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Michael Y. Grudic

Publications and source records attributed to Michael Y. Grudic.

17 recordsLinked to original sources

Non-ideal MHD and protostellar feedback effects on disc formation and evolution in numerical simulations of star cluster formation

While recent surveys have resolved hundreds of nearby protostellar discs, numerical simulations assuming ideal magnetohydrodynamics (MHD) have historically struggled to achieve disc formation due to efficient angular momentum removal by magnetic torques. Non-ideal MHD effects, relevant at the low ionization fractions typical of molecular clouds, have been shown to reduce the effectiveness of magnetic braking and promote disc formation. In this work, we present the results from a suite of calculations following the gravitational collapse of 50 $M_{\odot}$ turbulent molecular cloud cores down to the formation and evolution of stellar systems and protostellar discs. We use the radiation-MHD code GIZMO including non-ideal MHD (Ohmic resistivity, ambipolar diffusion, and the Hall effect) and the STARFORGE numerical framework for modeling star formation and stellar feedback. We compare the effects of assuming ideal vs. non-ideal MHD and including sub-grid protostellar jet feedback on disc formation and evolution. Discs form in all of our models but are least massive in the model with ideal MHD and sub-grid jet feedback. Apart from the ideal MHD$+$jets model, we do not observe any significant differences in disc properties between the ideal and non-ideal MHD models; however, ideal MHD discs are embedded in smaller rotating envelopes. Disc sizes are in general agreement with those of observed discs. Jet feedback increases core fragmentation and reduces final stellar masses. Our results suggest that magnetic braking does not efficiently suppress disc formation, regardless of whether ideal or non-ideal MHD is assumed, under the dynamical conditions in which multiple stellar systems form.

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The Evolution of Star-Forming Gas in STARFORGE: From Clouds, to Cores, to Stars

Star formation occurs within dense regions of giant molecular clouds (GMCs), however, exactly how gas collects and evolves to form individual stars and what role dense cores play remains unclear. We use the Lagrangian cell information in the STARFORGE simulation suite to track star-forming gas in three GMCs with varying magnetic field strengths. We find that, once a protostar forms, the lifetime of the unaccreted gas correlates with the final stellar mass, where low-mass stars ($M_*$ < 0.5 M$_\odot$) accrete for 0.5-0.6 Myr from a relatively local reservoir of gas, and high-mass stars ($M_*$ > 2 M$_\odot$) accrete over 3.3-4.7 Myr from a much larger volume. Although the protostellar accretion time increases weakly with magnetic field strength, the accreting gas radii, velocity dispersions, virial parameters, and magnetic energy ratios are largely insensitive to the global cloud properties. At the time of protostar formation, the unaccreted gas exhibits linewidth-size and mass-size relations characteristic of turbulently regulated, isothermal dense cores, following $σ_v \propto R^{0.47-0.55}$ and $M \propto R^{1.0-1.1}$, respectively. Low- and intermediate-mass stars undergo relatively continuous accretion and their accretion histories are well-fit by either isothermal sphere, turbulent core, or competitive accretion models, where no one model fits all masses. However, many high-mass stars experience intermittent accretion and their accretion histories are not well-fit by any of these models. While the distribution of accreting gas is more extended than typically-defined dense cores, the physical properties and structure of the star-forming gas resemble those of observed cores and are largely regulated by turbulence and feedback.

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The GHOSDT Simulations: II. Missing H$_2$ in Simulations of a Self-Regulated Interstellar Medium

Observations in the Galaxy and nearby spirals have established that the HI-to-H$_2$ transition at solar metallicity occurs at gas weight of $P_{\rm DE}/k_B\approx 10^4 \ \rm K \ cm ^{-3}$, similar to solar neighbourhood conditions. Even so, state-of-the-art models of a self-regulated interstellar medium underproduce the molecular fraction ($R_{\rm mol} \equiv M_{{\rm H}_2}/M_{HI}$) at solar neighbourhood conditions by a factor of $\approx2-4$. We use the GHOSDT suite of simulations at a mass resolution range of $100-0.25\ M_{\odot}$ (effective spatial resolution range of $\sim 20-0.05\ \rm pc$) run for 500 Myr to show how this problem is affected by modeling choices such as the inclusion of photoionizing radiation, assumed supernova energy, numerical resolution, inclusion of magnetic fields, and including a model for sub-grid clumping. We find that $R_{\rm mol}$ is not converged even at a resolution of 1 $M_{\odot}$, with $R_{\rm mol}$ increasing by a factor of 2 when resolution is improved from 10 to $1\ M_{\odot}$. Models excluding either photoionization or magnetic fields result in a factor 2 reduction in $R_{\rm mol}$. The only model that agrees with the observed value of $R_{\rm mol}$ includes our sub-grid clumping model, which enhances $R_{\rm mol}$ by a factor of $\sim3$ compared with our fiducial model. This increases the time-averaged $R_{\rm mol}$ to $0.25$, in agreement with the Solar circle value, and closer to the observed median value of $0.42$ in regions comparable to the solar neighbourhood in nearby spirals. Our findings show that small-scale clumping in the ISM plays a significant role in H$_2$ formation even in high-resolution numerical simulations.

