked spectra for different redshift windows. Multiple emission lines are simultaneously available for several windows in the redshift range from $z = 0.3$ to 2.3. The sample size indicated corresponds to sources that satisfy the criteria for our science results (criterion 1–8; see Section 7.1).</figcaption></figure>

showed an empirical precision of $\sigma_z/(1+z) = 0.00136$, which is in close agreement with the median value in the catalogue when accounting for the fact that the test combines the uncertainty of two line measurements.

(iv) grism coverage from [O II] to [S II] ($1.27 < z < 1.45$; maximum $\lambda$-coverage).

# 7 RESULTS

We demonstrate the utility of combining the WISP photometric and emission-line catalogues to study galaxy evolution by dividing the sample into four grism windows (redshift regimes) where different sets of emission lines are available in G102 and/or G141 (i.e. do not always require both) to constrain properties of the interstellar medium (ISM):

(i) grism coverage of $H\alpha + [N\ II]$, [S II], and [S III] doublet (0.30 < z < 0.73),

(ii) grism coverage of $H\alpha + [N\ II]$ and [S II] (0.30 < z < 1.45),

(iii) grism coverage of $H\beta$ and [O III] (0.74 < z < 2.31),

We do not examine the window where $H\beta$, [O III], and $H\alpha + [N\ II]$ are simultaneously covered to constrain the Balmer decrement ($H\alpha/H\beta$; $0.74 < z < 1.51$), which is a subset of sources in the third window above, because this was the focus of Battisti et al. (2022). Similarly, we do not examine the window where [O II], $H\beta$, and [O III] are covered ($1.27 < z < 2.31$; wider redshift than fourth window above) to constrain the metallicity via the $R_{23} \equiv ([O\ II]\lambda\lambda3726, 3729 + [O\ III]\lambda\lambda4959, 5007]/H\beta$ diagnostic because this was the focus of Henry et al. (2021). Both of those studies also supplement their samples with other HST grism surveys such that they have larger sample sizes than are available from WISP alone. A visual demonstration of the spectral coverage from WISP for these windows is shown in Fig. 13, together with the sample size satisfying the criteria for our science results (Section 7.1).
<figure><img src="image_15.png" /><figcaption>**Figure 14.** Top panel: grism redshift, $z_{\text{grism}}$, distribution for galaxies in the WISP sample that have robust photometric and spectroscopic data (criterion 1–4; black) and the subset that also have good SED fits, accurate stellar masses, and are not AGN candidates (criterion 1–7; orange), as described in Section 7.1. Bottom panel: stellar mass versus redshift. A representative median $1\sigma$ error bar for the criterion (1)–(7) sample (orange) is indicated in the lower left, with values of $\langle\sigma(z_{\text{grism}})\rangle = 0.0017$ (i.e. negligible) and $\langle\sigma(\log[M_*/M_{\odot})\rangle = 0.12$ dex. No significant selection effects on stellar mass are apparent with redshift.</figcaption></figure>

## 7.1 Sample selection criteria

Combining the overlapping sources in both the WISP photometric and emission-line catalogues provides us with a parent sample of 1937 galaxies that satisfy the following spectroscopic and photometric selection criteria:

(i) One emission line with $S/N \ge 3$ and one additional line with $S/N \ge 2$.

(ii) At least three bands of photometry with $S/N > 3$.

(iii) Independent redshift agreement between the two reviewers ($\text{REDSHIFT FLAG} = 0$).

(iv) Emission-line FWHM < 600Å (FWHM\_OBS<600).

Criteria (1) ensures an accurate $z_{\text{grism}}$, which is important for optimally aligning the spectra, as well as reducing false identifications. Criteria (2) ensures that we have adequate SED coverage for characterizing stellar masses, $M_*$, Criteria (3) removes ambiguous sources where the WISP pipeline reviewers have either assigned different redshift solutions or the spectrum was rejected by one of the reviewers (no confidence in redshift solution). We note that criteria (3) removes ~1/3 of the potential sample, which indicates the difficulty in determining reliable redshifts from low S/N spectra. Criteria (4) removes very broad emission-line sources (~1 per cent of sample). These broad profiles may be due to an AGN, which we want to exclude for our analysis. The redshift and stellar mass distribution of sources satisfying criterion (1)–(4) are shown in Fig. 14.

For creating stacked spectra according to stellar mass, we also impose additional cuts on SED goodness of fit and uncertainty on stellar mass:

(v) $\chi^2_{\text{red}} < 3$,

(vi) $\sigma(\log M_*) < 0.3$ dex,

which is detailed in Section 7.2. Together, criterion (5) and (6) remove 147 sources (6 fail both criteria) or 7.6 per cent of the sample. For reference, width of the stellar mass bins in our analysis are roughly 0.3 dex or larger to improve the reliability of bin assignment for each galaxy.

For the subset sources with grism coverage and detection of [O III] and $H\beta$, we also exclude AGN candidates based on the mass-excitation diagram (MEx, $\log[[O III]/H\beta]$ versus $\log[M_*/M_{\odot}]$; Juneau et al. 2014):

(vii) non-AGN in MEx diagram

which is detailed in Section 7.4.1. Criteria (7) removes an additional 59 sources. This leaves 1731 sources that satisfy criterion (1)–(7), and this sample is also shown in Fig. 14.

Finally, a criteria limiting the contamination of the main emission lines if that line is the focus of the stacking analysis:

(viii) neither reviewer marked line contamination ([LINE]_CONTAM<4 from both reviewers).

For example, we require $H\beta$ and [O III] are uncontaminated for the stacks in the $H\beta$ and [O III] window (Section 7.4.1). Depending on the window considered, this criteria typically removes an additional 15 per cent–20 per cent of sources in that window. This highlights the high rate of contamination that can occur in single-orientation grism data.

## 7.2 SED modelling for stellar masses

To estimate stellar masses, we perform SED fitting on our galaxy sample using the MAGPHYS (high-z) spectral modelling code (da Cunha et al. 2015; Battisti et al. 2020), adopting the grism redshift as the input redshift (i.e. fixed-z). Prior to fitting, the photometry is corrected for foreground MW extinction using the Galactic dust extinction maps from Schlafly & Finkbeiner (2011) via the NASA/IPAC Infrared Science Archive.<fnref n="14" /> MAGPHYS uses spectral population synthesis models of Bruzual & Charlot (2003), and we refer readers to that paper for details on the stellar tracks, templates, and isochones adopted in that model, also noting that it does include a prescription for thermally pulsing asymptotic giant branch stars. MAGPHYS adopts a Chabrier (2003) initial mass function (IMF) and has 14 free model parameters (high-z version), and for full details we refer readers to the documentation on the MAGPHYS website.<fnref n="15" /> In brief, they include: a uniform prior in metallicity from 0.2 to 2 times solar (one parameter); a parametric star formation history (SFH; three parameters), which rises linearly at early ages and then declines exponentially (delayed-tau model) with additional instantaneous bursts of star formation; the dust model of Charlot & Fall (2000), four parameters) for which the interstellar dust is distributed into two components, one associated with star-forming regions (migration time of 10 Myr) and the other with the diffuse ISM, with the addition of the 2175 Å absorption feature (Battisti et al. 2020); the dust emission models of da Cunha, Charlot & Elbaz (2008), which uses templates based on four components (five parameters); and a normalization that sets the stellar mass and star formation rate (SFR) from the SFH (one parameter). The adopted SFH parametrization may introduce systematic biases to the stellar mass estimates (e.g. Leja et al. 2019). For reference, when comparing overlapping WISP galaxies in Henry et al. (2021), who use similar photometry but adopt a non-parametric SFH for their SED modelling, we find their stellar

<footnote n="14">¹⁴https://irsa.ipac.caltech.edu/applications/DUST/</footnote>

<footnote n="15">¹⁵http://www.iap.fr/magphys/index.html</footnote>
<figure><img src="image_15.png" /><figcaption>**Figure 14.** Top panel: grism redshift, $z_{\text{grism}}$, distribution for galaxies in the WISP sample that have robust photometric and spectroscopic data (criterion 1–4; black) and the subset that also have good SED fits, accurate stellar masses, and are not AGN candidates (criterion 1–7; orange), as described in Section 7.1. Bottom panel: stellar mass versus redshift. A representative median $1\sigma$ error bar for the criterion (1)–(7) sample (orange) is indicated in the lower left, with values of $\langle\sigma(z_{\text{grism}})\rangle = 0.0017$ (i.e. negligible) and $\langle\sigma(\log[M_*/M_{\odot})\rangle = 0.12$ dex. No significant selection effects on stellar mass are apparent with redshift.</figcaption></figure>

## 7.1 Sample selection criteria

Combining the overlapping sources in both the WISP photometric and emission-line catalogues provides us with a parent sample of 1937 galaxies that satisfy the following spectroscopic and photometric selection criteria:

(i) One emission line with $S/N \ge 3$ and one additional line with $S/N \ge 2$.

(ii) At least three bands of photometry with $S/N > 3$.

(iii) Independent redshift agreement between the two reviewers ($\text{REDSHIFT FLAG} = 0$).

(iv) Emission-line FWHM < 600Å (FWHM\_OBS<600).

Criteria (1) ensures an accurate $z_{\text{grism}}$, which is important for optimally aligning the spectra, as well as reducing false identifications. Criteria (2) ensures that we have adequate SED coverage for characterizing stellar masses, $M_*$. Criteria (3) removes ambiguous sources where the WISP pipeline reviewers have either assigned different redshift solutions or the spectrum was rejected by one of the reviewers (no confidence in redshift solution). We note that criteria (3) removes ~1/3 of the potential sample, which indicates the difficulty in determining reliable redshifts from low S/N spectra. Criteria (4) removes very broad emission-line sources (~1 per cent of sample). These broad profiles may be due to an AGN, which we want to exclude for our analysis. The redshift and stellar mass distribution of sources satisfying criterion (1)–(4) are shown in Fig. 14.

For creating stacked spectra according to stellar mass, we also impose additional cuts on SED goodness of fit and uncertainty on stellar mass:

(v) $\chi^2_{\text{red}} < 3$,

(vi) $\sigma(\log M_*) < 0.3$ dex,

which is detailed in Section 7.2. Together, criterion (5) and (6) remove 147 sources (6 fail both criteria) or 7.6 per cent of the sample. For reference, width of the stellar mass bins in our analysis are roughly 0.3 dex or larger to improve the reliability of bin assignment for each galaxy.

For the subset sources with grism coverage and detection of [O III] and $H\beta$, we also exclude AGN candidates based on the mass-excitation diagram (MEx, $\log([\text{O III}]/H\beta)$ versus $\log[M_*/M_{\odot}]$; Juneau et al. 2014):

(vii) non-AGN in MEx diagram

which is detailed in Section 7.4.1. Criteria (7) removes an additional 59 sources. This leaves 1731 sources that satisfy criterion (1)–(7), and this sample is also shown in Fig. 14.

Finally, a criteria limiting the contamination of the main emission lines if that line is the focus of the stacking analysis:

(viii) neither reviewer marked line contamination ([LINE]_CONTAM<4 from both reviewers).

For example, we require $H\beta$ and [O III] are uncontaminated for the stacks in the $H\beta$ and [O III] window (Section 7.4.1). Depending on the window considered, this criteria typically removes an additional 15 per cent–20 per cent of sources in that window. This highlights the high rate of contamination that can occur in single-orientation grism data.

## 7.2 SED modelling for stellar masses

To estimate stellar masses, we perform SED fitting on our galaxy sample using the MAGPHYS (high-z) spectral modelling code (da Cunha et al. 2015; Battisti et al. 2020), adopting the grism redshift as the input redshift (i.e. fixed-z). Prior to fitting, the photometry is corrected for foreground MW extinction using the Galactic dust extinction maps from Schlafly & Finkbeiner (2011) via the NASA/IPAC Infrared Science Archive.<fnref n="14" /> MAGPHYS uses spectral population synthesis models of Bruzual & Charlot (2003), and we refer readers to that paper for details on the stellar tracks, templates, and isochones adopted in that model, also noting that it does include a prescription for thermally pulsing asymptotic giant branch stars. MAGPHYS adopts a Chabrier (2003) initial mass function (IMF) and has 14 free model parameters (high-z version), and for full details we refer readers to the documentation on the MAGPHYS website.<fnref n="15" /> In brief, they include: a uniform prior in metallicity from 0.2 to 2 times solar (one parameter); a parametric star formation history (SFH; three parameters), which rises linearly at early ages and then declines exponentially (delayed-tau model) with additional instantaneous bursts of star formation; the dust model of Charlot & Fall (2000), four parameters) for which the interstellar dust is distributed into two components, one associated with star-forming regions (migration time of 10 Myr) and the other with the diffuse ISM, with the addition of the 2175 Å absorption feature (Battisti et al. 2020); the dust emission models of da Cunha, Charlot & Elbaz (2008), which uses templates based on four components (five parameters); and a normalization that sets the stellar mass and star formation rate (SFR) from the SFH (one parameter). The adopted SFH parametrization may introduce systematic biases to the stellar mass estimates (e.g. Leja et al. 2019). For reference, when comparing overlapping WISP galaxies in Henry et al. (2021), who use similar photometry but adopt a non-parametric SFH for their SED modelling, we find their stellar

<footnote n="14">¹⁴https://irsa.ipac.caltech.edu/applications/DUST/</footnote>

<footnote n="15">¹⁵http://www.iap.fr/magphys/index.html</footnote>
masses are systematically larger than the MAGPHYS-derived values by 0.2 dex.

MAGPHYS does not include templates for emission-line fluxes and therefore we perform emission-line subtraction prior to SED fitting, when available. This is especially important for this study because we are using an emission-line-selected sample. If one assumes a roughly flat continuum (in $F_\lambda$), the average flux density measured in the photometry can be approximated as (e.g. Whitaker et al. 2014)

$$F_{\lambda} \approx F_{\lambda, \text{cont}} + F_{\text{line}}/\Delta\lambda, \quad (1)$$

where $F_{\lambda, \text{cont}}$ is the continuum-only flux density and $\Delta\lambda$ is the width of the filter, which we take to be its FWHM. We subtract emission-line fluxes for all lines with $S/N > 2$ from the photometric data. The impact of emission lines on photometry are the largest for galaxies with fainter continuum emission (typically lower $M_*$) and higher equivalent widths (EW = $F_{\text{line}}/F_{\lambda, \text{cont}}$). An example of a MAGPHYS fit for a WISP galaxy is shown in Fig. 15.

For each MAGPHYS fit, a goodness of fit is determined based on the best-fitting model using a reduced $\chi^2$ metric, $\chi^2_{\text{red}} = \chi^2/N_{\text{bands}}$, where $N_{\text{bands}}$ is the number of bands observed with non-zero flux. We exclude cases of poor-quality fits by removing galaxies with $\chi^2_{\text{red}} > 3$ from our analysis (criteria 5), which removes 140 of the criterion (1)–(4) sources. Cases of poor fits may be associated with poor/inconsistent photometric data and/or AGN contamination (AGN models are not included in the SED fitting). We also require accurate stellar masses because we will bin our data according to stellar masses, and exclude sources with $\sigma(\log M_*) > 0.3$ dex (based on the 16th and 84th percentiles of the posterior PDF (probability distribution function); $\sigma(\log M_*) = (\log M_{*, p84} - \log M_{*, p16})/2$; criteria 6). This occurs for 13 of the criterion (1)–(4) sources. The median values of the remaining WISP sample is $\bar{\chi}^2_{\text{red}} = 0.32$. The low $\chi^2$ values are due to the fact that the models tend to ‘overfit’ the data (more free parameters than data points).

Table 11 provides the $\log M_*$ and log SFR(SED) percentiles from MAGPHYS for our sample of 1937 galaxies that satisfy criterion (1)–(4) in Section 7.1. SFR(SED) represents the average SFR over the last 100 Myr of the SFH. For reference, the median $1\sigma$ uncertainty on $\log M_*$ and log SFR(SED) (taken as (84th–16th percentile)/2) is 0.12 and 0.25 dex, respectively. We note that our uncertainties may be underestimated due to the SFH parametrization used in MAGPHYS. For overlapping WISP galaxies in Henry et al. (2021), which uses a non-parametric SFH for SED modelling, their median $1\sigma$ uncertainties on $\log M_*$ and log SFR(SED) are larger by 0.03 and 0.04 dex, respectively. SED-derived SFRs have very large uncertainty when relying only on UV through NIR data. For this reason, we avoid using SED-derived SFRs for our analysis and instead use $H\alpha$-based estimates whenever possible. We note that the median number of bands available for the subsample is 5, with 85 per cent of the sample having coverage in IRAC (i.e. detection or an upper limit). The median uncertainty on $\log M_*$ for sources with 3, 4, 5, and 6 + bands available is 0.19, 0.13, 0.11, and 0.10 dex, respectively. We find that fields without IRAC coverage have only marginally higher stellar mass uncertainty (0.01 dex) and no significant bias. The difference in median value for the two samples is $\log M_*(\text{w/ IRAC}) - \log M_*(\text{no IRAC}) = 0.045$ dex and below the typical uncertainty and our binning size. We stress that these are formal uncertainties and that the true mass uncertainty is higher when accounting for systematic uncertainties arising from model assumptions (e.g. SFH). We include the number bands available in the SED modelling for each source as a column in Table 11.

## 7.3 Spectral stacking and emission-line fitting of stacked spectra

All galaxy spectra are stacked and fit following similar methods to those described in Dai et al. (2021), Henry et al. (2021), and Battisti et al. (2022). In brief, we use the continuum-subtracted spectra (using a cubic spline; see Section 5.3) and normalize them by the ‘typical’ brightest line in the spectral window considered, which for the windows we consider is either $H\alpha + [N\text{II}]$ (low-z windows) or [OIII] (high-z windows). The spectra are de-redshifted using a linear interpolation to shift them onto a common grid of rest wavelengths and we take the median of the normalized fluxes at each wavelength.

The procedure to fit the stacked spectra differs slightly from the method used for individual sources for the emission-line catalogue (Section 5.3) and this is due to the fact that the stacks reach greater depth such that more parameters are generally required for good fits (e.g. narrow + broad components). To fit the stacked spectra, we fit a set of Gaussian profiles to the emission lines in the region of interest. We adopt two Gaussian components for each line, one narrow and one broad component. Multiple components can arise due to kinematic differences among ionizing sources (e.g. HII versus AGN), but can also occur in grism spectra due to line profiles having a dependence on the spatial distribution of the emitting sources. The FWHM of the broad component is fixed to be the same for all of the lines and also required to be between 1–4× the FWHM of the narrow components. The amplitudes of the broad components for each line are allowed to vary independently (among positive values).

The emission lines are simultaneously fit with the following assumptions/restrictions: (1) the ratio of [OIII]$\lambda$5007/[OIII]$\lambda$4959 is fixed to 2.98:1 (Storey & Zeippen 2000) and [SIII]$\lambda$9532/[SIII]$\lambda$9069 is fixed to 2.47:1 (Berg et al. 2021), (2) single profiles are used for the closely spaced blends of [OII]$\lambda$3727, 3729, $H\alpha + [N\text{II}]\lambda$6548, 6583, and [SII]$\lambda$6716, 6731, (3) we require the narrow component FWHM of close pairs to match (e.g. $H\beta$ and [OIII], $H\alpha + [N\text{II}]$, and [SII]). We do not match all components in order to account for the effect that the spectral resolution difference between the G102 and G141 grisms can have on the profiles, (4) we require the FWHM of the narrow components to be within a factor of two with each other, (5) we allow a $\pm 10$ Å shift (rest frame) of the emission-line centroids to accommodate systematic uncertainties in the grism wavelength solution, and (6) we account for any (small) residual continuum offsets due to imperfect continuum subtraction by including free parameters for the spectra amplitudes (i.e. constant offsets) in the regions near emission-line groups (e.g. 4400 Å $< \lambda_{\text{rest}} < 5500$ Å for $H\beta$ and [OIII]; and 6000 Å $< \lambda_{\text{rest}} < 7100$ Å for $H\alpha + [N\text{II}]$ and [SII]).

Line flux measurements for the stacks are based on scaling the average flux of the normalized line in each bin (i.e. reversing the normalization). Line flux measurement uncertainties on the stacked spectra are obtained by bootstrapping with replacement. In brief, for each sample of N galaxies that are stacked, we draw N random galaxies from that sample, allowing individual objects to be selected more than once. We create a new stack from these objects and measure the lines and repeat this procedure 1000 times and calculate the standard deviation on the line fluxes from these realizations and adopt this as the uncertainty.

## 7.4 Stellar mass stack results

For all stellar mass bins, we require that they contain $N \gtrsim 100$ galaxies to ensure reliable recovery of faint emission lines and ensure stacks are not sensitive to any individual outlier galaxies in the stack. This also ensures that corrections, which are based on averages, are
masses are systematically larger than the MAGPHYS-derived values by 0.2 dex.

MAGPHYS does not include templates for emission-line fluxes and therefore we perform emission-line subtraction prior to SED fitting, when available. This is especially important for this study because we are using an emission-line-selected sample. If one assumes a roughly flat continuum (in $F_\lambda$), the average flux density measured in the photometry can be approximated as (e.g. Whitaker et al. 2014)

$$F_{\lambda} \approx F_{\lambda, \text{cont}} + F_{\text{line}}/\Delta\lambda, \quad (1)$$

where $F_{\lambda, \text{cont}}$ is the continuum-only flux density and $\Delta\lambda$ is the width of the filter, which we take to be its FWHM. We subtract emission-line fluxes for all lines with $S/N > 2$ from the photometric data. The impact of emission lines on photometry are the largest for galaxies with fainter continuum emission (typically lower $M_*$) and higher equivalent widths (EW = $F_{\text{line}}/F_{\lambda, \text{cont}}$). An example of a MAGPHYS fit for a WISP galaxy is shown in Fig. 15.

For each MAGPHYS fit, a goodness of fit is determined based on the best-fitting model using a reduced $\chi^2$ metric, $\chi^2_{\text{red}} = \chi^2/N_{\text{bands}}$, where $N_{\text{bands}}$ is the number of bands observed with non-zero flux. We exclude cases of poor-quality fits by removing galaxies with $\chi^2_{\text{red}} > 3$ from our analysis (criteria 5), which removes 140 of the criterion (1)–(4) sources. Cases of poor fits may be associated with poor/inconsistent photometric data and/or AGN contamination (AGN models are not included in the SED fitting). We also require accurate stellar masses because we will bin our data according to stellar masses, and exclude sources with $\sigma(\log M_*) > 0.3$ dex (based on the 16th and 84th percentiles of the posterior PDF (probability distribution function); $\sigma(\log M_*) = (\log M_{*, p84} - \log M_{*, p16})/2$; criteria 6). This occurs for 13 of the criterion (1)–(4) sources. The median values of the remaining WISP sample is $\bar{\chi}^2_{\text{red}} = 0.32$. The low $\chi^2$ values are due to the fact that the models tend to ‘overfit’ the data (more free parameters than data points).

