11institutetext: Département d’Astronomie, Université de Genève, Chemin Pegasi
51, CH-1290 Versoix, Switzerland 22institutetext: Centre for Astrophysics and
Space Sciences Maynooth, Department of Theoretical Physics, Maynooth
University, Maynooth, Ireland 33institutetext: Department of Physics and
Astronomy, Allen Building, 30A Sifton Rd, University of Manitoba, Winnipeg MB
R3T 2N2, Canada

# Explaining the high nitrogen abundances observed in high-z galaxies via
population III stars of a few thousand solar masses

Devesh Nandal 11 John A. Regan 22 Tyrone E. Woods 33 Eoin Farrell 11 Sylvia
Ekström 11 Georges Meynet 11

The chemical enrichment of the early Universe is a crucial element in the
formation and evolution of galaxies, and Population III (Pop III) stars must
play a vital role in this process. In this study, we examine metal enrichment
from massive stars in the early Universe’s embryonic galaxies. Using radiation
hydrodynamic simulations and stellar evolution modelling, we calculated the
expected metal yield from these stars. Specifically, we applied accretion
rates from a previous radiation-hydrodynamic simulation to inform our stellar
evolution modelling, executed with the Geneva code, across 11 selected
datasets, with final stellar masses between 500 and 9000 $\mathrm{M}_{\odot}$.
Our results demonstrate that the first generation of Pop III stars within a
mass range of 2000 to $9000\,\mathrm{M}_{\odot}$ result in N/O, C/O and O/H
ratios compatible with the values observed in very high-z galaxies GN-z11 and
CEERS 1019. The ejecta of these Pop III stars are predominantly composed of
4He, 1H, and 14N. Our Pop III chemical enrichment model of the halo can
accurately reproduce the observed N/O and C/O ratios, and, by incorporating a
hundred times more zero-metallicity interstellar material with the stellar
ejecta, it accurately attains the observed O/H ratio. Thus, a sub-population
of extremely massive Pop III stars, with masses surpassing approximately 2000
M⊙, effectively reproduces the CNO elemental abundances observed in high-z
JWST galaxies to date. We closely reproduced the observed Ne/O ratio in CEERS
1019 employing a model with several thousand solar masses and non-zero
metallicity, and we projected a ${}^{12}C/^{13}C$ ratio of 7, substantially
lower than the solar ratio of around 90. The significant nitrogen enrichment
predicted by Pop III stars with a few thousand solar masses not only
reinforces the argument for a heavy seed formation pathway for massive black
holes at redshifts as high as z=10.6 but it also accentuates the need for
deeper investigations into their complex nature and pivotal role in the early
Universe.

###### Key Words.:

Stars: evolution – Stars: Population III – Stars: massive – Stars: abundances

##  1 Introduction

The observation of nitrogen-enhanced high-$z$ galaxies, particularly in GN-z11
(Oesch et al. 2016) and CEERS-1019 (Finkelstein et al. 2017), has sparked a
revolution in the study of the Universe’s earliest star and galaxy formation.
GN-z11, located at a redshift of $\mathrm{z}=10.6$ (Bunker et al. 2023),
exhibits a N/O abundance ratio in its interstellar medium (ISM) that is more
than four times the solar value ($\log(\mathrm{N/O})>\sim-0.25$) (Cameron et
al. 2023; Senchyna et al. 2023). This ratio is not only significantly higher
than what is typically found in low-redshift galaxies and HII regions with a
comparable metallicity ($12+\log({\rm O/H})<\sim 8.0$) but it also slightly
exceeds the values observed in galaxies with super-solar metallicities
(Vincenzo et al. 2016; Berg et al. 2019). Although the C/O ratio of GN-z11 is
consistent with normal values, it is poorly constrained (Cameron et al. 2023).

Similarly, CEERS-1019, at a redshift of $z=8.678$, displays strong nitrogen
emission lines of N III and N IV, with the N IV] $\lambda 1486$ being the most
intense line in its rest-frame UV spectrum (Tang et al. 2023). This galaxy has
an unusually high N/O abundance ratio of $\log(\mathrm{N/O})=-0.13\pm 0.11$,
which is approximately 5.6 times the solar ratio. However, its C/O and Ne/O
ratios, with values of $\log(\mathrm{C/O})=-0.75\pm 0.11$ and
$\log(\mathrm{Ne/O})=-0.63\pm 0.07$ respectively, are relatively normal for
its metallicity (Marques-Chaves et al. 2023).

These observations challenge the conventional theories of stellar yields and
galactic chemical evolution, necessitating a reexamination of the dynamics of
the early Universe. In particular these unusual abundance patterns in high-z
galaxies may be a signature of massive, very massive, and supermassive stars
(MSs, VMSs, and SMSs) 111We consider stars to be massive within 10-100 M⊙,
very massive within 100-1000 M⊙, extremely massive within 1000-40,000 M⊙ and
supermassive with mass above 40,000 M⊙ as described in the work by Woods et
al. (2020) in early galaxies. Moreover, these massive objects may well explain
the appearance of central massive black holes in these galaxies as well (e.g.
Natarajan et al. 2023) and their role in the formation of supermassive black
holes (SMBHs) in the early Universe is a subject of ongoing research (Hosokawa
et al. 2010; Ekström et al. 2012; Woods et al. 2017; Haemmerlé et al. 2018;
Woods et al. 2021).

A number of recent studies have attempted to explain the unusually high
Nitrogen abundances (as well as the other metal abundances) observed in these
high-z galaxies. Kobayashi & Ferrara (2023) explain these signatures using a
rapid chemical enrichment mechanism via a dual-burst model where a quiescent
period lasting approximately 100 Myr separates the bursts. In their model,
Wolf-Rayet stars become the dominant enrichment source during the second burst
- enriching the ISM with heavy elements. Their single burst model, similar to
ours described here, requires the presence of massive stars with masses in
excess of $\sim 1000$ M⊙. Along similar lines both Charbonnel et al. (2023)
and Nagele & Umeda (2023) have studied the impact that metal enriched stars in
the mass range of $10^{3}$ \- $10^{5}$ M⊙ can have in high-z galaxies. In both
of these studies the authors have been able to reproduce the high
$\log(\mathrm{N/O})$ abundance ratios observed in GN-z11. Several other
studies have sought to explore different stellar evolution channels on the
early chemical evolution of the Universe. For instance, Meynet & Maeder (2006)
and Choplin et al. (2018) investigated the impact of fast-rotation on the
nucleosynthetic outputs of massive stars. These yields were then used in
models for the early chemical evolution of the Milky Way by Chiappini et al.
(2003, 2006); Cescutti et al. (2013) showing that the chemical composition of
the bulk of halo stars is compatible with yields coming from fast rotating
models. The potential role of pair-instability supernovae in the early
Universe was analysed by Heger et al. (2002). Although these studies have shed
light on different aspects, the exact elemental yields and enrichment
potential of VMSs and SMSs remain largely unexplored (Denissenkov & Hartwick
2014).

In this paper, we adopt a novel approach by combining radiation hydrodynamic
simulations and stellar evolution modelling to compute the expected metal
yield from a population of massive Population III (PopIII) stars. Using the
accretion rates from Regan et al. (2020b), we compute eleven PopIII models
from the pre-main sequence (PreMS) until the end of core helium burning. We
delve into the results of individual stellar models and the integrated halo
population, revealing new insights into the N/O, C/O, and O/H number
fractions, and taking into account the possibly diluting impact of an
additional population of one hundred 20 $\mathrm{M}_{\odot}$ stars.
Specifically, we find that chemical enrichment coming from the ejecta of very
massive stars, computed with a variety of assumptions can reproduce the
observed N/O number fractions, while we successfully match the observed C/O
abundances when pulsations from the massive PopIII stars remove all mass above
the CO core. Finally to match the O/H number fractions we require a dilution
factor (given by the ratio of the mass of the ejecta to that of the
interstellar medium with which the ejecta mixed) of 100, entirely consistent
with expected ratios chemical abundances in gas rich high-z galaxies. This
study not only provides significant insights into the chemical enrichment of
the early Universe and the role of supermassive PopIII stars, but also
underscores the necessity for further investigations into the complex but
pivotal role of massive PopIII stars in the early Universe.