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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.

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The Life and Times of Star-Forming Cores: an Analysis of Dense Gas in the STARFORGE Simulations

Dense gas in molecular clouds is an important signature of ongoing and future star formation. We identify and track dense cores in the STARFORGE simulations, following the core evolution from birth through dispersal by stellar feedback for typical Milky Way cloud conditions. Only $\sim$8% of cores host protostars, and most disperse before forming stars. The median starless and protostellar core lifetimes are $\sim 0.5-0.6$ Myr and $\sim0.8-1.1$ Myr, respectively, where the protostellar phase lasts $\sim 0.1^{+0.1}_{-0.05}$ Myr. While core evolution is stochastic, we find that virial ratios and linewidths decline in prestellar cores, coincident with turbulent decay. Collapse occurs over $\sim 0.1$ Myr, once the central density exceeds $\gtrsim 10^6$cm$^{-3}$. Starless cores, only, follow linewidth-size and mass-size relations, $σ\propto R^{0.3}$ and $M \propto R^1$. The core median mass, radius, and velocity dispersion scale weakly with the cloud magnetic field strength. We cluster the core properties and find that protostellar cores have $>80$% likelihood of belonging to three particular groups that are characterized by high central densities, compact radii, and lower virial parameters. Overall, core evolution appears to be universally set by the interplay of gravity and magnetized turbulence, while stellar feedback dictates protostellar core properties and sets the protostellar phase lifetime.

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FORGE'd in FIRE III: The IMF in Quasar Accretion Disks from STARFORGE

Recently, we demonstrated self-consistent formation of strongly-magnetized quasar accretion disks (QADs) from cosmological radiation-magnetohydrodynamic-thermochemical galaxy-star formation simulations, including the full STARFORGE physics shown previously to produce a reasonable IMF under typical ISM conditions. Here we study star formation and the stellar IMF in QADs, on scales from 100 au to 10 pc from the SMBH. We show it is critical to include physics often previously neglected, including magnetic fields, radiation, and (proto)stellar feedback. Closer to the SMBH, star formation is suppressed, but the (rare) stars that do form exhibit top-heavy IMFs. Stars can form only in special locations (e.g. magnetic field switches) in the outer QAD. Protostars accrete their natal cores rapidly but then dynamically decouple from the gas and wander, ceasing accretion on timescales ~100 yr. Their jets control initial core accretion, but the ejecta are swept up into the larger-scale QAD flow without much dynamical effect. The strong tidal environment strongly suppresses common-core multiplicity. The IMF shape depends sensitively on un-resolved dynamics of protostellar disks (PSDs), as the global dynamical times can become incredibly short ($\ll$ yr) and tidal fields are incredibly strong, so whether PSDs can efficiently transport angular momentum or fragment catastrophically at $\lesssim 10$ au scales requires novel PSD simulations to properly address. Most analytic IMF models and analogies with planet formation in PSDs fail qualitatively to explain the simulation IMFs, though we discuss a couple of viable models.