Table 11 provides the $\log M_*$ and log SFR(SED) percentiles from MAGPHYS for our sample of 1937 galaxies that satisfy criterion (1)–(4) in Section 7.1. SFR(SED) represents the average SFR over the last 100 Myr of the SFH. For reference, the median $1\sigma$ uncertainty on $\log M_*$ and log SFR(SED) (taken as (84th–16th percentile)/2) is 0.12 and 0.25 dex, respectively. We note that our uncertainties may be underestimated due to the SFH parametrization used in MAGPHYS. For overlapping WISP galaxies in Henry et al. (2021), which uses a non-parametric SFH for SED modelling, their median $1\sigma$ uncertainties on $\log M_*$ and log SFR(SED) are larger by 0.03 and 0.04 dex, respectively. SED-derived SFRs have very large uncertainty when relying only on UV through NIR data. For this reason, we avoid using SED-derived SFRs for our analysis and instead use $H\alpha$-based estimates whenever possible. We note that the median number of bands available for the subsample is 5, with 85 per cent of the sample having coverage in IRAC (i.e. detection or an upper limit). The median uncertainty on $\log M_*$ for sources with 3, 4, 5, and 6 + bands available is 0.19, 0.13, 0.11, and 0.10 dex, respectively. We find that fields without IRAC coverage have only marginally higher stellar mass uncertainty (0.01 dex) and no significant bias. The difference in median value for the two samples is $\log M_*(\text{w/ IRAC}) - \log M_*(\text{no IRAC}) = 0.045$ dex and below the typical uncertainty and our binning size. We stress that these are formal uncertainties and that the true mass uncertainty is higher when accounting for systematic uncertainties arising from model assumptions (e.g. SFH). We include the number bands available in the SED modelling for each source as a column in Table 11.

## 7.3 Spectral stacking and emission-line fitting of stacked spectra

All galaxy spectra are stacked and fit following similar methods to those described in Dai et al. (2021), Henry et al. (2021), and Battisti et al. (2022). In brief, we use the continuum-subtracted spectra (using a cubic spline; see Section 5.3) and normalize them by the ‘typical’ brightest line in the spectral window considered, which for the windows we consider is either $H\alpha + [N\text{II}]$ (low-z windows) or [OIII] (high-z windows). The spectra are de-redshifted using a linear interpolation to shift them onto a common grid of rest wavelengths and we take the median of the normalized fluxes at each wavelength.

The procedure to fit the stacked spectra differs slightly from the method used for individual sources for the emission-line catalogue (Section 5.3) and this is due to the fact that the stacks reach greater depth such that more parameters are generally required for good fits (e.g. narrow + broad components). To fit the stacked spectra, we fit a set of Gaussian profiles to the emission lines in the region of interest. We adopt two Gaussian components for each line, one narrow and one broad component. Multiple components can arise due to kinematic differences among ionizing sources (e.g. HII versus AGN), but can also occur in grism spectra due to line profiles having a dependence on the spatial distribution of the emitting sources. The FWHM of the broad component is fixed to be the same for all of the lines and also required to be between 1–4× the FWHM of the narrow components. The amplitudes of the broad components for each line are allowed to vary independently (among positive values).

The emission lines are simultaneously fit with the following assumptions/restrictions: (1) the ratio of [OIII]$\lambda$5007/[OIII]$\lambda$4959 is fixed to 2.98:1 (Storey & Zeippen 2000) and [SIII]$\lambda$9532/[SIII]$\lambda$9069 is fixed to 2.47:1 (Berg et al. 2021), (2) single profiles are used for the closely spaced blends of [OII]$\lambda$3727, 3729, $H\alpha + [N\text{II}]\lambda$6548, 6583, and [SII]$\lambda$6716, 6731, (3) we require the narrow component FWHM of close pairs to match (e.g. $H\beta$ and [OIII], $H\alpha + [N\text{II}]$, and [SII]). We do not match all components in order to account for the effect that the spectral resolution difference between the G102 and G141 grisms can have on the profiles, (4) we require the FWHM of the narrow components to be within a factor of two with each other, (5) we allow a $\pm 10$ Å shift (rest frame) of the emission-line centroids to accommodate systematic uncertainties in the grism wavelength solution, and (6) we account for any (small) residual continuum offsets due to imperfect continuum subtraction by including free parameters for the spectra amplitudes (i.e. constant offsets) in the regions near emission-line groups (e.g. 4400 Å $< \lambda_{\text{rest}} < 5500$ Å for $H\beta$ and [OIII]; and 6000 Å $< \lambda_{\text{rest}} < 7100$ Å for $H\alpha + [N\text{II}]$ and [SII]).

Line flux measurements for the stacks are based on scaling the average flux of the normalized line in each bin (i.e. reversing the normalization). Line flux measurement uncertainties on the stacked spectra are obtained by bootstrapping with replacement. In brief, for each sample of N galaxies that are stacked, we draw N random galaxies from that sample, allowing individual objects to be selected more than once. We create a new stack from these objects and measure the lines and repeat this procedure 1000 times and calculate the standard deviation on the line fluxes from these realizations and adopt this as the uncertainty.

## 7.4 Stellar mass stack results

For all stellar mass bins, we require that they contain $N \gtrsim 100$ galaxies to ensure reliable recovery of faint emission lines and ensure stacks are not sensitive to any individual outlier galaxies in the stack. This also ensures that corrections, which are based on averages, are
<figure><img src="image_16.png" /><figcaption>**Figure 15.** Top row: native resolution 10 arcsec × 10 arcsec image thumbnails (linear scale) of the available photometry for Par79_12 (i.e. parallel field 79, object 12). The last panel shows the SExTRACTOR segmentation map, based on F110W and F160W, which is an input for TPHOT, with object 12 indicated. Bottom left: the MAGPHYS best-fitting SED (black line) for Par79_12. The red squares are the observed photometry and the black circles are the corresponding model values. The blue line shows the predicted intrinsic stellar population SED (without attenuation). Bottom right: the posterior PDFs for stellar mass and SFR are also shown. The available photometric coverage is sufficient to accurately constrain stellar masses (~0.1 dex), however SFRs have poorer constraints due to the lack of rest-frame IR data (i.e. age/dust reddening degeneracy; ~0.3 dex).</figcaption></figure>

<table><caption>**Table 11.** Stellar mass and SFR percentiles from MAGPHYS for the 1937 WISP sources with 'robust' spectroscopy and photometry (criterion 1–4 in Section 7.1).</caption><thead><tr><th rowspan="2">Par</th><th rowspan="2">Obj</th><th rowspan="2">z<sub>grism</sub></th><th rowspan="2">z<sub>grism</sub>, err</th><th rowspan="2">AGN_flag<sup>a</sup></th><th colspan="3">log [M<sub>*</sub>/M<sub>☉</sub>]</th><th colspan="6">log [SFR(SED)/(M<sub>☉</sub>yr<sup>-1</sup>)]</th><th rowspan="2">χ<sup>2</sup><sub>red</sub></th><th rowspan="2">N<sub>bands</sub></th></tr><tr><th>2.5</th><th>16</th><th>50</th><th>84</th><th>97.5</th><th>2.5</th><th>16</th><th>50</th><th>84</th><th>97.5</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>0.5084</td><td>0.0013</td><td>0</td><td>9.92</td><td>10.03</td><td>10.15</td><td>10.26</td><td>10.40</td><td>0.01</td><td>0.73</td><td>1.16</td><td>1.58</td><td>1.90</td><td>0.011</td><td>5</td></tr><tr><td>1</td><td>13</td><td>0.5309</td><td>0.0011</td><td>0</td><td>9.80</td><td>9.94</td><td>10.02</td><td>10.13</td><td>10.21</td><td>-0.60</td><td>0.26</td><td>0.92</td><td>1.28</td><td>1.74</td><td>0.055</td><td>7</td></tr><tr><td>1</td><td>15</td><td>0.6699</td><td>0.0011</td><td>0</td><td>9.86</td><td>9.96</td><td>10.04</td><td>10.13</td><td>10.22</td><td>0.68</td><td>0.95</td><td>1.32</td><td>1.73</td><td>2.08</td><td>0.464</td><td>7</td></tr><tr><td>1</td><td>28</td><td>1.3443</td><td>0.0028</td><td>0</td><td>9.41</td><td>9.50</td><td>9.61</td><td>9.68</td><td>9.80</td><td>1.07</td><td>1.16</td><td>1.32</td><td>1.48</td><td>1.58</td><td>0.297</td><td>7</td></tr><tr><td>1</td><td>41</td><td>1.3065</td><td>0.0018</td><td>0</td><td>9.67</td><td>9.81</td><td>9.89</td><td>10.00</td><td>10.13</td><td>0.91</td><td>1.21</td><td>1.53</td><td>1.77</td><td>1.94</td><td>0.326</td><td>7</td></tr></tbody></table>

Notes. A full ASCII version of this table is available online. Percentiles provided are 2.5 per cent, 16 per cent, 50 per cent, 84 per cent, and 97.5 per cent. SFR(SED) corresponds to the average SFR over the last 100 Myr of the SFH. $\chi^2_{red} = \chi^2/N_{bands}$ is the reduced $\chi^2$ of the best-fitting model and $N_{bands}$ is the number of bands observed with non-zero flux.

<sup>a</sup>AGN_flag = 1 indicates sources that lie in the AGN region of the MEx diagram (Section 7.4.1).

reasonable for the sample (e.g. Section 7.4.2). Below we show our results using stellar mass stacks for four redshift windows.

### 7.4.1 Hβ and [O III] window ($0.74 < z < 2.31$)

We start with galaxies with both Hβ and [O III] grism coverage ($0.74 < z_{grism} < 2.31$) because it is one of the largest groups we consider ($N = 1040$ with criterion 1–8) and the ratio [O III]/Hβ as a function of stellar mass, known as a the MEx diagram, has been established as a reliable tool for distinguishing star forming galaxies (SFGs) and AGN at both low (Juneau et al. 2014) and high redshifts (Coil et al. 2015; Kashino et al. 2019). The results of Kashino et al. (2019) and Coil et al. (2015) suggest that the demarcation line to distinguish SFGs and AGN should shift to higher stellar masses with increasing redshift, requiring a 0.5 and 0.75 dex shift at $z \sim 1.6$ and $\sim 2.3$, respectively. We use the demarcation from Kashino et al. (2019) as our reference because we are examining similar redshifts ($z \sim 1.0$ and $\sim 1.6$). The position on the MEx diagram of individual galaxies in our subsample is shown in Fig. 16 (bottom). We find that

10.4 per cent of the WISP sources in this subsample are detected in both Hβ and [O III] (S/N > 3), 61.1 per cent detected only in [O III], and the rest are undetected in both lines (S/N < 3; 28.5 per cent). For Hβ undetected cases, we use the $3\sigma$ Hβ error and treat the ratio as a lower limit. We find 59 individual sources above the AGN lower boundary line, which are excluded from the stacks.

We subdivide galaxies in this window into two redshift ranges, $0.74 < z < 1.22$ and $1.22 \le z < 2.31$ ($z = 1.22$ is the median for this window), and each of those into five equal-number bins in stellar mass (10 bins total). The spectra of these stellar mass stacks and their position on the MEx diagram are shown in Fig. 16. The average galaxy properties and emission-line values for these stacks are listed in Table 12. As expected, most of the stacks lie in the SFG region of the diagram. However, despite excluding all individual galaxies with emission-line ratios or upper limits that lie in the AGN region of the MEx diagram prior to stacking (purple squares), the position of the highest mass stacks for each redshift remains on/above the lower AGN boundary. We attribute this result to the 28.5 per cent of individual sources that are unconstrained in the MEx diagram (i.e. those with S/N < 3 for both [O III] and Hβ), together with the fact
<figure><img src="image_16.png" /><figcaption>**Figure 15.** Top row: native resolution 10 arcsec × 10 arcsec image thumbnails (linear scale) of the available photometry for Par79_12 (i.e. parallel field 79, object 12). The last panel shows the SExTRACTOR segmentation map, based on F110W and F160W, which is an input for TPHOT, with object 12 indicated. Bottom left: the MAGPHYS best-fitting SED (black line) for Par79_12. The red squares are the observed photometry and the black circles are the corresponding model values. The blue line shows the predicted intrinsic stellar population SED (without attenuation). Bottom right: the posterior PDFs for stellar mass and SFR are also shown. The available photometric coverage is sufficient to accurately constrain stellar masses (~0.1 dex), however SFRs have poorer constraints due to the lack of rest-frame IR data (i.e. age/dust reddening degeneracy; ~0.3 dex).</figcaption></figure>

<table><caption>**Table 11.** Stellar mass and SFR percentiles from MAGPHYS for the 1937 WISP sources with 'robust' spectroscopy and photometry (criterion 1–4 in Section 7.1).</caption><thead><tr><th rowspan="2">Par</th><th rowspan="2">Obj</th><th rowspan="2">z<sub>grism</sub></th><th rowspan="2">z<sub>grism</sub>, err</th><th rowspan="2">AGN_flag<sup>a</sup></th><th colspan="3">log [M<sub>*</sub>/M<sub>☉</sub>]</th><th colspan="6">log [SFR(SED)/(M<sub>☉</sub>yr<sup>-1</sup>)]</th><th rowspan="2">χ<sup>2</sup><sub>red</sub></th><th rowspan="2">N<sub>bands</sub></th></tr><tr><th>2.5</th><th>16</th><th>50</th><th>84</th><th>97.5</th><th>2.5</th><th>16</th><th>50</th><th>84</th><th>97.5</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>0.5084</td><td>0.0013</td><td>0</td><td>9.92</td><td>10.03</td><td>10.15</td><td>10.26</td><td>10.40</td><td>0.01</td><td>0.73</td><td>1.16</td><td>1.58</td><td>1.90</td><td>0.011</td><td>5</td></tr><tr><td>1</td><td>13</td><td>0.5309</td><td>0.0011</td><td>0</td><td>9.80</td><td>9.94</td><td>10.02</td><td>10.13</td><td>10.21</td><td>-0.60</td><td>0.26</td><td>0.92</td><td>1.28</td><td>1.74</td><td>0.055</td><td>7</td></tr><tr><td>1</td><td>15</td><td>0.6699</td><td>0.0011</td><td>0</td><td>9.86</td><td>9.96</td><td>10.04</td><td>10.13</td><td>10.22</td><td>0.68</td><td>0.95</td><td>1.32</td><td>1.73</td><td>2.08</td><td>0.464</td><td>7</td></tr><tr><td>1</td><td>28</td><td>1.3443</td><td>0.0028</td><td>0</td><td>9.41</td><td>9.50</td><td>9.61</td><td>9.68</td><td>9.80</td><td>1.07</td><td>1.16</td><td>1.32</td><td>1.48</td><td>1.58</td><td>0.297</td><td>7</td></tr><tr><td>1</td><td>41</td><td>1.3065</td><td>0.0018</td><td>0</td><td>9.67</td><td>9.81</td><td>9.89</td><td>10.00</td><td>10.13</td><td>0.91</td><td>1.21</td><td>1.53</td><td>1.77</td><td>1.94</td><td>0.326</td><td>7</td></tr></tbody></table>

Notes. A full ASCII version of this table is available online. Percentiles provided are 2.5 per cent, 16 per cent, 50 per cent, 84 per cent, and 97.5 per cent. SFR(SED) corresponds to the average SFR over the last 100 Myr of the SFH. $\chi^2_{red} = \chi^2/N_{bands}$ is the reduced $\chi^2$ of the best-fitting model and $N_{bands}$ is the number of bands observed with non-zero flux.

<sup>a</sup>AGN_flag = 1 indicates sources that lie in the AGN region of the MEx diagram (Section 7.4.1).

reasonable for the sample (e.g. Section 7.4.2). Below we show our results using stellar mass stacks for four redshift windows.

### 7.4.1 Hβ and [O III] window ($0.74 < z < 2.31$)

We start with galaxies with both Hβ and [O III] grism coverage ($0.74 < z_{grism} < 2.31$) because it is one of the largest groups we consider ($N = 1040$ with criterion 1–8) and the ratio [O III]/Hβ as a function of stellar mass, known as a the MEx diagram, has been established as a reliable tool for distinguishing star forming galaxies (SFGs) and AGN at both low (Juneau et al. 2014) and high redshifts (Coil et al. 2015; Kashino et al. 2019). The results of Kashino et al. (2019) and Coil et al. (2015) suggest that the demarcation line to distinguish SFGs and AGN should shift to higher stellar masses with increasing redshift, requiring a 0.5 and 0.75 dex shift at $z \sim 1.6$ and $\sim 2.3$, respectively. We use the demarcation from Kashino et al. (2019) as our reference because we are examining similar redshifts ($z \sim 1.0$ and $\sim 1.6$). The position on the MEx diagram of individual galaxies in our subsample is shown in Fig. 16 (bottom). We find that

10.4 per cent of the WISP sources in this subsample are detected in both Hβ and [O III] (S/N > 3), 61.1 per cent detected only in [O III], and the rest are undetected in both lines (S/N < 3; 28.5 per cent). For Hβ undetected cases, we use the $3\sigma$ Hβ error and treat the ratio as a lower limit. We find 59 individual sources above the AGN lower boundary line, which are excluded from the stacks.

We subdivide galaxies in this window into two redshift ranges, $0.74 < z < 1.22$ and $1.22 \le z < 2.31$ ($z = 1.22$ is the median for this window), and each of those into five equal-number bins in stellar mass (10 bins total). The spectra of these stellar mass stacks and their position on the MEx diagram are shown in Fig. 16. The average galaxy properties and emission-line values for these stacks are listed in Table 12. As expected, most of the stacks lie in the SFG region of the diagram. However, despite excluding all individual galaxies with emission-line ratios or upper limits that lie in the AGN region of the MEx diagram prior to stacking (purple squares), the position of the highest mass stacks for each redshift remains on/above the lower AGN boundary. We attribute this result to the 28.5 per cent of individual sources that are unconstrained in the MEx diagram (i.e. those with S/N < 3 for both [O III] and Hβ), together with the fact
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Top: stacked spectra in the Hβ and [O III] window normalized to [O III] total flux in bins of stellar mass for our subsample at 0.74 < z < 2.31 (N = 1040 with criteria 1–8). The median log M* is indicated in each panel. The spectral fits are shown by the orange lines. Bottom: MEx diagram for our sample. The solid (dashed) red lines correspond to the lower (upper) boundaries of Juneau et al. (2014) shifted to higher masses by 0.5 dex (i.e. to the right), corresponding to the relation found at z ~ 1.6 by Kashino et al. (2019), and up by 0.13 dex to account for using total [O III] instead of only [O III]λ5007. Small black and grey points denote individual galaxies where MEx positions are constrained (71.5 per cent of sample), with median error bars given on the middle-left, and AGN candidates are indicated by purple squares. Hβ undetected cases are treated as lower limits (see Section 7.4.1). The large circles/triangles (colour based on median log M*), correspond to the *observed* values from the stacked spectra shown at the top (i.e. Hβ is not corrected for stellar absorption). Stack x-axis error bars denote the 1σ mass range spanned by each bin (Table 12 lists full mass range). The y-axis error bars denote the line ratio error on the stacked spectra, which are smaller than the symbol sizes in this case (<0.05 dex; see Table 12). Despite excluding AGN candidates in the stacking, the position of our highest mass stacks remain on/above the lower AGN boundary. We attribute this to the 28.5 per cent of our individual sources being unconstrained (S/N < 3 in both [O III] and Hβ), with larger log M* galaxies preferentially lacking detection in these lines (see Section 7.4.1).</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Top: stacked spectra in the Hβ and [O III] window normalized to [O III] total flux in bins of stellar mass for our subsample at 0.74 < z < 2.31 (N = 1040 with criteria 1–8). The median log M* is indicated in each panel. The spectral fits are shown by the orange lines. Bottom: MEx diagram for our sample. The solid (dashed) red lines correspond to the lower (upper) boundaries of Juneau et al. (2014) shifted to higher masses by 0.5 dex (i.e. to the right), corresponding to the relation found at z ~ 1.6 by Kashino et al. (2019), and up by 0.13 dex to account for using total [O III] instead of only [O III]λ5007. Small black and grey points denote individual galaxies where MEx positions are constrained (71.5 per cent of sample), with median error bars given on the middle-left, and AGN candidates are indicated by purple squares. Hβ undetected cases are treated as lower limits (see Section 7.4.1). The large circles/triangles (colour based on median log M*), correspond to the *observed* values from the stacked spectra shown at the top (i.e. Hβ is not corrected for stellar absorption). Stack x-axis error bars denote the 1σ mass range spanned by each bin (Table 12 lists full mass range). The y-axis error bars denote the line ratio error on the stacked spectra, which are smaller than the symbol sizes in this case (<0.05 dex; see Table 12). Despite excluding AGN candidates in the stacking, the position of our highest mass stacks remain on/above the lower AGN boundary. We attribute this to the 28.5 per cent of our individual sources being unconstrained (S/N < 3 in both [O III] and Hβ), with larger log M* galaxies preferentially lacking detection in these lines (see Section 7.4.1).</figcaption></figure>
<table><caption>**Table 12.** Average properties, emission-line luminosities, and line ratios for N = 1040 stacked spectra in the Hβ and [O III] window (0.74 < z < 2.31) that satisfy criterion (1)–(8).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>⟨log M<sub>*</sub>⟩</th><th>Hβ<br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>[O III]</th><th>[O III]<br>Hβ</th></tr></thead><tbody><tr><td></td><td></td><td>0.74 &lt; z<sub>grism</sub> &lt; 1.22 (z ~ 1.0)</td><td></td><td></td><td></td></tr><tr><td>104</td><td>[7.59, 8.82]</td><td>8.50</td><td>1.09 ± 0.06</td><td>7.27 ± 0.11</td><td>6.69 ± 0.37</td></tr><tr><td>104</td><td>[8.83, 9.27]</td><td>9.09</td><td>1.24 ± 0.06</td><td>7.24 ± 0.11</td><td>5.82 ± 0.31</td></tr><tr><td>104</td><td>[9.29, 9.71]</td><td>9.46</td><td>1.09 ± 0.06</td><td>5.01 ± 0.09</td><td>4.60 ± 0.28</td></tr><tr><td>104</td><td>[9.72,10.12]</td><td>9.93</td><td>1.42 ± 0.09</td><td>4.74 ± 0.11</td><td>3.34 ± 0.23</td></tr><tr><td>104</td><td>[10.12,11.60]</td><td>10.45</td><td>1.17 ± 0.11</td><td>2.92 ± 0.15</td><td>2.49 ± 0.27</td></tr><tr><td></td><td></td><td>1.22 ≤ z<sub>grism</sub> &lt; 2.31 (z ~ 1.6)</td><td></td><td></td><td></td></tr><tr><td>104</td><td>[7.77, 8.85]</td><td>8.58</td><td>2.11 ± 0.10</td><td>20.56 ± 0.25</td><td>9.72 ± 0.49</td></tr><tr><td>104</td><td>[8.86, 9.19]</td><td>9.03</td><td>3.60 ± 0.15</td><td>23.11 ± 0.18</td><td>6.42 ± 0.27</td></tr><tr><td>104</td><td>[9.19, 9.47]</td><td>9.31</td><td>4.70 ± 0.16</td><td>24.50 ± 0.18</td><td>5.22 ± 0.19</td></tr><tr><td>104</td><td>[9.47, 9.89]</td><td>9.67</td><td>3.82 ± 0.25</td><td>20.00 ± 0.31</td><td>5.24 ± 0.35</td></tr><tr><td>104</td><td>[9.89,11.26]</td><td>10.18</td><td>2.60 ± 0.29</td><td>10.89 ± 0.30</td><td>4.18 ± 0.48</td></tr></tbody></table>

Note. Hβ is not corrected for stellar absorption. [O III] is the sum of [O III]λλ4959, 5007.

that higher stellar mass galaxies have preferentially weaker [O III] and Hβ relative to Hα than lower stellar mass galaxies (e.g. fig. 5 of Battisti et al. 2022). As a reference, the lowest stellar mass bins for each redshift range have ~90 per cent of individual sources detected in [O III] or Hβ, whereas the highest stellar mass bins have 30 per cent–40 per cent of individual sources detected in [O III] or Hβ (for these cases, usually Hα and [S II] are detected). Thus, a majority of sources in the higher mass bins might be AGN that we are unable to identify individually using the MEx diagram. This indicates that there may be significant AGN contamination for WISP emission-line sources at high stellar masses.

