# FRESCO: The Paschen-$\alpha$ Star Forming Sequence at Cosmic Noon

Chloe Neufeld Astronomy Department, Yale University, 52 Hillhouse Ave, New
Haven, CT 06511, USA  Pieter van Dokkum Astronomy Department, Yale University,
52 Hillhouse Ave, New Haven, CT 06511, USA  Yasmeen Asali Astronomy
Department, Yale University, 52 Hillhouse Ave, New Haven, CT 06511, USA  Alba
Covelo-Paz Department of Astronomy, University of Geneva, Chemin Pegasi 51,
1290 Versoix, Switzerland  Joel Leja Department of Astronomy & Astrophysics,
The Pennsylvania State University, University Park, PA 16802, USA  Institute
for Computational & Data Sciences, The Pennsylvania State University,
University Park, PA 16802, USA  Institute for Gravitation and the Cosmos, The
Pennsylvania State University, University Park, PA 16802, USA  Jamie Lin
Department of Physics and Astronomy, Tufts University, 574 Boston Avenue,
Medford, MA 02155, USA  Jorryt Matthee Institute of Science and Technology
Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria  Pascal A. Oesch
Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix,
Switzerland  Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, København N, DK-2200, Denmark  Naveen A. Reddy
Department of Physics and Astronomy, University of California, Riverside, 900
University Avenue, Riverside, CA 92521, USA  Irene Shivaei Centro de
Astrobiología (CAB), CSIC-INTA, Carretera de Ajalvir km 4, Torrejón de Ardoz,
28850, Madrid, Spain  Katherine E. Whitaker Department of Astronomy,
University of Massachusetts, Amherst, MA 01003, USA  Cosmic Dawn Center
(DAWN), Niels Bohr Institute, University of Copenhagen, Jagtvej 128, København
N, DK-2200, Denmark  Stijn Wuyts Department of Physics, University of Bath,
Claverton Down, Bath, BA2 7AY, UK  Gabriel Brammer Cosmic Dawn Center (DAWN),
Niels Bohr Institute, University of Copenhagen, Jagtvej 128, København N,
DK-2200, Denmark  Danilo Marchesini Department of Physics and Astronomy, Tufts
University, 574 Boston Avenue, Medford, MA 02155, USA  Michael V. Maseda
Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter St.,
Madison, WI 53706 USA  Rohan P. Naidu NHFP Hubble Fellow  MIT Kavli Institute
for Astrophysics and Space Research, 77 Massachusetts Ave., Cambridge, MA
02139, USA  Erica J. Nelson Department for Astrophysical and Planetary
Science, University of Colorado, Boulder, CO 80309, USA  Anna Velichko
Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix,
Switzerland  Institute of Astronomy of V. N. Karazin Kharkiv National
University, Svobody square 4, 61022 Kharkiv, Ukraine  Andrea Weibel Department
of Astronomy, Université de Genève, Chemin Pegasi 51, 1290 Versoix,
Switzerland  Mengyuan Xiao Department of Astronomy, University of Geneva,
Chemin Pegasi 51, 1290 Versoix, Switzerland Chloe Neufeld
<EMAIL_ADDRESS>
###### Abstract

We present results from the JWST First Reionization Epoch Spectroscopically
Complete Observations survey (FRESCO) on the star forming sequence of galaxies
at $1.0<z<1.7$, around the peak of the cosmic star formation history. Star
formation rates (SFRs) are measured from the redshifted, nearly dust-
insensitive Paschen-$\alpha$ emission line, and stellar mass measurements
include the F444W (4.4 $\mu$m; rest-frame H) band. We find SFRs of galaxies
with $M*>9.5M_{\odot}$ that are lower than found in many earlier studies by up
to 0.6 dex, but in good agreement with recent results obtained with the
Prospector fitting framework. The difference
log(SFR(Pa$\alpha$)-SFR(Prospector)) is -0.09 $\pm$ 0.04 dex at
$10^{10-11}M_{\odot}$. We also measure the empirical relation between
Paschen-$\alpha$ luminosity and rest-frame H band magnitude and find that the
scatter is only 0.04 dex lower than that of the SFR-M* relation and is much
lower than the systematic differences among relations in the literature due to
various methods of converting observed measurements to physical properties. We
additionally identify examples of sources – that, with standard cutoffs via
the UVJ diagram, would be deemed quiescent – with significant, typically
extended, Paschen-$\alpha$ emission. Our results may be indicative of the
potential unification of methods used to derive the star forming sequence with
careful selection of star forming galaxies and independent star formation rate
and stellar mass indicators.

Galaxy evolution (594) — Galaxy properties (615) — Star formation (1569) —
Scaling relations (2031)

##  1 Introduction

The star forming sequence (SFS) of galaxies — the relation between star
formation rate (SFR) and stellar mass (M*) — is a useful probe of galaxy
evolution, with implications for how galaxies build up their mass and
eventually quench (e.g., Noeske et al., 2007; Elbaz et al., 2011; Speagle et
al., 2014; Whitaker et al., 2014; Lee et al., 2015; Renzini & Peng, 2015;
Salmon et al., 2015; Schreiber et al., 2015; Tomczak et al., 2016; Santini et
al., 2017; Leslie et al., 2020; Leja et al., 2022; Mérida et al., 2023;
Popesso et al., 2023). The relation has been measured in both observations and
simulations in a large number of previous studies (see Speagle et al., 2014
and Popesso et al., 2023 for reviews).

Generally, the relation is found to have very low scatter (0.2-0.3 dex in the
$10^{9}M_{\odot}<M*<10^{10}M_{\odot}$ mass regime). This tight relation
indicates that star formation histories (SFHs) are smooth: stellar mass grows
steadily with SFR at a consistent rate across these galaxies (Salmon et al.,
2015). Outside of this regime, at lower masses, higher scatter in the relation
has been observed, indicating that the SFHs for these galaxies are more bursty
and varied (Santini et al., 2017; Boogaard et al., 2018; Atek et al., 2022;
Mérida et al., 2023).

The normalization of the SFS increases with redshift, indicating that gas
accretion occurred at a higher rate earlier in the universe (Tomczak et al.,
2016), and the peak star formation for individual galaxies with high masses is
predicted to occur earlier than that of lower masses (Thomas et al., 2005).
Previous studies find that the sequence can be well fit by a broken power law
with a turnover that evolves with redshift; the slope below this turnover mass
is $\sim 1$, while above it is shallower, with suppressed specific SFR (e.g.,
Whitaker et al., 2014; Schreiber et al., 2015; Tomczak et al., 2016; Leja et
al., 2022). This has several physical implications: Popesso et al. (2023)
suggest that the time-dependence of the turnover mass is due to black hole
feedback and the availability of cold gas in the haloes. Looking at the bulge-
to-total mass ratios, Cooke et al. (2023) find evidence that the presence of
this turnover mass is due to the evolution of the specific star formation rate
of the disk rather than bulge growth (see also Abramson et al., 2014; Whitaker
et al., 2015).

