arXiv subjects

Carl L. Rodriguez

Publications and source records attributed to Carl L. Rodriguez.

At least 19 recordsLinked to original sources

arXiv2026

When the stars don't align: Investigating inconsistencies in binary black hole formation across population synthesis codes

Binary population synthesis (BPS) codes are extremely useful tools for investigating both the end-to-end lives of binary stars as well as a myriad of astrophysical phenomena observed in the Universe. Given the widespread use of BPS in modern astrophysical research, it is imperative to systematically compare BPS codes across the spectrum of computational efficiency, flexibility, and physical realism to gauge their consistency and robustness. In this work, we perform BPS using three modern codes---the rapid code $\texttt{COSMIC}$, the hybrid code $\texttt{METISSE}$ integrated into $\texttt{COSMIC}$, and the detailed code $\texttt{POSYDON}$---on three single-metallicity populations of identical initial binaries, ensuring consistent choices in physical parameterizations where possible. Investigating the final population of merging binary black holes (BBHs) as a test case, we find stark differences in the properties, formation pathways, and progenitors across the three codes. In an initial population of one million binary stars at $0.01 Z_\odot$, each code results in $\sim 5,000-9,000$ BBHs that merge within a Hubble time. However, only one initial binary becomes a BBH merger in all three codes, and $\lesssim 14 \%$ of BBH progenitors consistently merge in two codes. Binaries that become BBH mergers in two codes often go through different evolutionary pathways and result in different final properties. In short, the codes are inconsistent in predicting BBH merger properties, even for identical initial binary systems. Our results highlight the need for systematic comparisons of BPS techniques, for a deeper understanding of physical and computational differences between BPS codes, and for caution in over-interpreting the results from any BPS code. (Abridged)

astro-ph.HE↗

arXiv2026

Twin Peaks: Resolving Features in the Binary Black Hole Mass Function with COSMIC-METISSE

Gravitational waves from inspiraling binary black holes (BBHs) provide insights into the lives and deaths of massive stars. Population synthesis allows us to model these binaries through isolated binary evolution, but its predictive power is limited by difficulties in varying the stellar models and their associated uncertainties. We present a new grid of stellar tracks computed with the open-source stellar evolution code MESA, spanning metallicities $10^{-3} \le Z/Z_{\odot} \le 7$. We vary two stellar physics parameters: wind-driven mass loss and the convective boundary mixing (CBM) mechanism. We pair these models with the Method of Interpolation for Single Stellar Evolution (METISSE) and binary population synthesis code COSMIC to obtain synthetic populations of merging BBHs in the local Universe. We find a maximum in the primary mass spectrum near $10M_\odot$ which in most model variations is composed of two sub-populations at $\approx8M_{\odot}$ and $\approx13 M_\odot$, with the higher-mass population dominated by BBHs whose progenitors underwent a mass ratio reversal (MRR). This population also suggests an anticorrelation between higher primary masses and mass ratio, as BBHs with $m_1\gtrapprox10M_\odot$ preferentially undergo MRR and prefer a final mass ratio of $q\approx0.7$. However, the location and relative strength of these two sub-populations is sensitive to our assumed stellar physics: varying both the wind and CBM treatments can merge the MRR and non-MRR populations into a single peak near $9M_\odot$. Variations in our stellar tracks, especially CBM, lead to a factor of $\approx6$ difference in the rate, primarily due to modulation of the common envelope formation channel.

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arXiv2026

A Long Period Stellar-Mass Black Hole Binary in $\omega$ Centauri

Modern simulations of stellar dynamics in globular clusters peg a dominant role for stellar-mass black holes, but direct evidence for black holes in clusters remains limited. We present the discovery of an astrometric stellar-mass black hole--main sequence star binary in $\omega$ Centauri, the most massive Galactic globular cluster, using Hubble Space Telescope data from the oMEGACat project and additional JWST data that span a total of 23 years. The luminous companion to the black hole is a main-sequence turnoff star, and has a period of $94^{+63}_{-42}$ years, a semi-major axis of $31^{+15}_{-12}$ AU, and an eccentricity of $e=0.72^{+0.08}_{-0.13}$. Since we observe the binary during periastron, the mass of the black hole is well-constrained even though we only observe a partial orbit: the inferred black hole mass is $4.46^{+1.22}_{-1.01}$ M$_\odot$. We call this black hole oMEGACat BH-2. This is the first astrometric discovery of a stellar-mass black hole in a globular cluster, and is the longest period black hole binary system yet discovered. The low mass of this black hole is perhaps surprising given the low metallicity of the cluster, and shows that at least some low-mass black holes form at metallicity $Z<10^{-3}$. We find that the binary is almost certainly dynamically formed and is soft, with an expected binary disruption timescale of $\sim$800 Myr. While the total number of black hole binaries in $\omega$ Centauri is uncertain, we show that existing surveys only cover a small area of parameter space, and that the presence of additional detectable black hole binaries is likely.