These WISP results are consistent with Förster Schreiber et al. (2019), who examined AGN occurrence rates, $f_{AGN}$, in a sample of 600 galaxies at 0.6 < z < 2.7 in KMOS$^{3D}$ (K-band Multi Object Spectrograph). They found that galaxies with $log(M_*/M_\odot) < 10.2$ have an AGN occurrence rate of $f_{AGN} \lesssim 10$ per cent, with $f_{AGN}$ increasing dramatically with increasing mass (e.g. ~60 per cent at $log(M_*/M_\odot) = 11$; see their fig. 6). These results are also similar to findings in Henry et al. (2021), which included both the WISP and CLEAR + 3D-HST surveys. For the subsequent analysis, we do not exclude galaxies based on a stellar mass threshold (e.g. Battisti et al. 2022), but caution that AGN may contaminate bins above $log(M_*/M_\odot) \gtrsim 10.2$.

$$7.4.2 \quad H\alpha + [N\text{II}] \text{ and } [S\text{II}] \text{ window } (0.30 < z < 1.45)$$

Next, we consider galaxies with grism coverage of Hα + [N II] and [S II] (0.30 < z<sub>grism</sub> < 1.45; N = 1191 with criterion 1–8), which is our largest group size. This group can be used to examine how representative our sample is of typical SFGs at these redshifts. To do this, we characterize WISP galaxies relative to the star-forming galaxy MS (log SFR versus logM<sub>*</sub>; e.g. Brinchmann et al. 2004; Speagle et al. 2014; Leslie et al. 2020), using SFRs based on Hα (described below).

We divide galaxies in this window into three redshift ranges, 0.30 < z ≤ 0.83, 0.83 < z ≤ 1.15, and 1.15 ≤ z < 1.45 (equal number in each), and each of those into four equal-number bins in stellar mass (12 bins total). The spectra of these stellar mass stacks are shown in Fig. 17. The average galaxy properties and emission-line values for these stacks are listed in Table 13.

In order to estimate SFRs from Hα, we need to apply several corrections. We note that we only apply correction factors on stacked

spectra based on groups of N > 100 galaxies to minimize the impact of intrinsic variation of the correction factors. First, we deblend the Hα + [N II] line using the stellar mass- and redshift-dependent functional relation from Faisst et al. (2018), which used ~190 000 SDSS galaxies combined with the observed BPT locus evolution of SFGs from 0 < z < 2.5. These corrections were derived over the range of 0 < z < 2.7 and 8.5 < log(M<sub>*</sub>/M<sub>☉</sub>) < 11.0 and have an intrinsic scatter of ~0.2 dex. A small fraction of our stellar masses are log(M<sub>*</sub>/M<sub>☉</sub>) < 8.5 but extrapolating the Faisst et al. (2018) relation to lower masses should have minimal impact as the expected [N II] contribution is < 5 per cent at all redshifts in this mass regime. Based on this relation, the contribution of [N II] range from ~6 per cent for the lowest mass bins, up to ~35 per cent for the most massive bins.

Second, we correct Hα for stellar absorption, which cannot be directly fit in the low-resolution grism spectra. To correct for stellar absorption, we use the stellar mass- and SFR-dependent functional relation from Kashino & Inoue (2019), which is based on trends observed for ~190 000 SDSS galaxies. The fractional corrections were determined over the range of 7.2 < log(M<sub>*</sub>/M<sub>☉</sub>) < 11.4, with an intrinsic scatter of ~10 per cent–20 per cent. For each stack, we use the median value of stellar masses and SFRs from MAGPHYS. However, if the inferred SFR from MAGPHYS is lower than SFR(Hα<sub>obs</sub>) (corrected for [N II] blending), then we adopt the latter as the input to determine the fraction of stellar absorption because SFR(Hα<sub>obs</sub>) can be considered a lower limit. Due to the relatively high specific-SFR (SFR/M<sub>*</sub>) of WISP emission-line galaxies, the Hα absorption correction factor is negligible for most of the sample (~1 per cent).

Lastly, we correct for dust extinction. Due to the fact that Hβ is not available for most galaxies in this sample (due to coverage and/or depth), we cannot use the Balmer decrement for dust corrections. Instead, we use the $\tau'_B - \log M_*$ relation of SDSS galaxies (z ~ 0; Battisti et al. 2022), where $\tau'_B$ is the Balmer optical depth, and assume a 0.15 dex uncertainty on $\tau'_B$ for a given log M<sub>*</sub>. This relation appears to show minimal evolution with redshift (e.g. Battisti et al. 2022; Shapley et al. 2022). SFRs based on these corrections were found to be roughly consistent with SED-based SFRs in Battisti et al. (2022) for a similar sample. We adopt the MW extinction curve from Fitzpatrick et al. (2019), but note that most extinction curves have shapes that are very similar in the optical/NIR regime such that this choice has a smaller impact relative to the uncertainty on $\tau'_B$.
<table><caption>**Table 12.** Average properties, emission-line luminosities, and line ratios for N = 1040 stacked spectra in the Hβ and [O III] window (0.74 < z < 2.31) that satisfy criterion (1)–(8).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>log M<sub>*</sub></th><th>Hβ<br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>[O III]</th><th>[O III]<br>Hβ</th></tr></thead><tbody><tr><td></td><td></td><td>0.74 &lt; z<sub>grism</sub> &lt; 1.22 (z ~ 1.0)</td><td></td><td></td><td></td></tr><tr><td>104</td><td>[7.59, 8.82]</td><td>8.50</td><td>1.09 ± 0.06</td><td>7.27 ± 0.11</td><td>6.69 ± 0.37</td></tr><tr><td>104</td><td>[8.83, 9.27]</td><td>9.09</td><td>1.24 ± 0.06</td><td>7.24 ± 0.11</td><td>5.82 ± 0.31</td></tr><tr><td>104</td><td>[9.29, 9.71]</td><td>9.46</td><td>1.09 ± 0.06</td><td>5.01 ± 0.09</td><td>4.60 ± 0.28</td></tr><tr><td>104</td><td>[9.72,10.12]</td><td>9.93</td><td>1.42 ± 0.09</td><td>4.74 ± 0.11</td><td>3.34 ± 0.23</td></tr><tr><td>104</td><td>[10.12,11.60]</td><td>10.45</td><td>1.17 ± 0.11</td><td>2.92 ± 0.15</td><td>2.49 ± 0.27</td></tr><tr><td></td><td></td><td>1.22 ≤ z<sub>grism</sub> &lt; 2.31 (z ~ 1.6)</td><td></td><td></td><td></td></tr><tr><td>104</td><td>[7.77, 8.85]</td><td>8.58</td><td>2.11 ± 0.10</td><td>20.56 ± 0.25</td><td>9.72 ± 0.49</td></tr><tr><td>104</td><td>[8.86, 9.19]</td><td>9.03</td><td>3.60 ± 0.15</td><td>23.11 ± 0.18</td><td>6.42 ± 0.27</td></tr><tr><td>104</td><td>[9.19, 9.47]</td><td>9.31</td><td>4.70 ± 0.16</td><td>24.50 ± 0.18</td><td>5.22 ± 0.19</td></tr><tr><td>104</td><td>[9.47, 9.89]</td><td>9.67</td><td>3.82 ± 0.25</td><td>20.00 ± 0.31</td><td>5.24 ± 0.35</td></tr><tr><td>104</td><td>[9.89,11.26]</td><td>10.18</td><td>2.60 ± 0.29</td><td>10.89 ± 0.30</td><td>4.18 ± 0.48</td></tr></tbody></table>

Note. Hβ is not corrected for stellar absorption. [O III] is the sum of [O III]λλ4959, 5007.

that higher stellar mass galaxies have preferentially weaker [O III] and Hβ relative to Hα than lower stellar mass galaxies (e.g. fig. 5 of Battisti et al. 2022). As a reference, the lowest stellar mass bins for each redshift range have ~90 per cent of individual sources detected in [O III] or Hβ, whereas the highest stellar mass bins have 30 per cent–40 per cent of individual sources detected in [O III] or Hβ (for these cases, usually Hα and [S II] are detected). Thus, a majority of sources in the higher mass bins might be AGN that we are unable to identify individually using the MEx diagram. This indicates that there may be significant AGN contamination for WISP emission-line sources at high stellar masses.

These WISP results are consistent with Förster Schreiber et al. (2019), who examined AGN occurrence rates, $f_{AGN}$, in a sample of 600 galaxies at 0.6 < z < 2.7 in KMOS$^{3D}$ (K-band Multi Object Spectrograph). They found that galaxies with $log(M_*/M_\odot) < 10.2$ have an AGN occurrence rate of $f_{AGN} \lesssim 10$ per cent, with $f_{AGN}$ increasing dramatically with increasing mass (e.g. ~60 per cent at $log(M_*/M_\odot) = 11$; see their fig. 6). These results are also similar to findings in Henry et al. (2021), which included both the WISP and CLEAR + 3D-HST surveys. For the subsequent analysis, we do not exclude galaxies based on a stellar mass threshold (e.g. Battisti et al. 2022), but caution that AGN may contaminate bins above $log(M_*/M_\odot) \gtrsim 10.2$.

$$7.4.2 \quad H\alpha + [N\text{II}] \text{ and } [S\text{II}] \text{ window } (0.30 < z < 1.45)$$

Next, we consider galaxies with grism coverage of Hα + [N II] and [S II] (0.30 < z<sub>grism</sub> < 1.45; N = 1191 with criterion 1–8), which is our largest group size. This group can be used to examine how representative our sample is of typical SFGs at these redshifts. To do this, we characterize WISP galaxies relative to the star-forming galaxy MS (log SFR versus logM<sub>*</sub>; e.g. Brinchmann et al. 2004; Speagle et al. 2014; Leslie et al. 2020), using SFRs based on Hα (described below).

We divide galaxies in this window into three redshift ranges, 0.30 < z ≤ 0.83, 0.83 < z ≤ 1.15, and 1.15 ≤ z < 1.45 (equal number in each), and each of those into four equal-number bins in stellar mass (12 bins total). The spectra of these stellar mass stacks are shown in Fig. 17. The average galaxy properties and emission-line values for these stacks are listed in Table 13.

In order to estimate SFRs from Hα, we need to apply several corrections. We note that we only apply correction factors on stacked

spectra based on groups of N > 100 galaxies to minimize the impact of intrinsic variation of the correction factors. First, we deblend the Hα + [N II] line using the stellar mass- and redshift-dependent functional relation from Faisst et al. (2018), which used ~190 000 SDSS galaxies combined with the observed BPT locus evolution of SFGs from 0 < z < 2.5. These corrections were derived over the range of 0 < z < 2.7 and 8.5 < log(M<sub>*</sub>/M<sub>☉</sub>) < 11.0 and have an intrinsic scatter of ~0.2 dex. A small fraction of our stellar masses are log(M<sub>*</sub>/M<sub>☉</sub>) < 8.5 but extrapolating the Faisst et al. (2018) relation to lower masses should have minimal impact as the expected [N II] contribution is < 5 per cent at all redshifts in this mass regime. Based on this relation, the contribution of [N II] range from ~6 per cent for the lowest mass bins, up to ~35 per cent for the most massive bins.

Second, we correct Hα for stellar absorption, which cannot be directly fit in the low-resolution grism spectra. To correct for stellar absorption, we use the stellar mass- and SFR-dependent functional relation from Kashino & Inoue (2019), which is based on trends observed for ~190 000 SDSS galaxies. The fractional corrections were determined over the range of 7.2 < log(M<sub>*</sub>/M<sub>☉</sub>) < 11.4, with an intrinsic scatter of ~10 per cent–20 per cent. For each stack, we use the median value of stellar masses and SFRs from MAGPHYS. However, if the inferred SFR from MAGPHYS is lower than SFR(Hα<sub>obs</sub>) (corrected for [N II] blending), then we adopt the latter as the input to determine the fraction of stellar absorption because SFR(Hα<sub>obs</sub>) can be considered a lower limit. Due to the relatively high specific-SFR (SFR/M<sub>*</sub>) of WISP emission-line galaxies, the Hα absorption correction factor is negligible for most of the sample (~1 per cent).

Lastly, we correct for dust extinction. Due to the fact that Hβ is not available for most galaxies in this sample (due to coverage and/or depth), we cannot use the Balmer decrement for dust corrections. Instead, we use the $\tau'_B - \log M_*$ relation of SDSS galaxies (z ~ 0; Battisti et al. 2022), where $\tau'_B$ is the Balmer optical depth, and assume a 0.15 dex uncertainty on $\tau'_B$ for a given log M<sub>*</sub>. This relation appears to show minimal evolution with redshift (e.g. Battisti et al. 2022; Shapley et al. 2022). SFRs based on these corrections were found to be roughly consistent with SED-based SFRs in Battisti et al. (2022) for a similar sample. We adopt the MW extinction curve from Fitzpatrick et al. (2019), but note that most extinction curves have shapes that are very similar in the optical/NIR regime such that this choice has a smaller impact relative to the uncertainty on $\tau'_B$.
<figure><img src="image_18.png" /><figcaption>**Figure 17.** Top: similar to Fig. 16, but now for the $H\alpha + [N\text{II}]$ and $[S\text{II}]$ window and the stacked spectra are normalized to $H\alpha + [N\text{II}]$ total flux. Bottom: the galaxy MS (log SFR versus log$M_*$), for our sample binned by stellar mass (large coloured symbols) across three redshift ranges, which are distinguished by the line style connecting the filled data points (not a fit; $z \sim 0.6, 1.0$, and $1.3$ are solid, dashed, and dotted, respectively). Bins are based on stacked $H\alpha$ without dust corrections (SFR($H\alpha_{\text{obs}}$)) and with dust corrections (SFR($H\alpha_{\text{corr}}$)), where the latter is based on the log$M_*-\tau'_B$ relation (Battisti et al. 2022). The green lines are the galaxy MS from Leslie et al. (2020) at the median redshift of the groups (line styles match as above). Our sample mostly coincides with the MS except for a bias at low masses due to sensitivity limits. The median $H\alpha$ line detection threshold ($5\sigma$) for each redshift range is indicated (bottom left), but we note this has large variation due to differing opportunity lengths.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 17.** Top: similar to Fig. 16, but now for the $H\alpha + [N\,\text{II}]$ and $[S\,\text{II}]$ window and the stacked spectra are normalized to $H\alpha + [N\,\text{II}]$ total flux. Bottom: the galaxy MS (log SFR versus log$M_*$), for our sample binned by stellar mass (large coloured symbols) across three redshift ranges, which are distinguished by the line style connecting the filled data points (not a fit; $z \sim 0.6, 1.0$, and $1.3$ are solid, dashed, and dotted, respectively). Bins are based on stacked $H\alpha$ without dust corrections (SFR($H\alpha_{\text{obs}}$)) and with dust corrections (SFR($H\alpha_{\text{corr}}$)), where the latter is based on the log$M_*-\tau'_B$ relation (Battisti et al. 2022). The green lines are the galaxy MS from Leslie et al. (2020) at the median redshift of the groups (line styles match as above). Our sample mostly coincides with the MS except for a bias at low masses due to sensitivity limits. The median $H\alpha$ line detection threshold ($5\sigma$) for each redshift range is indicated (bottom left), but we note this has large variation due to differing opportunity lengths.</figcaption></figure>
<table><caption>**Table 13.** Average properties, emission-line luminosities, and line ratios for *N* = 1191 stacked spectra in the Hα + [N II] and [S II] window (0.30 < *z* < 1.45) that satisfy criterion (1)–(8).</caption><thead><tr><th rowspan="2">N</th><th rowspan="2">log M<sub>*</sub><br>range</th><th rowspan="2">log M<sub>*</sub></th><th colspan="2">log SFR</th><th rowspan="2">Hα + [N II]</th><th rowspan="2">[S II]</th><th rowspan="2">Hα<sub>obs</sub><br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th rowspan="2">Hα<sub>corr</sub></th></tr><tr><th>Hα<sub>obs</sub></th><th>Hα<sub>corr</sub></th></tr></thead><tbody><tr><td colspan="9" style="text-align:center;">0.30 &lt; z<sub>grism</sub> ≤ 0.83 (z ~ 0.6)</td></tr><tr><td>100</td><td>[7.25, 9.01]</td><td>8.66</td><td>-0.04 ± 0.01</td><td>0.13 ± 0.14</td><td>1.81 ± 0.02</td><td>0.35 ± 0.02</td><td>1.68 ± 0.04</td><td>2.49 ± 0.82</td></tr><tr><td>99</td><td>[9.01, 9.44]</td><td>9.20</td><td>0.11 ± 0.01</td><td>0.36 ± 0.14</td><td>2.73 ± 0.03</td><td>0.79 ± 0.02</td><td>2.40 ± 0.06</td><td>4.29 ± 1.41</td></tr><tr><td>99</td><td>[9.45, 9.84]</td><td>9.63</td><td>0.25 ± 0.02</td><td>0.59 ± 0.14</td><td>4.23 ± 0.05</td><td>1.13 ± 0.03</td><td>3.34 ± 0.13</td><td>7.25 ± 2.39</td></tr><tr><td>99</td><td>[9.84,10.92]</td><td>10.19</td><td>0.29 ± 0.02</td><td>0.75 ± 0.14</td><td>5.28 ± 0.06</td><td>1.28 ± 0.04</td><td>3.59 ± 0.16</td><td>10.58 ± 3.49</td></tr><tr><td colspan="9" style="text-align:center;">0.83 &lt; z<sub>grism</sub> ≤ 1.15 (z ~ 1.0)</td></tr><tr><td>100</td><td>[7.59, 8.93]</td><td>8.62</td><td>0.35 ± 0.01</td><td>0.51 ± 0.14</td><td>4.41 ± 0.04</td><td>0.43 ± 0.03</td><td>4.13 ± 0.08</td><td>6.03 ± 1.98</td></tr><tr><td>99</td><td>[8.94, 9.44]</td><td>9.17</td><td>0.46 ± 0.01</td><td>0.71 ± 0.14</td><td>6.01 ± 0.06</td><td>1.16 ± 0.05</td><td>5.38 ± 0.11</td><td>9.51 ± 3.12</td></tr><tr><td>99</td><td>[9.45,10.04]</td><td>9.76</td><td>0.61 ± 0.03</td><td>0.98 ± 0.14</td><td>9.60 ± 0.08</td><td>2.08 ± 0.06</td><td>7.65 ± 0.48</td><td>17.73 ± 5.90</td></tr><tr><td>99</td><td>[10.04,11.34]</td><td>10.37</td><td>0.72 ± 0.02</td><td>1.24 ± 0.14</td><td>15.04 ± 0.14</td><td>3.31 ± 0.09</td><td>9.84 ± 0.47</td><td>32.40 ± 10.71</td></tr><tr><td colspan="9" style="text-align:center;">1.15 ≤ z<sub>grism</sub> &lt; 1.45 (z ~ 1.3)</td></tr><tr><td>100</td><td>[7.54, 9.02]</td><td>8.63</td><td>0.54 ± 0.01</td><td>0.70 ± 0.14</td><td>6.83 ± 0.07</td><td>0.84 ± 0.07</td><td>6.42 ± 0.12</td><td>9.41 ± 3.08</td></tr><tr><td>99</td><td>[9.04, 9.50]</td><td>9.30</td><td>0.70 ± 0.01</td><td>0.97 ± 0.14</td><td>10.49 ± 0.10</td><td>1.80 ± 0.09</td><td>9.36 ± 0.17</td><td>17.47 ± 5.72</td></tr><tr><td>99</td><td>[9.50, 9.96]</td><td>9.74</td><td>0.77 ± 0.02</td><td>1.13 ± 0.14</td><td>13.35 ± 0.14</td><td>2.65 ± 0.11</td><td>11.04 ± 0.39</td><td>25.33 ± 8.33</td></tr><tr><td>99</td><td>[9.97,11.60]</td><td>10.30</td><td>0.89 ± 0.04</td><td>1.38 ± 0.15</td><td>21.22 ± 0.17</td><td>4.29 ± 0.12</td><td>14.29 ± 1.32</td><td>45.02 ± 15.30</td></tr></tbody></table>

Notes. [S II] is the sum of [S II]λλ6716, 6731. Hα<sub>obs</sub> are values after correcting for [N II] blending, where the uncertainty is the 1σ dispersion in correction values for individual galaxies and the line measurement uncertainties added in quadrature. Hα<sub>corr</sub> are values after also correcting for stellar absorption and dust extinction, with the latter introducing significant uncertainty (see Section 7.4.2).

A comparison of our sample, both before and after dust corrections, to the galaxy MS at these redshifts from Leslie et al. (2020) is shown in Fig. 17. The Leslie et al. (2020) relations are based on stacked radio data from ~200 000 galaxies in the COSMOS (COSMOlogical evolution Survey) field (we use their ‘All’ sample). For our SFRs, we adopt the conversion from Kennicutt & Evans (2012):

$$ \log \left[ \frac{\text{SFR}(\text{H}\alpha)}{\text{M}_\odot \text{yr}^{-1}} \right] = \log \left[ \frac{L(\text{H}\alpha)}{\text{erg s}^{-1}} \right] - 41.27 \quad (2) $$

which assumes the IMF of Kroupa & Weidner (2003), this is comparable to IMF used in MAGPHYS). All of the dust-corrected SFR values with log (M<sub>⋆</sub>/M<sub>☉</sub>) ≳ 9 appear roughly consistent with the MS, indicating they are fully representative of ‘normal’ star-forming galaxies at these redshifts. Even though our WISP galaxies are selected by emission-line strength, this provides a sample similar to those selected by traditional broad-band continuum photometry. This reflects the fact that all star-forming galaxies at z ≳ 0.5 have strong emission lines which WISP can detect.

At the lowest stellar masses (log (M<sub>⋆</sub>/M<sub>☉</sub>) ≲ 9), however, WISP galaxies tend to reside above the MS, which we attribute to the line detection threshold of WISP (~5 × 10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup>; Atek et al. 2010). In other words, WISP can only detect emission lines with high EWs at low stellar masses. We show the lower limit on SFR(Hα<sub>obs</sub>) for this line sensitivity at z = 0.6, 1.0, and 1.3 (median redshifts of our bins) in the lower left of Fig. 17.

### 7.4.3 Hα + [N II], [S II], and [S III] doublet window (0.30 < z < 0.73)

Next, we consider galaxies with grism coverage of Hα + [N II], [S II], and [S III] doublet (0.30 < z<sub>grism</sub> < 0.73; N = 318 with criterion 1–8). The S<sub>32</sub> ≡ [S III]λλ9069,9531/[S II]λλ6716,6731 ratio is a proxy for the ionization parameter of a galaxy and is relatively insensitive to the gas-phase metallicity and ISM pressure (Kewley, Nicholls & Sutherland 2019). However, there is considerable uncertainty regarding the exact conversion of S<sub>32</sub> to ionization parameter because [S II] lines are typically underestimated by photoionization models (Kewley et al. 2019). For this reason, we simply report the S<sub>32</sub> line

ratios instead of ionization parameter. For reference, 16.0 per cent of the WISP sources in our subsample are detected in both [S II] and [S III] (S/N > 3), 26.5 per cent detected only in [S II], and the rest are undetected in both lines (S/N < 3; 57.5 per cent).