This paper is set out as follows: Section 3 first explores the mechanisms
invoked for the transport of chemical special and calculates the integrated
abundances of the individual stars (we express $\mathbf{X}_{\mathbf{io}}$ as
the mass fraction of element $i$ in the ejecta a given star) and for the
entire halo ($\mathbf{X}_{\mathbf{ip}}$, the mean mass fraction of element $i$
in the ejecta coming from a population of stars). Section 4 explores the mass
ranges of individual stars that would reproduce the observed results and
predicts abundances based on our models, along with comparing our results to
previous studies. Section 5 sums up our findings and provides prospects for
future work.

##  2 Methods

###  2.1 Cosmological context

As discussed in the Introduction, the goal of this study is to calculate the
metal enrichement due to pulsational mass loss from massive stars in embryonic
haloes in the early Universe. To achieve this goal we utilise the radiation
hydrodynamical simulation of Regan et al. (2020b). We previously used the
calculated accretion rates from Regan et al. (2020b) to calculate the critical
accretion rates onto massive PopIII stars in the study by Nandal et al.
(2023b). In this study we take the stars found in Regan et al. (2020b) and
compute, in post-processing, the expected metal yield from these stars using
the same stellar evolution code as used in Nandal et al. (2023b).
For an in-depth discussion of both Regan et al. (2020b) and Nandal et al.
(2023b) we refer readers to the original papers but describe both papers
briefly here to provide context. Regan et al. (2020b) employed cosmological
zoom-in simulations utilising the Enzo code (Bryan et al. 2014; Brummel-Smith
et al. 2019) to investigate pristine, atomic cooling haloes, from the original
studies by Wise et al. (2019) and Regan et al. (2020a)222These simulation were
themselves rooted in the Renaissance simulation suite (Chen et al. 2014;
O’Shea et al. 2015; Xu et al. 2016). Using the canonical zoom-in technique
Regan et al. (2020b) study showed the formation of 101 (massive) stars in one
single halo. The cumulative stellar mass reached roughly 90,000
$\rm{M_{\odot}}\leavevmode\nobreak\ $after about 2 Myr of the first star’s
inception. Stellar masses ranged between 40
$\rm{M_{\odot}}\leavevmode\nobreak\ $to over 6000 $\rm{M_{\odot}}$, with a
simulation spatial resolution of $\Delta x\sim 1000$ au. Accretion rates onto
individual stars ranged from less than $10^{-3}$
$\rm{M_{\odot}\leavevmode\nobreak\ yr^{-1}}\leavevmode\nobreak\ $to close to 1
$\rm{M_{\odot}\leavevmode\nobreak\ yr^{-1}}\leavevmode\nobreak\ $at peak. It
is these accretion rates which serve as the input for our stellar evolution
modelling and is a key and unique component in this study.

In Nandal et al. (2023b) we selected 11 stellar evolution datasets from the
underlying cosmological simulations of R20b comprised of a variety of
accretion histories and final stellar masses (see Table 1). We use these same
11 datasets here. They contain final stellar masses from 491 $\rm{M_{\odot}}$
up to 6127 $\rm{M_{\odot}}$. These 11 stellar models, with fluctuating
accretion rates, were evolved from the pre-MS to the end of core helium
burning using the Geneva code (Genec) (Eggenberger et al. 2008). We adopted a
consistent chemical mix ($X$ = 0.7516, $Y$ = 0.2484, $Z$ = 0) and a deuterium
mass fraction $X_{2}=5\times 10^{-5}$ as per previous studies. Starting with a
2 M⊙ fully convective seed, accretion is modeled via a thin cold disc
(Haemmerlé et al. 2013, 2016), consistent with Palla & Stahler (1992) &
Hosokawa et al. (2010). The original study by Nandal et al. (2023b) required
several code enhancements in Genec including functionality to cater for
variable accretion rates from external files as well as improved spatial and
time resolution to account for the variable accretion history. However,
effects due to rotation and (explicit) mass loss are not considered, although
we note that our model hinges on the assumption that these massive stars do
suffer from some degree of mass loss through for example pulsations or due to
stellar winds triggered by the increase of the opacity at the surface due to
changes of the surface composition here by convection (see Figure 1 for a
graphical illustration). In this work, we do not model the mass loss
numerically, but test various hypothesis and assume that some amount occurs
during the evolution.

We discuss these underlying assumptions further in §2.2. In addition to the 11
models already computed in Nandal et al. (2023b) we computed an additional
model with a constant accretion rate of 3.5$\times 10^{-3}$$\
\mathrm{M}_{\odot}\,{\rm yr}^{-1}$and a final mass of 8904 M⊙ using the same
chemical composition as above. This model was computed to serve as a limiting
case for halo from the simulations of Regan et al. (2020b) to match the N/O,
C/O and O/H values with GN-z11 and CEERS 1019.

###  2.2 Massive PopIII Star (Nitrogen) Enrichment

To explain the abundances observed in high redshift candidates such as GN-z11
and CEERS1019, we invoke the very and extremely massive PopIII enrichment
scenario. In this scenario, a very and extremely massive star begins its
evolution as an accreting protostar during the pre-Main Sequence (pre-MS)
evolution that lasts for $\lesssim 10^{5}$ yr, see Figure 1. As the star
transitions to the main sequence the core hydrogen burning phase begins in the
blue with the star possessing a convective core and a radiative envelope as
shown in detail in Nandal et al. (2023b). If the star accretes sufficiently
rapidly (above approximately $2.5\times 10^{-3}$
$\rm{M_{\odot}\leavevmode\nobreak\ yr^{-1}}$) then the star can transition to
the red during the pre-MS or the MS phase. This transition is included in our
modelling. In either case at the end of the MS the star migrates to the red
and acquires a near fully convective structure before the start of core helium
burning. This allows the efficient transport of chemical species from the
interior to the surface. We next make the assumption, that due to the unstable
nature of such massive PopIII stars, they are unstable to mass loss, as
suggested by Nagele et al. (2022). The quantity of mass lost via winds and/or
pulsations is difficult to quantify and instead we parameterise this unknown
quantity by examining the impact of different mass loss amounts (see §3.3)333A
similar approach has been used by Liu et al. (2021) for investigating the
impact of winds of Pop III massive stars.. Following Helium burning and at the
end of core silicon burning, such an object may explode as a supernova (Nagele
& Umeda 2023) and produce a black hole or directly collapse into a black hole
with mass comparable to the Helium core mass Montero et al. (2012). For
massive stars with masses in excess of approximately 260
$\rm{M_{\odot}}\leavevmode\nobreak\ $a direct collapse black hole is always
the expected outcome. However, small mass islands leading to a supernova
explosions are predicted in some cases (e.g. Chen et al. 2014; Moriya et al.
2021) but there is currently no observational guidance to constrain these
islands. For the case of massive PopIII stars with masses in the range of
approximately $10^{3}-10^{4}$ $\rm{M_{\odot}}\leavevmode\nobreak\ $we find
that the expulsion of large quantities of surface material, which contains
unusually large nitrogen fractions, from the surface can lead to a black hole
accretion disc with an unusually large nitrogen abundance. This key signature
of massive PopIII mass loss episodes is highly relevant to other recent
observations of N-rich quasars as described in the works of (Bunker et al.
2023; Cameron et al. 2023).

Figure 1: Illustration depicting the massive PopIII enrichment scenario. From
left to right: (1) The formation of a massive PopIII star via accretion which
generally occurs during the pre-MS but some stars may undergo short accretion
phases during MS. If the accretion rate is below the critical limit described
in Nandal et al. (2023b), the star migrates to blue. (2) The transition to red
at the end of core helium burning leads to the formation of large convective
zones and pulsational mass loss as shown by the red mesh. (3) The collapse of
a MS may lead to additional mass ejected and the eventual formation of a black
hole. (4) Further accretion of ejected material onto the black hole creats the
conditions for allowing nitrogen absorption lines to appear, as in the case of
GN-z11 and CEERS 1019.

###  2.3 Model for the wind enrichment

In this study, we study a scenario where a star enriches the chemical
composition of its surrounding interstellar medium (ISM) by shedding some of
its mass during its evolution. This mass loss might occur through a series of
significant mass-loss episodes prior to the star’s final collapse for example.
Our understanding of the mass loss rates of present day massive stars is
incomplete (Sabhahit et al. 2023) and in the absence of observational guidance
our understanding of early Universe massive stars should certainly be seen as
incomplete. We therefore choose to parameterise the mass-loss rates of these
stars. We detail our parameterisation as follows.

