# WFC3 Infrared Spectroscopic Parallel (WISP) Survey: Photometric and Emission
Line Data Release

A. J. Battisti1,2, M. B. Bagley3, M. Rafelski4,5, I. Baronchelli6,7, Y.S.
Dai8, A. L. Henry4,5, H. Atek9, J. Colbert10, M. A. Malkan11, P. J.
McCarthy12, C. Scarlata13, B. Siana14, H. I. Teplitz10, A. Alavi10, K.
Boyett2,15, A. J. Bunker16, J. P. Gardner17, N. P. Hathi4, D. Masters10, V.
Mehta10, M. Rutkowski18, K. Shahinyan13, B. Sunnquist4, X. Wang19,20,21
1Research School of Astronomy and Astrophysics, Australian National
University, Cotter Road, Weston Creek, ACT 2611, Australia
2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia
3Department of Astronomy, The University of Texas at Austin, Austin, TX 78712,
USA
4Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218,
USA
5Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD
21218, USA
6INAF-Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna, Italy
7Italian ALMA Regional Centre, Via Gobetti 101, 40129 Bologna, Italy
8Chinese Academy of Sciences South America Center for Astronomy (CASSACA),
National Astronomical Observatories of China
(NAOC), 20A Datun Road, Beijing, 100012, China
9Institut d’Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard
Arago, 75014, Paris, France
10IPAC, California Institute of Technology, 1200 E. California Boulevard,
Pasadena, CA 91125, USA
11Department of Physics and Astronomy University of California, Los Angeles
Los Angeles, CA 90095-1547, USA
12National Optical-Infrared Astronomy Research Laboratory, Tucson, AZ 85719,
USA
13Minnesota Institute for Astrophysics, University of Minnesota, Minneapolis,
MN 55455, USA
14Department of Physics and Astronomy, University of California, Riverside,
900 University Avenue, Riverside, CA 92521, USA
15School of Physics, University of Melbourne, Parkville 3010, VIC, Australia
16Department of Physics, University of Oxford, Denys Wilkinson Building, Keble
Road, Oxford OX13RH, UK
17Astrophysics Science Division, NASA Goddard Space Flight Center, 8800
Greenbelt Rd, Greenbelt, MD 20771, USA
18Minnesota State University-Mankato, Telescope Science Institute, TN141,
Mankato, MN 56001, USA
19School of Astronomy and Space Science, University of Chinese Academy of
Sciences (UCAS), Beijing 100049, China
20National Astronomical Observatories, Chinese Academy of Sciences, Beijing
100101, China
21Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal
University, Beijing 102206, China<EMAIL_ADDRESS>0000-0003-4569-2285 0000-0002-9921-9218 0000-0002-9946-4731
0000-0003-0556-2929 0000-0002-7928-416X 0000-0002-6586-4446
0000-0002-7570-0824 0000-0001-6919-1237 0000-0002-9136-8876
0000-0002-4935-9511 0000-0002-7064-5424 0000-0002-8630-6435
0000-0003-4109-304X 0000-0002-8651-9879 0000-0003-2098-9568
0000-0001-6145-5090 0000-0001-5382-6138 0000-0001-7166-6035
0000-0001-7016-5220 0000-0001-5128-4160 0000-0003-3759-8707
0000-0002-9373-3865

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present reduced images and catalogues of photometric and emission line data
($\sim$230,000 and $\sim$8,000 sources, respectively) for the WFC3 Infrared
Spectroscopic Parallel (WISP) Survey. These data are made publicly available
on the Mikulski Archive for Space Telescopes (MAST) and include reduced images
from various facilities: ground-based $ugri$, HST WFC3, and Spitzer IRAC
(Infrared Array Camera). Coverage in at least one additional filter beyond the
WFC3/IR data are available for roughly half of the fields (227 out of 483),
with $\sim$20% (86) having coverage in six or more filters from $u$-band to
IRAC 3.6µm (0.35-3.6µm). For the lower spatial resolution (and shallower)
ground-based and IRAC data, we perform PSF-matched, prior-based, deconfusion
photometry (i.e., forced-photometry) using the TPHOT software to optimally
extract measurements or upper limits. We present the methodology and software
used for the WISP emission line detection and visual inspection. The former
adopts a continuous wavelet transformation that significantly reduces the
number of spurious sources as candidates before the visual inspection stage.
We combine both WISP catalogues and perform SED fitting on galaxies with
reliable spectroscopic redshifts and multi-band photometry to measure their
stellar masses. We stack WISP spectra as functions of stellar mass and
redshift and measure average emission line fluxes and ratios. We find that
WISP emission line sources are typically ‘normal’ star-forming galaxies based
on the Mass-Excitation diagram ([OIII]/$\mathrm{H}\beta$ vs. $M_{\star}$;
$0.74<z_{\mathrm{grism}}<2.31$), the galaxy main sequence (SFR vs.
$M_{\star}$; $0.30<z_{\mathrm{grism}}<1.45$), $S_{32}$ ratio vs. $M_{\star}$
($0.30<z_{\mathrm{grism}}<0.73$), and $O_{32}$ and $R_{23}$ ratios vs.
$M_{\star}$ ($1.27<z_{\mathrm{grism}}<1.45$).

###### keywords:

catalogues – surveys – galaxies: evolution – galaxies: general – galaxies:
photometry – ISM: evolution

††pubyear: 2024††pagerange: WFC3 Infrared Spectroscopic Parallel (WISP)
Survey: Photometric and Emission Line Data Release–E

##  1 Introduction

Slitless spectroscopy provides simultaneous spectra for every source in an
observed field of view (FOV). Such observations have the notable advantage
that they can be used to efficiently perform blind spectroscopic surveys over
large areas of the sky for the study of galaxy evolution, relative to slits,
fibers, or integral field spectroscopy (IFS) that cover much smaller FOVs.
This gain in mapping area from slitless spectroscopy usually comes at the
expense of reduced sensitivity due to a higher background, more source
confusion, and low to moderate spectral resolution ($R\sim 100-1000$) relative
to slits or IFS ($R\gtrsim 2000$). The latter limits dynamical analyses and
may result in lines blending together (e.g., $\mathrm{H}\alpha$+[NII]).

Blind surveys provide a unique and unbiased view of galaxy evolution by
avoiding issues of cosmic variance or photometric pre-selection. The grisms on
the Hubble Space Telescope (HST) have been widely utilised to perform slitless
spectroscopic surveys of thousands of galaxies at intermediate redshifts
($0.5\lesssim z\lesssim 2.5$; e.g., Pasquali et al., 2003, APPLES, Pirzkal et
al., 2004, GRAPES, Atek et al., 2010, WISP, Brammer et al., 2012, 3D-HST,
Pirzkal et al., 2013, PEARS, Treu et al., 2015, GLASS, Pirzkal et al., 2017,
FIGS, Wang et al., 2022, MAMMOTH–Grism, Simons et al., 2023, CLEAR, Revalski
et al., 2023, MUDF). Next generation facilities, including the James Webb
Space Telescope (JWST), Euclid, and the Nancy Grace Roman Space Telescope
(Roman), will revolutionise this capability by providing slitless spectroscopy
for millions of galaxies that span larger areas of the sky and a wider range
in cosmic time (e.g., Bagley et al., 2020).

The WFC3 (Wide Field Camera 3) Infrared Spectroscopic Parallel (WISP, Atek et
al., 2010) survey was the largest, multi-cycle HST pure-parallel grism
program. WISP obtained slitless spectroscopy for thousands of galaxies in 483
pointings using up to two near-IR grisms, G102 (0.80-1.15 µm, $R\sim 210$) and
G141 (1.08-1.69 µm, $R\sim 130$). Pure-parallel surveys, such as WISP, have
the benefit that the data are obtained ‘for-free’ for numerous random fields
that are independent and uncorrelated (i.e., unbiased). The versatility of
large slitless surveys like WISP are demonstrated by the range of science
cases that can be explored, such as: characterising the star forming galaxy
main sequence (Atek et al., 2014), characterising dust attenuation (Domínguez
et al., 2013) and dust attenuation curves (Battisti et al., 2022),
characterising the mass-metallicity relation (Henry et al., 2013, 2021),
characterising massive, quenched galaxies (Bedregal et al., 2013), identifying
galaxy pairs (Dai et al., 2021), identifying single spectral lines through
machine learning (Baronchelli et al., 2020, 2021), identifying Lyman-$\alpha$
emitters (Bagley et al., 2017), identifying bright, rare galaxies (Bagley et
al., 2024), predicting emission line galaxy number counts for future surveys
(Colbert et al., 2013; Mehta et al., 2015; Bagley et al., 2020), investigating
the mass-size relation of passive galaxies (Zanella et al., 2016),
crowdsourced analysis of slitless spectroscopic data (Dickinson et al., 2018),
nitrogen enhancement of star-forming galaxies (Masters et al., 2014), and the
discovery of very faint, distant (400pc) brown dwarfs (Masters et al., 2012).

A challenge for pure-parallel slitless surveys is that the random fields are
sporadic in position and typically do not have deep ancillary photometric data
available (e.g., compared to legacy deep fields). To remedy this, the WISP
team has carried out several supplementary observing programs to obtain
additional photometry with a variety of facilities, with priority given to the
deepest $\sim$200 WISP fields. These include HST WFC3/UVIS optical, ground-
based optical, and Spitzer/IRAC near-IR data.

This paper describes the public data release of a self-consistent photometric
catalogue, reduced images, and the emission line catalogue of WISP fields.
These data are hosted at the WISP
website111https://archive.stsci.edu/prepds/wisp/ on the Mikulski Archive for
Space Telescopes (MAST). Currently $\sim$50% of the WISP fields have
additional photometric data beyond WFC3/IR. These data provide a valuable
galaxy sample for legacy science and can serve as a useful reference for
ongoing and future grism surveys with JWST, Euclid, and Roman.

This paper is organised as follows: Section 2 describes the observational
data, Section 3 describes the WISP photometric pipeline, Section 4 presents
the WISP photometric catalogue, Section 5 describes the WISP spectroscopic
pipeline, Section 6 presents the WISP emission line catalogue, Section 7 shows
our results from combining both catalogues to study galaxies at
$0.3<z_{\mathrm{grism}}<2.3$, and Section 8 summarises our main conclusions.
Throughout this work we adopt a $\Lambda$-CDM cosmological model, with
$H_{0}=70$ km/s/Mpc, $\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$. All
magnitudes are in the AB magnitude system Oke & Gunn (1983).

##  2 Observations and Data Reduction

[width=0.48]Figures/WISPfields_c23.eps

Figure 1: Locations of the 483 WISP fields. These fields are primarily located
outside of the Galactic Plane. Most short parallel opportunities obtained
WFC3/IR G141 grism data along with one imaging filter (F140W or F160W) and
long opportunities obtained G102+G141 grisms and two imaging filters
(F110W+F140W or F110W+F160W).  Table 1: Summary of WISP HST Survey (PI: M
Malkan)

GO ID | Cycle | Observing Perioda | WFC3/UVISb | WFC3/IR | WFC3/IR Grism | Orbits
---|---|---|---|---|---|---
11696 | 17 | Nov 24, 2009 - May 1, 2011 | F475X,F600LP | F110W,F140W,F160W | G102,G141 | 250
12283 | 18 | Oct 6, 2010 - Mar 11, 2012 | F606W,F814Wc | F110W,F160W | G102,G141 | 280
12568 | 19 | Oct 29, 2011 - May 19, 2013 | None | F140W | G102,G141 | 260
12902 | 20 | Oct 16, 2012 - Mar 20, 2014 | F606W,F814W | F110W,F160W | G102,G141 | 260
13352 | 21 | Oct 31, 2013 - Jun 14, 2015 | F606W,F814W | F110W,F160W | G102,G141 | 375
13517 | 21 | Dec 8, 2013 - Feb 12, 2015 | F606W,F814W | F110W,F160W | G102,G141 | 200
14178 | 23 | Nov 30, 2015 - May 1, 2017 | F606W,F814W | F110W,F140W,F160W | G102,G141 | 520
|  |  |  |  | Total: | 2145

Notes. There are 184 short opportunity fields (one to three continuous
orbits), 180 fields with G141 and either F140W or F160W, and 4 fields with
G102 and F110W (see Section 2.1). There are 299 long opportunity fields (four
or more continuous orbits); these obtained G102+G141 and either F110W+F140W or
F110W+F160W, except for Cycle 19 which used F140W-only.
aObservations often extended beyond the nominal HST cycle period.
bUVIS data were only obtained for a subset of the deep fields (155 fields; See
Section 2.2).
cMost UVIS data in this cycle used 2x2 binning in the F475X and F600LP filters
and those are not included in the current data release.

###  2.1 WISP Survey - HST WFC3/IR Grism Spectroscopy and Imaging

The WISP survey (PI: M. Malkan; Atek et al., 2010) is a multi-cycle (cycles
17-23) HST pure-parallel program that obtained WFC3/IR observations for 483
pointings in random fields (i.e., location depended on the primary observing
target and its position angle). Of the 483 parallel pointings (which we denote
as ‘Par#’; e.g., Par1, Par2, etc.), there are 40 fields with partial overlap
(i.e., there are 443 unique fields). The position of the WISP pointings are
shown in Figure 1. The program IDs and details for the different HST cycles
are summarised in Table 1. The effective grism area of each WISP pointing is
$\sim$3.55 arcmin2 in G102 and $\sim$3.8 arcmin2 in G141, relative to the full
4.6 arcmin2 WFC3/IR FOV, due to area on both the left and right side of each
field being ‘lost’. On the left, this is because sources are not covered in
the direct images necessary for source identification and wavelength
calibration. On the right, this is because emission lines cannot be
distinguished from contaminating zero order images (Bagley et al., 2017). In
principle, high resolution ancillary data with a larger FOV, such as the
WFC3/UVIS data available for a subset of fields, could be used to locate
sources outside the WFC3/IR FOV. However, such an approach is not implemented
for the current data release. Thus, the effective imaging and grism areas of
the full WISP survey are $\sim$2200 arcmin2 and $\sim$1600 arcmin2,
respectively (this also accounts for field overlap). An overview of the
imaging and grism filters that are included in this data release are shown in
Figure 2.

[width=0.48]Figures/WISP_filters-crop.eps

Figure 2: Filters used in the WISP survey and follow-up observations separated
by (a) space-based and (b) ground-based facilities. The WISP survey obtained
WFC3/IR imaging together with the grism spectroscopy (dotted black curves) and
all WISP fields have either F140W or F160W data, with deep fields also having
F110W imaging. Additional photometry is inhomogenous and comprises of
WFC3/UVIS, Spitzer, and/or ground based optical data ($ugri$) from Magellan,
WIYN 3.5m, and Palomar. The F475X, F600LP, and IRAC ch2 curves are shown as
thinner lines to highlight that they are available for $<20$ fields (other
filters are $>20$ fields), with a breakdown shown in Table 5.