We divide galaxies in this window into three equal-number bins in stellar mass over the full redshift range and the spectra of these stacks are shown in Fig. 18 (top). We label the region where the Ca II triplet absorption features occur, which are not accounted for in the continuum fitting (simple polynomial spline), and it appears that this may affect the stacked spectrum in the region near the [S III]λλ9069 line, particularly for the largest stellar mass bin. We enforce a fixed [S III]λλ9532/[S III]λλ9069 ratio such that the impact should be mitigated, however the WISP values should be treated with caution. Attempting to account for this is beyond the scope of our results. The average galaxy properties and emission-line values for these stacks are listed in Table 14.

We show a comparison of the S<sub>32</sub> ratio versus log M<sub>⋆</sub> for WISP relative to the results for the MaNGA (Mapping Nearby Galaxies at Apache Point Observatory; z ~ 0) and MOSDEF (Multi-Object Spectrometer for infra-red exploration Deep Evolution Field; z ~ 1.5) samples (Sanders et al. 2020) in Fig. 18 (bottom). We show both the observed and extinction corrected line ratios. For MaNGA and MOSDEF, these extinction corrections are based on direct measurements of Balmer decrements (Hα/Hβ) and assuming an MW extinction curve (Cardelli, Clayton & Mathis 1989). For WISP, we do not have Hβ in our redshift window and, similar to the previous section, we adopt the τ<sub>B</sub>–log M<sub>⋆</sub> relation from Battisti et al. (2022, with 0.15 dex uncertainty) and the MW extinction curve from Fitzpatrick et al. (2019). We again note that different extinction curves give a similar outcome because of the similarity in their shape in the NIR (due to using a line ratio). The WISP sample shows similar values to the MaNGA sample relation prior to making corrections for diffuse-ionized gas (DIG). If the WISP galaxies (z ~ 0.55) have a similar component of DIG as MaNGA (z ~ 0), then this would imply they have comparable ionization parameter values as the MaNGA and MOSDEF samples. We also find a decreasing value S<sub>32</sub> with increasing log M<sub>⋆</sub>, similar to findings of Sanders et al. (2020) at both lower and higher redshifts, indicating
<table><caption>**Table 13.** Average properties, emission-line luminosities, and line ratios for N = 1191 stacked spectra in the Hα + [N II] and [S II] window (0.30 < z < 1.45) that satisfy criterion (1)–(8).</caption><thead><tr><th rowspan="2">N</th><th rowspan="2">log M<sub>*</sub><br>range</th><th rowspan="2">log M<sub>*</sub></th><th colspan="2">log SFR</th><th rowspan="2">Hα + [N II]</th><th rowspan="2">[S II]</th><th rowspan="2">Hα<sub>obs</sub><br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th rowspan="2">Hα<sub>corr</sub></th></tr><tr><th>Hα<sub>obs</sub></th><th>Hα<sub>corr</sub></th></tr></thead><tbody><tr><td colspan="9" style="text-align:center;">0.30 &lt; z<sub>grism</sub> ≤ 0.83 (z ~ 0.6)</td></tr><tr><td>100</td><td>[7.25, 9.01]</td><td>8.66</td><td>-0.04 ± 0.01</td><td>0.13 ± 0.14</td><td>1.81 ± 0.02</td><td>0.35 ± 0.02</td><td>1.68 ± 0.04</td><td>2.49 ± 0.82</td></tr><tr><td>99</td><td>[9.01, 9.44]</td><td>9.20</td><td>0.11 ± 0.01</td><td>0.36 ± 0.14</td><td>2.73 ± 0.03</td><td>0.79 ± 0.02</td><td>2.40 ± 0.06</td><td>4.29 ± 1.41</td></tr><tr><td>99</td><td>[9.45, 9.84]</td><td>9.63</td><td>0.25 ± 0.02</td><td>0.59 ± 0.14</td><td>4.23 ± 0.05</td><td>1.13 ± 0.03</td><td>3.34 ± 0.13</td><td>7.25 ± 2.39</td></tr><tr><td>99</td><td>[9.84,10.92]</td><td>10.19</td><td>0.29 ± 0.02</td><td>0.75 ± 0.14</td><td>5.28 ± 0.06</td><td>1.28 ± 0.04</td><td>3.59 ± 0.16</td><td>10.58 ± 3.49</td></tr><tr><td colspan="9" style="text-align:center;">0.83 &lt; z<sub>grism</sub> ≤ 1.15 (z ~ 1.0)</td></tr><tr><td>100</td><td>[7.59, 8.93]</td><td>8.62</td><td>0.35 ± 0.01</td><td>0.51 ± 0.14</td><td>4.41 ± 0.04</td><td>0.43 ± 0.03</td><td>4.13 ± 0.08</td><td>6.03 ± 1.98</td></tr><tr><td>99</td><td>[8.94, 9.44]</td><td>9.17</td><td>0.46 ± 0.01</td><td>0.71 ± 0.14</td><td>6.01 ± 0.06</td><td>1.16 ± 0.05</td><td>5.38 ± 0.11</td><td>9.51 ± 3.12</td></tr><tr><td>99</td><td>[9.45,10.04]</td><td>9.76</td><td>0.61 ± 0.03</td><td>0.98 ± 0.14</td><td>9.60 ± 0.08</td><td>2.08 ± 0.06</td><td>7.65 ± 0.48</td><td>17.73 ± 5.90</td></tr><tr><td>99</td><td>[10.04,11.34]</td><td>10.37</td><td>0.72 ± 0.02</td><td>1.24 ± 0.14</td><td>15.04 ± 0.14</td><td>3.31 ± 0.09</td><td>9.84 ± 0.47</td><td>32.40 ± 10.71</td></tr><tr><td colspan="9" style="text-align:center;">1.15 ≤ z<sub>grism</sub> &lt; 1.45 (z ~ 1.3)</td></tr><tr><td>100</td><td>[7.54, 9.02]</td><td>8.63</td><td>0.54 ± 0.01</td><td>0.70 ± 0.14</td><td>6.83 ± 0.07</td><td>0.84 ± 0.07</td><td>6.42 ± 0.12</td><td>9.41 ± 3.08</td></tr><tr><td>99</td><td>[9.04, 9.50]</td><td>9.30</td><td>0.70 ± 0.01</td><td>0.97 ± 0.14</td><td>10.49 ± 0.10</td><td>1.80 ± 0.09</td><td>9.36 ± 0.17</td><td>17.47 ± 5.72</td></tr><tr><td>99</td><td>[9.50, 9.96]</td><td>9.74</td><td>0.77 ± 0.02</td><td>1.13 ± 0.14</td><td>13.35 ± 0.14</td><td>2.65 ± 0.11</td><td>11.04 ± 0.39</td><td>25.33 ± 8.33</td></tr><tr><td>99</td><td>[9.97,11.60]</td><td>10.30</td><td>0.89 ± 0.04</td><td>1.38 ± 0.15</td><td>21.22 ± 0.17</td><td>4.29 ± 0.12</td><td>14.29 ± 1.32</td><td>45.02 ± 15.30</td></tr></tbody></table>

Notes. [S II] is the sum of [S II]λλ6716, 6731. Hα<sub>obs</sub> are values after correcting for [N II] blending, where the uncertainty is the 1σ dispersion in correction values for individual galaxies and the line measurement uncertainties added in quadrature. Hα<sub>corr</sub> are values after also correcting for stellar absorption and dust extinction, with the latter introducing significant uncertainty (see Section 7.4.2).

A comparison of our sample, both before and after dust corrections, to the galaxy MS at these redshifts from Leslie et al. (2020) is shown in Fig. 17. The Leslie et al. (2020) relations are based on stacked radio data from ~200 000 galaxies in the COSMOS (COSMOlogical evolution Survey) field (we use their ‘All’ sample). For our SFRs, we adopt the conversion from Kennicutt & Evans (2012):

$$ \log \left[ \frac{\text{SFR}(H\alpha)}{\text{M}_\odot \text{yr}^{-1}} \right] = \log \left[ \frac{L(H\alpha)}{\text{erg s}^{-1}} \right] - 41.27 \quad (2) $$

which assumes the IMF of Kroupa & Weidner (2003), this is comparable to IMF used in MAGPHYS). All of the dust-corrected SFR values with log(M<sub>*</sub>/M<sub>☉</sub>) ≳ 9 appear roughly consistent with the MS, indicating they are fully representative of ‘normal’ star-forming galaxies at these redshifts. Even though our WISP galaxies are selected by emission-line strength, this provides a sample similar to those selected by traditional broad-band continuum photometry. This reflects the fact that all star-forming galaxies at z ≳ 0.5 have strong emission lines which WISP can detect.

At the lowest stellar masses (log(M<sub>*</sub>/M<sub>☉</sub>) ≲ 9), however, WISP galaxies tend to reside above the MS, which we attribute to the line detection threshold of WISP (~5 × 10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup>; Atek et al. 2010). In other words, WISP can only detect emission lines with high EWs at low stellar masses. We show the lower limit on SFR(Hα<sub>obs</sub>) for this line sensitivity at z = 0.6, 1.0, and 1.3 (median redshifts of our bins) in the lower left of Fig. 17.

### 7.4.3 Hα + [N II], [S II], and [S III] doublet window (0.30 < z < 0.73)

Next, we consider galaxies with grism coverage of Hα + [N II], [S II], and [S III] doublet (0.30 < z<sub>grism</sub> < 0.73; N = 318 with criterion 1–8). The S<sub>32</sub> ≡ [S III]λλ9069,9531/[S II]λλ6716,6731 ratio is a proxy for the ionization parameter of a galaxy and is relatively insensitive to the gas-phase metallicity and ISM pressure (Kewley, Nicholls & Sutherland 2019). However, there is considerable uncertainty regarding the exact conversion of S<sub>32</sub> to ionization parameter because [S II] lines are typically underestimated by photoionization models (Kewley et al. 2019). For this reason, we simply report the S<sub>32</sub> line

ratios instead of ionization parameter. For reference, 16.0 per cent of the WISP sources in our subsample are detected in both [S II] and [S III] (S/N > 3), 26.5 per cent detected only in [S II], and the rest are undetected in both lines (S/N < 3; 57.5 per cent).

We divide galaxies in this window into three equal-number bins in stellar mass over the full redshift range and the spectra of these stacks are shown in Fig. 18 (top). We label the region where the Ca II triplet absorption features occur, which are not accounted for in the continuum fitting (simple polynomial spline), and it appears that this may affect the stacked spectrum in the region near the [S III]λλ9069 line, particularly for the largest stellar mass bin. We enforce a fixed [S III]λλ9532/[S III]λλ9069 ratio such that the impact should be mitigated, however the WISP values should be treated with caution. Attempting to account for this is beyond the scope of our results. The average galaxy properties and emission-line values for these stacks are listed in Table 14.

We show a comparison of the S<sub>32</sub> ratio versus log M<sub>*</sub> for WISP relative to the results for the MaNGA (Mapping Nearby Galaxies at Apache Point Observatory; z ~ 0) and MOSDEF (Multi-Object Spectrometer for infra-red exploration Deep Evolution Field; z ~ 1.5) samples (Sanders et al. 2020) in Fig. 18 (bottom). We show both the observed and extinction corrected line ratios. For MaNGA and MOSDEF, these extinction corrections are based on direct measurements of Balmer decrements (Hα/Hβ) and assuming an MW extinction curve (Cardelli, Clayton & Mathis 1989). For WISP, we do not have Hβ in our redshift window and, similar to the previous section, we adopt the τ<sub>B</sub>–log M<sub>*</sub> relation from Battisti et al. (2022, with 0.15 dex uncertainty) and the MW extinction curve from Fitzpatrick et al. (2019). We again note that different extinction curves give a similar outcome because of the similarity in their shape in the NIR (due to using a line ratio). The WISP sample shows similar values to the MaNGA sample relation prior to making corrections for diffuse-ionized gas (DIG). If the WISP galaxies (z ~ 0.55) have a similar component of DIG as MaNGA (z ~ 0), then this would imply they have comparable ionization parameter values as the MaNGA and MOSDEF samples. We also find a decreasing value S<sub>32</sub> with increasing log M<sub>*</sub>, similar to findings of Sanders et al. (2020) at both lower and higher redshifts, indicating
<figure><img src="image_19.png" /><figcaption>**Figure 18.** Top: similar to Fig. 16, but now for the $H\alpha + [N\text{II}]$, $[S\text{II}]$, and $[S\text{III}]$ window (0.30 < z < 0.73) and the stacked spectra are normalized to $H\alpha + [N\text{II}]$ total flux. The Ca II triplet absorption features are also indicated and appear to affect the stacked spectrum in the region near the $[S\text{III}]\lambda9069$ line, particularly for the largest stellar mass bin. Bottom: we compare the $S_{32}$ ratio versus stellar mass from WISP (z ~ 0.55) to the results in Sanders et al. (2020) for the MaNGA (z ~ 0) and MOSDEF (z ~ 1.5) samples. Small black and grey points denote individual galaxies where $S_{32}$ positions are constrained (42.4 per cent of sample), with median error bars given on the middle left. Coloured open and closed symbols correspond to the stellar mass stacks before and after dust extinction correction, labelled ‘obs’ and ‘dust-corr’, respectively (see Section 7.4.3). The WISP stacks appear most similar to the MaNGA relation before correcting for DIG, perhaps indicating a non-negligible DIG contribution in the WISP sample. All samples show a mildly decreasing $S_{32}$ with increasing log $M_*$.</figcaption></figure>

<table><caption>**Table 14.** Average properties, line luminosities, and line ratios for N = 318 stacked spectra in the $H\alpha + [N\text{II}]$, $[S\text{II}]$, and $[S\text{III}]$ doublet window (0.30 < z < 0.73) that satisfy criterion (1)–(8).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>⟨log M<sub>*</sub>⟩</th><th>Hα + [N II]</th><th>[S II]</th><th>[S III]</th><th>Hα<sub>obs</sub><br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>Hα<sub>corr</sub></th><th>[S II]<sub>corr</sub></th><th>[S III]<sub>corr</sub></th><th>[S III]<sub>corr</sub><br>/ [S II]</th><th>[S III]<sub>corr</sub><br>/ [S II]</th></tr></thead><tbody><tr><td>106</td><td>[7.25, 9.13]</td><td>8.88</td><td>1.72 ± 0.02</td><td>0.44 ± 0.01</td><td>0.35 ± 0.01</td><td>1.57 ± 0.04</td><td>2.49 ± 0.82</td><td>0.69 ± 0.22</td><td>0.47 ± 0.09</td><td>0.80 ± 0.04</td><td>0.67 ± 0.11</td></tr><tr><td>106</td><td>[9.13, 9.66]</td><td>9.44</td><td>3.19 ± 0.05</td><td>0.84 ± 0.04</td><td>0.60 ± 0.02</td><td>2.67 ± 0.11</td><td>5.29 ± 1.75</td><td>1.63 ± 0.52</td><td>0.89 ± 0.17</td><td>0.71 ± 0.04</td><td>0.55 ± 0.10</td></tr><tr><td>106</td><td>[9.66,10.83]</td><td>9.97</td><td>4.31 ± 0.05</td><td>1.15 ± 0.03</td><td>0.55 ± 0.02</td><td>3.06 ± 0.17</td><td>7.93 ± 2.63</td><td>2.87 ± 0.91</td><td>0.97 ± 0.19</td><td>0.48 ± 0.02</td><td>0.34 ± 0.06</td></tr></tbody></table>

*Notes.* [S II] is the sum of $[S\text{II}]\lambda\lambda6716$, 6731. [S III] is the sum of $[S\text{III}]\lambda\lambda9069$, 9532. $H\alpha_{\text{obs}}$ and $H\alpha_{\text{corr}}$ have same meaning as in Table 13. $[S\text{II}]_{\text{corr}}$ and $[S\text{III}]_{\text{corr}}$ are values after correcting for dust extinction (see Section 7.4.2).

a lower ionization parameter with increasing stellar mass. We highlight that $S_{32}$ is relatively insensitive to the shape of the ionizing spectrum (e.g. Sanders et al. 2020), and that studies favour a redshift evolution in the hardness of the ionizing spectrum (e.g. Steidel et al. 2016).

### 7.4.4 [O II] to [S II] window (1.27 < z < 1.45)

Finally, we consider galaxies with grism coverage from [O II] all the way to [S II], which occurs for only a narrow redshift window (1.27 < z<sub>grism</sub> < 1.45; N = 203 with criterion 1–8). This window is unique in that it provides coverage across most
<figure><img src="image_19.png" /><figcaption>**Figure 18.** Top: similar to Fig. 16, but now for the $H\alpha + [N\text{II}]$, $[S\text{II}]$, and $[S\text{III}]$ window (0.30 < z < 0.73) and the stacked spectra are normalized to $H\alpha + [N\text{II}]$ total flux. The Ca II triplet absorption features are also indicated and appear to affect the stacked spectrum in the region near the $[S\text{III}]\lambda9069$ line, particularly for the largest stellar mass bin. Bottom: we compare the $S_{32}$ ratio versus stellar mass from WISP (z ~ 0.55) to the results in Sanders et al. (2020) for the MaNGA (z ~ 0) and MOSDEF (z ~ 1.5) samples. Small black and grey points denote individual galaxies where $S_{32}$ positions are constrained (42.4 per cent of sample), with median error bars given on the middle left. Coloured open and closed symbols correspond to the stellar mass stacks before and after dust extinction correction, labelled ‘obs’ and ‘dust-corr’, respectively (see Section 7.4.3). The WISP stacks appear most similar to the MaNGA relation before correcting for DIG, perhaps indicating a non-negligible DIG contribution in the WISP sample. All samples show a mildly decreasing $S_{32}$ with increasing log $M_*$.</figcaption></figure>

<table><caption>**Table 14.** Average properties, line luminosities, and line ratios for N = 318 stacked spectra in the $H\alpha + [N\text{II}]$, $[S\text{II}]$, and $[S\text{III}]$ doublet window (0.30 < z < 0.73) that satisfy criterion (1)–(8).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>⟨log M<sub>*</sub>⟩</th><th>Hα + [N II]</th><th>[S II]</th><th>[S III]</th><th>Hα<sub>obs</sub><br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>Hα<sub>corr</sub></th><th>[S II]<sub>corr</sub></th><th>[S III]<sub>corr</sub></th><th>[S III]<sub>corr</sub><br>/[S II]</th><th>[S III]<sub>corr</sub><br>/[S II]</th></tr></thead><tbody><tr><td>106</td><td>[7.25, 9.13]</td><td>8.88</td><td>1.72 ± 0.02</td><td>0.44 ± 0.01</td><td>0.35 ± 0.01</td><td>1.57 ± 0.04</td><td>2.49 ± 0.82</td><td>0.69 ± 0.22</td><td>0.47 ± 0.09</td><td>0.80 ± 0.04</td><td>0.67 ± 0.11</td></tr><tr><td>106</td><td>[9.13, 9.66]</td><td>9.44</td><td>3.19 ± 0.05</td><td>0.84 ± 0.04</td><td>0.60 ± 0.02</td><td>2.67 ± 0.11</td><td>5.29 ± 1.75</td><td>1.63 ± 0.52</td><td>0.89 ± 0.17</td><td>0.71 ± 0.04</td><td>0.55 ± 0.10</td></tr><tr><td>106</td><td>[9.66,10.83]</td><td>9.97</td><td>4.31 ± 0.05</td><td>1.15 ± 0.03</td><td>0.55 ± 0.02</td><td>3.06 ± 0.17</td><td>7.93 ± 2.63</td><td>2.87 ± 0.91</td><td>0.97 ± 0.19</td><td>0.48 ± 0.02</td><td>0.34 ± 0.06</td></tr></tbody></table>

*Notes.* $[S\text{II}]$ is the sum of $[S\text{II}]\lambda\lambda6716$, 6731. $[S\text{III}]$ is the sum of $[S\text{III}]\lambda\lambda9069$, 9532. $H\alpha_{\text{obs}}$ and $H\alpha_{\text{corr}}$ have same meaning as in Table 13. $[S\text{II}]_{\text{corr}}$ and $[S\text{III}]_{\text{corr}}$ are values after correcting for dust extinction (see Section 7.4.2).

a lower ionization parameter with increasing stellar mass. We highlight that $S_{32}$ is relatively insensitive to the shape of the ionizing spectrum (e.g. Sanders et al. 2020), and that studies favour a redshift evolution in the hardness of the ionizing spectrum (e.g. Steidel et al. 2016).

### 7.4.4 [O II] to [S II] window (1.27 < z < 1.45)

Finally, we consider galaxies with grism coverage from [O II] all the way to [S II], which occurs for only a narrow redshift window (1.27 < z<sub>grism</sub> < 1.45; N = 203 with criterion 1–8). This window is unique in that it provides coverage across most
strong optical emission lines simultaneously, which is beneficial for characterizing various properties of the ISM, including: $O_{32} \equiv [O\text{III}]\lambda\lambda4959,5007/[O\text{II}]\lambda\lambda3726,3729$, a proxy for the ionization parameter (Kewley et al. 2019); $R_{23} \equiv ([O\text{II}]\lambda\lambda3726, 3729 + [O\text{III}]\lambda\lambda4959, 5007)/H\beta$, a proxy for gas-phase metallicity (e.g. Curti et al. 2017); and $H\alpha/H\beta$, a proxy for dust attenuation (Calzetti 2001). We note that unlike $S_{32}$, the relation between $O_{32}$ and ionization parameter is more sensitive to gas-phase metallicity and ISM pressure (Kewley et al. 2019).

We divide galaxies in this window into two equal-number stellar mass bins. The spectra of these stellar mass stacks are shown in Fig. 19. The average galaxy properties and emission-line values for these stacks are listed in Table 15. Unlike previous stacks, we can perform dust corrections based on the measured Balmer decrement. This is based on the methods detailed in Battisti et al. (2022), which require corrections for $H\alpha + [N\text{II}]$ blending and Balmer absorption based on empirical relations from Faisst et al. (2018) and Kashino & Inoue (2019), respectively. We note that the average dust attenuation based on SED modelling is systematically lower than that inferred from the Balmer decrement, with log SFR(SED) being ~0.2 dex lower than log SFR($H\alpha_{corr}$). This is consistent with the findings in Battisti et al. (2022) and is expected. In the absence of IR data, the age-dust degeneracy (older populations can produce redder colours) will result in older (lower SFR) templates in MAGPHYS being able to reproduce the data.

