# Building the First Galaxies — Chapter 2. Starbursts Dominate The Star
Formation Histories of 6$<$z$<$12 Galaxies

Alan Dressler The Observatories, The Carnegie Institution for Science, 813
Santa Barbara St., Pasadena, CA 91101, USA Alan Dressler
<EMAIL_ADDRESS>Marcia Rieke Steward Observatory, University of
Arizona, 933 N Cherry Ave, Tucson, AZ 85721, USA  Daniel Eisenstein Center for
Astrophysics Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
Daniel P. Stark Steward Observatory, University of Arizona, 933 N Cherry Ave,
Tucson, AZ 85721, USA  Chris Burns The Observatories, The Carnegie Institution
for Science, 813 Santa Barbara St., Pasadena, CA 91101, USA  Rachana
Bhatawdekar European Space Agency (ESA), European Space Astronomy Centre
(ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid,
Spain; European Space Agency, ESA/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, NL
Nina Bonaventura 1\. Cosmic Dawn Center (DAWN), Copenhagen, Denmark 2. Niels
Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200, Copenhagen,
Denmark 3.Steward Observatory University of Arizona 933 N. Cherry Avenue
Tucson AZ 85721, USA  Kristan Boyett School of Physics, University of
Melbourne, Parkville 3010, VIC, Australia  ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Andrew J. Bunker
Department of Physics, University of Oxford, Denys Wilkinson Building, Keble
Road, Oxford OX1 3RH, UK  Stefano Carniani Scuola Normale Superiore, Piazza
dei Cavalieri 7, I-56126 Pisa, Italy  Stephane Charlot Sorbonne Université,
CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014
Paris, France  Ryan Hausen Department of Physics and Astronomy, The Johns
Hopkins University, 3400 N. Charles St., Baltimore, MD 21218  Karl Misselt
Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ
85721, USA  Sandro Tacchella Cavendish Laboratory, University of Cambridge, 19
JJ Thomson Avenue, Cambridge, CB3 0HE, UK  Kavli Institute for Cosmology,
University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK  Christopher
Willmer Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson,
AZ 85721, USA

###### Abstract

We use _SEDz*_ — a code designed to chart star formation histories (SFHs) of
$6<z<12$ galaxies — to analyze the SEDs of 894 galaxies with deep
_JWST/NIRCam_ imaging by _JADES_ in the _GOODS-S_ field. We show how _SEDz*_
matches observed SEDs using stellar-population templates, graphing the
contribution of each epoch-by-epoch to confirm the robustness of the
technique. Very good SED fits for most SFHs demonstrates the compatibility of
the templates with stars in the first galaxies — as expected, because their
light is primarily from main-sequence A-stars, free of post-main-sequence
complexity and insensitive to heavy-element compositions. We confirm earlier
results from Dressler et al. (2023): (1) Four types of star formation
histories: SFH1 — burst; SFH2 — stochastic; SFH3 — ‘contiguous’ (3-epochs);
and SFH4 — ‘continuous’ (4-6 epochs); (2) Starbursts — both single and
multiple — are predominate ($\sim$70%) in this critical period of cosmic
history, although longer SFHs (0.5-1.0 Gyr) contribute one-third of the
accumulated stellar mass. These 894 SFHs contribute $10^{11.14}$,
$10^{11.09}$, $10^{11.00}$, and $10^{10.60}$ M⊙ for SFH1-4, respectively,
adding up to $\sim$4$\times 10^{11}$ M⊙ by $z=6$ for this field. We suggest
that the absence of rising SFHs could be explained as an intense dust-
enshrouded phase of star formation lasting tens of Myr that preceded each of
the SFHs we measure. We find no strong dependencies of SFH type with the
large-scale environment, however, the discovery of a compact group of 30
galaxies, 11 of which had first star formation at $z=11-12$, suggests that
long SFHs could dominate in rare, dense environments.

galaxies: evolution — galaxies: star formation — galaxies: stellar content

##  1 Star Formation Histories and the Birth of Galaxies — _JWST_ ’s “Prime
Mission”

The _HST & Beyond Committee_ (Dressler et al., 1996) chose a prime mission for
the space telescope that would become the extrordinary _JWST_. The
unanticipated reach of the ‘reborn’ _Hubble Space Telescope_ to galaxies with
redshifts $z=2-3$ — only 2 billion years after “the beginning” — held
extraordinary promise for learning how the modern universe actually _began_ ,
when first generations of stars collected into the first galaxies. Identifying
this as the key moment in our origins — rather than, for example, the Big Bang
— hinges on the idea that the miracle of _this universe_ , and more to the
point, of _life_ , is its incredible complexity. The chemical variety and
abundance that made this possible could never have built to a critical level
without multiple generations of heavy-element-producing stars, residing in
these giant reservoirs we know as _galaxies_.

_“The Hubble”_ as we now affectionately call it, took us to the trailhead of
one of humanity’s greatest journeys: traveling to this remote past to follow
the story of our origins back to the present day.

Central to that mission is the simple notion that galaxies began in very
different conditions — “cosmic environments” — at a time when dark matter was
sculpting a terrain of mountains and valleys in a formerly smooth-as-glass
universe. There and then, “ordinary matter” — the baryons that we would be
made of — were gathered and concentrated by gravity in a way that would
fundamentally alter the very nature of the universe. We had asked questions:
how fast, how turbulent, how explosive, how dynamic were the forces that
shaped these galaxies, so different from our times, when a slow and
irreversible decline dooms this universe to a grinding conclusion that we —
fortunately — will never see.

The tremendous effort and challenge of building _JWST_ is behind us. The
unearthly, spectacular views we now have of the universe — near and far — let
us start that remarkable journey with a large, representative sample of faint,
newborn galaxies, for a first look at how they survived their tumultuous
births.

Where to start? A long-standing and popular approach to the study of galaxy
formation and development has been to push to higher and higher redshift to
compare the properties of ever-younger galaxies. _JWST_ has already exceeded
expectations with images and confirming spectroscopy of starforming galaxies
at $z\sim 13$ (Robertson et al., 2023; Curtis-Lake et al., 2023), a scant 300
Myr after the Big Bang. Other studies identify candidates for even earlier
galaxies; deeper searches and microlensing by rich clusters (Treu et al.,
2022a) promise to provide candidates as early as redshift z$\sim$18\. However,
by their very nature, such searches find extraordinary objects — the brightest
sources at the earliest epochs. In order to assemble a representative sample
of the first galaxies, a later starting point is required: early _JWST_
results suggested z$\sim$12 as an epoch where dozens of galaxies could be
identified in the _JADES_ _GOODS-S_ field, with numbers increasing rapidly
into the many hundreds for z$\sim$6\. This motivated the choice of $6<z<12$
for the present study of the star formation histories. But for their number,
these are the ancestors of the common galaxies we find today.

The paper is organized as follows: Section 2 briefly reviews the methodology —
the program _SEDz*_ — details of of which can be also found in Dressler et al.
(2023), hereafter, Paper 1. Section 3 lays the foundation for this study,
showing and explaining a new format for _SEDz*_ results, with new data that
highlight the four types of SFHs. Section 4 explains how a robust,
representative sample of $\sim$900 galaxies was chosen from a catalog of
_GOODS-S_ sources with 9-band _NIRCam_ fluxes (SEDs) from the _JWST Advanced
Deep Extragalactic Survey_ — _JADES_. Section 5 shows 72 examples of SFHs for
four redshift ranges $6<z<12$, as measured by _SEDz*_. Section 6 looks for
changes in the mix of SFHs over time, and Section 7 presents a summary of the
birth of stellar mass — when, where, and how much — from z$\sim$12 down to
z$\sim$6\. Section 8 investigates correlations of SFHs with environment, and
Section 9 looks ahead to the implications of this study for future
observational and theoretical programs. Appendix A shows histograms of SFH
type with local density and nearest-neighbor distance, Appendix B shows
examples of SFH templates used by _SEDz*_ , and Appendix C discusses the
impact of emission lines on the continuum-dominated SEDs of this study.

A standard cosmology with $\Omega_{\rm m}=0.3$ $\Omega_{\Lambda}=0.7$ and
H0=70 km s-1 Mpc-1 is adopted throughout.

##  2 A Special Tool for a Special Time

The buildup of stellar mass in a galaxy is expressed as its star formation
history (SFH), that is, the rate of star formation changing with time.
Measuring the star formation histories of galaxies has proven more than
challenging, because while groups of young, massive stars are easy to
recognize, populations of stars older than a billion years — though still
young compared to the universe — age in such a way that it’s not possible to
tell a populatioh of old stars from another that is even older.

As part of a galaxy survey of 6 billion years of cosmic history, Kelson et al.
(2014) developed a tool for analyzing a galaxy’s “spectral energy
distribution”— SED, basically, its rainbow of color. By measuring SEDs for
galaxies observed $\sim$4 Gyr earlier in cosmic history, Kelson’s analysis
leveraged those observations to look back $\sim$2 Gyr further, to a time when
the universe was only around half its present age.111…an epoch we can see by
“looking back in cosmic time” — thanks to the late arrival of light in transit
for billions of years. Because of that, the part of a galaxy’s history that
_could_ be reliably measured was extended to when the universe had half its
present age, in this way revealing a substantial fraction of a galaxy’s growth
history. Applying this approach to a sample of a galaxies observed at redshift
$z\sim 0.4-0.8$, Dressler et al. (2018) discovered that $\sim$20% of galaxies
were still growing rapidly — with _increasing_ star formation rates (SFRs), in
an era that was thought to be a time of decline for _all_ galaxies as massive
as the Milky Way.

The motivation for this study, then, emerged directly from that one. The
ability to see only one billion years (or at most two) of star formation
history, a small part of a mature galaxy’s lifetime, stretches to “longer than
the age of the universe” during the period when _JWST’s_ prime mission kicks
in. Our job has been to gather sufficiently good SEDs, using _JWST’s_ near-
infrared camera, _NIRCam_ , to make accurate measurements of galaxy brightness
at a series of colors — infrared light from 1-5µm. Such data can fully
constrain the ages of populations of stars that make up a galaxy, and lining
up their stellar masses — epoch by epoch — constitutes a star formation
history of how the galaxy was built.

In this paper we show the results of our second attempt (see Paper 1) to
transform the flux measurements of each galaxy — its SED — into star formation
histories, the buildup of stellar mass over the first billion years. Our
subjects are a greatly-expanded sample of 894 galaxies at redshifts $6<z<12$
with 9-band near-infrared fluxes from _JWST/NIRCam_. We provide a short
description of a program code — _SEDz*_ — written expressly for the purpose of
reconstructing the histories of galaxies from the rich information encoded in
their SEDs. By choosing a sample of galaxies with ages less than billion
years, their fast-evolving stellar populations will be recorded, for us to
play back.

The development of _SEDz*_ followed Kelson’s maximum-likelihood Python code
for analyzing galaxy SEDs from the _Carnegie-Spitzer-IMACS Survey_ (Kelson et
al., 2014), through the combination of stellar population templates. The
program effectively isolated light from younger ($\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}1$ Gyr) populations of main-sequence
$A$-stars and led to the discovery of “late bloomers” — the $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$20% of galaxies at $z\sim 0.5$ that
produced at least 50% of their stellar mass in the previous 1 Gyr, that is,
_rising_ SFRs instead of the falling SFRs that are conventionally described as
predominant after $z=1$. These _late bloomers_ challenge theoretical models
that tightly couple the growth of galaxies to that of their dark matter halos,
because while it is possible to think of mechanisms that could delay star
formation, it is not easy to imagine why some halos might form so much later
than all the rest.