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arXiv2026

Modeling Globular Cluster Stellar Streams with a Basis-Expansion N-body Code

Globular cluster stellar streams probe galaxy-formation processes and can potentially reveal the distribution of dark matter in galaxies. In many theoretical studies, streams are modeled with particle-spray or direct N-body codes. But particle-spray methods abstract away the internal dynamics of the progenitor by making strong assumptions about the escape physics, while direct N-body is prohibitively expensive for realistic (N>10^5) systems. In this paper, we present the stream-modeling capabilities of KRIOS, a new basis-expansion N-body code for collisional stellar dynamics, that bridges this runtime vs. accuracy gap. We show that KRIOS reproduces NBODY6++GPU cluster models, and their associated streams, more accurately than particle spray in a fraction of the NBODY6++GPU wall-clock time. We then compare KRIOS to various particle-spray methods on 10 orbits similar to known Milky Way streams. The morphology and kinematics of these streams most disagree when the progenitor is tightly bound to the host, as these systems are often subject to stronger tidal forces. Finally, we discuss which elements of the progenitor physics are most important for modeling stellar streams and how these might be incorporated into particle-spray methods.

astro-ph.GA↗

arXiv2025

Breaking Down the $\textsf{CosmoGEMS}$: Toward Modeling and Understanding Globular Cluster Stellar Streams in a Fully Cosmological Context

Next-generation surveys are expected to uncover thousands of globular cluster (GC) stellar streams, motivating the need for a theoretical framework that produces realistic GC streams in a fully cosmological, Milky Way-like environment. We present $\textsf{CosmoGEMS}$, a star-by-star cosmological GC stream framework that self-consistently links small-scale cluster physics with large-scale Galactic dynamics. The initial phase-space positions of stream stars are informed by post-processed GC populations within the FIRE cosmological simulation. Escaped stars are orbit-integrated from their time of escape to the present day in a time-evolving Galactic potential extracted from the same simulation using a basis function expansion. We explore two example streams on different orbits. One forms a long, thin stream with a velocity dispersion consistent with Milky Way GC streams. However, it exhibits a clump and orbital-phase-dependent misalignments due to the evolving potential. The other stream develops both a thin component and a diffuse, shell-like structure, similar to features observed in streams like Jhelum. These results highlight the power of fully cosmological models in producing realistic stream morphologies and kinematics. Unlike idealized simulations, our models naturally incorporate time-dependent changes in the progenitor's orbit, including orbital plane evolution, which significantly affects stream structure. This challenges common assumptions in stream-finding algorithms and interpretation. $\textsf{CosmoGEMS}$ provides a key step toward connecting future stellar stream observations with the physics of globular cluster evolution and hierarchical galaxy formation in a cosmological context.

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arXiv2025

Growing the Intermediate-mass Black Hole in Omega Centauri

The recent detection of fast-moving stars in the core of Omega Centauri ($\omega$ Cen), the most massive globular cluster (GC) in the Milky Way, has provided strong evidence for the presence of an intermediate-mass black hole (IMBH). As $\omega$ Cen, is likely the accreted nucleus of a dwarf galaxy, this IMBH also represents a unique opportunity to study BH seeding mechanisms and their potential role in the formation of supermassive BHs. We present Monte Carlo $N$-body models of $\omega$ Cen with detailed treatments for the loss cone dynamics involving stars, binaries, and compact objects. Starting with BH seeds of $500-5000 \, M_{\odot}$ (consistent with runaway collisions of massive stars), our cluster models grow IMBHs with masses of $\sim50{,}000 \, M_{\odot}$ after 12 Gyr, while successfully reproducing the present-day surface brightness and velocity dispersion profiles of $\omega$ Cen. We find a population of fast stars similar to those observed in the core of $\omega$ Cen, with the fastest stars originating from binaries that were tidally disrupted by the IMBH. The IMBH growth is primarily driven by mergers with $30-40 \, M_{\odot}$ BHs, suggesting a present-day IMBH-BH merger rate of $\sim(4-8)\times10^{-8}~\rm{yr}^{-1}$ in $\omega$ Cen-like GCs. Our models also predict a similar rate of tidal disruption events ($\sim5\times10^{-8}~\rm{yr}^{-1}$) which, depending on the frequency of $\omega$ Cen-like GCs per galaxy, may represent anywhere from $0.1\%$ to $10\%$ of the observed TDE rate.

