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

We use SEDz * — a code designed to chart the star formation histories ( SFHs ) of 6 < z < 12 galaxies — to analyze the spectral energy distributions ( SEDs ) of 894 galaxies with deep JWST / NIRCam imaging by JADES in the GOODS-S ﬁ eld. We show how SEDz * matches observed SEDs using stellar-population templates, graphing the contribution of each epoch by epoch to con ﬁ rm the robustness of the technique. Very good SED ﬁ ts for most SFHs demonstrate the compatibility of the templates with stars in the ﬁ rst 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 con ﬁ rm earlier results from Dressler et al. ( 1 ) There are four types of SFHs: SFH1, burst; SFH2, stochastic; SFH3, “ contiguous ” ( three epochs ) , and SFH4, “ continuous ” ( four to six epochs ) . ( 2 ) Starbursts — both single and multiple — are predominant ( ∼ 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 e for SFH1 – 4, respectively, adding up to ∼ 4 × 10 11 M e by z = 6 for this ﬁ eld. 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 ﬁ nd 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 ﬁ rst star formation at z = 11 – 12, suggests that long SFHs could dominate in rare, dense environments.

The HST & Beyond Committee (Dressler et al. 1996) chose a prime mission for the extraordinary space telescope that would become 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 incredible complexity, fed by chemical variety that could never have built to the 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: travel to this remote past, and 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 smoothas-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 -lets us start that remarkable journey with a large, representative sample of faint, newborn galaxies, for a first look at how they survived their tumultuous beginning.
The paper is organized as follows: Section 2 briefly reviews the methodology, 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 ∼1000 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 the four types over four redshift ranges 6 < z < 12, as measured by SEDz*.Section 6 looks for changes in the mix of SFHs over time, Section 7 investigates correlations of SFHs with environment, and Section 8 presents a summary of the birth of stellar mass -when, where, and how much -we find for 6 < z < 12.

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 one old star from another that is even older.
As part of a galaxy survey of the last 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 colors) that leveraged observations of galaxies that reached back of 2 billion years to a time when the universe was itself much younger. 1 Because of that, the part of a galaxy's history that could be measured -a couple of billion years more -took us to when the universe was half its present age, in this way revealing a substantial fraction of the galaxy's growth history.Applying this approach to a sample of a galaxies observed at redshift z ∼ 0.4 − 0.8, Dressler et al. (2018) discovered ∼20% of galaxies were still growing rapidly, 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 1-2 billion years of a 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, NIR-Cam, 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 them upepoch by epoch -will constitute 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 -SEDs -into star formation histories, the buildup of stellar mass over the first billion years.Our subjects are a greatly-expanded sample of 982 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 the reconstructing the histories of galaxies from the rich information encoded in their SEDs.By choosing a sample of galaxies that are a billion years old or younger, 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. 2016), through the combination of stellar population templates.The program effectively isolated light from younger ( < ∼ 1 Gyr) populations of A-stars and led to the discovery of "late bloomers" -the 25% of galaxies at z ∼ 0.5 that produced at least 50% of their stellar mass in the previous 2 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 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 2 Gyr, a deficiency turned on its head when the the population under study has an age of < ∼ 1Gyr.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, the SFHs of Astar-dominated populations can be derived from SEDs, and vice-versa.A-stars are among the simplest mainsequence stars (Morgan & Keenan 1973), with a relatively simple structure and opacity produced by hydrogen absorption, 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.2SEDz* uses a nonnegative least squares (NNLS) engine (Lawson & Hanson 1995) and custom star-formation templates Robertson et al. 2010) 3 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 the 6 < z < 12 into integer steps,12,11...6 lasting (47.0,59.0,73.0,95.0,125.0,171.0,244.0 Myr,respectively.SEDz* operates with two sets of SED templates, one with 10 Myr bursts (unresolved after subsequent star formation) and another characterized by continuous star formation (CSF).The program builds up an 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 χ 2 .The epoch of observation (OE) is chosen as the lowest χ 2 and the star formation history is read off as the mass contributions for each scaled template that, in combination, make the best fit.This can include, at OE, the addition of a CSF template which signals constant star continuing from that point.SEDz* can combine the CSF template with a final burst template to expand the 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, allowing for a wide range of galaxy histories.
Paper I describes the working of the code in considerable detail, which we do not reproduce here.It also discusses tests of SEDz* , including its ability to reproduce the SEDs of synthesized galaxies in a simulated deep field, in 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 burst 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.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 when a period of tens of megayears of intense, dust-enshrouded star formation that was then cleared by its explosive feedback.

