# Adding Value to JWST Spectra and Photometry: Stellar Population and Star
Formation Properties of Spectroscopically Confirmed JADES and CEERS Galaxies
at $z>7$

Qiao Duan,1 Christopher J. Conselice,1 Qiong Li,1 Thomas Harvey,1 Duncan
Austin,1 Katherine Ormerod,1 E-mail<EMAIL_ADDRESS>James
Trussler,1 Nathan Adams1
1 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,
Manchester UK

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

###### Abstract

In this paper, we discuss measurements of the stellar population and star
forming properties for 43 spectroscopically confirmed publicly available high-
redshift $z>7$ JWST galaxies in the JADES and CEERS observational programs. We
carry out a thorough study investigating the relationship between
spectroscopic features and photometrically derived ones, including from
spectral energy distribution (SED) fitting of models, as well as morphological
and structural properties. We find that the star formation rates (SFRs)
measured from H$\beta$ line emission are higher than those estimated from
Bayesian SED fitting and UV luminosity, with ratios
$\text{SFR}_{\text{H}\beta}/\text{SFR}_{\text{UV}}$ ranging from $\sim 2-13$.
This is a sign that the star formation history is consistently rising given
the timescales of H$\beta$ vs UV star formation probes. In addition, we
investigate how well equivalent widths (EWs) of H$\beta$ $\lambda 4861$, [O
iii] $\lambda 4959$, and [O iii] $\lambda 5007$ can be measured from
photometry, finding that on average the EW derived from photometric excesses
in filters is 30% smaller than the direct spectroscopic measurement. We also
discover that a stack of the line emitting galaxies shows a distinct
morphology after subtracting imaging that contains only the continuum. This
gives us a first view of the line or ionized gas emission from $z>7$ galaxies,
demonstrating that this material has a similar distribution, statistically, as
the continuum. We also compare the derived SFRs and stellar masses for both
parametric and non-parametric star formation histories, where we find that 35%
of our sample formed at least 30% of their stellar mass in recent ($<10$ Myr)
starburst events.

###### keywords:

galaxies:high-redshift – galaxies: formation – galaxies: general – galaxies:
photometry – galaxies: star formation

††pubyear: 2023††pagerange: Adding Value to JWST Spectra and Photometry:
Stellar Population and Star Formation Properties of Spectroscopically
Confirmed JADES and CEERS Galaxies at $z>7$–14

##  1 Introduction

The high redshift universe is now being studied in depth by JWST as shown by a
slew of papers on early galaxy discoveries in the past year (Austin et al.,
2023; Adams et al., 2023a; Donnan et al., 2023; Finkelstein et al., 2023;
Harikane et al., 2022; Atek et al., 2022; Castellano et al., 2022; Donnan et
al., 2022; Trussler et al., 2023; Bouwens et al., 2023; McLeod et al., 2023;
Franco et al., 2023; Casey et al., 2023; Naidu et al., 2022; Curtis-Lake et
al., 2022; Hainline et al., 2023). These studies have found that there are
many more distant candidate galaxies at $z>7$ than inferred from before based
on HST observations. However, uncovering their properties is really just in
its infancy, and a major way to understand these systems is through
spectroscopy. There are also many questions which we need to answer before we
can reach the ultimate goal of using spectroscopy and imaging together to
infer the physical properties of galaxies and therefore to determine galaxy
evolution. A major one is how well spectra and imaging agree in terms of
deriving the physical properties of galaxies.

It is clear that spectroscopy with, in particular NIRSpec and also
NIRCam/NIRISS in grism mode, are and will continue to be of major importance
for the study of the first galaxies. At the same time, it will never be the
case that we will obtain spectroscopy for all, or even a large fraction, of
the most distant galaxies. The systems are too faint, and in many cases, too
abundant to effectively obtain many spectra. Thus, we must resort to imaging,
down to the completeness limit, to derive galaxy properties for understanding
the galaxy population. This is a well worn path and many papers have used
imaging for the measurements of photometric redshifts, stellar masses, and
derived star formation rates, amongst other properties (e.g., Adams et al.,
2023a; Austin et al., 2023; Fujimoto et al., 2023; Atek et al., 2023).

The purpose of this paper is therefore two-fold. We investigate how well we
can derive properties of distant galaxies from their photometry by comparing
the same properties as derived from spectroscopy. This includes a redshift
comparison: $z_{\text{Phot}}$ vs. $z_{\text{Spec}}$, as well as measures of
star formation rates and stellar masses. For example, it might be the case
that there is a systematic difference in the measurements of these quantities,
such that the ones derived from photometry are for example lower than
spectroscopy. If this is the case then we will need to account for this in
future analyses. We can also use spectroscopy and imaging together to derive
unique properties of galaxies. An example of this is using the location of
emission lines seen in spectroscopy which exist, and contribute flux, within
various imaging filters. When this is well understood and well known (e.g.,
without uncertain redshifts) we can obtain an image of the line emission alone
through subtracting filters that only contain continuum (no emission lines)
from filters with flux arising from emission lines (Hatch et al., 2013).

This type of analysis has been carried out in other ways before, but never
quite addressing the same questions we are here. Previous similar work
includes examining how well star formation and stellar masses can be measured
based on comparisons with models and with different fitting codes and methods
(e.g., Mobasher et al., 2015; Pacifici et al., 2023). This is also the case
for different photometric redshift codes (Dahlen et al., 2013), where tests
can be done to determine which methods and codes are the ‘best’ for recovering
correct photometric redshifts. Recently this has been examined in terms of the
stellar population properties of galaxies as derived through photometry,
finding that stellar mass is consistent between different codes, although
other properties derived from SED fitting can vary quite significantly
(Pacifici et al., 2023). Here we examine similar questions, but we take a more
detailed approach of comparing within the same code and same initial
conditions how well the properties of galaxies can be derived based on
photometry vs. spectroscopy. That is, we can determine the same features of
galaxies using spectroscopic measurements, sometimes within the line emission
detected, but otherwise fitting the spectrum.

Thus, in this paper we investigate the spectroscopic properties of a sample of
$z>7$ galaxies with reliable spectroscopic redshifts from NIRSpec on JWST
within two different fields - CEERS (Finkelstein et al., 2023) and JADES
(Rieke et al., 2023; Eisenstein et al., 2023).

The structure of this paper is outlined as follows. In Section 2, we detail
the dataset sourced from the JADES and CEERS fields. Our main findings and
analysis are presented in Section 3. A summary of our conclusions is provided
in Section 5. Throughout this work, we adhere to a standard cosmology with
$H_{0}=70\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$, $\Omega_{\rm M}=0.3$
and $\Omega_{\Lambda}=0.7$ to facilitate comparison with other observational
studies. All magnitudes reported are consistent with the AB magnitude system
(Oke, 1974; Oke & Gunn, 1983).

##  2 Data and Reduction

The launch of the James Webb Space Telescope in December 2021 (Rigby et al.,
2023) provides an unprecedented opportunity to study the distant universe.
Over the past year, several Cycle 1 observation programs have been conducted.
In this paper, we analyze data from the JADES and CEERS programs, both in
terms of imaging and spectroscopy. Below we give some details of which data we
use and how this data was reduced and processed.

###  2.1 JADES NIRSpec Observations

We use the first JADES released NIRSpec (Ferruit et al., 2022) data (PI:
Eisenstein, N. Lützgendorf, ID:1180, 1210), spanning the time-frame September
2022 to October 2022, with a focus on the publicly released data in GOODS-S
field. The spectra are obtained through the application of both
disperser/filter and PRISM/clear configurations. Specifically, the PRISM data
covers 253 galaxies, and 198 of them have disperser/filter data. Four
different disperser/filter combinations are used to acquire the spectroscopy:
G140M/F070LP, G235M/F170LP, G395M/F290LP, and G395H/F290LP, with a wavelength
coverage of $0.70-1.27\mu$m, $1.66-3.07\mu$m, $2.87-5.10\mu$m, and
$2.87-5.14\mu$m, respectively. The three medium resolution filters have a
nominal resolving power of R $\approx 1000$, while the high resolution data
can reach R $\approx 2700$. In this paper, we primarily utilize the PRISM
data, which covers a wavelength range of $0.6\,\mu\text{m}$ to
$5.3\,\mu\text{m}$, and exhibits a spectral resolution of $R\approx 30-330$
(Ji & Giavalisco, 2022).

Among the 253 observed galaxies, 13 are situated at $z_{\text{spec}}>7.0$,
with 11 of them having NIRCam observations. During these observations, three
micro-shutters were activated for each target. An exposure protocol was
implemented consisting of a three-point nodding sequence along the slit, with
each nod lasting 8403 seconds, and the entire sequence repeated four times.
This culminated in a total PRISM exposure time of up to 28 hours for some
sources. The subsequent extraction of flux-calibrated spectra was carried out
using specialized pipelines developed by both the ESA NIRSpec Science
Operations Team and the NIRSpec GTO Team (Bushouse et al., 2023). A more
detailed examination of the JADES/HST-DEEP spectra and the criteria used for
sample selection is provided by Eisenstein et al. (2023).

###  2.2 JADES NIRCam Observations

The JADES NIRCam imaging observations (Rieke et al., 2023) cover both the
GOODS-S and GOODS-N fields. In this paper, we focus on the GOODS-S field data
(PI: Eisenstein, N. Lützgendorf, ID:1180, 1210). The observations utilise nine
filter bands: F090W, F115W, F150W, F200W, F277W, F335M, F356W, F410M, and
F444W, encompassing a spatial extent of 24.4 - 25.8 arcmin2. A minimum of six
dither points was used for each observation, with exposure times spanning
14-60 ks. Correspondingly, the $5\sigma$ depths are within the range from 3.4
to 5.9 nJy, with flux aperture sizes varying between 1.26 and 1.52 arcsec.
Across all filter bands, JADES ensures a high level of pixel diversity (Rieke
et al., 2023), thereby significantly reducing the impact of flat-field
inaccuracies, cosmic ray interference, and other issues at the pixel level. In
this paper, we utilize the publicly released JADES data and reductions.