With this approach, the program _SEDz*_ was developed to exclusively measure
SFHs of the first galaxies. In Paper I we described the challenges associated
with measuring SFHs for stellar populations with ages of more than 1 Gyr, a
deficiency turned on its head when the the population under study has an age
of $\tau\mathrel{\raise 1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$1 Gyr. _SEDz*_ takes advantage of this
unique astrophysical opportunity that comes from the billion-year lifetimes of
$A$-stars (Dressler & Gunn, 1983; Couch & Sharples, 1987). Because they evolve
rapidly over a Gyr, it is possible to _derive_ SFHs from SEDs for $A$-star-
dominated populations, and vice-versa. $A$-stars are among the simplest main-
sequence stars (Morgan & Keenan, 1973): basically _black-body_ radiators with
a relatively simple internal structure and an opacity produced by hydrogen
absorption, thus free from the complications of chemical abundance and post-
main sequence evolution. These are critical and unique advantages for
measuring SFHs during the first billion years.

The data input to _SEDz*_ are SEDs — flux measurements in _NIRCam’s_ 7 wide
bands.222F090W, F115W, F150W, F200W, F277W, F356W, & F444W. Fluxes in the
narrower bands F335M and F410M are not used in the SED fit, but are valuable
in showing the presence of strong emission, particularly [O III] and H$\alpha$
at these redshifts. _SEDz*_ uses a non-negative least squares (NNLS) engine
(Lawson & Hanson, 1995) and custom star-formation templates (Robertson et al.,
2010)333The templates are based on Bruzual & Charlot (2003) models, but
include emission and non-stellar continuum from star forming regions in
calculating the fluxes. that are essentially a set of vectors which have a
significant amount of “orthnomality,” as can be seen in the plots in the
_Appendix B_ , where a more complete discussion of templates can be found.

For this study, _SEDz*_ divides redshifts $6<z<12$ into 7 integer steps,
$12,11...6$ lasting 42, 50, 61, 79, 101, 134, 186 Myr, respectively. _SEDz*_
operates with two sets of SED templates, one with 10 Myr bursts (unresolved
after subsequent star formation) and another characterized by constant star
formation (CSF). The program builds up a SED by adding stellar population
templates (starting at $z=12$ and working down) as needed to improve the fit,
and evolving them forward — adding up subsequent populations to improve the
fit, as measured by ${\chi}^{2}$. The epoch of observation (OE) is chosen as
the lowest ${\chi}^{2}$ and the star formation history is read off as the
stellar mass contributed by each scaled template that, in combination, make
the best fit. This can include the addition of a CSF template which signals
constant star formation at OE. _SEDz*_ can combine a CSF template with a final
burst template to expand its fitting possibilities, as shown in _Appendix B_.

_SEDz*_ requires no “priors” in the important sense that every trial solution,
as lower-redshift templates are added one-by-one, is fully independent of
previous ones. This allows for modeling free of any particular functional form
(e.g., non-parametric) and allowing for a range of galaxy histories. However,
that range is bounded: only 33 templates are used (28 burst, z=12 to z=6,
evolving, and 5 CSF, z=10, 9, 8, 7, 6 — at the epoch of observation). Since
flux ratios are fixed for each template, choosing a template constrains all 7
bands — there is no fitting of individual bands, so an acceptable solution is
not guaranteed: finding one indicates also that the SED _can_ be well-
described by the templates.444Since the templates come from present- epoch
stellar populations, suitability to very-high-redshift stellar populations was
unknown.

Paper I describes the working of the code in considerable detail, so we do not
repeat it here. Also discussed in Paper I are tests of _SEDz*_ , including its
ability to reproduce the SEDs of synthesized galaxies in a simulated deep
field, from the _NIRCam_ “Data Challenge” (Williams+2018). The _Appendix_ of
Paper 1 shows how test-SFHs generated by combining the stellar population
templates were recovered by _SEDz*_ , and how the distinction between bursts
and extended SFHs is robust.

As in Paper 1, we neglect the potential impact of dust. We note, as before,
that galaxies in our sample seem to be well described by SEDs with little or
no dust, consistent with the results of several papers showing that these
initial _JWST_ -selected samples are uniformly blue (Nanayakkara et al., 2022)
and fairly dust free. Our library of stellar population templates includes
sets with extinctions of $A_{v}$ = 0.4 & 1.0. We show in Figure 13 that
extinction at the level of $A_{V}$ = 0.4 is ruled out, in fact, even $A_{V}$ =
0.1 would produce a reddened SED not found in the 894-galaxy sample. While we
did find 27 other examples of steeply rising SEDs in the current work, their
identification as galaxies at high redshift is not possible with _SEDz*_ ,
because of its reliance on the A-star model.555If _SEDz*_ was applied with the
highly reddened A-stars of the dusty templates shown in Figure 13, the
variation caused by unknown amounts of dust would overwhelm the variation that
could be attributed to different ages of stars. We conclude from this that our
sample is by construction a “no-extinction” sample, and that it does describe
more than 95% of galaxies found by deep _NIRCam_ imaging in this field.

However, we do speculate here that the absence of rising SFHs in this and our
previous study could indicate that this phase of galaxy building is largely
hidden by dust, and that the SFHs we find began with 10–20 Myr of intense,
dust-enshrouded star formation, then cleared by its explosive feedback.

##  3 Deriving SFHs of the First Galaxies with SEDz

In Paper 1, we introduced and explained the _SEDz*_ code and applied it to
data from the _GLASS_ _JWST/ERO_ program (Treu et al., 2022b) from parallel
imaging with _NIRCam_ of _NIRISS_ grism spectroscopy of the cluster Abell 2744
(Merlin et al., 2022). Some challenges in processing and calibrating one of
the first deep-imaging programs — a crucial rationale for the _ERO_ program —
limited the targets of Paper 1 to only 24 galaxies that were judged suitable
for a first measurement of SFHs.

To that point _SEDz*_ had only been tested on simulated data of the _NIRCam_
deep imaging program (the _Data Challenge_ (Williams et al., 2018), and on
simulated SFHs produced using _SEDz*_ itself, an admittedly easier test to
pass. Valid questions had been raised about how different the SEDs of the
earliest galaxies might be from their descendants, particularly because the
nature of stellar populations at these early times was largely unknown.
However, the application of _SEDz*_ to the first such data produced
encouraging, and surprising results, in the sense that the program was able to
reproduce 24 complex 9-band SEDs with the code’s limited library of stellar
population templates.666In fact, our first attempt to apply _SEDz*_ to an
early photometric catalog, which expressed fluxes in micro-Jy instead of the
expected nano-Jy, produced only the SED-equivalent of gibberish. In other
words, SFHs with recognizable characteristics, bursts — single and multiple,
and multi-epoch star formation, with reasonable masses in the range of
$10^{8}$ to $10^{9}$ M⊙, fit all 24 SEDs within the errors of the photometry.
Considering the limited number of stellar population templates available to
_SEDz*_ , and their unique shapes, obtaining good fits from the ‘get-go’ was
surprising, and remarkable.

With the comparatively exquisite photometry from _NIRCam_ imaging of _GOODS-S_
for _JADES_ in late 2022, deeper imaging data have led to a $\sim$900-galaxy
sample at redshifts $6<z<12$, and our analysis of these new data confirms the
basic conclusions of Paper 1: good reproduction of observed SEDs and four SFH
‘types’ and, in particular, well-establishing the unexpected prominence of
starburst SFHs over longer, steadier runs of star formation. Moreover, we now
have sufficient data to begin to examine the dependence of these SFHs with
redshift, mass, environment, and large-scale structure.

We begin by revisiting the variation in SFH type. Figure 1 introduces a new
data format for _SEDz*_ output and gives examples of the four types of SFHs
found in Paper 1 and now in this paper, demonstrating both how the code
derives SFHs and that it does so with considerable fidelity. The left-hand box
displays the observed SED — fluxes in each of the 9 bands with 1$\sigma$ error
bars. The NNLS solution _SEDz*_ found by combining stellar population
templates is the magenta band — the quartile range of 21 iterations, each a
random perturbation of the SED by its errors. The ${\chi}^{2}$ of the fit is
inset in the upper-left: a prominent minimum in ${\chi}^{2}$ defines the
observed redshift, or OE. The solution and operation of _SEDz*_ is recorded in
the right box, which shows the stellar mass added at each of 7 epochs (integer
redshifts z = 12, 11…6). This is the how the SFH is calculated, by scaling and
combining stellar population templates to make the best NNLS fit to the
observed SED.

In Figure 1, this ‘best fit’ for the upper-left SED is a starburst — a single
epoch of star formation observed at $z=7$, in this case, a combination of a
burst and constant star formation — CSF. As shown in the left hand panel of
Figure 13 (_Appendix B_), the slope of CSF alone is more level, and a burst
alone much steeper, than what is observed. _SEDz*_ has determined that at a
ratio of 2:1 (more CSF than burst) is an excellent fit to the observed SED.
That is, this two-component stellar population model from present-epoch stars
in our Galaxy “works.” While it might seem remarkable that present epoch
stellar populations provide an almost perfect fit, in one sense this is
completely unremarkable: the $A$-stars that dominate the light of this
starburst at the OE are the least-complicated stars along the main sequence: a
fully convective core and a fully radiative envelope with opacity from
hydrogen ions — no metals required!

Figure 1: Examples of the four types of SFHs $5<z<12$ found with _SEDz*_ . The
text describes how, considered together, these examples demonstrate the
fidelity of _SEDz*_ -derived SFHs. The left box shows the observed SED (black
points with error bars) from 9-band _NIRCam_ imaging and the NNLS fit of
_SEDz*_ — the magenta band, showing the ‘quartile range’ of 21 trials, with
all data points perturbed by 1$\sigma$ random errors. The run of ${\chi}^{2}$
is shown in the insert at upper left; the dip (green star) marks the observed
redshift. Most important is the SFH corresponding to this best fit, shown in
the right box. Each epoch records the stellar mass from that epoch’s star
formation as a small colored box. For each epoch that contributes to the SED
fit, the flux contributed to the solution is plotted on the left box, as a
line of the same color (below the observed SED). Error bars, based on the
quartile ranges of the _SEDz*_ fit, are typically smaller than the boxes, but
a prominent exception is the $z=10$ burst in the lower-right SFH whose
contribution to the mass is uncertain within a factor of $\sim$5 and may or
may not contribute significantly. Error bars do not include systematic errors,
such as errors associated with photometry at these faint levels, but these are
unlikely to perturb the _shape_ of the _SEDz*_ solution. While error bars
corresponding to factors-of-two uncertainty in mass are common in the large
sample of the present work, such errors are not large enough to admit
distinctly different SFHs. The four panels show a starburst (SFH1 — upper-
left) and a double burst (SFH2 — upper-right), a ‘short’ but contiguous run of
star formation (SFH3 — lower-left) and a longer, continuous SFH (SFH4 — lower
right) covering half of the first $\sim$800 Myr of cosmic history to that
point. The expected locations of prominent emission lines are shown above the
SED, in blue; a larger green font marks a possible detection as excess flux
compared the best fit to the flux of continuum _with_ emission lines.

