arXiv subjects

Volker Bromm

Publications and source records attributed to Volker Bromm.

At least 73 records · Page 4Linked to original sources

arXiv2024

Rapidly rotating Population III stellar models as a source of primary nitrogen

The first stars might have been fast rotators. This would have important consequences for their radiative, mechanical and chemical feedback. We discuss the impact of fast initial rotation on the evolution of massive Population III models and on their nitrogen and oxygen stellar yields. We explore the evolution of Population III stars with initial masses in the range of 9Msol < Mini < 120Msol starting with an initial rotation on the Zero Age Main Sequence equal to 70% of the critical one. We find that with the physics of rotation considered here, our rapidly-rotating Population III stellar models do not follow a homogeneous evolution. They lose very little mass in case mechanical winds are switched on when the surface rotation becomes equal or larger than the critical velocity. Impact on the ionising flux appears modest when compared to moderately-rotating models. Fast rotation favours, in models with initial masses above ~20Msol, the appearance of a very extended intermediate convective zone around the H-burning shell during the core He-burning phase. This shell has important consequences on the sizes of the He- and CO-cores and thus impacts the final fate of stars. Moreover, it has a strong impact on nucleosynthesis boosting the production of primary 14N. Fast initial rotation impacts significantly the chemical feedback of Population III stars. Observations of extremely metal-poor stars and/or starbursting regions are essential to provide constraints on the properties of the first stars.

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arXiv2024

Distinguishing the impact and signature of black holes from different origins in early cosmic history

We use semi-analytical models to study the effects of primordial black hole (PBH) accretion on the cosmic radiation background during the epoch of reionization ($z\gtrsim 6$). We consider PBHs floating in the intergalactic medium (IGM), and located inside haloes, where star formation can occur. For stars with a mass $\gtrsim 25 \rm\ M_{\odot}$, formed in suitable host haloes, we assume they quickly burn out and form stellar remnant black holes (SRBHs). Since SRBHs also accrete material from their surroundings, we consider them to have similar radiation feedback as PBHs in the halo environment. To estimate the background radiation level more accurately, we take into account the impact of PBHs on structure formation, allowing an improved modeling of the halo mass function. We consider the radiation feedback from a broad suite of black holes: PBHs, SRBHs, high-mass X-ray binaries (HMXBs), and supermassive black holes (SMBHs). We find that at $z\gtrsim 30$, the radiation background energy density is generated by PBHs accreting in the IGM, whereas at lower redshifts, the accretion feedback power from haloes dominates. We also analyze the total power density by modeling the accretion spectral energy distribution (SED), and break it down into select wavebands. In the UV band, we find that for $f_{\rm PBH} \lesssim 10^{-3}$, the H-ionizing and Lyman-$α$ fluxes from PBH accretion feedback do not violate existing constraints on the timing of reionization, and on the effective Wouthuysen-Field coupling of the 21-cm spin temperature of neutral hydrogen to the kinetic temperature of the IGM. However, in the X-ray band, with the same abundance, PBHs contribute significantly and could account for the unresolved part of the cosmic X-ray background.

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arXiv2023

The first fireworks: A roadmap to Population III stars during the Epoch of Reionization through Pair Instability Supernovae

With the launch of JWST and other scheduled missions aimed at probing the distant Universe, we are entering a new promising era for high-$z$ astronomy. One of our main goals is the detection of the first population of stars (Population III or Pop III stars), and models suggest that Pop III star formation is allowed well into the Epoch of Reionization (EoR), rendering this an attainable achievement. In this paper, we focus on our chance of detecting massive Pop IIIs at the moment of their death as Pair-Instability Supernovae (PISNe). We estimate the probability of discovering PISNe during the EoR in galaxies with different stellar masses ($7.5 \leq \mathrm{Log}(M_\star/\mathrm{M_\odot}) \leq 10.5$) from six dustyGadget simulations of $50h^{-1}$ cMpc per side. We further assess the expected number of PISNe in surveys with JWST/NIRCam and Roman/WFI. On average, less than one PISN is expected in all examined JWST fields at $z \simeq 8$ with $Δz = 1$, and O(1) PISN may be found in a $\sim 1$ deg$^2$ Roman field in the best-case scenario, although different assumptions on the Pop III IMF and/or Pop III star-formation efficiency can decrease this number substantially. Including the contribution from unresolved low-mass halos holds the potential for increased discoveries. JWST/NIRCam and Roman/WFI allow the detection of massive-progenitor ($\sim 250 ~ \mathrm{M_\odot}$) PISNe throughout all the optimal F200W-F356W, F277W-F444W, and F158-F213 colors. PISNe are also predominantly located at the outskirts of their hosting haloes, facilitating the disentangling of underlying stellar emission thanks to the spatial-resolution capabilities of the instruments.