###  2.3 CEERS NIRSpec Observations

The CEERS NIRSpec spectroscopic data (Fujimoto et al., 2023; Haro et al.,
2023) were procured as part of the ERS program (PI: Steven L. Finkelstein,
ID:1345). This dataset was designed to optimize the overlap with observations
from both NIRCam and HST, using three medium resolution gratings $R\approx
1000$ and the PRISM $R\approx 100$. The PRISM data presented here are a
reschedule of the original observations affected by an electrical short in
CEERS Epoch 2 (December 2022). These rescheduled observations were executed in
CEERS Epoch 3, February 2023. During this period, both NIRSpec pointings,
namely NIRSpec11 and NIRSpec12, adhered to the standard CEERS MSA
observational guidelines. Specifically, they encompassed three integrations
with 14 groups in the NRSIRS2 readout mode per visit, leading to a total
exposure time of 3107 s. Within these observations a trio of shutters was used
to form slitlets, facilitating a three-point nodding sequence to enhance
background subtraction. The PRISM disperser, ranging in wavelength from
0.6–5.3 $\mu$m, is characterized by its capacity to provide varied spectral
details. In this paper, we use the NIRSpec data reduced by the Cosmic Dawn
Center, which is published on the DAWN JWST Archive (DJA).111https://dawn-
cph.github.io/dja/blog/2023/07/18/nirspec-data-products/. From this data set,
there are 32 galaxies at $z_{\text{spec}}>7$, which we analyse in the
following sections.

###  2.4 CEERS NIRCam Imaging

The CEERS (CEERS; ID=1345) NIRCam imaging (Bagley et al., 2023) includes data
across seven distinct filters: F115W, F150W, F200W, F277W, F356W, F410M, and
F444W, with a $5\sigma$ depth of 28.6 AB magnitudes using 0.1 arcsec circular
apertures. The dataset encompasses observations collected during June 2022,
accounting for 40% of the total NIRCam area covered for CEERS in the latter
half of the same year.

In this paper we utilise our own bespoke reduction of this data from the
Cosmic Evolution Early Release Science Survey in the Extended Groth Strip
field (EGS). We have reduced this data independently ourselves using a custom
set-up of the JWST pipeline version 1.6.2 using the in-flight calibration
files available through the CDRS 0942. We provide an extensive description of
this process and the resulting data quality in Ferreira et al. (2022); Adams
et al. (2023a).

In parallel, v1.9 EGS mosaics HST data from the CEERS team are used. These are
processed following the methodologies outlined in Koekemoer et al. (2011),
which notably include enhancements in calibration and astrometric accuracy
beyond what is available from the default HST archival pipeline, with a pixel
scale of 0.03". For the HST data, two filters, namely F606W and F814W, are
employed in our analyses due to their superior spatial resolution and depth
when compared to HST/WFC3 images, and the fact that they are bluer than the
JWST data. We find that using these two HST filters within CEERS is critical
for measuring accurate redshifts and other physical properties as this JWST
dataset is missing the crucially important F090W band.

###  2.5 Photometric Redshifts

Analysing the quality and robustness of photometric redshift estimates is a
key aspect of this paper, and thus we go into some detail in describing how
they are measured here. We use two different photometric redshift codes
throughout this paper - EAZY-PY (hereafter EAZY) is our primary code, and then
LePhare as a check on these values, both of which we describe below. Most of
our results however are discussed mainly in terms of the EAZY code.

Our primary photometric redshifts arise from fitting our derived SEDs from the
EAZY photometric redshift code (Brammer et al., 2008). This is the standard
code used to measure photo-zs from the EPOCHS sample (Adams et al. 2023a;
Conselice et al. 2023, in prep). To carry out the photometric redshift
analysis we use the BC03 template sets with a Chabrier initial mass function
for our analyses, with details discussed in Bruzual & Charlot (2003) and
Chabrier (2002), respectively. The templates we use include both exponential
and constant star formation histories, whereby we use within these 10
characteristic timescales ranging from $0.01<\tau<13$ Gyr. In addition to this
we use 57 different ages for the model galaxies spanning 0 to 13 Gyr. We
include galaxies models which are at redshifts that range from $0<z<25$. Dust
is accounted for by using the prescription of Calzetti et al. (2000). We allow
for $E(B-V)$ values up to 3.5, to include any very dusty galaxies that may
exist at these very high redshifts, and to determine the likely errors from
low redshift contamination. Our fitting of the photo-zs incorporates treatment
for emission lines, and we apply the intergalactic medium (IGM) attenuation
derived from Madau (1995) when considering our fits. The very blue templates
we use are presented in Larson et al. (2022) as well as those which used by
the JADES team (Hainline et al., 2023). These templates build upon the default
template sets and incorporate galaxies that exhibit bluer colors and stronger
emission lines, which are expected to be more appropriate for modelling the
spectral energy distributions (SEDs) for those systems that are at $z>7$.

In addition to EAZY we use photometric redshifts calculated with the LePhare
code. The setup that we use is the same as we have used for the EAZY results
described above. However, most of our results when using photometric redshifts
arise from EAZY, and LePhare is used as a check on these. By utilizing
multiple photometric redshift codes, we are able to cross-check the results
for consistency and identify potential contaminants, thus ensuring the
reliability of our final sample.

We do not use methods to fine-tune the zero points of the photometric bands,
as the NIRCam modules consist of multiple individual chips (8 in the blue and
2 in the red), each with their own independent calibrations and photometric
zero point offsets. Applying zero point modifications on a chip-by-chip basis,
instead of on the final mosaic, would be necessary due to the small field of
view covered by each chip, which results in a limited number of objects with
spectroscopic redshifts within each chip, and leads to potential unnecessary
biases determined by the positions of the galaxies in the NIRCam pointing.
Doing this would also introduce potential biases towards systems with certain
colors, which depend on the types of spectroscopically confirmed galaxies
within each module. Discussions with members of the community have indicated
that residual zero point errors were anticipated to be around 5 percent.
Therefore, we have implemented a minimum 5 percent error on the measured
photometry to account for potential zero point issues within the NIRCam
reduction pipeline.

##  3 Results

In this section we describe the basic results of our study by comparing
photometric and spectroscopic data, and what can be learned by combining the
two. We include a comparison of the galaxy properties derived separately from
the photometric and spectroscopic data, and how accurate we can derive
properties from photometry by comparing with spectroscopy, assuming that the
spectroscopic derivations are more accurate in some cases. We later discuss
the likelihood of this later case.

###  3.1 Photometric vs. Spectroscopic Redshifts

By far the most common way to estimate the distances of galaxies is through
photometric redshifts. This is due to the fact that photometric redshifts can
be measured when imaging is available for different galaxies in a variety of
filters; this allows us to compare to templates of known redshifts and thus
determine which is the best ‘fit’. In this section we carry out a comparison
of how we measure the photometric redshifts for distant galaxies and how well
these compare to the known high quality spectroscopic redshifts available from
NIRSpec JWST data.

There are however, two issues that we have to discuss concerning comparing the
photometric and spectroscopic redshifts. The first is the selection of
sources. It is not enough to blindly measure photometric redshifts for
everything that enters a catalogue, as the quality of those redshifts depends
strongly on the quality of the data at all wavelengths, and how many filters a
galaxy is detected within.

As described, the photometric redshift technique that we use to measure
redshifts comes from EAZY-PY (Brammer et al., 2008) and uses a variety of
approaches discussed in Section 2.5.1. These methods and details of the
photometric redshifts are further described in detail in Adams et al. (2023b)
and Conselice et al. (2023, in prep). For spectroscopic redshifts, we utilize
data from the publicly available JADES catalog (Bunker et al., 2023), as well
as from the DAWN JWST Archive (DJA) for CEERS galaxies. We re-measure these
spectroscopic redshifts ourselves using the [O iii] $\lambda 5007$ line and
find a good agreement with the published ones which we use throughout this
paper. For this initial comparison we just compare the photometric redshifts
we obtain for all 43 galaxies in our sample (11 from JADES and 32 from CEERS),
without consideration for whether these galaxies would be selected for
observation based on other criteria, which we discuss in more detail below.

The outcomes of our redshift comparison are visually represented in Figure 1.
We evaluate two statistical measures for all the galaxy samples: the outlier
fraction $\eta$ and the Normalised Median Absolute Deviation (NMAD). These two
parameters are defined by the following expressions:

$\eta=\frac{N_{115}+N_{85}}{N_{\text{total}}},$ (1)

where $N_{115}$ and $N_{85}$ represent the counts of points lying above the
line $z_{\text{phot}}=1.15\times(z_{\text{spec}}+1)$ and below the line
$z_{\text{phot}}=0.85\times(z_{\text{spec}}+1)$, respectively. These counts
indicate the presence of extreme outliers in the sample. The equation for
calculating the NMAD is given by (e.g., Duncan et al., 2019):

$\text{NMAD}=1.48\times\text{med}\left|\frac{z_{\text{spec}}-z_{\text{phot}}}{1+z_{\text{spec}}}\right|.$
(2)

The values for these parameters, as applied to our data set, are detailed in
Table 1. As is evident, our photometric redshift measurements show an
exceptional concordance with the spectroscopically measured values. Notably, a
mere 2.6% of our samples qualify as extreme outliers in terms of their
photometric redshifts. We find a very similar trend when using the LePhare
photometric redshifts.

We now would like to consider how the selection method we and others use in
high redshifts papers would allow these galaxies to be correctly identified as
high redshift (e.g., Adams et al. 2023a; Conselice et al. 2023, in prep). The
selection procedure in these papers, and others similar to them, uses more
than just the best-fitting photo-z solution, including issues such as the
limits on potential low-z solutions and the detection confidence of the
photometry. In addition to having a high-z solution, these high-z papers often
require that there be a low probability for the photometric redshift to be at
lower-z. Another criteria for robust selection of high-redshift galaxies
involves additional criteria, such as $>3\sigma$ detection in bands blueward
of the Lyman break, a PDF integral of photometric redshifts between $\pm 0.1z$
is greater than 60% of the total, and $\chi^{2}$ values less than 6. These
criteria are done to balance contamination with sample completeness. Thus we
can test our methodology with this sample to see how many galaxies from this
spectroscopic sample we would have included in our photometric samples in the
EPOCHS papers.