We assume that the stars lose their mass at or after the core He-burning
phase. This is a phase where the star is in the red part of the HR diagram
where pulsational instabilities can be large and also a phase where the
surface is enriched in heavy elements increasing the opacity. The total mass
of element $\mathbf{i}$ ejected by the star, denoted as $\mathbf{{M_{EJ}}(i)}$
in solar masses, is given by $\rm{\bar{X}_{i}M_{\rm EJ}}$, where
$\rm{\bar{X}{i}}$ is the mean mass fraction of element $\mathbf{i}$ in the
ejecta of the star and MEJ is the total mass ejected. $\rm{\bar{X}_{i}}$ is
given by

$\rm{\bar{X}_{i}}=\int_{M_{\rm cut}}^{M_{\rm tot}}X_{i}(M_{r}),dM_{r}/M_{\rm
EJ}$ (1)

where $\mathbf{M_{\mathbf{c}ut}}$ is the mass coordinate above which we assume
the mass to be lost, $\mathbf{M}_{\mathbf{r}}$ is the mass coordinate at which
$\mathbf{X}{\mathbf{i}}$ is chosen. Here we assume $\mathbf{M_{\mathbf{c}ut}}$
to take on three separate values: 1) 10% of the total stellar mass; 2) 40% of
the total stellar mass; and 3) all the stellar mass above CO core. The CO core
is defined as the mass coordinate below which less than $10^{-3}$ of Helium
mass fraction ($\mathbf{Y}_{c}$) is present. The mass below
$\mathbf{M_{\mathbf{c}ut}}$ is therefore assumed to be locked into the black
hole, and $\mathbf{M_{\mathbf{t}ot}}$ is the total actual mass of the star at
the moment of core collapse.

The ejected mass interacts with the interstellar medium (ISM), leading to a
mixture of the star’s ejecta and the ISM. The mass of the ISM involved in this
interaction is represented as $\mathbf{M_{\mathbf{I}SM}}$. We introduce a
dilution factor $\mathbf{f}$, which is the ratio $\rm{M_{ISM}/M_{EJ}}$. As
noted we treat $\mathbf{f}$ as a free parameter as it depends on a number of
unknown factors, such as the physics of the explosion and/or the collapse on
the one hand and on the exact state of the ISM on the other. To account for
our ignorance of both the exact mass lost values and the chemical composition
of the ISM we explore different possibilities here considering this
$\mathbf{f}$ factor as a free parameter, varying from 1 to 1000. We determine
$\mathbf{X}_{\mathbf{io}}$ as the mass fraction of element $\mathbf{i}$ in the
ISM at ejection time. The ejection of the mass from a star is assumed to occur
in the early stages of the halo evolution. As stars continue to eject matter
in their surroundings, the chemical composition changes as a function of time.
In other words, the initial chemical composition of the PopIII star is
pristine and only consists of hydrogen and helium but as these stars evolve
and eject the CNO rich material in the ISM, the chemical composition of the
ISM in the halo evolves as a function of time.

Using these parameters, we estimate the final composition of the chemical
mixture of the star’s ejecta and the ISM. This is a key objective of our
study. We define $\mathbf{X}_{\mathbf{im}}$ as the mass fraction of element
$\mathbf{i}$ in this mixture and calculate it using the principle of mass
conservation:

$\mathrm{X_{im}*(M_{EJ}+M_{ISM})=\bar{X}_{i}*M_{EJ}+X_{io}*M_{ISM}}$ (2)

By substituting the dilution factor f = MISM/MEJ into the equation, we can
simplify it to:

$\mathrm{X_{im}*(1+f)=\bar{X}_{i}+f*X_{io}}$ (3)

Furthermore, to extrapolate this to a galaxy containing $n$ stars is straight
forward. Let $\mathbf{n({\rm M}_{\rm ini})}$ be the number of stars in the
galaxy with masses between Mini and Mini \+ dMini. We obtain the mean mass
fraction of element $\mathbf{i}$ in the ejecta of all stars in the galaxy as

$\mathrm{X_{ip}=\sum_{M_{ini}}\frac{n(M_{ini})*\bar{X}_{i}(M_{ini})*M_{EJ}(M_{ini})}{n(M_{ini})*M_{EJ}(M_{ini})}}$
(4)

where $\mathbf{X}_{\mathbf{ip}}$ is the mass fraction of element $\mathbf{i}$
in the ejecta of all the stars. Now again assuming the dilution $\mathbf{f}$
as before we can compute the mass fraction in the ISM following the enrichment
from the stars as

$\mathrm{X_{imp}=\frac{X_{ip}+f*X_{io}}{1+f}}$ (5)

Finally, we assume the formation of stars in the galaxy occurs at zero
metallicity and therefore $\mathbf{X}_{\mathbf{io}}$ is taken as zero for C,
N, O and 0.7516 for $\mathbf{X}_{\mathbf{H,ini}}$. This means that for all
elements excluding Hydrogen we have that

$\mathrm{X_{imp}\approx\frac{X_{ip}}{1+f}}$ (6)

Therefore, the mass fraction of element $\mathbf{i}$ that exists in the ISM
following enrichment is given by the ejected fraction,
$\mathbf{X}_{\mathbf{ip}}$, divided by the dilution factor, $\mathbf{f}$, if
$\mathbf{f}$ is much larger than 1. The initial mass function for the halo is
given by the simulation, that is, the histograms shown in Fig. 3

The goal of this paper is to systematically explore the various integrated
abundances (i.e. $\mathbf{X}_{\mathbf{imp}}$) expected from very massive
PopIII stars in the first galaxies.

Table 1: Mean abundances in the mass fraction of different chemical species in the mass ejected by 11 massive PopIII star models. The first column shows the final mass of each model and the second column depicts the mass of CO core at the end of core helium burning. The next 5 columns depict the mean abundances (see Eq.1 in the mass fraction for ${}^{1}H$, ${}^{4}He$, ${}^{12}C$, ${}^{14}N$ and ${}^{16}O$ when the outermost 10% of total mass is ejected. The following five columns are the mean abundance in the ejecta when 40% of the outermost total mass is ejected and the final five columns when all the mass above CO core is ejected. $M_{\text{tot}}$ |  $M_{\text{CO}}$ |  $\bar{X}_{\text{H}}$ |  $\bar{X}_{\text{He}}$ |  $\bar{X}_{\text{C}}$ |  $\bar{X}_{\text{N}}$ |  $\bar{X}_{\text{O}}$ |  $\bar{X}_{\text{H}}$ |  $\bar{X}_{\text{He}}$ |  $\bar{X}_{\text{C}}$ |  $\bar{X}_{\text{N}}$ |  $\bar{X}_{\text{O}}$ |  $\bar{X}_{\text{H}}$ |  $\bar{X}_{\text{He}}$ |  $\bar{X}_{\text{C}}$ |  $\bar{X}_{\text{N}}$ |  $\bar{X}_{\text{O}}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
$(M_{\odot})$ |  $(M_{\odot})$ | 10% | 40% | CO core
491 |  104 |  0.360 |  0.430 |  0.002 |  0.056 |  0.150 |  0.256 |  0.450 |  0.002 |  0.079 |  0.210 |  0.235 |  0.451 |  0.002 |  0.084 |  0.224
771 |  165 |  0.319 |  0.460 |  0.002 |  0.053 |  0.162 |  0.235 |  0.466 |  0.002 |  0.074 |  0.218 |  0.217 |  0.465 |  0.002 |  0.079 |  0.232
778 |  163 |  0.299 |  0.473 |  0.003 |  0.038 |  0.180 |  0.240 |  0.454 |  0.002 |  0.058 |  0.235 |  0.220 |  0.447 |  0.002 |  0.065 |  0.253
932 |  247 |  0.339 |  0.588 |  0.002 |  0.056 |  0.015 |  0.185 |  0.682 |  0.002 |  0.102 |  0.028 |  0.161 |  0.695 |  0.003 |  0.108 |  0.031
1135 |  440 |  0.204 |  0.669 |  0.003 |  0.086 |  0.038 |  0.124 |  0.691 |  0.003 |  0.122 |  0.058 |  0.115 |  0.691 |  0.005 |  0.126 |  0.063
1331 |  317 |  0.293 |  0.519 |  0.005 |  0.067 |  0.114 |  0.201 |  0.528 |  0.003 |  0.103 |  0.163 |  0.186 |  0.528 |  0.003 |  0.108 |  0.172
1662 |  630 |  0.198 |  0.766 |  0.001 |  0.031 |  0.004 |  0.095 |  0.852 |  0.001 |  0.047 |  0.004 |  0.078 |  0.864 |  0.002 |  0.050 |  0.006
1923 |  746 |  0.232 |  0.577 |  0.001 |  0.046 |  0.137 |  0.181 |  0.573 |  0.001 |  0.061 |  0.174 |  0.171 |  0.571 |  0.001 |  0.064 |  0.183
3053 |  650 |  0.202 |  0.737 |  0.000 |  0.018 |  0.004 |  0.202 |  0.737 |  0.000 |  0.022 |  0.004 |  0.157 |  0.765 |  0.001 |  0.033 |  0.012
4477 |  759 |  0.297 |  0.687 |  0.000 |  0.015 |  0.001 |  0.153 |  0.816 |  0.001 |  0.029 |  0.001 |  0.073 |  0.884 |  0.003 |  0.034 |  0.006
6127 |  1252 |  0.173 |  0.779 |  0.001 |  0.039 |  0.006 |  0.079 |  0.855 |  0.001 |  0.056 |  0.008 |  0.040 |  0.875 |  0.004 |  0.060 |  0.017