astro-ph.HE↗

arXiv2025

KRIOS: A new basis-expansion $N$-body code for collisional stellar dynamics

The gravitational $N$-body problem is a nearly universal problem in astrophysics which, despite its deceptive simplicity, still presents a significant computational challenge. For collisional systems such as dense star clusters, the need to resolve individual encounters between $N$ stars makes the direct summation of forces - with quadratic complexity - almost infeasible for systems with $N\gtrsim 10^6$ particles over many relaxation times. At the same time, the most common Monte Carlo $N$-body algorithm - that of H\'enon - assumes the cluster to be spherically symmetric. This greatly limits the study of many important features of star clusters, including triaxiality, rotation, and the production of tidal debris. In this paper, we present a new hybrid code, KRIOS, that combines 3D collisionless relaxation using an adaptive self-consistent field method with collisional dynamics handled via H\'enon's method. We demonstrate that KRIOS can accurately model the long-term evolution of clusters and provide its complete phase-space information over many relaxation times. As a test of our new code, we present detailed comparisons to well-known results from stellar dynamics: (i) the collisional evolution of a family of Plummer spheres with varying anisotropy and rotation to core collapse, and (ii) the emergence of the radial-orbit instability in radially anisotropic star clusters, including its non-spherical effects.

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arXiv2025

Great Balls of FIRE IV. The contribution of massive star clusters to the astrophysical population of merging binary black holes

The detection of over a hundred gravitational wave signals from double compacts objects have confirmed the existence of such binaries with tight orbits. Two main formation channels are generally considered to explain the formation of these merging binary black holes (BBHs): the isolated evolution of stellar binaries, and the dynamical assembly in dense environments, namely star clusters. Although their relative contributions remain unclear, several analyses indicate that the detected BBH mergers probably originate from a mixture of these two distinct scenarios. We study the formation of massive star clusters across time and at a cosmological scale to estimate the contribution of these dense stellar structures to the overall population of BBH mergers. To this end, we propose three different models of massive star cluster formation based on results obtained with zoom-in simulations of individual galaxies. We apply these models to a large sample of realistic galaxies identified in the $(22.1\ \mathrm{Mpc})^3$ cosmological volume simulation \firebox. Each galaxy in this simulation has a unique star formation rate, with its own history of halo mergers and metallicity evolution. Combined with predictions obtained with the Cluster Monte Carlo code for stellar dynamics, we are able to estimate populations of dynamically formed BBHs in a collection of realistic galaxies. Across our three models, we infer a local merger rate of BBHs formed in massive star clusters consistently in the range $1-10\ \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$. Compared with the local BBH merger rate inferred by the LIGO-Virgo-KAGRA Collaboration (in the range $17.9-44\ \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$ at $z=0.2$), this could potentially represent up to half of all BBH mergers in the nearby Universe. This shows the importance of this formation channel in the astrophysical production of merging BBHs.

astro-ph.GA↗

arXiv2025

Realistic predictions for Gaia black hole discoveries: comparison of isolated binary and dynamical formation models