Key questions surrounding the relation remain. While there is general
agreement in a large number of studies about the scatter and the existence of
this tight relation, there are conflicting results about the exact
quantification of the normalization and slope of the SFS among observational
studies. Speagle et al. (2014) find that these conflicts can mostly be
ascribed to different methods used to infer the relation (i.e., inferring SFRs
and stellar masses), including selection effects, assumed IMFs, dust
extinction, and SED fitting methods, and those issues have not been fully
resolved in the years since. The normalization of the SFS determined from
galaxy formation simulations is also 0.2-0.5 dex lower than that found in
observational studies (Somerville & Davé, 2015; Tomczak et al., 2016; Popesso
et al., 2023). This was only recently mitigated with the use of updated masses
and SFRs from the Prospector Bayesian inference fitting framework and
spatially resolved star formation measurements (Leja et al., 2019; Nelson et
al., 2021; Leja et al., 2022). These differences lead to the question of what
the “true” relation is, and which method best recovers it.

Many studies use the observed bimodality between the rest-frame colors of
galaxies to select for star-forming galaxies, but this is highly dependent on
the methodology of color measurements due to spatially varying stellar
populations (Kriek et al., 2010; Whitaker et al., 2012; Belli et al., 2015). A
related method is to fit spectral energy distribution (SED) models and use a
threshold on the specific SFRs (sSFRs) to select quiescent galaxies (Merlin et
al., 2018), but lower sSFRs have associated uncertainties due to lower
intrinsic brightness and can be contaminated by emission from AGN or dust
heating by older stellar populations. Moreover, Eales et al. (2017) and
Feldmann (2017) argue that the distribution of galaxies is actually unimodal,
with no observable separation between star-forming and quenched galaxies.
Ambiguity between star-forming and quenched galaxies can lead to artificially
flattening the slope of the SFS at high masses (Renzini & Peng, 2015; Shivaei
et al., 2015), and Leja et al. (2022) measure differences of up to 0.5 dex in
the normalization of the SFS when using several standard pre-selection
methods.

Methods for inferring star formation rates and stellar masses can also affect
the measured SFS. For example, some studies measure the SFR using the UV
stellar continuum, which is ideal for high redshift observations where the
rest-UV emission is redshifted into optical wavelengths. This provides a
measure of the emission coming from massive young stars, which thus traces
recent star formation (Kennicutt & Evans, 2012). However, this method is
sensitive to interstellar dust attenuation, only probing starlight that is
unabsorbed by dust. A majority of star formation is obscured by dust,
particularly in massive galaxies; attempts to mitigate this are very sensitive
to the assumed attenuation laws (Salim & Narayanan, 2020). Other studies use
IR emission in conjunction with UV emission (e.g., Whitaker et al., 2014; Lee
et al., 2015; Tomczak et al., 2016; Shivaei et al., 2017; Popesso et al.,
2023), thus obtaining a combination of the unabsorbed UV light emitted by
young, massive stars and their re-radiated IR emission from dust. This too can
have associated uncertainties, as IR emission from dust heating can be
contaminated by asymptotic giant branch (AGB) stars in old stellar populations
and active galactic nuclei. Similarly, various studies look to the full
distribution of flux across different wavelengths using SED fitting to infer
SFRs (e.g., Salmon et al., 2015; Santini et al., 2017; Leja et al., 2022).
While this is the most self-consistent approach, it is difficult to assess
uncertainties: mass and SFR will be correlated and thus will lead to an
underestimate of the scatter in the SFR-stellar mass relation.

Another commonly used SFR indicator is nebular emission from hydrogen
recombination: recently formed massive stars ionize their surrounding gas, and
hydrogen recombination cascades produce emission lines (Kennicutt, 1998).
Unlike other indicators such as UV emission, nebular line SFRs are much less
sensitive to the assumed star formation history. In the optical regime,
previous studies have used H$\alpha$ or H$\beta$ (e.g., Whitaker et al., 2014;
Renzini & Peng, 2015; Shivaei et al., 2015). A common practice to correct for
optical dust attenuation is to measure the H$\alpha$/H$\beta$ Balmer
decrement. However, besides being a difficult measurement, as H$\beta$ is at
least $\sim 3$ times fainter than H$\alpha$, this correction misses any
emission that is not present in either line due to being fully obscured or
optically thick in these lines. Other studies have used longer wavelength
hydrogen recombination lines that are less sensitive to dust, such as the
Paschen series (e.g., Rieke et al., 2009; Cleri et al., 2022; Giménez-Arteaga
et al., 2022; Reddy et al., 2023), or the Brackett series (e.g., Pasha et al.,
2020). Using JWST NIRSpec observations, Reddy et al. (2023) find that SFRs
obtained using Paschen-$\alpha$ emission can be larger than those obtained
using Balmer lines by 25%, as expected if some of the star formation is
optically thick.

The SFS is especially important to study at cosmic noon ($z\sim 1-3$), when
the cosmic star formation density was at its peak (Madau & Dickinson, 2014).
While rest-frame NIR hydrogen recombination lines provide obvious benefits
over their optical counterparts for clean SFR determinations, they have until
recently only been accessible from the ground for the nearest galaxies, as
emission beyond $\sim$2.4$\mu$m is inaccessible (e.g., Paschen-$\alpha$
becomes inaccessible at $z>0.280$). With JWST, we can now observe longer
wavelength SFR tracers at cosmic noon. In this work, we use Pa$\alpha$ (1.875
$\mu$m), the n=4$\rightarrow$3 hydrogen recombination line, as a SFR indicator
to probe the relation between SFR and stellar mass in galaxies at redshifts
$z\sim 1.4$. Using JWST NIRCam/grism in the 4.4 $\mu$m band, we are able to
measure SFRs using Pa$\alpha$ emission lines, with stellar masses measured in
the rest-frame NIR, which allows us to measure the SFR-M* relation using a
relatively simple and independently derived method.

We use Pa$\alpha$ emission line data obtained using JWST NIRCam/grism
observations taken as part of the FRESCO survey, as described in Section 2. In
Section 3, we discuss the methods in which we derive physical properties of
galaxies in our sample, including obtaining stellar masses using rest-frame
NIR magnitude and SFR from Pa$\alpha$ emission, and in Section 3.4, we show
the resulting relation between SFR for our sample. We discuss our results in
the context of previous studies in Section 4 and provide a summary in Section
5.