Figure 2:  Test model with a final mass of 8904 M⊙ computed using a constant
accretion rate of 3.5$\ \mathrm{M}_{\odot}\,{\rm yr}^{-1}$until the end of
core helium burning. Left panel: The Kippenhahn diagram showing the evolution
of radius versus time. The blue and cream regions represents the convective
and radiative zones respectively. Core hydrogen burning is shown in dotted
zone and core helium burning in brown zone. The black lines represents the
iso-masses and the white lines depict the iso-thermal lines. Right panel: The
abundance profile inside the 8904 M⊙ model at the end of core helium burning.
The label for each element matches the corresponding line.

##  3 Results

###  3.1 Transport of chemical species

The evolution of a typical accreting massive Pop III star is shown in left
panel of Figure 2. The accretion history of this model is artificially
generated by assuming a constant accretion rate of 3.5$\times 10^{-3}$$\
\mathrm{M}_{\odot}\,{\rm yr}^{-1}$to produce a star with mass of 8904 M⊙. The
choice of constant accretion rate is motivated by the works of Nandal et al.
(2023a) where they compare the effects of a constant versus variable accretion
rate and find that evolution beyond core hydrogen burning is near identical in
both cases. Therefore, we present a new model (in addition to the 11 models
with variable accretion rates found in Nandal et al. (2023b)) that reproduces
the same chemical structure in advanced evolutionary stages as the model
computed with a variable accretion rate ending with a mass of 8904 M⊙. It must
be noted that the accretion history of this model was not obtained from the
hydrodynamic simulations and therefore, the contribution of its stellar yields
to the entire sub-population of mini halo are not included in the ejecta
calculations. We simply use this model to explain the structure of such stars
and explore its individual N/O, C/O and O/H ratios later on in this study.
After following a pre-MS evolution of $\lesssim 10^{5}$ years, the object
commences hydrogen burning in the blue region of HR diagram at log (T${}_{\rm
eff})=4.90$ (Nandal et al. 2023b). During the middle of hydrogen burning, at
an age of about 1.5 Myr the star begins its redward migration. The accretion
rate during this migration is below the critical value of
$\dot{M}_{\mathrm{crit,MS}}$ = 7.0$\times 10^{-3}$ found by Nandal et al.
(2023b), and the star therefore oscillates between red and blue until
$\approx$ 2 Myrs. As the core hydrogen is depleted, the star migrates to the
red and attains an effective temperature of log (T${}_{\rm eff})=3.70$. During
this final crossing of the HR gap, the structure that previously consisted of
a convective core and an extended radiative envelope, now consists of a
convective core, a series of intermediate convective zones and an extended
convective envelope. Such a near-fully convective structure allows the
transport of chemical species from the deep interior to the surface, thereby
promoting strong enrichment without the need of rotation. It is interesting to
note that the near-fully convective structure is only attained at the very end
of core hydrogen burning and is absent during the red-blue excursions that
occur from 1.5 - 2 Myrs, see left panel of Figure 2. The non-rotating models
produced in this study using Genec show that the structure of such stars is
independent of the choice of mass within the mass range of 200 - 105
$\mathrm{M}_{\odot}$.

The right panel of Figure 2 shows the abundance profile of the 8904 M⊙ star at
the end of core Helium burning stage. The convective core extends until the
mass coordinate of 1142 M⊙ beyond which the effects of large intermediate
convective zones become dominant as the profiles of various elements is flat
until 5800 M⊙, hinting at strong mixing in these zones. From 5800 to 7800 M⊙,
small intermediate convective are present which also promote mixing but to a
lesser extent, shown by the negative gradients of the abundance profile of all
elements in the right panel of Figure 2. Finally, a large convective zones
extends from a radius of 1600 to 15848 R⊙ and mass from 8000 to 8904 M⊙,
produces a flat abundance profile and affects the surface abundances of the
star. As a result of a near-fully convective structure, all chemical species
such as $\mathrm{{}^{1}H}$, $\mathrm{{}^{3}He}$, $\mathrm{{}^{4}He}$,
$\mathrm{{}^{12}C}$, $\mathrm{{}^{13}C}$ , $\mathrm{{}^{14}N}$,
$\mathrm{{}^{16}O}$, $\mathrm{{}^{20}Ne}$ and $\mathrm{{}^{22}Ne}$, shown in
the right panel of Figure 2 have their abundances strongly affected compared
to their initial abundances. Globally in the zone above the convective core,
hydrogen has been depleted (being transformed mainly into helium) and the
other chemical species have been synthesised.

Although such massive stars are expected to generate energy via the CNO cycle
already during core hydrogen burning, see Woods et al. (2017, 2021), the
amount of CNO material available is not sufficient for any significant 14N
production during this evolutionary stage. The production of 14N instead
occurs during the core helium burning stage. The first step in this process
occurs in the 4He rich convective core where 12C is produced via the
triple-$\alpha$ reaction. The 12C is then efficiently transported to adjacent
hydrogen burning shell via convection. This begins the second step where the
presence of 12C in the hydrogen burning shell allows it to capture hydrogen
and produce 13N, which emits a positron and produces 13C. In the final step,
13C captures a proton. This produces 14N. The intermediate convective zones
are present around the hydrogen burning shell and extend towards the surface,
thereby allowing the efficient transport of 14N in the stellar envelope. The
variation of the nitrogen abundance in mass fraction inside the star as a
function of the lagrangian mass coordinate is denoted by the red line in the
right panel of Figure 2 where the abundance of 14N is highest at the hydrogen
burning shell that begins at the mass coordinate of 1142 M⊙ and is the third
most abundant element (after 1H and 4He) at the surface. The production of 16O
is similarly related to the generation of 12C which for PopIII stars mainly
occurs during the core helium burning stage as seen above. Once 12C is
produced, it undergoes $\alpha$ capture to produce ${}^{16}O$ which is also
transported to the surface as shown by purple line in the right panel of
Figure 2. In the envelope we see thus material processed by both H- and He-
burning. The CNO cycle is responsible for building nitrogen. The He-burning is
responsible for making carbon and oxygen. The final abundances shown in the
right panel of 2 comes out from a complex interplay between nuclear reactions
and convection.

###  3.2 Integrated abundances

In Table 1 we show the mean mass fraction of various isotopes in the ejecta of
individual star with different final mass, $\bar{\rm X}_{i}$ of the 11 model
stars as discussed in §2.1. Firstly we see a clear trend in the ejected
abundances for hydrogen and helium that relates to the increasing mass of
stars. For example for 10% mass loss parametrisation the integrated mass
fraction of 1H left at the end of core hydrogen burning decreases from 0.36 to
0.17. This is due to the near fully convective structure of such stars that
allow the mixing of hydrogen and therefore fuse more hydrogen during their
lifetimes. As a consequence, the mean mass fraction of 4He increases with
increasing mass. The abundance trends for the CNO elements vary significantly
for individual models. Taking model 6127 as an example since it provides the
most significant contribution amongst the 11 stars. We find that within model
6127, 14N is evenly distributed in the interior and the mean mass fraction
varies from 0.039 in the outer 10% of total mass to 0.060 when considering all
mass above the CO core. A similar trend is seen for 12C where the mean
abundances vary from 0.001 for the 10% case to 0.004 when considering
everything above the core. The overall quantity of 12C for all three mass-loss
parameterisation is the lowest of all CNO elements and is due to the
conversion of 12C to 14N and 16O during the core helium burning stage. The
amount of integrated 16O varies from 0.006 at 10% to 0.017 for the mass above
the CO core. Once again, this highlights that most of 16O is stored in the
interior of the stars. Upon inspecting various integrated mass fractions in
Table 1, a general trend concerning the increase or decrease in abundances as
a function of mass can be observed, with the exception of models such as 1923.
This is likely due to the accretion history of such models where periodic
bursts in accretion after a quiescent phase occur well into core hydrogen
burning phase. This injects fresh elements, for instance hydrogen in the star
which leads to the envelope of such stars exhibhiting higher abundance of
hydrogen. In summary, high mass stars such as model 6127 have the highest mass
fraction of their chemical content in form of 4He and also have a significant
mass fraction of 14N when compared to other CNO elements. 1H plays a much
larger role in the overall mass fraction content of low mass models such as
491 and these models consist of larger mass fraction of 16O in comparison to
12C and 14N.