Astrometry from Gaia has enabled discovery of three dormant black holes (BHs) in au-scale binaries. Numerous models have been proposed to explain their formation, including several that have forecasted Gaia detections. However, previous works have used simplified detectability metrics that do not capture key elements of the Gaia astrometric orbit selection function. We apply a realistic forward-model of Gaia astrometric orbit catalogs to BH binary populations generated through (a) isolated binary evolution (IBE) and (b) dynamical formation in star clusters. For both formation channels, we analyze binary populations in a simulated Milky Way-like galaxy with a realistic metallicity-dependent star formation history and 3D dust map. We generate epoch astrometry for each binary from the Gaia scanning law and fit it with the cascade of astrometric models used in Gaia DR3. The IBE model of Chawla et al. (2022) predicts that no BH binaries should have been detected in DR3 and thus significantly underpredicts the formation rate of Gaia BHs. In contrast, the dynamical model of Di Carlo et al. (2024) overpredicts the number of BHs receiving DR3 orbital solutions by a factor of $\sim$8. The two models predict very different orbital period distributions, with the IBE model predicting only binaries that avoided common envelope evolution and have $P_{\text{orb}} \gtrsim 2,000$ d to be detectable, and the dynamical formation model predicting a period distribution that is roughly log-uniform. Adopting the dynamical channel as a fiducial model and rescaling by a factor of 1/8 to match DR3, we predict that $\sim$30 BH binaries will be detected in Gaia DR4, representing $\sim0.1\%$ of Milky Way BHs with luminous companions in au-scale orbits.

astro-ph.GA↗

arXiv2024

From Young Massive Clusters to Old Globular Clusters: Density Profile Evolution and IMBH Formation

The surface brightness profiles of globular clusters are conventionally described with the well-known King profile. However, observations of young massive clusters (YMCs) in the local Universe suggest that they are better fit by simple models with flat central cores and simple power-law densities in their outer regions (such as the Elson-Fall-Freeman, or EFF, profile). Depending on their initial central density, YMCs may also facilitate large numbers of stellar collisions, potentially creating very massive stars that will directly collapse to intermediate-mass black holes (IMBHs). Using Monte Carlo $N$-body models of YMCs, we show that EFF-profile clusters transform to Wilson or King profiles through natural dynamical evolution, but that their final $W_0$ parameters do not strongly correlate to their initial concentrations. In the densest YMCs, runaway stellar mergers can produce stars that collapse into IMBHs, with their final masses depending on the treatment of the giant star envelopes during collisions. If a common-envelope prescription is assumed, where the envelope is partially or entirely lost, stars form with masses up to $824\,M_{\odot}$, collapsing into IMBHs of $232\,M_{\odot}$. Alternatively, if no mass loss is assumed, stars as massive as $4000\,M_{\odot}$ can form, collapsing into IMBHs of $\sim 4000\,M_{\odot}$. In doing so, these runaway collisions also deplete the clusters of their primordial massive stars, reducing the number of stellar-mass BHs by as much as $\sim$ 40%. This depletion will accelerate the core collapse, suggesting that the process of IMBH formation itself may produce the high densities observed in some core-collapsed clusters.

astro-ph.GA↗

arXiv2024

Runaway and Hypervelocity Stars from Compact Object Encounters in Globular Clusters

The dense environments in the cores of globular clusters (GCs) facilitate many strong dynamical encounters among stellar objects. These encounters have been shown capable of ejecting stars from the host GC, whereupon they become runaway stars, or hypervelocity stars if unbound to the galactic potential. We study high speed stellar ejecta originating from GCs by using Monte Carlo N-body models, in particular focusing on binary-single encounters involving compact objects. We pair our model-discriminated populations with observational catalogs of Milky Way GCs to compose a present-day galactic population of stellar ejecta. We find that these kinds of encounters can accelerate stars to velocities in excess of 2000 km/s, to speeds beyond the previously predicted limits for ejecta from star-only encounters and in the same regime of galactic center ejections. However, the same ejections can only account for 1.5-20% of the total population of stellar runaways, and only 0.0001-1% of hypervelocity stars, with similar relative rates found for runaway white dwarfs. We also provide credible regions for ejecta from 149 Milky Way GCs, which we hope will be useful as supplementary evidence when pairing runaway stars with origin GCs.

astro-ph.GA↗

arXiv2023

Stellar Black Holes and Compact Stellar Remnants

The recent observations of gravitational waves (GWs) by the LIGO-Virgo-KAGRA collaboration (LVK) have provided a new opportunity for studying our Universe. By detecting several merging events of black holes (BHs), LVK has spurred the astronomical community to improve theoretical models of single, binary, and multiple star evolution in order to better understand the formation of binary black hole (BBH) systems and interpret their observed properties. The final BBH system configuration before the merger depends on several processes, including those related to the evolution of the inner stellar structure and those due to the interaction with the companion and the environment (such as in stellar clusters). This chapter provides a summary of the formation scenarios of stellar BHs in single, binary, and multiple systems. We review all the important physical processes that affect the formation of BHs and discuss the methodologies used to detect these elusive objects and constrain their properties.