Throughout the paper, we use a Chabrier (2003) IMF for stellar mass and SFR
calculations and give all magnitudes in the AB system (Oke & Gunn, 1983). We
assume a $\Lambda$CDM cosmology with $\Omega_{M}=0.3$, $\Omega_{\lambda}=0.7$,
and a Hubble constant $H_{0}=70$ km s-1 Mpc-1.

##  2 Data

###  2.1 FRESCO Survey

We use F444W NIRCam/grism spectra and imaging data in the GOODS North and
South fields, obtained between November 2022 and February 2023 from the First
Reionization Epoch Spectroscopically Complete Observations survey (FRESCO;
Cycle 1 GO-1895; PI Oesch, Oesch et al., 2023), a JWST cycle 1 53.8 hour
medium program. This survey covers an area of $\sim 60$ arcmin2 in each GOODS
field with two 2x4 NIRCam/grism mosaics. All the JWST data used in this paper
can be found in MAST: http://dx.doi.org/10.17909/gdyc-7g80 (catalog
10.17909/gdyc-7g80).

The FRESCO survey used grismR for a single dispersion direction over the
field, with spectra for most galaxies covering a maximal wavelength range of
3.8 to 5.0 $\mu$m. The spectroscopic exposure time per pointing was 7 ks,
allowing for a 5$\sigma$ line sensitivity of $2\times 10^{-18}$ erg s-1 cm-2
at a resolution of $R\sim 1600$ for compact sources, translating to
Paschen-$\alpha$ luminosities of $L_{\text{PaA}}=10^{40.57}$ erg s-1 at
redshift $z\sim 1.7$. Grism observations provide a complete sample of all
emission line sources in the field and reliable spectroscopic redshifts, as
well as emission line maps that can be useful for determining where exactly
emission is coming from in a galaxy. The wavelength coverage enables line
measurements and resolved maps of Pa$\alpha$ at $z\sim$ 1.4. In addition to
the F444W filter, the FRESCO survey includes medium band images using the
F182M and F210M filters. The exposure time per pointing for direct imaging was
0.9 ks, and the three filters (F182M, F210M, and F444W) have 5$\sigma$ depths
(measured in 0.32” diameter circular apertures) of 28.4, 28.2, and 28.2 mag,
respectively, as shown in Oesch et al. (2023).

The NIRCam slitless grism data were reduced using the grizli
software111https://github.com/gbrammer/grizli(Brammer, 2018) on the publicly
available NIRCam grism configuration
files222https://s3.amazonaws.com/grizli-v2/JwstMosaics/v7/index.html. A
detailed description of the data reduction process and the derivation of
photometric catalogs will be provided in Brammer et al. (in prep). To
summarize, raw files are obtained from the MAST archive, aligned to a Gaia-
matched reference frame, and each exposure is aligned to the direct images for
a given visit. Following Kashino et al. (2023), we obtain continuum-subtracted
spectra by using a running median filter along each row with a 12 pixel
central gap to subtract continuum emission and minimize self-subtraction.
Detection images for each field were obtained using a stack of F210M and F444W
FRESCO imaging. The GOODS fields have also been observed in several other
surveys, including 3D-HST333https://archive.stsci.edu/prepds/3d-hst/ (Brammer
et al., 2012; Skelton et al., 2014; Momcheva et al., 2016), a near-infrared
spectroscopic survey using the Hubble Space Telescope. Multi-wavelength
photometric catalogs were derived by running SExtractor (Bertin & Arnouts,
1996a) on HST and JWST images, ranging from $\sim$0.4-5.0 $\mu$m, PSF-matched
to the F444W filter. Fluxes were measured in circular apertures of radii
0.08”, 0.16”, 0.25” and 0.35” and corrected to total flux based on the
fraction of encircled flux in each circular aperture on the F444W PSF. All
fluxes were also corrected for Milky Way foreground extinction using the
extinction model from Fitzpatrick & Massa (2007).

###  2.2 Sample Selection

Sources with Paschen-$\alpha$ S/N $>$ 3 are selected from the grizli extracted
catalog. Subsequently, two individuals visually inspect each source using
SpecVizitor software444https://github.com/ivkram/specvizitor and categorize
them based on the quality of the line fit and redshift probability
distribution into five categories: 1) contaminated by bright sources in the
field, 2) absence of detectable lines, 3) uncertain about the line fit
quality, 4) robust fit with a single line and consistent morphological shape
between the line and imaging (F444W), and 5) robust fit with multiple lines.
The individual inspection catalogs are then merged to create the final
catalog. Sources flagged as robust (quality flags 4 and 5) by both or only one
of the inspectors are categorized as robust and semi-robust, respectively.
Where needed, we computed a weighting based on the flag distribution of each
inspector and down-weighted those flagged by the more lenient inspector. In
this study we adopt sources flagged as robust ($\sim$30% of the original
sample) and semi-robust ($\sim$40% of the original sample) in the final
catalog, as well as further cuts of Paschen-$\alpha$ SNR $>$ 5 and
$z_{\rm{width}}<$0.005555$z_{\rm{fit}}(z_{\rm{width}})=z_{\rm{fit}}(z_{975})-z_{\rm{fit}}(z_{025})/(1+z_{\rm{fit}}(z_{50}))/2$,
resulting in a sample of 609 galaxies with a redshift distribution shown in
Figure 1.

We use EA$z$Y (Brammer et al., 2008) SED fitting to estimate physical
properties in the following section, such as rest-frame colors and stellar
masses, from the flux corrected 0.7” diameter aperture photometry, with
redshifts set to those inferred from the grism spectrum of each galaxy. We
adopt a 14 template set666https://github.com/gbrammer/eazy-
photoz/tree/master/templates/sfhz with redshift-dependent SFHs that can be fit
as nonnegative linear combinations to allow for flexibility (see, e.g.,
Kokorev et al., 2022; Gould et al., 2023).

In Appendix A we compare our default EA$z$Y masses to those of other codes, in
particular Bagpipes (Carnall et al., 2018) and Prospector (Johnson et al.,
2021). We use EA$z$Y as the default for several reasons. With F444W (rest-
frame NIR) photometric measurements we should constrain the dominant mass
component of these galaxies, making a simple model favorable. EA$z$Y is one of
the simplest SED fitting methods available, and our results are thus easily
reproducible. Several previous studies also use similar EA$z$Y template sets
to obtain stellar masses (see, e.g., Sherman et al. (2020) for a discussion on
the reliability of EA$z$Y for obtaining stellar mass estimates).

Figure 1: Distribution of spectroscopic redshifts for our Paschen-$\alpha$
sample, which probes $1.0<z<1.7$, with a majority of sources around $z\sim
1.2-1.4$.