The stellar mass calculated for star formation at $z=7$ is $\sim$3$\times
10^{8}\rm{\hbox{$\,$M${}_{\odot}$}}$. The green arrow signifies the CSF
contribution, with ongoing star formation at OE.777A small arrow indicates
that less than half of the light comes from the CSF template (no arrow ==
none), and a larger arrow means more than half, and as much as ‘all.’ The CSF
template accounts for emission at OE, detected as the modest elevation of
F356W and F444W from the stellar continuum level (F410M) due to [O III]
emission. The CSF template only serves at OE, because stars formed in a prior
epoch are, by definition, old. In fact, although a burst or CSF is the way
_SEDz*_ models the growth of in stellar mass through the epochs, these are
indistinguishable by the next epoch, becoming an “old” population, regardless
of how the mass was spread over the interval. It is also important to remember
that, despite representing continuing CSF at OE, most of the light from the
CSF template is from young A-stars — the O & B stars, and any non-stellar
continuum and emission are gone, except for the last 10-20 Myr.

This starburst example begs the question, could another SFH — for example, a
combination of bursts — also reproduce the top-left SED? The top-right panel
shows that the answer is ‘no,’ by means of a SED that is perfectly fit with a
combination of _two_ bursts: one of $\sim$5$\times 10^{8}$ M⊙ at $z\approx 12$
and a $\sim$2$\times$108 M⊙ CSF+burst $\sim$500 Myr later (OE z$\approx$6).
The integrated mass of this SFH is the red-encircled black dot at
$\sim$7$\times$108 M⊙. Epochs without star formation are marked as lower
limits of $10^{6}$ M⊙. In this study, at the depth of the $JADES$ data for the
_GOODS-S_ field, detections as low as $10^{7}$ M⊙ have been made, but are
incomplete below $\sim$5$\times 10^{7}$ M⊙ (limited by the ‘noise’ from other
epochs of star formation), and severely so below $2\times 10^{7}$ M⊙ .
Nevertheless, it is clear that multiple epochs of star formation cannot
combine to produce the SED on the left, nor can a single epoch of star
formation imitate a double.

Perhaps the most revealing feature of this double-burst example is how clearly
it shows _SEDz*_ combining two widely-separated epochs of star formation to
match the observed SED. The two colored curves below the SED are A-star
templates that correspond to the age of the two bursts. The $z=12$ burst in
orange is that of an ‘old’ stellar population ($\sim$500 Myr before OE), while
the purple curve has the strong ultraviolet flux of a young population
($\sim$100 Myr), demonstrating the ability of _SEDz*_ to resolve $6<z<12$
epoch into old and young populations. This time it is the burst at $z=6$ that
dominates CSF, by 2:1, which accounts for the steeper slope of the purple
template, as shown in the right plot in Figure 13 (Appendix). It is the
striking difference between the two templates that together reproduce the
observed SED that shows how accurately _SEDz*_ can decompose a SED into
separate stellar populations, and how well a SFH can be matched with a
comparatively small number of A-star templates.888As in the single-burst case,
this double burst shows signs of star formation (elevation of the medium
bands) that is contributed by CSF at $z\sim$6\. As we discuss briefly in
Section 5, and show in detail in _Appendix C_ , this emission is not
responsible for the rise in red flux that is provided by star formation at
$z=12$. That contribution has already been accounted for in predicting the two
broad-band fluxes, F356W and F444W.

Before moving on to examples of longer SFHs, we want to clarify why these two
examples are called ‘starbursts,’ given that each represent a few hundred
million solar masses in approximately one hundred Myr. An averaged SFR of only
a few M⊙ yr-1 is not usually considered a ‘burst.’ However, we have no
information on the _history_ of star formation (SFRs) over these individual
epochs: we’re not measuring SFRs, but total stellar mass associated with that
epoch. What makes the top left example a ‘burst’ is that the $z=7$ epoch
contains only young A-stars — that is the template that fits the SED. _No
older A-stars — stars born in previous epochs — are detected_. As we discuss
in Section 9, we think it more likely that the stellar mass we find within a
single epoch was born in $\sim$10-20 Myr within the epoch, with SFRs in the
‘tens’ M⊙ yr-1), and a falling SFR (or even a shutdown) in the $50-100$ Myr
after. Such ‘more-likely’ SFHs would account for the a A-star dominated SED
and a corresponding absence of older A-stars, $\tau\mathrel{\raise
1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$150 Myr. And that is a ‘burst’, by any
definition.

The triple-epoch SFH shown in the bottom-left panel is common in the sample,
particularly at z$\sim$6–8. This example is particularly revealing because of
the flat (purple) SFH at $z=6$ from a CSF template that also produces [O III]
and H$\alpha$ emission, a burst that contributes the peak flux at $\lambda\sim
1\micron$, and a $\sim$200 Myr-‘old’, aging burst from $z\sim 8$ (green) burst
template (but indistinguishable as a burst after $z=8$) that produces the
rising flux beyond $\sim$3µm. In addition to “contiguous,” the three epochs of
star formation are close in mass at 2$\times 10^{8}$ M⊙, a near constant level
of SFH that might continue to $z=5$ and beyond. We note that a small but
significant fraction of these “triples” could be fit with only two contiguous
epochs of star formation, but none of them can be fit by a single epoch SFH.
And, at the redshift most are seen, two or three epochs amount to 300-400 Myr
in duration, long enough to host multiple generations of star formation.

This leads naturally into the the example in the lower right, where 4 epochs
of the possible 6 have substantial star formation that is both continuous and,
like the triple SFH, a coherent decline in added stellar mass. The most
important thing to recognize about these SFHs is that, again, they cannot be
reproduced by the single or a pair of bursts of star formation like upper left
and right, or by the shorter contiguous episodes that are shown in the bottom
left panel (see also the Appendices B & C of Paper I). A long continuous SFH
is defined here as (1) four epochs or more of star formation with less than
factor-of-two uncertainty in stellar mass, and (2) free of two-epoch gaps. The
example shown here, and those that follow in Figures 2—5 are representative of
8% of our $6<z<10$ sample. It is important to reiterate that what matters for
these longer, continuous SFHs is that they exist, rather than a dissection
into gaps, spikes, dips, and wiggles. The data for this study is insufficient
for _SEDz*_ to deliver such detail, and indeed, this might not even be
possible with higher resolution photometric filters or spectra, due to
limitations in NNLS fitting. For example, a single-epoch gap in one of the
continuous histories is likely a consequence of “non-negative solutions only”:
at any given redshift, adding star formation at that epoch may not improve the
SED fit and might even degrade it. For this reason, the longer SFHs we find
here are indicative of the general, not the detailed behaviour of star
formation in the galaxy.

The SEDs and solutions shown Figure 1 are exemplary: they display the very
good fits of a majority of SEDs to single-epoch templates (bursts), and the
ability of combinations templates to fit a range of SED shapes. That the
fraction of cases that ‘fail to find a good solution’ is small is, we think,
strong evidence that the principle behind _SEDz*_ is valid: an $A$-star
dominated stellar populations can be used to recover accurate SFHs for
galaxies in the $\tau<1$ Gyr period of cosmic history.

In the examples to follow, we will see that SFHs of significant duration are
all found to be declining or nearly flat. What is almost absent from the SFHs
shown here is a stretch of _rising_ star formation. As we explained in Paper
I, it is possible to attribute this to the difficulty of detecting a declining
but ‘current’ older population against a young one that was rising in flux but
is now fading — a simple selection affect. However, a more intriguing
possibility is that the flat/declining phase of nearly all first-galaxy-SFHs —
from bursts to long SFHs — were preceded by a strong, rapid burst of _dusty_
star formation lasting $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$50 Myr. Among the galaxies that were
excluded from our sample we find 27 with steep, red SEDs, but _SEDz*_ cannot
be used to determine their redshifts, so their connection to the unobscured
galaxies in our sample remains unknown.

##  4 Choosing a Sample of 6 $<$ z $<$ 12 Galaxies

_NIRCam’s_ exceptional performance and diversity of modes (Rieke et al.,
2023a), have supported Guaranteed Time Observations (GTO) that cover wide
variety of science programs, including exoplanets, star formation, and our
Galaxy with its neighbors. However, the largest component is devoted to the
study of the early universe (Eisenstein et al., 2023) — the era of galaxy
birth. The program described in this paper comes from deep-field imaging that
is beginning to answer longstanding questions about how the first generation
of stars — collected into galaxies that served as reservoirs for the buildup
of heavy chemical elements — fundamentally changed the evolution of our
universe.

This study uses nine-band _NIRCam_ imaging of a $\sim$25-sq-arcmin field of
the _JADES_ _GOODS-S_ survey. The images have been intensively processed, for
calibration, to remove instrument signatures, combine dithered exposures, and
characterize noise. These data were used to produced catalogs of objects (here
v0.7.2) that identifies stars and galaxies, deblend overlapping images, and
generates a number of different radial extractions of photometric measurements
in 9 filters, _NIRCam_ bands F090W, F115W, F150W, F200W, F277W, F335M, F356W,
F410M, and F444W. The catalog used here reached a depth of $\sim$30.0 AB mag
and contained 24,350 extended sources. Our study selected galaxies with
$S/N>5\sigma$ (F200W & F277W flux) within a 4-pixel-diameter circular
aperture, appropriate for the small size of $z>5$ galaxies. Details of data
quality, data reduction, and the production of photometric catalogs can be
found in Tacchella et al. (2023) and Rieke et al. (2023b). To establish our
sample, _SEDz*_ was run on the complete _GOODS-S_ v0.7.2 catalog, with results
sorted into four different redshift ranges, 6$<$z$<$7, 7$<$z$<$8, 8$<$z$<$10,
and 10$<$z$<$13\. To be precise, the actual ranges were shifted down by 0.25
in z, for example, $5.75<z<6.75$, in order to center on the epoch redshift (to
match the templates), in this case $z=6$. From the comparison of _SEDz*_
redshifts with the “known redshifts” of the synthetic _Data Challenge_ , SEDz
was found to have an accuracy of $\Delta\sigma_{z}\approx 0.15$ for $z>6$
galaxies. This better-than-expected performance meant that interpolation
between the templates used by _SEDz*_ was justified and, in fact, not
interpolating could add to systematic errors. For this reason, boundaries were
set as follows: z1: $5.75<z<6.75$, z2: $z<6.75<z<7.75$, z3: $7.75<z<9.75$, and
z4: $9.75<z<12.75$. Thus, when a galaxy’s redshift was found to be within the
range $5.75<z<6.25$, the z=6 template was used, but when $6.25<z<6.75$, a
50/50 interpolation between $z=6$ and $z=7$ templates was made (and so on for
the other samples). In effect, this is equivalent to saying, the ${\chi}^{2}$
for $z=6$ and $z=7$ are the same (within errors), so the program averages the
SED solutions (resulting SFHs), for those two redshifts.999In some cases,
averaging the two solutions appears to have stretched out the SFH by one
epoch, but we could not distinguish cases where this was the right thing to
do, as opposed to shifting one or the other solution. This is likely to have
produced some SFH3 types from 2-epoch SFH1 types. This potential and we
believe uncorrectable error does not alter the outcome or conclusions of our
study. Eventually, data for the separate redshift ranges would be combined
into a catalog spanning the full $5.75<z<12.75$ range, but the previous step
allowed an investigation of performance over the redshift range that was
helpful.