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 JWST ERO program GLASS (Treu et al. 2022) from parallel observations with NIRCam of NIRISS spectroscopy of the cluster Abell 2744 (Merlin et al. 2022).The area and depth of the direct imaging field of that ERO study, and some early 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 judged suitable for a first attempt to measure 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 surprising, and encouraging results, in the sense that the program was able to reproduce 24 complex 9-photometric-band SEDs with the code's limited library of stellar population templates. 4In other words, SFHs with recognizable characteristics, burstssingle and multiple, and multi-epoch star formationgently to steeply falling, 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, and their unique shapes, obtaining excellent 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 ∼ 1000-galaxy sample at redshifts 6 < z < 12, and our analysis of these new data confirms all the basic conclusions of Paper 1: good reproduction of observed SEDs and four SFH 'types,' and confirmation of the surprising 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 matter of SFH type.Figure 1 introduces a new data format for SEDz* output and gives examples of the four basic 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 1σ error bars.The NNLS solution SEDz* finds 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 χ 2 of the fit is inset in the upper-left: a prominent minimum in χ 2 defines the "epoch of observation" -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 8 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, corresponding to just one of the templates shown in the Appendix B. That is, a one-component stellar population model, based on stars at the present epoch, residing in our Galaxy, perfectly fits the SED of a galaxy at z = 7.Specifically, the template is that of a 10 Myr burst of star formation at the start of the z = 7 epoch, observed at the end of that epoch -here, 125 Myr later.What at first seems remarkable -the "perfect fit" -is in one sense 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!
The stellar mass calculated for the burst is just over 10 8 M ⊙ .The green arrow signifies star formation at OE: this SED is best fit by a combination of a z = 6 burst template and a z = 6 constant-star-formation (CSF) template. 5The need for the CSF template can only apply at OE since star formation from any previous epoch is 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 following epoch, becoming an "old" population and independent of how the mass was spread over the interval.
This starburst example begs the question, could any combination of bursts, also reproduce the top-left SED?The top-right panel shows why this is impossible, through an SED that is perfectly fit with a combination of a 4 × 10 8 M ⊙ burst at z = 11 and a ∼ 10 8 M ⊙ burst 400 Myr later, observed at z ≈ 6.The integrated mass of this SFH is the red-encircled black dot.The epochs without star formation are marked as lower limits of 10 6 M ⊙ .In this study, at the depth of the GOODS-S field, detections as low as 10 7 M ⊙ are made, but incomplete below ∼ 5 × 10 7 M ⊙ (depending on 'noise' from later star formation), and severely so below 2 × 10 7 M ⊙ .Clearly, the effect of multiple bursts together cannot produce the starburst on the left, nor vice-versa.
Perhaps the most revealing feature of the double-burst example is the way it shows how, specifically, the contribution of the two bursts combine to make up the observed SED.The SFH masses, color-coded by epoch, each produce the colored lines below the SED.The z = 11 burst in orange is that of an old stellar population, while the purple line shows the strong contrast with a burst of ultraviolet flux from a young population of < 100 Myr population, showing in very clear terms the ability of SEDz* to resolve the 6 < z < 12 epoch into old and young populations. 6he triple-epoch SFH shown in the bottom-left panel is very common in the sample, particularly at z ∼ 6.This example is particularly revealing because of the flat (purple) SFH coming from a CSF template that also produces [O III] and Hα emission, a young burst that contributes the peak flux at λ ∼ 1µm, and a ∼ 200 Myr-'old', aging burst from z ∼ 8 (green line) that produces the rise in flux beyond ∼ 3µm.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 several generations of star formation.
This leads naturally into the the example in the lower right, where 4 or 5 epochs of the possible 5 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 they cannot be reproduced by the single or a pair of bursts of star formation that are shown in upper left and right, or by the shorter contiguous episodes that are shown in the bottom left panel of this figure (see also the Appendix 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 the more that follow in Figures 2-5 are representative of 72 in our 6 < z < 10 sample (7%).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.
In summary, we believe the SEDs and solutions like those shown Figure 1 are more than exemplary -the excellent fits of single bursts, and the ability of combinations of such bursts to fit a wide range of SED shapes, with only a small fraction of outright 'failures' to find a good solution, is evidence that the principle behind SEDz* is valid: an A-star dominated stellar population can be used to recover accurate SFHs for galaxies in the τ < 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 least common for all the SFHs shown here is a stretch of rising star formation.As we said in Paper I, it is possible to attribute this to the difficulty of detecting a declining older population against the young one that is rising in flux -a simple selection affect.However, more intriguing is the possibility that the flat/declining phase of all first-galaxy-SFHs -from bursts to long SFHs -were preceded by a strong, rapid burst of dusty star formation lasting < ∼ 50 Myr.We see among the galaxies that were excluded from our sample ∼30 that have steep, red SEDs, but SEDz* cannot be used to determine their redshifts, so their connection to the unobscured galaxies in our sample is unknown.