We show a comparison of the $O_{32}$ and $R_{23}$ line ratios versus log $M_*$ for WISP relative to results from SDSS ($z \sim 0$) and the CLEAR survey ($1.1 < z < 2.3$; Papovich et al. 2022), which was an HST grism program in GOODS-N and GOODS-S (Great Observatories Origins Deep Survey-North and South; Simons et al. 2023). We show both the observed and extinction corrected line ratios for WISP (only extinction corrected for CLEAR). For CLEAR, the extinction corrections are based on the attenuation measurements from the SED fitting that assume the Calzetti et al. (2000) attenuation curve and assuming the nebular and continuum reddening are the same (see Papovich et al. 2022, for details). For WISP, we use Balmer decrements and the MW extinction curve from Fitzpatrick et al. (2019). The WISP sample has similar values and behaviour to the CLEAR stacks for both line ratios, which are offset above local galaxies based on SDSS. The SDSS contours are based on ~15 6000 galaxies at $z < 0.2$ (for selection criteria, see Battisti et al. 2022), noting that we use the stellar mass enclosed in the SDSS fibre and not the 'total' stellar mass. For $O_{32}$, the decreasing values in line ratios with increasing log $M_*$ suggests a lower ionization parameter and/or softer ionizing spectrum with increasing stellar mass. For $R_{23}$, the decreasing values in line ratios with increasing log $M_*$ reflects an increase in metallicity with increasing stellar mass. However, we note that our WISP $R_{23}$ values are close to the log $R_{23} \sim 1$ turnover in the $R_{23}$-metallicity relation (e.g. Curti et al. 2017), which introduces an ambiguity in relating $R_{23}$ to a metallicity. The CLEAR sample is representative of galaxies on the star-forming galaxy MS (see fig. 2 of Papovich et al. 2022) and our agreement with their trends further supports the argument that the WISP sample also reflects MS galaxies. For a more detailed analysis of the metallicity of WISP galaxies, we refer readers to Henry et al. (2021).

## 8 CONCLUSION

Slitless spectroscopic surveys are an efficient method to perform large spectroscopic surveys of galaxies across a wide range of cosmic time. We present the public data release of reduced ancillary photometric

images obtained for the WISP survey, a large pure-parallel HST program, as well as a consistent photometric catalogue containing ~230 000 sources. This catalogue is based on the SEXTRACTOR and TPHOT codes, the latter of which uses the high spatial resolution HST data to perform forced photometry on the low spatial resolution ground-based and Spitzer data. We also present the WISP emission-line catalogue containing ~8000 sources. This catalogue is based on a novel combination of an automated line detection algorithm and visual inspection. These data can be used to study a broad range of topics in galaxy evolution over ~60 per cent of cosmic time (0.3 $\le z \le 3$) and will serve as a useful reference sample for future slitless surveys with JWST, Euclid, and Roman.

We combine the WISP photometric and spectroscopic catalogues to examine the properties of WISP galaxies using stacked spectra in bins of stellar mass over four grism windows (redshift regimes) where specific emission-line ratios are available to study their ISM properties (Section 7.4):

(i) For $H\beta$ and [O III] coverage ($0.74 < z_{grism} < 2.31$), we bin 1040 galaxies and examine their position on the MEx diagram ([O III]/$H\beta$ versus $M_*$; Juneau et al. 2014). We find that our stacks at log ($M_*/M_\odot$) $< 10.2$ lie in the star-forming region of the diagram and log ($M_*/M_\odot$) $\gtrsim 10.2$ lie on/above the AGN region of the diagram. This suggests that there may be a non-negligible fraction of sources with AGN at higher masses and is qualitatively consistent with findings from other high-$z$ spectroscopic studies (e.g. Förster Schreiber et al. 2019).

(ii) For $H\alpha + [N\text{II}]$ and [S II] coverage ($0.30 < z_{grism} < 1.45$), we bin 1191 galaxies and examine their position on the galaxy MS (SFR versus $M_*$; Leslie et al. 2020). Bins with log ($M_*/M_\odot$) $\gtrsim 9$ appear roughly consistent with the 'star-forming MS', indicating they are representative of 'normal' star-forming galaxies. At log ($M_*/M_\odot$) $\le 9$, our bins reside above the MS.

(iii) For $H\alpha + [N\text{II}]$, [S II], and [S III] coverage ($0.30 < z_{grism} < 0.73$), we bin 318 galaxies to examine the [S III]/[S II] ratio (ionization parameter proxy). Our stacks are consistent with ratios found in MaNGA ($z \sim 0$) and MOSDEF ($z \sim 1.5$; Sanders et al. 2020) if WISP galaxies ($z \sim 0.5$) contain a similar [S II] contribution from DIG as MaNGA galaxies.

(iv) For [O II] to [S II] coverage ($1.27 < z_{grism} < 1.45$), we bin 203 galaxies to examine the [O III]/[O II] ratio (ionization parameter/spectral slope proxy) and ([O II] + [O III])/$H\beta$ ratio (metallicity proxy). Our stacks are consistent with line ratios found in CLEAR ($1.1 < z < 2.3$; Papovich et al. 2022). In particular, the relative strength of [O III] emission is substantially higher than in local star-forming galaxies observed by SDSS.

These results indicate that the majority of WISP galaxies are representative of typical MS galaxies.

Finally, we note that several current large-area photometric surveys, such as the Dark Energy Survey (grizY bands; Dark Energy Survey Collaboration 2016), the DECam Legacy Survey of the SDSS Equatorial Sky (grz bands; Dey et al. 2019), the Beijing–Arizona Sky Survey (gr bands; Zou et al. 2017), and the Mayall z-band Legacy Survey (MzLS, z band; Dey et al. 2019), provide shallow coverage (~22–24 AB mag) for some of the WISP fields that do not have existing coverage in this data release. In the future, the Legacy Survey of Space and Time (ugrizy bands; Ivezić et al. 2019) with the Rubin Observatory will provide more uniform and deeper coverage (final depth ~25–27 AB mag) that will supersede the depth of most existing optical data for WISP fields in the Southern Hemisphere (Dec. $< 0$). Incorporating these data sets may be the subject of a future data release.
strong optical emission lines simultaneously, which is beneficial for characterizing various properties of the ISM, including: $O_{32} \equiv [O\text{III}]\lambda\lambda4959,5007/[O\text{II}]\lambda\lambda3726,3729$, a proxy for the ionization parameter (Kewley et al. 2019); $R_{23} \equiv ([O\text{II}]\lambda\lambda3726, 3729 + [O\text{III}]\lambda\lambda4959, 5007)/H\beta$, a proxy for gas-phase metallicity (e.g. Curti et al. 2017); and $H\alpha/H\beta$, a proxy for dust attenuation (Calzetti 2001). We note that unlike $S_{32}$, the relation between $O_{32}$ and ionization parameter is more sensitive to gas-phase metallicity and ISM pressure (Kewley et al. 2019).

We divide galaxies in this window into two equal-number stellar mass bins. The spectra of these stellar mass stacks are shown in Fig. 19. The average galaxy properties and emission-line values for these stacks are listed in Table 15. Unlike previous stacks, we can perform dust corrections based on the measured Balmer decrement. This is based on the methods detailed in Battisti et al. (2022), which require corrections for $H\alpha + [N\text{II}]$ blending and Balmer absorption based on empirical relations from Faisst et al. (2018) and Kashino & Inoue (2019), respectively. We note that the average dust attenuation based on SED modelling is systematically lower than that inferred from the Balmer decrement, with log SFR(SED) being ~0.2 dex lower than log SFR($H\alpha_{corr}$). This is consistent with the findings in Battisti et al. (2022) and is expected. In the absence of IR data, the age-dust degeneracy (older populations can produce redder colours) will result in older (lower SFR) templates in MAGPHYS being able to reproduce the data.

We show a comparison of the $O_{32}$ and $R_{23}$ line ratios versus log $M_*$ for WISP relative to results from SDSS ($z \sim 0$) and the CLEAR survey ($1.1 < z < 2.3$; Papovich et al. 2022), which was an HST grism program in GOODS-N and GOODS-S (Great Observatories Origins Deep Survey-North and South; Simons et al. 2023). We show both the observed and extinction corrected line ratios for WISP (only extinction corrected for CLEAR). For CLEAR, the extinction corrections are based on the attenuation measurements from the SED fitting that assume the Calzetti et al. (2000) attenuation curve and assuming the nebular and continuum reddening are the same (see Papovich et al. 2022, for details). For WISP, we use Balmer decrements and the MW extinction curve from Fitzpatrick et al. (2019). The WISP sample has similar values and behaviour to the CLEAR stacks for both line ratios, which are offset above local galaxies based on SDSS. The SDSS contours are based on ~15 6000 galaxies at $z < 0.2$ (for selection criteria, see Battisti et al. 2022), noting that we use the stellar mass enclosed in the SDSS fibre and not the 'total' stellar mass. For $O_{32}$, the decreasing values in line ratios with increasing log $M_*$ suggests a lower ionization parameter and/or softer ionizing spectrum with increasing stellar mass. For $R_{23}$, the decreasing values in line ratios with increasing log $M_*$ reflects an increase in metallicity with increasing stellar mass. However, we note that our WISP $R_{23}$ values are close to the log $R_{23} \sim 1$ turnover in the $R_{23}$-metallicity relation (e.g. Curti et al. 2017), which introduces an ambiguity in relating $R_{23}$ to a metallicity. The CLEAR sample is representative of galaxies on the star-forming galaxy MS (see fig. 2 of Papovich et al. 2022) and our agreement with their trends further supports the argument that the WISP sample also reflects MS galaxies. For a more detailed analysis of the metallicity of WISP galaxies, we refer readers to Henry et al. (2021).

## 8 CONCLUSION

Slitless spectroscopic surveys are an efficient method to perform large spectroscopic surveys of galaxies across a wide range of cosmic time. We present the public data release of reduced ancillary photometric

images obtained for the WISP survey, a large pure-parallel HST program, as well as a consistent photometric catalogue containing ~230 000 sources. This catalogue is based on the SEXTRACTOR and TPHOT codes, the latter of which uses the high spatial resolution HST data to perform forced photometry on the low spatial resolution ground-based and Spitzer data. We also present the WISP emission-line catalogue containing ~8000 sources. This catalogue is based on a novel combination of an automated line detection algorithm and visual inspection. These data can be used to study a broad range of topics in galaxy evolution over ~60 per cent of cosmic time (0.3 $\le z \le 3$) and will serve as a useful reference sample for future slitless surveys with JWST, Euclid, and Roman.

We combine the WISP photometric and spectroscopic catalogues to examine the properties of WISP galaxies using stacked spectra in bins of stellar mass over four grism windows (redshift regimes) where specific emission-line ratios are available to study their ISM properties (Section 7.4):

(i) For $H\beta$ and [O III] coverage ($0.74 < z_{\text{grism}} < 2.31$), we bin 1040 galaxies and examine their position on the MEx diagram ([O III]/$H\beta$ versus $M_*$; Juneau et al. 2014). We find that our stacks at log ($M_*/M_\odot$) $< 10.2$ lie in the star-forming region of the diagram and log ($M_*/M_\odot$) $\gtrsim 10.2$ lie on/above the AGN region of the diagram. This suggests that there may be a non-negligible fraction of sources with AGN at higher masses and is qualitatively consistent with findings from other high-$z$ spectroscopic studies (e.g. Förster Schreiber et al. 2019).

(ii) For $H\alpha + [N\text{II}]$ and [S II] coverage ($0.30 < z_{\text{grism}} < 1.45$), we bin 1191 galaxies and examine their position on the galaxy MS (SFR versus $M_*$; Leslie et al. 2020). Bins with log ($M_*/M_\odot$) $\gtrsim 9$ appear roughly consistent with the 'star-forming MS', indicating they are representative of 'normal' star-forming galaxies. At log ($M_*/M_\odot$) $\le 9$, our bins reside above the MS.

(iii) For $H\alpha + [N\text{II}]$, [S II], and [S III] coverage ($0.30 < z_{\text{grism}} < 0.73$), we bin 318 galaxies to examine the [S III]/[S II] ratio (ionization parameter proxy). Our stacks are consistent with ratios found in MaNGA ($z \sim 0$) and MOSDEF ($z \sim 1.5$; Sanders et al. 2020) if WISP galaxies ($z \sim 0.5$) contain a similar [S II] contribution from DIG as MaNGA galaxies.

(iv) For [O II] to [S II] coverage ($1.27 < z_{\text{grism}} < 1.45$), we bin 203 galaxies to examine the [O III]/[O II] ratio (ionization parameter/spectral slope proxy) and ([O II] + [O III])/$H\beta$ ratio (metallicity proxy). Our stacks are consistent with line ratios found in CLEAR ($1.1 < z < 2.3$; Papovich et al. 2022). In particular, the relative strength of [O III] emission is substantially higher than in local star-forming galaxies observed by SDSS.

These results indicate that the majority of WISP galaxies are representative of typical MS galaxies.

Finally, we note that several current large-area photometric surveys, such as the Dark Energy Survey (grizY bands; Dark Energy Survey Collaboration 2016), the DECam Legacy Survey of the SDSS Equatorial Sky (grz bands; Dey et al. 2019), the Beijing–Arizona Sky Survey (gr bands; Zou et al. 2017), and the Mayall z-band Legacy Survey (MzLS, z band; Dey et al. 2019), provide shallow coverage (~22–24 AB mag) for some of the WISP fields that do not have existing coverage in this data release. In the future, the Legacy Survey of Space and Time (ugrizy bands; Ivezić et al. 2019) with the Rubin Observatory will provide more uniform and deeper coverage (final depth ~25–27 AB mag) that will supersede the depth of most existing optical data for WISP fields in the Southern Hemisphere (Dec. < 0). Incorporating these data sets may be the subject of a future data release.
<figure><img src="image_20.png" /><figcaption>**Figure 19.** Top: similar to Fig. 16, but now for the window covering [O II] to [S II] and the stacked spectra are normalized to $H\alpha + [N II]$ total flux. The numerous optical emission lines in this window allows several ISM diagnostics to be simultaneously available. The region around the Balmer break (0.3645 µm) shows a discontinuity, which may result from the simplistic treatment of the stellar continuum (see Section 5.3). Bottom: we compare the $O_{32}$ and $R_{23}$ ratios versus stellar mass from WISP ($z \sim 1.4$) to values from CLEAR ($1.1 < z < 2.3$; Papovich et al. 2022) and also show contours for SDSS ($z < 0.2$; coloured lines). Coloured open and closed symbols correspond to the stellar mass stacks before and after dust extinction correction, respectively, based on the measured Balmer decrement (see Section 7.4.4). The WISP stacks are in rough agreement with CLEAR, lying above the SDSS sample, and showing a decreasing $O_{32}$ and $R_{23}$ with increasing log $M_*$, Larger $O_{32}$ ratios indicate of higher ionization potential and/or harder ionizing spectrum. Larger $R_{23}$ indicate lower metallicities (for upper branch, $12 + \log(O/H) > 8.1$), however the $R_{23}$–metallicity relation has a turnover at $\log R_{23} \sim 1$ (e.g. Curti et al. 2017).</figcaption></figure>

<table><caption>**Table 15.** Average properties, emission-line luminosities, and line ratios for stacked spectra in the [O II] to [S II] window ($1.27 < z < 1.45$).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>⟨log M<sub>*</sub>⟩</th><th>[O II]</th><th>Hβ</th><th>[O III]<br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>Hα + [N II]</th><th>[S II]</th><th>Hα<sub>obs</sub></th><th>τ<sub>B</sub><sup>l</sup></th><th>log O<sub>32</sub></th><th>log R<sub>23</sub></th></tr></thead><tbody><tr><td>102</td><td>[7.54, 9.39]</td><td>9.01</td><td>5.03 ± 0.24</td><td>2.46 ± 0.14</td><td>16.41 ± 0.31</td><td>10.11 ± 0.09</td><td>1.45 ± 0.09</td><td>9.28 ± 0.26</td><td>0.27 ± 0.07</td><td>0.40 ± 0.06</td><td>0.95 ± 0.05</td></tr><tr><td>101</td><td>[9.40,11.26]</td><td>9.93</td><td>6.56 ± 0.35</td><td>2.39 ± 0.21</td><td>10.83 ± 0.32</td><td>18.29 ± 0.16</td><td>3.29 ± 0.11</td><td>14.50 ± 1.72</td><td>0.71 ± 0.19</td><td>-0.10 ± 0.11</td><td>0.94 ± 0.11</td></tr></tbody></table>

*Notes.* Hβ shown is not corrected for stellar absorption. [O III] is the sum of [O III]λλ4959, 5007. [S II] is the sum of [S II]λλ6716, 6731. The Balmer optical depth, $\tau_B^l = \ln((F(H\alpha)/F(H\beta))/2.86)$ is based on absorption-corrected lines (see Section 7.4.4). Values listed for $O_{32}$ and $R_{23}$ are after extinction correction.

ACKNOWLEDGEMENTS

The authors thank the anonymous referee, whose suggestions helped to clarify and improve the content of this work. AJB thanks the staff at the WIYN and Magellan facilities for their assistance with technical aspects of the observations. AJB is also thankful for attending ASTRO 3D writing retreats that provided a helpful environment to complete portions of this manuscript. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project

no. CE170100013. We acknowledge the invaluable labour of the maintenance and clerical staff at our institutions, whose contributions make our scientific discoveries a reality. This research was conducted on Ngunnawal Indigenous land, as well as within the traditional homelands of the Dakota people. This work is sponsored by the National Key R&D Program of China for grant no. 2022YFA1605300, the National Nature Science Foundation of China (NSFC) grants nos 12273051 and 11933003. HA is supported by CNES (Centre National d'Etudes Spatiales). AJ Bunker acknowledges funding from
<figure><img src="image_20.png" /><figcaption>**Figure 19.** Top: similar to Fig. 16, but now for the window covering [O II] to [S II] and the stacked spectra are normalized to $H\alpha + [N II]$ total flux. The numerous optical emission lines in this window allows several ISM diagnostics to be simultaneously available. The region around the Balmer break (0.3645 µm) shows a discontinuity, which may result from the simplistic treatment of the stellar continuum (see Section 5.3). Bottom: we compare the $O_{32}$ and $R_{23}$ ratios versus stellar mass from WISP ($z \sim 1.4$) to values from CLEAR ($1.1 < z < 2.3$; Papovich et al. 2022) and also show contours for SDSS ($z < 0.2$; coloured lines). Coloured open and closed symbols correspond to the stellar mass stacks before and after dust extinction correction, respectively, based on the measured Balmer decrement (see Section 7.4.4). The WISP stacks are in rough agreement with CLEAR, lying above the SDSS sample, and showing a decreasing $O_{32}$ and $R_{23}$ with increasing log $M_*$, Larger $O_{32}$ ratios indicate of higher ionization potential and/or harder ionizing spectrum. Larger $R_{23}$ indicate lower metallicities (for upper branch, $12 + \log(O/H) > 8.1$), however the $R_{23}$–metallicity relation has a turnover at $\log R_{23} \sim 1$ (e.g. Curti et al. 2017).</figcaption></figure>

<table><caption>**Table 15.** Average properties, emission-line luminosities, and line ratios for stacked spectra in the [O II] to [S II] window ($1.27 < z < 1.45$).</caption><thead><tr><th>N</th><th>log M<sub>*</sub><br>range</th><th>⟨log M<sub>*</sub>⟩</th><th>[O II]</th><th>Hβ</th><th>[O III]<br>(10<sup>41</sup> erg s<sup>-1</sup>)</th><th>Hα + [N II]</th><th>[S II]</th><th>Hα<sub>obs</sub></th><th>τ<sub>B</sub><sup>l</sup></th><th>log O<sub>32</sub></th><th>log R<sub>23</sub></th></tr></thead><tbody><tr><td>102</td><td>[7.54, 9.39]</td><td>9.01</td><td>5.03 ± 0.24</td><td>2.46 ± 0.14</td><td>16.41 ± 0.31</td><td>10.11 ± 0.09</td><td>1.45 ± 0.09</td><td>9.28 ± 0.26</td><td>0.27 ± 0.07</td><td>0.40 ± 0.06</td><td>0.95 ± 0.05</td></tr><tr><td>101</td><td>[9.40,11.26]</td><td>9.93</td><td>6.56 ± 0.35</td><td>2.39 ± 0.21</td><td>10.83 ± 0.32</td><td>18.29 ± 0.16</td><td>3.29 ± 0.11</td><td>14.50 ± 1.72</td><td>0.71 ± 0.19</td><td>-0.10 ± 0.11</td><td>0.94 ± 0.11</td></tr></tbody></table>

*Notes.* Hβ shown is not corrected for stellar absorption. [O III] is the sum of [O III]λλ4959, 5007. [S II] is the sum of [S II]λλ6716, 6731. The Balmer optical depth, $\tau_B^l = \ln((F(H\alpha)/F(H\beta))/2.86)$ is based on absorption-corrected lines (see Section 7.4.4). Values listed for $O_{32}$ and $R_{23}$ are after extinction correction.

## ACKNOWLEDGEMENTS

The authors thank the anonymous referee, whose suggestions helped to clarify and improve the content of this work. AJB thanks the staff at the WIYN and Magellan facilities for their assistance with technical aspects of the observations. AJB is also thankful for attending ASTRO 3D writing retreats that provided a helpful environment to complete portions of this manuscript. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project

no. CE170100013. We acknowledge the invaluable labour of the maintenance and clerical staff at our institutions, whose contributions make our scientific discoveries a reality. This research was conducted on Ngunnawal Indigenous land, as well as within the traditional homelands of the Dakota people. This work is sponsored by the National Key R&D Program of China for grant no. 2022YFA1605300, the National Nature Science Foundation of China (NSFC) grants nos 12273051 and 11933003. HA is supported by CNES (Centre National d'Etudes Spatiales). AJ Bunker acknowledges funding from
the 'FirstGalaxies' Advanced Grant from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 789056). Support for WISP (HST programs GO-11696, 12283, 12568, 12902, 13517, 13352, and 14178) was provided by NASA through grants from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This work uses data from WIYN. The WIYN Observatory is a joint facility of the NSF's National Optical-Infrared Astronomy Research Laboratory, Indiana University, the University of Wisconsin-Madison, Pennsylvania State University, the University of Missouri, the University of California-Irvine, and Purdue University. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. This work uses data from Palomar. The Palomar Observatory is a joint facility of the Caltech/Caltech Optical Observatories, Jet Propulsion Laboratory, Yale University, and National Astronomical Observatories of China. This work uses data from SDSS. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofísica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. This work uses data from PAN-STARRS. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation grant no. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

DATA AVAILABILITY

All of the WISP photometric and spectroscopic data used in this paper are publicly available through data releases on the WISP website.<fnref n="16" />

on MAST. This release adds the following data products to the WISP website: (1) fully reduced 5 arcmin × 5 arcmin cutouts (centred on WISP field) of ground-based observations, (2) fully reduced Spitzer images, (3) the photometric catalogue (FITS binary table; described in Table 6), (4) the emission-line catalogue (FITS binary table; described in Table 10), (5) the full versions of Table 2 (grism depths for each field), Table 7 (WFC/IR photometric depths/completeness for each field), Table 8 (photometric depths for each field), and Table 11 (MAGPHYS properties for subsample). Other data products can be made available upon reasonable request to the first author.

REFERENCES

Anders P., Fritze-v. Alvensleben U., 2003, A&A, 401, 1063

Astropy Collaboration, 2013, A&A, 558, A33

Astropy Collaboration, 2018, AJ, 156, 123

Atek H. et al., 2010, ApJ, 723, 104

Atek H. et al., 2014, ApJ, 789, 96

Bagley M. B. et al., 2017, ApJ, 837, 11

Bagley M. B. et al., 2020, ApJ, 897, 98

Bagley M. B. et al., 2024, ApJ, 961, 209

Baronchelli I. et al., 2020, ApJS, 249, 12

Baronchelli I. et al., 2021, ApJS, 257, 67

Battisti A. J., Cunha E. d., Shivaei I., Calzetti D., 2020, ApJ, 888, 108

Battisti A. J. et al., 2022, MNRAS, 513, 4431

Bedregal A. G. et al., 2013, ApJ, 778, 126

Berg D. A., Chisholm J., Erb D. K., Skillman E. D., Pogge R. W., Olivier G. M., 2021, ApJ, 922, 170

Bertin E., 2010, Astrophysics Source Code Library, record ascl:1010.068

Bertin E., Arnouts S., 1996, A&AS, 117, 393

Bertin E., Mellier Y., Radovich M., Missonnier G., Didelon P., Morin B., 2002, in Bohlender D. A., Durand D., Handley T. H., eds, ASP Conf. Ser. Vol. 281, Astronomical Data Analysis Software and Systems XI. Astron. Soc. Pac., San Francisco, p. 228

Bourque M., Baggett S., 2016, WFC3/UVIS Dark Calibration: Monitoring Results and Improvements to Dark Reference Files, Instrument Science Report WFC3 2016–08, The Association of Universities for Research in Astronomy, Inc.

