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Greg L. Bryan

Publications and source records attributed to Greg L. Bryan.

At least 37 records · Page 2Linked to original sources

The Origin of Da Scaling: Suppressed Cooling in Fast-Cooling Mixing Layers

In numerical experiments simulating Turbulent Radiative Mixing Layers (TRMLs) it is observed that as the cooling time in the mixed gas, $t_{\rm cool}$, becomes very short compared to the dynamical time of the turbulence, $t_{\rm eddy}/t_{\rm cool} \gg 1$, there is a change in the scaling behavior of the total energy radiated in the TRML as a function of this ratio, also known as the Damköhler number, ${\rm Da} \equiv t_{\rm eddy}/t_{\rm cool}$, from $\dot{E}_{\rm cool} \propto {\rm Da}^{1/2}$ to $\dot{E}_{\rm cool} \propto {\rm Da}^{1/4}$. The latter, so-called "fast-cooling," regime is of particular interest as many astrophysical mixing layers lie in this regime. We demonstrate that the origin of this change is the suppression of turbulent folding of the surface by the ram-pressure of the inflowing gas, which becomes much greater than the turbulent pressure in this regime. We present an argument that reproduces the $\dot{E}_{\rm cool} \propto {\rm Da}^{1/4}$ behavior by appealing to the suppression of the fractal structure of the interface by the ram-pressure of the inflowing gas.

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How High-Specific-Energy Winds Regulate the Circumgalactic Medium of Dwarf Galaxies

We investigate the role of ejective and preventive feedback in $\mathrm{\sim10^{10}-10^{11}\,M_\odot}$ dwarf halos using cosmological zoom-in simulations. These simulations use adaptive mesh refinement to capture high-specific-energy outflows, together with an implementation of discrete supernovae (SNe). We show that episodic, SNe-driven shock heating sustains the circumgalactic medium (CGM) at $\mathrm{\sim T_{vir}}$. This process also increases the ratio $\mathrm{t_{cool}/t_{ff} > 10}$ in the outer CGM and intergalactic medium (IGM), placing the gas in a radiatively stable regime. Hot outflows ($\mathrm{\gtrsim10^5\, K}$) dominate the energy budget, and their high specific energy allows them to traverse the CGM, escape the halo, and heat the IGM. In contrast, warm outflows ($\mathrm{\lesssim10^5\, K}$) dominate the mass budget and are largely recycled back into the interstellar medium (ISM), where they fuel future star formation. We identify a gradual transition at $\mathrm{\sim 5\, Gyr}$ that marks a shift in the balance between ejective and preventive feedback. At early times ($\mathrm{< 5\, Gyr}$), although the CGM cooling rate dominates for a larger fraction of time, the infrequent yet powerful SNe energy injection into the CGM is able to quickly dominate the cumulative energy balance. These outflows and their high specific energy are able to 'sweep' up mass in the CGM and IGM. At late times ($\mathrm{> 5\, Gyr}$), the CGM baryon fraction is only $\mathrm{\sim0.1}$, leading to a transition toward a preventive feedback mode in which SNe maintain $\mathrm{t_{cool}/t_{ff} > 10}$ and prevent $\mathrm{\sim75\%}$ of the expected baryon accretion rate.

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Probing the Hot Gaseous Halos of Milky Way-like Galaxies in the TNG50 simulation

The origin and structure of the hot ($T\gtrsim10^6$K) gaseous halo around Milky Way (MW)-mass galaxies provide a critical test for galaxy formation models. We perform a comprehensive comparison for a sample of MW analogues from the TNG50 cosmological simulation by generating synthetic soft X-ray emission and O VII/O VIII absorption lines, viewed from both internal (Solar) and external perspectives. The simulated halos successfully reproduce the observed global soft X-ray luminosity, inner-halo X-ray surface brightness, emission measure, and O VII absorption strength. However, two interconnected discrepancies are identified. First, the azimuthally averaged X-ray surface brightness profile from external viewpoints declines too steeply with radius compared to the extended emission detected in eROSITA stacking of SDSS galaxies, falling below the observations by up to $\sim 1$ dex at $R \gtrsim 100$ kpc. Second, the halos systematically underproduce O VIII absorption, with a median equivalent width $\sim 65\%$ lower than that observed in the Galactic halo, pointing to a deficit of hotter-phase gas at $T\sim(1.6-3.2)\times10^6$ K. These findings indicate that the simulated hot halos are too spatially compact and lack a hotter gas phase, suggesting that the TNG50 feedback model, while generating hot gas, deposits energy too centrally and too vigorously to sustain a gently extended, multi-phase corona.