Figure 3:  Mass ejected of various chemical species by each individual star in
the halo from Regan et al. (2020b). The first y-axis with lines and dots shows
the ejected masses in M⊙ for a given element for all the individual stars in
the simulation of Regan et al. (2020b). The dots connect the interpolated
values between the 11 computed models and each dot on lines correspond to the
11 models computed until the end of core Helium burning. The second y-axis
represents the number of stars in the histogram only. The bins in the
histogram cover a width of 100 M⊙ starting from 40 M⊙ and ending at 6200 M⊙.
The left panel shows the case when 10% of the total mass is ejected. The
middle and right panel, the cases when 40%, and respectively the whole mass
above the CO core is ejected.

To determine the mass of the different elements ejected by other initial mass
stars (not included among the 11 cases that have been computed here), formed
in the simulation of Regan et al. (2020b), we perform linear interpolation for
associating a CO core mass and an ejected mass of an isotope to the remaining
90 stars for which we did not compute a detailed evolutionary sequence. In
Fig. 3, we show how the ejected masses of different elements vary as a
function of the mass of the different stellar models.

Additionally, a histogram representing the mass distribution of all stars from
the cosmological simulation is over-plotted at the corresponding mass. A
general trend concerning all elements is visible in the three panels; the
total amount of any given element ejected (in M⊙) increases as a larger and
larger portion of star is considered for mass-loss. This is a quite obvious
fact but it also shows that all elements are well mixed in the interior and
envelope of all stars. As seen in all three panels of Figure 3, the integrated
ejected mass of 4He (orange line) increases as the mass of stars in the halo
increases. This is due to the fact that as the mass of a star increases,
larger portions of the convective core are able to sustain temperatures high
enough for 1H to fuse into 4He, thereby depleting the star of 1H and producing
an excess of 4He. The case of ejecting the entire mass above the CO core can
be examined in right panel of Figure 3, the total helium (orange line)
produced by a single 6200 M⊙ bin is an order of magnitude larger than any
single 600-700 M⊙ star, or is equal to all 12 stars in the 600-700 M⊙ mass
bin.
The trend for ejected mass of 1H (shown as blue line in all panels of Figure
3) is qualitatively similar to 4He but has a more complex profile for masses
ranging from 1000-6000 M⊙. The integrated ejecta mass of 1H increases for the
left panel of Figure 3 but in case of the middle and right panels, the value
peaks at around 3000 M⊙ and then decreases. This is due to a more efficient
core hydrogen burning shell that produces more 4He in stars with larger masses
above 3000 M⊙.
The integrated ejected mass of 14N (shown as red lines in Figure 3) also shows
an increasing trend similar to 4He with the most massive stars producing the
majority of 14N. However in the case of integrated ejecta for 16O (purple
line), the highest amount is produced by stars of 2000 M⊙ and decreases as
mass is further increased. This drop is more significant in 10% and 40% cases
and shows that most of 16O is locked in the deep interior of the star and is
less mixed when compared to other elements. The integrated ejecta for 12C
(green line) also appears to be locked in the deep interior, as seen when the
case of CO core (right panel of Figure 3) is considered. Here 12C integrated
ejecta mass follows a trend consistent with other chemical species but is
similar to 16O in 10% and 40% cases. These trends are due mainly to the fact
that nitrogen results from nuclear processes occurring in the H-burning shell,
while carbon and oxygen comes from the deeper He-burning regions and also from
the fact that more massive a star is, in general larger mixed zones appear.

Table 2: Table depicting the abundance ratios of various chemical species of
the entire halo. The first column indicates the assumption for the mass lost.
The columns 3 to 9 indicate the mean abundance (in mass fraction) of various
isotopes in the ejected material by all the stars in the halo simulation of
Regan et al. (2020b) with masses above 490 M⊙. The quantities in these columns
correspond to $X_{ip}$ defined by Eq. 4. The next five columns show the valuos
of log${}_{10}(N/O)$, log${}_{10}(C/O)$, log${}_{10}(O/H)+12$, log10(12C/13C)
and log10(22Ne/O) respectively, in the material composed from the sum of the
ejecta of all the stars. The ratios are in number fractions.

Fraction | $M_{\text{{ejecta}}}[M_{\odot}]$ | $X_{\rm H1,p}$ | $X_{\rm He4,p}$ | $X_{\rm C12,p}$ | $X_{\rm N14,p}$ | $X_{\rm O16,p}$ | $X_{\rm C13,p}$ | $X_{\rm Ne22,p}$ | log10(N/O) | log10(C/O) | log10(O/H)+12 | log10(12C/13C) | log10(22Ne/O)
---|---|---|---|---|---|---|---|---|---|---|---|---|---
10% of $M_{\text{tot}}$ | 8900.7 | 0.35 | 0.55 | 0.003 | 0.04 | 0.06 | 0.0004 | $5.7\times 10^{-5}$ | -0.17 | -1.30 | 11.23 | 0.875 | -3.02
40% of $M_{\text{tot}}$ | 32602.8 | 0.22 | 0.63 | 0.009 | 0.065 | 0.08 | 0.0005 | $7.7\times 10^{-5}$ | -0.09 | -0.95 | 11.56 | 1.25 | -3.02
Above CO core | 65866.5 | 0.20 | 0.65 | 0.012 | 0.07 | 0.07 | 0.0004 | $8.8\times 10^{-5}$ | 0.00 | -0.76 | 11.54 | 1.47 | -3.13

Figure 4: Abundance ratios (in number fractions) in the interstellar medium of
the halo as a function of O/H (expressed as log10(O/H)+12). The dilution
factor, $f$, is given by the colourbar. Dotted lines correspond to the
abundance in the ejecta of an individual stellar model. The mass is indicated
for each of them. The result for dilution factors equal to 1, 10, 100 and 1000
are shown by coloured circles. The solid lines show the abundances when the
ejecta of all the stars in the halo are mixed and mixed also with varying
amounts of pristine material: magenta line is for the case when the entire
mass above the CO core is assumed to be ejected by each star, brown and red
lines for the cases when 40%, respectively 10% of the total mass is ejected.
The coloured pentagons on the solid lines show the results for different
dilution factors. The grey trapezoid and the orange rectangle represent the
conservative and fiducial results for the abundances of GN-z11 by Cameron et
al. (2023). The yellow star with error bars correspond to the results of CEERS
1019 as shown in Marques-Chaves et al. (2023). Top Panel: The top panel shows
the N/O abundances as a function of the O/H abundances both in log base 10
scale. The red and brown stars in the top panel are the photoionisation
modelling results for GN-z11 by Senchyna et al. (2023). Bottom Panel: C/O
versus O/H ratios represented in the log base 10 scale.

Finally, to explore whether such a (progenitor) galaxy could produce the high
abundances observed in candidates such as GN-z11 and CEERS 1019, we sum up the
contributions of all the individual stars composing the population to one
isotopes and obtain the values in Table 2. The first striking feature is the
extremely high log10 N/O mass fraction ratio (-0.17 for 10% of total mass and
0.00 for the mass above CO core) and along with high O/H ratios (11.23 for 10%
of total mass and 11.54 for the mass above CO core). On the other hand, the
C/O ratio is quite low. This is due to the strongly depleted 12C in all models
(-1.30 for 10% of total mass and -0.76 for the mass above CO core). Driving
the depletion of 12C relative to 14N and 16O is the fusion of 12C to produce
the other two elements during the core helium burning stage and is similar to
the trend observed in massive stars, as seen in the works of Murphy et al.
(2021a).