Brammer G. B. et al., 2012, ApJS, 200, 13

Brammer G., Ryan R., Pirzkal N., 2015, Source-dependent Master Sky Images for the WFC3/IR Grisms, Instrument Science Report WFC3 2015–17, The Association of Universities for Research in Astronomy, Inc.

Brinchmann J., Charlot S., White S. D. M., Tremonti C., Kauffmann G., Heckman T., Brinkmann J., 2004, MNRAS, 351, 1151

Bruzual G., Charlot S., 2003, MNRAS, 344, 1000

Calzetti D., 2001, PASP, 113, 1449

Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J., Storchi-Bergmann T., 2000, ApJ, 533, 682

Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245

Chabrier G., 2003, PASP, 115, 763

Charlot S., Fall S. M., 2000, ApJ, 539, 718

Coil A. L. et al., 2015, ApJ, 801, 35

Colbert J. W. et al., 2013, ApJ, 779, 34

da Cunha E., Charlot S., Elbaz D., 2008, MNRAS, 388, 1595

da Cunha E. et al., 2015, ApJ, 806, 110

Curti M., Cresci G., Mannucci F., Marconi A., Maiolino R., Esposito S., 2017, MNRAS, 465, 1384

Dai Y. S. et al., 2021, ApJ, 923, 156

Dark Energy Survey Collaboration, 2016, MNRAS, 460, 1270

Dey A. et al., 2019, AJ, 157, 168

Dickinson H. et al., 2018, Res. Notes Am. Astron. Soc., 2, 120

Domínguez A. et al., 2013, ApJ, 763, 145

Du P., Kibbe W. A., Lin S. M., 2006, Bioinformatics, 22, 2059

<footnote n="16">¹⁶https://archive.stsci.edu/prepds/wisp/</footnote>
the 'FirstGalaxies' Advanced Grant from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 789056). Support for WISP (HST programs GO-11696, 12283, 12568, 12902, 13517, 13352, and 14178) was provided by NASA through grants from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This work uses data from WIYN. The WIYN Observatory is a joint facility of the NSF's National Optical-Infrared Astronomy Research Laboratory, Indiana University, the University of Wisconsin-Madison, Pennsylvania State University, the University of Missouri, the University of California-Irvine, and Purdue University. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. This work uses data from Palomar. The Palomar Observatory is a joint facility of the Caltech/Caltech Optical Observatories, Jet Propulsion Laboratory, Yale University, and National Astronomical Observatories of China. This work uses data from SDSS. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofísica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. This work uses data from PAN-STARRS. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation grant no. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

DATA AVAILABILITY

All of the WISP photometric and spectroscopic data used in this paper are publicly available through data releases on the WISP website.<fnref n="16" />

on MAST. This release adds the following data products to the WISP website: (1) fully reduced 5 arcmin × 5 arcmin cutouts (centred on WISP field) of ground-based observations, (2) fully reduced Spitzer images, (3) the photometric catalogue (FITS binary table; described in Table 6), (4) the emission-line catalogue (FITS binary table; described in Table 10), (5) the full versions of Table 2 (grism depths for each field), Table 7 (WFC/IR photometric depths/completeness for each field), Table 8 (photometric depths for each field), and Table 11 (MAGPHYS properties for subsample). Other data products can be made available upon reasonable request to the first author.

REFERENCES

Anders P., Fritze-v. Alvensleben U., 2003, A&A, 401, 1063

Astropy Collaboration, 2013, A&A, 558, A33

Astropy Collaboration, 2018, AJ, 156, 123

Atek H. et al., 2010, ApJ, 723, 104

Atek H. et al., 2014, ApJ, 789, 96

Bagley M. B. et al., 2017, ApJ, 837, 11

Bagley M. B. et al., 2020, ApJ, 897, 98

Bagley M. B. et al., 2024, ApJ, 961, 209

Baronchelli I. et al., 2020, ApJS, 249, 12

Baronchelli I. et al., 2021, ApJS, 257, 67

Battisti A. J., Cunha E. d., Shivaei I., Calzetti D., 2020, ApJ, 888, 108

Battisti A. J. et al., 2022, MNRAS, 513, 4431

Bedregal A. G. et al., 2013, ApJ, 778, 126

Berg D. A., Chisholm J., Erb D. K., Skillman E. D., Pogge R. W., Olivier G. M., 2021, ApJ, 922, 170

Bertin E., 2010, Astrophysics Source Code Library, record ascl:1010.068

Bertin E., Arnouts S., 1996, A&AS, 117, 393

Bertin E., Mellier Y., Radovich M., Missonnier G., Didelon P., Morin B., 2002, in Bohlender D. A., Durand D., Handley T. H., eds, ASP Conf. Ser. Vol. 281, Astronomical Data Analysis Software and Systems XI. Astron. Soc. Pac., San Francisco, p. 228

Bourque M., Baggett S., 2016, WFC3/UVIS Dark Calibration: Monitoring Results and Improvements to Dark Reference Files, Instrument Science Report WFC3 2016–08, The Association of Universities for Research in Astronomy, Inc.

Brammer G. B. et al., 2012, ApJS, 200, 13

Brammer G., Ryan R., Pirzkal N., 2015, Source-dependent Master Sky Images for the WFC3/IR Grisms, Instrument Science Report WFC3 2015–17, The Association of Universities for Research in Astronomy, Inc.

Brinchmann J., Charlot S., White S. D. M., Tremonti C., Kauffmann G., Heckman T., Brinkmann J., 2004, MNRAS, 351, 1151

Bruzual G., Charlot S., 2003, MNRAS, 344, 1000

Calzetti D., 2001, PASP, 113, 1449

Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J., Storchi-Bergmann T., 2000, ApJ, 533, 682

Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245

Chabrier G., 2003, PASP, 115, 763

Charlot S., Fall S. M., 2000, ApJ, 539, 718

Coil A. L. et al., 2015, ApJ, 801, 35

Colbert J. W. et al., 2013, ApJ, 779, 34

da Cunha E., Charlot S., Elbaz D., 2008, MNRAS, 388, 1595

da Cunha E. et al., 2015, ApJ, 806, 110

Curti M., Cresci G., Mannucci F., Marconi A., Maiolino R., Esposito S., 2017, MNRAS, 465, 1384

Dai Y. S. et al., 2021, ApJ, 923, 156

Dark Energy Survey Collaboration, 2016, MNRAS, 460, 1270

Dey A. et al., 2019, AJ, 157, 168

Dickinson H. et al., 2018, Res. Notes Am. Astron. Soc., 2, 120

Domínguez A. et al., 2013, ApJ, 763, 145

Du P., Kibbe W. A., Lin S. M., 2006, Bioinformatics, 22, 2059

<footnote n="16">¹⁶https://archive.stsci.edu/prepds/wisp/</footnote>
Faisst A. L., Masters D., Wang Y., Merson A., Capak P., Malhotra S., Rhoads
J. E., 2018, ApJ, 855, 132

Fitzpatrick E. L., Massa D., Gordon K. D., Bohlin R., Clayton G. C., 2019,
ApJ, 886, 108

Förster Schreiber N. M. et al., 2019, ApJ, 875, 21

Gonzaga S., Hack W., Fruchter A., Mack J., 2012, The DrizzlePac Handbook,
The Association of Universities for Research in Astronomy, Inc.

Henry A. et al., 2013, ApJ, 776, L27

Henry A. et al., 2021, ApJ, 919, 143

Hoffmann S. L., Mack J., Avila R., Martlin C., Cohen Y., Bajaj V., 2021,
American Astronomical Society Meeting Abstracts. p. 216.02

Ivezić Ž. et al., 2019, ApJ, 873, 111

Juneau S. et al., 2014, ApJ, 788, 88

Kashino D., Inoue A. K., 2019, MNRAS, 486, 1053

Kashino D. et al., 2019, ApJS, 241, 10

Kennicutt R. C., Evans N. J., 2012, ARA&A, 50, 531

Kewley L. J., Nicholls D. C., Sutherland R. S., 2019, ARA&A, 57, 511

Kroupa P., Weidner C., 2003, ApJ, 598, 1076

Kümmel M., Kuntschner H., Walsh J., 2007, Space Telesc. Eur. Coord. Facil.
Newsl., 43, 8

Kümmel M., Walsh J. R., Pirzkal N., Kuntschner H., Pasquali A., 2009, PASP,
121, 59

Leja J., Carnall A. C., Johnson B. D., Conroy C., Speagle J. S., 2019, ApJ,
876, 3

Leslie S. K. et al., 2020, ApJ, 899, 58

Lucy L. B., 1974, AJ, 79, 745

Malkan M. A. et al., 2021, PASSAGE-Parallel Application of Slitless
Spectroscopy to Analyze Galaxy Evolution, JWST Proposal. Cycle 1,
STSCI

Masters D. et al., 2012, ApJ, 752, L14

Masters D. et al., 2014, ApJ, 785, 153

Mehta V. et al., 2015, ApJ, 811, 141

Merlin E. et al., 2015, A&A, 582, A15

Merlin E. et al., 2016, A&A, 595, A97

Moré J. J., 1978, The Levenberg-Merquardt Algorithm: Implementation and
Theory. Springer-Verlag, Berlin

Oke J. B., Gunn J. E., 1983, ApJ, 266, 713

Osterbrock D. E., 1989, Astrophysics of Gaseous Nebulae and Active Galactic
Nuclei. University Science Books, Mill Valley, CA

Papovich C. et al., 2022, ApJ, 937, 22

Pasquali A., Pirzkal N., Walsh J. R., Rhoads J. E., Malhotra S., Tsvetanov
Z., Apples Team, 2003, in Shaver P. A., Dilella L., Giménez A.,
eds, Astronomy, Cosmology and Fundamental Physics. Springer-Verlag,
Berlin, p. 471

Pirzkal N. et al., 2004, ApJS, 154, 501

Pirzkal N. et al., 2013, ApJ, 772, 48

Pirzkal N. et al., 2017, ApJ, 846, 84

Pirzkal N. et al., 2018, ApJ, 868, 61

Prichard L. J. et al., 2022, ApJ, 924, 14

Rafelski M. et al., 2015, AJ, 150, 31

Revalski M. et al., 2023, ApJS, 265, 40

Richardson W. H., 1972, J. Opt. Soc. Am. (1917–1983), 62, 55

Sanders R. L. et al., 2020, ApJ, 888, L11

Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103

Shapley A. E. et al., 2022, ApJ, 926, 145

Simons R. C. et al., 2023, ApJS, 266, 13

Speagle J. S., Steinhardt C. L., Capak P. L., Silverman J. D., 2014, ApJS,
214, 15

Steidel C. C., Strom A. L., Pettini M., Rudie G. C., Reddy N. A., Trainor R.
F., 2016, ApJ, 826, 159

Storey P. J., Zeippen C. J., 2000, MNRAS, 312, 813

Tonry J. L. et al., 2012, ApJ, 750, 99

Treu T. et al., 2015, ApJ, 812, 114

van der Wel A. et al., 2014, ApJ, 788, 28

Wang X. et al., 2022, ApJ, 926, 70

Whitaker K. E. et al., 2014, ApJ, 795, 104

Zanella A. et al., 2016, ApJ, 824, 68

Zou H. et al., 2017, PASP, 129, 064101

## SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

### suppl.data

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

## APPENDIX A: TPHOT INPUT AND CONFIGURATION DETAILS

In order for TPHOT to obtain reliable measurements, the geometric centres of the sources detected in different bands must be perfectly aligned. To obtain this result, the coordinates of the sources originally extracted from the low-resolution images are refined by comparing the positions of the sources in the images at different wavelengths. This coordinate recentering is performed using an iterative procedure. Initially, source positions in the low-resolution data are determined by running SExTRACTOR on the original images. The most likely HST counterparts are identified using an initial search radius of 2 arcsec. At this stage, each source is associated to only one potential counterpart. Then, an average shift correction for the coordinates is computed by comparing the (RA, Dec.) positions of the counterparts in the two bands and the corresponding new set of WCS is applied to the low-resolution images. After this initial iteration, the entire process is repeated using this time, a shorter searching radius (0.75 arcsec). Therefore, the WCS correction is refined by performed the second iteration using only sources with a more secure counterpart identification. At the end of the process described, the coordinates in the low-resolution images are precisely recented to the HST reference frame.

TPHOT also requires input images with identical (or integer multiple) pixel-scale and identical pixel orientation. We use the SWARP software to obtain low-resolution images consistent with the HST reference images. We note that these SWARP intermediate products (i.e. images with identical pixel scales and orientations) are not provided in the current data release. TPHOT also requires both a catalogue of sources extracted in the high-resolution image (HST), and a corresponding segmentation map. In particular, the IDs reported in the input catalogue must be identical to the pixel values of the corresponding sources in the segmentation map. Our catalogues were created by merging catalogues of sources detected in the *J* and/or in the *H* band (plus a catalogue obtained from a sum of the *J* + *H* images). As a consequence, the IDs in our catalogues had to be re-assigned (and ordered on a brightness basis). Finally, not all the sources extracted (and included in the segmentation maps) were included in our catalogues. For example, we removed all the sources located in the image borders, characterized by bad photometric measurements.

Due to the fact that not all sources uniquely correspond to a counterpart across the different HST segmentation maps, we computed an appropriate unique segmentation image, from the original segmentation maps obtained by SExTRACTOR. In the new segmentation map, every source of the catalogue is uniquely related with a corresponding source (with identical ID) in the map. Moreover, all the sources removed from the catalogues are also removed from the final segmentation map.

In addition to the IDs, the TPHOT input catalogue must include, for each source, its (x,y) position in the HST reference image, the values $x_{min}$, $x_{max}$, $y_{min}$, and $y_{max}$ defining the borders of the source in
Faisst A. L., Masters D., Wang Y., Merson A., Capak P., Malhotra S., Rhoads
J. E., 2018, ApJ, 855, 132

Fitzpatrick E. L., Massa D., Gordon K. D., Bohlin R., Clayton G. C., 2019,
ApJ, 886, 108

Förster Schreiber N. M. et al., 2019, ApJ, 875, 21

Gonzaga S., Hack W., Fruchter A., Mack J., 2012, The DrizzlePac Handbook,
The Association of Universities for Research in Astronomy, Inc.

Henry A. et al., 2013, ApJ, 776, L27

Henry A. et al., 2021, ApJ, 919, 143

Hoffmann S. L., Mack J., Avila R., Martlin C., Cohen Y., Bajaj V., 2021,
American Astronomical Society Meeting Abstracts. p. 216.02

Ivezić Ž. et al., 2019, ApJ, 873, 111

Juneau S. et al., 2014, ApJ, 788, 88

Kashino D., Inoue A. K., 2019, MNRAS, 486, 1053

Kashino D. et al., 2019, ApJS, 241, 10

Kennicutt R. C., Evans N. J., 2012, ARA&A, 50, 531

Kewley L. J., Nicholls D. C., Sutherland R. S., 2019, ARA&A, 57, 511

Kroupa P., Weidner C., 2003, ApJ, 598, 1076

Kümmel M., Kuntschner H., Walsh J., 2007, Space Telesc. Eur. Coord. Facil.
Newsl., 43, 8

Kümmel M., Walsh J. R., Pirzkal N., Kuntschner H., Pasquali A., 2009, PASP,
121, 59

Leja J., Carnall A. C., Johnson B. D., Conroy C., Speagle J. S., 2019, ApJ,
876, 3

Leslie S. K. et al., 2020, ApJ, 899, 58

Lucy L. B., 1974, AJ, 79, 745

Malkan M. A. et al., 2021, PASSAGE-Parallel Application of Slitless
Spectroscopy to Analyze Galaxy Evolution, JWST Proposal. Cycle 1,
STSCI

Masters D. et al., 2012, ApJ, 752, L14

Masters D. et al., 2014, ApJ, 785, 153

Mehta V. et al., 2015, ApJ, 811, 141

Merlin E. et al., 2015, A&A, 582, A15

Merlin E. et al., 2016, A&A, 595, A97

Moré J. J., 1978, The Levenberg-Merquardt Algorithm: Implementation and
Theory. Springer-Verlag, Berlin

Oke J. B., Gunn J. E., 1983, ApJ, 266, 713

Osterbrock D. E., 1989, Astrophysics of Gaseous Nebulae and Active Galactic
Nuclei. University Science Books, Mill Valley, CA

Papovich C. et al., 2022, ApJ, 937, 22

Pasquali A., Pirzkal N., Walsh J. R., Rhoads J. E., Malhotra S., Tsvetanov
Z., Apples Team, 2003, in Shaver P. A., Dilella L., Giménez A.,
eds, Astronomy, Cosmology and Fundamental Physics. Springer-Verlag,
Berlin, p. 471

Pirzkal N. et al., 2004, ApJS, 154, 501

Pirzkal N. et al., 2013, ApJ, 772, 48

Pirzkal N. et al., 2017, ApJ, 846, 84

Pirzkal N. et al., 2018, ApJ, 868, 61

Prichard L. J. et al., 2022, ApJ, 924, 14

Rafelski M. et al., 2015, AJ, 150, 31

Revalski M. et al., 2023, ApJS, 265, 40

Richardson W. H., 1972, J. Opt. Soc. Am. (1917–1983), 62, 55

Sanders R. L. et al., 2020, ApJ, 888, L11

Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103

Shapley A. E. et al., 2022, ApJ, 926, 145

Simons R. C. et al., 2023, ApJS, 266, 13

Speagle J. S., Steinhardt C. L., Capak P. L., Silverman J. D., 2014, ApJS,
214, 15

Steidel C. C., Strom A. L., Pettini M., Rudie G. C., Reddy N. A., Trainor R.
F., 2016, ApJ, 826, 159

Storey P. J., Zeippen C. J., 2000, MNRAS, 312, 813

Tonry J. L. et al., 2012, ApJ, 750, 99

Treu T. et al., 2015, ApJ, 812, 114

van der Wel A. et al., 2014, ApJ, 788, 28

Wang X. et al., 2022, ApJ, 926, 70

Whitaker K. E. et al., 2014, ApJ, 795, 104

Zanella A. et al., 2016, ApJ, 824, 68

Zou H. et al., 2017, PASP, 129, 064101

## SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

### suppl.data

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

## APPENDIX A: TPHOT INPUT AND CONFIGURATION DETAILS

In order for TPHOT to obtain reliable measurements, the geometric centres of the sources detected in different bands must be perfectly aligned. To obtain this result, the coordinates of the sources originally extracted from the low-resolution images are refined by comparing the positions of the sources in the images at different wavelengths. This coordinate recentering is performed using an iterative procedure. Initially, source positions in the low-resolution data are determined by running SExTRACTOR on the original images. The most likely HST counterparts are identified using an initial search radius of 2 arcsec. At this stage, each source is associated to only one potential counterpart. Then, an average shift correction for the coordinates is computed by comparing the (RA, Dec.) positions of the counterparts in the two bands and the corresponding new set of WCS is applied to the low-resolution images. After this initial iteration, the entire process is repeated using this time, a shorter searching radius (0.75 arcsec). Therefore, the WCS correction is refined by performed the second iteration using only sources with a more secure counterpart identification. At the end of the process described, the coordinates in the low-resolution images are precisely recented to the HST reference frame.

TPHOT also requires input images with identical (or integer multiple) pixel-scale and identical pixel orientation. We use the SWARP software to obtain low-resolution images consistent with the HST reference images. We note that these SWARP intermediate products (i.e. images with identical pixel scales and orientations) are not provided in the current data release. TPHOT also requires both a catalogue of sources extracted in the high-resolution image (HST), and a corresponding segmentation map. In particular, the IDs reported in the input catalogue must be identical to the pixel values of the corresponding sources in the segmentation map. Our catalogues were created by merging catalogues of sources detected in the *J* and/or in the *H* band (plus a catalogue obtained from a sum of the *J* + *H* images). As a consequence, the IDs in our catalogues had to be re-assigned (and ordered on a brightness basis). Finally, not all the sources extracted (and included in the segmentation maps) were included in our catalogues. For example, we removed all the sources located in the image borders, characterized by bad photometric measurements.

Due to the fact that not all sources uniquely correspond to a counterpart across the different HST segmentation maps, we computed an appropriate unique segmentation image, from the original segmentation maps obtained by SExTRACTOR. In the new segmentation map, every source of the catalogue is uniquely related with a corresponding source (with identical ID) in the map. Moreover, all the sources removed from the catalogues are also removed from the final segmentation map.

In addition to the IDs, the TPHOT input catalogue must include, for each source, its (x,y) position in the HST reference image, the values $x_{min}$, $x_{max}$, $y_{min}$, and $y_{max}$ defining the borders of the source in
the segmentation map, a local background value (we set this value to 0 as the background was already subtracted from the images before running TPHOT), and the reference flux for each source in the high-resolution band.

One of the most important inputs required by TPHOT is the image of the kernel required to perform the inverse of the following convolution operation:

$$PSF(LRI) = \text{Kernel} * PSF(HRI), \qquad (A1)$$

where LRI and HRI stand for low- and high-resolution images, respectively. We obtain the convolution kernel image by deconvolving the low-resolution PSF using the HST PSF as a deconvolution kernel. For this, we adopt the Richardson-Lucy approach (Richardson 1972; Lucy 1974). The average low-resolution and HST PSFs are obtained averaging the PSFs of a selection of point-like, non-saturated sources detected in each image. In accordance with this choice, we set the TPHOT configuration parameter `usereal = True` (and `usemodels` and `useunresolved = False`).

The TPHOT algorithm is organized in different 'stages', each of which performs a specific task. The list and the order of the various stages in each iteration can be set by the user. As described in the user manual, the best results are obtained when the various stages are run in two separate iterations ('passes'). We proceed in the default manner, setting the keyword `order` to `standard` and to `standard2` in the two iterations, respectively.

For each source, TPHOT computes $(x,y)$ shifts during the first pass ('dance' stage). Using these corrections, in the second pass, local kernels are registered to each single source improving the accuracy of the outputs. This can be obtained by setting the keyword `mul-tikernel = true` for the second iteration. We set the size of the region in which the PSF shift is computed (`keyword dzonesize`) to 100 pixels and the maximum shift allowed (`keyword maxshift`) to 20 pixels. We reduce these two parameters to 50 and 1, respectively, for the second iteration. The shifts computed are smoothed over 100 and 50 neighbours in the two passes, respectively (`keyword nneigh interp`). Among the three different methods available for solving the linear systems during the fitting stage (i.e. LU, Cholesky and the iterative biconjugate gradient), we selected the matrix inversion method of LU (default). Additionally, we select the option to clip out large negative fluxes before obtaining the final fit. We set all the remaining TPHOT parameters to the default options.