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ArkenstoneBH. A model for high-specific energy black hole feedback in cosmological simulations

AGN feedback is a key piece of galaxy evolution but is difficult to model due to its high specific energies, multiphase nature, and limited simulation resolutions. Arkenstone is a subgrid framework for representing multiphase flows in coarse resolution simulations that has been used to model stellar feedback driven galactic winds. It ensures the correct treatment of high specific energy feedback that would otherwise be challenging to model accurately in Lagrangian simulations. We introduce the new Arkenstone BH model, which extends the Arkenstone framework to model black hole feedback. We focus on describing the first piece of this framework, which follows the hot, high specific energy phase of these outflows. The second piece, which treats their multiphase structure with a scheme for modeling unresolved cold clouds, will be implemented and described in a later paper. We present Arkenstone BH in simulations of an isolated galaxy to demonstrate the framework and its ability to capture high specific energy feedback that interacts only weakly with cold, dense gas. We show how these energetic outflows suppress star formation in our isolated galaxy by counteracting the inflow of gas from the circumgalactic medium into the interstellar medium. This work is part of the "Learning the Universe" collaboration, which aims to understand the Universe's underlying physics and initial conditions.

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Resolving the Unresolved Galactic Winds in Multi-phase Models. I. Methodology and Application

Galactic winds shape galaxy evolution; however, the outflowing gas is complex: it consists of multiple ionization phases, and its properties vary spatially. Therefore, methods that combine high-fidelity observations with state-of-the-art galactic-wind models are limited. Here we investigate methods for fitting the column density profiles derived from high-quality outflow observations with the multiphase, multiscale wind model from Fielding & Bryan 2022. We identify three key outflow parameters: the initial hot-phase mass-loading factor ($η_\text{ M,hot,0}$), the initial cool-phase mass-loading factor ($η_\text{ M,cool,0}$), and the initial cool-cloud mass. We obtain good fits for most galaxies, with tight constraints on $η_\text{ M,cool,0}$ and moderate constraints on the other two parameters. We find the inferred $η_\text{ M,cool,0}$ and $η_\text{ M,hot,0}$ are mostly of order unity, with significant scatter. The constraints on $η_\text{ M,hot,0}$ suggest that the interaction between the cool and hot phases allows us to indirectly constrain the properties of the hot wind from cool-outflow observations. The model also predicts various radial trends. First, for all galaxies, the cool-phase outflow velocity increases between $1-2$ times of the half-light radius, then reaches a plateau. Second, most galaxies exhibit increasing $η_\text{ M,cool}$ and decreasing $η_\text{ M,hot}$ with radius, with a few showing the reverse trends. These results are effective, model-conditional constraints, and are consistent with other recent multiphase simulations and observations. This highlights that the velocity-radius mapping encoded in UV absorption profiles enables recovery of outflow spatial structures from spatially integrated spectra. Our method paves the way for future broad parameter studies and guides updates of outflow simulations in future work.

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The Thermodynamic and Kinematic Evolution of Circumgalactic Gas around $z=1$ in the IllustrisTNG model

The circumgalactic medium (CGM) is known to contain multiphase gas in various stages of evolution and interaction with the galaxy. In order to characterize its detailed behavior on short timescales, we use a subregion of the TNG100 cosmological simulation to study the evolution of the $z=1$ CGM around six galaxies in $10^{11.5}-10^{12}$ $M_{\odot}$ halos at a high time cadence of $\approx2$ Myr. We use Monte Carlo tracer particles to follow this CGM gas forward in time in a Lagrangian way and determine how its thermodynamic and kinematic properties change. We find that CGM gas mixes between different temperature and density phases quickly and within $\approx500$ Myr evolves into distinct cold ($T\approx10^4$ $\rm{K}$) and warm-hot ($T\approx10^{5.5}$ $\rm{K}$) phases at small and large distances from the galaxy, respectively, regardless of its initial ($z=1$) halo-centric radius. This is largely driven by feedback from the galaxy, which heats and ejects cold gas that had previously cooled and accreted toward and occasionally into the galaxy from the outer CGM. We see signatures of this process in autocorrelations of kinematic quantities, which take $\approx400$ Myr to fully decorrelate from their initial values, suggesting a timescale over which feedback disrupts and reprocesses CGM gas. We also examine gas in narrow temperature and density ranges associated with commonly observed ions and find that gas that is O VI-like stays in its phase for hundreds of Myr longer than gas that is Mg II-like or C IV-like, suggesting that CGM observations of different species could probe gas in different evolutionary states, even if the gas is cospatial.