In accordance with the selection criteria explained in our previous work
(Adams et al. 2023b; Conselice et al. 2023, in prep), 16 out of the 32 CEERS
galaxies would be categorized as robust galaxies. The reasons that 16 galaxies
would not have survived our selection are varied and depend on a few factors.
Among the 16 galaxies that would make up this non-robust sample, 4 systems are
excluded due to being near image edges or diffraction spikes. 1 galaxy is
excluded for lacking observations in bands blueward of the Lyman break, and 11
are rejected owing to flux detections below $5\sigma$ above the noise in the
first, second, or both bands redward of the Lyman break. It is noteworthy that
the CEERS team likely selected these 11 galaxies based on using smaller,
$0.2\,\text{arcsec}$ apertures for their photometry. Despite their faintness,
our analysis still gets their redshifts correct. Thus, overall we only miss
those galaxies which are too faint for reliable photometric redshifts or those
that are in non-ideal regions of the images.

We generate both primary and secondary photometric redshift solutions for each
galaxy in our study. The secondary redshift solutions are constrained to have
a maximum allowable redshift of $z=6$. In our robust galaxy samples, these
secondary solutions typically exhibit an inferior fit quality compared to the
primary solutions. This is substantiated by an average $\Delta\chi^{2}$ value
which is $\sim$ 35 higher than that of the primary solutions, for which the
mean $\chi^{2}$ is $7.47$.

Table 1: Values of $\eta$ and NMAD for JADES, CEERS, and Joint Data. The outlier fraction, $\eta$, expressed as a percentage and defined by Equation 1, measures the proportion of extreme outliers in the redshift comparison. The NMAD, calculated using equation Equation 2, estimates the scatter in the redshift differences, adjusted for scale. The low values of both metrics attest to the accurate measurement of our photometric redshifts. Parameters | JADES | CEERS | Joint
---|---|---|---
$\eta$ | 0.0 % | 3.6 % | 2.6 %
NMAD | 0.027 | 0.036 | 0.035
Figure 1: Comparison of spectroscopic redshifts with photometric redshifts
from EAZY, for 11 JADES and 32 CEERS galaxies. A scatter plot between these
values is presented and shown with an inset histogram at the bottom right
corner, displaying the frequency distribution of the quantity
$(z_{\text{spec}}-z_{\text{phot}})/(1+z_{\text{spec}})$ of our galaxy samples.

###  3.2 Galaxy Intrinsic Properties

We analyze the intrinsic properties of our galaxy samples, both
spectroscopically and photometrically, using various methodologies.
Specifically, we use Bagpipes (Carnall et al., 2018) to fit the photometric
and spectroscopic galaxy data separately with six parametric SFH models—log-
normal, delayed, constant, exponential, double delayed, and delayed
burst—along with a non-parametric Continuity model (Leja et al., 2019), while
fixing the redshift to the spectroscopic redshift in both cases. We use Log10
priors for dust, metallicity, and age. The reason for selecting Log10 priors
is because we expect high redshifts galaxies to be young, with lower
metallicity and for being less dusty. We set prior limits for metallicity in
the range of $[1\text{e-06},10.0]\,\text{Z}_{\odot}$, dust prior in the range
of $[0.0001,10.0]$ in $A_{\text{V}}$, the time assumed for star formation to
start at 0.001 Gyr, the time assumed for star formation to stop at
$t_{\text{U}}$, with $t_{\text{U}}$ denoting the age of the Universe. In
addition, Kroupa (2001) IMF, Bruzual & Charlot (2003) SPS model, and the
Calzetti et al. (2000) dust attenuation model is implemented. For each model,
we examine no effects other than using different SFR timescales — 5 Myr, 10
Myr, and 100 Myr — on the derived properties. These timescales only impact the
measured SFR.

Since there are no significant differences in galaxy parameters derived from
various models, we have chosen to focus our analysis on the results obtained
using the log-normal SFH model. For each property computed from Bagpipes, the
derived values are represented by the median of their respective PDF. The
lower and upper uncertainties are determined as the differences between the
50th percentile and the 16th, and between the 84th and the 50th percentiles,
respectively.

In our spectroscopic fitting, we incorporate three additional considerations
(Carnall et al., 2019): velocity dispersion, flux calibrations, and noise. The
velocity dispersion is modelled by setting the width of the Gaussian kernel in
velocity space to be convolved with the spectroscopic output, within a range
of $[1,1000]$ km/s. For flux calibrations, we address potential discrepancies
between photometric and spectroscopic measurements by fitting a Chebyshev
polynomial perturbation to the spectroscopic data (Carnall et al., 2019). This
method assists in correcting calibration issues and aligning the models. To
account for noise, we introduce a factor that applies a multiplicative
adjustment to all spectroscopic uncertainties. Moreover, to evaluate potential
slit losses, we simulate photometric flux using the observed spectral data.
Our analysis reveals a maximum discrepancy of $\sim$20% between the observed
photometric flux points and the simulated data, predominantly in the NIRCam
filter F090W. This discrepancy is likely attributed to the fact that this band
is blueward of the Lyman break for our sample galaxies at redshifts $z>7$,
resulting in a significant drop in flux. Consequently, the noise dominates in
this band. For other filter bands, no discernible differences are observed.

We produce a scatter plot with photometrically-derived values on the y-axis
and spectroscopically-derived values on the x-axis, for Bagpipes derived
stellar masses, formed masses, SFRs, and dust extinction values
(A${}_{\text{V}}$). Using the Bayesian Markov Chain Monte Carlo (MCMC) method,
we compute the line of best fit for each plot via the emcee package (Foreman-
Mackey et al., 2013). Specifically, we employ 100,000 steps and 50 walkers to
generate candidate gradients and y-intercept values. For both sets of values,
we adopt the mean as the representative value and use the 1$\sigma$ deviation
as the associated uncertainty, as the distributions follow a perfect Gaussian.
In addition, the Pearson correlation coefficient between the spectroscopic and
photometrically derived values is determined, and its uncertainty is
calculated using the Fisher transformation. Specifically, the Pearson
correlation coefficient $r$ is transformed into a $z$-score using the Fisher
transformation, which is given by
$z=\frac{1}{2}\ln\left(\frac{1+r}{1-r}\right)$. This transformation ensures
that the distribution of $z$ is approximately normal. Once $z$ is obtained,
the 95% confidence interval for it is calculated. Subsequently, this
confidence interval is transformed back to the correlation coefficient scale
using the inverse Fisher transformation, represented by
$r=\frac{e^{2z}-1}{e^{2z}+1}$. Thus, providing the 95% confidence interval for
the original correlation coefficient $r$. The results of gradients,
intercepts, and correlation coefficients using 100 Myr SFR timescale are
presented in Table 2.

Table 2: Linear regression and Pearson correlation analysis between spectroscopic and photometric results for different galaxy properties derived from Bagpipes using 100 Myr SFR timescale. The gradient and y-intercept of the regression model are computed, and the uncertainty in the correlation coefficient is calculated using the Fisher transformation. The 1$\sigma$ values (or scatter) for residuals between the best fit line and scatter points are shown. Property | Correlation | Gradient | Intercept | Residual $1\sigma$
---|---|---|---|---
Stellar Mass [log${}_{10}(\text{M}_{\odot})$] | $0.62^{+0.39}_{-0.28}$ | $0.55\pm 0.11$ | $3.49\pm 0.90$ | 0.37 [log${}_{10}(\text{M}_{\odot})$]
Mass Formed [log${}_{10}(\text{M}_{\odot})$] | $0.58^{+0.34}_{-0.35}$ | $0.53\pm 0.12$ | $3.72\pm 0.95$ | 0.41 [log${}_{10}(\text{M}_{\odot})$]
Star Formation Rate [$\text{M}_{\odot}\,\mathrm{yr}^{-1}$] | $0.64^{+0.15}_{-0.22}$ | $0.67\pm 0.13$ | $0.42\pm 0.30$ | 1.37 [$\text{M}_{\odot}\,\mathrm{yr}^{-1}$]
Dust Extinction (Av) [AB mag] | $0.61^{+0.16}_{-0.24}$ | $0.49\pm 0.1$ | $0.15\pm 0.04$ | 0.20 [AB mags]

####  3.2.1 Quality of the Bagpipes fits

In this short section we discuss how well we can fit the SEDs of our galaxies
with the Bagpipes fits and the underlying models which we use. These are
standard models which have been used throughout the literature for years, but
it might be the case that at these higher redshifts galaxy SEDs might be
better fit by, for example, models in which the IMF differs from the
assumption (perhaps top-heavy) or by models which incorporate binary stars
(e.g., BPASS) (e.g., Eldridge & Stanway, 2009). One way to determine this is
through examining how well our SEDs are fit by these models as determined
through the $\chi^{2}_{\text{reduced}}$ values of these fits.

We evaluate the goodness of fit for our models by calculating the
$\chi^{2}_{\text{reduced}}$ for both photometric and spectroscopic fitting.
Both our JADES and CEERS samples exhibit comparable photometric
$\chi^{2}_{\text{reduced}}$ values, meaning that there is not one particular
sample which is better fit by our methods than the other. Precisely, the mean
photometric $\chi^{2}_{\text{reduced}}$ for the JADES samples is $1.5\pm 0.6$,
whereas for CEERS samples, it stands at $2.0\pm 1.1$. This indicates a similar
and good level of photometric fitting quality for these two sets of galaxy
samples.

However, the spectroscopic fitting quality for CEERS samples appears to be
slightly inferior based on this statistic. The mean
$\chi^{2}_{\text{reduced}}$ for JADES is $1.54\pm 0.65$. In contrast, the
corresponding value for the CEERS sample rises to $3.19\pm 1.34$, nearly
double that of JADES. We speculate that the worse fitting quality for CEERS is
primarily attributed to its shorter exposure time. Some JADES galaxies have
exposure times extending up to 28 hours, whereas CEERS employs an exposure
time of less than an hour. Whilst the larger errors on the fainter
observations should account for this, it is possible that these are being
underestimated in our fits, and therefore resulting in higher
$\chi^{2}_{\text{reduced}}$ values. In any case, we do not observe large
$\chi^{2}_{\text{reduced}}$ values that would suggest the models we fit are
inherently flawed. However, a more detailed analysis is warranted and
necessary, but this is beyond the scope of this paper.