## APPENDIX B: WISP PHOTOMETRIC CATALOGUE FLAG DESCRIPTION

There are two entries for quality flags in the photometric catalogue, each consisting of a sum of bit flags (i.e. sum of powers of 2). One is for the default SExTRACTOR 'internal' flags<fnref n="17" /> (`FLAG_[NIRFILTER]`) and the other is for the default TPHOT flags (Merlin et al. 2015, TPHOT_FLAGS_[FILTER]). These are described below.

`FLAG_[NIRFILTER]` contains a sum of 8 flag bits (i.e. sum of powers of 2):

(i) 1 = photometry likely to be biased by neighbouring sources or bad pixels;

(ii) 2 = object has been deblended;

(iii) 4 = at least one object pixel is saturated;

(iv) 8 = object is close to image boundary;

<figure><img src="image_21.png" /><figcaption>**Figure C1.** The Ricker wavelet used for emission-line detection in the CWT. It is proportional to the second derivative of a Gaussian function and is defined by a width parameter, $\sigma$.</figcaption></figure>

(v) 16 = at least one photometric aperture is incomplete or corrupted;

(vi) 32 = the isophotal footprint is incomplete or corrupted;

(vii) 64 = a memory overflow occurred during deblending;

(viii) 128 = a memory overflow occurred during extraction.

For example, a saturated detection close to an image boundary will have `FLAG_[NIRFILTER] = 4 + 8 = 12`.

`TPHOT_FLAGS_[FILTER]` contains a sum of three flag bits:

(i) 1 = the prior has saturated or negative flux;

(ii) 2 = the prior is blended;

(iii) 4 = the source is at the border of the image.

## APPENDIX C: WISP CONTINUOUS WAVELET TRANSFORM ALGORITHM

Starting from the 1D spectra extracted and calibrated by AXE, we perform a CWT on the spectrum using a Ricker wavelet, which is proportional to the second derivative of a Gaussian function. The Ricker wavelet models the function

$$f = \frac{2}{\sqrt{3\sigma\pi^{\frac{1}{4}}}} \left(1 - \frac{x^2}{\sigma^2}\right) e^{-\frac{x^2}{2\sigma^2}}, \qquad (C1)$$

and is illustrated in Fig. C1.

The transform is performed using $N_\sigma = 10$ kernels or wavelets of varying widths, with the minimum width set to 1.5 pixels, corresponding to ~36 Å (~70 Å) in G102 (G141), and the maximum width equal to twice the FWHM estimate for the object. Spectra obtained in slitless mode are essentially images of the source at each wavelength, and so the width of emission lines will be correlated with the source size. We approximate the FWHM as twice the dispersion measured along the semimajor axis (A_IMAGE reported by SExTRACTOR), and use this FWHM$_{est}$ to define upper bounds for both the wavelet widths and the FWHM of the emission-line profile fits described in Section 5.3.

The CWT transform compares the wavelet with the 1D spectrum, shifting the wavelet to cover all wavelengths and scaling or stretching to cover all input widths. The resulting array of CWT coefficients is a matrix of dimension $N_\sigma \times N_\lambda$ representing the correlation of the spectrum and wavelet at each scale and wavelength. Large CWT coefficients indicate regions of the spectrum with a strong correlation with the wavelet, and so the largest coefficients will occur where both the position and width of the wavelet best match a spectral feature. An example coefficient matrix is displayed in the bottom panel of Fig. C2.

<footnote n="17">¹⁷https://astromatic.github.io/sextractor/Flagging.html</footnote>
the segmentation map, a local background value (we set this value to 0 as the background was already subtracted from the images before running TPHOT), and the reference flux for each source in the high-resolution band.

One of the most important inputs required by TPHOT is the image of the kernel required to perform the inverse of the following convolution operation:

$$PSF(LRI) = \text{Kernel} * PSF(HRI), \qquad (A1)$$

where LRI and HRI stand for low- and high-resolution images, respectively. We obtain the convolution kernel image by deconvolving the low-resolution PSF using the HST PSF as a deconvolution kernel. For this, we adopt the Richardson-Lucy approach (Richardson 1972; Lucy 1974). The average low-resolution and HST PSFs are obtained averaging the PSFs of a selection of point-like, non-saturated sources detected in each image. In accordance with this choice, we set the TPHOT configuration parameter `usereal = True` (and `usemodels` and `useunresolved = False`).

The TPHOT algorithm is organized in different 'stages', each of which performs a specific task. The list and the order of the various stages in each iteration can be set by the user. As described in the user manual, the best results are obtained when the various stages are run in two separate iterations ('passes'). We proceed in the default manner, setting the keyword `order` to `standard` and to `standard2` in the two iterations, respectively.

For each source, TPHOT computes $(x,y)$ shifts during the first pass ('dance' stage). Using these corrections, in the second pass, local kernels are registered to each single source improving the accuracy of the outputs. This can be obtained by setting the keyword `mul-tikernel = true` for the second iteration. We set the size of the region in which the PSF shift is computed (`keyword dzonesize`) to 100 pixels and the maximum shift allowed (`keyword maxshift`) to 20 pixels. We reduce these two parameters to 50 and 1, respectively, for the second iteration. The shifts computed are smoothed over 100 and 50 neighbours in the two passes, respectively (`keyword nneigh interp`). Among the three different methods available for solving the linear systems during the fitting stage (i.e. LU, Cholesky and the iterative biconjugate gradient), we selected the matrix inversion method of LU (default). Additionally, we select the option to clip out large negative fluxes before obtaining the final fit. We set all the remaining TPHOT parameters to the default options.

## APPENDIX B: WISP PHOTOMETRIC CATALOGUE FLAG DESCRIPTION

There are two entries for quality flags in the photometric catalogue, each consisting of a sum of bit flags (i.e. sum of powers of 2). One is for the default SExTRACTOR 'internal' flags<fnref n="17" /> (`FLAG_[NIRFILTER]`) and the other is for the default TPHOT flags (Merlin et al. 2015, TPHOT_FLAGS_[FILTER]). These are described below.

`FLAG_[NIRFILTER]` contains a sum of 8 flag bits (i.e. sum of powers of 2):

(i) 1 = photometry likely to be biased by neighbouring sources or bad pixels;

(ii) 2 = object has been deblended;

(iii) 4 = at least one object pixel is saturated;

(iv) 8 = object is close to image boundary;

<figure><img src="image_21.png" /><figcaption>**Figure C1.** The Ricker wavelet used for emission-line detection in the CWT. It is proportional to the second derivative of a Gaussian function and is defined by a width parameter, $\sigma$.</figcaption></figure>

(v) 16 = at least one photometric aperture is incomplete or corrupted;

(vi) 32 = the isophotal footprint is incomplete or corrupted;

(vii) 64 = a memory overflow occurred during deblending;

(viii) 128 = a memory overflow occurred during extraction.

For example, a saturated detection close to an image boundary will have `FLAG_[NIRFILTER] = 4 + 8 = 12`.

`TPHOT_FLAGS_[FILTER]` contains a sum of three flag bits:

(i) 1 = the prior has saturated or negative flux;

(ii) 2 = the prior is blended;

(iii) 4 = the source is at the border of the image.

## APPENDIX C: WISP CONTINUOUS WAVELET TRANSFORM ALGORITHM

Starting from the 1D spectra extracted and calibrated by AXE, we perform a CWT on the spectrum using a Ricker wavelet, which is proportional to the second derivative of a Gaussian function. The Ricker wavelet models the function

$$f = \frac{2}{\sqrt{3\sigma\pi^{\frac{1}{4}}}} \left(1 - \frac{x^2}{\sigma^2}\right) e^{-\frac{x^2}{2\sigma^2}}, \qquad (C1)$$

and is illustrated in Fig. C1.

The transform is performed using $N_\sigma = 10$ kernels or wavelets of varying widths, with the minimum width set to 1.5 pixels, corresponding to ~36 Å (~70 Å) in G102 (G141), and the maximum width equal to twice the FWHM estimate for the object. Spectra obtained in slitless mode are essentially images of the source at each wavelength, and so the width of emission lines will be correlated with the source size. We approximate the FWHM as twice the dispersion measured along the semimajor axis (A_IMAGE reported by SExTRACTOR), and use this FWHM$_{est}$ to define upper bounds for both the wavelet widths and the FWHM of the emission-line profile fits described in Section 5.3.

The CWT transform compares the wavelet with the 1D spectrum, shifting the wavelet to cover all wavelengths and scaling or stretching to cover all input widths. The resulting array of CWT coefficients is a matrix of dimension $N_\sigma \times N_\lambda$ representing the correlation of the spectrum and wavelet at each scale and wavelength. Large CWT coefficients indicate regions of the spectrum with a strong correlation with the wavelet, and so the largest coefficients will occur where both the position and width of the wavelet best match a spectral feature. An example coefficient matrix is displayed in the bottom panel of Fig. C2.

<footnote n="17">¹⁷https://astromatic.github.io/sextractor/Flagging.html</footnote>
<figure><img src="image_22.png" /><figcaption>**Figure C2.** An example of the emission-line detection algorithm. Top panel: The input spectrum is plotted in black. The filtered spectrum (blue curve) is used as an estimate of the continuum. The purple curve is the detection threshold, defined as a minimum S/N ≥ 2.31 above the continuum. Bottom panel: the 2D CWT coefficient matrix represents the correlation of the spectrum and wavelet at each scale and wavelength. Larger coefficients (yellow colours) identify regions of higher correlation. Emission lines are correlated with the wavelet at many scales, creating connected ridge lines in the CWT matrix. The dashed grey lines in the top panel show the positions of detected ridge lines. The yellow solid lines show the ridges that passed our additional selection criteria to be identified as true emission-line candidates.</figcaption></figure>

As can be seen in the bottom panel of Fig. C2, strong emission peaks in the spectrum are strongly correlated with the Ricker wavelet at many scales. The resulting peaks in the 2D CWT coefficient matrix extend to multiple scales and can be visualized as mountain ridges. Emission-line features in the spectrum can now be identified using the ridges in the CWT coefficient matrix. For this step, we use the SCIPY program `findPeaks_cwt`, which is an implementation of the procedure presented in Du, Kibbe & Lin (2006). We briefly summarize the process here and refer the reader to Du et al. (2006) for a full description of the algorithm.

The first step in the peak identification process involves identifying ridge lines in the coefficient matrix. At each scale, a local maximum is matched with the nearest maximum calculated for the adjacent scale. The two local maxima constitute a ridge provided they are within

a set distance, $dist_{max}$, which we define as one pixel larger than the width of the wavelet at the given scale. A ridge line continues through the matrix as long as the local maximum at each scale is within $d_{max}$ of the previously identified maximum. The ridge line is terminated if a local maximum is not matched at more than $g_{thresh}$ consecutive kernels. We conservatively use $g_{thresh} = 1$ kernel.

The second step is to identify peaks from the detected ridge lines. We only consider ridge lines that cover at least $l_{min} = 3$ scales and have a ridge signal-to-noise of $S/N_{min, CWT} \ge 1$. The ridge S/N is estimated at each scale, and is taken to be the maximum CWT coefficient value on the ridge divided by the overall noise floor. The noise floor is calculated as the 10th percentile of the coefficients around the ridge line at the smallest scale ($\sigma_{min}$). These identified peaks are represented as dashed grey lines in the top panel of Fig. C2.

Following the peak finder, we additionally screen the selected peaks to remove sources that are likely to be spurious. The spectrum is filtered to remove noise using a median filter with a window size of 31 pixels, corresponding to ~760 Å in G102 and ~1440 Å in G141. The purpose of this filtering is to obtain a crude measure of the continuum, which is used in evaluating the strength of any identified peaks. The large window is chosen so that emission lines will not significantly affect the continuum measurement. From this continuum estimate, the contrast between the peak and the continuum is calculated $C = (f_{\lambda, peak} - f_{\lambda, continuum})/f_{\lambda, continuum}$, and any peak with $C < C_{min} = 0.15$ is rejected. This criterion is approximately equivalent to a cut on very low EW emission lines and is implemented in order to remove noise spikes. Next, all peaks that overlap with zeroth orders of nearby bright ($m < 23.5$ in the corresponding direct image) sources are rejected. Recall that we also do not consider any spectra on the right edge of the detector where we cannot determine the position of zeroth orders. We additionally remove peaks that are within $d_{edge} = 5$ pixels of the edge of the spectrum to avoid convolution edge effects. Finally, we require that emission-line candidates have an overall signal-to-noise for the emission line of $S/N_{line} \ge 4$. For a line consisting of three contiguous pixels, this corresponds to $S/N_{min, pix} \ge 2.31$, where here $S/N$ is defined traditionally as the flux in the continuum divided by the error. This resulting noise threshold is displayed as the purple curve in Fig. C2. A summary of the emission line detection parameters is provided in Table C1.

<table><caption>**Table C1.** Emission-line detection parameters.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Description</th></tr></thead><tbody><tr><td colspan="3" style="text-align: center;">Continuous wavelet transform</td></tr><tr><td>N<sub>σ</sub></td><td>10</td><td>Number of CWT kernels (widths) used in transform</td></tr><tr><td>σ<sub>min</sub></td><td>1.5 [pixels]</td><td>Minimum CWT kernel width</td></tr><tr><td>σ<sub>max</sub></td><td>2.0</td><td>Maximum CWT kernel width, fraction of FWHM<sub>est</sub></td></tr><tr><td colspan="3" style="text-align: center;">Ridge and peak definitions</td></tr><tr><td>d<sub>max</sub></td><td>σ + 1 [pixels]</td><td>Maximum acceptable separation distance between local maxima at each scale on the same ridge line</td></tr><tr><td>g<sub>max</sub></td><td>1 [kernels]</td><td>Maximum acceptable gap between connected ridges</td></tr><tr><td>l<sub>min</sub></td><td>3 [kernels]</td><td>Minimum acceptable no. of kernels in which peak is significant</td></tr><tr><td>S/R<sub>min, CWT</sub></td><td>1</td><td>Minimum acceptable ridge S/N at each scale</td></tr><tr><td colspan="3" style="text-align: center;">Requirements for real lines</td></tr><tr><td>C<sub>min</sub></td><td>0.15</td><td>Minimum acceptable contrast between peak and continuum fluxes</td></tr><tr><td>d<sub>edge</sub></td><td>5 [pixels]</td><td>Minimum acceptable distance to edge of spectrum</td></tr><tr><td>n<sub>min</sub></td><td>3 [pixels]</td><td>Minimum number of pixels above the noise threshold</td></tr><tr><td>S/N<sub>min, pix</sub></td><td>2.31</td><td>Minimum S/N per pixel</td></tr></tbody></table>
<figure><img src="image_22.png" /><figcaption>**Figure C2.** An example of the emission-line detection algorithm. Top panel: The input spectrum is plotted in black. The filtered spectrum (blue curve) is used as an estimate of the continuum. The purple curve is the detection threshold, defined as a minimum S/N ≥ 2.31 above the continuum. Bottom panel: the 2D CWT coefficient matrix represents the correlation of the spectrum and wavelet at each scale and wavelength. Larger coefficients (yellow colours) identify regions of higher correlation. Emission lines are correlated with the wavelet at many scales, creating connected ridge lines in the CWT matrix. The dashed grey lines in the top panel show the positions of detected ridge lines. The yellow solid lines show the ridges that passed our additional selection criteria to be identified as true emission-line candidates.</figcaption></figure>

As can be seen in the bottom panel of Fig. C2, strong emission peaks in the spectrum are strongly correlated with the Ricker wavelet at many scales. The resulting peaks in the 2D CWT coefficient matrix extend to multiple scales and can be visualized as mountain ridges. Emission-line features in the spectrum can now be identified using the ridges in the CWT coefficient matrix. For this step, we use the SCIPY program `findPeaks_cwt`, which is an implementation of the procedure presented in Du, Kibbe & Lin (2006). We briefly summarize the process here and refer the reader to Du et al. (2006) for a full description of the algorithm.

The first step in the peak identification process involves identifying ridge lines in the coefficient matrix. At each scale, a local maximum is matched with the nearest maximum calculated for the adjacent scale. The two local maxima constitute a ridge provided they are within

a set distance, $dist_{max}$, which we define as one pixel larger than the width of the wavelet at the given scale. A ridge line continues through the matrix as long as the local maximum at each scale is within $d_{max}$ of the previously identified maximum. The ridge line is terminated if a local maximum is not matched at more than $g_{thresh}$ consecutive kernels. We conservatively use $g_{thresh} = 1$ kernel.

The second step is to identify peaks from the detected ridge lines. We only consider ridge lines that cover at least $l_{min} = 3$ scales and have a ridge signal-to-noise of $S/N_{min, CWT} \ge 1$. The ridge S/N is estimated at each scale, and is taken to be the maximum CWT coefficient value on the ridge divided by the overall noise floor. The noise floor is calculated as the 10th percentile of the coefficients around the ridge line at the smallest scale ($\sigma_{min}$). These identified peaks are represented as dashed grey lines in the top panel of Fig. C2.

Following the peak finder, we additionally screen the selected peaks to remove sources that are likely to be spurious. The spectrum is filtered to remove noise using a median filter with a window size of 31 pixels, corresponding to ~760 Å in G102 and ~1440 Å in G141. The purpose of this filtering is to obtain a crude measure of the continuum, which is used in evaluating the strength of any identified peaks. The large window is chosen so that emission lines will not significantly affect the continuum measurement. From this continuum estimate, the contrast between the peak and the continuum is calculated $C = (f_{\lambda, peak} - f_{\lambda, continuum})/f_{\lambda, continuum}$, and any peak with $C < C_{min} = 0.15$ is rejected. This criterion is approximately equivalent to a cut on very low EW emission lines and is implemented in order to remove noise spikes. Next, all peaks that overlap with zeroth orders of nearby bright ($m < 23.5$ in the corresponding direct image) sources are rejected. Recall that we also do not consider any spectra on the right edge of the detector where we cannot determine the position of zeroth orders. We additionally remove peaks that are within $d_{edge} = 5$ pixels of the edge of the spectrum to avoid convolution edge effects. Finally, we require that emission-line candidates have an overall signal-to-noise for the emission line of $S/N_{line} \ge 4$. For a line consisting of three contiguous pixels, this corresponds to $S/N_{min, pix} \ge 2.31$, where here $S/N$ is defined traditionally as the flux in the continuum divided by the error. This resulting noise threshold is displayed as the purple curve in Fig. C2. A summary of the emission line detection parameters is provided in Table C1.

<table><caption>**Table C1.** Emission-line detection parameters.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Description</th></tr></thead><tbody><tr><td colspan="3" style="text-align: center;">Continuous wavelet transform</td></tr><tr><td>N<sub>σ</sub></td><td>10</td><td>Number of CWT kernels (widths) used in transform</td></tr><tr><td>σ<sub>min</sub></td><td>1.5 [pixels]</td><td>Minimum CWT kernel width</td></tr><tr><td>σ<sub>max</sub></td><td>2.0</td><td>Maximum CWT kernel width, fraction of FWHM<sub>est</sub></td></tr><tr><td colspan="3" style="text-align: center;">Ridge and peak definitions</td></tr><tr><td>d<sub>max</sub></td><td>σ + 1 [pixels]</td><td>Maximum acceptable separation distance between local maxima at each scale on the same ridge line</td></tr><tr><td>g<sub>max</sub></td><td>1 [kernels]</td><td>Maximum acceptable gap between connected ridges</td></tr><tr><td>l<sub>min</sub></td><td>3 [kernels]</td><td>Minimum acceptable no. of kernels in which peak is significant</td></tr><tr><td>S/R<sub>min, CWT</sub></td><td>1</td><td>Minimum acceptable ridge S/N at each scale</td></tr><tr><td colspan="3" style="text-align: center;">Requirements for real lines</td></tr><tr><td>C<sub>min</sub></td><td>0.15</td><td>Minimum acceptable contrast between peak and continuum fluxes</td></tr><tr><td>d<sub>edge</sub></td><td>5 [pixels]</td><td>Minimum acceptable distance to edge of spectrum</td></tr><tr><td>n<sub>min</sub></td><td>3 [pixels]</td><td>Minimum number of pixels above the noise threshold</td></tr><tr><td>S/N<sub>min, pix</sub></td><td>2.31</td><td>Minimum S/N per pixel</td></tr></tbody></table>
## APPENDIX D: WISP SURVEY COMPLETENESS SIMULATIONS

The selection function in slitless spectroscopic data is complex, depending on line S/N, EW, galaxy size and concentration, and observed wavelength. Extensive simulations exploring the full parameter space are required. Moreover, the completeness strongly depends on the observing strategy and depth of the data sets. We therefore perform two sets of simulations, one each for the shallow and deeper WISP fields. We add synthetic sources to a selection of real WISP fields and reprocess the fields through the WISP pipeline and line finding procedures presented in Section 5. We describe the full process below.

We create 10 000 simulated galaxies and divide them equally between the shallow and deep fields. All sources are assigned a spectral template from the models of Bruzual & Charlot (2003) created with a Chabrier (2003) IMF, a constant SFH observed 100 Myr after the beginning of star formation, and one of three metallicities: $Z/Z_\odot$ = 0.02, 0.2, or 1. The template spectra are redshifted to the observed frame such that all emission-line and continuum fluxes are normalized to the desired observed values. We add the following emission lines to the spectra: [O II]λ3727, [O III]λ4363, Hβ, [O III]λ4959, [O III]λ5007, Hα, [S II]λ6716, [S II]λ6730, [S III]λ9069, and [S III]λ9531. Each emission line is modelled as a Gaussian with $\sigma = 3$ Å.

The basic question addressed by completeness corrections is whether an input source or emission line is recovered by the reduction and processing performed on real data. As it is not a measure of the rates of source misclassification or redshift misidentification, the inputs need not represent the physical distributions observed in the universe. Unless otherwise noted, we therefore uniformly populate the input parameter space so we can determine the ranges most affected by incompleteness.

For each parameter, we choose input ranges that bracket the observed values. Source redshifts are pulled from a uniform distribution ranging from the redshift at which $H_\alpha$ enters the wavelength coverage to that at which [O III]λ5007 leaves the wavelength coverage.<fnref n="18" /> We adopt conservative wavelength cutoffs for each grism to avoid the wavelengths where the sensitivity drops rapidly: $8500 \le \lambda_{G102} \le 11200$ Å and $11200 \le \lambda_{G141} \le 16500$ Å for the G102 and G141 grisms, respectively. Real emission lines that lie outside of these wavelength ranges are flagged in the catalogue (see Appendix E for details). These cut-offs correspond to redshift ranges of $0.3 \le z \le 2.3$ for the deep fields with coverage in both grisms and $0.7 \le z \le 2.3$ for the shallow fields. Input $H_\alpha$ fluxes for sources in shallow fields are pulled uniformly from $5 \times 10^{-17} \le f_{H\alpha} \le 1 \times 10^{-15}$ erg s⁻¹ cm⁻², with a lower limit of $1 \times 10^{-17}$ erg s⁻¹ cm⁻² in the deep fields. We increase the number of faint line fluxes in the deep fields by separating the synthetic sources into two groups: half with fluxes pulled from a uniform distribution with a maximum at $1 \times 10^{-16}$ erg s⁻¹ cm⁻² and half with fluxes extending up to $1 \times 10^{-15}$. Using two upper flux limits allows us to populate the bright end where sources should be easily detected in the deep fields, while ensuring we have an adequate number of faint objects even if the recovered fraction

is small. The input observed EW distribution is uniform across the range $20 \le \text{EW}_{H\alpha, \text{obs}} \le 700$ Å. The flux density in the continuum at the observed wavelength of $H_\alpha$ – that is, the ratio of input $H_\alpha$ flux and EW – is used to normalize the spectral template to the desired observed units and brightness.