Due to the nature of parallel observations, the integration times for each
field was set by the primary target observations. We refer the reader to Atek
et al. (2010) for a complete description of the observing strategy and data
reduction. In brief, short opportunities (one to three continuous orbits; 180
fields) usually obtained G141 and one WFC3/IR filter, either F140W or F160W.
However, a handful of short opportunities obtained G102 and F110W instead (4
fields). Long opportunities (four or more continuous orbits; 299 fields)
obtained G102+G141 and two WFC3/IR filters, either F110W+F140W or F110W+F160W,
except for Cycle 19 which used F140W-only. Cycle 20 and beyond are almost
exclusively deep fields (G102+G141; See Table 1). In general, grism
integration times are $\sim$6$\times$ those for the direct images. For the
long opportunities, the integration times in the two grisms were set to
achieve approximately uniform sensitivity for an emission line of a given flux
across the full wavelength range ($\sim$5:2 for G102:G141). The median
$5\sigma$ detection limit for emission lines fluxes (point source) in both
grisms is $\sim 5\times 10^{-17}$ erg s-1 cm-2 (Atek et al., 2010), but we
stress that this varies considerably with the length of the opportunity and
variation in background levels (zodiacal light, Earth limb brightening, and
telescope thermal emission). The line detection limits for each individual
WISP fields are presented in Figure 3 and Table 2.

[width=0.48]Figures/WISPdepths.pdf

Figure 3: The $5\sigma$ emission line sensitivities in the individual WISP
fields (light grey curves). The blue dashed line indicates the median
$5\sigma$ field depth. The depth varies significantly field-to-field due to
variations in the exposure time and background levels in each field.  Table 2:
WISP emission line depths for the 419 fields in the emission line catalogue

Par | RA | Dec |  $1\sigma$ Depth G102a |  $1\sigma$ Depth G141a
---|---|---|---|---
|  |  | (erg s-1 cm-2) | (erg s-1 cm-2)
1 | 01:06:35.29 |  $+$15:08:53.8 | $9.67\times 10^{-18}$ | $9.57\times 10^{-18}$
2 | 01:25:10.02 |  $+$21:39:13.7 | … | $1.17\times 10^{-17}$
5 | 14:27:06.64 |  $+$57:51:36.2 | $7.72\times 10^{-18}$ | $5.30\times 10^{-18}$
6 | 01:50:17.18 |  $+$13:04:12.8 | $1.15\times 10^{-17}$ | $8.76\times 10^{-18}$
7 | 14:27:05.90 |  $+$57:53:33.7 | $1.54\times 10^{-17}$ | $8.56\times 10^{-18}$
…

Notes. A full ASCII version of this table is available online.
aGrism flux limits depend on wavelength (see Figure 3). Values presented here
are at $\lambda=1.1\mu\mathrm{m}$ for G102 and $1.5\mu\mathrm{m}$ for G141.

Due to HST only having a single dispersion direction for each grism, and
position/orientation being tied to the Primary observing target, all grism
data are single orientation. We note that multi-orientation pure-parallel
observations are possible on JWST due to the availability of multi-directional
grisms, and that this is already being utilised (e.g., Cycle 1 PASSAGE survey
with NIRISS, GO 1571; PI: M. Malkan, Malkan et al. 2021). Multi-orientation
grism data can be used to construct spatially resolved emission line maps
(e.g., Pirzkal et al., 2018; Wang et al., 2022).

All WISP data are reduced and calibrated with the WFC3 pipeline calwf3,
together with custom scripts to improve the calibration and account for the
specific challenges of undithered, pure-parallel observations. The foundation
of the WISP reduction pipeline is described in Atek et al. (2010). Here we
additionally implement a multiple component fit to the sky background in the
grism images. While the “input” spectrum of the sky can be considered uniform
across the field-of-view, the sky emission is not uniform on the detector.
Typically a single master sky image is scaled and fit to remove the background
in each grism image, under the assumption that the relative strength of the
background components remain the same exposure to exposure. However, as noted
by Brammer et al. (2012), the structure in the sky of WFC3 grism images is
highly variable, with zodiacal light and a helium emission line at 1.083 µm
contributing. While the zodiacal component should stay relatively constant
throughout a full set of exposures taken on the same date, the helium emission
comes from Earth’s upper atmosphere and can vary on timescales shorter than
the length of an exposure as HST moves closer or farther from Earth and the
telescope pointing changes. We model and subtract the background in each grism
exposure with a linear combination of the zodiacal light and helium sky images
created by Brammer et al. (2015), calculating the amplitudes of each sky
component with two iterations of a least squares fit.

We use the AstroDrizzle and TWEAKREG routines of DrizzlePac (Gonzaga et al.,
2012; Hoffmann et al., 2021) to combine the individual exposures, correcting
for astrometric distortions and any alignment issues between exposures. The IR
direct and grism images are drizzled onto a 0.08"/pixel scale. Object
detection in the IR direct images (F110W, F140W, and F160W) is performed with
Source Extractor (version 2.5; Bertin & Arnouts, 1996). For fields with
imaging in two filters, we create a combined detection image and supplement
the catalog with sources detected individually in only one of the filters. We
use the aXe software package (Kümmel et al., 2009) to extract and calibrate
the spectra, using the Source Extractor catalogs as inputs.

###  2.2 HST WFC3/UVIS Imaging

For 155 of the long opportunity fields, WFC3/UVIS (FOV = 2.7′$\times$2.7′)
imaging data were also obtained with some combination of F475X, F606W, F600LP,
and/or F814W filters (only 2 of these at most for a single field). These
observations were all carried out as part of the main parallel survey (PI: M.
Malkan; see Table 1 for cycles and GO IDs). The variety in UVIS photometric
filters used is a result of a change in strategy between cycles. Specifically,
in the first cycle of WISP observations (Cycle 17), the F475X and F600LP
filters were utilised to maximise throughput. However, it was realised that
the less-wide filters provided more information for spectral energy
distribution (SED) fitting, and thus future observations switched to F606W and
F814W. In Cycle 18, we switched to 2x2 binned observations for the UVIS
imaging, although it was later realised that the combination of lack of binned
calibrations and pixel based charge transfer efficiency corrections made the
data less useful. In Cycle 19, we only obtained short parallel opportunities,
and thus none included UVIS imaging. Starting with Cycle 20 and onwards, all
UVIS observations were obtained in un-binned F606W and F814W data. In total we
have 70 and 43 fields with two and one un-binned UVIS filters, respectfully,
for a total of 113 fields with G102+G141 grism spectroscopy and excellent UVIS
imaging.

####  2.2.1 HST Data Reduction and Co-addition

The UVIS images are also reduced through calwf3, along with additional custom
calibrations described in Rafelski et al. (2015) including custom dark
calibration files to address hot pixel masking, background gradients, and
blotchy background patterns. These calibrations only apply to unbinned WFC3
data and, as a result, the binned UVIS data in Cycle 18 are not included in
this data release. We first applied a pixel-based Charge Transfer Efficiency
(CTE) correction on all individual raw dark files. When post-flashed dark
files were available, we used those. The Cycle 17 UVIS data (F475X and F600LP)
had high background and minimal CTE degradation. All UVIS data since Cycle 20
(F606W and F814W) use post-flash or have sufficient background on their own
based on the recommendations at the time. We then used the dark files from a
3-5 day window to create a super dark to identify the hot pixels. These hot
pixels use a lower threshold to identify hot pixels otherwise lost due to CTE
degradation. We also create a master superdark that stacks all dark
observations within the same anneal cycle as the observations, which we
subtract from the data within calwf3 to reduce the blotchy patterns and
gradients. The details of all these steps are outlined in the Appendix of
Rafelski et al. (2015). This dark calibration methodology was partly
incorporated as part of UVIS 2.0 (Bourque & Baggett, 2016) utilizing post-
flashed CTE corrected darks. Then later in 2020 the dark reference files moved
to contemporaneous darks. The pipeline still does not include improvements for
hot pixels. For future reductions, we point to the hot pixel treatment in
Prichard et al. (2022) and Revalski et al. (2023), which also includes
additional improvements to artifacts caused by CTE degradation such as matched
amplifier backgrounds and read out cosmic rays (ROCRs).

The UVIS image mosaics were created with AstroDrizzle and TWEAKREG. The images
where corrected for cosmic rays and aligned to the NIR images. The final image
drizzle parameters are set to have final_scale of 0.04"/pixel,
final_pixfrac=0.75, and The final_wht_type=IVM (inverse-variance weighting
map). We also create NIR and UVIS image mosaics with matched plate scales
(final_scale) of 0.04"/pixel, 0.08"/pixel, and 0.13"/pixel. The use of
final_scale of 0.08"/pixel or 0.13"/pixel for UVIS data produces significantly
undersampled images, and we therefore use the 0.04"/pixel NIR and UVIS mosaics
for matched photometry. These images are then convolved with a kernal to match
the point spread-function (PSF) of all the images to that of the F160W filter.
We used the IRAF task PSFMATCH to calculate the matching kernals and convolve
the images. Additionally, RMS images are created by taking
$1/\sqrt{(\mathrm{IVM})}$ and cleaned images of the UVIS data are generated by
masking edges, chip gaps, and bad pixels with randomly generated Gaussian
noise. The pixel-matched imaging data in both WFC3/UVIS and WFC3/IR were made
available in previous data releases from the WISP team via the survey website
on MAST222https://archive.stsci.edu/prepds/wisp/.

###  2.3 Ground-based Imaging

The ground-based data were taken between the 2010A-2019A semesters from
various PIs across several independent programs. The data were taken with
Palomar/LFC (31 nights), Palomar/WaSP (2 nights), WIYN/MiniMosaic (12 nights),
WIYN/ODI (9.5 nights), and Magellan/Megacam (3.5 nights). A summary of the
programs, including their IDs, PIs, dates, and the number of nights, are
listed in Table 3.

Table 3: Summary of ground-based imaging campaigns on WISP fields included in
this release

ID | PI(s) | Telescope/Instr. | Semester | Bands | Nights
---|---|---|---|---|---
P-23 | B. Siana | Palomar/LFC | 2010A | $gi$ | 4
H-05 | B. Siana | Palomar/LFC | 2010B | $gi$ | 2
J-06 | C. Scarlata | Palomar/LFC | 2010B | $gi$ | 3
0438 | A. Henry | WIYN/MiniMo | 2010B | $gri$ | 4
0160 | A. Henry | WIYN/MiniMo | 2011A | $gi$ | 5
0222 | A. Henry | WIYN/MiniMo | 2011B | $g$ | 3
J-18 | H. Telpitz | Palomar/LFC | 2012A | $gi$ | 3
J-01 | M. Rafelski | Palomar/LFC | 2013A | $gi$ | 2
J-10 | M. Rafelski | Palomar/LFC | 2013B | $gi$ | 3
J-23 | M. Rafelski | Palomar/LFC | 2014A | $gi$ | 2
J-05 | Y. Dai | Palomar/LFC | 2014B | $gi$ | 2
J-16 | J. Colbert | Palomar/LFC | 2015A | $gi$ | 3
J-12 | Y. Dai | Palomar/LFC | 2016A | $g$ | 1
J-14 | Y. Dai | Palomar/LFC | 2016B | $gi$ | 3
J-14 | I. Baronchelli | Palomar/LFC | 2017B | $gi$ | 3
0298 | A. Battisti | WIYN/ODI | 2017B | $ugr$ | 2.5
… | P. McCarthy | Magellan/Megacam | 2017B | $ugr$ | 1.5
| & A. Battisti |  |  |  |
0275 | A. Battisti | WIYN/ODI | 2018A | $ugr$ | 2.5
… | A. Battisti | Magellan/Megacam | 2018A | $ugr$ | 2
0140 | A. Battisti | WIYN/ODI | 2018B/19A | $ugr$ | 4.5a
N-115 | Y. Dai | Palomar/WASP | 2019A | $g$ | 2

Notes. Columns list the (1) Program ID, (2) Principal Investigator, (3)
Telescope and instrument used, (4) Semester observed, (5) Bands observed, (6)
Number of nights where data was taken. aThree of these nights were provided as
additional technical time

The observing campaign can be broadly divided into two categories: (1)
programs with Palomar (LFC or WASP) and WIYN/MiniMosaic focused on
observations in the $g$ and $i$ bands, where $i$-band was only obtained for
fields without HST/UVIS F814W or F600LP data (these filters have similar
effective wavelengths), with the goal of improving stellar mass estimates for
WISP galaxies; (2) programs with WIYN/ODI and Magellan/Megacam focused on
observations in $u$, $g$, and $r$ bands, where $r$-band was only obtained for
cases without HST/UVIS F606W data (similar in wavelength), with the goal of
providing rest-frame UV measurements to constrain reddening from dust
attenuation (Battisti et al., 2022). The WIYN/ODI and Magellan/Megacam
instruments have large fields-of-views (FOVs, 40′$\times$48′and
24′$\times$24′, respectively), which are significantly larger than the HST
WFC3/IR footprint (FOV = 2.3′$\times$2.2′). Whenever possible, observations
were optimised to observe multiple WISP fields simultaneously.

The desired depths of the programs varied, but for WIYN/ODI and
Magellan/Megacam they were AB mag=26, 26, 25.3 in $u$, $g$, and $r$ (5$\sigma$
point-source), respectively. These depths were typically achieved for the
Magellan runs but not for most of the WIYN runs, due to poor weather and/or
observing conditions (e.g., lunar phase). A detailed summary on the depths for
each facility is given in Section 4.2.

####  2.3.1 Ground-based Data Reduction and Co-addition

Below we describe the data reduction process for each telescope individually,
but note that they follow a similar overall procedure that includes bias,
flat, and dark-subtraction. All images were astrometrically aligned to the
World Coordinate System (WCS) using the astrometry.net software package,
unless otherwise specified. Flux calibrations were also performed in similar
ways, unless otherwise specified, and is summarised in Section 3.1.

  * •

Palomar/LFC – The Palomar/LFC WISP observations spanned the largest number of
different observers among our datasets. All raw images were re-reduced
following the same procedure for self-consistency. The LFC consists of six
chips (each 6.14′$\times$12.29′; referred to as chip0 through chip5), covering
a circular area with a $\sim$24′ diameter, and the WISP field was always
centered on chip0. Basic data reduction steps were only performed on the chip0
data. We note that dark frames were not always available for subtraction,
however, this has a minimal impact on the final photometric quality because
the LFC has very little dark
current333https://sites.astro.caltech.edu/palomar/observer/200inchResources/lfccookbook.html#dark.