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Too Big to Quench? I. Constraining ISM Stripping of Dwarf Satellites in Milky Way-like Halos

Galaxy environment plays a crucial role in quenching star formation in dwarf galaxies. In Milky Way (MW)-like environments, dwarf satellite quenching is primarily driven by ram pressure stripping (RPS), the direct removal of satellite gas by the host halo gas. Using a suite of 20-pc resolution hydrodynamical wind tunnel simulations, we constrain the satellite mass scale at which the stripping of a dwarf galaxy's interstellar medium (ISM) becomes inefficient in MW-like halos. The simulations include radiative cooling in a multiphase satellite ISM, star formation, and stellar feedback, and vary both satellite masses ($M_{\star}=10^{6.2}, 10^{6.8}, 10^{7.2}\ M_{\odot}$) and host halo gas densities along a first-infall and post-pericentric orbit. We find that the degree of ISM stripping in our dwarf galaxies is consistent with the analytical prediction by McCarthy et al. (2008). Star formation is rapidly quenched when RPS is effective, but can be mildly enhanced or temporarily quenched and subsequently reignited when RPS is incomplete. ISM stripping is efficient for satellites with $M_{\star} \lesssim 10^{7}\ M_{\odot}$ (or $M_{200} \lesssim 10^{10}\ M_{\odot}$) but highly inefficient above this scale. This transitional mass ($M_{\star} \approx 10^{7}\ M_{\odot}$) is 0.5-1 dex lower than that found in observations and cosmological simulations, suggesting that additional mechanisms are needed to quench more massive satellites, such as tidal stripping of the satellite dark matter or RPS from a clumpy gaseous halo.

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Identifying signatures of inflow onto face-on galaxies using the Balmer decrement

Isolated star-forming galaxies require inflows of fresh gas from the surrounding medium to sustain episodes of star formation over time. However, there are very few direct detections of accretion onto external galaxies. Studies in absorption can only observe along limited sightlines, while those in emission can have difficulty distinguishing inflowing gas in the foreground of the galactic disk from similarly Doppler-shifted outflowing gas in the background. We explore the possibility of using the Balmer decrement (H$α$/H$β$) in low-inclination systems as a diagnostic for disentangling the flow geometry in disk-like galaxies. We leverage mock spatial-spectral observations of an isolated Milky Way-mass galaxy simulated using the radiation-hydrodynamics code AREPO-RT and post-processed with the Monte Carlo radiative transfer code COLT. We find that gas components located in front of the disk exhibit systematically lower Balmer decrements than gas embedded in or behind the disk, with a mean front-back offset of $Δ(\text{H}α/\text{H}β) \approx -0.14$. The ability to differentiate between the disk and far-side components is limited by the extremely clumpy, multiphase dust distribution along the line of sight introducing substantial scatter. Overall, the results provide a useful observational diagnostic of inflow and outflow in dusty face-on galaxies.

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Mainly on the Plane: Observing the Extended, Ionized Disks of Milky Way Analogs in IllustrisTNG

This paper explores the extent to which the circumgalactic medium (CGM) of Milky Way-like galaxies is located in an extended, ionized, disklike structure. To test this hypothesis, we analyze the spatial and kinematic distributions of different ion species within a sample of MW-like systems in IllustrisTNG. We model commonly observed ions (HI, MgII, SiIV, CIV and OVI) and calculate (1) their angular momentum misalignment from the star-forming disk ($θ$) and (2) the fraction of absorption consistent with galaxy rotation ($f_\mathrm{EWcorot}$). We find that 63% of MgII, 45% of SiIV, 38% of CIV, and 35% of OVI mass along the major axis have kinematics aligned with the galaxy angular momentum axis. We extend this to a mock absorption line survey and quantify $f_\mathrm{EWcorot}$. We find that $f_\mathrm{EWcorot}$(MgII) $\sim80\%$ and $f_\mathrm{EWcorot}$(OVI) $\sim60\%$ at $\sim0.5\ \mathrm{R_{200c}}$, in agreement with recent observational work. We find that in the typical MW analog, there is evidence of cool-warm material in an extended, corotating structure, regardless of whether the angular momentum or observational definition is used. Hence, we expect that the typical MW CGM, especially in the low ions, should be mainly on the plane.