####  3.2.2 Measuring Galaxy Stellar masses

In this section, we examine the various different ways in which stellar mass
and formed mass are derived from Bagpipes using the spectroscopic and
photometric data. Stellar mass represents the present-day mass of the galaxy,
while the formed mass incorporates the observed mass plus the return mass,
accounting for the mass from exploded stars that contribute to the formation
of new stars. Consequently, the formed mass is always greater than the stellar
mass. Also, the stellar mass is the only quantity we can directly compare with
given that this is what we are observing. In addition, different SFR
timescales dictate the duration over which the star formation rate is
averaged, and these do not influence the derived galaxy masses. Thus, we
present only the 100 Myr averaged SFR results here. In Table 2, we show the
correlation coefficient and the parameters of the best-fit line for the
spectroscopically and photometrically derived values of these two quantities.
Generally speaking, these two masses derived from both methods are in moderate
agreement, with high scatter.

We present a graphical comparison for stellar masses in Figure 2. For our
galaxy samples, the stellar masses for both CEERS and JADES range from
$\log_{10}(\text{M}_{*}/\text{M}_{\odot})=6.8$ to 9.3, with individual means
of 8.0 for both fields, consistent with the findings of Fujimoto et al.
(2023). The correlation coefficient for spectroscopically and photometrically
derived stellar masses is $0.62^{+0.39}_{-0.28}$, which indicates moderate
agreement between these two methods. However, the $1\sigma$ residual of 0.37
$\log_{10}(\text{M}_{*}/\text{M}_{\odot})$ from the best fit line suggests
high scatter in the data. We hypothesize that this scatter arises from some
photometric bands being affected by strong emission lines of H$\beta$ and [O
iii], thereby reducing the accuracy of the stellar masses. Further
investigation reveals that galaxies with this pronounced scatter generally
exhibit high star formation rates. Although there isn’t a universally strong
agreement across all mass ranges, a notably better alignment is observed
within the mass range $\log_{10}(\text{M}_{*}/\text{M}_{\odot})=[7.6,8.2]$.

Figure 2: The comparison of galaxy stellar masses derived from spectroscopic
and photometric data using Bagpipes fitting, based on a log-normal star
formation history with a 100 Myr SFR timescale. The best fit line for all data
points has a gradient of $0.55\pm 0.11$, and an interception of $3.49\pm 0.90$
$\log_{10}(\text{M}_{*}/\text{M}_{\odot})$, as shown by the dashed line. The
solid line shows the 1:1 relation between the two masses. The correlation
coefficient between the spectroscopic and photometric measurements is
$0.62^{+0.39}_{-0.28}$. In general, we find a better agreement between these
methods of measuring stellar masses at intermediate masses. At the lowest
masses the photometric method gives larger masses, whereas at the higher
masses the spectroscopic measurement of stellar mass is larger.

####  3.2.3 Measuring Star Formation Rates

In this section, we employ three methods to measure the SFR: which we name as:
Bagpipes, UV luminosity, and H$\beta$ line luminosity. For the Bagpipes
method, we not only analyze the correlation in SFR derived both
photometrically and spectroscopically, but also study the variations in the
derived SFR values when employing different timescales: 100 Myr, 10 Myr, and 5
Myr. We use this to investigate the star formation history of our sample and
to determine when the stellar masses of these galaxies formed. We then compare
these SFR measurements with those from direct line and UV measures. The
specific parameters for the Bagpipes fitting are detailed in Section 3.2.

Beyond the insights provided by the Bagpipes method, we further measure the
SFR directly using H$\beta$ line luminosity from spectrum, and UV luminosity
derived from the photometry. Each technique, as elaborated in this section,
calculates the SFR over distinct timescales. For instance, the Hydrogen
$\beta$ method predominantly captures recent SFRs—about 10 Myr prior to
observations. In contrast, the UV luminosity method gauges the SFR over a
longer window, specifically the $\sim 100$ Myr preceding the observations
(Kennicutt Jr & Evans, 2012).

For SFRs measured from the H$\beta$ line, we employ the calibration proposed
by Kennicutt Jr & Evans (2012). The approach harnesses synthetic stellar
populations and SEDs to calibrate various SFR tracers, relying on a standard
IMF for enhanced results over previous calibrations. Typically, the H$\alpha$
luminosity is used for SFR calculations due to its direct relationship with
recent star formation, and this relationship is expressed as:

$\log\dot{M_{*}}(\text{M}_{\odot}\text{yr}^{-1})=\log L_{\text{H}\alpha}-\log
C_{\text{H}\alpha},$ (3)

where $L_{\text{H}\alpha}$ is the H$\alpha$ luminosity and
$C_{\text{H}\alpha}$ is the calibration constant with $\log
C_{\text{H}\alpha}=41.27$. However, in our high-redshift galaxy samples, the
H$\alpha$ line is redshifted beyond the NIRSpec wavelength range. We therefore
measure the H$\beta$ line luminosity, from which we derive the H$\alpha$
luminosity using the ratio $L_{\text{H}\alpha}/L_{\text{H}\beta}=2.86$,
applicable in dust-free star-forming regions (Kennicutt Jr & Evans, 2012). We
later discuss how viable this assumption is and how it might influence our
measurements.

To estimate SFRs directly from the photometry, we employ the conversion from
the UV luminosity directly measured $L_{\text{UV}}$ to SFR as presented in
Equation 4. In this case we do correct for dust obscuration by measuring the
rest-frame UV using a technique that involves utilising the UV $\beta$ slope.
We fit a power law to the rest-frame UV photometry of the galaxy to determine
the proportionality constant, $\beta$. The dust corrected SFR in solar mass
per year is then computed using the equation from Madau & Dickinson (2014):

$\mathrm{SFR}_{\mathrm{UV}}=\kappa\cdot L_{\mathrm{UV}}\cdot
10^{0.4(4.43+1.99\beta)},$ (4)

where $\kappa=1.15\times
10^{-28}\,\mathrm{M}_{\odot}\,\mathrm{yr}^{-1}\,\mathrm{erg}^{-1}\,\mathrm{s}\,\mathrm{Hz}$,
is the proportionality constant that accounts for the efficiency of star
formation and the IMF (Salpeter, 1955), $4.43+1.99\beta$ is the dust
correction factor $A_{\text{UV}}$ (Meurer et al., 1999), and $L_{\mathrm{UV}}$
is the UV luminosity of the galaxy. We use these star formation calibrations
and measurements in the following subsections.

####  3.2.4 Photometry vs. Spectroscopy SFRs

In this subsection we investigate how well fits to spectroscopy compare with
fits to the photometry for measuring star formation rates within our sample of
galaxies. The reason for doing this is to determine how well we can measure
the SFR in terms of internal consistency, but also if we assume that the star
formation rate measured from spectroscopy is somehow more ’correct’ than with
photometry, how different these two measures would be. In Figure 3 we show a
comparison of Bagpipes derived spectroscopic and photometric SFR using a 100
Myr timescale. In our sample, the majority of galaxies exhibit an SFR ranging
from $\sim 0.3$ to $\sim 3\,\text{M}_{\odot}\text{yr}^{-1}$, with a number of
systems having higher SFRs, reaching up to $\sim
9\,\text{M}_{\odot}\text{yr}^{-1}$. We find that the JADES sources with
NIRSpec data typically exhibit a lower mean SFR of
$1.6\,\text{M}_{\odot}\text{yr}^{-1}$, compared to those from the CEERS field
which have a mean SFR of $5.6\,\text{M}_{\odot}\text{yr}^{-1}$. However, it is
important to note that this is within the errors of these measurements. These
differences underline the significance of selection biases in studying diverse
high-redshift galaxies, emphasizing the need for a more comprehensive
spectroscopic approach in future endeavors.

Furthermore, the correlation coefficient between these star formation
measurements is $0.64^{+0.15}_{-0.22}$, signifying a good agreement between
the two methods. Notably, there is an especially strong concordance between
photometrically and spectroscopically derived SFRs, for SFR values up to $2$
$\text{M}_{\odot}\text{yr}^{-1}$. It is only at the higher end of the star
formation where we find that the photometry is higher. However, it is
important to keep in mind that these differences are at about the level of the
uncertainty in these values.

####  3.2.5 Bursty Star Formation Events

In this section, we present three ways in which the bursty SFH nature for our
galaxy sample is identified and verified within these high redshift galaxies.
We are able to do this as we have the ability to determine the SFR accurately
knowing the correct redshift of our systems.

Firstly, we turn our attention to the comparison between SFR derived from
H$\beta$ line emission and the UV luminosity. Of our samples, 5 out of 11
JADES galaxies and 20 out of 32 CEERS galaxies exhibit an H$\beta$ line which
we can measure. The comparison for these galaxies is illustrated in Figure 4.
Given that the H$\beta$ results have not been corrected for dust, we opted for
a consistent comparison by assuming a dust-free condition for the UV-derived
SFR as well. As these are low mass high redshift galaxies, they are unlikely
to be very dusty in any case. Consequently, the term
$10^{0.4(4.43+1.99\beta)}$ as outlined in Equation 4 is omitted from these
comparisons.

It is worth noting that if dust correction is taken into account, then the
effect is stronger in the rest-frame UV than in the rest-frame optical where
H$\beta$ is located. Upon analysis, 60% of the CEERS samples show a higher SFR
from the H$\beta$ line luminosity measurement compared to that from the UV
luminosity, while this observation is true for all the JADES samples. The SFR
derived from H$\beta$ line luminosity can be as much as 2.4 times higher for
JADES samples and 13.5 times for CEERS samples, which may well be due to
photometric selection biases in the way these galaxies are selected.