  * •

Palomar/WaSP – Basic reduction steps were identical to Palomar/LFC, except
that WaSP has 4 large chips (square FOV: 18.4′$\times$18.5′) and all chips
were reduced.

  * •

WIYN/Minimosaic – the raw archival WIYN data were obtained via the NOAO
Science Archive (now known as the NOIRLab Astro Data
Archive444https://astroarchive.noirlab.edu). Basic reduction steps were
similar to Palomar, except that Minimosaic has 2 large chips (square FOV:
9.6′$\times$9.6′) and both chips were used.

  * •

WIYN/ODI – basic reduction, WCS-alignment, and photometric calibration was
performed using the ODI Pipeline, Portal, and Archive (PPA)
system555https://portal.odi.iu.edu/index/front. PPA is a service provided by
the WIYN Consortium, Inc., and hosted at Indiana University. The photometric
calibration in the ODI PPA is based on measurements from the SDSS ($ugriz$)
and Pan-STARRS ($grizy$). We note that for a few fields outside the SDSS
footprint, the $u$-band ODI data required manual photometric calibration,
which is discussed in Section 3.1.

  * •

Magellan/Megacam – images with basic reduction and WCS-alignment were provided
by the OIR Telescope Data Center at Harvard’s Center for Astrophysics (CfA),
supported by the Smithsonian Astrophysical Observatory.

The process for co-adding images was the same for all ground-based data.
First, images are normalised by exposure time. Second, normalised images are
combined using the SWarp software (Bertin et al., 2002; Bertin, 2010). During
SWarp, images are background subtracted using a 128 pixel background mesh
unless saturated stars bleed onto a significant portion of field. In such
cases, a 32 pixel background is adopted to minimise the area affected by
saturation. During this step we also mask out satellite trails from individual
exposures if they overlap with the WISP field (satellite trails outside the
WISP area are ignored). For convenience, the publicly released images are
cropped into 5′$\times$5′ regions centered on the WISP fields. For reference,
the HST/UVIS FOV is 2.70′$\times$2.70′ and the HST/IR FOV is
2.05′$\times$2.27′.

###  2.4 Spitzer IRAC Imaging

Spitzer IRAC/channel 1, 3.6 µm imaging (warm mission; PI: J Colbert) was
obtained for $\sim$200 of the deepest WISP field over multiple cycles (GO
80134 (Cycle 8), 90230 (Cycle 9), 10041 (Cycle 10), 12093 (Cycle 12)), with
the primary goal of providing accurate stellar masses for galaxies in the WISP
survey. For a handful of WISP fields, IRAC/channel 2, 4.5µm data were also
obtained.

####  2.4.1 Spitzer Data Reduction and Co-addition

Roughly half of the WISP parallels are in low background fields ($\sim$0.08
MJy/sr at 3.6µm), while the remainder are in fields with medium backgrounds
($\sim$0.12 MJy/sr). To achieve similar sensitivity for all the targeted
fields (5$\sigma$ depth of 0.9$\mu$Jy), we split the observations into two
integration times, 25 versus 35 minutes on-source. The variation of the
background with observing window does not significantly change the required
exposure time. For the observations, we use a medium dither pattern with 100
second frames and either 15 or 21 exposures, depending on the total
integration time. For the small subset of fields observed with the 4.5µm
filter, we always used the 21 exposure (35 minute) observation.

Individual calibrated IRAC exposures are referred to as Basic Calibrated Data,
or BCDs. However, IRAC BCD data contain several artifacts, including mux-
bleed, mux-stripe, column droop, and bright star
ghosts666https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/35/.
The IRAC pipeline therefore also produces corrected BCD images (cBCD), which
attempt to mitigate these artifacts. We start with the cBCDs for all of our
data reduction and analysis.

All the IRAC mosaics are generated using the Spitzer MOsaicker and Point
source EXtractor (MOPEX) package. Before generating mosaics, problematic cBCDs
– those with unusually high noise, extreme saturation, or other unexplained
large artifacts – are removed. Such problematic cBCDs only make up a small
fraction (<5%) of the input cBCDs and do not significantly affect total
exposure times for any observations. The first frame of all IRAC Astronomical
Observation Requests (AORs) has decreased sensitivity and was not included in
the mosaics. The MOPEX Overlap pipeline subtracts the estimated background
from Zodiacal light from each CBCD and then matches the background level in
all frames with an additive correction. The MOPEX Mosaic pipeline then
performs outlier rejection to remove cosmic rays, moving objects, and other
artifacts, before re-sampling the images onto a common reference frame.
Finally, the images are combined to produce a weighted mean and median mosaic
along with associated coverage, uncertainty, and standard-deviation maps.

##  3 WISP Photometric Pipeline

The methods to obtain zeropoints and photometry differ between the HST data
(high spatial resolution) and the ground-based and Spitzer data (both low
spatial resolution). In this section we describe the data processing workflow
used to create the WISP photometric catalogue.

###  3.1 Photometric Zeropoints

####  3.1.1 HST Zeropoints

The HST WFC3/UVIS and WFC3/IR zeropoints are taken from the STScI calibration
website777https://www.stsci.edu/hst/instrumentation/wfc3/data-
analysis/photometric-calibration. We note that the WFC3 zeropoint solutions
change slightly over time and different zeropoint values are applied to data
from different HST cycles over the course of the program.

####  3.1.2 Ground-based Data Zeropoints

For all ground-based imaging, the flux zeropoints were determined, in order of
priority, from: (1) direct comparison to SDSS ($ugri$; $110\degree\lesssim
RA\lesssim 265\degree$ and $Dec>0\degree$), (2) direct comparison to Pan-
STARRS ($gri$; full sky for $Dec>-30\degree$), (3) using standard fields
(i.e., fields with (1) or (2)) at different airmasses (atmospheric extinction)
for individual nights of each observation. Option (3) was necessary when
neither SDSS or Pan-STARRS are available for calibration. This was required
for many of the southern WISP fields observed with Magellan, particularly for
the $u$-band imaging.

First, we extract psfMag values for stars (PhotoType=6) in the SDSS DR14 and
Pan-STARRS DR2 public catalogues to use as our reference values. Magnitudes in
Pan-STARRS were converted into the SDSS system using the relationships in
Tonry et al. (2012). Second, we run SExtractor (Bertin & Arnouts, 1996) with
similar parameters across facilities, for consistency, on our reduced, co-
added images (Section 2.3.1). A summary of the most relavant SExtractor
parameters are listed in Table 4. Third, magnitude zeropoints are determined
by cross-matching close sources and comparing MAG_AUTO values from SExtractor
to the catalogue psfMag values (both represent total magnitudes). A distance
threshold of $\sim$1″ was typically adopted, but this varied with seeing
conditions (maximum of 3″).

The filters for all of the ground-based data (see Figure 2b) are similar to
SDSS. As a result, colour differences tend to be small, however, this was
still accounted for during the ZP determination. In particular, the Magellan
$g$ and $r$ and Palomar $i$ filters show the largest deviations from SDSS.
These colour corrections are based on fitting the zeropoint magnitudes as a
function of $u-g$, $g-r$, $g-r$, and, $r-i$ colours for the $u$, $g$, $r$, and
$i$ filters, respectively.

The typical precision of the ZPs are $\sigma_{ZP}\sim 0.05$ mag for
Magellan/Megacam ($ugr$), WIYN/ODI ($ugr$), WIYN/MiniMosaic ($gri$), and
Palomar/WaSP ($g$). For Palomar/LFC ($gi$), the typical precision is slightly
worse, $\sigma_{ZP}\sim 0.1$ mag, due to the smaller FOV with fewer reference
stars for calibration. We recommend adopting a minimum uncertainty of 0.1 mag
for all ground-based optical data to account for potential systematic ZP
offsets.

Table 4: Summary of SExtractor parameters used on the ground-based data for
determining zeropoints

Parameter | Value
---|---
DETECT_THRESH | 1.5
ANALYSIS_THRESH | 1.5
DEBLEND_NTHRESH | 32
DEBLEND_MINCONT | 0.005
DETECT_MINAREA | 6
BACK_SIZE | 64
BACK_FILTERSIZE | 3
FILTER | Y
FILTER_NAME | gauss_2.0_5x5.conva

Notes. The photometry from SExtractor is used only for constraining magnitude
zeropoints for the ground-based data. We use TPHOT to measure photometry for
the WISP catalogue (see Section 3.3). a5$\times$5 convolution mask of a
Gaussian PSF with FWHM = 2.0 pixels.

For rare instances of overlapping data (e.g., both Magellan and Palomar data
are available in the $g$ filter), we adopt the case with better seeing
(typically also deeper), unless there is a dramatic difference in depth
relative to the poorer seeing case ($\gtrsim 1$ mag difference). A few
comparisons between overlapping data from different telescopes with roughly
similar imaging quality (depth, seeing) were possible and used as a check on
zeropoints and colour-corrections. We find that cases of overlapping data
agree to within 1$\sigma$ for $\sim$60-70% of sources, as expected. We find
that the agreement gets poorer (larger scatter) when comparing datasets with
larger quality differences (e.g., 1" vs 1.7" seeing), however the median ZP
offsets remain consistent with zero.

[width=0.98]Figures/Pipeline_example-crop.eps

Figure 4: HST images and segmentation maps are used to perform ‘forced’
photometry on the lower-resolution data (ground-based and Spitzer) by
combining the PSFs of both HST and the lower-resolution data (detailed in
Section 3.3). As an example, we show data from Par 104: (left) the HST F110W
image, (middle) the Magellan $g$ image, and (right) the residual of the
Magellan $g$ image after running through TPHOT. Instances of over-subtracted
residuals (black circles) are expected to occur for sources that are saturated
in the HST image (mostly foreground stars); for these cases the HST (deeper)
light-profile models are less accurate relative to the same sources in the
unsaturated (shallower) low-resolution data. The HST WFC3/IR FOV
(2.05′$\times$2.27′) is indicated by the green box in all panels.  Table 5:
Summary of the number of fields, $N$, with each filter in the WISP Photometric
catalogue

Filter | $u$ | $g$ | F475X | F606W | $r$ | F600LP | $i$ | F814W | F110W | F140W | F160W | I1 | I2
---|---|---|---|---|---|---|---|---|---|---|---|---|---
$\lambda_{\mathrm{eff}}(\mu\mathrm{m})$ | 0.3551 | 0.4686 | 0.4939 | 0.5893 | 0.6165 | 0.7444 | 0.7481 | 0.8060 | 1.1534 | 1.3923 | 1.5396 | 3.550 | 4.493
$N$ | 113 | 167 | 19 | 43 | 68 | 19 | 57 | 99 | 233 | 168 | 261 | 175 | 3

Notes: I1=IRAC1, I2=IRAC2. The catalogue contains data for 439 out of 483 WISP
fields. For details on individual fields, refer to Table 8.

####  3.1.3 Spitzer Zeropoints

Similar to HST, the Spitzer zeropoints are taken from the IRAC instrument
handbook
website888https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/14/.
We note that the WISP data were obtained during the Spitzer warm-mission,
which had a different zeropoint solution to the cold-mission.

###  3.2 HST PSF- and Aperture-matched Isophotal Photometry (high spatial
resolution)

The methods used to obtain the HST photometry are described in Bagley et al.
(2017) and Henry et al. (2021). In brief, a segmentation map is first
generated from the F110W and F160W detections using SExtractor on the
0.08"/pixel mosaics and then re-gridded to the 0.04"/pixel scale mosaics. The
photometry is deteremined using photutils in Astropy (Astropy Collaboration et
al., 2013, 2018) to derive isophotal fluxes in all HST bands using the re-
gridded segmentation map and includes local sky subtraction. SExtractor
photometry is also performed on WFC3/IR (0.08"/pixel) images (prior to PSF-
matching), in order obtain the total magnitudes (MAG_AUTO).

For the WFC3/UVIS data, we determine aperture corrections, APCOR, using the
difference between MAG_AUTO and the isophotal magnitude, MAG_ISO, in the F160W
HST filter and list these values in our catalogue (i.e.,
APCOR_UVIS=MAG_AUTO_F160W-MAG_ISO_F160W). This is similar to the method used
in Henry et al. (2021); Battisti et al. (2022). We recommend total magnitudes
to be estimated for UVIS filters using
$m_{\mathrm{tot}}$=MAG_ISO_[UVISFILTER]+APCOR_UVIS. For the WISP subsample
used in our results (Secton 7), the median value of these aperture corrections
(APCOR_UVIS) is $\Delta m=-0.11$ mag.

###  3.3 Ground-based and Spitzer Forced Photometry (low spatial resolution)

We performed template-fitting or ‘forced’ photometric measurements on the
lower-resolution data (ground-based and IRAC; both datasets follow the same
procedure) by exploiting the coordinates of the HST-detected sources as
priors. Figure 4 demonstrates an example of the photometric fitting from the
TPHOT WISP pipeline on the ground-based data.

The core of this computation is performed using the TPHOT software (v2; Merlin
et al., 2015, 2016), which we summarise below, and provide in more detail in
Appendix A. In brief, TPHOT requires two images at different resolutions and a
list of detected objects. The algorithm transforms the low resolution image
into a (simulated) high-resolution image. To do this, TPHOT “distributes” the
flux of the sources in the low-resolution image according to the flux
distribution in the high-resolution image using a deconvolution kernel
(provided by the user). Compared to aperture photometry (and closest-
counterpart associations), this technique allows us to obtain more accurate
photometric estimates, especially when multiple HST sources appear blended in
the low-resolution images. For all of the HST sources undetected in the low-
resolution bands, we set their fluxes as an upper limit to the 3$\sigma$
detection limit.

##  4 WISP Photometric Catalogue

###  4.1 Photometric Catalogue Description

The WISP photometric catalogue contains $\sim$230,000 sources in 439 WISP
fields. These sources include stars, galaxies, and active galactic nuclei
(AGN). Fields that are absent are cases where the WISP photometric pipeline
failed, which most commonly occurred due to overcrowding, bright stars, or
persistence. We note that the filter availability is quite inhomogeneous among
WISP fields and entries for fields without data in a given filter have values
of ‘-99’ for their photometry. We provide a summary of the number of fields
with individual filters in this data release in Table 5. The photometry in
this catalogue are not corrected for foreground Milky Way extinction.