###  3.3 Impact of dilution factor

The abundance ratios obtained from individual models and the entire galaxy
represent the amount that will be ejected by the respective object(s) and take
no account of pre-existing enrichment. However, in order to account for pre-
existing enrichment of the ISM, a dilution factor ($f$ =
$M_{\mathrm{ISM}}/M_{\mathrm{EJ}}$ ) is included in further calculations. Due
to the complexity in determining the precise value of the dilution factor, we
assume values of 1, 10, 100, 500 and 1000. The results are then compared to
the observational data for GN-z11 and CEERS 2019 and are shown in Figure 4. In
Figure 4 we show a selection of individual models as well as the results from
when all of the stars are included. The model with a final mass of 6127 M⊙
reproduces the N/O, C/O and O/H values very well over a wide range of dilution
factor ($f=10\rightarrow 100$). The values for the composition of the ejecta
coming from all the stars using three different cutoff values can also
reproduce the N/O number fractions of -0.13, -0.04 and 0.05 for 10%, 40% and
above the CO core respectively - entirely consistent with observations.
However, the C/O number fraction (bottom panel) of -0.64 is the closest of the
observed ratios in the two considered high redshift galaxies when the entire
mass above the CO core is assumed to be ejected. The O/H number fractions of
7.70, 7.80 and 8.75 for 10%, 40% of total mass and all mass above the CO core
for the entire galaxy come close to the observations if a dilution factor of
100 is considered. A dilution factor of 100 is exactly what we expect for a
10% ejection fraction combined with a star formation rate of 0.1. This is
compatible with a situation in where the masses of stars represents only 10%
of the total mass (stars and gas) of the clusters, and where 10% of the
stellar mass is ejected.

###  3.4 Massive PopIII stars as efficient Nitrogen enrichers and the
progenitors of high-z N-loud Quasars

The evolution of accreting massive Pop III stars demonstrates profound
nitrogen enrichment of the outer envelope, as depicted in Figure 2. Such
enrichment is principally driven during the core helium burning phase, where
the presence of 12C advances the production of 14N. However, these stars tend
to nearly exhaust their ${}^{12}{\rm C}$ reservoirs in this enrichment
process. Delving into the integrated abundances across an entire (sub-)galaxy
population, there’s an evident correlation: as stellar mass increases, the
remaining fraction of 1H decreases while 4He exhibits the opposite trend.
Specifically, in the first galaxy simulations of R20b, the stellar mass range
leads to remarkably high N/O and O/H ratios, with a diminished C/O ratio,
attributed to the pronounced carbon depletion across models. Introducing the
concept of dilution to assess the impact on the interstellar medium, the 6127
M⊙ model aligns very well with observed ratios such as N/O, C/O, and O/H over
a dilution factor spectrum of 10-100. Moreover, considering realistic mass
cutoffs and a dilution factor of 100, the integrated values from all of the
massive stars agrees very closely with observational benchmarks as shown in
Figure 4. What this tells us is that a sub-population of very massive PopIII
stars can reproduce the elemental abundances as seen by JWST and in particular
explains very well the unusually high nitrogen abundances.

##  4 Discussion

###  4.1 Mass ranges

The chemical signatures exhibited by the massive PopIII stars are strongly
dependent on their mass during the various mass-loss events and at the time of
collapse. Figure 4 shows both the impact from the individual stars from the
simulations of Regan et al. (2020b) and those from all of the stars. An
individual star with mass less than 1923 M⊙ results in a log10(N/O) ratio of
-0.37, which is on the lower end of observed values. The log10(C/O) ratio on
the other hand misses the observed values entirely. The next mass in the
simulation (not shown in Figure 4) that produces a log10(N/O) ratio of 0.1 and
log10(C/O) ratio of -0.7 is 2479 M⊙. There also exists an upper mass limit for
haloA beyond 8904 M⊙ where the log10(N/O) ratio exceeds 0.85 and log10(C/O)
reduces below -0.6, thereby missing the observational window for GN-z11 and
CEERS 1019. Such a conclusion is strictly time dependent as continual
pollution of ISM by the next generations of stars would change the log10(N/O)
value. Interestingly supermassive PopIII stars with masses above 100,000 M⊙
cannot produce the observed values as they experience a premature collapse
during core hydrogen burning (Haemmerlé et al. 2018). This evolutionary stage,
prior to helium burning, is devoid of any substantial production of CNO
elements which only occur during the later core helium burning stage. This
result demonstrated that there exists both an upper and lower mass limit where
massive PopIII are capable of producing the observed signatures. We note that
this does imply that such massive stars do not exist - simply that stars in
the mass range of approximately $10^{3}-10^{4}$ are required to re-produce the
abundances signatures seen by JWST.

###  4.2 Predicted abundances

Here we attempt to predict abundances of additional elements that have not yet
been observed so as to make the model falsifiable. The goal here is to provide
some additional values to better constrain future observations of objects such
as GN-z11 and CEERS 1019. While our study primarily focuses on a specific
stellar mass range, it represents only a fraction of the total stellar mass.
However, the significance of our work lies in demonstrating the capability of
these supermassive stars (SMSs) to both produce substantial amounts of
Nitrogen and seed massive black holes. Additionally, various works have shown
that Late (z¡ 7) Pop III star formation might also have occurred in pristine
regions due to in-homogeneous metal enrichment of the first galaxies
(Tornatore et al. 2007; Salvaterra et al. 2011; Vanzella et al. 2020). With
this in mind, we find the integrated ejected mass in our simulated galaxy to
be primarily enriched in helium with 0.55 mass fraction for 10% of total mass
and 0.65 for all mass ejected above CO core. This mass fraction allows us to
predict the undiluted log10(He/H) for 10% and above CO core ratios of all
stars for entire halo to be -0.40 and -0.09. Once the helium and hydrogen rich
ejecta is exposed to the ISM, we can further predict the diluted log10(He/H)
ratios. For an equal contribution from the total stellar ejecta of all stars
and the ISM, f = 1, we obtain log10(He/H) = -0.62. For stronger dilutions of f
= 10, 100 and 1000, the ratio decreases to -0.99, -1.07 and -1.08
respectively. Given that observing He/H ratios is an important observable
signature for massive stars (Schaerer & Pelló 2003), these predicted ratios
are useful for future JWST observations.

The log10(12C/13C) is found to be 0.87 for the 10% case and 1.47 for the CO
core case. To provide a comparison, the solar composition material shows a
ratio 12C/13C around 60 (see Table 2 in Ekström et al. 2012, and references
therein). Once these isotopes reach an equilibrium state (i.e. when the
process has reached a stationary regime and the abundances of the CNO elements
no longer vary) in material that has been processed by CNO burning reactions,
the ratio decreases to value around 4. The 12C/13C ratios from the integrated
population when considering 10% and all mass above CO cases at the end of core
helium burning are found to be 8 and 25 respectively, which clearly show the
sign of CNO burning. It is also important to note that the absolute values of
both 12C and 13C are boosted by the mixing between the helium and hydrogen
burning regions. Fast rotating massive stars would also produce 12C/13C ratios
around similar values as the very massive stars considered here (Chiappini et
al. 2008).

The right hand panel of Figure 2 shows that Neon abundance of such stars is
strongly dominated by the 22Ne isotope, which is formed via the fusion of 14N.
However, such stars also have a high 16O abundance which reduces the overall
log10(22Ne/O) ratio to -3.02 for the 10% case and -3.13 for the CO core case.
Comparing these values to the log10(Ne/O) ratio of -0.63 obtained by Marques-
Chaves et al. (2023), we find that PopIII stars in a halo such as ours cannot
produce the observed Ne/O ratios, at least for galaxies such as CEERS 1019. To
further explore the possibility of such massive stars producing the required
Ne/O ratios, we invoke a scenario where the very and extremely massive stars
form in an already enriched halo by previous generations of stars. We compute
one model with a final mass of 3200 M⊙ at Z = 10-6 until the end of core
helium burning and calculate the mean abundances in mass fractions for various
elements in its ejecta, assuming all the mass above the CO core is lost at the
end of its evolution. Upon ejection of the chemical species by this model, the
ejecta is mixed with the non zero metallicity ISM with a dilution factor
ranging from 1 to 1000. The results for a dilution factor 100 show a number
fraction ratio of log10(Ne/O) = -0.58. Additional number fractions of CNO are;
log10(N/O) = -0.52, log10(C/O) = -1.29 and log10(O/H)+12 = 8.03. The N/O and
C/O ratios for this single model is lower than the observed ratios for GN-z11
and CEERS 1019 but such ratios will likely be different if a population of
such stars with different masses are considered in a given halo (as we did for
the Pop III case). At least, the numerical example shown here indicates that
there is good hope that starting from a non-zero metallicity would still allow
strong enrichment in CNO elements compatible with high redshift star forming
zones, while also compatible with the high Ne/O ratio.