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Suppressed Cosmic Ray Energy Densities in Molecular Clouds From Streaming Instability-Regulated Transport

Cosmic rays (CRs) are the primary driver of ionization in star forming molecular clouds (MCs). Despite their potential impacts on gas dynamics and chemistry, no simulations of star cluster formation following the creation of individual stars have included explicit cosmic ray transport (CRT) to date. We conduct the first numerical simulations following the collapse of a $2000 M_{\odot}$ MC and the subsequent star formation including CRT using the STARFORGE framework implemented in the GIZMO code. We show that when CR-transport is streaming-dominated, the CR energy in the cloud is strongly attenuated due to energy losses from the streaming instability. Consequently, in a Milky Way like environment the median CR ionization rate (CRIR) in the cloud is low ($ ζ\lesssim 2 \times 10^{-19} \rm s^{-1}$) during the main star forming epoch of the calculation and the impact of CRs on the star formation in the cloud is limited. However, in high-CR environments, the CR distribution in the cloud is elevated ($ζ\lesssim 6 \times 10^{-18}$), and the relatively higher CR pressure outside the cloud causes slightly earlier cloud collapse and increases the star formation efficiency (SFE) by $50 \%$ to $\sim 13 \%$. The initial mass function (IMF) is similar in all cases except with possible variations in a high-CR environment. Further studies are needed to explain the range of ionization rates observed in MCs and explore star formation in extreme CR environments.

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FORGE'd in FIRE: Resolving the End of Star Formation and Structure of AGN Accretion Disks from Cosmological Initial Conditions

It has recently become possible to zoom-in from cosmological to sub-pc scales in galaxy simulations to follow accretion onto supermassive black holes (SMBHs). However, at some point the approximations used on ISM scales (e.g. optically-thin cooling and stellar-population-integrated star formation [SF] and feedback [FB]) break down. We therefore present the first cosmological radiation-magnetohydrodynamic (RMHD) simulation which self-consistently combines the FIRE physics (relevant on galactic/ISM scales where SF/FB are ensemble-averaged) and STARFORGE physics (relevant on small scales where we track individual (proto)stellar formation and evolution), together with explicit RMHD (including non-ideal MHD and multi-band M1-RHD) which self-consistently treats both optically-thick and thin regimes. This allows us to span scales from ~100 Mpc down to <100 au (~300 Schwarzschild radii) around a SMBH at a time where it accretes as a bright quasar, in a single simulation. We show that accretion rates up to $\sim 10-100\,{\rm M_{\odot}\,yr^{-1}}$ can be sustained into the accretion disk at $\ll 10^{3}\,R_{\rm schw}$, with gravitational torques between stars and gas dominating on sub-kpc scales until star formation is shut down on sub-pc scales by a combination of optical depth to cooling and strong magnetic fields. There is an intermediate-scale, flux-frozen disk which is gravitoturbulent and stabilized by magnetic pressure sustaining strong turbulence and inflow with persistent spiral modes. In this paper we focus on how gas gets into the small-scale disk, and how star formation is efficiently suppressed.

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FORGE'd in FIRE II: The Formation of Magnetically-Dominated Quasar Accretion Disks from Cosmological Initial Conditions

In a companion paper, we reported the self-consistent formation of quasar accretion disks with inflow rates $\sim 10\,{\rm M_{\odot}\,yr^{-1}}$ down to <300 Schwarzschild radii from cosmological radiation-magneto-thermochemical-hydrodynamical galaxy and star formation simulations. We see the formation of a well-defined, steady-state accretion disk which is stable against star formation at sub-pc scales. The disks are optically thick, with radiative cooling balancing accretion, but with properties that are distinct from those assumed in most previous accretion disk models. The pressure is strongly dominated by (primarily toroidal) magnetic fields, with a plasma $β\sim 10^{-4}$ even in the disk midplane. They are qualitatively distinct from magnetically elevated or arrested disks. The disks are strongly turbulent, with trans-Alfvenic and highly super-sonic turbulence, and balance this via a cooling time that is short compared to the disk dynamical time, and can sustain highly super-Eddington accretion rates. Their surface and 3D densities at $\sim 10^{3}-10^{5}$ gravitational radii are much lower than in a Shakura-Sunyaev disk, with important implications for their thermo-chemistry and stability. We show how the magnetic field strengths and geometries arise from rapid advection of flux with the inflow from much weaker galaxy-scale fields in these 'flux-frozen' disks, and how this stabilizes the disk and gives rise to efficient torques. Re-simulating without magnetic fields produces catastrophic fragmentation with a vastly smaller, lower-$\dot{M}$ Shakura-Sunyaev-like disk.

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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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What Causes The Formation of Disks and End of Bursty Star Formation?