We present an explanation of the WISP photometric catalogue entries in Table
6. These include RA, Dec, sizes and position angles (based on HST), and Kron-
like elliptical aperture magnitude (MAG_AUTO; only WFC3/IR filters) from
SExtractor. There are two additional aperture measurements available for HST
data: (1) isophotes (ISO) based on the F110W and F160W segmentation map and
(2) fixed circular apertures (APER; radii $r$ = 0.2, 0.5, 1.0, 1.5″). A visual
representation of these apertures is shown in Figure 5. For the ground-based
and Spitzer data, photometry based on TPHOT is provided. For consistent
‘total’ photometry, we recommend using MAG_AUTO for WFC3/IR,
MAG_ISO+APCOR_UVIS for WFC3/UVIS, and AB_MAG (TPHOT values) for ground-based
and Spitzer data.

There are also two quality flags in the photometric catalogue. A description
of these flags is provided in Appendix B. These flags should be carefully
considered when selecting sources from the catalogue to avoid use of
unreliable photometry.

[width=0.48]Figures/wisp_apertures_v2-crop.pdf

Figure 5: A demonstration of the three types of apertures available for HST
imaging data in the photometric catalogue.  Table 6: Description of WISP
Photometric catalogue

Title | Description
---|---
PAR | WISP field ID number
OBJ | Object ID number
RA | Decimal RA from HST images [deg]
DEC | Decimal Dec from HST images [deg]
A_WORLD |  SExtractor profile RMS along major axis in world coordinates, measured on HST images [arcsec]
B_WORLD |  SExtractor profile RMS along minor axis in world coordinates, measured on HST images [arcsec]
THETA_WORLD | Position angle measured counter-clockwise from world x-axis, measured on HST images [deg]
X_IMAGE_040 | Object x pixel coordinate in 0.04″/pixel scale image [pixels]
Y_IMAGE_040 | Object y pixel coordinate in 0.04″/pixel scale image [pixels]
A_IMAGE_040 |  SExtractor profile RMS along major axis measured on 0.04″/pixel HST images [pixels]
B_IMAGE_040 |  SExtractor profile RMS along minor axis measured on 0.04″/pixel HST images [pixels]
THETA_IMAGE_040 | Position angle counter-clockwise from x-axis, measured on 0.04″/pixel HST images [deg]
X_IMAGE_080 | Object x pixel coordinate in 0.08″/pixel scale image [pixels]
Y_IMAGE_080 | Object y pixel coordinate in 0.08″/pixel scale image [pixels]
A_IMAGE_080 |  SExtractor profile RMS along major axis measured on 0.08″/pixel HST images [pixels]
B_IMAGE_080 |  SExtractor profile RMS along minor axis measured on 0.08″/pixel HST images [pixels]
THETA_IMAGE_080 | Position angle counter-clockwise from x-axis, measured on 0.08″/pixel HST images [deg]
FLUX_[APTYPE]_[HSTFILTER]a | Sky-subtracted signal within aperture [$\mu$Jy]
FLUXERR_[APTYPE]_[HSTFILTER]a | Aperture signal uncertainty [$\mu$Jy]
MAG_[APTYPE]_[HSTFILTER]a | Magnitude for FLUX_[APTYPE]_[HSTFILTER]; -99 for undetected sources [AB mag]
MAGERR_[APTYPE]_[HSTFILTER]a | Magnitude uncertainty; -99 for undetected sources [AB mag]
FLUX_SKY_[HSTFILTER]a | Background used for sky subtraction in all apertures; use 10″ rectangle with sources masked [$\mu$Jy]
FLUXERR_SKY_[HSTFILTER]a | Sky aperture signal uncertainty [$\mu$Jy]
MAG_AUTO_[NIRFILTER]b |  SExtractor Kron-like elliptical aperture magnitude; limit reported for undetected sources [AB mag]
MAGERR_AUTO_[NIRFILTER]b |  SExtractor RMS error for AUTO magnitude; -99 for undetected sources [AB mag]
FLAG_[NIRFILTER]b |  SExtractor extraction flags (8 bit flags; see Appendix B)
AB_MAG_[FILTER]c | Filter magnitude from T-PHOT output; limiting magnitude for undetected sources [AB mag]
AB_MAGERR_[FILTER]c | Filter magnitude uncertainty from T-PHOT output; -99 for undetected sources [AB mag]
TPHOT_FLAG_[FILTER]c |  T-PHOT extraction flags (3 bit flags; see Appendix B)
INSTR_FLAG_[GROUNDFILTER]d | String indicating ‘Telescope-instrument’ for ground-based data (e.g., ‘Magellan-Megacam’).
APCOR_UVIS | Aperture correction to convert WFC3/UVIS isophotal magnitudes to total magnitude [AB mag]

Notes: a[ATYPE] is one of: ISO (isophotes based on the F110W and F160W
segmentation map) or APER (circular apertures of radii $r$ = 0.2, 0.5, 1.0,
1.5″; array has dimensions of ($n_{\mathrm{obj}}$, 4)). [HSTFILTER] is one of:
F475X, F475Xc, F606W, F606Wc, F600LP, F600LPc, F814W, F814Wc, F110W, F110Wc,
or F160W. ‘c’ refers to photometry on images convolved to match the PSF of
F160W. Only convolved fluxes are available for the ISO apertures. b[NIRFILTER]
is one of: F110W, F140W, or F160W. c[FILTER] is one of: $u$, $g$, $r$, $i$,
I1, or I2. d[GROUNDFILTER] is one of: $u$, $g$, $r$, $i$.

Table 7: Summary of WFC3/IR imaging depth and completeness for WISP fields in
the photometric catalog

|  |  F110W Depth (AB mag) |  |  F140W Depth (AB mag) |  |  F160W Depth (AB mag)
---|---|---|---|---|---|---
Par | $N$ | Aperture | Point-source | Galaxy | $N$ | Aperture | Point-source | Galaxy | $N$ | Aperture | Point-source | Galaxy
1 | 425 | 26.28 | 26.26 | 25.25 | 355 | 25.65 | 25.78 | 24.77 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
2 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | 354 | 25.52 | 25.58 | 24.59 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
3 | 622 | 26.27 | 26.41 | 25.43 | 413 | 25.65 | 25.68 | 24.65 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
5 | 502 | 26.48 | 26.42 | 25.42 | 520 | 26.23 | 26.28 | 25.28 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
6 | 346 | 25.86 | 25.87 | 24.84 | 415 | 25.78 | 25.86 | 24.89 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
…

Notes: $N$ is the number of detected objects in WISP photometric pipeline.
‘Aperture’ is the average 5$\sigma$ depth within 0.5″ sky regions. ‘Point-
source’ and ‘Galaxy’ are the 50% completeness depths for injected simulated
point-sources and galaxies, respectively (see Section 4.2 and Figure 6). A
full ASCII version of this table is available online.

Table 8: Summary of photometric availability and depth (AB mag) for WISP
fields in this data release

Par | $u$ | $g$ | F475X | F606W | $r$ | F600LP | $i$ | F814W | F110W | F140W | F160W | I1 | I2
---|---|---|---|---|---|---|---|---|---|---|---|---|---
$\lambda_{\mathrm{eff}}(\mu\mathrm{m})$ | 0.3551 | 0.4686 | 0.4939 | 0.5893 | 0.6165 | 0.7444 | 0.7481 | 0.8060 | 1.1534 | 1.3923 | 1.5396 | 3.550 | 4.493
1 | 25.06 | 26.29 | $\bm{--}$ | $\bm{--}$ | 25.82 | $\bm{--}$ | 26.35 | $\bm{--}$ | 26.02 | 25.59 | $\bm{--}$ | 23.88 | $\bm{--}$
2 | $\bm{--}$ | 27.16 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | 26.28 | $\bm{--}$ | $\bm{--}$ | 24.94 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$
3 | $\bm{--}$ | 26.68 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | 26.14 | $\bm{--}$ | 25.91 | 25.42 | $\bm{--}$ | 23.75 | $\bm{--}$
5 | 24.48 | 26.90 | $\bm{--}$ | $\bm{--}$ | 24.64 | $\bm{--}$ | 26.23 | $\bm{--}$ | 26.36 | 25.97 | $\bm{--}$ | 23.53 | $\bm{--}$
6 | $\bm{--}$ | 26.91 | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | $\bm{--}$ | 26.06 | $\bm{--}$ | 25.68 | 25.38 | $\bm{--}$ | 23.85 | $\bm{--}$
…

Notes: The filters available for each field are indicated in green with the
median 5$\sigma$ magnitude (AB) for detected sources (red dashes indicate no
data). Rows highlighted in orange have ‘full’ UV to near-IR coverage (6 or
more filters). The $g$-band and F475X cover roughly similar wavelengths and
typically only one of these were obtained. This similarly occurs for
F606W/$r$-band, F600LP/$i$-band/F814W, and F140W/F160W. I1=IRAC1, I2=IRAC2. A
full ASCII and PDF version of this table is available online.

###  4.2 Summary of Imaging Depth and Completeness

Since the segmentation maps of sources from WFC3/IR imaging data are used as
priors for the shallower and/or lower-resolution imaging data, we only
formally characterise the depth and completeness for the WFC3/IR images. This
is because, by design, every source detected in the WFC3/IR catalogue has an
entry for each additional filter with data (either a detection or upper limit;
i.e., 100% ‘complete’). Below we outline the method for estimating these
values for the WFC3/IR images. We also provide a representative depth for each
filter based on median 5$\sigma$ magnitude (AB) for detected sources, which we
also describe below.

For the HST imaging data, there are considerable differences in the depths and
completeness achieved from field to field. This arises from the parallel
nature of the program, where exposure times are set by the Primary
observation. To estimate this, we use the code described in Prichard et al.
(2022)999https://github.com/lprichard/hst_sky_rms and briefly summarise here.
First, the code determines the rms background value in 1000 randomly selected
empty sky regions, where the segmentation map from SExtractor is used to
exclude regions overlapping with sources. Next, it generates a histogram of
the rms values and fits this distribution with a Gaussian profile to determine
the sigma-clipped median. The median rms value is multiplied by the correlated
pixel noise correction factor for that filter (for details, see Section 3.3 of
the DrizzlePac Handbook101010https://hst-docs.stsci.edu/drizzpac). For the
drizzle parameters of the WFC3/IR images, as described in Section 2.2.1, the
correlated noise correction factor is 1.678. The corrected median rms is then
converted into a limiting magnitude using the zero-point and a specified
aperture size. We provide an estimate of depth for the WFC3/IR filters for a
fixed-aperture size of 0.5″ radius in Table 7.

To measure the completeness, we inject simulated sources of varying brightness
into the images and estimate their recoverability with SExtractor, following
methodology similar to Revalski et al. (2023). First, we inject point-sources
modeled as the PSF for each WFC3/IR filter. We adopt the PSFSTD
models111111https://www.stsci.edu/hst/instrumentation/wfc3/data-analysis/psf,
taking the average across the detector (3$\times$3 array), and resampling it
to match the 0.08″ resolution of the drizzled images. We inject 40 sources
into each image and require that these do not overlap with themselves or with
real sources, as determined from the SExtractor segmentation map from the
photometric pipeline. The magnitudes of the sources is scaled from [-3 mag,+1
mag], in steps of 0.1 mag (40 steps), relative to the filter zeropoint
magnitude. This process is then repeated for a simulated galaxy, which is
modeled as a Sérsic profile with $n=2$, inclined at 45°, and an effective
radii of 0.48″. This corresponds to the average size of a
$\log[M_{\star}/M_{\odot}]=10$ star-forming galaxy at $z=1$ using the size-
mass relation of van der Wel et al. (2014). The simulated galaxies are also
convolved with each filter PSF. The resulting completeness measurements are
shown in Figure 6. The point-source completeness values show close agreement
($\lesssim 0.2$ mag) with the 5$\sigma$ depth based on 0.5″ apertures.

$\begin{array}[]{ccc}\includegraphics[width=0.31]{Figures/WISP_{H}ST_{F}110W_{c}ompletion.eps}&\includegraphics[width=0.31]{Figures/WISP_{H}ST_{F}140W_{c}ompletion.eps}&\includegraphics[width=0.31]{Figures/WISP_{H}ST_{F}160W_{c}ompletion.eps\vspace{2mm}}\\\
\includegraphics[width=0.32]{Figures/WISP_{H}ST_{F}110W_{n}umber_{c}ount.eps}&\includegraphics[width=0.32]{Figures/WISP_{H}ST_{F}140W_{n}umber_{c}ount.eps}&\includegraphics[width=0.32]{Figures/WISP_{H}ST_{F}160W_{n}umber_{c}ount.eps}\\\
\end{array}$

Figure 6: Top row: Comparison of the fraction of artificial sources that are
recovered as a function of magnitude for the WISP WFC3/IR images. The thin
gray and red lines show the simulated point-source and galaxy completeness,
respectively, for individual fields. The thick black and red lines are the
medians of the point-source and galaxy completeness, respectively, across all
fields. The completeness (adopted as the 50% detection fraction) varies by up
to 1.8 mag across the sample due to the varying exposure length of the visits.
The completeness values for each individual field are provided in Table 7. The
median 50% completeness for each source type is indicated at the bottom of
each panel. Bottom row: Histograms of SExtractor MAG_AUTO values for the
WFC3/IR images in the WISP catalog. The black vertical dashed line denoted the
median 50% completeness of point sources for all fields (same as top panles).

A full list of the median depth in each filter, based on median 5$\sigma$
magnitude (AB; $0.15<m_{\mathrm{err}}<0.25$ mag) for detected sources, are
provided in Table 8 and summarised in Figure 7. We note that this depth value
is the median of the entire sample of 5$\sigma$ sources in each field, which
span a range of sizes/surface brightness and hence is a not a uniform
representation of depth. With regard to the WFC3/IR data, the depths reported
here typically lie in-between the depth values for the point-source and
simulated galaxies provided in Table 7. We provide some additional details on
the variation in depth for the ground-based and Spitzer imaging data. For the
ground-based data, there are considerable differences in the depths achieved
from field to field. This difference is a result of the ground-based data
being obtained through numerous programs, with different
facilities/instruments and different science goals (see Table 3), and due to
variations in the observing conditions. For Spitzer, the programs run over the
different cycles (see Section 2.4) used slightly different exposures that were
intended to achieve roughly uniform depth for each targeted field (see Section
2.4.1).

