# EPOCHS Paper V. The dependence of galaxy formation on galaxy structure at
$z<7$ from JWST observations

Christopher J. Conselice,1 Justin T.F. Basham, 1 Daniel O. Bettaney,1 Leonardo
Ferreira,2 Nathan Adams,1 Thomas Harvey,1 Katherine Ormerod,1 Joseph
Caruana,3,4 Asa F. L. Bluck,5 Qiong Li,1 William J. Roper,${}^{{}^{6}}$ James
Trussler,1 Dimitrios Irodotou,7 Duncan Austin1
1 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,
Manchester UK
2 School of Physics and Astronomy, University of Victoria, Victoria, BC,
Canada
3 Department of Physics, University of Malta, Msida MSD 2080, Malta
4 Institute of Space Sciences & Astronomy, University of Malta, Msida MSD
2080, Malta
5 Stocker AstroScience Center, Department of Physics, Florida International
University, 11200 SW 8th Street, Miami, 33199, USA
6 Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH, UK
7 Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2,
FI-00014, Helsinki, Finland E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We measure the broad impact of galaxy structure on galaxy formation by
examining the ongoing star formation and integrated star formation history as
revealed through the stellar masses of galaxies at $z<7$ based on JWST CEERS
data from the Extended Groth Strip (EGS). Using the morphological catalog of
3965 visually classified JWST galaxies from Ferreira et al. (2023), we
investigate the evolution of stars, and when they form, as a function of
morphological type as well as galaxies classified as passive and starburst
through spectral energy distributions. Although disk galaxies dominate the
structures of galaxies at $z<7$, we find that these disks are in general
either ‘passive’, or on the main-sequence of star formation, and do not
contain a large population of starburst galaxies. We also find no significant
correlation between morphological type and the star formation rate or colours
of galaxies at $z<7$. In fact, we find that the morphologically classified
‘spheroids’ tend to be blue and are not found to be predominately passive
systems at $z>1.5$. We also find that the stellar mass function for disk
galaxies does not evolve significantly during this time, whereas other galaxy
types, such as the peculiar population, evolve dramatically, declining at
lower redshifts. This indicates that massive peculiars are more common at
higher redshifts. We further find that up to $z\sim 7$, the specific star
formation rate (sSFR) does not vary with visual morphology, but strongly
depends on stellar mass and internal galaxy mass density. This demonstrates
that at early epochs galaxy assembly is a mass-driven, rather than a
morphologically-driven, process. Quenching of star formation is therefore a
mass-dominated process throughout the universe’s history, likely due to the
presence of supermassive black holes.

###### keywords:

keyword1 – keyword2 – keyword3

††pubyear: 2024††pagerange: EPOCHS Paper V. The dependence of galaxy formation
on galaxy structure at $z<7$ from JWST observations–EPOCHS Paper V. The
dependence of galaxy formation on galaxy structure at $z<7$ from JWST
observations

##  1 Introduction

For nearly a century the process of galaxy formation and evolution has
remained one of the primary unsolved problems in astrophysics. These systems,
and the dark matter they contain, dominate the universe’s structure, and
therefore understanding them is a key part of our knowledge of how the
universe came to be. One basic question is: how (and when) do galaxies that we
see in the local universe form? This can be divided into other sub-questions,
including: when did various aspects of galaxies that we see in the nearby
universe come to be – such as their structure, morphology, and masses? Similar
studies have also been interested in uncovering the physical processes which
have driven galaxy evolution and formation since the initial onset of star
formation in the universe. In essence, the study of galaxy evolution is one of
the history of galaxy properties, and then using that information to determine
the physical driving mechanisms behind this observed formation (Bluck et al.,
2014; Conselice et al., 2014; Paulino-Afonso et al., 2017; Osborne et al.,
2020; Huertas-Company et al., 2023).

One aspect of this is the formation of the structures of galaxies. This can be
considered in a few ways, including the quantitative evolution of galaxies, as
well as morphological ‘type’ evolution (Conselice et al., 2003; Bluck et al.,
2012; Mortlock et al., 2013). This morphological and structural evolution of
galaxies can be viewed as the change in their resolved appearance and
structure over time (e.g., Mortlock et al., 2013; Conselice, 2020; Ferreira et
al., 2023; Jacobs et al., 2023; Margalef-Bentabol et al., 2022). These changes
are influenced by a variety of factors, including the effects of gravity,
merging, the presence of gas and dust, and the formation and subsequent
evolution of stars, given a still unknown initial mass function that may vary
with time (Trussler et al., 2022). All of these physical effects can drive and
change the morphologies and structures of galaxies, which can then be further
examined with quantitative tools (e.g., Bershady et al., 2000; Conselice et
al., 2003) or machine learning (Cheng et al., 2020, 2021; Euclid Collaboration
et al., 2023).

One of the major motivations for JWST is to understand how and when early
galaxy formation occurred. One of the main routes by which we can address this
is through the structural evolution of galaxies at high redshifts $z>3$.
Specifically on account of the finite speed of light, we are viewing and
imaging galaxies as they looked billions of years ago (e.g., Conselice, 2014;
Mortlock et al., 2015; Ferreira et al., 2022). By comparing these observations
with nearby galaxies we can determine how galaxies of different types have
changed throughout time. From the earliest galaxy studies astronomers have
been able to resolve these systems, and this has long provided information
about the history of the formation of these objects (e.g., Hubble, 1926).

A major factor in the structural evolution of galaxies is the process of
interactions and mergers with other galaxies. Over time, galaxies interact and
merge with each other, resulting in the formation of larger, and potentially
more complex structures that can have distinct morphological appearances
(e.g., Conselice, 2014; Mortlock et al., 2013; Duncan et al., 2019; Ferreira
et al., 2023; Huertas-Company et al., 2023). This process also triggers the
formation of new stars, AGN, and central massive black holes, and the
redistribution of matter within galaxies, changing appearances dramatically
(e.g., Conselice et al., 2003). Overall, the structural evolution of galaxies
is a complex process that is influenced and determined by most galaxy
formation processes. As galaxies form new stars and accrete matter they
continue to change and evolve over all of cosmic time.

JWST has now enabled us to investigate this problem at the highest redshifts,
whereby galaxy morphology in the rest-frame optical can now be examined up to
$z\sim 8$ (Ferreira et al., 2022, 2023; Fudamoto et al., 2022; Kartaltepe et
al., 2022). We can now look further into this problem, with this paper
representing the next step in the process following the initial determination
of morphological evolution of galaxies (e.g., Ferreira et al., 2022, 2023;
Fudamoto et al., 2022; Kartaltepe et al., 2022). One of the first major
discoveries with JWST was the finding that disk galaxies dominate the
morphology of galaxies all the way back to $z\sim 7$ or even to higher
redshifts (e.g., Ferreira et al., 2022; Treu et al., 2023). Before this
discovery, HST observations largely pointed to peculiars as being the most
common galaxy type at $z>1.5$ (e.g., Conselice et al., 2005). In fact, it is
now clear that there exists a large population of disk galaxies back to these
early times, which have also been found by other studies (e.g., Carnall et
al., 2022; Fudamoto et al., 2022; Kartaltepe et al., 2022; Jacobs et al.,
2022).

Whilst we now have a good idea of overall galaxy morphology as a function of
redshift, it is critical to investigate how galaxy formation up to $z\sim 8$
is driven by, or dependent on, galaxy structure and morphology. We know that
in the local universe there is a strong dependence of galaxy morphology on
star formation and stellar mass (e.g. Bluck et al., 2014; Thanjavur et al.,
2016). This correlation is such that systems classified visually as
ellipticals or spheroids are the most massive galaxies which contain the
lowest star formation rates (e.g., Conselice, 2006b; Kelvin et al., 2014).
When does this relationship between structure and physical properties become
established? This is now a question we can answer with JWST data, which has
provided rest-frame optical structural properties of these galaxies for the
first time at $z>3$ at a higher resolution than can be provided by any
previous telescope.

Previous to JWST we thought we had a good idea of how morphology and structure
evolve in terms of other galaxy physical properties, namely the star formation
rate and stellar masses. It was already clear even based on HST that does not
exist a strong correlation between the morphology of a galaxy and its past and
ongoing star formation rate at $z>1.5$ (e.g., Conselice et al., 2011; Tohill
et al., 2021; Papaderos et al., 2023). Investigations of this included looking
at how stellar mass correlates with morphology up to $z\sim 3$ using HST data
(e.g., Brinchmann & Ellis, 2000; Conselice et al., 2005; Bluck et al., 2022).
Within this paper, we investigate this process back to the earliest times we
currently can at $z<7$, using the best morphologies that we can currently
obtain with any telescope (Ferreira et al., 2023).