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Evolution of Nuclear Star Cluster in Dwarf Galaxy through Mergers and In-Situ Star Formation

Nuclear Star Clusters (NSCs) are dense stellar systems located at the centers of galaxies. Employing Enzo-Abyss, which integrates hydrodynamics with a direct N-body solver, we introduce a simulation capable of resolving the evolution of NSCs within a live galaxy. This includes live dark matter, gaseous dynamics, star formation and feedback, collisional dynamics for star clusters. The evolution of NSCs is typically shaped by two main processes: mergers of star clusters and in-situ star formation. Our simulation enables investigation of the contributions of these mechanisms to the growth of NSCs. This work focuses on the impact of stellar physics and gas content on the growth of NSCs within a dwarf galaxy. To this end, we carry out four simulations, a fiducial simulation, one without supernova feedback, one with low star formation efficiency, and one with higher galactic gas content. This study shows a likelihood that both mergers and in-situ star formation contribute to NSC evolution comparably. In addition, mergers result in disruption of dense gas clumps within star clusters, indicating that in-situ star formation is suppressed when mergers occur. However, the limitations -- such as the lack of individual star physics and limited spatial/particle mass resolution -- hinder drawing a definite conclusion. Nevertheless, with further development, our simulations will serve as a cornerstone that untangles the complex interplay between mergers and in-situ star formation in shaping the structure and mass of NSCs, thereby providing insights into their formation and evolution.

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Chemical Signatures of Population III Stars in Damped Lyman-$α$ Absorption Systems at $z \approx 6$

Recently, Sodini et al. (2024) presented a sample of OI damped Lyman-$α$ absorption system (DLA) analogs at $z\sim6$ that contain possible chemical signatures of Population III (Pop III) stars. In this paper, we use an N-body simulation-based semi-analytic model of the first stars and galaxies to predict the impact of Pop III stars on high-redshift DLAs. These Pop III DLA predictions are the first to include a number of important physical effects such as Lyman-Werner (LW) feedback, reionization, and external metal enrichment (all of which account for three-dimensional spatial fluctuations caused by halo clustering). We predict the abundance of DLAs as a function of their carbon-to-oxygen ratios ([C/O]). We find that our fiducial model is strongly ruled out by the data as it contains too few high-[C/O] DLAs, which have metals primarily from Pop III stars. However, increasing the delay time between Pop III and metal-enriched star formation due to supernovae feedback leads to better agreement with the data. Our results suggest that DLA analogs at $z\sim6$ are a promising probe of Pop III star formation for two key reasons. First, for reasonable parameter choices there are significant numbers of DLAs with metals primarily originating from Pop III stars. Second, we find that the number of DLAs with substantial Pop III contributions depends strongly on the Pop III star formation efficiency and the delay time between Pop III and metal-enriched star formation.

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Blue Monsters and Dusty Descendants: Reconciling UV and IR Emission from Galaxies from z=7, up to z= 14

Recent JWST observations reveal massive, UV-bright galaxies at $z > 10$ with little apparent dust attenuation, whereas ALMA detections at $z \simeq 7$ show similarly massive systems that are already dust-rich and IR-luminous. This raises a fundamental question: can a single physical model of star formation and dust production explain both populations across cosmic time? We address this using a minimal framework with only two free parameters--the instantaneous star formation efficiency ($ε_\star$) and the dust yield per Type II supernova ($y_d$)--and predict the rest-frame UV and IR luminosity functions (LFs) from $z \simeq 14$ to 7. For a uniform ISM, we find a UV-IR tension at the bright end of the LFs at $z \ge 7$. The UV LF requires low dust yields ($y_d \lesssim 0.01\,M_\odot$), whereas the $z=7$ IR LF requires higher yields ($y_d \sim 0.1\,M_\odot$) unless the star formation efficiency is boosted above $ε_\star \approx 5$-10%. We show that incorporating a porous, turbulent ISM largely resolves this tension: turbulence opens low-column-density sightlines that enhance the UV escape fraction while leaving the total absorbed energy--and thus the IR luminosity--nearly unchanged once radiative-transfer--induced flattening of the attenuation curve is included. Large-grain dust distributions, while reducing UV opacity, play a secondary role once ISM porosity and radiative transfer are taken into account. At $z > 10$, however, even strong turbulence cannot reproduce the bright end of the UV LF at high dust yield. This could be resolved either by efficient dust removal in early massive systems or by substantial ISM dust growth by $z \simeq 7$. Our results highlight dust physics as a key lever for interpreting the rapidly growing UV and IR constraints within the broader context of early galaxy formation.