$\begin{array}[]{cc}\includegraphics[width=0.38]{Figures/depth_{H}ST_{U}VIS_{w}isp.eps}&\includegraphics[width=0.38]{Figures/depth_{H}ST_{I}R_{w}isp.eps\vspace{2mm}}\\\
\includegraphics[width=0.38]{Figures/depth_{u}{}_{w}isp.eps}&\includegraphics[width=0.38]{Figures/depth_{g}{}_{w}isp.eps\vspace{2mm}}\\\
\includegraphics[width=0.38]{Figures/depth_{r}{}_{w}isp.eps}&\includegraphics[width=0.38]{Figures/depth_{i}{}_{w}isp.eps\vspace{2mm}}\\\
\lx@intercol\hfil\includegraphics[width=0.38]{Figures/depth_{S}pitzer_{I}RAC_{w}isp.eps}\hfil\lx@intercol\\\
\end{array}$

Figure 7: Comparison of the median magnitude for sources detected at
$\sim$5$\sigma$ significance (sources with $0.15<m_{\mathrm{err}}<0.25$ mag;
$S/N\sim 5$) for all WISP fields in this data release. Panels show (left to
right, top to bottom) HST WFC3/UVIS, WFC3/IR, ground-based $u$, $g$, $r$, $i$,
and Spitzer/IRAC. The vertical dashed lines denote the median magnitude value
of 5$\sigma$-detected sources for a given filter (i.e., image depth). The
range in depths are mainly due to the varying length of exposure times,
observing conditions, and/or field crowding (see Section 4.2).

###  4.3 Comparison of ground-based catalogue photometry to SDSS

For the fraction of WISP fields that overlap with SDSS, we can make a
comparison of the values in our photometric catalogue to values in the SDSS
photometric catalogue. Due to SDSS being much shallower (5$\sigma$ point-
source depth for $u,g,r,i$ is 22.15, 23.13, 22.70, 22.20 mag, respectively)
than our data (see Figure 7), this comparison is quite limited (particulaly
for $u$-band) and only possible for the brightest galaxies in each WISP field.
We restrict our comparison to galaxies (SDSS PhotoType=4) and extract PetroMag
values from SDSS DR14 public catalogues to use as our reference values. The
PetroMag values are the most suitable for representing total galaxy flux that
will be similar to our TPHOT photometry (psfMag was used to compare stars for
the zeropoints in Section 3.1.2). However, the TPHOT photometry is based on
priors from the deeper HST data such that the aperture sizes are likely to
differ with respect to SDSS. A distance threshold of $\sim$0.5″ is adopted,
and we only compare sources with $S/N\geq 5$ in both datasets. A comparison
for the $u,g,r,i$ filters is shown in Figure 8.

$\begin{array}[]{cc}\includegraphics[width=0.4]{Figures/photo_{c}ompare_{u}{}_{w}isp.eps}&\includegraphics[width=0.4]{Figures/photo_{c}ompare_{g}{}_{w}isp.eps\vspace{2mm}}\\\
\includegraphics[width=0.4]{Figures/photo_{c}ompare_{r}{}_{w}isp.eps}&\includegraphics[width=0.4]{Figures/photo_{c}ompare_{i}{}_{w}isp.eps}\\\
\end{array}$

Figure 8: Comparison of the magnitude offset for galaxies detected at $S/N\geq
5$ in optical bands from SDSS (PetroMag) and our WISP catalogue (AB_Mag). The
vertical dashed lines denote the median 5$\sigma$ point-source limit for SDSS.
We note that the magnitude limit for galaxies is fainter than this (e.g.,
Figure 6). The median offsets are typically $\lesssim$0.2 mag and agree within
the variance of the data. There are very few $u$-band galaxies bright enough
for reliable comparison. The solid and dashed lines shows the median and $\pm
1\sigma$ values combining all data in equal-number bins of 50 galaxies. For
each instrument we provide the median magnitude difference (i.e., y-axis) and
its variance in the legend, with the number of available sources shown in
parentheses.

We find good general agreement in the photometry, with median offsets of
$\lesssim$0.2 mag, although a slight bias (0.2 mag) may exist for the $r$ and
$i$ bands. However, these offsets are within the variance for each band
indicating they may not be significant. These results support or previous
claim that the optical zeropoints have a typical accuracy of $\sim$0.1 mag.
Individual sources with large differences ($\Delta>0.5$ mag) are likely due to
source blending and/or incorrect cross-matching. We note that the sample
available for this comparison is much smaller than the sample used in the
zeropoint determination for each image because the zeropoint estimate made use
of the entire instrument FoV (>15$\times$ the area of WFC3/IR) whereas the
catalogue only includes the small region overlapping with the WFC3/IR data.

##  5 WISP Spectroscopic Pipeline

The WISP emission line catalogue is created in three steps. First, an
automatic detection algorithm examines every extracted spectrum to identify
emission line candidates. Next, each candidate is independently inspected by
two reviewers both for confirmation and to measure the source redshift and
emission line properties. These first two steps are performed by the
wisp_analysis121212https://github.com/HSTWISP/wisp_analysis software package.
Finally, the output from the two reviewers is combined to create one catalogue
entry for each emission line source. We describe each step in this process in
the following sections.

###  5.1 Emission Line Candidate Identification

We identify emission line candidates with a peak detection algorithm that uses
a continuous wavelet transform (CWT) to select appropriately-shaped peaks in
one-dimensional spectra. A wavelet transform breaks a signal into its base
components, each of which is a modified version of the same “mother” wavelet
function. This process is similar to Fourier analysis, but rather than
sinusoidal components of varying frequencies, the base components identified
by a wavelet analysis are scaled or shifted versions of the mother wavelet.
The CWT is an improvement over the previous WISP line detection method, which
identified emission lines as contiguous pixels above a signal-to-noise (S/N)
threshold (Colbert et al., 2013). The previous amplitude-based peak finding
process was strongly dependent on the fit to the continuum and the amount of
smoothing applied to the spectrum. It also resulted in many spurious
detections as noise spikes can be misidentified as faint emission lines. The
CWT technique identifies emission line features in the spectrum based on their
shape as well as their amplitude, and therefore reduces the number of spurious
emission line candidates that reviewers need to inspect. A detailed
description of the steps in applying our CWT algorithm and using the results
to identify emission line candidates is provided in Appendix C.

Emission line identification using the CWT algorithm is performed on the one-
dimensional spectra extracted and calibrated by aXe (Kümmel et al., 2009). We
first remove from each spectrum the flux introduced by the overlapping
continua from nearby objects. For this purpose we use the contamination model
created by aXe during spectral extraction, where all objects detected in the
direct images are approximated as two-dimensional Gaussians defined by the
size and shape measured by SExtractor. This process is performed on the one-
dimensional spectra of each grism individually, allowing for 500Å of overlap
between the two grisms. We next require that at least two reviewers inspect
each emission line candidate, both to confirm the candidates and to measure
the line properties.

###  5.2 Emission Line Candidate Inspection

The original, amplitude-based WISP line detection software resulted in a false
detection rate of $\gtrsim 70$%, depending on the depth of the fields.
Although the improvements presented here — identifying emission lines using
both amplitude and shape combined with the EW criterion — reduce this rate
significantly to approximately 55%, the visual inspection remains necessary
for constructing a clean catalogue. This inspection is especially crucial for
undithered parallel data, which cannot be properly cleaned of artifacts.

For each emission line candidate, reviewers simultaneously inspect the direct
images of the source, the two-dimensional spectral stamps, the one-dimensional
extracted spectrum in units of $f_{\lambda}$, and a spectrum in units of S/N.
An example of the full display from the interactive portion of the process is
shown in Figure 9.

We now briefly describe the inspection process and the series of checks
reviewers perform for each candidate. The source displayed in Figure 9, object
93 from WISP field Par94 (hereafter 94-93), is used as an example to
illustrate the process. The two main questions reviewers must answer are
whether the emission line candidate identified by the detection algorithm is
real, and whether it belongs to the object to which it is associated. In the
first case, reviewers are validating the results of the detection software. In
the second, they are considering and ruling out possible sources of
contamination.

[width=0.48]Figures/display.pdf

Figure 9: The display from the interactive portion of the emission line
finding process. Reviewers inspect all available information for a given
object. Top row: The two-dimensional spectral stamps for G102 (left) and G141
(right) are displayed with a green box indicating the trace of the spectra.
Red circles identify the positions of zeroth orders of bright ($m<23$) objects
that may contaminate the spectra. Middle row: The direct images in all
available filters, F110W (left) and F160W (right), with the positions of all
objects and their corresponding magnitudes marked. The source of interest,
here object 93, is centered in the direct images. Bottom panel: The one-
dimensional spectrum is displayed in both flux units ($f_{\lambda}$, top) and
signal-to-noise (bottom). In the example shown here, the emission features
identified in the spectrum of object 93 are not centered in the green box
because they are coming from object 77. The emission line offset is clearest
in the G102 spectrum. Object 93 was rejected as an emission line candidate and
these emission features were instead measured for object 77.

Candidate confirmation is required because spurious or false emission lines
are occasionally identified by the detection program. False emission lines
typically arise in two cases, when detector artifacts are identified as lines
and when the continuum is improperly fit. The first case is a particular
problem for a pure parallel survey such as WISP, since the telescope is not
dithered between exposures. Combining multiple exposures therefore does not
remove all cosmic rays, hot pixels, and other artifacts. Those that remain are
sometimes selected as emission line candidates. Reviewers can often reject
these by comparing the shape of the emission line candidate in the two-
dimensional spectral stamp (top row of Figure 9) with the source shape in the
direct image (middle row). Recall that an emission line in the spectral stamp
is an image of the source at the given wavelength. The size, ellipticity, and
position angle of the source are expected to be reflected to some degree in
the emission line. This comparison is approximate, however, since the emission
regions in a galaxy need not directly correlate with the broadband continuum
emission detected in the imaging filters.

In the second case, false emission line candidates are identified in objects
with continua that are poorly fit by the automatic software, which uses a
cubic spline to fit the spectrum at eight wavelengths nodes. A steep rise in
the continuum of an object, often caused by contamination from the spectrum of
a nearby object, that is not reflected in the model fit can be incorrectly
selected as a spectral peak. Given the large range of object sizes, fluxes,
and levels of spectral confusion, one set of parameters will not work
perfectly for all objects. The software’s continuum fit is therefore treated
as a first pass. The dashed blue line in Figure 9 is the continuum model for
object 94-93, which in this case represents a good fit to the observed
continuum. For objects with improperly fit continua, reviewers can tweak the
model by adding, removing, or changing the wavelengths of the nodes used in
the spline fit (black circles).

The reviewers must next determine whether the identified emission feature
belongs to the source in question. With only a single roll angle, WISP spectra
are often contaminated by overlapping spectra from other sources along the
dispersion direction. This check generally involves four parts. First, the
comparison between source and emission line shape described above can help
identify emission lines coming from another object. We do not expect a galaxy
to be much larger or much brighter in an emission line than it is in imaging.

Second, the emission should be vertically centered in the trace of the
spectral stamps, indicated by the green box in the top panels of Figure 9. We
can see that the line candidates in the spectrum of 94-93 are not centered,
evidence that they likely belong to the nearby, brighter object 77. We note
that it is of course possible that the emitting region of a source may not be
centered on the continuum emission, and by rejecting emission lines that are
off the centre of the trace we may also be rejecting real emission line
galaxies.

Third, if there are multiple emission lines visible in the spectrum, their
relative wavelengths should match. The wavelength solution of the grism is
determined by the source position in the direct image, and will therefore only
be correct for the spectrum of that source. For example, in Figure 9, given
the assumed redshift for this object, the spectral peak around $\lambda\sim
10500$Å should be [OII]$\lambda 3727$. However, it does not line up exactly
with the expected wavelength for [OII] at this redshift (indicated by the blue
vertical line), further indication that these emission lines are contaminants
from object 77.

Finally, the reviewers must consider the position of zeroth orders. We
consider a portion of a spectrum to suffer from “major” zeroth order
contamination if it directly overlaps with a zeroth order from a bright source
($m<23$ magnitude). The position of these bright zeroth orders are indicated
by red circles in the grism stamps in Figure 9. The chance alignment of a
bright zeroth order, especially from a compact source, can appear as a very
convincing emission line. Spectral peaks that suffer from this major
contamination are automatically rejected by the automatic software. Meanwhile,
“minor” zeroth order contamination could be caused by (1) bright zeroth orders
that are close to but not directly overlapping the spectral trace or (2) from
direct overlap with zeroth orders of fainter sources ($m>23$). In some cases,
again especially for the most compact objects, these fainter zeroth orders can
be bright enough to masquerade as emission lines, and so the reviewers must
remain vigilant for this possibility. The minor zeroth order contamination
regions for object 94-93 are shown as orange bands in the spectrum of Figure
9.

###  5.3 Emission Line Measurements

Once an emission line candidate has been confirmed, the reviewers fit a model
to the spectrum. The fitting is performed via Levenberg-Marquardt least-
squares minimisation. It is implemented with the software mpfit, based on the
MINPACK-1 FORTRAN package (Moré, 1978) and translated to Python by Mark
Rivers131313University of Chicago,
http://cars9.uchicago.edu/software/python/mpfit.html. With mpfit, each
parameter can be held fixed or can be constrained with upper and lower bounds.
The full model includes over 20 parameters, which are described below and
listed in Table 9.

Table 9: Model Spectrum Parameters

Parameter | Description | Initial Value | Limits
---|---|---|---
$n_{\mathrm{nodes}}$ | Number of spline nodes used in continuum fit | 8 | Fixed
$\Delta\lambda_{\mathrm{fitting}}$ | Size of region used for line fitting | 1500 Å | Fixed
$z_{\mathrm{init}}$ | Input redshift |  $\left(\frac{\lambda_{\mathrm{obs}}}{\lambda_{\mathrm{H}\alpha}}-1\right)$a | $\pm 0.02$
$\Delta z_{\mathrm{[OIII]}}$ | Shift in redshift allowed for [OIII] profile fit | 0 | $\pm 0.02$
$\Delta z_{\mathrm{[OII]}}$ | Shift in redshift allowed for [OII] profile fit | 0 | $\pm 0.02$
$\Delta z_{\mathrm{[SIII,HeI]}}$ | Shift in redshift allowed for [SIII] and HeI fits | 0 | $\pm 0.02$
FWHMinit | Input FWHM |  $2a\>\Delta\lambda_{\mathrm{G141}}$ Åb | ${}^{-0.3\mathrm{FWHM}_{\mathrm{init}}}_{+2.0\mathrm{FWHM}_{\mathrm{init}}}$
$A_{\mathrm{line}}$ | Input amplitude for each emission line |  $\dotsb$c | 0,1c
$r_{\mathrm{[SIII]}\lambda 9532/\lambda 9069}$ | Ratio of [SIII]$\lambda 9532$ to [SIII]$\lambda 9069$ fluxes | 2.48 | Fixed
$\lambda_{\mathrm{T}}$ | Grism transition wavelength | 11200 Å | Fixed
$\lambda_{\mathrm{blue}}$ | Blue wavelength cutoff for the G102 grism | 8100 Å | Fixed
$\lambda_{\mathrm{red}}$ | Red wavelength cutoff for the G141 grism | 17000 Å | Fixed

Notes: aThe input redshift is that which will give $\mathrm{H}\alpha$ for the
current line, or is a redshift guess provided by the user.

bFWHMinit is taken as twice the source semi-major axis (A_IMAGE) multiplied by
the dispersion in the red grism.

cEmission line amplitudes are estimated as the flux value at line centre and
are constrained to be positive.