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arXiv2023

The Complete CEERS Early Universe Galaxy Sample: A Surprisingly Slow Evolution of the Space Density of Bright Galaxies at z ~ 8.5-14.5

We present a sample of 88 candidate z~8.5-14.5 galaxies selected from the completed NIRCam imaging from the Cosmic Evolution Early Release Science (CEERS) survey. These data cover ~90 arcmin^2 (10 NIRCam pointings) in six broad-band and one medium-band imaging filter. With this sample we confirm at higher confidence early JWST conclusions that bright galaxies in this epoch are more abundant than predicted by most theoretical models. We construct the rest-frame ultraviolet luminosity functions at z~9, 11 and 14, and show that the space density of bright (M_UV=-20) galaxies changes only modestly from z~14 to z~9, compared to a steeper increase from z~8 to z~4. While our candidates are photometrically selected, spectroscopic followup has now confirmed 13 of them, with only one significant interloper, implying that the fidelity of this sample is high. Successfully explaining the evidence for a flatter evolution in the number densities of UV-bright z>10 galaxies may thus require changes to the dominant physical processes regulating star formation. While our results indicate that significant variations of dust attenuation with redshift are unlikely to be the dominant factor at these high redshifts, they are consistent with predictions from models which naturally have enhanced star-formation efficiency and/or stochasticity. An evolving stellar initial mass function could also bring model predictions into better agreement with our results. Deep spectroscopic followup of a large sample of early galaxies can distinguish between these competing scenarios.

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arXiv2023

CEERS Key Paper I: An Early Look into the First 500 Myr of Galaxy Formation with JWST

We present an investigation into the first 500 Myr of galaxy evolution from the Cosmic Evolution Early Release Science (CEERS) survey. CEERS, one of 13 JWST ERS programs, targets galaxy formation from z~0.5 to z>10 using several imaging and spectroscopic modes. We make use of the first epoch of CEERS NIRCam imaging, spanning 35.5 sq. arcmin, to search for candidate galaxies at z>9. Following a detailed data reduction process implementing several custom steps to produce high-quality reduced images, we perform multi-band photometry across seven NIRCam broad and medium-band (and six Hubble broadband) filters focusing on robust colors and accurate total fluxes. We measure photometric redshifts and devise a robust set of selection criteria to identify a sample of 26 galaxy candidates at z~9-16. These objects are compact with a median half-light radius of ~0.5 kpc. We present an early estimate of the z~11 rest-frame ultraviolet (UV) luminosity function, finding that the number density of galaxies at M_UV ~ -20 appears to evolve very little from z~9 to z~11. We also find that the abundance (surface density [arcmin^-2]) of our candidates exceeds nearly all theoretical predictions. We explore potential implications, including that at z>10 star formation may be dominated by top-heavy initial mass functions, which would result in an increased ratio of UV light per unit halo mass, though a complete lack of dust attenuation and/or changing star-formation physics may also play a role. While spectroscopic confirmation of these sources is urgently required, our results suggest that the deeper views to come with JWST should yield prolific samples of ultra-high-redshift galaxies with which to further explore these conclusions.

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arXiv2023

Hypernova signatures of the first stars in dwarf galaxies in the Local Group

Observing the first generation of stars, Population III (Pop III), is still a challenge even with the James Webb Space Telescope (JWST) due to their faintness. Instead, searching for fossil records of Pop III stars in nearby dwarf galaxies provides an alternative method for studying their physical properties. It is intriguing that a star recently discovered in the Sculptor dwarf galaxy, named AS0039, is considered to show the unique signature of a Pop~III star. The detailed abundance patterns of AS0039 are well-matched with those predicted by nucleosynthesis models for Pop~III exploding as an energetic hypernova (HN), confirming its potential to provide insight into the properties of the first stars. This study aims to explore the environmental conditions required for the formation of such a unique star using cosmological hydrodynamic zoom-in simulations on dwarf galaxies with a mass of M_vir~10^8 solar mass at z=0 while varying the fraction of Pop~III stars that undergo HNe. Our simulations identify rapid gas inflow (~0.08 solar mass/yr) as a possible factor in facilitating the formation of stars similar to AS0039. Alternatively, the delayed formation of subsequent Pop~II stars in the gas-enriched environment may lead to low-metallicity stars like AS0039. Additionally, using the A-SLOTH code, we investigate the probability of finding remnants of Pop II stars with HN signatures in nearby dwarf satellite galaxies. We suggest that the most likely dwarf galaxies to contain HN signatures are massive satellites with a probability of 40% in the range of M_peak~10^{10}-10^{11} solar mass and M_star~10^7-10^8 solar mass, considering observational limitations.