##  3 Deriving the Star Forming Sequence

The FRESCO survey is well-suited for observing the SFS at cosmic noon. At
redshifts of $z\sim 1-2$, the 4.4 micron band targets the rest-frame near
infrared (NIR) emission of galaxies. This filter is thus especially suited for
tracing the dominant stellar mass component - low-mass stars, which typically
make up most of the total luminosity in the NIR (e.g., Wen et al., 2013;
Nagaraj et al., 2021). Additionally, Paschen-$\alpha$ ($\lambda=1.8751\mu$m)
falls in the rest-frame NIR, so we can observe this dust-insensitive SFR
tracer as well. We are then able to independently observe the relation between
SFR (derived from Pa$\alpha$) and $M^{*}$ (derived using SED fitting that
incorporates the rest-frame NIR) at cosmic noon.

###  3.1 Rest-frame Colors

We differentiate between quenched and star forming galaxies in our sample
using the rest-frame U-V and V-J colors via the UVJ diagnostic, which is a
standard method of separating star forming and quenched systems into distinct
regions while breaking the degeneracy between quiescence and dust content
(e.g., Labbé et al., 2005; Wuyts et al., 2007; Williams et al., 2009; Bundy et
al., 2010; Cardamone et al., 2010; Whitaker et al., 2011; Brammer et al.,
2011; Patel et al., 2012). The EA$z$Y SED fits include interpolated rest-frame
fluxes in the U, V, and J bands, from which we derive rest-frame U-V and V-J
colors. We use the selection criteria for quiescent galaxies in the redshift
range for our sample ($z\sim 1-2$) as described in Muzzin et al. (2013) and
Mowla et al. (2019):

$U-V>1.3$
---
$V-J<1.5$
$U-V>0.88(V-J)+0.59$
(1)

From this, we determine which galaxies are classically defined as “quenched”
or “star forming,” with the two regimes and the boundaries separating them
shown in Figure 2. 13 galaxies - $\sim 2$% of our sample - would be classified
as quenched via the UVJ diagram despite being selected for having
Paschen-$\alpha$ emission lines and thus active star formation. We discuss the
caveats of using this method to select star-forming galaxies in the context of
spatially resolved emission line maps in Section 4.3.

We also use our spectral data and the SED fits to measure fluxes in the rest-
frame H band ($1.6\mu$m); this NIR band is directly observed for our sample of
$z=1-1.7$ galaxies.

Figure 2: SED fitting derived rest-frame U-V vs. V-J colors (the UVJ diagram)
for the 609 galaxies in our Paschen-$\alpha$ selected sample. We use the Mowla
et al. (2019) criteria to separate quenched (red) vs. star forming (blue)
galaxies. Note that there is a population of quenched galaxies in this
emission-line-selected sample.

###  3.2 EAzY Rest-frame NIR Magnitudes and Stellar Masses

As noted aboved, including rest-frame NIR bands in SED fitting should lead to
more reliable masses, as we incorporate the dominant stellar component in SED
fitting rather than relying on extrapolations using other bands. Previous
studies have observed a correlation between absolute magnitude in NIR bands
and stellar mass at $z=0$ (e.g., Wen et al., 2013; Nagaraj et al., 2021), and
here we can explore this relation at $z\sim 1.4$.

We show the tight correlation between stellar mass and rest-frame H band
magnitude in Figure 3, as well as the best fit linear relation between the two
properties. We note that the stellar masses are derived from SED fitting using
photometric data across a wide range of wavelengths ($0.4-5.0\mu$m) and thus
are not determined solely by the rest-frame H band. The equation that directly
gives stellar mass from rest-frame H band magnitude, with parameters obtained
using bootstrapping and 3$\sigma$ outlier removal, is

$\log(M^{*})[M_{\odot}]=(-0.461\pm 0.004)H_{\text{mag}}-(0.32\pm 0.09),$ (2)

where ${H}_{\mathrm{mag}}$ is the absolute magnitude at rest-frame 1.6 micron.
There is little scatter in the rest-frame H-band M/L ratio at fixed mass, with
a biweight scatter around the best-fit of 0.17 dex. A slope of -0.4 would
imply a constant rest-frame H band mass-to-light ratio (M/L), but we find a
slightly steeper slope, indicating that the M/L in the H-band is a function of
mass and that not all of the galaxies in our Paschen-$\alpha$ sample have
identical mass-to-light ratios in the rest-frame H band.

Figure 3: Rest-frame H band magnitude vs. log stellar mass as inferred from
EA$z$Y SED fitting using photometric data across a wide range of wavelengths
($0.4-5.0\mu$m), along with 1$\sigma$ errorbars on both variables for the best
fit model. The best fit linear relation (using bootstrapping and 3$\sigma$
outlier removal) is shown in black, with a slope of $\sim$0.46, implying a
rest-frame H-band mass-to-light ratio that is not constant with mass.

###  3.3 Paschen-$\alpha$ Star Formation Rates

We use a relatively simple model for calculating SFR (see also, e.g., Papovich
et al., 2009 and Cleri et al., 2022 for similar Paschen line conversions) and
discuss further complexities that may be introduced in the SFR conversion in
Section 3.5. We derive P$\alpha$ SFRs using the procedure outlined in
Kennicutt & Evans (2012) for H$\alpha$, adopting the atomic ratio between
H$\alpha$ and Pa$\alpha$ to be 8.575 assuming Case B recombination and
T=$10^{4}$K (Osterbrock, 1989). We assume a Chabrier IMF and use the SFRHα
calibration derived by Murphy et al. (2011) and Hao et al. (2011); we note
that the Kroupa (2001) and Chabrier (2003) IMFs are functionally equivalent
(Chomiuk & Povich, 2011; Speagle et al., 2014). With our Pa $\alpha$ emission
line measurements, we use the following conversion of L(Pa$\alpha$) to
SFR${}_{\text{Pa}\alpha}$:

$\text{SFR}_{\text{Pa}\alpha,\mathrm{corr}}[M_{\odot}/\text{yr}]=4.6\times
10^{-41}\times L_{\text{Pa}\alpha,\mathrm{corr}}[\text{ergs^{-1}}]$ (3)

where $L_{\text{Pa}\alpha,\mathrm{corr}}$ is the dust-corrected Pa$\alpha$
luminosity, which we derive by applying a dust extinction correction to the
measured emission line fluxes from FRESCO spectroscopic data and the
luminosity distance using the grism redshifts for the default cosmology. The
extinction in the V-band, A(V), is derived using EA$z$Y SED fitting, which we
convert to an extinction correction for Pa$\alpha$ using a Calzetti
attenuation law (Calzetti et al., 2000). We also calculate the corresponding
extinction specifically around star forming regions, AHII(V), found by Price
et al. (2014) to be AHII(V)=1.86A(V). We find that A(Pa$\alpha$) increases
with galaxy mass, with a majority of A(Pa$\alpha$) values for sources in our
sample falling below 0.2 mag, which corresponds to a relatively small
extinction correction of $10^{0.4A(\text{Pa}\alpha)}\approx 1.2$ that is
applied to L(Pa$\alpha$). In comparison, using the same conversions for
H$\alpha$ emission, A(H$\alpha$) would be about fives time greater than
A(Pa$\alpha$), leading to significantly larger extinction corrections than
those needed for Paschen-$\alpha$ emission.