CHOOSING A SAMPLE OF 6 < z < 12 GALAXIES
The Guaranteed Time Observations (GTO) awarded to the NIRCam team of JWST has supported a wide variety of science programs covering exoplanets, star formation, and our Galaxy with its neighbors (Rieke et al. 2023, submitted to ApJ).However, the largest component is devoted to the study of the early universe (Eisen-stein++2023, submitted to ApJ) -the era of galaxy birth.The program described in this paper comes from deep-field imaging that will begin to answer longstanding questions about how the first generation of starscollected 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 ∼30sq-arcmin field of the GOODS-S survey (Rieke et al.).The images were intensively processed for calibration, removing instrument signatures, combining dithered exposures, and noise characterization.These data were used to produced a catalog of objects (v0.7.2) that identifies stars and galaxies, deblends overlapping images, and generates a number of different radial extractions of photometric measurements for 24,350 sources in NIR-Cam bands F090W, F115W, F200W, F277W, F335M, F356W, F410M, and F444W reaching a depth of ∼30.0 AB mag.Our study selected galaxies with S/N > 5σ (F200W & F277W flux) within a 4-pixel diameter circular aperture, appropriate for the small size of z > 5 galaxies.Details of the NIRCam data quality, reduction, and photometric catalog's creation can be found in Robertson et al. (2023, submitted to ApJ) and Tacchella et al. (2023, submitted to ApJ).
To establish the sample, SEDz* was run on the complete GOODS-S v0.7.2 catalog in four different redshift ranges, 6<z<7, 7<z<8, 8<z<10, and 10<z<13.To be more 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.SEDz* was found to have a accuracy of σ z ≈ 0.10 for z > 6 galaxies, from comparing SEDz* redshifts with the "known redshifts" of the Data Challenge.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 rson, boundaries were set as follows: 5.75 < z < 6.75, z < 6.75 < z < 7.75, etc.Thus, when a galaxy's redshift was found to be within the range 5.75 < z < 6.25 the the z=6 template was used, but when 6.25 < z < 6.75, a 50/50 interpolation between the z = 6 and z = 7 were made, and so on for the other samples.Eventually these would be combined into a catalog spanning the full 5.75 < z < 12.75 range, but this 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 ∼ 2 galaxies where NIR-Cam's range of 1 − 5µm translates into a rest frame coverage of ∼ 0.3 − 1.7µm, typically covering a Balmerbreak over an otherwise flat SED.When very faint galaxies are the targets, these are easily mistaken for a z ∼ 6−8 galaxy 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 χ 2 curve when two minima were found, one for z ∼ 2 and another for the higher redshift.During the 'Data Challenge' tests, we found the overall slope of the run of χ 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 2.5σ 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. (2023, submitted to ApJ).
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, 82 galaxies at z6-7, z7-8, z8-10, and z10-12.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 446,183,174,and 12 'confirmed' objects." This left 321,191,155, and 70 objects with z SED unconfirmed by z a. Their SEDs were inspected, one-by-one, to decide if the Lyman-break was sufficiently well defined to indicate a low-redshift 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 ∼737 inspections, 223, 126, 103, and 57 galaxies were rejected.The remaining 88, 65, 52, and 13 galaxies were added to the "gold sample," based on judgement that at least half of these were at the redshift found by SEDz* .The final count for the four redshift slices were: z6 7-534, z7 8-249, z8 10-176, and z10 12-23 -a total of 982 galaxies,