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arXiv2023

A CEERS Discovery of an Accreting Supermassive Black Hole 570 Myr after the Big Bang: Identifying a Progenitor of Massive z > 6 Quasars

We report the discovery of an accreting supermassive black hole at z=8.679, in CEERS_1019, a galaxy previously discovered via a Ly$α$-break by Hubble and with a Ly$α$ redshift from Keck. As part of the Cosmic Evolution Early Release Science (CEERS) survey, we observed this source with JWST/NIRSpec spectroscopy, MIRI and NIRCam imaging, and NIRCam/WFSS slitless spectroscopy. The NIRSpec spectra uncover many emission lines, and the strong [O III] emission line confirms the ground-based Ly$α$ redshift. We detect a significant broad (FWHM~1200 km/s) component in the H$β$ emission line, which we conclude originates in the broad-line region of an active galactic nucleus (AGN), as the lack of a broad component in the forbidden lines rejects an outflow origin. This hypothesis is supported by the presence of high-ionization lines, as well as a spatial point-source component embedded within a smoother surface brightness profile. The mass of the black hole is log($M_{BH}/M_{\odot})=6.95{\pm}0.37$, and we estimate that it is accreting at 1.2 ($\pm$0.5) x the Eddington limit. The 1-8 $μ$m photometric spectral energy distribution (SED) from NIRCam and MIRI shows a continuum dominated by starlight and constrains the host galaxy to be massive (log M/M$_{\odot}$~9.5) and highly star-forming (SFR~30 M$_{\odot}$ yr$^{-1}$). Ratios of the strong emission lines show that the gas in this galaxy is metal-poor (Z/Z$_{\odot}$~0.1), dense (n$_{e}$~10$^{3}$ cm$^{-3}$), and highly ionized (log U~-2.1), consistent with the general galaxy population observed with JWST at high redshifts. We use this presently highest-redshift AGN discovery to place constraints on black hole seeding models and find that a combination of either super-Eddington accretion from stellar seeds or Eddington accretion from massive black hole seeds is required to form this object by the observed epoch.

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arXiv2023

Observability of Low-Luminosity AGN in the Early Universe with JWST

Active galactic nuclei (AGN) in the early Universe are thought to be prominent sources of energy and ionizing photons that affected the growth of their host galaxy and their environment. However, it is still unclear how the supermassive black holes (SMBHs) that fuel these AGN grew to the observed high masses already at high redshifts. Observations of high-redshift SMBH progenitors or lower-luminosity AGN will thus help characterize the evolution of SMBHs and their impact on the surroundings. With the launch of the JWST, fainter objects at high redshifts can now be detected, including lower-luminosity AGN. We assess the observability of such low luminosity AGN, using the cosmological simulation code GIZMO to provide a realistic environment for black hole growth in the early Universe. Soon after the first stars are born in the simulation run, we insert stellar-remnant black hole seeds of various initial masses, between $300$ and $10^4 {\rm \ M}_{\odot}$, at the center of a dark matter halo and follow their growth until $z\sim6$. Such stellar black hole seeds placed in a typical high-$z$ environment do not significantly accrete and grow to reach masses that can be observed with the JWST under conditions of standard Bondi-Hoyle accretion, as energy input from stellar feedback and chaotic dynamics prevent efficient gas accretion onto the black holes. To be observed with the JWST, rarer but still physically feasible growth regimes, involving Eddington or super-Eddington accretion, would be required. Alternatively, AGN observability may be boosted under even rarer conditions of extreme gravitational lensing.