The empirical relation between rest-frame H band magnitude (tracing stellar
mass) and uncorrected Paschen-$\alpha$ luminosity (tracing SFR) is shown in
Figure 4. Binned median luminosities, obtained via bootstrapping in each bin,
are shown, and the biweight scatter in the relation is $\sim$0.25 dex. The
completeness limits shown in this figure correspond to the detection limits
for compact sources described in Section 2.

Figure 4: The directly observed relation between rest-frame H band absolute
magnitude and Paschen-$\alpha$ luminosity, uncorrected for dust effects.
Square points are median luminosities in H magnitude bins of width $\sim$1
mag, with with uncertainties estimated via bootstrap sampling in each bin. The
biweight scatter of the relation is small at 0.25 dex. The horizontal dashed
line corresponds to the Pa$\alpha$ flux detection limits for compact galaxies
in our sample, below which we are not complete in luminosity, nor are we
complete for larger galaxies.

###  3.4 The Star Forming Sequence

We show the dust-corrected SFR (obtained from Pa$\alpha$ emission in Section
3.3) against the stellar mass (derived from EA$z$Y SED fitting that
incorporates the rest-frame NIR bands as described in Section 3.2), for our
sample of galaxies in Figure 5, where the horizontal dashed line indicates the
SFR completeness limit. We calculate this from the flux detection limit for
compact sources of $2\times 10^{-18}$ erg s-1, corresponding to a
Paschen-$\alpha$ luminosity limit of $\sim 10^{40.57}$ erg s-1 at the highest
redshift probed in our sample ($z=1.68$). We then convert this luminosity
limit to a SFR limit based on the conversion in Equation 3, noting that this
is applicable for compact sources and thus we are not complete below this line
nor are we complete for more extended sources.

Quantifying a best fit line is nontrivial with scatter and uncertainties in
both directions in the SFR-M* plane (Hogg et al., 2010). While many studies
fit the relation with a broken power law, with a flattened linear relation at
higher masses (e.g., Whitaker et al., 2014; Lee et al., 2015; Leja et al.,
2022), we do not have enough data at the high mass end to motivate fitting a
broken power law. We instead focus on analyzing the general trends we see here
for the SFR-M* relation for galaxies in our sample. We calculate binned median
values for mass bins of 0.4 dex width and present them in Figure 6, with
uncertainties in the SFR medians for each mass bin obtained from bootstrap
resampling.

While we include all galaxies in our binned median SFRs, we color data points
by whether a galaxy is considered star forming (blue) or quenched (red), as
determined in Section 3.1 by position in UVJ space. It is interesting to note
that several quenched galaxies have significant residual Paschen-$\alpha$
emission but were identified as quenched with the UVJ diagram. With slitless
grism spectra, we have access to spatially resolved Paschen-$\alpha$ emission
line maps, from which we can see where star formation, unobscured by dust, is
occurring in these galaxies. In Figure 5, we display several examples of these
line maps in different regions throughout our SFR-M* distribution. One can see
where star-forming clumps — where Paschen-$\alpha$ emission is concentrated —
are present, and where our 0.7” circular photometric apertures are placed in
relation. We return to this intriguing subsample of galaxies in Section 4.3.

Figure 5: SFR, derived from Pa$\alpha$ emission line measurements, plotted
against stellar mass, derived from EA$z$Y SED fitting. Galaxies in our sample
are shown as either star forming (blue points) or quenched (red points),
defined using the UVJ diagram in Figure 2. The SFS scatter is similar to that
found in the empirical relation between L(PaA) and rest-frame NIR magnitude.
The dashed grey horizontal line indicates our completeness limit for compact
sources, below which we cannot make any definitive statements on the SFR
distributions. Spatially resolved Paschen-$\alpha$ emission line maps are
shown for a selection of galaxies in our sample, with their locations relative
to the distribution of data. For each galaxy, the left panel shows the RGB
image, constructed by combining the F182M, F210M, and F444W bands, and the
right panel shows the Paschen-$\alpha$ emission line map with 1” scaling
shown. The size of the 0.7” circular aperture used for the photometric
measurements are shown in both panels as well. Figure 6: Top: Binned median
points for our SFR-M* data compared to the relations found by Speagle et al.
(2014) (green), Whitaker et al. (2014) (blue), Tomczak et al. (2016) (red),
Leslie et al. (2020) (yellow), Leja et al. (2022) (purple), Mérida et al.
(2023) (magenta), with the horizontal dashed line indicating our SFR
completeness limit and our distribution shown as a kernel density estimation.
Bottom: Differences in SFRs between previous studies and our median values,
with the horizontal dashed line indicating equality. We are offset from many
earlier studies at intermediate masses and are most consistent with results
from Leja et al. (2022) at masses of $\sim 10^{10-11}M_{\odot}$, where the
solid and dashed purple lines indicate the mode (star forming sample only) and
mean (star forming and quenched sample) relations from Leja et al. (2022).

###  3.5 Uncertainties and Caveats

Here we explore caveats and uncertainties that may affect our measurements of
the properties of the observed SFS. Our sample is most likely not complete at
lower masses. We calculate the completeness limit of our sample, from
detection and selection effects, and plot this as the dashed horizontal line
in Figure 4 at $L_{\text{PaA}}=10^{40.57}$ erg s-1. This corresponds to the
5$\sigma$ detection limit ($2\times 10^{-18}$ erg s-1) of the grism spectra at
the highest redshift in our sample ($z=1.68$), below which we are most likely
not complete. We note that this limit applies to compact galaxies, and the
completeness is expected to be a function of size, with the sample likely
being more complete for smaller galaxies and less complete for larger
galaxies. This luminosity limit corresponds to SFR${}_{\text{Pa}\alpha}=1.7$
M⊙ yr-1, which we show as the dashed horizontal line in Figure 5.

There are uncertainties associated with grism spectroscopy, such as
overlapping spectra and spectral extraction uncertainties, which may affect
our measurements for SFR from Pa$\alpha$ emission lines; the uncertainties
associated with Paschen-$\alpha$ flux are incorporated into the errorbars
shown for individual datapoints in Figure 5. There are uncertainties
associated with SED fitting, which may affect our measurements for M*; the 68%
confidence intervals are incorporated into the errorbars on the median stellar
masses.