By fitting combinations of stellar population templates, _SEDz*_ found
maximum-likelihood fits to SEDs that yielded redshifts in these four redshift
intervals. A well-recognized problem in deriving $z>4$ redshifts from SEDs is
a degeneracy with $z\sim 2$ galaxies where _NIRCam_ ’s range of $1-5\micron$
translates into a rest frame coverage of $\sim 0.3-1.7\micron$, typically
covering a Balmer-break over an otherwise flat SED. When very faint galaxies
are the targets, these are easily mistaken for $z\sim 6-8$ galaxies with a
Lyman-break. We used three different methods to mitigate the problem. First,
we wrote code in _SEDz*_ that compared the shape of the ${\chi}^{2}$ curve
when _two_ minima were found, one for $z\sim 2$ and another for the higher
redshift. During the ‘Data Challenge’ tests, we found that using the overall
slope of the run of ${\chi}^{2}$ with redshift, the depth and width of the
minima, and the color of the _SEDz*_ itself, removed roughly 50% of cases. We
also used archived _HST_ data to find at least two 2.5$\sigma$ detections in
three visible bands of the _WFC3_ imaging, F606W, F775W, and F814W. Flux below
the Lyman-break is the best rejection method, but we have found that, for
galaxies this faint in the near-infrared, only about one-third of low-redshift
galaxies are detected in these bands, even with the deepest _HST_ imaging
available. The third check was to use EAZY ‘photo-z’ redshifts for the
cataloged objects, part of _JADES_ team data processing for internal and
eventual community use (Hainline et al., 2020).

The procedure was to run _SEDz*_ for each redshift interval using only (1) the
rejection of low-z objects by detection of visible flux and (2) the internal
_SEDz*_ $z<4$ rejection. This produced four subsets with 759, 374, 277, 61
galaxies at z6-7, z7-8, z8-10, and z10-13, defined in Section 4 as z1, z2, z3,
and z4 (shifted by -0.25 from integer z values). Taking the _SEDz*_ redshift
(hereafter, $z_{SED}$) as the adopted redshift was required, because that is
the value for which the SFH is derived, but comparing $z_{SED}$ with EAZY-
derived redshift, $z\\_a$, and finding them consistent was taken as the next
level of “qualification.” This was termed the “gold sample,” and amounted to
446, 183, 115, and 15 ‘confirmed’ objects.” This left 313, 191, 162, and 46
objects with $z_{SED}$ _unconfirmed_ by $z\\_a$. Their SEDs were inspected,
one-by-one, to decide if the Lyman-break range was sufficiently well defined
to suggest a low-redshift for the galaxy. If so, the 7 wide-band images
(readily accessed through a ‘ _FitsMap_ ’ viewer from the _JADES_ image-
processing team) in particular, the F090W, F115W, and F150W images, were
inspected in order to evaluate _visual_ evidence for a Lyman-break. From these
$\sim$712 inspections, 225, 123, 103, and 38 galaxies were rejected. The
remaining 88, 68, 59, and 8 galaxies were added to the “gold sample,” based on
judgement that at least half of these were at the higher redshift found by
_SEDz*_. The count for the four redshift slices was then: z1—534, z2—251,
z3—174, and z4—23, a total of 982 galaxies.

Subsequent to the first release of this paper, we “pruned” the data sample
further. An additional 72 galaxies were deleted from z1, 18 were deleted from
z2, and 2 were moved from z2 to z3. About half had been removed in ‘FitsMap’
inspection for proximity to diffraction spikes; the remaining half was split
between marginal ‘S/N$\approx$5’ cases and poor overall fits of the model to
the data. The final numbers for this study are z1—462, z2—233, z3—176, and
z4—23 (unchanged), a total of 894 galaxies.

##  5 Further Examples of SFHs

To expand on the introduction of the four SFH types we showed in Figure 1, we
show 18 examples for each of four redshift ranges in Figures 2, 3, 4, and 5.
In each, there is a row-by-row progression, starting from the top, from a
single burst population, through stochastic (multiple bursts), to contiguous
epochs of star formation, and finally longer, continuous over four or more
epochs.

_SEDz*_ plots, like the ones that follow, and their associated data, will be
available for the full 894-galaxy sample at
https://obs.carnegiescience.edu/SEDz-star/SFHs.

Beginning with Figure 2, we see three examples of a $z=6$ starburst, each with
a mass of $\sim$2$\times 10^{8}$ M⊙. As in the discussion for the burst SFH in
Figure 1, a single epoch of star formation — both occurring and observed at
$z\sim 6$ — is a very good fit to each observed SED101010Recall that the
magenta band shows the quartile ranges of solutions while the single purple
line shows a _single_ solution that is used to break down the SED into its
component parts, epoch by epoch.. For all three, the solution is a combination
of a burst and continuing “constant” star formation (CSF) with less than a 50%
contribution to the flux(denoted by the small green arrow). (A confirmation of
the redshift found by _SEDz*_ is the [O III] emission in the top left case,
detected in the medium band filter F335M.) Again, the excellent fit found for
such cases validates that the stellar population templates are correct for the
task. Single bursts are the most common SFHs in our study — 473 cases, 53% of
the full sample.

We also identify the next two examples (second row, left and center,
hereafter, ‘2l, 2c’) as _single bursts_. Their _two-adjacent epochs of star
formation_ , may be unresolved, that is, one event that is best fit by using
consecutive templates. In both 2l & 2c the burst at $z=7$ would have been very
blue, but one epoch later – when these galaxies are observed — their
contribution rises to the red, causing the elevation in each spectra. It seems
reasonable that star formation episode of $\tau\sim 100$ Myr could produce
this _SEDz*_ result by spanning the relatively long “integer-redshift” epochs
of $z=6$ and $z=7$. Under this interpretation of a single event, we include
later examples where the two masses differ by as much as an-order-of
magnitude, implying a sharply rising or falling episode of star formation.

Figure 2: Examples of the identified four types of SFHs of this study observed
at redshifts $z\sim 6$ ($5.75<z<6.75$), starting with three examples of single
starbursts in the top row and continuing in order, across the rows and and
down, to multi-burst “stochastic” histories, three-epoch _contiguous_ runs,
and finishing with long SFHs of four epochs or more. Detailed explanations of
the salient characteristics of these types are described in the text.

Figure 3: A virtual ‘replay’ of the types in Figure 3 for 18 galaxies at
$z\sim 7$ ($6.76<z<7.75$), as described in the text. This set includes five
examples with very high S/N [Row(1-5):position(left-right-center)] = 1l, 2l,
2r, 3r, and 4c, that are exquisitely fit by _SEDz*_ with its “present-epoch”
templates, demonstrating the fidelity of the SFHs that _SEDz*_ can deliver.

The next examples, which exhibit well separated bursts, are additional
demonstrations of the ability of _SEDz*_ to reveal dominant early star
formation in galaxies observed $\sim$500 Myr later, giving confidence in its
identification of SFHs that extend over the $6<z<12$ range of our study.
Comparing the stellar population templates shown in the _Appendix B_ , it is
clear that these three examples show histories that cannot be reproduced by
_any single stellar population_. Figure 2 shows 3 examples (2r, 3l, 3c) of
strong, well-separated bursts of star formation. We call these _stochastic_
SFHs because it seems unlikely that these separate bursts can be “tied
together,” not even if there was weaker, undetected star formation in-between
(which would be at least an order-of-magnitude smaller in mass). The following
SFH (3r) is interpreted as either 3 or 4 epochs of star formation starting at
$z=10$). All four are graphic illustrations of very young, blue stellar
population whose red flux has been ‘boosted’ by older populations, at
$z=10-12$. For all four of these _stochastic_ SFHs, redshifts are again
confirmed by [O III] emission in the F335M band. Stochastic star formation, by
our definition, is almost as common as the single bursts (in total epochs of
star formation), adding 165 cases (19%) of two or more bursts. Together,
‘bursts’ and ‘stochastic’ make up 72% of SFHs found here: clearly, this is a
strong and, we believe, unexpected, _dominant mode_ of galaxy building in its
beginnings.

However, the bottom 3 rows of Figure 2 remind us that a significant fraction
of early galaxies are undergoing more orderly, gradual growth. In examples 4l,
4c, 4r and 5l three stellar populations are required to fit the observed SEDs.
SFH3 star formation is usually “contiguous,” but sometimes with a one-epoch
gap, likely due to ‘noise’ or the asymmetry in NNLS solutions — no negative
star formation. (See Figure 3, the gap in 4c, but note the $z=9$ star
formation 4l that shows the opposite — a _detection_ that is dubious). SFH3
describes 21% of full sample (25% of the $z=6$ sample). All three have final
star formation at $z=6$ with and added CSF components, hence the very flat
purple CSF contributions (see _Appendix B_). Again, it is also clear that no
amount of $z=6$ or $z=7$ star formation can produce the ‘rising-to-the-red,’
in all but 4r, with its uncertain star formation at $z=8$ and noisy SED.
Although they look short, these last 3 epochs add up to half-a-billion years,
or half of the time since the Big Bang, so these are a substantial departure
from what seem to be the dominant SFH mode — $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$100 Myr starbursts.

The final 5 examples, 5c, 5r and row 6, are longer, more-continuous histories
(SFH4) that stretch over the full redshift range, with 4 to 6 epochs of star
formation. Although two have a 2-epoch gap that could have landed them in the
‘stochastic’ category, for all there is an orderly history of constant or
declining star formation. These are pronounced examples of young stellar
populations with a history of very early star formation that accounts for
their strongly ‘rising-to-the-red’ SEDs. All five show $z=11$ and $z=12$ star
formation, however it is likely that this period of $\sim$100 Myr is not
“resolved,” so the SED could be reproduced by only one, with the combined
mass. Although they represent only 3% of the $z=6$ population and only 69
galaxies in the 894-galaxy sample (8%), the persistence of SFH4 over the full
time range explored here suggests a different environment, one where galaxies
can evolve more slowly and relatively undisturbed, for example, experiencing
only minor mergers.

From this first set we see the prevalent signature of early (z
$\mathrel{\raise 1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}10$) star formation: a SED rising to the
red, often accompanied by substantial star formation at OE. This is best seen
by the different levels for the medium bands F335M and F410M than is defined
by the 7 broad-bands. This raises the question of whether strong emission
lines could be boosting the far red fluxes and mimicking early star formation.
We show in _Appendix C_ that this should not be the case, because the CSF
templates _include_ active star formation, so that the level of the broad
bands cannot be ‘raised’ by emission — it’s already included.111111The caveat
is emission is much stronger than in the present-epoch star-formation _SEDz*_
templates: the “rise-to-the-red” could be mistaken for star-formation hundreds
of Myr earlier. This effect is likely to be seen in the present study, at a
level of ‘factor-of-2 or less’ excess stellar mass for a $<$10% fraction of
the SFHs (see _Appendix C_). For example, SEDs 5l and 5r of Figure 3 are very
similar, with strong [O III] emission the only high points, suggesting that
the SED rise is due to stronger emission than in the templates. In contrast,
the center SED has a steadily rising fit that is certainly the result of the
$z=12$ star formation. The medium bands F335M and F410M (open circles — not
used in the NNLS fit) provide good reference points for the presence of
emission and the level in the continuum, because emission-line strengths were
not calculated for the narrower bands. _Appendix C_ provides more examples and
discussion.