The higher SFR from the H$\beta$ line method most likely arises from the
differing timescales each method probes. The UV luminosity reflects the SFR
over the previous 100 Myr, while H$\beta$ traces the SFR over much shorter
timescales of $\sim$10 Myr. Such findings suggest a bursty phase of star
formation in these galaxies over the recent few million years (see below for
further proof of this). One factor that may bias the sample towards higher SFR
during the past 10 Myr is that we are only showing the H$\beta$ SFRs for
galaxies with an identifiable H$\beta$ detection. Another issue which we have
ignored in this calculation is the dust content. It might be the case that the
dust extinction is high enough to attenuate the UV light more than the
H$\beta$ line flux such that it only appears to be lower. We investigate the
dust in more detail in Section 3.2.6, however we give some indication for its
impact here. Using the Calzetti et al. (2000) dust law we find an attenuation
of A${}_{\mathrm{UV}}=0.25$, A${}_{\mathrm{H}\beta}=0.13$ for our galaxies.
This leads to a relative increase in UV SFR over H$\beta$ by about 10% (25%
increase in UV vs. a 12% increase in H$\beta$ flux) which is not nearly enough
to create UV star formation rates that match the observed H$\beta$. Thus, we
can conclude that there is an intrinsic difference in what these two star
formation rates are measuring.

To investigate the bursty nature of the SFH of these galaxies more thoroughly,
we utilize the non-parametric ’Continuity’ model presented by Leja et al.
(2019). Our analyses yield consistent findings: galaxies with higher
H$\beta$-derived SFR do indeed exhibit a notable burst in their SFH when
interpreted through the Continuity model. Specifically, for a majority of
these cases, the timing of these star formation bursts is identified to occur
within a timeframe spanning $0.3$ to $0.7$ Gyr.

Another aspect that indicates a bursty SFH is from the specific star formation
rate, defined as

$\text{sSFR}=\frac{\text{M}_{\text{formed}}(<t)/t}{\text{M}_{*}},$ (5)

where $\text{M}_{\text{formed}}$ represents the mass formed within the past
$t$ years, and $\text{M}_{*}$ is the observed stellar mass of the galaxy. If a
galaxy formed all its mass within the past $t$ years, then
$\text{M}_{\text{formed}}=\text{M}_{*}$, neglecting any stellar mass loss
through stellar evolution processes, resulting in a maximum sSFR of
$\text{sSFR}=(1/t)$.

We utilise Bagpipes to derive the sSFR both spectroscopically and
photometrically. The majority of our sample display higher values of
photometrically derived $\log_{10}(\text{sSFR})$ compared to the
spectroscopically derived values, with the most significant discrepancy being
11% observed in both the CEERS and JADES samples. Furthermore, in Figure 5, we
show $\log_{10}(\text{sSFR})$ for our samples derived from Bagpipes
spectroscopic fitting under 10 Myr and 100 Myr SFR timescale. Most galaxies
attain the maximum $\log_{10}(\text{sSFR})$ value of $\log_{10}(1/t)=-8$ using
a 100 Myr SFR timescale. This implies that most galaxies are consistent with
forming most of their stars within the past 100 Myr. Additionally, we also
find $45\%\pm 20\%$ of JADES galaxies and $34\%\pm 11\%$ of CEERS galaxies
formed 30% of their total mass within the past 10 Myr. In addition, from this
10 Myr timescale model, two CEERS samples achieve a $\log_{10}(\text{sSFR})$
value of $-7$, suggesting they formed their entire stellar mass within this
period, while two JADES galaxies reach $-7.2$, indicating approximately 60% of
their stellar mass was formed during the past 10 Myr, both signifying periods
of intense star formation. These observations underscore the bursty nature of
star formation in the last few million years for these galaxies. A comparative
analysis using a 5 Myr SFR timescale does not produce results significantly
different in sSFR from those obtained with a 10 Myr SFR timescale, indicating
a relatively stable star formation rate across these two timescales.

Figure 3: Comparison of SFR derived from spectroscopic and photometric
Bagpipes fitting for 43 galaxies using a 100 Myr SFR timescale. That is the
measured SFR using the same way with the same code, but one axis shows the
photometric values while the other the spectroscopic results. We find a
correlation coefficient of $0.64^{+0.15}_{-0.22}$ and that 80% of the galaxies
have SFRs in the range $[0.3,3]\,\mathrm{M}_{\odot}\,\mathrm{yr}^{-1}$. Figure
4: Comparison of SFR derived from H$\beta$ lines and UV luminosity for 25
galaxies exhibiting H$\beta$ lines under dust free assumption. 68 % galaxies
have higher H$\beta$ derived SFR values than that obtained using the UV
luminosity method, with a factor up to $2.4-13.5$. Figure 5: Comparison of
$\log_{10}(\text{sSFR})$ derived from Bagpipes spectroscopic fitting for two
distinct SFR timescales: 10 Myr (top) and 100 Myr (bottom). In the 100 Myr SFR
timescale graph, 61% of CEERS galaxies and 73% of JADES galaxies reach the
$\log_{10}(\text{sSFR})=-8$ limit, suggesting these galaxies formed their
entire stellar mass within the past 100 Myr. Conversely, in the 10 Myr graph,
only 2 galaxies from both CEERS and JADES achieve $\log_{10}(\text{sSFR})=-7$
limit. This evidence advocates for the appropriateness of a 10 Myr timescale
over a 100 Myr timescale, especially in light of bursty star formation
patterns observed in recent million years.

####  3.2.6 Dust attenuation and Star Formation Rate

It is crucial to emphasize the dust correction factor used in our SFR
measurements across different methodologies, as well as when we do and do not
use it. As mentioned, we employ three methods to derive SFR measures: this
includes the measurements from the Bagpipes code, SFR derived from UV
luminosity with dust corrections, and SFR calculated from the H$\beta$ line
luminosity. Dust attenuation effects are only considered for the SFR derived
using the first two methods, assuming a (Calzetti et al., 2000) dust
attenuation model.

Specifically, Bagpipes fitting applies this dust law to derive $A_{\text{V}}$,
representing the attenuation in the V-band. In contrast, when calculating SFRs
via the UV luminosity method, we utilize the same dust model but determine
$A_{\text{UV}}$ using the formula by Meurer et al. (1999):
$A_{\text{UV}}=4.43+1.99\beta$. Essentially this formula allows us to
determine the dust extinction in the UV by measuring the UV slope $\beta$,
which we do using methods outlined in Austin et al. (2023). It is worth noting
that the dust law from Meurer et al. (1999) is primarily tailored for $z\sim
4$ galaxies and thus may not be directly applicable for our sample at $z>7$.
We chose to use it in the absence of a currently widely accepted dust
attenuation law for high-redshift galaxies. A comprehensive discussion
regarding this choice can be found in Austin et al. (in prep). One way that we
can see this problem is that some of the values for the $A_{\text{UV}}$ are
actually negative using this method, which is meaningless in this context.

Considering the potential unsuitability of the Meurer et al. (1999) dust
attenuation relation for our high-redshift samples, it is essential to gauge
its influence. We address this by comparing the dust-corrected SFR values
derived from UV luminosity with those derived from Bagpipes. As the UV
luminosity method computes the SFR over an approximate 100 Myr timescale,
assuming a lognormal SFH, we adhere to the same parameters in our Bagpipes
fits. In addition, while both methodologies employ the Calzetti et al. (2000)
dust model, their applications differ. The UV luminosity method calculates the
attenuation $A_{\text{UV}}$ in the UV band, whereas Bagpipes determines the
attenuation $A_{\text{V}}$ in the V band. To ensure a consistent comparison we
convert the UV luminosity’s dust correction factor from $A_{\text{UV}}$ to
$A_{\text{V}}$, accounting for the discrepancies in dust attenuation between
the two methods. This conversion leverages the relationship
$A_{\text{UV}}/A_{\text{V}}=S$, with $\log_{10}{S}=0.40$ (Salim & Narayanan,
2020).

After these SFR values measured using both methods are aligned in terms of the
same dust correction factor ($A_{\text{V}}$), we can assess the potential
discrepancies between the two. The comparison of SFR derived from these two
methods is shown in Figure 6. Yellow points in this figure indicate galaxies
with negative $A_{\text{UV}}$ and, consequently, $A_{\text{V}}$ values. For
our analyses, we treat these negative values as zero - implying that these
galaxies are ‘dust free’. We will further elaborate on the rationale and
implications of this decision in the subsequent paragraph. From this figure,
we find the correlation coefficient is $\sim 0.7$. This discrepancy, resulting
from the application of the dust attenuation relation in the UV luminosity
method, underscores the necessity for a refined scaling relation, which will
likely bring the correlation coefficient closer to equality, assuming that
this dust measurement method is the culprit.

Building upon the above discussion, we detail the values of $A_{\text{UV}}$
and $A_{\text{V}}$ utilised in our study to appreciate the scale and
implications of our dust corrections. By employing the dust scaling relation
from Meurer et al. (1999) to determine $A_{\text{UV}}$ and hence
$A_{\text{V}}$, we find that 55% of JADES samples and 73% of CEERS samples
exhibit negative $A_{\text{V}}$ values. These negative values indicate both an
absence of dust corrections and issues with calibration; consequently, they
are reset to zero. This is due to the very blue nature of the SEDs of these
high-redshift galaxies. These are bluer than the systems that were used to
calibrate the Meurer relation. The comparison between
$\mathrm{A}_{\mathrm{V}}$ derived from UV $\beta$ slope and Bagpipes is shown
in Figure 7. Among the galaxies that have positive $A_{\text{V}}$ values
derived from the UV $\beta$ slope, most of the JADES and CEERS sample exhibit
$A_{\text{V}}$ values below 0.5, with a median value of 0.10. Taking into
account that 68% of total samples exhibit negative $A_{\text{V}}$, this
suggests that even for the cases with accurate dust attenuation correction,
the magnitude of the necessary correction is typically modest. This conclusion
is also shown in Figure 6, where there are no discernible observations showing
that the dust-corrected UV SFR deviates from the uncorrected samples.

Our findings underscore the importance of a refined dust scaling relation for
high redshift samples. New UV dust scaling relations are being developed, and
are needed to make progress on this front. For instance, a comprehensive
cosmological hydrodynamical simulation of dust attenuation is presented in
Wilkins et al. (2018). Moreover, a promising technique to recover the dust
content of galaxies using machine learning methods is being explored (Fu et
al. 2023, in prep). Concurrently, a new empirical relation is also under
construction (Austin et al. 2023, in prep).