We also note that, while Paschen-$\alpha$ is relatively dust-insensitive and
the dust corrections that we measure are small, dust attenuation measurements
obtained from SED fitting as well as the attenuation law used are a source of
systematic uncertainty for our sample (Salim & Narayanan, 2020) and most
likely depend on sSFR, stellar mass, and metallicity (e.g., Reddy et al.,
2015; Shivaei et al., 2020). Additionally, the conversion between nebular line
luminosity and SFR depends on the hardness of the ionizing spectrum, which in
turn depends on the assumption of binary stars, stellar rotation, stellar
metallicity, the chosen stellar population model, and the IMF. We assume a
Solar metallicity calibration, which would be different for low metallicity
and mass (see, e.g., Reddy et al., 2023 for a mass- and metallicity-dependent
conversion). Both of the main systematics (assuming binary stars and/or using
lower metallcities) would lower our inferred SFRs further and we thus note
that our SFR measurements are upper bounds. We emphasize that a main point of
this paper is to directly observe the SFS at cosmic noon with the use of a
novel dataset containing direct tracers of SFR (Paschen-$\alpha$ luminosity)
and stellar mass (rest-frame H band magnitudes), and we use this direct
conversion between Paschen-$\alpha$ luminosity and SFR.

Additionally, we do not fit the SFS as a function of redshift. Our redshift
bin is thus larger than most used in previous studies ($z=$1.1-1.7), which can
affect the shape of the relation (e.g., Popesso et al., 2023). However, our
sample has relatively few galaxies at $z>1.4$, and when comparing to previous
studies we use their result at a redshift or range of redshifts similar to the
majority of our sample ($z\sim 1.3$ and $z=1.0-1.5$). Previous studies find
that the normalization of the SFS evolves roughly as $(1+z)^{2.8}$ (Speagle et
al., 2014; Popesso et al., 2023). Performing a differential redshift
correction — shifting the SFR of each source based on this redshift evolution
in normalization — reduces the biweight scatter in our relation by only
$\sim$0.02 dex, and the binned median SFRs shift by at most 0.05 dex.

##  4 Discussion

###  4.1 Scatter

It is interesting to explore the different features in the structure of our
SFR-M* data. In Figure 5, one can see the general trend of how galaxies fall
along and scatter around the SFS when using star formation rates and masses
derived from our rest-frame NIR observations. We also show a comparison to a
line of unity to demonstrate how different parts of the distribution deviate
from a 1-1 relation between log(SFR) and log(M*), though we cannot make
definitive statements about the slope of our relation at the low mass end due
to completeness limits.

The average binned biweight scatter is around 0.29 dex — there is a tight
relation between SFR-M*, indicating that most galaxies have similar star
formation processes. Surprisingly, the scatter is 0.04 dex larger than the
purely empirical relation between Paschen-$\alpha$ luminosity and rest-frame H
band magnitude found in Section 3. The increase in scatter is likely largely
due to the assumptions introduced in the conversions to SFR and stellar mass.
This, in turn, suggests that the freedom in M/L ratios in the model fits to
the data is larger than the variation in the actual universe.

###  4.2 Comparison to Previous Studies

Directly comparing the measured relations between SFR and M* is not trivial -
Speagle et al. (2014) find about 0.25-0.5 dex offset between relations in the
literature due to various reasons (e.g., different SFR indicators and effects
of preselection of star forming galaxies). Here, we attempt to compare our
data with previous studies, specifically focusing on the use of this
independent method of obtaining SFRs and stellar masses.

####  4.2.1 Slope and Scatter

In Figure 6, we show our median datapoints and parametric relations for the
SFS found by other studies; solid points indicate where our sample is
complete. We compare our SFR-M* relation to six other studies, including
Whitaker et al. (2014) and Leja et al. (2022), which use 3D-HST data to
measure SFRs using UV+IR and state-of-the-art SED fitting (Prospector),
respectively. Additional studies shown in this figure use deep-IR observations
to construct the SFR-M* relation (Tomczak et al., 2016), rest-frame UV data
(Mérida et al., 2023), or radio data (Leslie et al., 2020). We also include
the relation found by Speagle et al. (2014), which combines relations by
several studies using mixed methods.

We compare with relations that apply to the average redshift of our sample
(Figure 1), and we correct these relations to a Chabrier IMF to match this
work. We do not include the offset factor of 0.3 dex for the stellar masses
found by Leja et al. (2022) as Popesso et al. (2023) does in their
comparisons, as we find masses consistent with those obtained using the
Prospector framework (see Figure 7 and Appendix A).

We measure a scatter in SFRs at fixed mass of 0.29 dex, which is similar to
that found by previous studies. It is important to keep in mind that
Paschen-$\alpha$ SFRs probe shorter timescales, similarly to H$\alpha$
emission line tracers (Kennicutt & Evans, 2012), as compared to UV+IR SFR
timescales. Paschen-$\alpha$ emission line tracers are also sensitive to the
assumed SFH, dust attenuation curve, and the assumption of the hardness of the
ionizing radiation field when converting nebular line fluxes. The similar
scatter with literature measurements then implies that there is no evidence
for strong stochasticity on $\sim$10 Myr timescales that would be averaged out
when using UV+IR tracers that are sensitive only to $\sim$100 Myr timescales.

Most studies predict a steeper relation at lower masses (e.g., Mérida et al.
(2023) measure the SFS down to $10^{8}M_{\odot}$ at $z=1$, finding a slope of
0.97) and a flattening at high masses (e.g., with the flattening at the high
mass end found by Whitaker et al. (2014) and Leja et al. (2022)). Comparing
the slope, we can see that our relation has a shallower slope at lower masses
and a steeper slope (closer to unity) at higher masses. However, we cannot
completely quantify the slope below SFR${}_{\text{Pa}\alpha}=1.7$ M⊙ yr-1 at
the low mass end because of our detection-limited sample.

On the bottom panel of Figure 6, we show the differences between previous
relations and our median SFR data points at our binned mass values. The black
dashed line is where our data is equal to the compared data. At
$M>9.5M_{\odot}$, we are offset from many earlier studies, with a relation
that is up to 0.6 dex lower. Our results are the least offset with recent
results obtained in the Prospector fitting framework (Leja et al., 2022), with
a mean difference of 0.09$\pm$0.04 dex at $M*\sim 10^{10}-10^{11}M_{\odot}$
when comparing to the mean relation (dashed purple line in Figure 6).

The main point of this paper is not necessarily to more correctly characterize
the SFS, but rather to probe a simpler, more independent method of determining
the general shapes and trends in the relation without relying on the more
complicated methods used in the studies shown here. There is not currently an
observationally motivated way to tell whether or not this simpler method
performs better or worse. We find that our relation is different than the
relation predicted in other studies (lower measured SFRs or higher inferred
masses), but we have agreement with Leja et al. (2022) at the high mass end.
As noted in Section 4.1, the method that produces the lowest scatter would be
to apply direct comparisons to Paschen-$\alpha$ luminosity and rest-frame H
band magnitude.