For further examples of SFHs, Figure 3 shows for $z\sim 7$ a virtual replay of
the $z\sim 6$ population: 5 individual bursts (4 single, 1 ‘twin’), 4 well
separated “stochastic” events, 3 more triples, 3 noisy SFH3/SFH4 histories,
and 3 long SFHs, none with a gap of more than 1 epoch, and two cases with star
formation in all 6 epochs. (Some have large error-bars that remind us that
these are “representative” star formation histories, not to be considered
faithful “epoch-by-epoch.)” As in Figure 2, but not explicitly called out, are
very high S/N examples, in particular, examples 1l, 2l, 2r, 3r, and 4c are
well-defined SED solutions that match the fluxes of the data with remarkable
fidelity. Considering the relatively crude redshift-resolution of the stellar
population templates, the agreement of model and data is convincing evidence
that the modeling works and the templates are fully “descriptive:” 3 or 4
templates are usually all that’s needed, and that’s good, because that’s all
that are available!

Figure 4: The persistence of the four SFH types reaches back $\sim$700 Myr
from $z\sim 6$. No obvious _evolution_ of the mix of types is apparent,
although changes in “proportions” may be appearing (see Figure 6). At this
earlier epoch the prominence of the Lyman-break is a strong factor in finding
the redshift and establishing the SFH. More than half of these $8<z<10$
galaxies show detected star formation back to $z\sim 11-12$.

Figure 5: 18 of the 25 examples $z\sim 10-12$ in our 894-galaxy sample. The
Lyman-break now extends from F090W into the F115W filter as well. The
timescale covered in this figure is only $\sim$200 Myr, shorter than most of
the longer histories we find at lower redshift, but there are three cases —
2c, 3c, 5l — that seem to cover this whole period.

Extending the redshift coverage up to $z=8-10$ in Figure 4 shows that the
classification into the four types of SFHs continues to earlier times. All are
represented in similar frequency to those at lower observed redshift. The
Lyman-break is, of course, pronounced, which helps with constraining the
_SEDz*_ fiting. Most of the the bursts (single and double) in the top three
rows rise sharply to the (rest-frame) ultraviolet — signaling very young
populations, but conversely, the bottom two roles show the steepest rise to
the red in the sample, in this case signaling strongly declining rates of star
formation since $z=12$.

Finally, in Figure 5, we see 18 of the 23-galaxy-sample of the highest
redshifts. The Lyman-breaks are clifflike, and the SEDs are all blue within
this sample that covers only $150$ Myr, only $\sim$200 Myr since $z=20$ when
the first “modern” galaxies were likely born. Rapid evolution of the universe
at this time, especially the strong growth of dark-matter halos and rapidly
decreasing density of large-scale structure, suggests star formation that
might be itself changing in character or composition. Yet, remarkably, the
stellar populations we observe are all matched by the stars that we have all
around us today, some 13 billion years later.

##  6 SFHs Across Time

Does the population of SFHs itself ‘evolve’? Figure 6 plots SFH type for 894
different galaxies as measured at their epoch of observation, color-coded to
show burst SFHs as red and orange (single and multiple), with contiguous
‘triples,’ and continuous ‘long SFHs,’ as green and blue. To first order, we
see two things: (1) the “final” masses of all 894 in our SFHs sample are
largely confined to $10^{8}$–$10^{10}$ M⊙, and (2) all four types are
represented over the full redshift range covered in this study. That there are
some “accumulated” stellar mass below $10^{8}$ M⊙, but none below $5\times
10^{7}$ M⊙, is a simple detection limit: the fluxes would generally fall below
the $S/N>5$ limit we have chosen. On the other hand, the steep falloff in
numbers above $M>3\times 10^{9}$ M⊙ is probably a reflection of astrophysics,
for example, stellar feedback suppression in the environment of rapid star
formation in the compressed volumes of these sub-kpc-sized sources. Powerful
feedback is probably expected in the case of the bursts, but it is less
obvious why the longer histories, with lifetimes of hundreds of Myr, would be
subject to the same limitations, and yet the distribution here suggests,
interestingly, that they are. This, and the clear result that most of the
stellar mass in this formative time is made in relatively large starbursts,
should place strong constraints on numerical simulations of galaxy growth.

The ‘evolution’ of the proportions SFHs over time is harder to parameterize,
but it is clear from the fact that all types show up over the diagram that
there is no strong evolution of the _population_ of SFHs. Figure 7 shows a
crude graph of the frequency of the four SFH types for the sample in Figure 6.
With the exception of the 70% fraction of bursts at the highest
redshifts121212This probably not a result of small-number statistics as it is
the smaller interval of time to express the four SFH types, the variation in
the rest of the plot is ‘factors-of-two’ and not much in the way of trends.

We should add that there is some non-statistical “bunchiness” in Figure 6,
such as the ‘swells’ of SFH3 ‘contiguous’ at $z\sim 6.5$ and SFH4 ‘long-SFHs’
at $z\sim 7.5$, and the ‘valley’ of single-bursts at $z\approx 6.5$, but we
believe that these are more likely _SEDz*_ “preferences” associated with
interpolating between the epochs, rather than a real effect. A denser sampling
of epochs, with twice the time resolution for the templates, would likely
resolve this, but for now we focus on broad trends.

The lack of strong change over time (for this early period) provides little in
the way of clues about the nature or “causes” of the different histories. This
suggests that dependencies based on space, rather than time, might provide
more insight. We investigate this in Section 8.

Figure 6: The stellar masses associated with the four SFH types displayed over
the full $6<z<12$ time frame of this study. The bottom scales are the age of
the universe in megayears, and the duration of each of the 7 epochs of this
study. Each dot represents a galaxy at the epoch-of-observation, at its final
mass, with SFH type indicated by dot-color. (Figure 8 & Figure 9 show the
period spanned _by each SFH_ by “connecting the dots” from the beginning to
end of stellar mass growth.) The most important feature in this figure is the
presence of all four types over the full range of epochs. Proportions of the
four SFH types appear to change over the distribution (for a rough picture,
see Figure 7), like the apparent “swells” in long-SFHs (SFH4) that appear at
$z\sim 7.5$, or contiguous histories (SFH3) at $z\sim 6.5$. These may be the
result of a biases in _SEDz*_ or, for example, large-scale structure, but the
full coverage of each SFH type in both epoch and mass is the takeaway.

Figure 7: The rough proportions of the four SFH types with redshift, derived
from the distribution in Figure 6.

Figure 8: (_left_) The contribution to the stellar mass during the period
$6<z<12$ from galaxies dominated by bursts. Galaxies with SFH1 histories are
red dots; with ‘handles’ mark their epoch. Orange tracks — SFH2 — begin with
the first epoch of star formation and connect to the last, showing that such
systems do not grow more than factors of 3 or 4. Instead, new systems appear:
that is how total stellar mass grows during this period. The single burst
cases do not add substantial mass until $z\sim 9$ (see Figure 9.) (_right_)
The longer SFHs, both 3-epoch contiguous (SFH3) and 4-or-more-epochs
continuous (SFH4) show substantial growth from $z\sim 12$ to $z\sim 6$,
reaching a similar level of contributed mass in the range of $10^{8}$–$10^{9}$
M⊙ (Figure 9), but a factor of 3 less than the SFH2 multiple bursts. For both
SFH3 and SFH4, the stellar mass accrues over $\sim$0.5–1.0 Gyr, perhaps
suggesting less volatile surroundings and circumstances in their development
compared to the SFH1 and SFH2 burst histories.

Figure 9: The combined diagram showing all (beginning-to-end) histories,
summed to produce the integrated mass (recorded as the colored lines above).
The substantial growth in stellar mass that happens in this volume of space
from $z=12$ to $z=6$ is mostly from adding sources, amounting to the 894 we
collected for our study. SFH1 and SFH3 rise rapidly and reach nearly the same
value of $\sim$1011 M⊙ . SFH2 accumulates as much mass, but is flatter
because, typically, these begin with an strong early burst and end with a
much-later, smaller one. The contribution of SFH4 is also flatter, rising by
only a factor of $\sim$3, due to declining mass contributions, in this case.
SFH4 histories contribute a factor-of-three less mass than the others, the
result of their lower frequency of 8%. Making the principle point of this
paper again, SFH1 & SFH2 combine to contribute 2.6$\times$ 10${}^{(}11)$ M⊙ of
the total stellar mass — 66%. Starbursts rule.

##  7 A Galaxy is Born

Returning to our theme, we want to explore how the results obtained in this
study can help in understanding how galaxies began to grow and build up the
essential elements for planets and life. Specifically, how has the progress of
star formation proceeded in the first billion years of cosmic history,
birthing and growing new galaxies in a environment more gas-rich and more
turbulent than we easily imagine? At the same time, these young galaxies are
likely fed continuously by smooth inflow of gas, incorporating less massive
galaxies and adding their moderately metal-enriched stellar populations. All
this continues as young galaxies are vulnerable to violent major mergers and
the huge energy released in massive starbursts, and possible large-scale
changes through black hole formation and growth. It is not likely that such
questions will be answered solely through observations but, rather — as always
— theory will be required to explore the physics of each of these elements.
Numerical simulations should benefit greatly from these kind of data,
replacing previous and various speculations, where the manifestations of star
formation that set the course are reproduced, and, we hope _understood_.

What we have found in this study already confirms the dynamism of the epoch
where galaxies achieved masses of $10^{8}$–$10^{10}$ M⊙. We find large
contributions to the growth of stellar populations by bursts unlike any we see
today, strong enough to produce a stellar mass of $10^{8}$–$10^{9}$ M⊙ in an
episode lasting only $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$100 Myr — little more than a dynamical
time — and, apparently, strong enough to ward off further star formation for
more than $\sim$500 Myr, and maybe even a Gyr. And yet, we also see common
cases of multiple bursts over which the total stellar mass can reach well over
$10^{10}$ M⊙. What is the difference, then, between these and systems making
the similar amounts of stellar mass, but over the same long period of time
where bursting galaxies seems to go dormant?

A good way to appreciate the power of these data can be seen in Figure 8 and
Figure 9, where we plot the mass buildup over $6<z<12$ from these different
modes of star formation. These plots use the _SEDz*_ star formation histories
for our 894-galaxy sample to graph the onset of star formation and, in the
cases of longer SFHs, its subsequent addition of stellar mass. Here we have
“connected the dots” — from when star formation began to the last epoch where
it is detected — to show stellar mass buildup. (Color coding is the same as
for previous figures.)