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What Suppresses Star Formation in Bulge-Dominated Early-Type Galaxies?

We investigate the physical origin of star formation suppression in gas-rich early-type galaxies using five high-resolution hydrodynamical idealized galaxy simulations, performed with the moving-mesh code AREPO. These simulations include one Milky Way-like galaxy and four early-type galaxies, of which one early-type galaxy is found to have significantly less star formation despite a substantial molecular gas reservoir. We apply a modified virial theorem to the overdensities in each galaxy to quantify the forces regulating their stability and thus star formation. We find evidence that, in the suppressed galaxy, strong Coriolis forces driven by elevated galactic shear may inhibit gravitational collapse. This is caused by the galaxy's high central compactness, providing a physical mechanism for the suppression of star formation that does not require the removal of molecular gas. In contrast, less compact early-type galaxies host more gravity-dominated clouds and therefore exhibit higher star formation rates. However, we find that this gravitational stability occurs without significantly increasing the classical Toomre-Q parameter, and therefore a new criterion for suppressed star formation may be needed. We also discuss the impact of our choice of overdensity scale and connections to observations of molecular clouds.

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Aeos: The Impact of Population III Initial Mass Function and Star-by-Star Models in Galaxy Simulations

We explore the effect of variations in the Population III (Pop III) initial mass function (IMF) and star-by-star feedback on early galaxy formation and evolution using the Aeos simulations. We compare simulations with two different Pop III IMFs: $M_\text{char} = 10 \, \mathrm{M}_\odot$ and $M_{\rm max} = 100 \, \mathrm{M}_\odot$ (Aeos10) and $M_\text{char} = 20 \, \mathrm{M}_\odot$ and $M_{\rm max} = 300 \, \mathrm{M}_\odot$ (Aeos20). Aeos20 produces significantly more ionizing photons, ionizing 30% of the simulation volume by $z \approx 14$, compared to 9% in Aeos10. This enhanced ionization suppresses galaxy formation on the smallest scales. Differences in Pop III IMF also affect chemical enrichment. Aeos20 produces Population II (Pop II) stars with higher abundances, relative to iron, of light and $α$-elements, a stronger odd-even effect, and a higher frequency of carbon-enhanced metal-poor stars. The abundance scatter between different Pop II galaxies dominates the differences due to Pop III IMF, though, implying a need for a larger sample of Pop II stars to interpret the impact of Pop III IMF on early chemical evolution. We also compare the Aeos simulations to traditional simulations that use single stellar population particles. We find that star-by-star modeling produces a steeper mass-metallicity relation due to less bursty feedback. These results highlight the strong influence of the Pop III IMF on early galaxy formation and chemical evolution, emphasizing the need to account for IMF uncertainties in simulations and the importance of metal-poor Pop II stellar chemical abundances when studying the first stars.

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RIGEL: Feedback-regulated cloud-scale star formation efficiency in a simulated dwarf galaxy merger

Major mergers of galaxies are likely to trigger bursty star formation activities. The accumulation of dense gas and the boost of star formation efficiency (SFE) are considered to be the two main drivers of starbursts. However, it remains unclear how each process operates on the scale of individual star-forming clouds. Here, we present a high-resolution (2 Msun) RHD simulation of a gas-rich dwarf galaxy merger using the RIGEL model to investigate how mergers affect the properties of the structure of dense star-forming gas and the cloud-scale SFE. We tracked the evolution of sub-virial dense clouds in the simulation by mapping them across successive snapshots taken at intervals of 0.2 Myr. We find that the merger triggers a 130 fold increase in the SFR and shortens the galaxy-wide gas-depletion time by two orders of magnitude compared to those in two isolated galaxies. However, the depletion time of individual clouds and their lifetime distribution remained unchanged over the simulation period. The cloud life cycles and cloud-scale SFE are determined by the local stellar feedback rather than such environmental factors as tidal fields regardless of the merger process, and the integrated SFE ($ε_{\rm int}$) of clouds in complex environments remains well-described by an $ε_{\rm int}-Σ_{\rm tot}$ relation found in idealized isolated-cloud experiments. During the peak of the starburst, the media SFE was lower by only 0.17-0.33 dex compared to the value when the galaxies were not interacting. The merger boosts the SFR through the accumulation and compression of dense gas fueling star formation. Strong tidal torques assemble $>10^5$ Msun clouds, which seed massive star clusters. The average separation between star-forming clouds decreases during the merger, which in turn decreases the cloud--cluster spatial de-correlation from >1 kpc to 0.1 kpc depicted in tuning fork diagrams.