####  4.2.2 GOODS Fields SFRs and Masses

We can isolate uncertainties associated with stellar mass and SFR measurements
by looking directly at how different methods fare for the same sources in the
GOODS fields. Various studies have constructed the SFS using the GOODS fields,
including Whitaker et al. (2014) and Leja et al. (2022), who measure SFRs from
UV+IR and masses from FAST SED fitting, and SFRs and masses from Prospector
SED fitting, respectively. Because we measure the SFRs and masses for the same
sample of galaxies in the GOODS-N and GOODS-S fields, we can directly compare
our method of using Paschen-$\alpha$ emission as a SFR indicator and SED
fitting incorporating rest-frame NIR bands as a stellar mass indicator. We
show the differences between these measurements (Leja et al., 2022 in purple
and Whitaker et al., 2014 in blue) for cross-matched sources with $\Delta
z<0.05$ in Figure 7, plotted against our measured masses.

The top panel in Figure 7 shows comparisons in SFR measurements. We are
consistent with both Whitaker et al. (2014) and Leja et al. (2022), with mean
differences of around 0.1 dex and a distribution that falls between the two
previous studies. There is a larger deviation in the differences with Leja et
al. (2022) at the low mass end; previous studies have found an increase in
scatter between different SFR indicators for galaxies at the lower end of the
SFR distribution. Cleri et al. (2022) find this when comparing between UV and
Pa$\beta$ measurements at low redshift ($z\leq 0.3$), and Reddy et al. (2023)
find at $z>1$ that this effect also exists when comparing UV SFRs to Paschen
lines.

We compare our EA$z$Y mass measurements, which incorporate rest-frame NIR
photometry, to those obtained using SED fitting with UV-IR photometry from the
3D-HST survey (Brammer et al., 2012; Skelton et al., 2014), for the same
sources in the GOODS fields in middle panel. We find that we are more
consistent with the Prospector framework, with a difference of 0.0-0.2 dex
across the entire mass range and a biweight scatter of $\sim$0.2 dex. We
consistently measure higher masses than those measured using FAST SED fitting
by $\sim$0.2-0.4 dex. This comparison between the masses of individual sources
can explain why our SFR-M* relation has better agreement with Leja et al.
(2022) and is around 0.3 dex lower than the relation found by Whitaker et al.
(2014). Leja et al. (2019) find that the difference between stellar masses
inferred from Prospector and FAST are due to the nonparametric SFHs in the
Prospector-$\alpha$ template, which produces older stellar ages and favors a
smooth SFH. FAST is sensitive to luminosity weighted ages and produces a large
population of $\lesssim$ 1 Gyr old galaxies at this redshift (see Appendix A
for further discussion).

Our inferred stellar masses thus contribute to the offset in the SFS with many
previous studies: when comparing sSFR measurements (bottom panel of Figure 7,
we are most consistent with the Prospector masses, and our offset in sSFR from
Whitaker et al. (2014) stems mostly from the offset in stellar mass. We find
that our SFRs are consistent within the distributions of both Whitaker et al.
(2014) and Leja et al. (2022) despite using a relatively simple conversion
between Paschen-$\alpha$ and SFR.

Figure 7: Comparison of SFRs and stellar masses for the same galaxies, cross-
matched between FRESCO and 3D-HST catalogs with $\Delta z<0.05$, in the GOODS
fields. We plot the difference between our measurements for SFR (top), stellar
mass (middle), and sSFR (bottom) and the measurements from Prospector SED
fitting (Leja et al., 2022) and FAST (Whitaker et al., 2014) in purple and
blue, respectively. We plot the running medians for the distributions in the
differences as solid lines, and dashed horizontal lines indicate equality. We
are consistent in SFR with both previous studies, but our stellar masses from
EA$z$Y are more consistent with those from Prospector, with an offset of
0.1-0.2 dex. Our stellar masses are further offset by $\sim 0.3$ dex from
those obtained with FAST.

###  4.3 UVJ Quenched Galaxies with Paschen-$\alpha$ Emission

We separate the star-forming and quenched galaxies in our sample to explore
the distinguishing properties between the two regimes and the efficacy of the
UVJ diagram. We can see where different populations of galaxies fall along the
general shape of the SFS in Figure 5, and there are interesting implications
when looking at the locations of classically defined quenched galaxies along
the SFS. While we do not have enough data points to fit a broken power law at
the high mass end, we do see that most of the UVJ quenched galaxies, which
tend to drive down the median SFR, fall within the high mass, low sSFR regime.
This may be important to consider when fitting the relation to a selection of
star-forming galaxies, especially if using the UVJ method: when not including
the UVJ quenched galaxies in our star-forming selection, our median SFR values
in the highest mass bins increase by up to 0.05 dex; while not significant for
the case of this relatively small quenched sample, this may be important for
larger surveys and cause an artificially high normalization when using UVJ
selection criteria at these masses. This is especially seen in the comparisons
between the mean and mode relations from Leja et al. (2022) in Figure 6.

As seen in Figure 6, several quenched galaxies also fall near the binned
median SFR values, indicating that these galaxies have a significant amount of
Paschen-$\alpha$ emission. Thus the bimodal classification system may not be
reliable with the use of small, centrally-focused apertures that miss star
formation in the outskirts. Looking at the spatially resolved line maps in
Figure 5 of a subsample of galaxies, we can see that in most of the star-
forming galaxies, star formation is concentrated in the central regions,
whereas for some of the quenched galaxies, star formation is occurring mostly
on the outskirts and is missed with the 0.7” circular apertures used in the
photometric measurements. This could explain why some galaxies with
significant Paschen-$\alpha$ emission are defined as quenched: their central
regions may be dusty or are no longer star-forming, and thus in a small enough
circular aperture, their color gradient would indicate quiescence. With an
aperture size of 0.7” diameter, we detect 13 UVJ quenched galaxies; when
decreasing the aperture size to a diameter of 0.32”, we record an additional 5
UVJ quenched galaxies while gaining no star forming galaxies. Further
explorations of color gradients and photometric aperture sizes in relation to
the bimodal classification system are needed to improve global definitions of
quenched galaxies.