Figure 6: Comparison of the SFR determined from UV luminosity to those derived
via Bagpipes spectroscopic fitting, using log-normal SFH and a 100 Myr SFR
timescale. We convert the UV luminosity dust attenuation from $A_{\text{UV}}$
to $A_{\text{V}}$ to ensure consistency in the dust attenuation factor with
Bagpipes. Yellow points represent galaxies with negative $A_{\text{UV}}$,
which is physically meaningless and are thus set to $=0$ (dust-free). Overall,
the correlation coefficient is $\sim 0.7$, although an ideal correlation would
yield a value of 1. This discrepancy stems from the erroneous $A_{\text{UV}}$
value we calculated, using the scaling relation from Meurer et al. (1999),
which is only applicable at lower redshifts ($z\sim 4$). Figure 7: Comparison
of $A_{\mathrm{V}}$ values obtained from Meurer et al. (1999) and those
determined through spectroscopic fitting using Bagpipes. Points marked in
yellow represent negative $A_{\mathrm{V}}$ values as per Meurer et al. (1999),
which we reset to zero (dust free). These instances constitute 55% of the
JADES samples and 73% of the CEERS samples. The best-fit line for data points
with positive $A_{\mathrm{V}}$ values yields a gradient $m=0.24\pm 0.02$. The
1$\sigma$ scatter of the residuals, defined as the differences $x-y$, is
measured to be 0.79, indicating high scatter.

####  3.2.7 Relations of SFR, Mass and Redshift

In this section we aim to determine the relationship between SFR, masses, and
redshifts for our samples. To illustrate our findings, we have created several
figures.

Figure 8 presents the plot of SFR versus stellar masses, derived from Bagpipes
using a short 10 Myr SFR timescale. This is compared with the results from the
FLARES simulation (Wilkins et al., 2022) and the main sequence relations at
$z\sim 2$ (Iyer et al., 2018) and $z\sim 6$ (Santini et al., 2017). Our
findings are in close alignment with these three established studies. We
determine a best-fit line, represented by $y=0.61x-4.49$, and find that the
1$\sigma$ scatter of the residuals is 0.43, indicating low scatter. Although
the gradient of our best-fit line is less steep than those found in the
aforementioned studies, it should be noted that this discrepancy may be
attributable to bias in the selection of our sample.

We present two sets of scatter plots that illustrate the relationships among
SFR, stellar masses, and redshifts, as shown in Figure 9 and Figure 10. Each
set contains two sub-plots: in the left sub-plot, the SFR is calculated using
H$\beta$ line emission and UV luminosity, while the stellar mass is derived
using Bagpipes. In the right sub-plot, both the SFR and stellar mass are
determined via Bagpipes. We subsequently compute the ratio
$\mathrm{SFR_{\mathrm{H}\beta}}/\mathrm{SFR_{\mathrm{UV}}}$ for the left plot,
and $\mathrm{SFR}_{\mathrm{10Myr}}/\mathrm{SFR}_{\mathrm{100Myr}}$ for the
right plot, for further analysis. Dust corrections are only considered in the
Bagpipes case.

From the right panel (derived SFR using Bagpipes) of Figure 9, it is evident
that more massive galaxies generally exhibit comparable SFR values derived
from both 10 Myr and 100 Myr timescales, consistent across all redshifts in
our samples. This demonstrates the absence of a significant recent burst in
SFR for high-redshift galaxies that are more massive
$\log_{10}(\text{M}_{*}/\text{M}_{\odot})>8.6$. However, this observation is
not mirrored in the left panel which might be largely attributable to the
absence of a dust attenuation correction for the SFR derived from UV and
H$\beta$ luminosity. If an accurate dust scaling relation for UV luminosity is
developed, then we expect the left result to be similar to the right.

From Figure 10, we find that the
$\text{SFR}_{10\,\text{Myr}}/\text{SFR}_{100\,\text{Myr}}$ ratio is higher on
average for galaxies with a lower SFR as determined by the 100 Myr timescale.
The results from this figure’s left and right images support this observation.
This underscores the recent bursty star-formation patterns, and such bursty
star formation histories are particularly pronounced in younger and less
massive galaxies, aligning with the findings of Looser et al. (2023).
Furthermore, we do not observe any significant correlations between redshifts
and either stellar mass or SFRs for our sample galaxies in the range
$z_{\text{spec}}=7-13.2$. This suggests that galaxies within this high-
redshift interval may exhibit a diverse range of behaviors.

Figure 8: Plot of SFR from Bagpipes with a 10 Myr timescale versus stellar
masses. Results from the FLARES simulation with a 10 Myr timescale and main
sequence relation at $z\sim 2$ (Iyer et al., 2018) and $z\sim 6$ (Santini et
al., 2017) are also shown. The best-fit line is characterized by $0.61\pm
0.01$. Despite the slightly lower gradient in our results, close agreement
with these established studies is observed. Figure 9: Scatter plots depicting
the relationship between stellar masses and the redshift, with color coding
representing the SFR ratio (10 Myr / 100 Myr) values. Stellar masses are
derived from Bagpipes in both plots. The left plot showcases the SFR
calculated using the H$\beta$ line emission and UV luminosity methods, while
the right plot displays the SFR as determined by Bagpipes over 10 Myr and 100
Myr timescales. Only the Bagpipes-derived SFR adopts a dust correction factor.
The left figure has fewer data points because not all galaxies exhibit an
H$\beta$ emission line (26/43). As can be seen from the right plot, galaxies
with higher masses tend to have more comparable SFR derived between 10 Myr and
100 Myr timescales. Figure 10: Plots akin to Figure 9, but with the y-axis
representing the SFR ratio and the x-axis displaying the average SFR over a
100 Myr timescale, while the color denotes redshifts. The SFR ratio is more
noticeable for galaxies with lower average SFR during the past 100 Myr.

###  3.3 Emission Line Characteristics

We investigate the emission line attributes in the four distinct JADES
galaxies that prominently display strong H$\beta$ $\lambda 4861$, [O iii]
$\lambda 4959$, and [O iii] $\lambda 5007$ emission lines, using the specutils
package (Astropy-Specutils Development Team, 2019). These lines, within the
NIRSpec wavelength range coverage, exhibit the strongest S/N ratio compared to
other potential lines. Our choice of these galaxies is informed by two primary
factors. Firstly, these JADES galaxies have longer NIRSpec exposure times than
the CEERS galaxies, leading to a superior S/N ratio. Secondly, of the 13 JADES
galaxies with $z_{\text{spec}}>7$, two systems are without NIRcam images, and
4 (at $z$ = 10.3 - 13.2) are identified as metal-poor galaxies (Curtis-Lake et
al., 2022). Among the remaining 7, only 4 of these galaxies distinctly exhibit
the aforementioned three emission lines. The associated spectra for these
galaxies are laid out in Appendix A, and Table 3 shows the line flux and
equivalent width (EW) of these three lines.

To compare the spectra of these systems with their photometry we attempt to
estimate equivalent widths from the photometry. This is a technique to learn
about galaxy emission lines without spectra, something which has been done
using Spitzer photometry to determine properties of high redshift galaxies
(e.g., Smit et al., 2016). To test this idea using JWST data we compare the
sum of the equivalent widths for these three lines as derived
spectroscopically with their photometric counterparts. The computation of
photometric equivalent widths hinges on the differential broad-band
magnitudes, specifically between the bands featuring emission lines and those
devoid of them. The aggregate equivalent width inherent within the band
harboring emission lines can be mathematically expressed as:

$\Delta\text{m}=-2.5\log\left(1+\frac{\text{EW}_{\text{Sum}}(1+z)}{\text{Bandwidth}}\right),$
(6)

where $\Delta m$ is the magnitude differences between the filter band with
emission line and the continuum, ’Bandwidth’ represents the width of the band
that includes the emission lines, $\text{EW}_{\text{Sum}}$ represents the
cumulative equivalent width of all emission lines within that filter band. A
detailed introduction of this equation is in Duncan et al. (2023); Mármol-
Queraltó et al. (2016). This formula succinctly captures the incremental
contribution of the emission line to the overall flux of the band. Among our
four JADES galaxies, two display emission in the F444W band, using the F410M
band as continuum. The other two show emission in the F410M band, with F356W
band serving as the continuum.

Figure 11 presents a comparative analysis of the sum of the EW of H$\beta$
$\lambda 4861$, [O iii] $\lambda 4959$, and [O iii] $\lambda 5007$ lines as
determined through both photometric and spectroscopic techniques. To ensure a
comprehensive study, we incorporate all JADES galaxies at $z\approx 3$ that
display these three emission lines in the F200W filter. Additionally, six
JADES galaxies at $z\approx 6$ with these lines detected in the F335M filter
are also included. The gradient of the line of best fit for all samples is
$0.49\pm 0.11$, indicating a moderate agreement between the results obtained
from both spectroscopic and photometric approaches. Generally, the photometric
method yields sums of EW that are about $30\%\pm 20\%$ lower compared to those
derived spectroscopically. We attribute this discrepancy to a potential
overestimation of the photometric continuum, leading to diminished EW
measurements. While the spectroscopic spectra are uncontaminated, there can be
sources of contamination in the photometric data. One possible cause is the
assumption that the continuum in the spectrum is flat within the filter band’s
wavelength range; however, spectra can display various shapes across these
wavelengths. In addition, the presence of noise in the spectra can directly
influence the size of the continuum, thereby affecting the spectroscopic EW
values.

Among the four $z>7$ JADES galaxies, those with the presence of the three
specific emission lines in the F410M medium band (indicated by blue stars in
Figure 11) exhibit more precise photometrically-derived EW values in
comparison to galaxies with emission lines in the wide band (F444W). However,
this conclusion does not hold as strongly for the $z\approx 3$ samples, which
have emissions in the F200W wide band. We believe that the primary underlying
factor is still the detection of the continuum. From the spectra of the
$z\approx 3$ samples, the continuum is clearly observable and detectable. In
contrast, for the four high-redshift samples, the continuum is hardly
discernible, as evidenced in Appendix A. As a result, when deriving the
spectroscopic EW, the continuum introduces uncertainty, leading to deviations
from its photometric counterparts. Given the above considerations, some
caution should be used when measuring and interpreting EW measurements from
broad-band photometry, especially for galaxies with high EW emission lines.

Finally, we compare our results with Withers et al. (2023), which studies the
sum of the EWs of the same emission lines (H$\beta$ and [O iii]) for galaxies
at redshifts between $1.7$ and $6.7$, and find a good agreement with our
samples within this redshift range.