astro-ph.SR↗

arXiv2023

Great Balls of FIRE III: Modeling Black Hole Mergers from Massive Star Clusters in Simulations of Galaxies

After the nearly hundred gravitational-wave detections reported by the LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of merging binary black holes (BBHs) remains open. The two main formation channels generally considered are from isolated field binaries or via dynamical assembly in dense star clusters. Here, we focus on understanding the dynamical formation of merging BBHs within massive clusters in galaxies of different masses. To this end, we apply a new framework to consistently model the formation and evolution of massive star clusters in zoom-in cosmological simulations of galaxies. Each simulation, taken from the FIRE project, provides a realistic star formation environment with a unique star formation history and hosts realistic giant molecular clouds that constitute the birthplace of star clusters. Combined with the code for star cluster evolution CMC, we are able to produce populations of dynamically formed merging BBHs across cosmic time in different environments. As the most massive star clusters preferentially form in dense massive clouds of gas, we find that, despite their low metallicities favourable to the creation of black holes, low-mass galaxies contain few massive clusters and therefore have a limited contribution to the global production of dynamically formed merging BBHs. Furthermore, we find that massive clusters can host hierarchical BBH mergers with clear identifiable physical properties. Looking at the evolution of the BBH merger rate in different galaxies, we find strong correlations between BBH mergers and the most extreme episodes of star formation. Finally, we discuss the implications for future LIGO-Virgo-KAGRA gravitational wave observations.

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arXiv2023

Modelling stellar evolution in mass-transferring binaries and gravitational-wave progenitors with METISSE

Massive binaries are vital sources of various transient processes, including gravitational-wave mergers. However, large uncertainties in the evolution of massive stars, both physical and numerical, present a major challenge to the understanding of their binary evolution. In this paper, we upgrade our interpolation-based stellar evolution code METISSE to include the effects of mass changes, such as binary mass transfer or wind-driven mass loss, not already included within the input stellar tracks. METISSE's implementation of mass loss (applied to tracks without mass loss) shows excellent agreement with the SSE fitting formulae and with detailed MESA tracks, except in cases where the mass transfer is too rapid for the star to maintain equilibrium. We use this updated version of METISSE within the binary population synthesis code BSE to demonstrate the impact of varying stellar evolution parameters, particularly core overshooting, on the evolution of a massive (25M$_\odot$ and 15M$_\odot$) binary system with an orbital period of 1800 days. Depending on the input tracks, we find that the binary system can form a binary black hole or a black hole-neutron star system, with primary(secondary) remnant masses ranging between 4.47(1.36)M$_\odot$ and 12.30(10.89)M$_\odot$, and orbital periods ranging from 6 days to the binary becoming unbound. Extending this analysis to a population of isolated binaries uniformly distributed in mass and orbital period, we show that the input stellar models play an important role in determining which regions of the binary parameter space can produce compact binary mergers, paving the way for predictions for current and future gravitational-wave observatories.

astro-ph.SR↗

arXiv2023

Young Star Clusters Dominate the Production of Detached Black Hole-Star Binaries

The recent discovery of two detached black hole-star (BH-star) binaries from Gaia's third data release has sparkled interest in understanding the formation mechanisms of these systems. We investigate the formation of these systems by dynamical processes in young open star clusters (SCs) and via isolated binary (IB) evolution, using a combination of direct $N$-body models and population synthesis simulations. By comparing dynamical and isolated systems created using the same model of binary stellar evolution, we find that dynamical formation in SCs is nearly 40 times as efficient per unit of star formation at producing BH-star binaries compared to IB evolution. We expand this analysis to the full Milky Way (MW) using a FIRE-2 hydrodynamical simulation of a MW-mass galaxy. Even assuming that only $10\%$ of star formation produces SCs with masses $> 1000\,\mathrm{M_{\odot}}$, we find that the MW contains $\sim 2 \times 10^5$ BH-star systems, with approximately 4 out of every 5 systems being formed dynamically. Many of these dynamically-formed systems have larger orbital periods, eccentricities, and black hole masses than their isolated counterparts. For binaries older than 100 Myr, we show that any detectable system with $e\gtrsim0.5$ or $M_{\rm BH}\gtrsim 10\,\mathrm{M_{\odot}}$ can only be formed through dynamical processes. Our MW model predicts between 61 and 210 such detections from the complete DR4 Gaia catalog, with the majority of systems being dynamically formed in massive and metal-rich SCs. Finally, we compare our populations to the recently discovered Gaia BH1 and Gaia BH2, and conclude that the dynamical scenario is the most favorable formation pathway for both systems.