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.Beginning with Figure 2, we see three examples of a z = 6 starburst, each with a mass of ∼ 2 × 10 9 M ⊙ .As in the discussion for the burst SFH in Figure 1, a single epoch of star formation, in these cases both occurring and ob-served at z ∼ 6, fits the SED near-perfectly7 .This solution is, then, a combination of both a burst and continuing "constant" star formation (CSF), the latter with less than 50% contribution to the flux.A confirmation of the redshift found by SEDz* is the [O III] emission in each 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 -550 cases, more than half the sample (56%).
We also identify the next two examples, with twoadjacent epochs of star formation, as single bursts, either unresolved, that is, one event that is best fit by consecutive templates, or a result of the "interpolation" between templates described earlier.It seems reasonable that star formation episode of > ∼ 100 Myr could produce this SEDz* result in the comparably long "integer-redshift" epochs used here.Under this interpretation of a single event, we include examples where the mass varies by as much as an-order-of magnitude, implying a rising or falling episode of star formation for these cases.
The next two examples (2nd row right and 3rd row left, hereafter, 2r and 3l) are additional demonstrations of the ability of SEDz* to reveal dominant early star formation in galaxies observed ∼500 Myr later, giving confidence in its production of full SFHs over the 6 < z < 12 range of our study.Comparing the stellar population templates shown in the Appendix B, it is clear that these two examples show histories that cannot be reproduced by any single stellar population.Figure 2 shows 4 examples of strong, well-separated bursts of star formation.We call these stochastic SFHs because it seems unlikely that these can 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 lower in mass.The triple-burst in the middle of row 3 (and the very similar "quad" to its right) are graphic illustrations of very young, blue stellar population whose red flux has been 'boosted' older populations, at z = 10 and z = 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, adding up to 204 cases (21%).Together with starbursts amount to 77% of SFHs found here: clearly, this is a strong and, we believe, unexpectedly, the dominant mode of galaxy building in its beginnings.
But, the bottom 3 rows remind us that a significant fraction of early galaxies are undergoing more orderly, gradual growth.In rows 4 and 5 are four examples of triple-epoch SFHs, 23% of galaxies in the z = 6 sample.In each case, three separate stellar populations -usually "continguous," but occasionally with a one-epoch gap -are needed to reproduce the such SEDs.All four have final star formation, at z = 6, with CSF components, hence the very flat purple CSF contribution (Appendix B ).But it is also apparent that no amount of z = 6 or z = 7 star formation can lead to the 'risingto-the-red' in each.Although they look short, these 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 -∼ 100 Myr starbursts.
The final 4 examples are long, more-continuous histories, only 3% of the z ∼ 6 subset, the stretch over the full range.Although two have a 2-epoch gap and could have been called 'stochastic,' what seems clear is an orderly history of declining star formation.These are further, pronounced examples of young stellar populations with a history of very early star formation that accounts for their 'rising-to-the-red' SEDs.In all four, both z = 11 and z = 12 star formation is found, however it is likely that this period of ∼ 100Myr is not "resolved," so the SED could be reproduced by only one, with the mass combined.Although they represent only 3% of the z = 6 population and only 72 galaxies in total (7%), the persistence of these over the full time range explored here suggests a very different environment where some galaxies can evolve more slowly and relatively undisturbedfor example, experiencing only minor mergers.
From this first set we see the prevalent signature of early (z > ∼ 10) star formation -an SED rising to the red, is 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 is not the case, the main point being that the CSF templates include active star formation, so that the level of the broad bands cannot be 'raised' by emission -it's already included, and that 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 the templates were not calculated for the narrower bands.Appendix C provides more examples and discussion.
Returning to the examples SFHs, in Figure 3 shows for z ∼ 7 a virtual replay of the z ∼ 6 population: 5 individ-  ual bursts (3 single, 2 'twin'), 4 well separated "stochastic" events, 3 more triples, and 5 long SFHs, none with a gap of more than 1 epoch, and two cases where all epochs are filled, but with some large error-bars that remind that these are "representative" star formation histories, not to be considered strictly as "epoch-by-epoch."As in Figure 2, but not explicitly called out, are very high S/N examples, in particular, examples 2r, 3r, 4l, 4c along the "sequence" (code: row#, lcr=left, center, right), are extremely 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 compelling evidence that the modeling works and the templates are fully "descriptive:" 3 or 4 templates are all that's needed, and that's good, because that's all that are available!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, much more pronounced.Most of the the bursts, in the top three rows, rise sharply to the (rest-frame) ultraviolet -signaling some 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 cliff-like, and the SEDs are all blue with this sample that covers only 150 Myr, only ∼ 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, 13 billion years later.