As they grow, galaxies can transition from irregular/spheroidal with 'bursty' star formation histories (SFHs), to disky with smooth SFHs. But even in simulations, the direct physical cause of such transitions remains unclear. We therefore explore this in a large suite of numerical experiments re-running portions of cosmological simulations with widely varied physics, further validated with existing FIRE simulations. We show that gas supply, cooling/thermodynamics, star formation model, Toomre scale, galaxy dynamical times, and feedback properties do not have a direct causal effect on these transitions. Rather, both the formation of disks and cessation of bursty star formation are driven by the gravitational potential, but in different ways. Disk formation is promoted when the mass profile becomes sufficiently centrally-concentrated in shape (relative to circularization radii): we show that this provides a well-defined dynamical center, ceases to support the global 'breathing modes' which can persist indefinitely in less-concentrated profiles and efficiently destroy disks, promotes orbit mixing to form a coherent angular momentum, and stabilizes the disk. Smooth SF is promoted by the potential or escape velocity (not circular velocity) becoming sufficiently large at the radii of star formation that cool, mass-loaded (momentum-conserving) outflows are trapped/confined near the galaxy, as opposed to escaping after bursts. We discuss the detailed physics, how these conditions arise in cosmological contexts, their relation to other correlated phenomena (e.g. inner halo virialization, vertical disk 'settling'), and observations.

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Novel Conservative Methods for Adaptive Force Softening in Collisionless and Multi-Species N-Body Simulations

Modeling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve adaptively, in any high-dynamic range simulation, but this poses unique challenges of consistency, conservation, and accuracy, especially in multi-physics simulations where species with different softening laws may interact. We therefore derive a generalized form of the energy-and-momentum conserving gravitational equations of motion, applicable to arbitrary rules used to determine the force softening, together with consistent associated timestep criteria, interaction terms between species with different softening laws, and arbitrary maximum/minimum softenings. We also derive new methods to maintain better accuracy and conservation when symmetrizing forces between particles. We review and extend previously-discussed adaptive softening schemes based on the local neighbor particle density, and present several new schemes for scaling the softening with properties of the gravitational field, i.e. the potential or acceleration or tidal tensor. We show that the tidal softening scheme not only represents a physically-motivated, translation and Galilean invariant and equivalence-principle respecting (and therefore conservative) method, but imposes negligible timestep or other computational penalties, ensures that pairwise two-body scattering is small compared to smooth background forces, and can resolve outstanding challenges in properly capturing tidal disruption of substructures (minimizing artificial destruction) while also avoiding excessive N-body heating. We make all of this public in the GIZMO code.

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Why do Black Holes Trace Bulges (& Central Surface Densities), Instead of Galaxies as a Whole?

Previous studies of fueling black holes (BHs) in galactic nuclei have argued (on scales ~0.01-1000pc) accretion is dynamical with inflow rates $\dot{M}\simη\,M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass $M_{\rm gas}$, dynamical time $t_{\rm dyn}$, and some $η$. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency $f_{\rm wind}=M_{\rm ejected}/M_{\rm total}$ scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim\bar{a}_{\rm grav}/\langle\dot{p}/m_{\ast}\rangle\sim Σ_{\rm eff}/Σ_{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\,M_{\rm tot}(<r)/r^{2}$ and $\langle\dot{p}/m_{\ast}\rangle$ is the momentum injection rate from young stars. Adopting this as the simplest correction for stellar feedback, $η\rightarrow η\,(1-f_{\rm wind})$, we show this provides a more accurate description of simulations with stellar feedback at low densities. This has immediate consequences, predicting e.g. the slope and normalization of the $M-σ$ and $M-M_{\rm bulge}$ relation, $L_{\rm AGN}-$SFR relations, and explanations for outliers in compact Es. Most strikingly, because star formation simulations show expulsion is efficient ($f_{\rm wind}\sim1$) below total-mass surface density $M_{\rm tot}/π\,r^{2}<Σ_{\rm crit}\sim3\times10^{9}\,M_{\odot}\,{\rm kpc^{-2}}$ (where $Σ_{\rm crit}=\langle\dot{p}/m_{\ast}\rangle/(π\,G)$), BH mass is predicted to specifically trace host galaxy properties above a critical surface brightness $Σ_{\rm crit}$ (B-band $μ_{\rm B}^{\rm crit}\sim 19\,{\rm mag\,arcsec^{-2}}$). This naturally explains why BH masses preferentially reflect bulge properties or central surface-densities ($Σ_{1\,{\rm kpc}}$), not 'total' galaxy properties.