Table 3: NIRSpec Emission Line Measurements for Four JADES Galaxies: Fluxes and equivalent widths (EWs) for H$\beta$ $\lambda 4861$, [O iii] $\lambda 4959$, and [O iii] $\lambda 5007$ are detailed. Intriguingly, for each galaxy, the ratio of line fluxes does not align with the ratio of their corresponding EWs. This discrepancy may arise from the continuum. The continuum surrounding these emission lines for the four galaxies is scarcely detectable, hence influencing the derived values. NIRSpec ID | $z_{\text{spec}}$ | H$\beta$ $\lambda 4861$ | [O iii] $\lambda 4959$ | [O iii] $\lambda 5007$ | H$\beta$ | [O iii] $\lambda 4959$ | [O iii] $\lambda 5007$
---|---|---|---|---|---|---|---
|  | Line Flux | Line Flux | Line Flux | EW | EW | EW
|  | $(10^{-20}\text{ erg s}^{-1}\text{ cm}^{-2})$ | $(10^{-20}\text{ erg s}^{-1}\text{ cm}^{-2})$ | $(10^{-20}\text{ erg s}^{-1}\text{ cm}^{-2})$ | (Å) | (Å) | (Å)
8013 | 8.473 | $20.59\pm 2.38$ | $34.53\pm 2.83$ | $93.54\pm 6.80$ | $160.3\pm 72.3$ | $341.9\pm 67.4$ | $1102.6\pm 66.3$
21842 | 7.98 | $35.40\pm 3.13$ | $64.78\pm 3.54$ | $184.81\pm 3.76$ | $278.1\pm 76.1$ | $620.8\pm 66.7$ | $1950.4\pm 67.4$
20961 | 7.045 | $46.91\pm 8.34$ | $41.97\pm 6.57$ | $105.04\pm 5.40$ | $18.3\pm 133.1$ | $12.2\pm 92.5$ | $315.8\pm 83.5$
10013682 | 7.275 | $10.10\pm 2.34$ | $25.06\pm 3.11$ | $61.44\pm 3.48$ | $81.4\pm 57.4$ | $351.8\pm 71.4$ | $1039.8\pm 70.3$
Figure 11: Comparison of the sum of EWs calculated using photometric and
spectroscopic methods. The sum represents the combined values of H$\beta$
$\lambda$4861, [O iii] $\lambda$4959, and [O iii] $\lambda$5007\. The red and
blue colors denote the emissions from these three lines in wide and medium
filter bands, respectively. Galaxies at different redshifts are labelled with
circles, diamonds, and stars for $z_{\text{spec}}\sim 3,6,\text{ and }>7$ ,
respectively.

###  3.4 Morphological and Photometric Size Effects from Line Emission

In our study of the line-emitting sample, we note that the photometric fluxes
in line-emitting bands are sometimes stronger than neighboring bands. This
brightness can likely be attributed to line emission, as discussed in the
previous section. Our primary inquiry in this section is to discern the impact
of this line emission on the morphological attributes of galaxies. This is
achieved by subtracting and subsequently analyzing the residuals from bands
that exhibit line emissions in contrast to those that do not.

A particular focus of our examination are the emission lines
$\text{H}\beta\,\lambda 4861$, $[\text{O}\textsc{iii}]\,\lambda 4959$, and
$[\text{O}\textsc{iii}]\,\lambda 5007$, evident in four high-redshift JADES
galaxies as discussed in Section 3.3. Of these galaxies, two display the lines
in the F444W band (NIRSpec ID: 8013, 21842), while the others do so in the
F410M band (NIRSpec ID: 20961, 10013682). To delineate further, the F410M and
F356W bands act as the continuum for these sets respectively. We use these as
the continuum as they are the bands closest to those with emission lines,
without themselves having emission lines present. Thus, our dataset
encompasses two galaxy sets, each offering data from a pair of filter bands –
one with emission lines present and its counterpart containing only the
continuum. These can be subtracted from each other to show the location of the
line emission spatially.

Our methodology of subtraction is very similar to that used in Hatch et al.
(2013), whereby essentially the line emission structure is found by
subtracting a normalised image which contains no lines from the image in the
filter where line emission exists. The idea is that the residuals show the
distribution of the gas which produces the line emission. To do this we carry
out a background subtraction for each image. We do this by masking each galaxy
and other galaxies in each image, we then derive the median value for the
background level, which is then subtracted from each image. This is followed
by the normalization of every galaxy image set, this is a critical step as we
have to ensure that all the continuum light is removed from the band with the
line emission to reveal that underlying emission. To do this we use an
aperture of consistent size across the frames (154 pixels roughly the size of
all our galaxies) for each of the galaxies within these images, we compute the
total flux within this aperture. The image with the highest flux summation is
used for normalization, from which the normalization constants for other
images are determined. The latter is accomplished by dividing the flux
summation by their individual flux sums. These constants are then multiplied
with the background-subtracted images, resulting in images that are both
normalized and devoid of background.

We used this procedure on individual galaxies, however, when this was carried
out no single galaxy was found to show line emission that could be detected.
Therefore, we concluded that stacking of these images was potentially a way to
retrieve a signal. To do this for every galaxy set, a weighted stack of these
images – both emission and continuum – is created. This involves calculating
the standard deviation of the background noise for each image and subsequently
assigning weights to each, based on the inverse of the noise standard
deviation. The final stacked image is constructed by achieving a weighted flux
sum and then dividing this by the total weight (the sum of the weights of all
images). This procedure is executed separately for the emission and continuum
images of every galaxy set.

To ensure the consistency of the PSF with the F444W band, we employ a two-step
process involving the convolution of emission and continuum images with their
respective PSF kernels. The PSF models for our bands are generated using
WebbPSF (Perrin et al., 2012; Perrin et al., 2014). The kernels for this
convolution are derived using pypher (Boucaud et al., 2016). These kernels are
designed such that when convolved with the PSFs of their specific bands
(either emission or continuum), the resultant PSFs are then such that they
match that of the F444W band. Due to the emission and continuum residing in
different bands, two distinct kernels were crafted and applied for the
convolution. After this, the continuum images are subtracted from the emission
ones, effectively revealing the location of the material producing the line
emission. This assumes that the underlying continuum light in the emission
line band is similarly distributed at similar wavelengths. We test this with
measuring the flux below and find a good agreement, revealing that we are
indeed retrieving the line emission. Notably, this emission is accentuated in
the galaxy set associated with the F410M band as the emission band, as
depicted in Figure 12. To quantify the flux of the line emission, eight equal-
area apertures are positioned around the emission domain, and the flux sum
within these is computed. Through the standard deviation of these sums, we
deduce that the core line emission flux sum is elevated at $\sim 11\sigma$
above the background threshold.

We use these normalization constants to scale the photometric fluxes we
measure. Upon analyzing the photometric line flux of this region, as revealed
in this image, we obtain a flux measurement of $(203.4\pm 36)\times
10^{-20}\,\text{erg/s/cm}^{2}$. This closely aligns with the direct line flux
measurements (the sum of the lines in the galaxies stacked), which is found to
be $(247.01\pm 12.86)\times 10^{-20}\,\text{erg/s/cm}^{2}$, as reported by the
JADES team for the same lines in the same galaxies (Bunker et al., 2023). This
is a strong indication that we are indeed seeing the spatial extent of the
line emission for these systems, and not as a result of a colour gradient or
stellar continuum excess at the emission line band wavelength.

Furthermore, to measure the structure of this line emitting gas we employed
the GALFIT software (Peng et al., 2002, 2010) for a detailed morphological
analysis. The radii and Sérsic indices of the two galaxies (NIRSpec ID: 20961,
10013682) across different filter bands are presented in Table 4. The
photometric band with the stacked line emission has a fitted radius of
$0.61\pm 0.02$ kpc and a Sérsic index of $n=$ $0.27\pm 0.09$. These values
align with the average dimensions of the corresponding galaxies in their
individual emission bands. Moreover, as emphasized in Table 4, the size of the
galaxy gaseous region is slightly larger than stellar contributions, but the
errors on these measurements are quite large. Therefore, we can only conclude
with this information that the sizes of the emission line regions are
statistically similar to the continuum size. However, the Sérsic index for the
line emission image is much lower than for the galaxy continuum images that go
into the stack, showing that it is perhaps less concentrated (diffuse) than
the stellar light itself.

Lastly, we measure the sizes of the four JADES galaxies with emission lines
that overlap in wavelength with the NIRCam filters using GALFIT. After
visually inspecting the sizes in these bands, we discard any data exhibiting
notably high uncertainties or large $\chi^{2}_{\text{reduced}}$ values. The
final results are found in Figure 13. Notably, we identified a consistent
pattern, mirroring findings from the stacked data: bands exhibiting line
emission consistently display a slightly larger size relative to those of the
continuum bands, with the exception of NIRSpec ID: 10013683. It is not clear
why in that particular case the sizes are not as large. We do note that in
this galaxy, however, we find the weakest emission lines amongst these four
systems, which may be the reason.

Figure 12: Line emission image obtained by subtracting the stacked continuum-only images from the stacked emission images for the subset of galaxies exhibiting emission lines in the F410M band (NIRSpec ID: 20961, 10013682). A pronounced line emission detection, registering $11.08\sigma$ above the background, is clearly visible, with a possible distinct shape. Table 4: Morphological parameters for two JADES galaxies and the attributes of their stacked images are detailed. The stacked residual is calculated by subtracting the Stacked Continuum from the Stacked Emission, highlighting the contribution from gas emission. The uncertainties associated with the radius and Sérsic Index derived from GALFIT are purely statistical, and do not represent physical errors. Galaxy | Band | Radius (Kpc) Error | Sérsic Index
---|---|---|---
20961 | Emission | $0.48\pm 0.01$ | $0.59\pm 0.10$
20961 | Continuum | $0.41\pm 0.01$ | $0.31\pm 0.11$
10013682 | Emission | $0.73\pm 0.64$ | $0.05\pm 0.29$
10013682 | Continuum | $1.87\pm 0.25$ | $1.03\pm 0.50$
Stacked Emission | Emission | $0.66\pm 1.14$ | $0.03\pm 0.2$
Stacked Continuum | Continuum | $0.49\pm 1.87$ | $0.05\pm 0.72$
Stacked Residual | Line Emission | $0.61\pm 0.02$ | $0.27\pm 0.09$
Figure 13: Size comparisons of four JADES galaxies with prominent emission
lines. To the right of each individual galaxy plot, the average representative
radius error for each galaxy is displayed, while each point on the plots
indicates the radius that minimises the $\chi^{2}_{\text{reduced}}$ value. We
discard any data exhibiting notably high uncertainties or large
$\chi^{2}_{\text{reduced}}$ values. Typically, the band with the emission line
shows a larger radius compared to other filter bands. This implies an extended
gas emission region around these galaxies that extends beyond their star-
forming regions. The errors are statistically derived from GALFIT and do not
necessarily represent physical uncertainties, and are lower limits.