Figure 8 (left) shows this for single bursts and bursty ‘stochastic’
histories, SFH1 & SFH2, and (right) longer “contiguous” and “continuous”
histories, SFH3 & SFH4. In an effort to provide guidance to numerical-
simulation modelers trying to answer such questions, we now express the data
we have described here in terms of the growth of galaxies with such different
histories in mass-buildup diagrams. The plot is for mass versus time, as in
Figure 6, but now with tracks that connect the first and last epochs of
recorded star formation within the $6<z<12$ era. In Figure 8, SFH1 — a single
burst, shows up as a dot with a handle marking its epoch, while an SFH2 —
“stochastic,” in orange, appears as a shallow rise, since the two bursts are
usually well separated. It is also easy to see that, while the single bursts
are the most common SFH type, multiple bursts are both larger in mass to begin
with (we find mostly declining SFHs) growing with subsequent bursts, such that
they add the most mass over most of this era. A critical point, though, is
that the mass from these burst-dominant galaxies is growing through the
appearance of new bursts. The most frequent number of bursts for SFH2 galaxies
is just 2 — a single added burst rather than a several. Stellar mass is
primarily growing by adding bursting objects, single and multiple, not by many
smaller bursts in each galaxy.131313Recall that, although we use a burst to
represent each epoch of recorded star formation, the stellar mass formed is –
from later epochs – unresolved. The “dot-like” representation of SFH in the
_SEDz*_ plots is only symbolic. The same diagram for the 3-epoch ‘contiguous’
(SFH3) and 4-epoch or more ‘continuous’ (SFH4) histories shows more tilt in
its tracks: this is most obvious in the 3-epoch tracks that become more and
more dominant from redshift $z=9$ down.

Putting it all together in Figure 9, we combine the burst and longer
histories, summing and integrating to learn how the stellar mass of this
collection of 894 galaxies grew from $z=12$ to $z=6$. We see the contribution
of single bursts grow strongly, while the average mass for SFH1 — the lowest
of the 4 types — does not increase over the full redshift range. By $z\sim 6$
the single-burst, stochastic, and continuous histories have each added
$\sim$$10^{11}$ M⊙ to this volume of space. The SFH4 galaxies have contributed
a factor-of-three less mass, but most of this is the result of their lower
frequency of 8%, so this means that all 4 types contribute a similar amount of
stellar mass from $6<z<12$. Finally, we plot the integrated stellar mass for
this special epoch, which reaches $4\times 10^{11}$ M⊙ in this volume at
$z=6$, and is growing at a rate of $\sim$500 M⊙Myr-1.

We hope that both the rates and manner of star formation in these youngest of
galaxies will provide the first meaningful constraints for numerical modeling
studies of the evolution of the universe at the end of the first billion years
of cosmic history.

##  8 SFHs Across Space

SFHs are known to have a strong spatial variance, in the sense that different
kinds of galaxies (for example, ellipticals as opposed to spirals) are found
to dominate in different environments (Dressler, 1980), and the different SFHs
of these have clearly differed greatly. Recognizing this, we looked at the
spatial distributions to see if galaxy ‘environment’ could be connected to the
four types of SFHs. Figure 10 shows the distribution on the sky of the four
SFHs (again with the same color encoding). There is obvious large-scale
structure in the z1, z2, and z3 maps, especially in the lowest redshift $z\sim
6$ map, where the contrast between large voids and substantial clustering is
strong. This is probably both a result of the growing clustering with epoch,
but also because our much larger sample makes any contrast more discernible.
Still, there is a strong impression of substantial large-scale structure over
the period $6<z<10$ — covering most of the epoch of reionization. A map of
only the 23 galaxies in the z4 sample is not useful, of course, but we have
made another view of the $z=11-12$ universe that we discuss below.

It is not surprising that there are no _visual_ spatial distribution
differences in the four SFHs, but it is reasonable to expect that correlations
of SFH types with local-density, or with nearest-neighbor distance, might
provide some insight into whether the environments of these galaxies influence
their SFHs. In Figure 11 (_A_ ppendix A) we show histograms of local-density
and nearest-neighbor-distance for the $z\sim$, $z\sim 7$, and $z\sim 8-z9$
redshift ranges (aka, z1, z2, z3). The left three panels show density ranges
that vary from a few to tens of galaxies arcmin-2. As with Figure 6, the most
notable feature of these diagrams are ups-and-downs likely associated with
density fluctuations, with no clean separation by type. Perhaps there is a
slight preference for the longer SFHs to be in denser regions or closer to
their neighbors, but nothing clear enough to be helpful.

Figure 10: The distribution on the sky for the three redshifts ranges z1, z2,
& z3, along with a map of galaxies found by _SEDz*_ to have had ‘first star
formation’ at $z\sim 11-12$ (lower right — see text). The four square figures
essentially cover the full period of reionization. Large-scale structure, in
the form of large voids and swaths of higher galaxy density, is evident in
each map, for the z1, z2, & z3 samples. The SFH of each galaxy is represented
by color: SFH1: burst = _red_ ; SFH2: stochastic (multiburst) = _orange_ ;
SFH3: 3-contiguous epochs of star formation = _green_ ; SFH4: long, continuous
star formation = _blue_. However, there are no obvious correlations between
location with respect to other galaxies of different SFH types visible from
these maps, so if these exist, they must hold for higher density contrasts.
The bottom-right square map shows just such a higher concentration of galaxies
— those with ‘first star formation’ at $z=11-12$ (this tight group is also
visible in the panel above), with the surprisingly clear result that the
rarest of our SFHs — long and continuous — are highly represented compared to
the study sample. An enlargement of the area ($\sim$2 arcmin) appears on the
right.

However, in the sky maps of Figure 10, the fourth panel may hold an important
clue about the role of environment. Here we have done something new, based on
the ability of _SEDz*_ to identify prior star formation from galaxies observed
at later epochs — galaxy star-formation histories. We made this map by
choosing galaxies for which _substantial_ star formation has been detected at
$z=11$ or $z=12$,141414We consider these epochs to be effectively
indistinguishable and in doing so, selected 201 galaxies of our sample of 894
that had their _first epoch_ of star formation at that time: we plot in the
fourth panel what a sky with galaxies forming stars at z=11-12 might have
looked like.

Remarkably, we see a relatively tight galaxy group of 30 members in an area
less than $\sim$2 arcmin-2. Eleven of those, 37%, are SFH4 —long, continuous
SFHs, only 8% of the full sample in this study. We claim that this detection
of many long SFHs ‘spatially,’ while not statistically conclusive, is a unique
data point in the search for an environmental dependence of SFH type.
Furthermore, this distribution further confirms that _SEDz*_ actually works:
there is no other explanation for how these two quantities — position on the
sky and SFH — could be well-correlated. If the star formation at $z=11-12$
_SEDz*_ detected were bogus, these galaixes would spread randomly across the
field.151515(Dressler et al., 2018) found a similar spatial dependence for
_Late Bloomers_ and argued that their affinity for other late bloomers
confirmed the legitimacy of their unconventional SFHs The clustering, and also
what appears to be large-scale structure for the full sample of galaxies,
confirms these ‘earliest’ SFHs. In addition, above and below the circled area,
the density remains high and appears to contain a higher fraction of SFH4
galaxies, compared to the much larger sample of the left side of the figure.

Subsequently, we noticed that this this higher-galaxy-density region also
shows in the upper right panel, $6.75<z<7.75$. In fact, this galaxy group had
already been independently discovered by members of the _JADES_ team (Endsley
et al., 2023), at an _observed_ redshift of $z\sim 7.5$, further confirming
their long SFHs. Even more members are observed at the later epoch.

This fortunate ‘feature’ of the _GOODS-S_ field called to mind that, for the
original morphology-density relationship, Dressler (1980) and Postman & Geller
(1984) found no gradient in morphological type beyond the rich-cluster
boundaries, that is, no slowly changing populations beyond the effective
radius of the cluster. This and other evidence convinced Dressler (see Section
IV-C) that the origin of the morphology-density relation lay not in the late-
time evolution of the cluster or its galaxies. Rather, it pointed to an
environmental dependence arising at the epoch of galaxy birth: the different
morphological types were foretold by their birth environment, a kind of _early
nurture_ that is in fact _nature_.

Soon there will be more deep-field imaging like _GOODS-S_ and more groups will
be found at — incredibly — at $z\sim 12$. This result, if confirmed by many
other cases, might suggest a rather obvious conclusion about the different
SFHs we have found here: burst histories are most common in the equivalent of
the lower density “field” of the modern universe, probably the result of
stochastic merger events that reflect the sparser environment. In this
picture, long SHFs are destined for the richer, denser environments of the
future. They would be galaxies that, unlike the “bursts,” were built up in a
more orderly series of accretion events and minor mergers.

##  9 Writing Chapter 3: The Age of Starbursts?

Observations of the early universe with the incomparable _JWST_ already have
already had a profound effect on our ideas about how the first galaxies were
born and how they grew. In scarcely more than a year, hundreds of studies have
feasted on galaxy samples that are large, deep, various, and multiplexed. They
have been probed with diverse modes of cameras and spectrographs that are
unprecedented in a space telescope, offering factors of hundreds to thousands
greater sensitivity in the near-to-mid-IR: the early universe is viewed anew.

Our study is but one of multitudes focused on the rise of stars and galaxies,
the elements that redefined the universe at the very epoch we now explore —
for the first time. So far, this wealth of _JWST_ data tells a new story: that
the birth of galaxies appears to be a volatile affair. Specifically, a central
theme has been that “starbursts” are prevalent in this first billion years, or
at the very least, that they play a critical role in understanding what see.
Before comparing the present work to a small sample of these papers, it is
important to reiterate why — for a majority of galaxies in our _GOODS-S_ field
— we identify their SFH as “bursts.” Our study has particular significance
because it was the first to trace the buildup of the stellar mass in the first
galaxies (Dressler et al., 2023), and because it is the only one to rely
solely on the light of main-sequence A-stars. The mass-to-light ratios of
these stars are thus accurately-known and independent of chemical composition.
Furthermore, a stellar population with an age of between 100 and 1000 Myr is
not a dusty one: even while O & B stars are still forming in HII regions,
A-stars have already migrated into near-dustless environments.

Our study of 894 newborn galaxies at $6<z<12$ has shown that their star
formation was predominately in bursts: we have called these histories
“starbursts”(single) and “stochastic” (multiple). Because of the methodology
of this study and the limitations of SEDs with 7 broad-bands fluxes, we
actually know little about the nature of these bursts that we find dominating
the SFHs of the first galaxies. For these, we observe primarily, almost
exclusively, the light of A-stars whose ages range between $\sim$50–150 Myr.
It is likely that the mass of stars _born during_ the full epoch was much less
than that born in the first $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$50 Myr of explosive star formation that
preceded it. In other words, most of the observed A-stars came from a shorter
period that started earlier in the epoch. By this reasoning, we suggest that
star formation rates of 10-30 M⊙ yr-1 characterized the dust-enshrouded phase
we have imagined, and it is during this phase that the $\sim$50–120 Myr-old
A-stars that define our SEDs were born. We can estimate the SFRs of the CSF at
OE and imagine them to be typical of the SFR over the whole epoch: that might
only be 1-10 M⊙ yr-1 (see, for example Emami et al. (2019); Faisst et al.
(2019); Rezaee et al. (2023)), but we will be hard-pressed to make a SED
measurement, or any other we can think of, that can recover that _history_ of
the SFR with a resolution of tens of megayears — for any given
object.161616Alternatively, spectroscopic measurements of emission-line
spectra for these kinds of galaxies could be used in a statistical way to
estimate the range of SFRs and the level of “burstiness” for the sample, and
by comparing SFRs from UV flux to those from H$\alpha$ for large samples.