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FIRE-3: Updated Stellar Evolution Models, Yields, & Microphysics and Fitting Functions for Applications in Galaxy Simulations

Increasingly, uncertainties in predictions from galaxy formation simulations (at sub-Milky Way masses) are dominated by uncertainties in stellar evolution inputs. In this paper, we present the full set of updates from the FIRE-2 version of the Feedback In Realistic Environments (FIRE) project code, to the next version, FIRE-3. While the transition from FIRE-1 to FIRE-2 focused on improving numerical methods, here we update the stellar evolution tracks used to determine stellar feedback inputs, e.g. stellar mass-loss (O/B and AGB), spectra (luminosities and ionization rates), and supernova rates (core-collapse and Ia), as well as detailed mass-dependent yields. We also update the low-temperature cooling and chemistry, to enable improved accuracy at $T \lesssim 10^{4}\,$K and densities $n\gg 1\,{\rm cm^{-3}}$, and the meta-galactic ionizing background. All of these synthesize newer empirical constraints on these quantities and updated stellar evolution and yield models from a number of groups, addressing different aspects of stellar evolution. To make the updated models as accessible as possible, we provide fitting functions for all of the relevant updated tracks, yields, etc, in a form specifically designed so they can be directly 'plugged in' to existing galaxy formation simulations. We also summarize the default FIRE-3 implementations of 'optional' physics, including spectrally-resolved cosmic rays and supermassive black hole growth and feedback.

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Radiative Stellar Feedback in Galaxy Formation: Methods and Physics

Radiative feedback (RFB) from stars plays a key role in galaxies, but remains poorly-understood. We explore this using high-resolution, multi-frequency radiation-hydrodynamics (RHD) simulations from the Feedback In Realistic Environments (FIRE) project. We study ultra-faint dwarf through Milky Way mass scales, including H+He photo-ionization; photo-electric, Lyman Werner, Compton, and dust heating; and single+multiple scattering radiation pressure (RP). We compare distinct numerical algorithms: ray-based LEBRON (exact when optically-thin) and moments-based M1 (exact when optically-thick). The most important RFB channels on galaxy scales are photo-ionization heating and single-scattering RP: in all galaxies, most ionizing/far-UV luminosity (~1/2 of lifetime-integrated bolometric) is absorbed. In dwarfs, the most important effect is photo-ionization heating from the UV background suppressing accretion. In MW-mass galaxies, meta-galactic backgrounds have negligible effects; but local photo-ionization and single-scattering RP contribute to regulating the galactic star formation efficiency and lowering central densities. Without some RFB (or other 'rapid' FB), resolved GMCs convert too-efficiently into stars, making galaxies dominated by hyper-dense, bound star clusters. This makes star formation more violent and 'bursty' when SNe explode in these hyper-clustered objects: thus, including RFB 'smoothes' SFHs. These conclusions are robust to RHD methods, but M1 produces somewhat stronger effects. Like in previous FIRE simulations, IR multiple-scattering is rare (negligible in dwarfs, ~10% of RP in massive galaxies): absorption occurs primarily in 'normal' GMCs with A_v~1.

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FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation

The Feedback In Realistic Environments (FIRE) project explores feedback in cosmological galaxy formation simulations. Previous FIRE simulations used an identical source code (FIRE-1) for consistency. Motivated by the development of more accurate numerics - including hydrodynamic solvers, gravitational softening, and supernova coupling algorithms - and exploration of new physics (e.g. magnetic fields), we introduce FIRE-2, an updated numerical implementation of FIRE physics for the GIZMO code. We run a suite of simulations and compare against FIRE-1: overall, FIRE-2 improvements do not qualitatively change galaxy-scale properties. We pursue an extensive study of numerics versus physics. Details of the star-formation algorithm, cooling physics, and chemistry have weak effects, provided that we include metal-line cooling and star formation occurs at higher-than-mean densities. We present new resolution criteria for high-resolution galaxy simulations. Most galaxy-scale properties are robust to numerics we test, provided: (1) Toomre masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved. Stellar masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followed by properties of winds and circum-galactic media (CGM). Central (~kpc) mass concentrations in massive (L*) galaxies are sensitive to numerics (via trapping/recycling of winds in hot halos). Multiple feedback mechanisms play key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels late star formation; radiative feedback suppresses accretion onto dwarfs and instantaneous star formation in disks. We provide all initial conditions and numerical algorithms used.

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Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.

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