##  4 Discussion

Our results show that photometric quantities are fairly good at representing
the properties of galaxies that can be derived through spectroscopy. This is
under the assumption however, that the quantities we derive from spectroscopy
are standard ’correct’ values. Whilst this is true for the spectroscopic
redshift which is very unlikely to be ambiguous or wrong, this is not
necessary the case for star formation and stellar mass, which we discuss
below. Even the measurement of line fluxes for SFR values can be incorrect,
despite the common lore that these values are better than others. It is
especially not clear if the measurements of stellar mass and star formation
rates are better measured spectroscopically than with photometry. Under the
same assumptions about the underlying process for fitting, that is the same
code and same star formation history models, we find that galaxy properties
are within 60 % the same between measurements done with the photometry and
spectroscopy for $z>7$ galaxies. This is often below the typical random
uncertainty limits for these quantities from any measurements we can do now.

We have also shown in this paper that our methods for deriving photometric
redshifts using the EPOCHS methods (Adams et al., 2023a) reveal a good
agreement with spectroscopic redshift measurements. Obtaining reliable
photometric samples is crucial for subsequent spectroscopic redshift follow-
up. Given that spectroscopic redshifts are resource-intensive and expensive,
we cannot anticipate every galaxy to undergo a spectroscopic analysis due to
the associated costs. Consequently, the reliance on photometric redshifts
remains paramount for studying the broader galaxy population for the
foreseeable future. This dependence is underscored by the fact that these
photometric redshifts play a fundamental role in our analyses to decipher
evolutionary patterns across various fields. This includes datasets like the
PEARLS data (Windhorst et al., 2023) and the recent public releases from JWST.
Thus tests such as this one are critical for determining the quality of the
photometric redshifts as well as determining what fraction of high redshift
galaxies at $z>7$ would even be included in samples of distant galaxies with
photometric redshifts. One caveat to all of this, which we showed in this
paper, is that the spectroscopic samples from JADES and CEERS are quite
different in their underlying properties and these certainly are not
representative of the distant galaxy population. More full and complete
redshift surveys are needed at these redshifts to determine absolutely how
well photometric and selection methods work.

Beyond this we are finding that the gas properties, as measured through
emission lines, of these earliest galaxies can be measured with the comparison
of spectroscopy and photometry. This involves extracting the equivalent widths
of lines that are present within the photometric bands. This is the method of
finding fluxes or equivalent widths by using the excess in a filter over a fit
continuum. We find that this can be done; however, in some instances, the
equivalent widths derived from photometry are about $30\%\pm 20\%$ smaller
than those measured with spectroscopy. Our conclusion from this is that any
measurements made outside of spectroscopy should be carefully done when trying
to measure emission line properties from fluxes within filters.

We also show that new approaches towards understanding galaxy structure in
line emission at $z>7$ can be carried out by subtracting filters with emission
lines from those without emission lines to view the entire line emitting
structure. We carry this out on a limited sample here, showing that the
structure of the gas is slightly diffuse within galaxies. This is an
indication that this gas is perhaps not as concentrated as the stars, and
gives further evidence for an outside-in formation in these galaxies, assuming
that the line emission is produced from star formation events, which from line
ratios of these galaxies appears to be the case (Rinaldi et al., 2023; Sun et
al., 2023).

##  5 Conclusions

In this paper we investigate galaxies that have spectroscopy taken with
NIRSpec with JWST and are confirmed to be at $z>7$. Our primary sample is
those galaxies that have NIRSpec data taken as part of the JADES GTO and the
CEERS ERS data sets. Our primary goal is to use this spectroscopy and imaging
to determine how well photometrically derived quantities, using methods we
have developed, compare with those based on the more possibly reliable
spectroscopic measurements. Our findings include:

I. We find that there is an excellent agreement in the comparison of
photometric redshifts to spectroscopic redshifts using the EAZY code. Only two
galaxies are classed as outliers within the full sample of 43 galaxies. We
also discuss in this paper which galaxies in the spectroscopic sample would
not be selected using normal procedures for finding high-z galaxies depending
on their properties.

II. We find a correlation coefficient $r\sim 0.60$ between the stellar masses
derived both photometrically and spectroscopically, and a similar correlation
for the SFR, using exactly the same Bagpipes setup to measure both. The
moderate agreement between results obtained from these two methods underscores
the accuracy of the photometric method, given the assumption that
spectroscopically derived values are correct.

III. By comparing the star formation rate measurements for our galaxies using
the H$\beta$ line and UV luminosity, we find that there is a ’mismatch’ in the
spectroscopic properties of the galaxies compared to those derived through
photometry. In nearly all cases we find a systematically higher star formation
rate (range from ratios of 2.4 to 13.5) as derived through the spectroscopic
line fluxes than we get from the photometry itself. This is an indication that
the star formation rate is increasing with time, as the H$\beta$ is measuring
more recent star formation.

IV. Furthermore, we find that using broad-band filters to measure emission
line equivalent widths is possible, but can lead to high uncertainties and
possible underestimates by $30\%\pm 20\%$. Thus, any measurements of line
fluxes or equivalent widths using these filter sets should be done with some
caution.

V. We also use a new method to find the spatial distribution of the line
emission by subtracting NIRCam filter with and without emission lines present.
Using this method we find that there are no detections of line emission in the
individual subtracted images of these galaxies. However, a stacked version of
this method with several galaxies finds a significant detection from which we
show that the line emission has a spatial distribution similar to the
continuum light.

VI. We measure the morphological and structural properties (size and Sérsic
indices) of this sample of galaxies as a function of wavelength in the broad-
band and medium-band filters. We find that in three out of four cases the
sizes of these galaxies are slightly larger in the bands that contain the
emission lines compared to neighboring bands which are emission line free.
This gives some indication that perhaps the line emission is slightly more
extended or less concentrated than the older stellar population. However, when
we subtract off the continuum from the bands with emission lines we find that
statistically the sizes of the emission region are similar to the size of the
continuum light.

Overall, we have shown in this paper that the use of photometry to measure
galaxy properties is a reliable method of measuring photometric redshifts,
stellar masses (or mass to light ratios) and star formation rates. There are
slight differences with spectral derived properties and these should be taken
into account when trying to calibrate an absolute scale for star formation and
stellar mass histories of galaxies which have been derived based on
photometry. In the future, it is clear that more general spectroscopy is
needed for early galaxies where tests like these can be done over a broader
range of intrinsic properties.

## Data Availability

Some of the data underlying this article is made available by Adams et al.
(2023c), and the DAWN JWST Archive (DJA). The remainder of the data set will
be released together with Conselice et al. (2023, in prep). The catalogues of
the sample discussed herein may be acquired by contacting the corresponding
author.

## Acknowledgement

We thank Elizabeth Stanway for suggestions and thoughts on comparing spectral
energy distribution models. We acknowledge support from the ERC Advanced
Investigator Grant EPOCHS (788113), as well as a studentship from STFC. LF
acknowledges financial support from Coordenação de Aperfeiçoamento de Pessoal
de Nível Superior - Brazil (CAPES) in the form of a PhD studentship. DI
acknowledges support by the European Research Council via ERC Consolidator
Grant KETJU (no. 818930). CCL acknowledges support from the Royal Society
under grant RGF/EA/181016. CT acknowledges funding from the Science and
Technology Facilities Council (STFC). This work is based on observations made
with the NASA/ESA Hubble Space Telescope (HST) and NASA/ESA/CSA James Webb
Space Telescope (JWST) obtained from the Mikulski Archive for Space Telescopes
(MAST) at the Space Telescope Science Institute (STScI), which is operated by
the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST, and NAS 5–26555 for HST. Some of the data
products presented herein were retrieved from the Dawn JWST Archive (DJA). DJA
is an initiative of the Cosmic Dawn Center, which is funded by the Danish
National Research Foundation under grant No. 140. This research made use of
the following Python libraries: Numpy (Harris et al., 2020); Scipy (Virtanen
et al., 2020); Matplotlib (Hunter, 2007); Astropy (Astropy Collaboration et
al., 2013, 2018, 2022); EAZY-PY (Brammer et al., 2008); LePhare (Arnouts et
al., 1999; Ilbert et al., 2006); Bagpipes (Carnall et al., 2018); mpi4py
(Dalcin & Fang, 2021); specutils (Astropy-Specutils Development Team, 2019);
Pickle (Van Rossum, 2020).

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##  Appendix A JADES galaxies Spectrum and Sizes

In this appendix, we present the spectra of four selected JADES galaxies
referenced in Sections 3.3 and 3.4. Each figure displays both the simulated
and observed photometric flux for each band, with all emission lines labeled.
Notably, out of these four galaxies, three exhibit solely the H$\beta$
$\lambda 4861$, [O iii] $\lambda 4959$, and [O iii] $\lambda 5007$ emission
lines. Additionally, we observe slit losses predominantly in the F090W band.
We attribute this discrepancy primarily to the F090W band lying blueward of
the Lyman break, causing a significant flux drop, especially for our sample
galaxies in the redshift range $z>7$, which makes the band highly susceptible
to noise domination.

Figure 14: Spectra of four JADES galaxies exhibiting prominent emission lines.
Red and blue points denote observed and simulated photometric fluxes,
respectively. We find that slit loss occurs only in the F090W band.
Additionally, three galaxies exhibit only H$\beta$ $\lambda 4861$, [O iii]
$\lambda 4959$, and [O iii] $\lambda 5007$. The relevant line flux and
equivalent widths of emission lines are shown in Table 3.