SFHS ACROSS TIME
Does the population of SFHs itself 'evolve' ? Figure 6 plots the SFHs of different galaxies as measured at their epoch of observation, color-coded to show burst SFHs as red and orange (single and multiple) and contiguoustriples & continuous-long SFHs as green and blue.To first order, we see two things: (1) the masses of all 982 in our SFHs sample are largely confined to 108 -10 10 M ⊙ , and (2) all four types are represented over the full redshift range covered in this study.The first 'limit', that there are few "accumulated" stellar mass below 10 8 M ⊙ , and none below 5 × 10 7 M ⊙ , is probably a simple de-tection 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 × 109 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 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 redshifts 8 , the variation in the rest of the plot is 'factors-of-two' and not much in the way of trends. 9 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 look into this possibility in the next section.

SFHS ACROSS SPACE
SFHs are known to have a strong spatial variance, in the sense that different kinds of galaxies (ellipticals vs. 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 8 shows the distribution on the sky of the four SFHs (again with the same color encoding).There is obvious largescale structure in the z1, z2, and z3 samples, especially in the lowest z ∼ 6 map, where the contrast between large voids and substantial clustering very strong.This is probably both a result of the growing clustering with   11 include this information by "connecting the dots" from the beginning to end of stellar mass growth.)The most important feature here is the representation of all four types over the full time range.While it is clear that proportions change over the distribution (for a rough picture, see Figure 7), like the apparent "surges" in long-SFHs (SFH4) that appear at z ∼ 10 and z ∼ 8, or the dominance of three-epoch contiguous histories (SFH3) starting at z ∼ 7, it is not clear if these are the result of a biases in SEDz* , or large-scale structure, for example.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 the 22 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 localdensity, or with nearest-neighbor distance, might provide some insight into whether the environments of these galaxies influence their SFHs.In Figure 12 (Appendix  A) we show histograms of local-density and nearestneighbor-distance for the z6, z7, and z8 redshift ranges.The left three panels show density ranges that vary from a few to tens of galaxies per arcmin.As with Figure 6, the most notable feature of these diagrams are ups-anddowns 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.
However, in the sky maps of Figure 8, 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 histories.We made this map by choosing galaxies for which substantial star formation has been detected at z = 11 or z = 1210 , and in doing so, selected 274 galaxies of our sample of 982 that had their first epoch of star formation at that time: what we plot in the fourth panel is what a sky with galaxies forming stars at z=11-12 might have looked like.
Remarkably, we see a tight galaxy group of 16 members in an area only bit larger than ∼ 1 arcmin −2 .Nine of those 16 galaxies are the long, continuous SFHs, the ones that make up only 7% of the full sample: here they are more than half.We claim that this detection of many long SFHs spatially -not a statistical result but a unique data point -is further confirmation that SEDz* actually works: there is no other explanation for how these two quantities -position on the sky and SFH -could be so strongly correlated.If the z = 11 − 12 star formation SEDz* has detected was bogus, they should spread randomly across the field.The clustering, and also what appears to be large-scale structure for the full sample of galaxies, confirms these 'earliest-star-formation' SFHs.
Subsequently, we noticed that this this tight group also shows in the upper left panel, 6.75 < z < 7.75.In fact, this galaxy group had already been independently discovered by members of the JADES team, at an observed redshift of z ∼ 7.5, further confirming their long SFHs.Even more members are observed at the later epoch.
This fortunate 'feature' of the GOOD-S field called to mind that, for the original morphology-density relationship (Dressler 1980), Postman & Geller (1984) found no gradient in morphological type beyond the cluster boundaries, that is, no slowly changing populations beyond the effective radius of the cluster.This and other evidence convinced Dressler that the origin of the morphology-density relation lay not in the latecluster evolution of the cluster or its galaxies, it pointed to the relationship 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 fields like this GOOD-S and more groups will be found at -incredibly -z ∼ 12.This result, if confirmed by many other cases, will 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 en-Figure 8.The distribution on sky for the three redshifts intervals, z1, z2, & z3, along with a map of galaxies found by SEDz* to have had 'first star formation' at z ∼ 11 − 12 (lower right -see text).The four 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 low-right 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 (∼2 arcmin) appears on the right.
vironments 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.