The paper is organized as follows. In § 2 we describe the data products we use
from previous work including the visual classifications. § 3 includes the
results from the analysis examining the structures of galaxies and how they
relate to star formation and stellar masses from $z=1.5$ to 7. In §4 we
discuss our results and what they imply for how galaxy formation occurs at
$z<8$ and we summarise our findings from this paper in § 5. Throughout this
paper when quanitites that require a cosmology are used (namely stellar masses
and star formation rates) we use a $\Lambda$-CDM cosmology ($H_{0}=70$
kms-1Mpc-1, $\Omega_{m}=0.3$ and $\Omega_{\Lambda}=0.7$). The values we use
for these quantities are calculated using this cosmology unless explicitly
stated otherwise. This is, the measured SFR and inferred stellar masses scale
as $h^{-2}$.

##  2 Data and Methods

This paper is one of series of papers from the EPOCHS survey, which is a
reduction and analysis of several deep JWST imaging and spectroscopy fields.
These fields include the early Release Observations of GLASS, JADES, CEERS,
and SMACS 0723, along with the PEARLS GTO Survey fields: El Gordo, MACS-0416
and the North Ecliptic Pole (NEP) (Windhorst et al., 2023). The data we use
are mostly from observations taken with the Near Infrared Camera of these
various fields. In this paper we utilise NIRCam JWST observations using our
bespoke reduction from the Cosmic Evolution Early Release Science Survey
(CEERS; ID=1345). Specifically, we use the part of this data that overlaps
with the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS;
Grogin et al. 2011; Koekemoer et al. 2011) 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 on-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. (2023); Adams et al.
(2023) and Conselice et al. (2024, in prep). Our reduction includes all of the
observed JWST bands, which includes F115W, F150W, F200W, F277W, F356W, F410W
and F444W. These bands are used in three different way thoughout this paper -
for redshfit measurements, stellar masses and star formation rates, as well as
for morphological measurements, both in fitting sizes as well as within visual
classifications.

Our analysis follows the same 3965 sources at $z>1.5$ taken from the CANDELS
catalogs, as explained in Ferreira et al. (2023). This remains at the time of
writing one of the largest catalogs of galaxy classifications at $z>2$ with
JWST. We use our well calibrated and robust photometric redshifts, star
formation rates, and stellar masses derived for these CANDELS data (Duncan et
al., 2014, 2019; Whitney et al., 2021) to conduct this analysis. We do not use
morphological information for the selection of sources. We also do not use
magnitude cuts, as we want to ensure that sources possibly faint in HST but
easily visible in the JWST observations are included.

As explained in Ferreira et al. (2023), two different approaches are used to
manage these data: first we perform visual classifications for all sources,
which is described in detail in Ferreira et al. (2023). We also carry out
quantitative structural measures through the code GALFIT (Peng et al., 2010b)
where parametric light profile fitting is carried out to measure sizes and
Sersic indices for our sample. See Ferreira et al. (2023); Ormerod et al.
(2024) for more descriptions of how these morphologies match with the
quantitative structural measurements.

###  2.1 Photometric Redshifts, Stellar Masses, and Star Formation Rates

The photometric redshifts we use in this paper originate from the redshifts
calculated in Duncan et al. (2019) for the Extended Groth Strip (EGS) field,
although these have been checked with new JWST-based photometric redshifts
using all the JWST bands mentioned above. We use the HST based one ultimately
as most of our galaxies are at lower redshifts, as well as to match the well
calibrate star formation rates and stellar masses we measure.

We use the photometric redshift software eazy (Brammer et al., 2008) for
template fitting of our SEDs, such that three separate template sets are used
and fit to the photometric bands. These templates include zero-point offsets
altering the input fluxes and fixing additional wavelength-dependent errors.
We also use with these redshifts a Gaussian process code (GPz; Almosallam et
al. (2016)) to measure further empirical estimates using a subset of our
photometric bands. Individual redshift posteriors are calculated, and all four
of these measurements are combined in a statistical framework via a
hierarchical Bayesian combination to create a final redshift estimate. For
these quantities we use all of the HST data in this field as well as Spitzer
and ground based imaging. This includes the bands F435W, F606W, F775W, F814W,
F850LP, F098M, F105W, F125W, F160W, while for Spitzer the 3.6 and 4.5 $\mu$m
bands, with the ground-based data including the CTIO U band, VLT/VIMOS U band,
VLT/ISAAC Ks and VLT/HAWK-I Ks data. For a more in-depth description of the
process, see section 2.4 of Duncan et al. (2019). We use the U-band and HST
based photometric redshifts as they cover most of the light where photometric
redshifts are sensitive to in the redshift ranges we are probing. However, as
a cross check we also examine how JWST based SEDs would differ from the ones
based on HST and find essentially no difference. All the results in this paper
remain the same using either version. At $z>3$ we find that the $\sigma_{\rm
NMAD}=0.12$ when comparing over all redshifts between the HST and JWST based
photometric redshifts.

These data used to measure these redshifts are calculated from the original
CANDELS+GOODS WFC3/ACS imaging and data, Spitzer/IRAC S-CANDELS (Ashby et al.,
2015), and ground-based observations with CFHT (Stefanon et al., 2017) as well
as with the JWST bands. The overall method for this is described in more
detail in Duncan et al. (2019). The redshifts that we use have a high accuracy
at the redshifts of interests, when compared with the spectroscopic redshifts
available within the EGS field (Duncan et al., 2019).

Our galaxy stellar masses are measured using a modified version of the
spectral energy distribution (SED) code which is described in detail in Duncan
et al. (2014). Using this code the stellar mass is measured at all redshifts
in the photo-$z$ fitting range. These masses also have what is called a
‘template error function’, described in Brammer et al. (2008) which accounts
for uncertainties driven by the template set and any wavelength effects.

The mass measuring technique uses Bruzual & Charlot (2003) templates from
which we fit out data. and we include a wide range of stellar population
parameters that are meant to represent the possible forms of the galaxy
populations up to such high redshifts. Our method is essentially the same as
used in previous work on this sample (Duncan et al., 2019). To calculate these
stellar masses we use a Chabrier initial mass function for the stellar
populations, with a range of possible star formation histories. The star
formation histories we apply follow exponential $\tau$-models for both
positive and negative values of $\tau$. The timescales we use include:
$\left|\tau\right|$ = 0.25, 0.5, 1, 2.5, 5, and 10, along with a short burst
model ($\tau$ = 0.05). Furthermore we also consider continuous star formation
models (with $\tau\gg$ 1/$H_{0}$).

To ensure our masses are reliable we compare to masses calculated
independently by several other teams within the CANDELS collaboration (Santini
et al., 2015). We do this to ensure that the stellar mass estimates do not
suffer from systematic biases. We find some minor scatter between different
mass estimates at the level of 0.15 dex; however, the masses we use are not
affected by any significant biases compared to others. More details on the
method and models used can be found in previous work on this sample Duncan et
al. (2019).

The star formation histories we use are from the SEDs of these galaxies. We
examine the UV light from these galaxies and correct for dust using the UV
slope of the spectral energy distribution ($\beta$). This gives us a measure
of the dust attention in the galaxy, which we correct to obtain the total star
formation rate. These star formation rates agree well with the star formation
rates derived directly from the SED fitting (Duncan et al., 2014). For more
information see the papers where these measurements are described in greater
detail (Duncan et al., 2014, 2019).

###  2.2 Galaxy Classifications

The classifications we use throughout this paper arise from the work by
Ferreira et al. (2023) who classified in total 3965 sources in the EGS field
as observed with the CEERS ERS project. These classifications were done into
four main types, and were carried out by eye through the participation of five
different expert classifiers. These classifications are: disk, elliptical,
peculiar, and ambiguous. These classifications are done solely based on the
F444W morphology of each galaxy based on its appearance. No information about
the stellar populations, star formation rates, or colours of the galaxies was
used to determine the morphological type.

These types are somewhat self explanatory, but we give a brief discussion here
for completeness, although see Ferreira et al. (2023) for a more detailed
description of how these types are determined and the pitfalls and biases that
might be present in our derived morphologies. Examples of our various types of
galaxies are shown in Figure 1. For completeness we give a brief description
of how these different galaxies are classified into their various types.

First, the disk galaxies are those that appear to have a disk — this can be
pure disks, edge-on disks, or systems with a central concentration (such as a
bulge) with an outer disk system. The spheroids are compact, smooth and have
no obvious irregularity that changes their basic morphological structure,
although very minor differences from a pure symmetry are acceptable to be
considered part of this class. The 3rd main type is the peculiars, which look
like galaxies in some type of active formation or disruption - essential these
are analogous to those galaxies in the local universe which appear to be
mergers or those dominated by star formation, although this interpretation is
not used to classify these systems. Essentially anything that is resolved and
has a morphological appearance is classified as a peculiar if it cannot be
classified as an elliptical or a spiral due to the structure generally not
being symmetric. The galaxy type “ambiguous” are those galaxies that cannot be
classified as they are too faint and/or too small to have any reliable
classification. Examples of these various types, besides the "ambiguous" type
which are typically just small and faint featureless ‘blobs’ are shown in
Figure 1 and discussed in more detail in Ferreira et al. (2023).