The model spectrum fit to the data consists of a continuum with the following
emission lines added: [OII]$\lambda\lambda 3727+3729$, H$\gamma$,
$\mathrm{H}\beta$, [OIII]$\lambda\lambda 4959+5007$, $\mathrm{H}\alpha$,
[SII]$\lambda\lambda 6716+6730$, [SIII]$\lambda 9069$, [SIII]$\lambda 9531$,
and HeI$\lambda 10830$. The continuum is modeled using a cubic spline fit to a
series of $n_{\mathrm{nodes}}$ spectral nodes, and emission lines are modeled
as Gaussians, where the line centre is determined by the redshift guess for
the source, the input amplitude is estimated separately for each line within
$\pm\Delta\lambda_{\mathrm{fitting}}$ of line centre, and the standard
deviation depends on the source size and the dispersion of the grism in which
the line appears. Emission lines are not fit individually. The entire spectrum
— continuum plus all lines — is fit simultaneously, and all line profiles are
constrained to have the same FWHM in pixels, not in Å. Hence, lines in the
higher dispersion G102 will have smaller FWHM by a factor of two. This
approach is reasonable under the assumption that all emission lines are images
of the same host source. The source redshift is determined by the centre of
the profile fit to the $\mathrm{H}\alpha$ line at $z\lesssim 1.6$ and [OIII]
at $z\gtrsim 1.6$ (when $\mathrm{H}\alpha$ has redshifted out of the G141
grism). The centres of each additional line are allowed to vary up to a
maximum wavelength equivalent to $\Delta z_{\mathrm{line}}=0.02$. In the
absence of multiple emission lines, single lines are assumed to be
$\mathrm{H}\alpha$ unless the clear asymmetry of the
[OIII]$+$$\mathrm{H}\beta$ line profile is visible.

As a consequence of the use of a full spectral model, all emission lines
listed above are fit provided they fall within the grism wavelength coverage
at the assigned redshift. Emission lines that were not identified by the
detection algorithm will therefore be measured along with the identified
lines. We refer to the lines strong enough to have been identified by the
detection algorithm as “primary lines”, while the remaining lines are called
“secondary lines”. This distinction is an important one for the emission line
catalogue completeness, which is discussed in the next section (Section 5.4).

Lines with a flux S/N$<$1 are set at 1$\sigma$ and reported as upper limits in
flux and therefore EW. These limits are calculated by summing in quadrature
the error array within $2\times$FWHM of line center. We find, however, that
the error arrays calculated by aXe are underestimates of the spectral noise
properties. The 1$\sigma$ limits are all systematically lower than the
sensitivity limits measured for the fields. We therefore apply a correction
factor to the flux limits, correcting the amplitude of the limits while
preserving the scatter in the measurements.

We note several emission lines — $\mathrm{H}\alpha$ and [NII], the
[SII]$\lambda\lambda 6716+6731$ doublet, the [OII]$\lambda\lambda 3727+3730$
doublet, and the [OIII]$\lambda 4959+5007$ doublet — are blended at the
resolution of the WFC3 grisms. The fluxes measured for $\mathrm{H}\alpha$
therefore include the contribution from [NII]$\lambda 6583$ and [NII]$\lambda
6550$, and those for [OII], [SII], and [OIII] each include both doublet lines.
The flux ratio [SIII]$\lambda$9532/[SIII]$\lambda$9069 is fixed to 2.48:1.

While inspecting each spectrum, reviewers can change multiple parameters in
order to improve the fit to the spectrum. In addition to moving, adding, or
subtracting nodes for the continuum fit, they can provide a new redshift guess
for the source; modify the wavelength ranges of each grism to fit emission
lines at the grism edges (changing the transition between grisms,
$\lambda_{\mathrm{T}}$, and their wavelength cutoffs $\lambda_{\mathrm{blue}}$
and $\lambda_{\mathrm{red}}$); or provide a new guess for the FWHMinit,
usually decreasing the default guess for sources where the dispersion axis is
along the minor-axis. Finally, reviewers can mask regions of the spectrum that
suffer from severe contamination from either zeroth orders or nearby continua,
thereby making sure they do not affect the full spectral model. The emission
line candidate vetting, spectral fitting and cataloguing are all performed as
part of one streamlined process. The results from the two reviewers are then
combined for each object, and a series of quality flags are assigned to the
emission line object determined by the level of redshift, flux and EW
agreement between the reviewers’ classifications (see Section 6 and Appendix
E).

###  5.4 Completeness Corrections

The completeness of a survey or catalogue is a description of how accurately
the detected sample represents the true population in the universe.
Understanding a survey’s completeness is necessary before the results can be
used to conclude anything about the true underlying distribution of sources
and source properties. A survey such as WISP can suffer from incompleteness
for a variety of reasons. Sources may be lost amidst the noise in images if
their fluxes are close to the detection limit. Some sources may not be
detected, or their emission lines missed in their spectra, because they
overlap or are blended with nearby bright objects. The completeness of a
survey depends on the specific selection function used to detect sources. In
the case of the WISP emission line catalogue, the selection function includes
the detection of sources in the direct images, the identification of emission
line candidates via the detection algorithm, and the acceptance during the
visual inspection. We also only look for emission lines of continuum-detected
sources in the images. We must understand the fraction of sources and emission
lines that are not detected through this full process as a function of their
properties such as size, shape, and the strength of their emission.

In quantifying the completeness corrections that must be applied to a
catalogue, we are determining the types and numbers of sources that are
missed. To do so, we create a simulated catalogue of 10,000 sources and their
spectra, 5,000 each for the shallow and deep portions of the WISP Survey. The
simulated sources have $H$-band magnitudes in the range $16.8\leq m_{H}\leq
26.2(27.6)$ and observed $\mathrm{H}\alpha$ fluxes in the range of $5\times
10^{-17}(1\times 10^{-17})\leq f\leq 1\times 10^{-15}$ erg s-1 cm-1 for the
shallow (deep) fields. See Table 17 for the full list of input parameters and
values. We insert these simulated sources into real WISP images, 25 sources at
a time, and run them through the full WISP pipeline and emission line
detection software. The creation of the simulated data is described in
Appendix D. In order to save time and the effort required during the visual
inspection stage, the reviewers only inspect the spectra of simulated sources
that were identified by the line finding algorithm. Yet not all of the
emission line candidates were real. Some were noise spikes, contamination, or
the result of poorly fit continua. We note, however, that because of this
choice we cannot use the simulations to measure the rates of contamination or
redshift mis-identification in the catalogue.

Of the 10,000 input sources, 7,721 were recovered by the WISP reduction
pipeline, with an equal number recovered in the shallow and deep fields. This
77% recovery fraction represents the overall imaging completeness given the
imaging depths and our set of source detection parameters. The majority of the
sources that are not recovered in the imaging catalogue, and which therefore
have no extracted spectra, are faint and/or extended. In Figure 10 the input
semi-major axis sizes (before convolution with the PSF) are shown as a
function of magnitude for the simulated sources that were input and recovered.
The distributions of real sources are shown for reference. The sources that
are not recovered in imaging mainly have a semi-major axis of $a\geq
0.7\arcsec$ and are fainter than 24.5 magnitudes in the $H$ band.

[width=0.48]Figures/recoveredmags.pdf

Figure 10: The semi-major axis as a function of the $H$-band magnitude for all
input sources (grey) and those recovered in imaging (blue contours). The real
sources from the photometric and emission line catalogues are shown in red.
The imaging completeness is a function of the magnitude and size of the
sources. The recovery fraction drops for large ($a\geq 0.7\arcsec$) and faint
($H>24.5$) sources.

For the simulated sources recovered in imaging, we calculate the fraction of
these that are recovered by the full line finding process. We find that the
completeness depends on source size and shape and emission line EW and S/N.
The S/N dependence is essentially a dependence on line flux, but includes the
effects of the variable depths of the WISP fields (see Figure 3). While we can
measure the S/N of observed emission lines, there is no analogous definition
of the input S/N for the simulated lines. The input template spectra do not
include noise, and while we have added shot noise to the simulated grism data
based on the integration times of the exposures into which they are added,
this is not the only source of noise that will affect the flux measurements.
The depths reached in each field depend also on the level of the zodiacal
background for each pointing. We therefore instead characterise the
completeness as a function of emission line “scaled flux”, or the emission
line flux (input or recovered) divided by the sensitivity limit of the field
at the wavelength of the line.

[width=0.48]Figures/completeness.png

Figure 11: The completeness of the emission line catalogue as a function of
the scaled flux and observed EW of the strongest line for each source. The
dashed horizontal line indicates the EW completeness limit 40 Å. The small,
transparent points indicate the lines with EW$<$40 Å and/or S/N$<$5\.

As discussed in Section 5.3, a source will enter the catalogue because of the
detection of the primary lines. We consider only one line per spectrum — both
for the input simulated and the output measured spectra — taking the line with
the brightest scaled flux as the source’s primary line. As we are not
attempting to quantify the rates of redshift mis-identification, we consider a
detected emission line recovered regardless of whether the reviewers have
properly identified it (i.e., regardless of what redshift is assigned to the
object). We recover 868 of the 5000 simulated sources added to deep WISP
fields covered by both grisms and 1541 of the 5000 added to shallow, G141-only
fields. This recovery reflects the completeness due to both the imaging and
the spectroscopic selection functions, and is heavily influenced by source
size and shape as discussed below.

The object size and shape will strongly affect the completeness, as large, low
surface brightness emission lines may be missed by the peak finder. However,
the large sources that suffer from the highest levels of incompleteness, those
with $a\geq 0.7\arcsec$, constitute less than 1% of the total catalogue. We
simulate sources with a uniform distribution of sizes, but then weight the
input sources by the distribution of observed sizes in the emission line
catalogue. This step both reflects the observed distribution and allows us to
consider a two-parameter completeness correction, maintaining sufficient
number counts for the completeness analysis without requiring reviewers to
visually inspect tens of thousands of sources.

The completeness is calculated in four bins of scaled flux and five bins of
EW. The bin edges are determined by the distribution of sources in the real
WISP emission line catalogue such that there are an approximately equal number
of real sources in each bin. The one exception is the bin of lowest EW, which
we add in order to probe an area of the parameter space with low completeness
(EW${}_{\mathrm{obs}}<40$Å, see Colbert et al., 2013). We use a radial basis
function to approximate the three-dimensional surface formed by the bin
centers and recovery fractions calculated in each bin. The resulting
completeness corrections calculated for each source in the WISP emission line
catalogue are shown in Figure 11. They are applied according to the scaled
flux and observed EW of the strongest line in the spectrum, which is most
often $\mathrm{H}\alpha$ or [OIII] but is occasionally [OII] when
$\mathrm{H}\alpha$ or [OIII] are masked out due to overlap with a bright
zeroth order or other major contaminant. These completeness corrections are
applicable at the source level or for the primary lines for each source. They
are not appropriate for secondary lines. As expected, very few low-EW emission
lines were recovered in the simulations, making the completeness corrections
calculated in bins with EW${}_{\mathrm{obs}}<40$Å very uncertain. We therefore
find that the EW criterion presented in Colbert et al. (2013) applies to the
new version of the line finding process as well (see Bagley et al. 2020 for a
comparison of these completeness corrections with those calculated by Colbert
et al. 2013). We also recommend applying an emission line flux S/N cut at
S/N$>$5 when using this catalogue.

##  6 WISP Emission Line Catalogue

###  6.1 Emission Line Catalogue Description

The WISP emission line catalogue contains 8,192 sources in 419 WISP fields.
These sources include only galaxies and AGN (spanning
$0.137<z_{\mathrm{grism}}<2.785$; no stars included). Fields that are absent,
relative to the photometric catalogue, fall into one of a few categories: they
were too crowded (a few WISP fields captured portions of dwarf galaxies),
heavily contaminated by bright stars, or suffered from poor and uneven
background subtraction in the grism data. We note that line availability is
dependent on the grism coverage and galaxy redshift and that sources without
data in a given emission line have values of ‘-1’ for their entries. The S/N
and EW of all emission lines in the catalogue are shown in Figure 12. The vast
majority of the $\mathrm{H}\alpha$ emission lines (blue circles) have a S/N
greater than 4 (vertical dashed line), indicating that $\mathrm{H}\alpha$ is
most often the primary line in a spectrum. Emission line fluxes to the left of
the dashed line were likely fit as secondary lines and are therefore at a
lower S/N. The emission lines in this catalogue are not extinction-corrected
(neither foreground Milky Way nor internal extinction applied).

[width=0.48]Figures/snr.png

Figure 12: The emission line S/N and EW of all emission lines in the
catalogue. $\mathrm{H}\alpha$ is the two most commonly identified “primary
line” and therefore the majority of $\mathrm{H}\alpha$ in the catalogue has a
S/N$>$4\. The majority of the lower-S/N lines were fit as a consequence of the
redshift assigned by identification of a primary line.

We present an explanation of the WISP emission line catalogue entries in Table
10. These include RA, Dec, WFC3/IR total magnitudes, sizes (based on HST),
spectroscopic redshift, and the FWHM used for all emission lines. There are
also emission line flux, flux error, EW, and observed wavelength, for nine
lines ([OII], H$\gamma$, $\mathrm{H}\beta$, [OIII], $\mathrm{H}\alpha$+[NII],
[SII], [SIII]$\lambda$9069, [SIII]$\lambda$9532, and HeI$\lambda$10830).

There are also nine quality flags in the emission line catalogue. A
description of these flags is provided in Appendix E. These flags should be
carefully considered when selecting sources from the catalogue. For the most
robust selection of emission line sources, we recommend only using cases with
REDSHIFT_FLAG=0 (5054 sources) to avoid cases with ambigious redshift
determinations. Cases with REDSHIFT_FLAG$>$0 indicate some type of redshift
disagreement between the reviewers or redshift uncertainty for single line
emitters. The majority of sources with REDSHIFT_FLAG$>$0 are those that were
identified by only a single reviewer (REDSHIFT_FLAG$\geq$16; 2061 sources).
These cases are likely marginal detections where one reviewer did not consider
the identified emission feature to be real above the noise or rejected the
emission feature as some type of artifact or contamination. Sources with
REDSHIFT_FLAG$\geq$16 should therefore be considered with caution.