It is more accurate, then, to say that our study has concluded that starbursts
dominate not because we see signatures of $10^{8}-10^{9}$ M⊙ of stars _forming
over an epoch_ , but because we see a population of A-stars in that epoch that
are limited to ages less than $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle<$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$150 Myr. Most likely, they were born in
a much shorter period within that epoch. What defines our result that
“starbursts dominate” is that we see _no_ A-stars _older_ than, say, 150 Myr,
that is, _from a prior epoch._ That’s why we call these SFHs bursts, not
because we are seeing the burst (although we may be, in some cases), but
because the only stars we do see are _young._

We think that the principal benefit of our observations of the prominent role
of starbursts will be to help inform theory, and numerical simulations models,
about the growth of the baryonic component of the universe that winds up as
_galaxies_. The prevalence of bursts of star formation in the first billion
years should be influential in guiding theoretical work to understand galaxy
growth in a dynamic environment. It also seems that there are environmental
factors that might send galaxies down one path rather than another that could
help constrain numerical simulations.

Early results from _JWST_ have focused on a the large population of bright
galaxies, particularly at $z>10$, e.g., Donnan et al. (2023), Harikane et al.
(2024), and Finkelstein et al. (2023), suggesting that the luminosity function
of the first-galaxies evolved less slowly with redshift.171717That is, the
luminosity function not declining as rapidly as pre-_JWST_ (_HST_)
observations and derived predictions. Observations of _brighter-than-expected_
, _more-numerous-than-expected_ , or _evolving-less-rapidly-than-expected_ ”
galaxies have promoted “burstiness” as a way to reconcile these findings
(e.g., Looser et al. (2023)) with previous models (e.g., Wilkins et al.
(2022)). However, those galaxies are higher redshift, and/or rarer (and more
massive?) than those studied here, so our sample adds little to that
discussion.

On the other hand, Sun et al. (2023a) and Sun et al. (2023b) have in
particular suggested that lower-mass galaxies, with an abundance and mass
predicted pre-_JWST_ models, have been elevated in luminosity by bursts,
specifically that their _light-to-mass ratios_ have risen through substantial
bursts of star formation. While again, those samples are not a comparable our
own, we can by analogy question this explanation. Our study finds a high level
of ‘burstiness’ through measurements of _stellar mass_ — the mass of A-stars
from the SEDs. Likewise, the $z>10$ ‘bright’ examples may be cases of galaxies
forming more _stellar mass_ — in bursts.

In a study that also seeks to measure a change in SFHs over $6<z<12$, Ciesla
et al. (2023) use a very different method than our own to extract such
information from SEDs. Their analysis correlates SED-shape with position on
_the starforming-main-sequence_ to characterize whether a galaxy’s SFH is
‘stochastic,’ like our definition — bursty over multiple epochs, or ‘secular,’
— longer and steadier, like our SFH3 and SFH4 types. They posit a smooth
transition from mostly-stochastic to mostly-secular at around $z\sim 9$.
Although our sample is relatively small beyond $z>9$, Figure 6 shows no clear
transition at $z>9$, with a similar fraction of SFH1+SFH2 and SFH3+SFH4 down
to $z\sim 7$. There seems to be a strong upturn in the both SFH1 andd SFH3
below $z\sim 7$ (see Figure 7 with the ratio between ‘stochastic’ (SFH1) and
‘secular’ (SFH3) basically unchanged. Again, our methodology is more
straightforward — _SEDz*_ actually derives SFHs from ages of A-star
populations, but this important issue requires further study.

About this important matter, what seems clear is that the most of the youngest
galaxies do not grow steadily in a calm, peaceful environment. Rather, their
journey to what we today regard as “galaxy-sized” may be more chaotic, or even
explosive. Perhaps these are gas-rich mergers dominating in lower density
regions, manifesting in “one- or two-event” growth spurts in the first billion
years, reaching $\sim$$10^{9}$ M⊙ (what we now call galaxy-sized) when this
first phase completes. Importantly, however, by $z\sim 2$ — “cosmic noon” —
these galaxies should grow by an order-of-magnitude in mass to reach a halfway
point for _L ∗_. It will be important, and challenging, to relate that later,
more-easily observed universe to what we have witnessed for the earliest
galaxies. These starburst galaxies at $6<z<12$ neither seem poised for another
burst, nor prepared to settle into steadier star-formation histories. The
simple fact that most of our 894 galaxies do not show star formation over many
epochs precludes the notion that these bursty objects are ‘picking up’ again
before $z\sim 6$. Perhaps the “contiguous” SFH3 galaxies, common in our $z=6$
sample, are destined to become those L* galaxies. We note that almost all show
the signatures of continuing star formation at $z=6$, so perhaps they will
grow into the most common galaxies of today, just beginning in earnest their
journey to maturity. It is undeniable that a transition from ‘stochastic’ to
‘secular’ (to use Ciesla et al.’s term) _did_ occur, so a focused study on
$4<z<6$ galaxies, by whatever means their SFHs can be characterized, seems a
priority, and imperative for “Chapter 3.”

Finally, pursuing our suggestion that the starbursts we have observed were the
consequence of intense, extreme-density, dust-enshrouded bursts of star
formation, we hope an effort can be made to match up this population of
growing galaxies to a coeval population of heavily-dust-obscured proto-
galaxies that will come from _JWST/MIRI_ and perhaps _ALMA_. That our sample
seems effectively dust-free strongly suggests that there is a ‘just-before’
phase of tens of millions of years in which explosive star formation ignited
in gas-rich protogalaxies, leading directly to the objects we have been
studying. Forming stars rapidly in these sub-kiloparsec volumes is a
formidable challenge to our considerable knowledge of how stars form. In
particular, the feedback from the supernovae of such starbursts should blow
things apart!

We have taken note, with great interest, of work suggesting that such feedback
can be suppressed if, at that time, supernovae of mass M $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}10$ M⊙ collapsed directly into black
holes. Renzini et al. (2022) have suggested that this extraordinary
explanation is near ‘mandatory’ to explain the multiple stellar populations
observed for many globular clusters, traditionally thought to be limited to a
single generation by supernovae-driven feedback. It appears that the same
challenge applies towards our understanding of the earliest galaxies. We find
first “bursts” of star formation with stellar masses $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$108 M⊙ — a scaled-up version of the
largest globular clusters — similarly in need of a physics miracle (see Dekel
et al. (2023)) to avoid destruction before fulfillment.

Travelers on _JWST_ — the ultimate spacetimeship, we seek answers to questions
first asked a century ago. Wonderfully, we are fortunate to be grasping this
‘once in a species’ opportunity to know our origins.

AD gratefully acknowledges the support of the _NIRCam_ team for the
opportunity to contribute to the _NIRCam_ science program on the earliest
galaxies, and for prior funding from the _JWST/NIRCam_ contract, NAS5-02015.
The DC2 “deep field” simulation was a Herculean task that provided the
essential guidance for the program described here, and for the _NIRCam_ GTO
program in general. This work is based on observations made with the
NASA/ESA/CSA James Webb Space Telescope, using imaging data processed by the
_NIRCam_ project team in collaboration with _JADES_ , a extragalactic project
team consisting of members in the _NIRCam_ and _NIRSpec_ teams. D.S., K.M.,
M.R. and A.D. have been supported by _JWST/NIRCam_ contract to the University
of Arizona, NAS5-02015. N. Bonaventura acknowledges support from The Cosmic
Dawn Center (DAWN), funded by the Danish National Research Foundation under
grant no.140. K. Boyett acknowledges partial support by the Australian
Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D), through project number CE170100013. A. Bunker acknowledges funding
from the “FirstGalaxies” Advanced Grant from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (Grant agreement No. 789056) S. Cariani acknowledges support by
European Union’s HE ERC Starting Grant No. 101040227 - WINGS. D. Eisenstein is
supported as a Simons Investigator and by _(_ JWST/NIRCam) contract to the
University of Arizona, NAS5-02015 R. Hausen acknowledges funding for this
research from the Johns Hopkins University, Institute for Data Intensive
Engineering and Science (IDIES)

##  Appendix A SFHs vs Environment at z $>$ 6

Figure 11: Histograms of the incidence of the different SFH types with local
density (_left_) and as a function of nearest-neighbor-separation (_right_).
No clear trends are apparent, that is, SFH types at this early time do not
depend on local environment as they do after z$\sim$2 The three vertical
panels are for the 3 redshift ranges, z $\approx$ 6, 7, and 8-10 (bottom to
top). The chief differences are in terms of scale, for example, the peak of
both distributions shifts to lower density and to larger separation with
increasing redshifts, as expected for a sample limited by apparent brightness.
Density contrasts in this _GOODS-S_ field are modest, but Figure 10 shows
signs of a correlation of longer SFHs with higher density groups.

The histograms of Figure 11 show distributions of the four SFH types with
local density — calculated using the area of the 10 nearest neighbors
galaxies, and distance to the single nearest neighbor galaxy. The absence of
any obvious trends between SFH type and environment seems at-odds with results
for environmental dependencies later in cosmic history, for example, the
obviously difference in SFHs of rapidly growing elliptical galaxies compared
to the drawn-out SFHs of spirals like the Milky Way. However, from another
perspective, the lack of environmental dependence is reminiscent of studies of
the environment around rich clusters in the early 1980’s (Dressler, 1980;
Postman & Geller, 1984) who found that a steep dependence of galaxy morphology
with local density within the effective radius of a cluster did not continue
to the lower density “field” beyond. In this study, Figure 10 shows a hint of
the same behavior: in the region of higher density, a $z\sim$7 rich group, the
long-SFH types are strongly represented, a correlation that is not expressed
in lower-density surroundings.

##  Appendix B Stellar Population Templates of _SEDz*_

In this section we show samples of the stellar population templates used by
_SEDz*_ to characterize the SFHs of $5<z<12$ galaxies. Figure 12 plots the
fluxes of 10 stellar population templates with a 10 Myr burst of star
formation (at 1 M⊙ yr-1= $10^{7}$ M⊙) at the start of epoch $z=12$, “observed”
to evolve at epochs $z=11...3$ — later epochs without further star formation.
For this study _SEDz*_ uses 7 templates, for bursts starting at z = 11, 10…6.
The principal feature of this plot is that the templates are largely non-
conformal, that is, not a conformal set of curves scaled by some parameter or
set of parameters. These “vectors” describing stellar populations are
different enough — sufficiently _orthonormal_ — that a least-squares
combination of them is substantially ‘resolved’ from any other combination.
This property allows _SEDz*_ to ‘calculate’ the history of a stellar
population — essentially, by vector algebra: finding the coefficients of the
vector sum that best represent the observed SED.181818Another way of thinking
about these templates is to consider them as musical“chords,” all playing the
same 7 “notes” (the wavelengths of the 7 wide-bands), but differing in the
volume (flux) from templates to template. Since all notes sound together,
there are limited combinations available to fit the SED (the music), and there
is no way to make changes in individual bands to improve the sound (fit). This
is why the good SED fits found in this study — with the restricted number of
A-star-dominated templates from present-day populations — provide a “self-
verification” of the method. What makes this particular application of the
method potent is the non-conformal character of SEDs for stellar populations
of ages $\tau<1~{}Gyr$ — the templates covering the early universe for $z=12$
to $z=5$ whose light is dominated by main-sequence A-stars. The figure shows
why, as has been known for half-a-century, finding the ages of stellar
populations with stars only _older_ than 2 Gyr is, in practice, impossible:
note how the templates $z=5,4,3$ are becoming a simple scaling of a single
shape, as the universe reaches an age of 2 Gyr at $z\sim 3$.