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arXiv2023

Constraints on the Cosmological Coupling of Black Holes from the Globular Cluster NGC 3201

Globular clusters are among the oldest stellar populations in the Milky Way; consequently, they also host some of the oldest known stellar-mass black holes, providing insight into black hole formation and evolution in the early ($z\gtrsim 2$) Universe. Recent observations of supermassive black holes in elliptical galaxies have been invoked to suggest the possibility of a cosmological coupling between astrophysical black holes and the surrounding expanding Universe, offering a mechanism for black holes to grow over cosmic time, and potentially explaining the origin of dark energy. In this paper, I show that the mass functions of the two radial velocity black hole candidates in NGC 3201 place strong constraints on the cosmologically-coupled growth of black holes. In particular, the amount of coupling required to explain the origin of dark energy would either require both NGC 3201 black holes to be nearly face on (a configuration with probability of at most $10^{-4}$) or one of the BHs would need to have formed with a mass below that of the most massive neutron stars ($2.2M_{\odot}$). This emphasizes that these and other detached black hole-star binaries can serve not only as laboratories for compact object and binary astrophysics, but as constraints on the long-term evolution of astrophysical black holes.

astro-ph.CO↗

arXiv2023

Great Balls of FIRE II: The evolution and destruction of star clusters across cosmic time in a Milky Way-mass galaxy

The current generation of galaxy simulations can resolve individual giant molecular clouds, the progenitors of dense star clusters. But the evolutionary fate of these young massive clusters, and whether they can become the old globular clusters (GCs) observed in many galaxies, is determined by a complex interplay of internal dynamical processes and external galactic effects. We present the first star-by-star $N$-body models of massive ($N\sim10^5-10^7$) star clusters formed in a FIRE-2 MHD simulation of a Milky Way-mass galaxy, with the relevant initial conditions and tidal forces extracted from the cosmological simulation. We select 895 ($\sim 30\%$) of the YMCs with $ > 6\times10^4M_{\odot}$ from Grudić et al.~2022 and integrate them to $z=0$ using the Cluster Monte Carlo Code, \texttt{CMC}. This procedure predicts a MW-like system with 148 GCs, predominantly formed during the early, bursty mode of star formation. Our GCs are younger, less massive, and more core-collapsed than clusters in the Milky Way or M31. This results from the assembly history and age-metallicity relationship of the host galaxy: younger clusters are preferentially born in stronger tidal fields and initially retain fewer stellar-mass black holes, causing them to lose mass faster and reach core collapse sooner than older GCs. Our results suggest that the masses and core/half-light radii of GCs are shaped not only by internal dynamical processes, but also by the specific evolutionary history of their host galaxies. These results emphasize that $N$-body studies with realistic stellar physics are crucial to understanding the evolution and present-day properties of GC systems.

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arXiv2022

Great Balls of FIRE I: The formation of star clusters across cosmic time in a Milky Way-mass galaxy

The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium (ISM) conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modeling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 MHD galaxy simulation onto a cluster population according to a GMC-scale cluster formation model calibrated to higher-resolution simulations, obtaining detailed properties of the galaxy's star clusters in mass, metallicity, space, and time. We find $\sim 10\%$ of all stars formed in the galaxy originate in gravitationally-bound clusters overall, and this fraction increases in regions with elevated $Σ_{\rm gas}$ and $Σ_{\rm SFR}$, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies -- no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as $7\times 10^6 M_\odot$ form in massive, dense clouds with high star formation efficiency. The initial mass-radius relation of young star clusters is consistent with an environmentally-dependent 3D density that increases with $Σ_{\rm gas}$ and $Σ_{\rm SFR}$. The model does not reproduce the age and metallicity statistics of old ($>11\rm Gyr$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at $z>3$.

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