There is a range of observed emission-line ratios in the WISP catalogue, which we account for in the simulations by varying the input $H_\alpha/[\text{O III}]\lambda5007$ ratios in the synthetic spectra. Although we are not attempting to quantify the redshift misidentification in the catalogue, simulating emission lines with a variety of flux ratios is necessary to include any biases related to single versus multiline emitters. For example, reviewers are more likely to identify low S/N lines if there are additional emission lines visible in the spectrum to confirm the source's redshift. Input $\log_{10}(H_\alpha/[\text{O III}]\lambda5007)$ ratios are drawn from a Gaussian distribution centred at $\mu = 0$ with $\sigma = 0.2$, matching the observed distribution in the catalogue but with a slightly larger FWHM. The intrinsic $H_\alpha/H\beta$ ratio for case B recombination is adopted for all sources, 2.86 (Osterbrock 1989). For the remaining emission lines, we adopt the ratios from Anders & Fritze-v. Alvensleben (2003) with respect to [O III]λ5007 for each metallicity assuming an electron density of $n_e = 100$ cm⁻³ and electron temperature of $T_e = 10000$ K. The input H-band magnitudes are not assigned to the sources, but instead are the result of the flux normalization of the template spectral continua and depend on the $H_\alpha$ fluxes and EWs of each source. We do not add the effects of dust to the spectra, but instead rely on the range of line ratios to cover observed values. We note that the adopted case B Balmer decrement, $H_\alpha/H\beta$, is the only line ratio that remains unchanged and therefore always exhibits the value expected for dust-free galaxies. However, we remind the reader that as we are not trying to replicate reality, this choice will not affect the resulting completeness calculations.

The completeness of sources in the WISP catalogue depends strongly on object size and shape. Object size first affects the completeness in imaging, where the low surface brightness of faint, extended objects may fall below the adopted SExTRACTOR detection thresholds, while the higher surface brightnesses of more compact sources are detected. In addition, the pipeline removes the most extremely elongated detected sources from the catalogue in an attempt to remove artefacts such as diffraction spikes and persistence from bright first orders. Since emission lines observed via slitless spectroscopy are essentially images of the sources at the given wavelengths, the source shape and size will also affect the completeness of the line finding procedure. Extended sources with a low EW are missed by the peak finder, and reviewers are more consistent with their treatment of compact, high-S/N emission lines. We therefore assign each object a profile RMS along the major (minor) axis pulled from a uniform distribution in the range 0.05 arcsec $\le a \le 1.2$ arcsec (0.05 arcsec $\le b \le a$), again matching the range but not the shape of the observed distribution in the catalogue. The input parameter distributions are summarized in Table D1.

We add 25 simulated sources at random locations to the raw images for a set of WISP fields, using the AXESIM (Kümmel et al. 2007) software package to create the synthetic direct and grism images of each source. These fields are then fully processed as real data, including the visual inspection by two reviewers. As mentioned in Section 5.4, in order to save on the time and effort required for this step, the reviewers only inspect the spectra of simulated sources that were identified by the line finding algorithm. This is not to say that all emission-line candidates were real. Some were noise spikes, contamination, or the result of poorly fit continua. However, it does mean we cannot use the simulations to measure the rates of contamination or redshift misidentification in the catalogue.

<footnote n="18">¹⁸We do not add any emission lines to the spectrum in the two narrow wavelength ranges that AXESIM uses for spectral normalization: 10 400–10 600 (G102) and 15 400–15 600 Å (G141). Emission lines in these ranges would artificially boost the normalization factor thereby significantly reducing the simulated continuum of the spectrum. For more information, see the AXESIM (Kümmel, Kuntschner & Walsh 2007) manual available at axe.stsci.edu/axesim/. There are therefore several narrow redshift ranges that we do not populate with synthetic sources.</footnote>
## APPENDIX D: WISP SURVEY COMPLETENESS SIMULATIONS

The selection function in slitless spectroscopic data is complex, depending on line S/N, EW, galaxy size and concentration, and observed wavelength. Extensive simulations exploring the full parameter space are required. Moreover, the completeness strongly depends on the observing strategy and depth of the data sets. We therefore perform two sets of simulations, one each for the shallow and deeper WISP fields. We add synthetic sources to a selection of real WISP fields and reprocess the fields through the WISP pipeline and line finding procedures presented in Section 5. We describe the full process below.

We create 10 000 simulated galaxies and divide them equally between the shallow and deep fields. All sources are assigned a spectral template from the models of Bruzual & Charlot (2003) created with a Chabrier (2003) IMF, a constant SFH observed 100 Myr after the beginning of star formation, and one of three metallicities: $Z/Z_\odot$ = 0.02, 0.2, or 1. The template spectra are redshifted to the observed frame such that all emission-line and continuum fluxes are normalized to the desired observed values. We add the following emission lines to the spectra: [O II]λ3727, [O III]λ4363, Hβ, [O III]λ4959, [O III]λ5007, Hα, [S II]λ6716, [S II]λ6730, [S III]λ9069, and [S III]λ9531. Each emission line is modelled as a Gaussian with $\sigma = 3$ Å.

The basic question addressed by completeness corrections is whether an input source or emission line is recovered by the reduction and processing performed on real data. As it is not a measure of the rates of source misclassification or redshift misidentification, the inputs need not represent the physical distributions observed in the universe. Unless otherwise noted, we therefore uniformly populate the input parameter space so we can determine the ranges most affected by incompleteness.

For each parameter, we choose input ranges that bracket the observed values. Source redshifts are pulled from a uniform distribution ranging from the redshift at which $H_\alpha$ enters the wavelength coverage to that at which [O III]λ5007 leaves the wavelength coverage.<fnref n="18" /> We adopt conservative wavelength cutoffs for each grism to avoid the wavelengths where the sensitivity drops rapidly: $8500 \le \lambda_{G102} \le 11200$ Å and $11200 \le \lambda_{G141} \le 16500$ Å for the G102 and G141 grisms, respectively. Real emission lines that lie outside of these wavelength ranges are flagged in the catalogue (see Appendix E for details). These cut-offs correspond to redshift ranges of $0.3 \le z \le 2.3$ for the deep fields with coverage in both grisms and $0.7 \le z \le 2.3$ for the shallow fields. Input $H_\alpha$ fluxes for sources in shallow fields are pulled uniformly from $5 \times 10^{-17} \le f_{H\alpha} \le 1 \times 10^{-15}$ erg s⁻¹ cm⁻², with a lower limit of $1 \times 10^{-17}$ erg s⁻¹ cm⁻² in the deep fields. We increase the number of faint line fluxes in the deep fields by separating the synthetic sources into two groups: half with fluxes pulled from a uniform distribution with a maximum at $1 \times 10^{-16}$ erg s⁻¹ cm⁻² and half with fluxes extending up to $1 \times 10^{-15}$. Using two upper flux limits allows us to populate the bright end where sources should be easily detected in the deep fields, while ensuring we have an adequate number of faint objects even if the recovered fraction

is small. The input observed EW distribution is uniform across the range $20 \le EW_{H\alpha, \text{obs}} \le 700$ Å. The flux density in the continuum at the observed wavelength of $H_\alpha$ – that is, the ratio of input $H_\alpha$ flux and EW – is used to normalize the spectral template to the desired observed units and brightness.

There is a range of observed emission-line ratios in the WISP catalogue, which we account for in the simulations by varying the input $H_\alpha/[O III]λ5007$ ratios in the synthetic spectra. Although we are not attempting to quantify the redshift misidentification in the catalogue, simulating emission lines with a variety of flux ratios is necessary to include any biases related to single versus multiline emitters. For example, reviewers are more likely to identify low S/N lines if there are additional emission lines visible in the spectrum to confirm the source's redshift. Input $\log_{10}(H_\alpha/[O III]λ5007)$ ratios are drawn from a Gaussian distribution centred at $\mu = 0$ with $\sigma = 0.2$, matching the observed distribution in the catalogue but with a slightly larger FWHM. The intrinsic $H_\alpha/H\beta$ ratio for case B recombination is adopted for all sources, 2.86 (Osterbrock 1989). For the remaining emission lines, we adopt the ratios from Anders & Fritze-v. Alvensleben (2003) with respect to [O III]λ5007 for each metallicity assuming an electron density of $n_e = 100$ cm⁻³ and electron temperature of $T_e = 10000$ K. The input H-band magnitudes are not assigned to the sources, but instead are the result of the flux normalization of the template spectral continua and depend on the $H_\alpha$ fluxes and EWs of each source. We do not add the effects of dust to the spectra, but instead rely on the range of line ratios to cover observed values. We note that the adopted case B Balmer decrement, $H_\alpha/H\beta$, is the only line ratio that remains unchanged and therefore always exhibits the value expected for dust-free galaxies. However, we remind the reader that as we are not trying to replicate reality, this choice will not affect the resulting completeness calculations.

The completeness of sources in the WISP catalogue depends strongly on object size and shape. Object size first affects the completeness in imaging, where the low surface brightness of faint, extended objects may fall below the adopted SExTRACTOR detection thresholds, while the higher surface brightnesses of more compact sources are detected. In addition, the pipeline removes the most extremely elongated detected sources from the catalogue in an attempt to remove artefacts such as diffraction spikes and persistence from bright first orders. Since emission lines observed via slitless spectroscopy are essentially images of the sources at the given wavelengths, the source shape and size will also affect the completeness of the line finding procedure. Extended sources with a low EW are missed by the peak finder, and reviewers are more consistent with their treatment of compact, high-S/N emission lines. We therefore assign each object a profile RMS along the major (minor) axis pulled from a uniform distribution in the range 0.05 arcsec $\le a \le 1.2$ arcsec (0.05 arcsec $\le b \le a$), again matching the range but not the shape of the observed distribution in the catalogue. The input parameter distributions are summarized in Table D1.

We add 25 simulated sources at random locations to the raw images for a set of WISP fields, using the AXESIM (Kümmel et al. 2007) software package to create the synthetic direct and grism images of each source. These fields are then fully processed as real data, including the visual inspection by two reviewers. As mentioned in Section 5.4, in order to save on the time and effort required for this step, the reviewers only inspect the spectra of simulated sources that were identified by the line finding algorithm. This is not to say that all emission-line candidates were real. Some were noise spikes, contamination, or the result of poorly fit continua. However, it does mean we cannot use the simulations to measure the rates of contamination or redshift misidentification in the catalogue.

<footnote n="18">¹⁸We do not add any emission lines to the spectrum in the two narrow wavelength ranges that AXESIM uses for spectral normalization: 10 400–10 600 (G102) and 15 400–15 600 Å (G141). Emission lines in these ranges would artificially boost the normalization factor thereby significantly reducing the simulated continuum of the spectrum. For more information, see the AXESIM (Kümmel, Kuntschner & Walsh 2007) manual available at axe.stsci.edu/axesim/. There are therefore several narrow redshift ranges that we do not populate with synthetic sources.</footnote>
<table><caption>**Table D1.** Input parameters for simulated sources.</caption><thead><tr><th>Parameter</th><th>Deep fields</th><th>Shallow fields</th></tr></thead><tbody><tr><td>Redshift</td><td>0.3 ≤ z ≤ 2.3</td><td>0.7 ≤ z ≤ 2.3</td></tr><tr><td>Semimajor axis<sup>a</sup></td><td>0.05 arcsec ≤ a ≤ 1.2 arcsec</td><td>0.05 arcsec ≤ a ≤ 1.2 arcsec</td></tr><tr><td>Elongation<sup>b</sup></td><td>1 ≤ a/b ≤ 24</td><td>1 ≤ a/b ≤ 24</td></tr><tr><td>Observed Hα flux (erg s<sup>-1</sup> cm<sup>-2</sup>)</td><td>1 × 10<sup>-17</sup> ≤ f ≤ 1 × 10<sup>-15</sup></td><td>5 × 10<sup>-17</sup> ≤ f ≤ 1 × 10<sup>-15</sup></td></tr><tr><td>Observed Hα EW (Å)</td><td>20 ≤ EW<sub>obs</sub> ≤ 700</td><td>20 ≤ EW<sub>obs</sub> ≤ 700</td></tr><tr><td>Hα/[O III]λ5007 ratio</td><td>Gaussian: μ = 0, σ = 0.2</td><td>Gaussian: μ = 0, σ = 0.2</td></tr><tr><td>H-band magnitude<sup>c</sup></td><td>16.8 ≤ m<sub>H</sub> ≤ 27.6</td><td>16.8 ≤ m<sub>H</sub> ≤ 26.2</td></tr></tbody></table>

Notes. Parameters indicated with a range are uniformly populated between that range.

<sup>a</sup>The semimajor axis *a* is treated as the profile RMS along the major axis.

<sup>b</sup>The semiminor axis *b* values are pulled from the range 0.05 arcsec ≤ *b* ≤ *a*, and so these elongations *a/b* list the minimum and maximum possible values.

<sup>c</sup>The H-band magnitude is computed from the input template spectra normalized according to the Hα flux and EW. The *m*<sub>H</sub> here list the minimum and maximum possible values.

The WISP completeness calculations, described in Section 5.4, involve determining the fraction of sources that have been recovered in bins of source size and emission-line flux and EW. After the simulated sources are fully processed through the WISP software, we compare all properties of the recovered sources with their input values. This step is necessary to confirm that the recovered sources are counted in the proper bins, that is, that the parameter values are not systematically different due to the simulation and reduction processes. The input and output fluxes for Hα and [O III] show a clear correlation down to $f \sim 7 \times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$. At fainter fluxes, there is a slight trend toward brighter output fluxes, which may be caused by spectral contamination. Overlapping spectra can boost a source's measured emission-line flux, and we expect the severity of this contamination to increase with decreasing line flux. Yet there are far too few recovered Hα or [O III] lines with fluxes <7 × 10$^{-17}$ erg s$^{-1}$ cm$^{-2}$ to properly evaluate the trend. The other emission lines are almost always fit as secondary lines and will therefore be fainter and at a lower S/N than the primary lines. There is a similarly good agreement between input and output Hα and [O III] EWs.

A comparison of the source sizes, however, shows that the inputs are systematically larger than the outputs. This effect is not surprising, since the flux in the wings of the simulated Gaussian sources can fall below the SExTRACTOR detection limit. The extracted 'footprints' of the sources are then smaller than what was simulated. We must understand the relationship between the input and output sizes in order to properly determine the number of sources that are recovered as a function of size. We model this relationship with a combination of a fourth-order polynomial for semimajor and minor axes $\le 0.6$ arcsec and a linear fit for larger sizes. The WISP survey completeness is applied to sources according to their observed fluxes, EWs, and sizes, as their intrinsic values are unknown. The completeness is therefore calculated as a function of the output values measured for the simulated sources rather than the input values. We use the models to scale the input *a* and *b* to their measured values. This step is necessary to ensure that input sources that are not recovered are counted in the correct bins.

## APPENDIX E: WISP EMISSION-LINE CATALOGUE FLAG DESCRIPTION

There are nine entries for quality flags in the emission-line catalogue, all consisting of a sum of bit flags (i.e. sum of powers of 2). These are described below.

`FILTER_FLAG` indicates the filter coverage as a sum of 10 flag bits:

(i) 1 = F110 coverage;

(ii) 2 = F140 coverage;

(iii) 4 = F160 coverage;

(iv) 8 = UVIS1 coverage (F475X or F606W);

(v) 16 = UVIS2 coverage (F600LP or F814W);

(vi) 32 = IRAC coverage (Ch1 and/or Ch2);

(vii) 64 = *u* coverage;

(viii) 128 = *g* coverage;

(ix) 256 = *r* coverage;

(x) 512 = *i* coverage.

`GRISM_FLAG` contains a sum of two flag bits:

(i) 1 = G102 coverage;

(ii) 2 = G141 coverage.

`[GRISM_FILTER] FILTER` contains a sum of five flag bits:

(i) 1 = Artefact, a satellite trail, strange features, significant persistence, etc.

(ii) 2 = Sky subtraction problem, residual sky, or structure remaining in the background.

(iii) 4 = One or more bright sources present that significantly contaminate the field.

(iv) 8 = A very crowded field, usually indicating some type of star cluster.

(v) 16 = Scattered light, leading to sensitivity depths that vary significantly depending on source position.

`EDGE_FLAG` contains a sum of five flag bits:

(i) 0 = Object is not near an image edge in direct image.

(ii) 1 = Object is within ~20 pixels of bottom edge of direct image.

(iii) 2 = Object is within ~20 pixels of top edge of direct image.

(iv) 4 = Object is within ~20 pixels of left edge of direct image.

(v) 8 = Object is potentially within the region along the right edge in which the position of zeroth orders is unknown. The exact x-position is different for both grisms and the wavelength of the emission line must also be considered. The line-finding algorithm takes these details into account.

`REDSHIFT_FLAG` contains a sum of eight flag bits:

(i) 0 = Redshift agreement within 1σ errors.

(ii) 1 = Redshift disagreement within 1σ errors; adopted redshift taken as the case with three or more lines with S/N > 3.

(iii) 2 = Redshift disagreement within 1σ errors; adopted redshift taken as the case with line identified as Hα. If both reviewers
<table><caption>**Table D1.** Input parameters for simulated sources.</caption><thead><tr><th>Parameter</th><th>Deep fields</th><th>Shallow fields</th></tr></thead><tbody><tr><td>Redshift</td><td>0.3 ≤ z ≤ 2.3</td><td>0.7 ≤ z ≤ 2.3</td></tr><tr><td>Semimajor axis<sup>a</sup></td><td>0.05 arcsec ≤ a ≤ 1.2 arcsec</td><td>0.05 arcsec ≤ a ≤ 1.2 arcsec</td></tr><tr><td>Elongation<sup>b</sup></td><td>1 ≤ a/b ≤ 24</td><td>1 ≤ a/b ≤ 24</td></tr><tr><td>Observed Hα flux (erg s<sup>-1</sup> cm<sup>-2</sup>)</td><td>1 × 10<sup>-17</sup> ≤ f ≤ 1 × 10<sup>-15</sup></td><td>5 × 10<sup>-17</sup> ≤ f ≤ 1 × 10<sup>-15</sup></td></tr><tr><td>Observed Hα EW (Å)</td><td>20 ≤ EW<sub>obs</sub> ≤ 700</td><td>20 ≤ EW<sub>obs</sub> ≤ 700</td></tr><tr><td>Hα/[O III]λ5007 ratio</td><td>Gaussian: μ = 0, σ = 0.2</td><td>Gaussian: μ = 0, σ = 0.2</td></tr><tr><td>H-band magnitude<sup>c</sup></td><td>16.8 ≤ m<sub>H</sub> ≤ 27.6</td><td>16.8 ≤ m<sub>H</sub> ≤ 26.2</td></tr></tbody></table>

Notes. Parameters indicated with a range are uniformly populated between that range.

<sup>a</sup>The semimajor axis *a* is treated as the profile RMS along the major axis.

<sup>b</sup>The semiminor axis *b* values are pulled from the range 0.05 arcsec ≤ *b* ≤ *a*, and so these elongations *a/b* list the minimum and maximum possible values.

<sup>c</sup>The H-band magnitude is computed from the input template spectra normalized according to the Hα flux and EW. The *m*<sub>H</sub> here list the minimum and maximum possible values.

The WISP completeness calculations, described in Section 5.4, involve determining the fraction of sources that have been recovered in bins of source size and emission-line flux and EW. After the simulated sources are fully processed through the WISP software, we compare all properties of the recovered sources with their input values. This step is necessary to confirm that the recovered sources are counted in the proper bins, that is, that the parameter values are not systematically different due to the simulation and reduction processes. The input and output fluxes for Hα and [O III] show a clear correlation down to $f \sim 7 \times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$. At fainter fluxes, there is a slight trend toward brighter output fluxes, which may be caused by spectral contamination. Overlapping spectra can boost a source's measured emission-line flux, and we expect the severity of this contamination to increase with decreasing line flux. Yet there are far too few recovered Hα or [O III] lines with fluxes <7 × 10$^{-17}$ erg s$^{-1}$ cm$^{-2}$ to properly evaluate the trend. The other emission lines are almost always fit as secondary lines and will therefore be fainter and at a lower S/N than the primary lines. There is a similarly good agreement between input and output Hα and [O III] EWs.

A comparison of the source sizes, however, shows that the inputs are systematically larger than the outputs. This effect is not surprising, since the flux in the wings of the simulated Gaussian sources can fall below the SExTRACTOR detection limit. The extracted 'footprints' of the sources are then smaller than what was simulated. We must understand the relationship between the input and output sizes in order to properly determine the number of sources that are recovered as a function of size. We model this relationship with a combination of a fourth-order polynomial for semimajor and minor axes $\le 0.6$ arcsec and a linear fit for larger sizes. The WISP survey completeness is applied to sources according to their observed fluxes, EWs, and sizes, as their intrinsic values are unknown. The completeness is therefore calculated as a function of the output values measured for the simulated sources rather than the input values. We use the models to scale the input *a* and *b* to their measured values. This step is necessary to ensure that input sources that are not recovered are counted in the correct bins.

## APPENDIX E: WISP EMISSION-LINE CATALOGUE FLAG DESCRIPTION

There are nine entries for quality flags in the emission-line catalogue, all consisting of a sum of bit flags (i.e. sum of powers of 2). These are described below.

`FILTER_FLAG` indicates the filter coverage as a sum of 10 flag bits:

(i) 1 = F110 coverage;

(ii) 2 = F140 coverage;

(iii) 4 = F160 coverage;

(iv) 8 = UVIS1 coverage (F475X or F606W);

(v) 16 = UVIS2 coverage (F600LP or F814W);

(vi) 32 = IRAC coverage (Ch1 and/or Ch2);

(vii) 64 = *u* coverage;

(viii) 128 = *g* coverage;

(ix) 256 = *r* coverage;

(x) 512 = *i* coverage.

`GRISM_FLAG` contains a sum of two flag bits:

(i) 1 = G102 coverage;

(ii) 2 = G141 coverage.

`[GRISM_FILTER] FILTER` contains a sum of five flag bits:

(i) 1 = Artefact, a satellite trail, strange features, significant persistence, etc.

(ii) 2 = Sky subtraction problem, residual sky, or structure remaining in the background.

(iii) 4 = One or more bright sources present that significantly contaminate the field.

(iv) 8 = A very crowded field, usually indicating some type of star cluster.

(v) 16 = Scattered light, leading to sensitivity depths that vary significantly depending on source position.

`EDGE_FLAG` contains a sum of five flag bits:

(i) 0 = Object is not near an image edge in direct image.

(ii) 1 = Object is within ~20 pixels of bottom edge of direct image.

(iii) 2 = Object is within ~20 pixels of top edge of direct image.

(iv) 4 = Object is within ~20 pixels of left edge of direct image.

(v) 8 = Object is potentially within the region along the right edge in which the position of zeroth orders is unknown. The exact x-position is different for both grisms and the wavelength of the emission line must also be considered. The line-finding algorithm takes these details into account.

`REDSHIFT_FLAG` contains a sum of eight flag bits:

(i) 0 = Redshift agreement within 1σ errors.

(ii) 1 = Redshift disagreement within 1σ errors; adopted redshift taken as the case with three or more lines with S/N > 3.

(iii) 2 = Redshift disagreement within 1σ errors; adopted redshift taken as the case with line identified as Hα. If both reviewers