A GALAXY IS BORN
To end where we began, we want to explore how the results obtained in this study can help in understanding how galaxies began to grow and change their chemical composition.
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 imag-ine.At the same time, these young galaxies are also fed continuously by smooth inflow of gas and incorporating less massive galaxies, adding already more mature, moderately metal-enriched stellar populations.All this would continue while young galaxies are also vulnerable to violent mergers and the huge energy release of massive starbursts, and 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 9−10 M ⊙ .We find large contributions to the growth of stellar populations by bursts unlike any we see today, strong enough to make 10 8−9 M ⊙ in an episode lasting only ∼100 Myr -little more than a dynamical time -strong enough to ward off further star formation for more than ∼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 over the same long time in period where a bursting galaxy goes quiet.
The best way to appreciate the power of these data can be seen in Figure 9, Figure 10, and Figure 11, 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 982-galaxy sample to graph the onset of star formation and, in the cases of longer SFHs, its subsequent adding of stellar mass.Here we have "connected the dots" -from when star formation began to the last epoch where it is detected -to show the buildup.(Color coding is the same as for previous figures.) Figure 9 shows this for single bursts and bursty 'stochastic' histories, as we have called them.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, beginning with Figure 9.The plot is for mass vs. time, as in Figure 6, but now with tracks that connect the first epoch of recorded star formation with the last, within the 6 < z < 12 era.In Figure 9, SFH1 star formation -single bursts, are shown as dots with handles covering the their epoch, while the SFH2 "stochastic" histories, in orange, show up mostly as a shallow rise, but with occasional steep ascents.It is also easy to see that, while the single bursts are the most common SFH (of all SFH types), the multiple bursts are both large in mass to begin with and grow with subsequent bursts, such that they add the most mass in this era.A critical point, though is that the mass from these burstdominant galaxies is growing through the appearance of new bursts -'-the most frequent number of bursts for SFH2 galaxies is only 2. Stellar mass is growing by adding bursting objects, single and multiple, not by many smaller bursts in each galaxy.
The same diagram for the 3-epoch 'contiguous' (SFH3) and 4-epoch or more 'continuous' (SFH4) his-tories shows more tilt in its tracks: this is most obvious in the 3-epoch tracks that become more and more dominant from z = 10 down, but, of course, the many epochs of star formation of the SFH4 histories show up as a greater 'tilt.'Both SFH3 and SFH4 result in a very similar distribution of mass, but lower by a factor-of-3 than that of SFH2.
Putting it all together in Figure 11, we combine the burst and longer histories, summing and integrating to learn how the stellar mass of this collection of 982 galaxies grew from z = 12 to z = 6.We see the contribution of single bursts grow strongly, without the mass of individual bursts increasing in time.By z ∼ 6 the single-burst, contiguous, and continuous histories have each added almost 10 11 M ⊙ to this volume of space.The largest contribution, from multiple-burst, stochastic histories is around twice what the other types have added.
Finally, we plot the integrated stellar mass for this special epoch, which reaches 2.3×10 12 M ⊙ in this volume at z = 6, and is growing at a rate of ∼ 2300 M ⊙ yr −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.