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arXiv2023

Probing the Nature of the First Galaxies with JWST and ALMA

By implementing a model of primordial dust emission, we predict dust-continuum fluxes for massive galaxy sources similar to those recently detected by JWST at $z \gtrsim 7$. Current upper flux limits, obtained with ALMA for some of these sources, can constrain gas metallicity and dust fraction of the first galaxies. Encouragingly, if assuming expected properties for typical first galaxies (i.e., dust-to-metal mass ratio: $D/M = 5 \times 10^{-3}$, gas metallicity: $Z_{\rm g} = 5 \times 10^{-3}~Z_{\odot}$, star formation efficiency: $η= 0.01$), model far-infrared (FIR) fluxes are consistent with current upper flux limits inferred from ALMA bands 6 and 7 ($\lesssim 10^4$ nJy). Such low $D/M$ values and metallicities are in agreement with some scenarios proposed in the literature to explain the non-detection of the FIR dust continuum for high-$z$ JWST galaxy candidates. On the other hand, higher values of model parameters $D/M$ ($\gtrsim 0.06$) and $Z_{\rm g}$ ($\gtrsim 5 \times 10^{-2}~Z_{\odot}$) are ruled out by observational data, unless a higher $η$ is assumed. According to our findings, ALMA multi-band observations could constrain the dust chemistry and dust grain size distribution in the early universe. In this context, future observational challenges would involve not only reaching higher FIR sensitivities, but also increasing the wavelength coverage by exploring distinct ALMA bands.

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arXiv2022

Impact of Population III homogeneous stellar evolution on early cosmic reionisation

Context: Population III (Pop III) stars may be fast rotating. An expected consequence of fast rotation is strong internal mixing that deeply affects their evolutionary tracks in the Hertzsprung-Russell diagram and hence their ionising power. aims: We investigate the impact on the ionising power of Pop III stars in an extreme case of internal mixing, the one leading to chemically homogeneous evolution (CHE). In that situation, during the main sequence phase, the star keeps the same chemical composition from its center to its surface. Homogeneous stars have larger effective temperatures and luminosities than stars evolving non-homogeneously and thus are stronger ionising sources. Methods: The stellar evolution models are based on $n=3$ polytropes with a time varying hydrogen mass fraction. The ionisation model employs the self-similar champagne flow solution from Shu et al. (2002), as well as numerical simulations for the stochastic treatment of star clusters over a grid of redshifts and halo masses. Results: We find that haloes containing chemically homogeneous stars have an escape fraction of ionising photons about twice that of haloes containing classical Pop III stars. By extrapolating the high-$z$ ionisation history powered by Pop III stars (at $z\gtrsim 15$) to the post-reionisation epoch, we derive the Thomson scattering optical depth $τ$, which is compared with the value measured by $\textit{Planck}$. We find that $τ$ is overproduced by $\sim1.5- 5σ$, when all Pop III stars evolve homogeneously. This indicates that CHE is unlikely to be realised in the majority of Pop III stars, although the present study cannot exclude that a fraction of them undergoes CHE. Conclusions: Fast rotation might have a significant impact on the ionising budget of Pop III stars, and thus on early cosmic reionisation.

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arXiv2022

Dwarf galaxy formation with and without dark matter-baryon streaming velocities

We study how supersonic streaming velocities of baryons relative to dark matter -- a large-scale effect imprinted at recombination and coherent over $\sim 3$ Mpc scales -- affects the formation of dwarf galaxies at $z \gtrsim 5$. We perform cosmological hydrodynamic simulations, including and excluding streaming velocities, in regions centered on halos with $M_{\rm vir}(z=0) \approx 10^{10}$ M$_{\odot}$; the simulations are part of the Feedback In Realistic Environments (FIRE) project and run with FIRE-3 physics. Our simulations comprise many thousands of systems with halo masses between $M_{\rm vir} = 2\times10^{5}$ M$_{\odot}$ and $2\times10^9$ M$_{\odot}$ in the redshift range $z=20-5$. A few hundred of these galaxies form stars and have stellar masses ranging from 100 to $10^7$ M$_{\odot}$. While star formation is globally delayed by approximately 50 Myr in the streaming relative to non-streaming simulations and the number of luminous galaxies is correspondingly suppressed at high redshift in the streaming runs, these effects decay with time. By $z=5$, the properties of the simulated galaxies are nearly identical in the streaming versus non-streaming runs, indicating that any effects of streaming velocities on the properties of galaxies at the mass scale of classical dwarfs and larger do not persist to $z=0$.