Figure 1: A subset of the images of galaxies used in this work, the image cut-
outs were derived using the pipeline, outlined and described in detail in
(Ormerod et al., 2024). The images are ordered in increasing redshift from the
top row downwards. The columns show an example of each morphology, in each
redshift bin. (SF)/(P) denotes those that have been defined as star-
forming/passive in the study of the main sequence. Each cut-out has a
resolution of 0.03"" per pixel, and are constructed such that the background
of each is scaled equally, for direct comparison. More examples are discussed
and presented in Ferreira et al. (2023).

###  2.3 Galaxy Size Measurements

We examine the half light radii of our galaxies with the JWST images, using
the GALFIT software to fit a Sérsic light profile to each galaxy. GALFIT is a
least squares fitting algorithm which finds the optimum solution to a fit by
using a Levenberg-Marquardt algorithm. Based on this, Galfit determines the
goodness of fit via $\chi^{2}$ calculations, and adjusts parameters until the
$\chi^{2}$ no longer improves. Galfit uses the reduced chi-squared,
$\chi_{\nu}^{2}$, determined by

$\chi_{\nu}^{2}=\frac{1}{N_{\mathrm{DOF}}}\sum_{x=1}^{nx}\sum_{y=1}^{ny}\frac{\left(f_{\mathrm{data}}(x,y)-f_{\mathrm{model}}(x,y)\right)^{2}}{\sigma(x,y)^{2}}$
(1)

summed over $nx$ and $ny$ pixels, and where $N_{DOF}$ is the number of degrees
of freedom. As seen in Equation 1, Galfit requires a data image,
$f_{data}(x,y)$ and a sigma image, $\sigma(x,y)$, which are used to calculate
the model image, $f_{model}(x,y)$ (Peng et al., 2002, 2010a).

A full description of this method can be found in Ormerod et al. (2024),
although the methodology we use to carry out these measurements is fairly
straightforward.To summarise, we use a custom pipeline, taking the input
parameters from the SExtractor catalogue, use PSFs created with Perrin et al.
(2015), and we quote the results obtained the rest-frame optical filter for
each object. Many more details are presented in Ormerod et al. (2024). We also
run our objects through another surface brightness fitting code, IMFIT, which
gives very similar results.

We use the fitted sizes and Sersic indices from these measurements within this
paper to investigate how quantitative structures correlate with the star
formation and mass assembly of galaxies, although this is a limited study. A
larger study investigating the issues of the sizes and Sersic indices of these
galaxies will be discussed in (Ormerod et al., 2024).

##  3 Results

In the following sections we describe the main results of this paper,
especially our investigation of how galaxy properties vary as a function of
morphological type in terms of measured stellar masses and star formation
rates at $z<7$.

We first describe the stellar mass evolution and the characteristics of the
evolution of galaxy stellar masses for systems at a given morphological type
at these redshifts. We later investigate the star formation rate for these
galaxies, and how the star formation rate varies with a combination of stellar
mass and morphology.

In this way we measure the dominant processes which are driving galaxy
evolution at $z<7$. Ultimately, we are interested in discovering what are the
processes assembling galaxy mass in the universe. This paper allows us to
start investigating this question in terms of galaxy morphology at $z>3$ for
the first time with the advent of JWST data. To do this we investigate three
different quantities in this paper and how they correlate with the morphology,
masses, and mass densities of galaxies. These are ongoing star formation
(SFR), the observed stellar mass (M∗), and galaxies which have since largely
stopped star forming (quenched systems.). The star formation rate can be
thought of as the total mass formed within a galaxy over a certain amount of
time $\delta t$, or:

${\rm SFR_{\rm obs}}=\frac{\int_{t_{0}}^{t_{obs}}dM_{SFR}dt}{\delta t}$ (2)

where $\delta t=(t_{\rm obs}-t_{0})$, the time in which the star formation
rate is being measured. As we use ultraviolet star formation rate measures,
this time-scale is roughly $\delta t=100$ Myr. Likewise, we can the stellar
mass in terms of the star formation as:

$M_{*}=\int_{0}^{t_{rmobs}}{\rm SFR}(t)dt$ (3)

where the value of the SFR is a function of time, divided into arbitrarily
small amounts. From this equation we can also write that the SFR $\sim$
dM∗/dt, that is, that the SFR is the time derivative of the stellar mass. In
this sense, we use the stellar mass as the integrated formation history and
the SFR as the derivative of this formation, at least averaged over the past
100 Myr.

###  3.1 Galaxy measurements with redshift

One of the issues we investigate to get a sense of the nature of our data are
the trends of star formation rate and mass with redshift for our different
morphological types. In Figure 2 we show the scatter of distribution of
stellar masses for galaxies in our sample as a function of redshift. As can be
immediately seen, there is no obvious pattern for lower or higher mass
galaxies to be of any particular morphological type. Likewise, we show a
redshifts vs. star formation rate in Figure 3, which also does not demonstrate
any strong trend with any particular morphological type to be more massive or
to contain higher/low star formation rates than others. We however plot the
averages of these stellar masses and star formation rates for different galaxy
morphologies, showing slight differences. One of these is that on average the
spheroid types appear to have smaller star formation rates, particularly at
lower redshifts.

Based on this, and from the analysis in Ferreira et al. (2023), we conclude
that there must be multiple modes of galaxy formation occurring to produce
star formation in different types of galaxies, or alternatively that different
modes of star formation have different morphological outcomes as they evolve
through the mechanisms responsible for triggering this star formation. For
more detail on how star formation rates correlated with galaxy types see
Ferreira et al. (2023). This however is a very broad correlation we are
finding here without any subtleties or details that can be examined from this.
To understand this better we explore in more detail in the remainder of the
paper how the gross morphology of a galaxy drives its past (stellar mass) and
ongoing (SFR) formation history. We carry this out by examining in some detail
how galaxy morphology is distrbuted within stellar mass and star formation
rates.

Figure 2: The plot of stellar mass as a function of redshift for our sample of
galaxies with visual morphological classifications. The different morphologies
are plotted as different points, as shown in the inner caption of the figure.
In section §3, and throughout we investigate this relationship between the
stellar mass, morphology, and star formation, and how these properties vary
with redshift. Figure 3: Plot of the scatter of the star formation rate (SFR)
as a function of redshift. The points here are coloured in terms of their
morphological type, which is shown in the caption. As can be seen, the lack of
an obvious correlation between SFR and morphology can be observed. Note that
the SFR measures which are less than $\sim 1$ M0 year-1 have errors larger
than the measured value, such that there actual SFR is effectively $<1$ M0
year-1.

###  3.2 Stellar mass function evolution

One of the primary methods of examining galaxy formation is to determine the
stellar mass evolution of galaxies (e.g., Mortlock et al., 2011; Duncan et
al., 2014; Mortlock et al., 2015; Navarro-Carrera et al., 2023). This quantity
is the amount of stars that have formed in galaxies by a given observed time.
Effectively it is the integral of the star formation rate at all times prior
to observing the galaxy at its given redshift (Conselice et al., 2022; Bluck
et al., 2023).

Figure 4: A comparison of our derived stellar mass functions at z $\sim$ 2
through to $z\sim 7$ with comparisons from Duncan et al. (2014), Muzzin et al.
(2013), Gonzalez et al. (2012), and Santini et al. (2012). The blue (solid)
line is the total mass function obtained in this work; whilst the green
(dotted) line is the fit for these mass functions obtained by Duncan et al.
(2014). The black (dashed) mass function is that obtained for the galaxy
sample used throughout this paper; but using the masses calculated from
similar studies (e.g., Stefanon et al., 2017) Figure 5: Corner plot from the
MCMC analysis of a single mass function fit with the parameters of the fits
shown in Table 2. This is an example for the disk population in the redshift
range 2.0 < z < 3.0, with similar fits carried out for the other redshift and
sub-divisions into morphology ranges. Figure 6: Derived stellar mass
functions, as a function of both morphological classification type and
redshift. The associated $\chi_{R}^{2}$ for the emcee fitting is given in the
associated legend of each subplot. The lines and points are similar to what is
shown in Figure 4. It is clear that at some redshifts we do not have an
extensive amount of data to fit these mass functions accurately for some
types, which is reflected in the limited Schechter function fits.  Figure 7:
Visualisation of how the Schechter parameters vary through redshift as a
function of morphological type. In the shaded region, at redshifts higher than
the bin $4<z<5$, we fixed the value of $M^{*}$ when carrying out these fits.
This is due to the turnover mass difficult to constrain given the limited
amount of data.

Previous to JWST, Duncan et al. (2014, 2019) measured the stellar masses for
galaxies in the EGS field using the HST CANDELS data. We use these stellar
masses in this paper to determine the stellar mass function evolution as a
function of morphology up to $z\sim 7$, and listed in Table 2. We show our
reconstruction of the total mass function in Figure 4. We recalculated the
Schechter (1976) function fit parameters using our fitting methodology, which
is described in detail below, and we find a good agreement with the previous
work on this topic from Duncan et al. (2014) amongst others, as can be seen in
Figure 4.