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LAP1-B is the First Observed System Consistent with Theoretical Predictions for Population III Stars

Recently, Nakajima et al. (2025) presented James Webb Space Telescope observations of the $z=6.6$ Population III (Pop III) candidate LAP1-B, which is gravitationally lensed by galaxy cluster MACS J0416. We argue that this is the first object to agree with three key theoretical predictions for Pop III stars: (1) formation in extremely low-metallicity halos with virial temperatures ranging from $T_{\rm vir}\sim 10^3-10^4~{\rm K}$, (2) a top-heavy initial mass function, and (3) formation of low-mass clusters with ${\sim}{\rm a ~few}\times 1000~M_\odot$ in massive Pop III stars. LAP1-B is consistent with recently formed Pop III stars hosted in a $\sim 5\times 10^7~M_\odot$ dark matter halo, some of which have enriched their surrounding gas either with supernovae or stellar winds. We use the semi-analytic model of Visbal et al. (2020) to predict the abundance of Pop III clusters observable at the high magnification provided by the foreground galaxy cluster MACS J0416. Using fiducial parameters unmodified from previous work, we expect about one observable Pop III galaxy similar to LAP1-B in the range $z=6-7$. At earlier times, the intrinsic abundance is higher, but Pop III systems would not have been detected because of their increased luminosity distance and lower mass dark matter halos, which would host fewer stars. Thus, we find that LAP1-B was found at the redshift theoretically expected, given current observable limits, despite the fact that most Pop III systems form much earlier.

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From Primordial Stars to Early Galaxies: A Semi-Analytic Model Calibrated with Aeos and Renaissance

We present an extension of our semi-analytic model that follows the formation of Population III stars and their metal-enriched descendants, incorporating dark matter halo merger trees from cosmological $N$-body simulations and feedback from reionization. Our extended model is calibrated using two complementary cosmological hydrodynamical simulations: Aeos, which resolves individual Population III and II stars to $z\sim14.6$, and Renaissance, which is lower resolution but follows large-scale metal-enriched star formation to $z \sim 11$. With a combined calibration, we capture small-scale physics of primordial star formation over a large range in halo mass. We find good agreement between our calibrated model and Aeos, reproducing the evolution in number of star-forming halos and total stellar mass. Achieving this agreement requires increasing the normalization of, flattening the redshift dependence of, and adding scatter to the commonly used critical mass threshold $M_{\mathrm{crit}}$. Our treatment of the delay between Pop III stellar death and subsequent Pop II star formation emphasizes the need to account for halos that have yet to transition to Pop II, since incomplete sampling of this delay in simulations limits physically motivated calibrations. Finally, we apply our model to larger-volume dark matter only simulations and predict $\sim10$ active Pop III sources at $z = 10$ lie within the area strongly lensed by galaxy cluster MACS J0416 with a magnification exceeding $μ> 30$. These results demonstrate that semi-analytic approaches, when calibrated to hydrodynamical simulations, can provide accurate, computationally efficient predictions for the earliest stages of cosmic star formation.

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Aeos is Mixing it Up: The (In)homogeneity of Metal Mixing Following Population III Star Formation

Stellar surface abundances are records of the state of the gas from which stars formed, and thus trace how individual elements have mixed into the surrounding medium following their ejection from stars. In this work, we test the common assumption of instantaneous and homogeneous metal mixing during the formation of the first Population II stars by characterizing the chemical homogeneity of the gas in simulated star-forming environments enriched by Population III stellar feedback. Testing the homogeneity of metal mixing in this time period is necessary for understanding the spread of abundances in the most metal-poor stars, and the (in)homogeneity of individual sites of star formation. Using Aeos, a suite of star-by-star cosmological simulations, we quantify how gas abundances change over space and time relative to Population II stellar abundances using Mahalanobis distances, a measure of covariance-normalized dissimilarity. We find that the homogeneous mixing assumption holds only within $\sim100$ pc of a star-forming region and $\sim 7$ Myr following the star formation event. Beyond this regime, deviations between stellar and gas abundances increase until they become indistinguishable from assuming a homogeneous mix of metals averaged over the initial mass function. This highlights the limited applicability of assuming instantaneous and homogeneous mixing in realistic halo environments at high redshift. We identify critical mixing scales that are necessary to explore chemical evolution in the early Universe. These scales can be applied to determine the precision needed for accurate chemical tagging of observed data and to explore parameter space with analytical models.

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