###  4.3 Impact of a population of 20 M⊙ stars

Due to the constraints in resolution of the hydrodynamic simulations of Regan
et al. (2020b), stars with masses less than 40 M⊙ are likely to be unresolved
but should exist in real proto-galaxies of this mass. We can nonetheless
estimate their impact on the N/O, C/O and O/H abundances by assuming 100
PopIII stars with 20 M⊙ are born in addition within the halo. This is likely
to be a very conservative estimate. Although the outcome of core collapse of
20 M⊙ is realistically unknown, we assume these 20 M⊙ models without rotation
to undergo classical core-collapse which we expect will eject a huge portion
of the star beyond the CO core, see works by Murphy et al. (2021b).

The ejecta from an individual 20 M⊙ will contain 9.6 M⊙ of 1H, 6.2 M⊙ of 4He,
1.4 M⊙ of 16O, 0.6 M⊙ of 12C and merely 1.2$\times 10^{-7}$ M⊙ of 13C. Using
these values, we can estimate the impact of 100 of 20 M⊙ stars on the mass
fraction values of log (N/O), log (C/O) and log (O/H) found in table 2. For
the case of 10% of the total mass ejected from all stars without accounting
for dilution ($\mathbf{i}$ = 0), we find a value of log (N/O) = -0.27,
log(C/O) = -0.87 and log(O/H) + 12 = 11.21. These values when compared to row
1, column 10, 11 and 12 of Table 2 show a decrease in log (N/O) mass fraction
values (from -0.17 to -0.27), an increase in log(C/O) values (from -1.30 to
-0.87) and a near identical log(O/H) + 12 values (from 11.23 to 11.21).
However, the impact of adding these 100 20 PopIII stars would be smaller for
the cases 40% and ‘above the CO core’. Conclusively, these values are not
significantly affected by 100 20 M⊙ stars however if the halo were to contain
an excess of a 104 stars, the impact will be enhanced. However, addition of 20
M⊙ PopIII stars would improve our agreement for the log (C/O) and log (Ne/O)
ratio in the bottom panel of Figure 4.

###  4.4 Comparison with previous studies

The presence of strong NIII] $\lambda$ 1750 and CIII] $\lambda\lambda$1909
lines observed in GN-z11 by Bunker et al. (2023) present unusually high N/O
ratios at a redshift of z = 10.6. Using the emission line fluxes from Bunker
et al. (2023), Cameron et al. (2023) derived the abundance ratios
quantitatively and found log (N/O) ¿ -0.25, log (C/O) ¿ -0.78 and log (O/H)
$\approx$ 7.82 for their fiducial model and log (N/O) ¿ -0.49, log (C/O) ¿
-0.95 and log (O/H) $\leq$ 8.60 for their conservative models as denoted by
orange and grey box in Figure 4.

Using the runaway collision scenario proposed by Gieles et al. (2018),
Charbonnel et al. (2023) were the first to explore the N/O, C/O and Ne/O of
GN-z11. Using a SMS model with a characteristic mass of 104 M⊙ and
metallicities ([Fe/H]) ranging from -1.76 to -0.78. The mechanism of transport
of chemical species in their work is the presence of a fully convective SMS
that grows via collisions with smaller objects throughout its lifetime.
Additionally, they predict the Ne/O in GN-z11 to be higher than other high-z
objects when compared to normal galaxies with similar metallicity. In contrast
we invoke a more conservative massive PopIII formation scenario where the
transition to the later stages of evolution, specifically post H-burning
allows the structure to become convective and transport the elements to the
surface more efficiently. Our single star models such as 6127 produce a higher
N/O and C/O ratio whereas the O/H ratios match for a dilution factor between
10-100. Our integrated abundances for our total population of massive stars
provide a closer match to the observed values of N/O and C/O, whereas the O/H
matches if the dilution factor is around 100. We also find that the 22Ne/16O
ratio for the population to be around -3.0 which is much lower than the values
of GN-z11 predicted in their work.

Nagele & Umeda (2023) compute metal-enriched SMS models with rotation, stellar
winds and SMS explosions to explain the high nitrogen pollution in GN-z11. The
four models in their study were generated at ZAMS with initial masses of 103,
104, 5$\times$104 and 105. Each model was evolved either until the late carbon
burning phase or until the GR instability was reached. The total 12C, 14N and
16O values were 9.91, 17 and 27 M⊙ respectively for the 103 M⊙ model. In
comparison, 12C, 14N and 16O values for our 932 M⊙ model are 0.741, 26.76 and
7.657 M⊙ if all the mass above CO core is assumed to be ejected. The
difference in the ejected masses is likely due to their inclusion of the
effects of mass-loss, rotation and high metallicity in their models; our
models are instead computed without mass-loss and rotation and have zero
metallicity. Furthermore, Nagele & Umeda (2023) favour their high mass models
when explaining the abundances of GN-z11 over a range of dilution factors
whereas our models at 105 M⊙ produce a log10(N/O) = 2.2, log10(C/O) = 0.45 and
log10(O/H)+12 varying from -2.3 to 0.8 over a range of dilution factors from 1
to 1000. This difference is possibly due to the difference in metallicity and
structure of such objects.
Finally, Kobayashi & Ferrara (2023) advocate for a dual starburst model to
explain the high Nitrogen abundances in GN-z11. By assuming that star
formation in GN-z11 begins at z $\sim$ 16.7 and continued for 100 Myr before a
quisient phase also lasting approximately 100 Myr Kobayashi & Ferrara (2023)
show that WR stars at [Fe/H] = 0, -1, -2 and -3 in the second star burst phase
are potential sources of high (C,N)/O ratios. When considering their fiducial
model following the dual starburst formation scenario and fixing the star
formation age to match the log (O/H)+12 ratio , the log (N/O) ratio is found
to be 0.246. They also conclude that very massive stars (VMS ¿ 100M⊙) with Z =
0 and 0.0002 as sources do not lead to a sufficient increase in N/O and pair
instability supernovae (PISNe) lead to decrease in N/O ratio. They also show a
single star burst model which requires stars with masses in excess of 1000
$\rm{M_{\odot}}\leavevmode\nobreak\ $to explain the abundances - consistent
with what we show here. Kobayashi & Ferrara (2023) also concluded that the
impact of adding normal massive stars (typically of 20 M⊙, as we did here)
does not affect the overall N/O ratio of GN-z11.
Another high-z JWST galaxy discovered by the CEERS survey team - CEERS 1019 -
displays similar abundances to GN-z11. Investigating CEERS 1019 Marques-Chaves
et al. (2023) found strong emission of NIII and NIV lines and obtained log
(N/O) = -0.13 $\pm$ 0.11, log (C/O) = -0.75 $\pm$ 0.11, log (O/H)+12 = 7.78
$\pm$ 0.18 and log (Ne/O) = -0.63 $\pm$ 0.07. Furthermore, Marques-Chaves et
al. (2023) invoke (super-massive) stars with masses in excess of 1000
$\rm{M_{\odot}}\leavevmode\nobreak\ $to explain the unusual abundances
(consistent also with similar anomalies observed in present day globular
clusters (e.g. Denissenkov & Hartwick 2014; Gieles et al. 2018)).

##  5 Conclusion

The research presented here has delved into the intricacies of massive PopIII
stars and their pivotal roles in influencing the chemical constitution of
specific galaxy environments. Through a meticulous analysis of an expansive
dataset and detailed simulations, the study elucidates how the mass,
evolution, and environmental interactions of massive PopIII stars are
instrumental in deciphering the observed chemical signatures from early epochs
of the Universe. Herein, we encapsulate the salient findings and their
ramifications for forthcoming research.