Redshift Range | $M^{*}$ | $\log\phi_{*}$ | $\alpha$ | $\chi_{R}^{2}$
---|---|---|---|---
$1.5<z<2$ | 10.86 $\pm$ 0.17 | -2.92 $\pm$ 0.18 | -1.54 $\pm$ 0.18 | 1.16
$2<z<3$ | 10.40 $\pm$ 0.21 | -2.80 $\pm$ 0.17 | -1.48 $\pm$ 0.16 | 1.63
$3<z<4$ | 10.51 $\pm$ 0.24 | -3.24 $\pm$ 0.18 | -1.48 $\pm$ 0.16 | 2.40
$4<z<5$ | 10.51 $\pm$ 0.24 | -3.65 $\pm$ 0.22 | -1.52 $\pm$ 0.14 | 0.88
$5<z<6$ | 10.42 $\pm$ 0.32 | -4.02 $\pm$ 0.30 | -1.56 $\pm$ 0.16 | 0.32
$6<z<7$ | 10.39 $\pm$ 0.28 | -4.55 $\pm$ 0.34 | -1.65 $\pm$ 0.20 | 0.77
Table 1: The single Schechter function fitted parameters for the total galaxy stellar mass function for our whole data set, encompassing all morphology types. Shown are the error bars for these fits which were derived using our MCMC fitting methods. Our results agree well with previous mass function measurements, including from Duncan et al. (2014). Redshift Range | Type | $M^{*}$ | $\log\phi_{*}$ | $\alpha$ | $\chi_{R}^{2}$
---|---|---|---|---|---
$1.5<z<2$ | Disk | 11.09 $\pm$ 0.46 | -3.26 $\pm$ 0.30 | -1.52 $\pm$ 0.14 | 1.38
$2<z<3$ | Disk | 10.78 $\pm$ 0.38 | -3.26 $\pm$ 0.23 | -1.48 $\pm$ 0.11 | 0.98
$3<z<4$ | Disk | 10.54 $\pm$ 0.38 | -3.39 $\pm$ 0.23 | -1.45 $\pm$ 0.12 | 1.20
$4<z<5$ | Disk | 10.53 $\pm$ 0.41 | -3.83 $\pm$ 0.27 | -1.51 $\pm$ 0.10 | 0.65
$5<z<6$ | Disk | 10.41 $\pm$ 0.28 | -4.49 $\pm$ 0.35 | -1.59 $\pm$ 0.19 | 0.47
$6<z<8$ | Disk | 10.49 $\pm$ 0.00 (Fixed) | -4.75 $\pm$ 0.31 | -1.58 $\pm$ 0.17 | 0.21
$6<z<8$ | Disk | 10.39 $\pm$ 0.28 | -5.17 $\pm$ 0.28 | -1.62 $\pm$ 0.20 | 0.40
$1.5<z<2$ | Peculiar | 10.44 $\pm$ 0.39 | -3.31 $\pm$ 0.27 | -1.49 $\pm$ 0.11 | 0.72
$2<z<3$ | Peculiar | 10.57 $\pm$ 0.39 | -3.29 $\pm$ 0.22 | -1.49 $\pm$ 0.08 | 0.57
$3<z<4$ | Peculiar | 10.64 $\pm$ 0.46 | -3.61 $\pm$ 0.24 | -1.47 $\pm$ 0.07 | 1.13
$4<z<5$ | Peculiar | 10.79 $\pm$ 0.51 | -4.11 $\pm$ 0.29 | -1.50 $\pm$ 0.09 | 0.56
$5<z<6$ | Peculiar | 10.65 $\pm$ 0.52 | -4.59 $\pm$ 0.39 | -1.59 $\pm$ 0.20 | 0.96
$6<z<8$ | Peculiar | 10.65 $\pm$ 0.00 (Fixed) | -5.43 $\pm$ 0.40 | -1.61 $\pm$ 0.20 | 0.29
$1.5<z<2$ | Spheroid | 10.60 $\pm$ 0.49 | -3.75 $\pm$ 0.38 | -1.65 $\pm$ 0.22 | 1.67
$2<z<3$ | Spheroid | 10.72 $\pm$ 0.51 | -3.74 $\pm$ 0.35 | -1.51 $\pm$ 0.16 | 1.51
$3<z<4$ | Spheroid | 10.77 $\pm$ 0.50 | -3.85 $\pm$ 0.28 | -1.42 $\pm$ 0.12 | 0.45
$4<z<5$ | Spheroid | 10.69 $\pm$ 0.32 | -4.21 $\pm$ 0.34 | -1.48 $\pm$ 0.17 | 0.54
$5<z<6$ | Spheroid | 10.65 $\pm$ 0.51 | -4.54 $\pm$ 0.41 | -1.52 $\pm$ 0.21 | 0.79
$6<z<8$ | Spheroid | 10.63 $\pm$ 0.52 | -5.15 $\pm$ 0.42 | -1.52 $\pm$ 0.22 | 0.84
Table 2: The single Schechter parameters for the total galaxy stellar mass
function as a function of morphological type. Shown are the fitted parameters
assuming that the mass function is well fit by this function. We also note on
this Table when the value of $M^{*}$ is held constant when the other Schechter
function parameters are fit. We also list the value of the reduced-chi-squared
for each fit ($\chi^{2}_{R}$).

We fit the Schechter function parameters for our sample of galaxies using the
following procedure. We compute the number densities of galaxies as the number
of galaxies in a given stellar mass bin normalised by the co-moving volume in
the corresponding redshift bin. We also correct our counts for incompleteness
using the results from Duncan et al. (2019), analysing the completeness of the
EGS Wide 1 subfield. These inferred mass functions are then fit by creating an
array of all the computed number densities in order of the centre of the
stellar mass bin. We then fit for each bin a Schechter function (Schechter
1976) of the form:

$\phi(M)=\phi^{*}\cdot\rm\ln(10)\cdot[10^{(M-M^{*})}]^{(1+\alpha)}\cdot\rm\exp[-10^{(M-M^{*})}]$
(4)

the value $\phi^{*}$ is the normalisation, $M^{*}$ is the value of the so-
called turn-over mass in dex units, while $\alpha$ is the slope of the low-
mass end distribution.

The parameter determination was conducted via use of the Markov Chain Monte
Carlo (MCMC) sampler emcee (Foreman-Mackey, 2016a), in which we take the
likelihood function to be of Gaussian form, and maximise this with a uniform
prior. The sampling of the posterior is done using emcee to draw probable
parameter arrays from the posterior probability distribution. We experiment
with other prior distributions, finding the outcome of these results very
similar to the main process we describe here. This method is visualised using
the plotting software corner (Foreman-Mackey, 2016b). For example, histograms
of the posterior distribution for the disk galaxy population between $1.5<z<2$
are shown in Figure. 5. The other morphological types show similar features
and similar corner plots from our MCMC fitting of these mass functions. The
best fits for these mass functions is shown in Table 2 as a function of
morphology, while the total mass function fits are shown in Table 1.

At the highest redshifts we are limited to a sample of a few dozen galaxies
for each of the three major morphological types, as well within the lower
redshift bins, there are a few hundred. These limited numbers should be kept
in mind when interpreting the results and trends that we find in this paper.

###  3.3 Mass functions of morphological types

We now examine how the different morphological types of our sample are
distributed as a function of stellar mass. This is shown in Figure 6, where as
a function of redshift we have plotted the stellar mass function for galaxies
in the classified morphological types of disks, peculiars, and spheroidal
galaxies. The Schechter function parameters for each of the morphological
types are listed as a function of redshift in Table 2. The fitted Schechter
function parameters are also plotted in Figure 7. Note that in several
versions of the fits, we hold the values of M∗ constant, as otherwise we do
not have enough data to fully fit these. As can also be seen, it becomes
progressively harder to measure accurately points at the highest redshifts
(Figure 6). These mass functions will be better measured when larger
morphological samples of galaxies become available.

The largest difference we see within these fits, is the high density of disk
galaxies as shown by the values of $\phi$ amongst all the redshifts. As shown
in Figure 7, the disk galaxies have a higher normalisation than any other
morphological types at all redshifts, which is another reflection of the fact
that the disks dominate the galaxy population at these redshifts (Ferreira et
al., 2023). The spheroid galaxies have the lowest densities, particularly at
the lower redshifts. However at $z>5$ we find that the values of $\phi$ are
fairly similar for all morphological types. One caveat to this is that we have
held the value of M∗ constant at these highest redshifts which may affect the
fits of the other parameters, although the value of M∗ is fairly constant at
the higher redshifts (e.g., Duncan et al., 2014; Harvey et al., 2024) so the
effect is likely small. Interestingly, we find that the values of $\phi$ grow
at very similar rates for the different morphological types. It is not clear
however if between these redshifts we are seeing a growth in the number of
galaxies that, for whatever reason, are distributed equally between types, but
we cannot determine from this work alone how the morphologies between
redshifts might be evolving into each other.

Remarkably perhaps, we find no significant difference in the value of the
faint-end slope, $\alpha$ for the galaxies classified into different
morphological types. This however is more or less only the case at the highest
redshifts at $3<z<5$. At the lowest redshifts we find that there are fewer
lower-mass spheroid galaxies, and a relatively higher number of disks and
peculiars at the faint end of the mass function.