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arXiv2022

Accelerating early massive galaxy formation with primordial black holes

Recent observations with JWST have identified several bright galaxy candidates at $z\gtrsim 10$, some of which appear unusually massive (up to $\sim 10^{11}\ \rm M_{\odot}$). Such early formation of massive galaxies is difficult to reconcile with standard $Λ\rm CDM$ predictions, demanding very high star formation efficiency (SFE), possibly even in excess of the cosmic baryon mass budget in collapsed structures. With an idealized analysis based on linear perturbation theory and the Press-Schechter formalism, we show that the observed massive galaxy candidates can be explained with lower SFE than required in $Λ\rm CDM$, if structure formation is accelerated/seeded by massive ($\gtrsim 10^{9}\ \rm M_{\odot}$) primordial black holes (PBHs) that make a up a small fraction ($\sim 10^{-6}-10^{-3}$) of dark matter, considering existing empirical constraints on PBH parameters. We also discuss the potential observational signatures of PBH cosmologies in the JWST era. More work needs to be done to fully evaluate the viability of such PBH models to explain observations of the high-$z$ Universe.

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arXiv2022

Public Release of A-SLOTH: Ancient Stars and Local Observables by Tracing Halos

The semi-analytical model A-SLOTH (Ancient Stars and Local Observables by Tracing Halos) is the first public code that connects the formation of the first stars and galaxies to observables. After several successful projects with this model, we publish the source code and describe the public version in this paper. The model is based on dark matter merger trees that can either be generated based on Extended Press-Schechter theory or that can be imported from dark matter simulations. On top of these merger trees, A-SLOTH applies analytical recipes for baryonic physics to model the formation of both metal-free and metal-poor stars and the transition between them with unprecedented precision and fidelity. A-SLOTH samples individual stars and includes radiative, chemical, and mechanical feedback. It is calibrated based on six observables, such as the optical depth to Thomson scattering, the stellar mass of the Milky Way and its satellite galaxies, the number of extremely-metal poor stars, and the cosmic star formation rate density at high redshift. A-SLOTH has versatile applications with moderate computational requirements. It can be used to constrain the properties of the first stars and high-z galaxies based on local observables, predicts properties of the oldest and most metal-poor stars in the Milky Way, can serve as a subgrid model for larger cosmological simulations, and predicts next-generation observables of the early Universe, such as supernova rates or gravitational wave events.

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arXiv2022

A Long Time Ago in a Galaxy Far, Far Away: A Candidate z ~ 12 Galaxy in Early JWST CEERS Imaging

We report the discovery of a candidate galaxy with a photo-z of z~12 in the first epoch of the JWST Cosmic Evolution Early Release Science (CEERS) Survey. Following conservative selection criteria we identify a source with a robust z_phot = 11.8^+0.3_-0.2 (1-sigma uncertainty) with m_F200W=27.3, and >7-sigma detections in five filters. The source is not detected at lambda < 1.4um in deep imaging from both HST and JWST, and has faint ~3-sigma detections in JWST F150W and HST F160W, which signal a Ly-alpha break near the red edge of both filters, implying z~12. This object (Maisie's Galaxy) exhibits F115W-F200W > 1.9 mag (2-sigma lower limit) with a blue continuum slope, resulting in 99.6% of the photo-z PDF favoring z > 11. All data quality images show no artifacts at the candidate's position, and independent analyses consistently find a strong preference for z > 11. Its colors are inconsistent with Galactic stars, and it is resolved (r_h = 340 +/- 14 pc). Maisie's Galaxy has log M*/Msol ~ 8.5 and is highly star-forming (log sSFR ~ -8.2 yr^-1), with a blue rest-UV color (beta ~ -2.5) indicating little dust though not extremely low metallicity. While the presence of this source is in tension with most predictions, it agrees with empirical extrapolations assuming UV luminosity functions which smoothly decline with increasing redshift. Should followup spectroscopy validate this redshift, our Universe was already aglow with galaxies less than 400 Myr after the Big Bang.

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arXiv2022

Impact of magnetic fields on Population III star formation

The theory of the formation of the first stars in the Universe, the so-called Population III (Pop III), has until now largely neglected the impact of magnetic fields. Complementing a series of recent studies of the magneto-hydrodynamic (MHD) aspects of Pop III star formation, we here carry out a suite of idealized numerical experiments where we ascertain how the fragmentation properties of primordial protostellar discs are modified if MHD effects are present. Specifically, starting from cosmological initial conditions, we focus on the central region in a select minihalo at redshift $z\sim$ 25, inserting a magnetic field at an intermediate evolutionary stage, normalized to a fraction of the equipartition value. To explore parameter space, we consider different field geometries, including uniform, radial, toroidal, and poloidal field configurations, with the toroidal configuration being the most realistic. The collapse of the gas is followed for $\sim$8 orders of magnitude in density after the field was inserted, until a maximum of $10^{15}{\rm \,cm}^{-3}$ is reached. We find that the magnetic field leads to a delay in the collapse of the gas. Moreover, the toroidal field has the strongest effect on the collapse as it inhibits the fragmentation of the emerging disc surrounding the central core and leads to the formation of a more massive core. The full understanding of the formation of Pop~III stars and their mass distribution thus needs to take into account the effect of magnetic fields. We further conclude that ideal MHD is only a first step in this endeavor, to be followed-up with a comprehensive treatment of dissipative effects, such as ambipolar diffusion and Ohmic dissipation.