Table 10: Description of WISP Emission Line catalogue

Title | Description
---|---
PAR | WISP field ID number
OBJ | Object ID number
RA | Decimal RA from HST images [deg]
DEC | Decimal Dec from HST images [deg]
JMAG | J-band magnitude; SExtractor MAG_AUTO_F110W from WISP Photometric Catalogue [mag]
HMAG | H-band magnitude; SExtractor MAG_AUTO_[F140W or F160W] from WISP Photometric Catalogue [mag]
A_IMAGE |  SExtractor profile RMS along major axis measured on 0.08″/pixel HST images [pixels]
B_IMAGE |  SExtractor profile RMS along minor axis measured on 0.08″/pixel HST images [pixels]
FILTER_FLAG | Flag identifying filter coverage for field (10 bit flags; see Appendix E)
GRISM_FLAG | Integer flag identifying grism coverage for field; (1=G102, 2=G141, 3=G102+G141)
[GRISM_FILTER]_FLAGa | Flags identifying any problems with the grism data for this field (5 bit flags; see Appendix E)
EDGE_FLAG | Flag identifying objects close to edges of direct image (5 bit flags; see Appendix E)
NNEIGHBORS | Number of sources in WISP Photometric Catalogue within 1″ of object
NLINES | Number of lines detected at $>2\sigma$ for object
REDSHIFT | Redshift from simultaneous fit to all lines in spectrum
REDSHIFT_ERR | Redshift 1$\sigma$ uncertainty
dz_OIII | Shift in redshift of the [OIII] profile fit compared with reported REDSHIFT for object
dz_OII | Shift in redshift of the [OII] profile fit compared with reported REDSHIFT for object
dz_SIII_HE1 | Shift in redshift of the [SIII] and HeI profile fit compared with reported REDSHIFT for object
DELTA_REDSHIFT | Difference in redshift fits of the two reviewers
REDSHIFT_FLAG | Flag identifying quality of redshift fit (6 bit flags; see Appendix E)
FWHM_OBS | FWHM used for all emission line profile fits; observed frame using the 46.5 Å/pix dispersion in G141 grism [Å]
FWHM_OBS_ERR | FWHM 1$\sigma$ uncertainty [Å]
FWHM_FLAG | Flag identifying quality of reported FWHM (5 bit flags; see Appendix E)
COMPLETENESS | Source completeness reflecting the selection function of the full line-finding procedure (See Section 5.4)
[LINE]_NREVSb | Number of reviewers who measured emission line
[LINE]_FLUXb | Emission line flux from profile fit [erg s-1 cm-2]
[LINE]_FLUX_ERRb | Emission line flux 1$\sigma$ uncertainty [erg s-1 cm-2]
[LINE]_DELTA_FLUXb | Difference in emission line fluxes of the two reviewers [erg s-1 cm-2]
[LINE]_EW_OBSb | Emission line equivalent width reported in observed frame; -1 for undetected lines [Å]
[LINE]_DELTA_EWb | Difference in emission line EWs of the two reviewers [Å]
[LINE]_FLAGb | Flag identifying quality of emission line measurements (6 bit flags; see Appendix E)
[LINE]_CONTAMb | Flag identifying the contamination noted by each reviewer (‘a’ and ‘b’); String has form ‘a.b’ (4 bit flags; see Appendix E)
[LINE]_WAVEOBSb | Observed wavelength of emission line [Å]
[LINE]_EDGE_FLAGb | Flag identifying emission lines close to edges of grism where sensitivity decreases (4 bit flags; see Appendix E)

Notes: a[GRISM_FILTER] is one of: G102 or G141. b[LINE] is one of: OII, Hg,
Hb, OIII, HaNII, SII, SIII_9069, SIII_9532, or He1_10830.

###  6.2 Grism Redshift Accuracy and Precision

The redshift accuracy of the grism data are primarily driven by the number of
available lines, with a greater number of lines generally providing more
reliable redshifts. For example, Baronchelli et al. (2020) show that the
default choice of assuming WISP single-line emitters are $\mathrm{H}\alpha$ is
incorrect for $\sim$30% of cases, where most of these are likely to be the
[OIII]$\lambda$5007 emission line. Therefore, in the absence of other
independent information that can inform how to break single-emitter
degeneracies, such as photometric redshifts (photo-$z$) and/or machine
learning (e.g., Baronchelli et al., 2020, 2021), we urge caution in using
sources with only a single emission line (NLINES$\leq$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\sim 6000$; 0.8-2.5µm) were made on sources
with $S/N\gtrsim 10$ (from grism) in [OIII] and/or $\mathrm{H}\alpha$. They
found very good agreement in line identification (close to 100%) 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 ($R\sim 1200$;
0.51-0.85µm) will be presented in Boyett et al. (in prep), which we briefly
highlight here. This program observed 85 emission line galaxies out of 138
potential emission sources in the 4 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% 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/pix and a FWHM$\sim$110Å. We characterise the
precision as $\sigma_{z}/(1+z)$ (i.e., REDSHIFT_ERR /(1+REDSHIFT), which has a
median value of 0.00088 ($\sim$0.09%) 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 $\sim$140 sources that
were observed multiple times, often with very different exposure times (field
depths) and roll angles. This comparison 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.

##  7 Results

[width=0.7]Figures/WISP_stack_spectra_windows.eps

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 (criteria 1-8; see Section 7.1).

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:

  * •

grism coverage of $\mathrm{H}\alpha$+[NII], [SII], and [SIII] doublet
($0.30<z<0.73$)

  * •

grism coverage of $\mathrm{H}\alpha$+[NII] and [SII] ($0.30<z<1.45$)

  * •

grism coverage of $\mathrm{H}\beta$ and [OIII] ($0.74<z<2.31$)

  * •

grism coverage from [OII] to [SII] ($1.27<z<1.45$; maximum $\lambda$-coverage)

We do not examine the window where $\mathrm{H}\beta$, [OIII], and
$\mathrm{H}\alpha$+[NII] are simultaneously covered to constrain the Balmer
decrement ($\mathrm{H}\alpha$/$\mathrm{H}\beta$; $0.74<z<1.51$), 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 [OII],
$\mathrm{H}\beta$, and [OIII] are covered ($1.27<z<2.31$; wider redshift than
fourth window above) to constrain the metallicity via the
$R_{23}\equiv(\mathrm{[OII]}\lambda\lambda$3726, 3729 +
[OIII]$\lambda\lambda$4959, 5007)/$\mathrm{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 Figure 13, together
with the sample size satisfying the criteria for our science results (Section
7.1).

###  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:

  1. (1)

One emission line with $S/N\geq 3$ and one additional line with $S/N\geq 2$

  2. (2)

At least three bands of photometry with $S/N>3$

  3. (3)

Independent redshift agreement between the two reviewers (REDSHIFT_FLAG=0)

  4. (4)

Emission line $\mathrm{FWHM}<600$Å (FWHM_OBS$<$600)

Criteria (1) ensures an accurate $z_{\mathrm{grism}}$, which is important for
optimally aligning the spectra, as well as reducing false identifications.
Criteria (2) ensures that we have adequate SED coverage for characterising
stellar masses, $M_{\star}$. 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 $\sim$1/3 of the potential
sample, which indicates the difficulty in determining reliable redshifts from
low signal-to-noise spectra. Criteria (4) removes very broad emission line
sources ($\sim$1% 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 criteria (1)-(4) are shown in Figure 14.

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

  1. (5)

$\chi_{\mathrm{red}}^{2}<3$

  2. (6)

$\sigma(\log M_{\star})\,<0.3$ dex

which is detailed in Section 7.2. Together, criteria (5) and (6) remove 147
sources (6 fail both criteria) or 7.6% 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 [OIII] and
$\mathrm{H}\beta$, we also exclude AGN candidates based on the Mass-Excitation
diagram (log[[OIII]/$\mathrm{H}\beta$] vs. log[$M_{\star}/M_{\odot}$]; Juneau
et al. 2014):

  1. (7)

non-AGN in MEx diagram

which is detailed in Section 7.4.1. Criteria (7) removes an additional 59
sources. This leave 1731 sources that satisfy criteria (1)-(7), and this
sample is also shown in Figure 14.

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

  1. (8)

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

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

[width=0.5]Figures/WISP_z_logM.png

Figure 14: Top panel: grism redshift, $z_{\mathrm{grism}}$, distribution for
galaxies in the WISP sample that have robust photometric and spectrocopic data
(criteria 1-4; black) and the subset that also have good SED fits, accurate
stellar masses, and are not AGN candidates (criteria 1-7; orange), as
described in Section 7.1. Bottom panel: stellar mass vs. redshift. A
representative median 1$\sigma$ errorbar for the criteria (1)-(7) sample
(orange) is indicated in the lower-left, with values of
$\langle\sigma(z_{\mathrm{grism}})\rangle=0.0017$ (i.e., negligible) and
$\langle\sigma(\log[M_{\star}/M_{\odot}])=0.12$ dex. No significant selection
effects on stellar mass are apparent with redshift.

###  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 Milky Way extinction using the Galactic dust extinction maps from
Schlafly & Finkbeiner (2011) via the NASA/IPAC Infrared Science
Archive141414https://irsa.ipac.caltech.edu/applications/DUST/. 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 AGB 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 website151515http://www.iap.fr/magphys/index.html. In brief, they
include: a uniform prior in metallicity from 0.2 to 2 times solar (1
parameter); a parametric star-formation history (SFH; 3 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) (4 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 interstellar medium
(ISM), with the addition of the 2175Å absorption feature (Battisti et al.,
2020); the dust emission models of da Cunha et al. (2008), which uses
templates based on four components (5 parameters); and a normalisation that
sets the stellar mass and star formation rate (SFR) from the SFH (1
parameter). The adopted SFH parametrisation 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 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)

$F_{\lambda}\simeq
F_{\lambda,\mathrm{cont}}+F_{\mathrm{line}}/\Delta\lambda\,,$ (1)

where $F_{\lambda,\mathrm{cont}}$ 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 $M_{\star}$) and higher
equivalent widths ($EW=F_{\mathrm{line}}/F_{\lambda,\mathrm{cont}}$). An
example of a MAGPHYS fit for a WISP galaxy is shown in Figure 15.

[width=0.95]Figures/WISP_MAGPHYS_example-crop.pdf

Figure 15: Top row: Native resolution $10\arcsec\times 10\arcsec$ 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-fit 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 probability distribution functions (PDFs) for stellar mass and SFR
are also shown. The available photometric coverage is sufficient to accurately
constrain stellar masses ($\sim$0.1 dex), however SFRs have poorer constraints
due to the lack of rest-frame IR data (i.e., age/dust reddening degeneracy;
$\sim$0.3 dex).  Table 11: Stellar mass and SFR percentiles from MAGPHYS for
the 1937 WISP sources with ‘robust’ spectroscopy and photometry (criteria 1-4
in Section 7.1)

Par | Obj | $z_{\mathrm{grism}}$ | $z_{\mathrm{grism,err}}$ | AGN_flaga | $\log[M_{\star}/M_{\odot}]$ | $\log[\mathrm{SFR}(\mathrm{SED})/(M_{\odot}\mathrm{yr}^{-1})]$ | $\chi^{2}_{\mathrm{red}}$ | $N_{\mathrm{bands}}$
---|---|---|---|---|---|---|---|---
2.5 | 16 | 50 | 84 | 97.5 | 2.5 | 16 | 50 | 84 | 97.5
1 | 10 | 0.5084 | 0.0013 | 0 | 9.92 | 10.03 | 10.15 | 10.26 | 10.40 | 0.01 | 0.73 | 1.16 | 1.58 | 1.90 | 0.011 | 5
1 | 13 | 0.5309 | 0.0011 | 0 | 9.80 | 9.94 | 10.02 | 10.13 | 10.21 | -0.60 | 0.26 | 0.92 | 1.28 | 1.74 | 0.055 | 7
1 | 15 | 0.6699 | 0.0011 | 0 | 9.86 | 9.96 | 10.04 | 10.13 | 10.22 | 0.68 | 0.95 | 1.32 | 1.73 | 2.08 | 0.464 | 7
1 | 28 | 1.3443 | 0.0028 | 0 | 9.41 | 9.50 | 9.61 | 9.68 | 9.80 | 1.07 | 1.16 | 1.32 | 1.48 | 1.58 | 0.297 | 7
1 | 41 | 1.3065 | 0.0018 | 0 | 9.67 | 9.81 | 9.89 | 10.00 | 10.13 | 0.91 | 1.21 | 1.53 | 1.77 | 1.94 | 0.326 | 7
…

Notes. A full ASCII version of this table is available online. Percentiles
provided are 2.5%, 16%, 50%, 84%, and 97.5%. SFR(SED) corresponds to the
average SFR over the last 100 Myr of the SFH.
$\chi_{\mathrm{red}}^{2}=\chi^{2}/N_{\mathrm{bands}}$ is the reduced
$\chi^{2}$ of the best-fit model and $N_{\mathrm{bands}}$ is the number of
bands observed with non-zero flux.
aAGN_flag=1 indicates sources that lie in the AGN region of the Mass-
Excitation diagram (Section 7.4.1).

For each MAGPHYS fit, a goodness-of-fit is determined based on the best-fit
model using a reduced $\chi^{2}$ metric,
$\chi_{\mathrm{red}}^{2}=\chi^{2}/N_{\mathrm{bands}}$, where
$N_{\mathrm{bands}}$ is the number of bands observed with non-zero flux. We
exclude cases of poor-quality fits by removing galaxies with
$\chi_{\mathrm{red}}^{2}>3$ from our analysis (criteria 5), which removes 140
of the criteria (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 $\sigma(\log M_{\star})>0.3$ dex (based on the 16th and 84th percentiles
of the posterior PDF; $\sigma(\log M_{\star})$=($\log
M_{\star\mathrm{,p84}}-\log M_{\star\mathrm{,p16}})/2$; criteria 6). This
occurs for 13 of the criteria (1)-(4) sources. The median values of the
remaining WISP sample is $\bar{\chi}_{\mathrm{red}}^{2}=0.32$. The low
$\chi^{2}$ values are due to the fact that the models tend to ‘over-fit’ the
data (more free parameters than datapoints).