###  3.4 Evolution of the Main Sequence (MS): Passive, Starbursts and MS
galaxies

####  3.4.1 Definitions

Galaxies come in different types, not only morphological, but also in terms of
different ongoing star formation rates. Some galaxies are undergoing star
formation in a burst mode, some are passive (with little star formation),
whilst others are present in what is called the ‘main-sequence’ of star
formation. It is clear that especially at high redshifts, there is no obvious
correlation between the morphology of a galaxy and its star formation rate
(e.g., Conselice et al., 2011; Mortlock et al., 2013). However, a strong
dependence of sSFR on quantitative structure has been found, including bulge
mass, central mass density and the stellar potential (e.g. Cheung et al.,
2012; Fang et al., 2013; Lang et al., 2014; Bluck et al., 2022, 2023). It is
interesting that these structural relations do not appear to result in strong
morphological dependence on star formation.

As part of this we investigate the so-called "main-sequence" of galaxy
formation for our sample and how morphological properties relate to this. This
main-sequence is a (sub-)linear relationship between the star formation rate
of galaxies and their past integrated star formation as demonstrated by their
measured stellar mass (e.g., Noeske et al., 2007; Bhatawdekar & Conselice,
2021). These systems can be thought of as ‘normal’ galaxies that are neither
passive nor star bursting. We use our data to define passive, starbursting,
and main-sequence types at each redshift galaxies by fitting the main sequence
and determining the different star forming types based on the position of
individual galaxies relative to this fit, with star forming galaxies defined
as those systems which are $>1\sigma$ above the main sequence, and passives
those which are $<1\sigma$ below the main sequence.

Our definition of the main sequence originates via the assumption of a simple
power law relation between star formation rate and the stellar mass (Pearson
et al., 2018). A straight line fit to the $\log_{10}($SFR$)$ vs
$\log_{10}$(M∗) data is performed using emcee, wherein the vertical scatter of
each point from this straight line is found to be normally distributed.
Galaxies within one vertical standard deviation of this fit were then isolated
for fitting via emcee. This produces a final straight line that defines our
main sequence, of the form:

$\log_{10}\left(\frac{\textrm{SFR}}{\textrm{M}_{\odot}\textrm{yr}^{-1}}\right)=\gamma\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)+\beta.$
(5)

With respect to this line, each galaxy’s $\log_{10}($SFR$)$ has a vertical
deviation ($\delta$) that is normally distributed across the population. The
width of this distribution ($\sigma$) was calculated, such that the
starbursting, main sequence, and passive populations are defined as:

Starbursting : $\delta>\sigma$

Main Sequence : $|\delta|<\sigma$

Passive : $\delta<-\sigma$

This procedure was repeated within redshift bins at z = (1.5, 2, 3, 4, 7),
providing the fractional starforming history makeup of the starbursting, main
sequence, and passive populations as a function of redshift.To be clear, we
carry out this fit to determine this criteria for all the galaxies within a
redshift bin; we not fit this for the individual morphological types. Thus the
fits shown in the overall stellar mass vs. SFR plane are the fits over all
galaxies within that redshift bin.

Figure 8: Plot showing the densities of galaxies in the main sequence plane by
morphological type, wherein the over-plotted straight in each redshift bin has
been obtained via a fit to ourSFR and M∗ values. The colours of the symbols
show the morphological type of the galaxies plotted. The blue points are for
the disk galaxies, the red are those for the spheroids, the green are
peculiars, and the ambiguous galaxies are plotted as purple.

####  3.4.2 Main-sequence types

The results of this exercise are shown in Figure 8 where we have divided up
the main sequence fitting into different redshift and morphological bins.
There are a few things to take away from this figure. The first is that there
is well defined main sequence for galaxies at most morphologies, with the
exception of the classified spheroids, up to $z\sim 3$. This can be seen as
the line showing the best fit to the data. It is also the case that there is
not a great deal of difference in the main sequence fitting and distribution
of galaxies in terms of morphology up to $z\sim 3$. In the upper panels of
Figure 8 it can be seen clearly that the distribution is very similar and that
there are no ‘offsets’ for the main sequence at $1.5<z<3$. This also means
that the main sequence is made up of all morphology types in this epoch, which
is a bit different from the local universe where it is found in general that
the morphological make up of the main sequence is primarily from disk galaxies
(e.g., Brinchmann et al., 2004; Noeske et al., 2007).

At the higher redshifts at $z>3$, where we now have the first reliable
morphological types, we do not see as clear of a pattern. The main sequence is
still present to some degree, but there is a larger scatter of points. None
the less, these points seem to fall into the same part of the parameter space
for the different galaxy morphologies.

The best way to determine how the different galaxy types change along the main
sequence, or are defined as passive or starburst is to plot the change in the
morphological types as a fraction of these main sequence based derived star
formation states. The results of this are shown in Figure 9 and Figure 10. It
is important to note how many galaxies we have within each of these
morphological bins at different redshifts. At $z=1.5-2$ we have 507 disk
galaxies, 268 peculiar galaxies, and 149 spheroid galaxies within these plots.
This changes at $z\sim 3$ to be 463 peculiars, 619 disks, and 214 spheroids,
while at $z\sim 6.5$ we are left with 29 peculiars, 34 disks, and 16
spheroids.

To determine which star formation type a galaxy is we use its distance from
the main-sequence, which we determine by fitting within each redshift bin, all
galaxies, regardless of morphology, to defined the main-sequence. Then the
various criteria are applied in reference to this fit. The first plot in
Figure 9 shows the fraction of the star forming types as a function of
morphological type — the starbursts, main-sequence galaxies and those which
are passives. We divide up this trend in this way as we know from our
definition that a large fraction of all galaxies will naturally be defined as
main-sequence using our definition. However, this does not mean that there
should be any particular biases for any morphological type of galaxy to be
found on the main-sequence or within the passives or starbursts.

As deduced from the plot of the main sequence itself, we find a mixture of
galaxy morphologies that make up the main-sequence, although we do see some
evolution. At the highest redshifts where we can carry out this test, at
$z\sim 6$, we find that the relative contributions of spheroid, disk and
peculiar are fairly similar, at about a third of the population each, with
spheroids dropping quickly at the next lower redshift bin to be only about 10%
of the population. At lower redshifts we increasingly see that the disk
galaxies make up a large fraction of the main-sequence galaxy population, such
that it constitutes about 60% of the main sequence at $z\sim 1.5$. This
compares well with the total fraction of disk galaxies that make up the entire
galaxy population at this redshift (Ferreira et al., 2023), demonstrating
again that disk galaxies are dominating the typical star formation in the
universe at all epochs up to $z\sim 6$.

Peculiar galaxies have a slightly declining contribution to the fraction of
galaxies on the main-sequence, whilst the spheroids continue to have a lower
contribution and become, on average, more passive. This is essentially
evidence that we are witnessing the formation of the Hubble sequence. Galaxies
must by nature form in some type of irregular/peculiar way and transform into
normal galaxies at lower redshifts. Thus, we are finding at the lowest
redshifts the expected and typical trend of galaxy morphology correlating with
the star forming properties of galaxies with different morphologies.

The starburst population, those defined as above the main sequence, are
equally dominated by disk galaxies and peculiars. In fact these are about
equally represented, while ellipticals again represent a very small fraction
of this population. On the other hand, the ‘passive’ types are seen to have
more similarities to the ‘main-sequence’, such that the three types are fairly
equal at the highest redshifts. However at lower redshifts we see that the
disk galaxies become the dominant type, again at about 60% of the population
at the lowest redshifts. The major difference between this and the main
sequence galaxies is that the peculiars decline more rapidly — there are in
fact very few passive peculiar galaxies at the lowest redshifts.

We can reverse this view and ask the question in terms of the morphological
types, essentially - what fraction of each type is classified within the
different star formation categories as based on the main sequence? This is
shown in Figure 10 where the dissection of each morphological type is shown in
terms of these star forming properties. The trends here reflect what we see
when we examine the evolution of the star forming types in terms of
morphology.

The disk galaxies display a high fraction of their number on the main-
sequence, which by their dominance and the definition of our main sequence, is
not a surprise. However, we can see that there is gradual evolution in terms
of the fraction, such that they evolve away from being starbursts and slightly
more on the main-sequence, particularly at redshifts $z<3$. However, it is
still the case that even at redshift $z\sim 6$, 60% of disk galaxies are on
the main sequence. Spheroids show similar trends, and again this is consistent
with a gradual formation of the Hubble sequence, although the early onset of
this is actually at redshifts higher than our highest redshift at $z>6$.
Deeper and more imaging data are needed to probe this in more detail at these
earlier times, which might be possible with MIRI and deep NIRCam observations.
Peculiars show different trends, whereby they increase slightly their fraction
in the starburst class at lower-z, while retaining a fairly flat evolution
with redshift in the main-sequence.