##  5 Conclusion

With the capabilities of JWST, we can now use Paschen-$\alpha$ as an
independent, dust-insensitive tracer of SFR at cosmic noon in addition to
incorporating rest-frame NIR photometry in derivations of stellar mass. This
allows for a direct, independent measurement of the star forming sequence of
galaxies at $z\sim 1-2$. We summarize our main results as follows:

  * •

We find that there is low scatter (0.25 dex) in the directly observed relation
between the rest-frame H band magnitude — which traces the dominant stellar
mass component in a galaxy — and dust-uncorrected Paschen-$\alpha$ luminosity
— which traces SFR. The scatter increases slightly in the relation between
log(SFR) and log(M*) (likely due to assumptions introduced in the conversions
to stellar mass and SFR) and is consistent with previous studies at $\sim
0.29$ dex. Various assumptions used and disagreements in masses inferred from
different SED codes lead to increased scatter among SFR-M* relations in the
literature, and we note that the scatter in the relationship between
Paschen-$\alpha$ luminosity and rest-frame H band magnitude is much smaller
than these systematic differences.

  * •

At $\sim 10^{10-11}M_{\odot}$, our relation is offset from most studies. It is
in good agreement with results obtained using the Prospector fitting framework
(Leja et al., 2022); we find that this is mostly attributed to the
similarities between the masses obtained from the EA$z$Y redshift-dependent
SFH templates and the nonparametric SFHs implemented in Prospector.

  * •

Some UVJ defined quenched galaxies fall close to the relation, and spatially
resolved emission line maps obtained from grism spectroscopic data allow us to
probe exactly where star formation is occurring in these galaxies. The bimodal
system of selecting star forming galaxy is highly sensitive to color
gradients, and it is thus important for larger surveys of the SFS to use
carefully selected photometric aperture sizes.

With more incoming data from JWST, this method will be able to expand our
understanding of the SFR-M* relation through simpler, independent measurements
of SFR and stellar mass at cosmic noon. The process of quenching can be
further explored by looking at the morphology of Paschen-$\alpha$ emission
using emission line maps produced by grism spectroscopy. Our methods can also
be applied to larger samples to better measure the SFS in this redshift regime
and constrain the low mass end of the relation.

## Acknowledgments

This work is based on observations made with the NASA/ESA/CSA James Webb Space
Telescope. The data were obtained from the Mikulski Archive for Space
Telescopes at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST. These observations are associated with program
# 1895.

Support for this work was provided by NASA through grant JWST-GO-01895 awarded
by the Space Telescope Science Institute, which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract NAS
5-26555.

This work has received funding from the Swiss State Secretariat for Education,
Research and Innovation (SERI) under contract number MB22.00072, as well as
from the Swiss National Science Foundation (SNSF) through project grant
200020_207349. The Cosmic Dawn Center (DAWN) is funded by the Danish National
Research Foundation under grant No. 140.

RPN acknowledges funding from JWST programs GO-1933 and GO-2279. Support for
this work was provided by NASA through the NASA Hubble Fellowship grant HST-
HF2-51515.001-A awarded by the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy,
Incorporated, under NASA contract NAS5-26555

Cloud-based data processing and file storage for this work is provided by the
AWS Cloud Credits for Research program.

This paper made use of several publicly available software packages. We thank
the respective authors for sharing their work: IPython (Pérez & Granger,
2007), matplotlib (Hunter, 2007), seaborn (Waskom et al., 2018), numpy (Harris
et al., 2020), scipy (Virtanen et al., 2020), jupyter (Kluyver et al., 2016),
Astropy (Astropy Collaboration et al., 2013, 2018), grizli (Brammer 2018;
Brammer et al. 2022), Prospector (Leja et al., 2019, 2017; Johnson et al.,
2021), FSPS (Conroy et al., 2009a, 2010; Conroy & Gunn, 2010a, b; Foreman-
Mackey et al., 2014), dynesty (Speagle, 2018), EAZY (Brammer et al., 2008),
Bagpipes (Carnall et al., 2018), SExtractor (Bertin & Arnouts, 1996b).

##  Appendix A Mass measurements

In this work, we infer masses using EA$z$Y SED templates due to the ease of
use of the code and the reproducibility of our results, as discussed in
Section 3.2. While several previous studies use similar EA$z$Y templates to
infer masses (see, e.g., Sherman et al., 2020; Labbé et al., 2023), we
acknowledge that EA$z$Y has not been traditionally used in the context of
inferring physical properties of galaxies. We thus compare the stellar masses
used in this work to stellar masses from other SED fitting codes, namely,
Bagpipes (Carnall et al., 2018) and Prospector (Johnson et al., 2021). For all
fits, we use grism redshifts and 0.7” photometric apertures.

We specifically use Prospector-$\alpha$, which includes non-paramtetric SFHs,
nebular emission treatment, and stellar population synthesis (SPS) models
using FSPS (Conroy et al., 2009b; Conroy & Gunn, 2010c), following the
parameters outlined in Leja et al. (2019). We use a delayed tau model with SPS
models from Bruzual & Charlot (2003) for the Bagpipes runs. For the Prospector
masses, we check the chi squared value for each fit and discard those with bad
fits from our results.

Our comparison is shown in Figure 8, with differences between the EA$z$Y
stellar masses used in this work and stellar masses from Prospector (top) and
Bagpipes (bottom). Our masses are higher than the results from each of the
other SED fitting codes, but we are most consistent with Prospector with a
median offset of 0.20 dex and a biweight scatter of 0.19 dex, which is around
the scatter expected between different SED fitting codes (see, e.g., Pacifici
et al., 2023 for a discussion on the scatter in physical properties between
different SED fitting codes), whereas we measure higher masses than Bagpipes
by a median offset of 0.46 dex and 0.35 biweight scatter. These results are
indicative of the differences in the SFH implementations in these codes; the
Prospector-$\alpha$ model implements non-paramtric SFHs and captures the mass
contribution from older stellar populations (e.g., Leja et al., 2019; Lower et
al., 2020), while Bagpipes, like FAST, is sensitive to the youngest stars.
This is especially evident in Figure 9: we see that the mass-weighted ages
from Bagpipes are significantly and consistently lower than those derived from
Prospector, implying that Bagpipes models a much younger stellar population
than Prospector. Using SED template superposition with EA$z$Y, which allows
for multi-component SFHs rather than a unimodel SFH, we also infer higher
stellar masses and thus obtain similar results to Prospector.

Figure 8: Stellar mass comparisons between the masses used in this work,
derived with EA$z$Y, and masses derived using Prospector (top) and Bagpipes
(bottom). We are more consistent with masses derived with Prospector (0.2 dex
median offset) because both template superposition (EA$z$Y) and non-parametric
SFHs (Prospector-$\alpha$) allow for multi-component SFHs, whereas SED fitting
codes such as Bagpipes and FAST implement parametric SFHs. Figure 9:
Comparisons between the mass-weighted ages derived using Prospector (solid
purple) and Bagpipes (hatched blue). Prospector includes the mass contribution
from an older population of stars, thus resulting in older mass-weighted ages.

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