Table 11 provides the $\log M_{\star}$ and $\log\mathrm{SFR(SED)}$ percentiles
from MAGPHYS for our sample of 1937 galaxies that satisfy criteria (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 $\log M_{\star}$ and
$\log\mathrm{SFR(SED)}$ (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 parametrisation 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 $\log M_{\star}$ and $\log\mathrm{SFR(SED)}$
are larger by 0.03 and 0.04 dex, respectively. SED-derived SFRs have very
large uncertainty when relying only on UV through near-IR data. For this
reason, we avoid using SED-derived SFRs for our analysis and instead use
$\mathrm{H}\alpha$-based estimates whenever possible. We note that the median
number of bands available for the subsample is 5, with 85% of the sample
having coverage in IRAC (i.e., detection or an upper limit). The median
uncertainty on $\log M_{\star}$ 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 $\log M_{\star}(\mathrm{w/~{}IRAC})-\log
M_{\star}(\mathrm{no~{}IRAC})=0.045$ 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 Henry et al. (2021); Dai et al. (2021); Battisti et al. (2022).
In brief, we use the continuum-subtracted spectra (using a cubic spline; see
Section 5.3) and normalise them by the ‘typical’ brightest line in the
spectral window considered, which for the windows we consider is either
$\mathrm{H}\alpha$+[NII] (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 normalised
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 ionising sources (e.g., HII vs 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 1-4x 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\lambda$3727, 3729, $\mathrm{H}\alpha$+[NII]$\lambda\lambda$6548,
6583, and [SII]$\lambda\lambda$6716, 6731, (3) we require the narrow component
FWHM of close pairs to match (e.g., $\mathrm{H}\beta$ and [OIII],
$\mathrm{H}\alpha$+[NII], 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 2 with each other, (5) we allow a
$\pm 10\text{\AA}$ 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.,
$4400\text{\AA}<\lambda_{\mathrm{rest}}<5500\text{\AA}$ for $\mathrm{H}\beta$
and [OIII]; $6000\text{\AA}<\lambda_{\mathrm{rest}}<7100\text{\AA}$ for
$\mathrm{H}\alpha$+[NII] and [SII]).

Line flux measurements for the stacks are based on scaling the average flux of
the normalised line in each bin (i.e., reversing the normalisation). 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 realisations 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 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 $\mathrm{H}\beta$ and [OIII] Window ($0.74<z<2.31$)

We start with galaxies with both $\mathrm{H}\beta$ and [OIII] grism coverage
($0.74<z_{\mathrm{grism}}<2.31$) because it is one of the largest groups we
consider ($N$=1040 with criteria 1-8) and the ratio [OIII]/$\mathrm{H}\beta$
as a function of stellar mass, known as a the Mass-Excitation (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,
requring a 0.5 dex and 0.75 dex shift at $z\sim 1.6$ and $z\sim 2.3$,
respectively. We use the demarcation from Kashino et al. (2019) as our
reference because we are examining similar redshifts ($z\sim 1.0$ and $z\sim
1.6$). The position on the MEx diagram of individual galaxies in our subsample
is shown in Figure 16, bottom. We find that 10.4% of the WISP sources in this
subsample are detected in both $\mathrm{H}\beta$ and [OIII] ($S/N>3$), 61.1%
detected only in [OIII], and the rest are undetected in both lines ($S/N<3$;
28.5%). For $\mathrm{H}\beta$ undetected cases, we use the 3$\sigma$
$\mathrm{H}\beta$ 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 sub-divide galaxies in this window into two redshift ranges, $0.74<z<1.22$
and $1.22\leq z<2.31$ (z=1.22 is the median for this window), and each of
those into 5 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
Figure 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% of individual sources that are unconstrained in the
MEx diagram (i.e., those with $S/N<3$ for both [OIII] and $\mathrm{H}\beta$),
together with the fact that higher stellar mass galaxies have preferentially
weaker [OIII] and $\mathrm{H}\beta$ relative to $\mathrm{H}\alpha$ than lower
stellar mass galaxies (e.g., Figure 5 of Battisti et al., 2022). As a
reference, the lowest stellar mass bins for each redshift range have $\sim$90%
of individual sources detected in [OIII] or $\mathrm{H}\beta$, whereas the
highest stellar mass bins have 30-40% of individual sources detected in [OIII]
or $\mathrm{H}\beta$ (for these cases, usually $\mathrm{H}\alpha$ and [SII]
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.

Table 12: Average properties, emission line luminosities, and line ratios for
$N$=1040 stacked spectra in the $\mathrm{H}\beta$ and [OIII] window
($0.74<z<2.31$) that satisfy criteria (1)-(8)

$N$ | $\log M_{\star}$ | $\left\langle\log M_{\star}\right\rangle$ | $\mathrm{H}\beta$ | [OIII] | $\dfrac{\mathrm{[OIII]}}{\mathrm{H}\beta}$
---|---|---|---|---|---
range | ($10^{41}$ erg s-1)
$0.74<z_{\mathrm{grism}}<1.22$ ($z\sim 1.0$)
104 | [ 7.59, 8.82] | 8.50 | 1.09$\pm$0.06 | 7.27$\pm$0.11 | 6.69$\pm$0.37
104 | [ 8.83, 9.27] | 9.09 | 1.24$\pm$0.06 | 7.24$\pm$0.11 | 5.82$\pm$0.31
104 | [ 9.29, 9.71] | 9.46 | 1.09$\pm$0.06 | 5.01$\pm$0.09 | 4.60$\pm$0.28
104 | [ 9.72,10.12] | 9.93 | 1.42$\pm$0.09 | 4.74$\pm$0.11 | 3.34$\pm$0.23
104 | [10.12,11.60] | 10.45 | 1.17$\pm$0.11 | 2.92$\pm$0.15 | 2.49$\pm$0.27
$1.22\leq z_{\mathrm{grism}}<2.31$ ($z\sim 1.6$)
104 | [ 7.77, 8.85] | 8.58 | 2.11$\pm$0.10 | 20.56$\pm$0.25 | 9.72$\pm$0.49
104 | [ 8.86, 9.19] | 9.03 | 3.60$\pm$0.15 | 23.11$\pm$0.18 | 6.42$\pm$0.27
104 | [ 9.19, 9.47] | 9.31 | 4.70$\pm$0.16 | 24.50$\pm$0.18 | 5.22$\pm$0.19
104 | [ 9.47, 9.89] | 9.67 | 3.82$\pm$0.25 | 20.00$\pm$0.31 | 5.24$\pm$0.35
104 | [ 9.89,11.26] | 10.18 | 2.60$\pm$0.29 | 10.89$\pm$0.30 | 4.18$\pm$0.48

Notes. $\mathrm{H}\beta$ is not corrected for stellar absorption. [OIII] is
the sum of [OIII]$\lambda\lambda$4959, 5007.

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 KMOS3D. They found that galaxies with
$\log(M_{\star}/M_{\odot})<10.2$ have an AGN occurrence rate of
$f_{AGN}\lesssim 10$%, with $f_{AGN}$ increasing dramatically with increasing
mass (e.g., $\sim$60% at $\log(M_{\star}/M_{\odot})=11$; see their Figure 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
$\log(M_{\star}/M_{\odot})\gtrsim 10.2$.

$\begin{array}[]{c}\includegraphics[width=0.95]{Figures/WISP_{M}Ex_{c}ompare_{p}anel1-crop.png\vspace{1mm}}\\\
\includegraphics[width=0.7]{Figures/WISP_{M}Ex.png}\\\ \end{array}$

Figure 16: Top: Stacked spectra in the $\mathrm{H}\beta$ and [OIII] window
normalised to [OIII] total flux in bins of stellar mass for our subsample at
$0.74<z<2.31$ ($N$=1040 with criteria 1-8). The median $\log M_{\star}$ is
indicated in each panel. The spectral fits are shown by the orange lines.
Bottom: Mass-Excitation (MEx) diagram for our sample. The solid (dashed) red
lines corresponds 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 $z\sim 1.6$ by Kashino et al. (2019), and up by 0.13 dex to
account for using total [OIII] instead of only [OIII]$\lambda$5007\. Small
black and gray points denote individual galaxies where MEx positions are
constrained (71.5% of sample), with median errorbars given on the middle-left,
and AGN candidates are indicated by purple squares. $\mathrm{H}\beta$
undetected cases are treated as lower-limits (see Section 7.4.1). The large
circles/triangles (colour based on median $\log M_{\star}$), correspond to the
observed values from the stacked spectra shown at the top (i.e,
$\mathrm{H}\beta$ is not corrected for stellar absorption). Stack x-axis
errorbars denote the 1$\sigma$ mass range spanned by each bin (Table 12 lists
full mass range). The y-axis errorbars 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% of our individual sources being unconstrained
($S/N<3$ in both [OIII] and $\mathrm{H}\beta$), with larger $\log M_{\star}$
galaxies preferentially lacking detection in these lines (see Section 7.4.1).

####  7.4.2 $\mathrm{H}\alpha$+[NII] and [SII] Window ($0.30<z<1.45$)

Next, we consider galaxies with grism coverage of $\mathrm{H}\alpha$+[NII] and
[SII] ($0.30<z_{\mathrm{grism}}<1.45$; $N$=1191 with criteria 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 characterise
WISP galaxies relative to the star-forming galaxy Main Sequence (MS; logSFR
vs. log$M_{\star}$; e.g., Brinchmann et al., 2004; Speagle et al., 2014;
Leslie et al., 2020), using SFRs based on $\mathrm{H}\alpha$ (described
below).

We divide galaxies in this window into three redshift ranges, $0.30<z\leq
0.83$, $0.83<z\leq 1.15$ and $1.15\leq z<1.45$ (equal-number in each), and
each of those into 4 equal-number bins in stellar mass (12 bins total). The
spectra of these stellar mass stacks are shown in Figure 17. The average
galaxy properties and emission line values for these stacks are listed in
Table 13.

Table 13: Average properties, emission line luminosities, and line ratios for
$N$=1191 stacked spectra in the $\mathrm{H}\alpha$+[NII] and [SII] window
($0.30<z<1.45$) that satisfy criteria (1)-(8)

$N$ | $\log M_{\star}$ | $\left\langle\log M_{\star}\right\rangle$ | $\left\langle\log\mathrm{SFR}\right\rangle$ |  $\mathrm{H}\alpha$+[NII] | [SII] |  $\mathrm{H}\alpha$obs |  $\mathrm{H}\alpha$corr
---|---|---|---|---|---|---|---
range | $\mathrm{H}\alpha_{\mathrm{obs}}$ | $\mathrm{H}\alpha_{\mathrm{corr}}$ | ($10^{41}$ erg s-1)
$0.30<z_{\mathrm{grism}}\leq 0.83$ ($z\sim 0.6$)
100 | [ 7.25, 9.01] | 8.66 | -0.04$\pm$0.01 | 0.13$\pm$0.14 | 1.81$\pm$0.02 | 0.35$\pm$0.02 | 1.68$\pm$0.04 | 2.49$\pm$ 0.82
99 | [ 9.01, 9.44] | 9.20 | 0.11$\pm$0.01 | 0.36$\pm$0.14 | 2.73$\pm$0.03 | 0.79$\pm$0.02 | 2.40$\pm$0.06 | 4.29$\pm$ 1.41
99 | [ 9.45, 9.84] | 9.63 | 0.25$\pm$0.02 | 0.59$\pm$0.14 | 4.23$\pm$0.05 | 1.13$\pm$0.03 | 3.34$\pm$0.13 | 7.25$\pm$ 2.39
99 | [ 9.84,10.92] | 10.19 | 0.29$\pm$0.02 | 0.75$\pm$0.14 | 5.28$\pm$0.06 | 1.28$\pm$0.04 | 3.59$\pm$0.16 | 10.58$\pm$ 3.49
$0.83<z_{\mathrm{grism}}\leq 1.15$ ($z\sim 1.0$)
100 | [ 7.59, 8.93] | 8.62 | 0.35$\pm$0.01 | 0.51$\pm$0.14 | 4.41$\pm$0.04 | 0.43$\pm$0.03 | 4.13$\pm$0.08 | 6.03$\pm$ 1.98
99 | [ 8.94, 9.44] | 9.17 | 0.46$\pm$0.01 | 0.71$\pm$0.14 | 6.01$\pm$0.06 | 1.16$\pm$0.05 | 5.38$\pm$0.11 | 9.51$\pm$ 3.12
99 | [ 9.45,10.04] | 9.76 | 0.61$\pm$0.03 | 0.98$\pm$0.14 | 9.60$\pm$0.08 | 2.08$\pm$0.06 | 7.65$\pm$0.48 | 17.73$\pm$ 5.90
99 | [10.04,11.34] | 10.37 | 0.72$\pm$0.02 | 1.24$\pm$0.14 | 15.04$\pm$0.14 | 3.31$\pm$0.09 | 9.84$\pm$0.47 | 32.40$\pm$10.71
$1.15\leq z_{\mathrm{grism}}<1.45$ ($z\sim 1.3$)
100 | [ 7.54, 9.02] | 8.63 | 0.54$\pm$0.01 | 0.70$\pm$0.14 | 6.83$\pm$0.07 | 0.84$\pm$0.07 | 6.42$\pm$0.12 | 9.41$\pm$ 3.08
99 | [ 9.04, 9.50] | 9.30 | 0.70$\pm$0.01 | 0.97$\pm$0.14 | 10.49$\pm$0.10 | 1.80$\pm$0.09 | 9.36$\pm$0.17 | 17.47$\pm$ 5.72
99 | [ 9.50, 9.96] | 9.74 | 0.77$\pm$0.02 | 1.13$\pm$0.14 | 13.35$\pm$0.14 | 2.65$\pm$0.11 | 11.04$\pm$0.39 | 25.33$\pm$ 8.33
99 | [ 9.97,11.60] | 10.30 | 0.89$\pm$0.04 | 1.38$\pm$0.15 | 21.22$\pm$0.17 | 4.29$\pm$0.12 | 14.29$\pm$1.32 | 45.02$\pm$15.30

Notes. [SII] is the sum of [SII]$\lambda\lambda$6716, 6731.
$\mathrm{H}\alpha$obs are values after correcting for [NII] blending, where
the uncertainty is the $1\sigma$ dispersion in correction values for
individual galaxies and the line measurement uncertainties added in
quadrature. $\mathrm{H}\alpha$corr are values after also correcting for
stellar absorption and dust extinction, with the latter introducing
significant uncertainty (see Section 7.4.2).

In order to estimate SFRs from $\mathrm{H}\alpha$, we need to apply several
corrections. We note that we only apply correction factors on stacked spectra