Redshift Range | $\gamma$ | $\beta$ | $\sigma$
---|---|---|---
$1.5<z<2.0$ | 0.85 $\pm$ 0.22 | -7.91 $\pm$ 2.09 | 0.62
$2.0<z<3.0$ | 0.82 $\pm$ 0.22 | -7.29 $\pm$ 1.98 | 0.69
$3.0<z<4.0$ | 0.73 $\pm$ 0.18 | -6.36 $\pm$ 1.68 | 0.72
$4.0<z<8.0$ | 0.85 $\pm$ 0.22 | -7.14 $\pm$ 2.12 | 0.92
Table 3: The total main sequence fitting parameters, irrespective of
morphology, as a function of redshift range. Figure 9: The morphological
fractional composition of the ”main-sequence" method of defining star forming
types, which are: starbursting, main sequence, and passive galaxies divided by
visual morphology as a function of redshift. Plotted are the fraction of
galaxies defined as starbursts, main sequence, and passive as a function of
redshift. The different colours and symbols show the breakdown of the fraction
of each star formation type as a function of redshift. Compare this to Figure
10 where these morphological main-sequence types are plotted in terms of
morphological type. Figure 10: The main-sequence defined star formation types
fractional composition of the disk, peculiar, spheroidal and ambiguous
morphologically classified galaxies by star forming category as a function of
redshift. The different colours and symbols show the breakdown of the fraction
of each morphology within a given star forming type as a function of redshift.

###  3.5 Passive and Star Forming from UVJ Diagrams

As noted in papers previously (e.g., Williams et al., 2009; Ownsworth et al.,
2016), the position of galaxies at high redshift in a so-called UVJ diagram
can reveal their star forming nature. Within this space there is a region
where passive galaxies are found, while we also find systems that are star
forming are found in a lower part the diagram. Whilst this may seem redundant
to the star formation analyses we preform in the last section, we carry out
this UVJ analysis as a complement to that work and also a way to better
understanding the physical nature of morphology and how it correlates with
current stellar population properties. In principle, the UVJ gives some idea
of the existing stellar population and whether the galaxy is ‘passive’ or not
and using colours we have a longer time-scale in which to determine this than
compared to the star formation rate which is more of an instantaneous
measurement when the galaxy is observed.

The colours for the UVJ analyses here are from the catalog provided by
(Stefanon et al., 2017). These colours are derived from a BC03 SPS template,
and an exponentially declining SFH; with $\tau$ = [ 0.1, 0.3, 0.6, 1, 2, 3, 5,
9, 15 Gyrs]. Both Calzetti and SMC dust extinction laws are implemented, with
the code deciding the extinction model which gives the better fit. No nebular
emission is added, additionally an array of metallicities is used, including a
subset of models with young ages and low metallicities. See Stefanon et al.
(2017) and Mobasher et al. (2015) for greater discussion of how these colours
are synthesised.

Figure 11: UVJ colours and diagram which are used to define the population
cuts in the 1.5 < z < 2.5 bin based on the star formation rate of these
galaxies. Galaxies are colour-coded by sSFR (as measured in Gyr-1), and those
which have log(sSFR) < -1 are circled in red. This is an example redshift bin,
other redshifts show similar results and trends.

We use the full CANDELS EGS catalog to define the redshift dependent cuts,
identifying the galaxies in which the sSFR fell below a threshold. We
therefore compare the position of galaxies in the UVJ plane with those which
are passive based on their low sSFR. The threshold for finding passive
galaxies was taken to be $-1$ Gyr-1, as plottedin Figure 11. The selection
region for quiescent galaxies is defined as,

$U-V>1.19-0.07(1+z)\\\ V-J<1.93-0.07(1+z)\\\ U-V>0.88(V-J)-0.014(1+z)+0.476\\\
$ (6)

These cuts share the same gradient as in the work done by Lovell et al.
(2022), although we introduce a redshift dependent V$-$J bound, accounting for
the migration of the galaxies into more positive values of U$-$V and V$-$J
towards the present. Once these cuts are defined for each redshift bin in the
range $1.5<z<7$, we compare the morphologically classified regions to this.
Overall, however, it is important to note that we find a very good agreement
between the sSFR of galaxies and their position in the UVJ colour space.
Galaxies which are defined as passive due to their position in this space have
the lowest sSFR values (Figure 11). In fact, we find that it is the galaxies
which are the bluest in both colours, shown in the bottom left part of the
diagram, are most likely to have a high sSFR. Thus, we can use this diagram
with some confidence to understanding the past history and the state of the
stellar populations within galaxies for different morphological types.

When we apply the UVJ cut method in our sample as labelled by morphological
type, we obtain Figure. 12, whereby the morphologically classified subset is
denoted within this space. By doing this we can determine how UVJ space is
morphologically dependent, finding that there is very little to no correlation
between galaxy morphology and the position in the UVJ space. This is a sign
that at the highest redshifts, there is no obvious correlation between a
morphological type and the age of its most recent stellar population,
consistent with Section 3.4. This morphological treatment does change however
as we go to lower redshifts, whereby the Hubble sequence is established.

It is also worth remarking that we find very few of the spheroid types in the
passive region of the UVJ space. In fact at $z>3.5$ we find that there is no
correlation between UVJ colour and the morphological type. While at the lower
redshifts, we do see at least some division of types. In general, we find that
the spheroid types are at the blue end of both colours, while the disk
galaxies are redder. We also see a significant overlap of the position of the
spheroids with those of the peculiars, suggesting perhaps some association.
This is consistent with the findings of the main-sequence, whereby we find
that a significant fraction of the spheroids are located in the starburst or
main-sequence of star formation region of this parameterisation. This is due
to the fact that these spheroids are actively forming. These high-z systems
could be the ancestors of ellipticals today, but in a formation mode from some
type of merging activity or otherwise a collapse of gas into a small volume.
In the next sections we directly investigate the sSFR patterns for these
galaxies.

We can use the models of stellar population evolution shown in Figure 13 to
determine the likely time-scales in which at least the spheroid systems remain
below the passive region on this diagram. We show in this figure models from
Bruzual & Charlot (2003) with 2016 Miles Stellar population synthesis models,
with a Chabrier IMF and BPASS models (Eldridge et al., 2017) with the same
Chabrier IMF and stellar mass range from 0.1-100 M0 . The markers on the plots
are (from the bluest, bluest point redward) 10, 50, 100, 250, 500, 750, 1000
and 2000 Myr. We also include one dusty galaxy model at solar metallicity.

If we examine the location of the spheroids in this space, we find that they
have a stellar population with an age of about 100 Myr, assuming a solar type
metallicity. These same models show that these galaxies would be within the
passive region of UVJ space after another few hundred million years. In this
sense the UVJ diagram is revealing that the star formation activity is more
prolonged than the morphological evolution for these galaxies, assuming that
these are transiting from peculiars into spheriods, a topic we discuss in more
detail in the discussion section.

Figure 12: A division of UVJ diagrams for our subset of morphologically
classified galaxies up to redshifts $z=6.5$. Redshift dependent cuts derived
in both this work, and that done by Lovell et al. (2022) are shown; dividing
the population into passive and star-forming regions. No true bi-modality can
be seen at these high redshifts, and the two regions can be seen to be
populated by a varying amount at all morphologies. Although a lower proportion
of peculiars are seen in the passive domain at late-times, at early-times this
proportion can be seen to increase. We see surprisingly very little
correlation between morphological type and the location of galaxies on these
UVJ diagrams.

Figure 13: The UVJ diagrams, but now showing models of where galaxies of
different metallcities (Z) evolve in terms of U-V and V-J colours from 10 Myr
to 2Gyr. On the left we show BC03 (Bruzual & Charlot, 2003) with 2016 Miles
Stellar population synthesis models, with a Chabrier IMF; on the right panel
we show BPASS models (Eldridge et al., 2017) also with a Chabrier IMF. Most
models show the intrinsic stellar spectra, with no dust included. The markers
are (from the bluest, bluest point redward) 10, 50, 100, 250, 500, 750, 1000
and 2000 Myr. Also shown are the $z=2$ and $z=8$ quiescent defined regions
which we use in Fig 12 at different redshifts.

###  3.6 Specific star formation rate evolution

Star formation is the derivative of the stellar mass within galaxies. It gives
us an idea of the rate at which stars in galaxies are forming at a given
instance. Another approach we use is investigating the specific star formation
rate (sSFR), which gives the relative amount of star formation for an already
formed amount of stellar mass. For a given observed star formation rate (SFR),
the specific star formation rate is simply defined and measured as sSFR = SFR
/ M∗. In our notation this is the derivative of the change in mass divided by
the integral of the star formation rate over all of time. The observed
distributions of star formation rates with redshifts are asymmetric, as
measured SFRs span many orders of magnitude. We report the median sSFR with
associated error bars as the 16th and 84th percentile values, as to enclose a
68% confidence region of the measurement.

In a sense this is an indication of how important the ongoing star formation
rate is within a galaxy compared to the past integrated star formation rate,
as measured by the stellar mass. We then take the average for the sSFR for
each galaxy morphological type at each redshift and plot the results in Figure
14.