CONCLUSION
Our study of ∼1000 newborn galaxies at 6 < z < 12 has shown that their star formation is dominated by bursts: we have called these histories "starbursts"(single) and "stochastic" (multiple).
On the other hand, a substantial minority of galaxies in our study do have traditional τ -model growth histories, what we have called "contiguous" and "continuous" SFHs that last at least 500 − 1000 Myr.Though less numerous than the starburst histories, they are roughly equivalent in their production of stellar mass over the first billion years.
We think that the principal benefit of this result will be to help inform numerical simulations in their modeling of the growth of the baryonic component of the universe that winds up in 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 differences in environment that sends galaxies down one path rather than the other.
We also 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 Figure 9.The contribution to the stellar mass during the period 6 < z < 12 from galaxies dominated by bursts.Red dots, with 'handles' showing their epoch.Orange tracks begin with the first epoch of star formation and connect to the last, showing that such systems do not grow substantially -factors of 3 or 4 at most.Instead, new systems appear, and during this period, that is how the total stellar mass grows.Remarkably, the single burst cases do not add any substantial mass until z=6.
there is a 'just-before' phase of tens of millions of years in which explosive star formatioh ignited in the abundant gas, leading directly to the objects we have been studying.
What seems clear is that the majority of these youngest galaxies do not grow steadily in a calm, peaceful environment.Rather, their journey to what we today regard as "galaxy-sized" seems explosive and chaotic.Perhaps these are gas-rich mergers dominating in lower density regions, manifesting in "one-or twoevent" growth spurts in the first billion years, reaching ∼10 9 M ⊙ (what we call galaxy-sized) when this first phase completes.In another 2 billion years, by z ∼ 2 -"cosmic noon" -these galaxies should have grown by an order-of-magnitude in mass to reach a halfway point for L * It will be important, and challenging, to match their continuing growth to the growth we see for the earliest galaxies, the population of this study.These starburst galaxies neither seem poised for another burst, nor prepared to settle into steadier star-formation histories.Perhaps the "contiguous" SFHs, very common in our Figure 10.The longer SFHs, both 3-or-more epoch contiguous (SFH3) and 4-or-more epoch continuous (SFH4) show substantial growth from z ∼ 12 to z ∼ 6, reaching a similar level of mass per galaxy in the range of 10 8 -10 9 M⊙ , a factor of 3 less than the SFH2 multiple bursts.For both SFH3 and SFH4, the the stellar mass accrues over ∼ 0.5 − 1.0 Gyr, suggesting less volatile surroundings and circumstances in their development compare to the SFH1 and SFH2 burst histories.z = 6 sample, are destined to be those L * galaxies.We note that most have continuing star formation at z = 6, so perhaps they will become the most common galaxies of today, just beginning in earnest their journey to maturity.
Figure 11.The combined diagram shows all the histories, taken together, sum to produce the mass recorded in the colored (dotted) lines above.The substantial growth in stellar mass that happens in this volume of space from z = 12 to z = 6 is mostly from the adding of sources, leading to the 982 we collected for our study.SFH2 -the multiple-burst "stochastic" history, contributes the most, more than the sum of SFH1, SFH3, and SFH4, and despite the strong rise in the number of sources toward z ∼ 6 (which our data suggests continues to z ∼ 5), SFH2 -by virtue of its larger bursts and repeats -makes the largest contribution to stellar mass in the first epoch of star formation where the stellar masses of galaxies grows enough to overlap the mass distribution we see today, but by a very different path with respect to its mode of star formation.

APPENDIX
A. SFHS VS ENVIRONMENT AT z >6 The histograms of Figure 12 the 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 three vertical panels are for the 3 redshift ranges, z ≈ 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.
The absence of any obvious trends between SFH type and environment by these measures 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 there is a hint of the same behavior: in the one region of much higher density, the long-SFH types are strongly represented, a correlation that is not expressed in the lower-density surroundings.

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 13 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 star formation.For this study SEDz* uses 8 templates, for bursts starting at z = 11, 10...5.The principal feature of this plot is that the templates show a considerable amount of non-conformalism, that is, they are 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 'derive' the history of a stellar population -essentially, vector algebraby finding the coefficients of the vector sum that best represents the SED.What makes this particular application of the method potent is the non-conformal character of stellar populations of ages τ < 1 Gyr -the templates covering the early universe for z = 12 to z = 5.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 ∼ 3. 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 were not representative of stellar populations at z > 5 this attempt to reproduce observed SEDs would fail badly; quite the opposite is true.
The bottom half of Figure 14 shows the templates for constant-star-formation 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.At the time resolution offered by broad-band SEDs, no further information is available, including no signature that would distinguish CSF from a more complex behavior over the ∼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 ∼ 2µm at z ∼ 6 to ∼ 3.5µm at z ∼ 10, and from the jaggedness of the SED from 3µm to 5µm -due to [O III] and Hα emission.This flatness, when combined with bursts of previous epochs, is responsible for much of 'character' of the long SFHs.The top of Figure 14 shows that combining a burst (at the beginning of an epoch) with a 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 ∼ 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.