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arXiv2022

Maximal X-ray feedback in the pre-reionization universe

X-ray feedback in the pre-reionization Universe provided one of the major energy sources for reionization and the thermal evolution of the early intergalactic medium. However, X-ray sources at high redshift have remained largely inaccessible to observations. One alternative approach to study the overall effect of X-ray feedback in the early Universe is a full cosmological simulation. Toward this goal, in this paper we create an analytic model of X-ray feedback from accretion onto supermassive black holes (SMBHs), to be used as a sub-grid model in future cosmological simulations. Our analytic model provides a relation between the mass of a dark matter halo and the SMBH it hosts, where the efficiency is governed by an energy balance argument between thermal feedback and the confining gravitational potential of the halo. To calibrate the model, we couple the halo-level recipe with the Press-Schechter halo mass function and derive global mass and energy densities. We then compare our model to various observational constraints, such as the resulting soft X-ray and IR cosmic radiation backgrounds, to test our choice of model parameters. We in particular derive model parameters that do not violate any constraints, while providing maximal X-ray feedback prior to reionization. In addition, we consider the contribution of SMBH X-ray sources to reionization and the global 21 cm absorption signal.

astro-ph.CO↗

arXiv2022

On the probability of the extremely lensed $z$=6.2 Earendel source being a Population~III star

The recent discovery of the extremely lensed Earendel object at $z=6.2$ is remarkable in that it is likely a single star or stellar multiple, observed within the first billion years of cosmic history. Depending on its mass, which is still uncertain but will soon be more tightly constrained with the James Webb Space Telescope, the Earendel star might even be a member of the first generation of stars, the so-called Population~III (Pop~III). By combining results from detailed cosmological simulations of the assembly of the first galaxies, including the enrichment of the pristine gas with heavy chemical elements, with assumptions on key stellar parameters, we quantify the probability that Earendel has indeed a Pop~III origin. We find that this probability is non-negligible throughout the mass range inferred for Earendel, specifically ranging from a few percent at the lower-mass end to near unity for some Pop~III initial mass function (IMF) models towards the high-mass end of the allowed range. For models that extend the metal-enriched IMF to $500$\,M$_\odot$, the likelihood of Earendel being a Pop~III star stays at the few to ten percent level. We discuss the implications of such a discovery for the overall endeavor to probe the hitherto so elusive first stars in the universe.

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arXiv2022

Effects of stellar-mass primordial black holes on first star formation

We use cosmological hydrodynamic zoom-in simulations and semi-analytical models to study the effects of primordial black holes (PBHs) on first star formation. Our models self-consistently combine two competing effects: initial (isocurvature) perturbations induced by PBHs and BH accretion feedback. Focusing on PBHs with masses $\sim 30\ \rm M_{\odot}$, we find that the standard picture of first star formation in molecular-cooling minihaloes is not changed by PBHs, as the simulated star-forming gas clouds in the central parsec are very similar to those in the $\rm ΛCDM$ case when PBHs make up $f_{\rm PBH}\sim 10^{-4}-0.1$ of dark matter. With a dynamical friction timescale of $\sim 2-10\ \rm Myr$ when the central gas density reaches $10^{5}\ \rm cm^{-3}$, it is also unlikely that PBHs can sink into star-forming discs and affect the evolution of protostars, although they may interact with the stars during the main-sequence stage. At larger scales, PBHs tend to shift star formation to more massive haloes, and accelerate structure formation. The latter effect is stronger in regions with higher initial overdensities. For $f_{\rm PBH}\sim 10^{-4}-0.01$ (allowed by observational constraints), the collapsed mass fraction of haloes hosting Population III stars is similar (within a factor of $\sim2$ at $z\lesssim 30$) to that in $\rm ΛCDM$, implying that the impact of stellar-mass PBHs on the cosmic star formation history at $z\gtrsim 10$ is small. We also find that the Lyman-Werner photons from PBH accretion in atomic-cooling haloes may facilitate the formation of direct-collapse BHs.

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