We model the evolution of this sSFR evolution through redshift by a simple
power law of the form,

$\left(\frac{\textrm{sSFR}}{\textrm{Gyr}^{-1}}\right)=a(1+z)^{b}$ (7)

where the parameters $a$ and $b$ are free and fit parameters. We calculate
these free parameters for the entire population within the survey and further
investigate this fit in relation to the differing morphological and stellar
mass bins.

Comparing the individual morphologies to the power law relation found for the
entire population, we see no distinction in sSFR in terms of morphological
type, as can be seen in Figure 14. This implies that the construction of new
stellar mass in galaxies during the $1.5<z<7$ epoch does not depend on the
overall morphology. This strongly implies that there are several ways in which
the star formation in a galaxy can be triggered with different effective
morphologies and resulting structures. It also may imply that galaxy
morphology is established first and the star formation occurs within this
structure without dramatically changing the overall appearance of a galaxy.
This issue is addressed in more detail in Ormerod et al. (2024).

Probing the form of this power-law for galaxies of varying stellar masses,
however, yields a more diverse array of free parameters, and one that
correlates with the value of the stellar mass. This measurement shows that
there is a strong correlation between the evolution of the sSFR and the
stellar masses of galaxies (Figure 15) which is tabulated in Table 4. This
evolution reflects a tendency for the higher mass galaxies to drop in sSFR at
lower redshifts, while the lower mass galaxies still tend to contain a high
star formation rate. In fact, we find that the fitted parameters for the sSFR
evolution finds significant differences between the lowest mass galaxies and
the highest in terms of the normalisation parameter $a$, while the slope for
all types, the $b$ value, is quite similar. This is another indication of the
so-called galaxy downsizing, whereby the highest stellar mass galaxies decline
in their star formation rate and AGN activity before lower mass galaxies
(e.g., Bundy et al., 2006). We discuss these results in the discussion section
along with the other findings of the paper to develop hypotheses for how
galaxy formation is driven at early times in the universe’s history.

Stellar Mass |  $a$ [Gyr${}^{-1}]$ | b | $\chi^{2}_{\textrm{red}}$
---|---|---|---
$8.5<\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)<9.0$ | 0.26 $\pm$ 0.18 | 2.41 $\pm$ 0.28 | 3.3
$9.0<\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)<9.5$ | 0.11 $\pm$ 0.09 | 2.36 $\pm$ 0.27 | 11.8
$9.5<\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)<10.0$ | 0.044 $\pm$ 0.034 | 2.36 $\pm$ 0.27 | 3.7
$10.0<\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)<10.5$ | 0.007 $\pm$ 0.004 | 2.34 $\pm$ 0.26 | 15.3
$10.5<\log_{10}\left(\frac{\textrm{M}_{*}}{\textrm{M}_{\odot}}\right)$ | 0.007 $\pm$ 0.003 | 2.39 $\pm$ 0.27 | 47.6
Table 4: The power-law fitting parameters for $\log_{10}$[sSFR] values as a
function of redshift for various stellar mass ranges of galaxies. As shown,
the slopes (the $a$ parameter) of these fits change with redshift, getting
progressively steeper at the highest stellar masses.  Figure 14: The median
specific star formation rates for galaxies grouped by morphology as a function
of redshift. The distribution of the sSFR values for the different
morphological types are also shown plotted as different colours and symbols.
Also plotted for reference are individual sSFRs from previous work. Figure 15:
The specific star formation rates for galaxies as a function of stellar mass.
The symbols are the same as in Figure 14. However, in this instance we have
plotted our sample in terms of stellar mass cuts as opposed to morphological
type. A much stronger dependence on stellar mass is seen.

###  3.7 Galaxy Size and Internal Stellar Mass Density

Using the galaxy sizes and the masses we have calculated for these objects, we
investigate the relation between galaxy morphology/structure and quenching or
the ending of star formation. There are reasons to think that galaxy density,
or rather, galaxy mass divided by the radius (essentially the stellar
potential) correlates strongly with the quenching in a galaxy. This has been
seen at redshifts $z=0-2$ (Bluck et al., 2023), and is related to the idea
that these systems are predicted to host higher central supermassive black
holes, which facilitates the quenching of galaxies (Piotrowska et al., 2022;
Bluck et al., 2023).

If we examine the distribution of mass density $\rho_{*}$ values in terms of
the sSFR in units of Gyr-1 we find that the lower sSFR galaxies tend to have a
higher internal mass density, as seen in Figure 16. This relation is not
however perfect, and it is clear that some galaxies with low sSFR rates are in
low mass density systems. It appears that the stellar potential may do better
at predicting quiescence (e.g., Bluck et al., 2024). This is a sign, along
with the mass as we have already discussed, which indicates what is likely
producing the truncation of star formation in our sample of galaxies. Thus,
whilst we find that mass is a factor, we find that as well the density is also
a factor in producing a change in the star formation in galaxies. Although we
find that even though overall morphology is not a critical factor in
determining the star formation rate and quenching of galaxies, mass density
and the stellar mass of a galaxy is proportional to the quenching effect. We
discuss the reasons this might be the case in the discussion section of this
paper (§4).

Figure 16: The distribution of internal mass density for our galaxies and how
these depend on the sSFR values, shown as histograms. As can be seen those
objects with the highest densities have the the lowest specific star formation
rates at the lower values.

##  4 Discussion

There are several ways in which we can measure how galaxy formation and
evolution occur. With the advent of JWST we now have the ability to determine
how galaxy morphology is part of this process up to the earliest times where
galaxies can be found. This is due to the recent morphological catalogue of
Ferreira et al. (2022) whereby a new direction can be taken as we have
reliable visually-classified morphologies for galaxies at these early times.
The question we address here is what role morphology plays in the formation of
galaxies at $z<7$ and whether there is a correlation between these
morphologies and the way that galaxies have, and are, formed. We use the star
formation rate as a proxy for the ongoing formation rate of galaxies, and the
stellar mass as the integrated history of all mass assembly. While we know
that mergers are important at this epoch and may dominate mass assembly (e.g.,
Duncan et al., 2019), we are not able to measure this directly, although we
can get some idea of its presence through morphology.

The summary of our results is such that we find that galaxy morphology does
not appear to be a critical aspect for the formation of galaxies, at least in
terms of their star formation rates at $3<z<7$. This means that there are
systems which have low and high star formation rates at every visible
morphology that we classify our systems into. It is therefore not the case
that only peculiar or disk like morphologies are those that contain a high
star formation rate – we can see that galaxies we classify into spheroid-types
also have a high star formation rate quite often in the early universe. We in
fact see very little correlation between properties, except for the trends of
sSFR with redshift at different stellar masses, which are significantly
different. Whether these objects are true spheroids, or forming spheroids, is
another question. What is likely shows is that morphology is set early in a
galaxy and events such as star formation do not significantly alter these
structures. Mergers may do so and these will be examined in future studies.

From previous results, mostly from HST, we know that there is an apparent
correlation between the redshifts of galaxies and their structures as given by
the redshift-morphology relation (e.g., Conselice, 2014; Mortlock et al.,
2013). In addition, processes such as mergers can be seen up to these high
redshifts through using pairs of galaxies (e.g., Duncan et al., 2019), and
these mergers can have an influence on the galaxy structures present, as well
as their measured star formation rates. Furthermore, now that we have this new
parameter space of morphology for distant galaxies we can test whether and how
correlations exist that might suggest causality, or to lead to further
investigations of why and how galaxy structure and formation of mass in
galaxies might be correlated (Conselice, 2006a; Kelvin et al., 2014; Bluck et
al., 2023).

In this paper, using JWST observations we find that galaxy morphology, at
least as classified by eye into the classic spheroid, disk, and peculiar types
is not a dominating feature in the formation of galaxies at $z>3$. Whilst we
do find a strong differential in morphological types at lower redshifts at
$z<1$ this difference does not appear to exist at higher redshifts as
strongly. In fact, we find that galaxy mass functions are clearly different
for galaxies that are classified as disks vs. those which are classified as
ellipticals at lower redshifts. We find that galaxy morphology does not
correlate strongly with specific star formation rate, or with the fraction of
passive galaxies as seen at high redshift. Essentially, we are finding that
galaxy structure and galaxy formation processes are largely decoupled to some
extent at high redshifts, as has also been previously claimed for deep HST
observations with WFC3 (Conselice et al., 2011). We can measure the time-
scales for this, given the SFR measurements and the colours of our various
morphological types. First, we know that the SFR we calculate through UV
emission has a time-scale of roughly 100 Myr, thus if some galaxies are formed
in bursts and little subsequent formation, such as ellipticals and spheroids,
then we would expect them to have low SFR and sSFRs after 100 Myr. Likewise,
we can investigate the colours of our galaxies within the UVJ diagram and use
stellar population models to put limits on the morphological and star
formation time-scales.