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 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, τ ≤ 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 ∼100 Myr of cosmic history, any object selected through broad-band photometry will by necessity require star formation to have been either a large burst of short duration or continuous star formation during most if not all of the epoch.Thus, the effect of the youngest populations through their emission lines is likely to be modest at best.
Figure 15 verifies that this is the case 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 Hα lines over the redshift range 6 < z < 9.
The medium bands often provide good evidence of emission because their width is ∼40% of the broad bands, and and they can also, in cases that exhibit emission, establish the continuum level at that color, sometimes considerably below that of the broad bands11 The close agreement in flux of both broad and narrow bands in the upper left and lower left examples shows that there is little or no detected emission in these two cases, which is typical of our ∼ 1000-galaxy sample.Note how the level of F356W and F444W are close.The center-left SED shows moderate emission in F444W and detection of the continuum in F335M, and here the F444W appears to be elevated above F356W: indeed, the emission -[O III] -is detected in both bands.The case in the upper-right is a stronger example of the same pattern: 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?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 included hydrogen lines (Robertson et al. 2010), based on Osterbrock tabulations and case B recombination) and metallic lines (Z = 0.2 Z⊙, 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 ∼ 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 typical closeness to F356W level, but the SEDz* model passes through both points because emission is included.The same for the upper-right example with strong emission in F335M -among the strongest in our sample.In this case, at least, the continuum level of F410M, compared to the elevated value of F356W, comes in at the proper ratio of 2.5:1.
In the middle-right and bottom-right examples we again see the SEDz* model passing through F356W and F444W -the emission, in these cases -[O III] and Hα -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.The continuum is matched by z = 11 − 12 and z = 8 flux to complete the fit.
To conclude, the examples with little-or-no emission suggest, and the examples on the right confirm, that "red rise" found in the SEDs of more than 100 galaxies of our sample, is flux from older stellar populations, in other words, the SEDz* star formation history confirmed.

Figure 1 .
Figure 1.Examples of the four types of SFHs 5 < z < 12 found by SEDz* .The text describes how, considered together, these examples demonstrate the fidelity of SEDz* -derived SFHs.The left box of each panel 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 1σ random errors.The run of χ 2 is shown in the insert at upper left; the dip marks the observed redshift.Most important is the SFH corresponding to this best fit, shown in the box to the right, where each epoch of star formation, in solar masses, is recorded as a box with colors corresponding to the different epochs.For each epoch that contributes to the SED fit, the flux contributed to the solution is plotted on he left box, as a line of the same color below the 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 ∼ 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 larger sample that underlies the present work, such errors are not large enough to admit distinct, alternative SFHs.The four panels show a starburst (upper-left) and a double burst (upper-right), a 'short' but contiguous run of star formation (lower-left) and a longer, continuous SFH covering half of the first ∼800 years of cosmic history to that point.The positions of prominent emission lines are shown above the SED, in blue, with a larger green font marking a possible detection by excess flux compared the best fit to the flux of continuum with emission lines.

Figure 2 .
Figure 2. Examples of the identified four types of SFHs of this study observed at redshifts z ∼ 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 continguous runs, and finishing with long SFHs of four epochs or more.Detailed explanations of the salient characteristics of these types are explained in the text.

Figure 3 .
Figure3.A virtual 'replay' of the types in Figure3for 18 galaxies at z ∼ 7 (6.76 < z < 7.75), as described in the text.This set includes four examples with very high S/N (Row:left-right-center = 2l, 3r, 4l, 4c) that are exquisitely fit by SEDz* with its "present-epoch" templates, demonstrating the fidelity of the SFHs that SEDz* can deliver.

Figure 4 .
Figure 4.The persistence of the four SFH types reaches back ∼ 700 Myr from z ∼ 6.No obvious evolution of the mix of types is apparent, although changes in "proportions" may be appearing (see Figure6).At this earlier epoch the prominence of the Lyman break is a strong factor in finding the reshift and establishing the SFH.More than half of these 8 < z < 10 galaxies show detected star formation at z ∼ 11 − 12

Figure 6 .
Figure6.The stellar masses associated with the four SFH types displayed over the full 6 < z < 12 time frame of this study.Each dot represents the epoch-of-observation, but the period of star formation is indicated only by color.(Figure9through (Figure11include this information by "connecting the dots" from the beginning to end of stellar mass growth.)The most important feature here is the representation of all four types over the full time range.While it is clear that proportions change over the distribution (for a rough picture, see Figure7), like the apparent "surges" in long-SFHs (SFH4) that appear at z ∼ 10 and z ∼ 8, or the dominance of three-epoch contiguous histories (SFH3) starting at z ∼ 7, it is not clear if these are the result of a biases in SEDz* , or large-scale structure, for example.

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

Figure 14 .
Figure 14.Bottom: Templates for CSF (constant star formation) at epochs 5 through 10.Top: Combinations of burst and CSF templates at z = 7. Ratios are CSF-to-burst (see text).