  * •

Mass ranges’ importance: The mass of the PopIII stars was found to be a
determining factor in their resultant chemical signature. Specifically, stars
less than $\sim$$1900\,\mathrm{M}_{\odot}$ produce a $\log_{10}$ (N/O) ratio
of -0.37, which is on the lower end of observed values. Stars beyond
$8900\,M_{\odot}$ exceed the observed ratios for GN-z11 and CEERS 1019 and
hence may be rare, at least in these galaxies. Only massive PopIII stars
within the range of $1900\,\mathrm{\rm M}_{\odot}$ to
$8900\,\mathrm{M}_{\odot}$ appear to align with the observed chemical
signatures.

  * •

A population of very massive PopIII stars: A sub-population of very massive
PopIII stars produces an abundance pattern of nitrogen which is consistent
with current observations by JWST of GN-z11 and CEERS 1019. The high nitrogen
abundances are driven solely by the most massive stars among that population.
Lower mass stars will dilute that abundance pattern as they do not produce
sufficient Nitrogen to be consistent with observations. Hence, it appears that
some early galaxies must contain a minority population of very massive PopIII
stars (i.e. stars with masses in excess of 1000 $\rm{M_{\odot}}$) in order to
be consistent with observations.

  * •

Predicted halo abundance: The mass of individual massive PopIII stars
significantly influences the chemical outputs of entire halos. For instance,
the integrated ejected mass due to all of the massive stars in our model
resulted in enrichment in 4He with a mass fraction of 0.55 for 10% of total
mass and 0.65 for all mass ejected above the CO core. As a result, the
integrated ejected mass of 1H varied from 0.35 to 0.20. Hence, our model
predicts H helium rich environments in these embryonic galaxies. Additionally,
low mass (M${}_{*}\lesssim 2000$ $\rm{M_{\odot}}$) PopIII stars are found to
be the strong polluters in 16O whereas the ejecta of stars with masses above
2000 M⊙ are enriched in 14N. Overall, after 4He and 1H, 14N dominates the
ejecta of high mass PopIII stars.

  * •

Matching abundances with GN-z11 and CEERS 1019: If all massive PopIII stars
eject a fraction of their total mass, we can closely reproduce the log (N/O),
log (C/O) and log (O/H)+12 ratios over a range of dilution factor. Our massive
PopIII models predict that N-loud quasars should be a key signature of a
previous episode of massive PopIII star formation with the seed for the
quasars possible originating from one of the PopIII stars responsible for the
initial nitrogen enrichment.

  * •

The origin of the high Ne/O ratio in CEERS 1019: As mentioned above, our model
produces very low Ne/O ratio (-3.02) compared to CEERS 1019 (-0.63). In the
present models, neon is under the form of the 22Ne isotopes. It comes from the
transformation of the 14N at the beginning of the core He-burning phase. The
low value that we obtain indicates that this process alone is not efficient
enough to produce Ne/O ratios compatible with the one observed in CEERS 1019.
Additionally, we find that stars with mass around 3200 M⊙ at 10-6 Z can
reproduce accurately the log10(Ne/O) ratio of -0.58, but the N/O, C/O values
are below the observed value. This concludes that it is difficult to reproduce
all the observed ratios with just one generation of PopIII models; a more
complex analysis of star formation history is needed.

  * •

Abundance predictions: It is important to emphasise that the current model
predicts the abundances resulting from a first generation of extremely massive
stars. As previously mentioned, these predictions are specifically applicable
to a unique stage in the evolution of such systems. In this context, we also
outline potential abundance signatures characteristic of these systems. Carbon
ratios: The $\log_{10}$ (12C/13C) ratio for the 10% case and CO core case was
found to be 0.87 and 1.47 respectively, showing a strong signature of CNO
cycle. The Ne/O ratios predicted in this study were found to be around -3.0
for the halo. These additional abundance ratios provide an estimated value for
future observations of JWST. We encourage observers to seek out for these
ratios in future observations.

  * •

Impact of 20 $M_{\odot}$ stars: Incorporating 100 stars of 20 $M_{\odot}$ mass
within the stellar population provides pivotal insights into the role of these
less massive stars. Specifically, the contribution of these stars leads to
$\log$10 (N/O) and $\log$10 (O/H)+12 values of -0.27 and 11.21 respectively,
indicating their negligible effect on these ratios (i.e. PopIII stars of this
mass cannot account for anomalously high N abundances). However, the addition
of these stars into the halo increased the $\log$10 (C/O) from -1.30 to -0.87
and would likely increase the Ne/O ratio, thereby providing a better fit to
the observed values of GN-z11 and CEERS 1019.

As future studies continue to explore the possible scenarios for high red-
shift candidates such as GN-z11 and CEERS 1019, our models robustly predict
significant N enrichment from massive PopIII stars. If such stars exist, and
they eject mass, it would be entirely unsurprising to find strong N-enrichment
in the very early Universe. It is important to recognise that nitrogen
enrichment can also result from fast-rotating massive stars with masses
ranging between 8 and approximately 100 M⊙ (Meynet & Maeder 2006; Chiappini et
al. 2003, 2006; Cescutti et al. 2013). Fast rotating models have been
suggested to account for the value of about -1.5 (log(N/O)) observed in iron-
poor halo stars. This value is more than an order of magnitude lower than what
is displayed by high-redshift galaxies such as GN-z11 and CEERS 1019. However,
it is worth noting that the chemical enrichment model for the halo of our
Galaxy significantly differs from the one discussed here. In future research,
it would be insightful to explore the influence of fast-rotating massive, very
massive, and even supermassive stars within this context

The influx of observations by JWST via the JADES (Maiolino et al. 2023a, b),
CEERS (Larson et al. 2023) and UNCOVER (Goulding et al. 2023) surveys have
revealed the existence of a population of massive black holes with masses
ranging from as low as $4\times 10^{5}$ $\rm{M_{\odot}}\leavevmode\nobreak\
$up to $\lesssim 10^{8}$ $\rm{M_{\odot}}\leavevmode\nobreak\ $at redshifts as
high as z = 10.6. The masses of these black holes as well as their sub-
Eddington accretion rates, in most cases, appears to strengthen the case for a
heavy seed formation pathway with the seed being a massive PopIII or SMS the
most likely candidate (e.g. Natarajan et al. 2023). Our investigation here
adds extra weight to the heavy seed argument by showing that massive PopIII
stars enrich the environment surrounding the (mini)-quasar with metal
abundances consistent with observations. In light of the above, it is
paramount for future investigations to further probe into the multifaceted
nature of massive PopIII stars, either to affirm, challenge, or elaborate on
the narratives and interpretations offered in this study.

## Acknowledgements

D.N., S.E. and G.M. have received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 833925, project STAREX). JR acknowledges support
from the Royal Society and Science Foundation Ireland under grant number
URF\R1\191132. JR also acknowledges support from the Irish Research Council
Laureate programme under grant number IRCLA/2022/1165. T.E.W. acknowledges
support from the National Research Council of Canada’s Plaskett Fellowship.
E.F. and G.M. have received funding from the SNF project 200020-212124.

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##  Appendix A Impact of evolutionary stages on the integrated abundances

To explore the impact of late stages of evolution on the abundances, we
calculated the integrated abundances of Hydrogen, Carbon, Nitrogen and Oxygen
for the 3053 M⊙ model as shown in table 3. We find that the integrated
abundances do no vary significantly beyond the core Helium burning phase. This
is due to the very short timescale of the subsequent phases which barely
alters the total composition of the model.Therefore the 11 models computed
until the end of core Helium burning provide sufficienlty accurate results.
The core is defined as the mass coordinate in star below which $10^{-3}$ mass
fraction of the previous chemical species is left. For instance, CO core has
$10^{-3}$ mass fraction of helium (Yc) is left in the core.

Table 3: Integrated abundance of various elements inside a 3053M⊙ model at
zero metallicity computed until the end of core Si burning. Column 1 indicates
various evolutionary stages. The integrated mass fraction of a given element
is presented in columns 2, 3, 4 and 5.

Evolutionary stage | $\begin{aligned} \rm{\bar{X}_{i}}=\int_{M_{\rm cut}}^{M_{\rm tot}}X_{i}(M_{r})dM_{r}/M_{\rm EJ}\end{aligned}$
---|---
Z = 0.0 |  1H |  12C |  14N |  16O
End He burning | 0.1570 | 0.00160 | 0.0380 | 0.0130
End C burning | 0.1570 | 0.0008 | 0.0330 | 0.0120
End Si burning | 0.1570 | 0.0008 | 0.0330 | 0.0120