Figure 12: Templates for a 10 Myr burst of star formation at $z=12$ evolved
(aged and observed) at lower redshifts. With good data (S/N $\mathrel{\raise
1.50696pt\hbox{$\scriptstyle>$}\kern-6.00006pt\lower
1.72218pt\hbox{{$\scriptstyle\sim$}}}$ 7), the distinctive shapes of these
templates allow _SEDz*_ to make essentially unique SFH solutions. This
character changes for $z\leq$ 5 as the templates become scaled versions of
each other, the reason that distinguishing stellar populations with $\tau>$2
Gyr are basically indistinguishable, a behavior attributable to the very
similar _giant branches_ of older stars.

Figure 13: _top-left_ : Templates for CSF (constant star formation) at epochs
5 through 10. _Right_ : Combinations of burst and CSF templates at $z=7$.
Ratios are CSF-to-burst (see text). _left-bottom_ : The affect of dust on the
z=7 CSF template shown for $A_{V}$ = 0.4, a factor-of-two in the 1.15$\micron$
band, and $A_{V}$ = 1.0, a factor-of-ten, demonstrating the galaxies in the
894 sample analyzed here show little if any dust. Even a 30% decline across
the SED from 4.44$\micron$ to 1.15$\micron$ — equivalent to $A_{V}$ $\sim$ 0.1
— would have adversely impacted the SEDz* fit compared to the no-dust
solution.

The signature of a burst of star formation is a very blue SED at that epoch,
but for the subsequent epochs, the history of star formation _within that
epoch_ is unresolved. Therefore, _SEDz*_ accumulates the sum of bursts as the
stellar masses of each: this is indistinguishable from continuous star
formation over the prior epochs.

A final point of note is that _SEDz*_ works because it is strongly constrained
by the shape of each template, which means that variation of the coefficients
in the maximum likelihood solution cannot either make or break the fit. If
these templates, made from present-epoch stars in our Galaxy, were not
representative of stellar populations at $z>5$, this attempt to reproduce
observed SEDs would fail badly. Quite the opposite is true.

The top-right panel of Figure 13 shows templates for 6 templates, from $z=10$
to $z=5$, corresponding to the flux resulting from 1.0 M⊙ yr-1 of constant
star formation (CSF) over that particular epoch. Unlike bursts, there is no
evolution of stellar population over subsequent epochs, because ongoing star
formation can only be recorded in the SED from the epoch of observation. Prior
epochs of CSF are indistinguishable from bursts of the same mass. With the
time resolution offered by broad-band SEDs, no additional information is
available: there is no signature to distinguish CSF from a more complex
behavior over the $\sim$100 Myr duration of each epoch.

Clearly, the distinguishing feature of the 6 CSF templates is that they are
all flat — as conformal as it gets — in comparison to the burst templates. The
modulation that _is_ apparent comes from the Balmer break — moving from $\sim
2\micron$ at $z\sim 6$ to $\sim 3.5\micron$ at $z\sim 10$, and from the
jaggedness of the SED from $3\micron$ to $5\micron$ — due to [O III] and
H$\alpha$ emission lines. This flatness, when combined with bursts of previous
epochs, is responsible for much of ‘character’ of the long SFHs. The right
panel of Figure 13 shows that combining a burst, early in an epoch), with CSF
at that same epoch, produces signatures that are found in many $z>5$ SEDs. The
ratios of 3:1 to 1:2 for the burst/CSF flux, shown in this case for $z\sim 7$,
are apparent in hundreds of the SEDs in our sample. It is worth remembering
that this combination is just equivalent to ongoing star formation that is
declining, rather than constant, over the epoch.

The bottom-left panel shows the attenuation in the SED expected for different
values of $A_{V}$, as described in Section 2.

##  Appendix C Do Emission Lines Impact Derivations of SFH with _SEDz*_ ?

In general, the influence of emission lines in photometric studies using broad
bands, like this one, are only significant if the line-to-continuum ratio is
very large. For example, a moderate-resolution spectrograph (with resolutions
of 100s) is effective at detecting even weak lines only when the continuum
level is low, and that is true only for young stellar populations, $\tau\leq
20$ Myr. In contrast, broad photometric bands like the ones used in this study
select against such populations because the continuum flux is weak (the
objects are faint).

Because our detections of faint galaxies rely on the sensitivity to small
fluxes, the equivalent width of an emission line must be enormous, that is, a
low continuum flux. Since the “integer epochs” of this study cover $\sim$100
Myr of cosmic history, any object selected through broadband photometry will
by necessity require a large burst of star formation compared to the stellar
mass generated over the epoch. Thus, the contribution to the flux from the
youngest populations, through emission lines, should be modest.

Figure 14 verifies that by selecting cases of relatively strong star emission
lines (the right-side examples) and comparing to SEDs on the left with little
evidence of star formation. Our SEDs are made up of 7 broad bands (filled
circles) and the two medium bands, F335M and F410M (open circles, not used in
the _SEDz*_ fitting). In particular, these and the F356W and F444W broad-bands
are sampling the [O III] and H$\alpha$ lines over the redshift range $6<z<9.$

The medium bands often provide good evidence of emission because their width
is $\sim$40% of the broad bands, so they can also — in cases that exhibit
emission — establish the continuum level at that color, sometimes considerably
below that of the broad bands.191919It is significant, though, that none of
our SEDs show a continuum detection near zero, as would be the case for a pure
emission-line spectrum, consistent with our claim that this is not possible
with broad bands and long epochs. The close agreement in flux of both broad
and narrow bands in the top and bottom left examples shows that there is
little or no detected emission in these cases, which is common in our
894-galaxy sample. Note how the levels of F356W and F444W are close. The
middle left SED shows moderate emission in F444W and detection of the
continuum in F335M, and here F444W appears to be elevated above F356W by [O
III] emission. The case in the top right is a stronger example: strong
detected emission in F356W and F335W, also [O III] , at this lower redshift.

When compared to the flat blue (CSF) templates on the left, and purple on the
right (excluding middle right), these SEDs all show a substantial rise in flux
over the F356–F444 region. What is the contribution of emission lines to this
rise?

For most of our sample, the answer is: little to none. This is because the CSF
templates _include_ the emission line fluxes for the appropriate stellar
population, for both the broad and narrow bands. As explained in Stark et al.
(2013) the SEDs of these templates include hydrogen lines (Robertson et al.,
2010), based on Osterbrock tabulations and case B recombination) and metallic
lines (Z = 0.2 Z$\odot$, likely appropriate for our high-z galaxies) and
continuum radiation, calculated and described by Stark et al. (2013). Of
course, the strength of these lines should vary from object to object, and
perhaps systematically from $z\sim 0$ to $z>5$, but examination of dozens of
our sample suggests that such variations, though present, are smaller than the
effect of “line vs. no-line.” However, the existence of variation, as well as
not knowing the redshift well enough to place the emission lines accurately,
prevent us from making detailed arguments about whether these low-z line
ratios are in fact a good match for very young galaxies.

Knowing that the emission lines are appropriately included in the templates we
use, is it easier to understand the examples we show here. Since emission is
included, the F356W and F444W fluxes of the upper and lower left SEDs show no
emission, indeed, if their ‘elevation’ from a flat SED were due to emission,
the narrow bands would show higher, not at the same level. The middle-left
example does show elevation of F444W compared to its more typical closeness to
the level of F356W, but the _SEDz*_ model passes through both points because
_emission is included._ (This indicates that the ’present-epoch’ templates are
appropriate.) The same goes for the top right example with strong emission in
F335M. In this case and most others, the continuum level of F410M, compared to
the elevated value of F356W, comes in at the proper ratio of 2.5:1.

Figure 14: These _SEDz*_ plots address the influence of emission lines on SFHs
derived in this study. The SFHs on top and bottom left have little or no
emission, as shown by the fact that the medium bands (2.5 times smaller
bandwidth than broad bands) share the same flux level as the broad bands. The
middle left shows a modest level of emission — elevation of F410M over F444W,
and the top right evidence for moderate emission. The fact that the stellar
population templates include emission-line flux representative of typical
star-forming-regions is obvious from the middle and bottom right examples,
demonstrating that the “rise of the red continuum” in these 6 cases must be
due to flux from older stellar populations, unless significant contributions
from emission only [O III] and/or H$\alpha$ are _substantially stronger than
for present-day star-formation regions._

In the middle and bottom right examples we again see the _SEDz*_ model passing
through F356W and F444W, the emission — here [O III] and H$\alpha$ — is
_included_. The continuum below is sampled in each by both medium bands. Here
we also see that the continuum level is provided by a single, older, $z=11$
population, which is boosting the level of F356W and F444 to give the SED its
distinctive shape, one that is _inconsistent with any single population_. For
the bottom-right example the continuum is matched by $z=11-12$ and $z=8$ flux
to complete the fit. The only way emission could contribute significantly
would be if [O III] and H$\alpha$ emission were substantially stronger in
these regions of star formation in $z>6$ galaxies than in galaxies of today.

To look for galaxies with stronger-than-present-day emission, we examined SEDs
to find cases where the points indicating emission had fluxes systematically
higher than the values of the five bands F090W, F115W, F150W, F200W, and
F277W. There were few among the 690 cases of the z1 and z2 samples, $z<7.75$,
but 50 of the 128 galaxies in the redshift range $7.75<z<9.75$ showed
conspicuous [O III] emission in the F444 band. Among these, 28 had SEDs that
rose steadily through F356W, which _SEDz*_ attributed to earlier star
formation, $z\geq 10$. For the remaining 22 the lack of such a clear trend
suggested that these were, in fact, cases of [O III] emission much stronger
than represented by the templates. For such cases the “earlier” stellar mass
found by _SEDz*_ was incorrect. By examining the $z\geq 10$ contribution, we
determined that for such galaxies total stellar mass had been overestimated by
factors of 1.5 to 3.5. This is important for future _SEDz*_ studies. At the
same time, it does not alter the conclusions of this study, in fact, it moves
some SFH2 types (an early and late burst) back to the SFH1 category,
reaffirming our principal result of the prominence of starbursts in the early
universe.

Since these strong emission cases are a small part of the study, this result,
added to the cases with little-or-no emission, confirms that “red rise” we
find for $\sim$100 galaxies is flux from older stellar populations, in other
words, _SEDz*_ star formation histories confirmed.

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