We show the result of this in Figure 13, which we have previously discussed
when introducing the UVJ results. As shown there, the time-scale for the
spheroids to move from the star forming region into the passive one is several
hundred Myr. This would imply that by the time these morphological types are
at $z=1.5$ we would find them in the passive region, thus establishing the
traditional Hubble sequence of finding a correlation between galaxy morphology
(appearance) and star forming properties. These galaxies must therefore form
their morphology and structure more rapidly than ending their star formation.
If this star formation is truncated by feedback, then this feedback occurs in
a longer period of time than the processing resulting in the morphological
establishment of these systems (Hopkins et al., 2010). We also find that the
peculairs are in the similar region of the UVJ space as shown in Figure 12.
This may indicate that these galaxies are rapidly evolving into spheroids
whilst still undergoing star formation. As these effects are decoupled and the
dynamical effects of changing the morphology can occur within $<0.5$ Gyr
(Whitney et al., 2021) it seems likely that this is why we are finding
spheroids in the part of the UVJ space at $z>1.5$. The high merger rate for
galaxies suggests that this is the reason for the delayed formation of passive
spheroids (e.g., Duncan et al., 2019; Whitney et al., 2021).

Throughout the redshift bins we have studied in this paper at $z<7$, we also
investigate the distribution of SFR within each morphological type, finding
similar conclusions. Stellar mass however strongly correlates with the sSFR,
which we can see as well when comparing our observations to theory from the
FLARES simulation (e.g., Lovell et al., 2021; Roper et al., 2022), as shown in
Figure 17, where galaxies with stellar masses > $10^{10}\textrm{M}_{\odot}$
were decomposed into a bulge and a disc component based on the method
introduce by Irodotou & Thomas (2021).

Another way to investigate these questions is to probe how much star formation
is within each morphological type as a function of redshift. This was
presented to some degree already in the study of overall morphology in
Ferreira et al. (2023). Here we look at this in a very broad way. As shown in
Figure 18, there is a difference in the relative contribution of galaxy types
to the star formation rate density. As can be seen, there is no particular
morphological type that dominates the star formation of the universe at $z<7$.
Again, this demonstrates that there are different modes of producing star
formation, at least assuming these are reflected in the morphologies of
galaxies, but there is a range of these structures at the high end of the star
formation rate distribution at $z>3$. If anything we see that there is a
divergence of the star formation rate for spheroids at $z<2$, which may
signify that this type of star formation, producing a spheroidal structure, is
petering out at lower redshifts. One obvious explanation is that these
spheroidal morphologies are formed from mergers of galaxies, and thus when the
merger rate declines (Duncan et al., 2019; Conselice et al., 2022) steeply at
lower redshifts, this results in fewer compact elliptical like galaxies
forming.

Figure 17: The results of theory for measuring these quantities as taken from
the FLARES simulation from (Roper et al., 2022) . As can be seen we find a
stronger relation between the stellar mass selection for the sSFR evolution,
than we do in the morphological cuts, here taken as bulge to total ratios,
which correlate to some degree with morphological types (Ormerod et al.,
2024).

Likewise, we see that the galaxies classified as disks dominate the fraction
of ongoing star formation rate at all redshifts, with this especially being
the case at the lower redshifts (see also (Ferreira et al., 2023) where this
is also discussed in detail). This means that physics of galaxy and star
formation is likely dominated by whatever processes triggers this in disk
galaxies. The answer to this is beyond the scope of this current paper. This
is likely either from gas accretion or perhaps merging galaxies that produces
a disk galaxy as a final product, although this must happen very early in the
universe. Some analyses show that within a mass selected sample it is indeed
gas accretion which dominates the star formation (e.g., Conselice, 2012), and
it is likely this mode which keeps these galaxies from quenching. However,
more studies are needed to investigate the ways in which star formation is
triggered and sustained in disk galaxies at high redshifts to indeed
investigate this idea.

However, what we are also interested in is inferring how star formation is
quenched in distant galaxies. This is a separate question to that of how star
formation is triggered. What we find is that stellar mass is a factor in this,
but we also find that galaxy density, as defined as the stellar mass divided
by the radius or size squared tends to be a factor in which galaxies have a
lower star formation rate. This implies that galaxies which are denser in
matter have a lower star formation rate. This is also seen for nearby galaxies
(e.g., Bluck et al., 2024), and is likely, or probably, a result of having
more super massive black holes in these lower star forming systems. This is an
example of quenching formed by ’mass’ or by feedback from AGN, something that
we investigate more in Bluck et al. (2024)

Figure 18: The SFR density of the universe at different epochs of time. We
obtain this for each morphology by integrating the corresponding SFR
functions, that is number of galaxies at a given star formation rate, in
redshift bins. For comparison we include data points from Adams et al. (2023);
Bouwens et al. (2023, 2022). The blue (dashed) line is the constant star
formation efficiency model from Harikane et al. (2023), whereas the orange
(dotted) line is the double power law derived by Madau & Dickinson (2014).

Another issue that our results imply is that galaxy morphology in the
traditional Hubble division of spheroid/disk/peculiar is not sufficient to
trace the major formation mechanisms occurring at high redshifts. It is
possible, or perhaps even likely, that there are other classes of galaxies
that can be developed at higher redshifts that correlate better with ongoing
physical processes driving galaxy assembly and the quenching of galaxies.
Tohill et al. (2023) in fact suggests using JWST imaging that there are other
groups in which galaxies should be classified based on unsupervised machine
learning. Time will tell how well this new approach is towards understanding
the evolution and establishment of galaxy structure and morphology in the
universe.

##  5 Conclusions

As part of our series of papers using EPOCHS data, we describe the dependence
of morphology on the star formation and stellar mass assembly history of
galaxies. In this paper we investigate the morphological evolution of galaxies
of various types and compare this with their stellar mass, stellar
populations, and star formation rates. Our primary findings include:

I. The stellar mass function for these galaxies evolves such that the disk
galaxies have a very similar pattern of stellar mass distributions at all
redshifts $z<7$, whereas the peculiar galaxies decrease in average stellar
mass over this time. The spheroid galaxies have the lowest number densities
and flattest $\alpha$ slopes at the lower redshifts.

II. The specific star formation rate (sSFR) for galaxies as a function of
morphology is very similar between the different morphological types. That is,
the relative amount of star formation in a galaxy at $z<7$ does not strongly
depend upon its morphology – we find that spheroids, disks and peculiars all
appear to have the same amount of average star formation, for a given stellar
mass. This signifies that star formation can be produced in different ways in
early galaxies and these can produce morphologies that at least appear to
resemble later galaxy morphological types, or are established in those forms
whilst undergoing star formation events that do not alter the overall
morphologies.

III. We find very little correlation between the morphology of a galaxy and
its star formation rate, both past, and current. We find that all
morphological classes of galaxies can have high star formation rates, with no
significant difference in the fractions of galaxies of various types found to
be in different morphological states. Most notably we find that galaxies
classified by eye as spheroids have a range of star formation rates, and thus
they are not perfect analogs to the ellipticals that we find in the nearby
universe, which are for the most part passive galaxies.

IV. We find that stellar mass is the dominant property which determines when a
galaxy will start to lower its star formation rate by comparing the sSFR of
galaxies as a function of mass and redshift. This is further seen in
simulations of galaxy formation. We further show that the mass density within
galaxies has an important effect on the star formation rate, with the highest
density objects tending to have the lowest star formation rates, although
there is not a 1:1 correlation here.

Overall our results suggest, within the milieu of stellar mass measurements
being correct, that there is a strong trend during all of cosmic time for the
mass of galaxies to strongly depend upon their formation histories. These
formation histories of galaxies are not reflected in any obvious way with the
underlying morphologies of galaxies, such that we cannot use morphology to
predict the star formation rate, which is possible to some degree within the
nearby universe (e.g., Conselice, 2006b; Kelvin et al., 2014). Morphology
therefore might be a very stable feature of galaxies, that are imprinted very
early in their history and outside of major dynamical events or accretion,
they retrain the same morphology over most of cosmic time.

In the future, efforts to quantify the amount of light in these galaxies and
how they are distributed will help resolve some of these questions. This
sample is also investigated in companion papers include Ormerod et al. (2024).
By examining features such as the Sersic index as well as the radius of these
galaxies, and also their non-parametric morphologies, we obtain a better idea
of how galaxy structure influences the star formation and mass assembly of
distant galaxies. This is also the case for methods such as those that utlise
machine learning (Tohill et al., 2023), finding new classes of galaxies that
can then be studied for their properties as a function of redshift as well as
how these evolve with time.

## Acknowledgements

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).
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.

This research made use of the following Python libraries: Astropy (Astropy
Collaboration et al., 2022); Morfometryka (Ferrari et al., 2015); Pandas
(Reback et al., 2022); Matplotlib (Hunter, 2007); photutils (Bradley et al.,
2020)

## Data Availability

The specific observations analyzed can be accessed via
https://doi.org/10.17909/xm8m-tt59, and the visual classifications from
(Ferreira et al., 2023) are publicly available at
https://github.com/astroferreira/CEERS_EPOCHS_MORPHO/.

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