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Philip F. Hopkins

Publications and source records attributed to Philip F. Hopkins.

At least 271 records · Page 15Linked to original sources

No Assembly Required: Mergers are Mostly Irrelevant for the Growth of Low-mass Dwarf Galaxies

We investigate the merger histories of isolated dwarf galaxies based on a suite of 15 high-resolution cosmological zoom-in simulations, all with masses of $M_{\rm halo} \approx 10^{10}\,{\rm M}_{\odot}$ (and M$_\star\sim10^5-10^7\,{\rm M}_{\odot}$) at $z=0$, from the Feedback in Realistic Environments (FIRE) project. The stellar populations of these dwarf galaxies at $z=0$ are formed essentially entirely "in situ": over 90$\%$ of the stellar mass is formed in the main progenitor in all but two cases, and all 15 of the galaxies have >70$\%$ of their stellar mass formed in situ. Virtually all galaxy mergers occur prior to $z\sim3$, meaning that accreted stellar populations are ancient. On average, our simulated dwarfs undergo 5 galaxy mergers in their lifetimes, with typical pre-merger galaxy mass ratios that are less than 1:10. This merger frequency is generally comparable to what has been found in dissipationless simulations when coupled with abundance matching. Two of the simulated dwarfs have a luminous satellite companion at $z=0$. These ultra-faint dwarfs lie at or below current detectability thresholds but are intriguing targets for next-generation facilities. The small contribution of accreted stars make it extremely difficult to discern the effects of mergers in the vast majority of dwarfs either photometrically or using resolved-star color-magnitude diagrams (CMDs). The important implication for near-field cosmology is that star formation histories of comparably massive galaxies derived from resolved CMDs should trace the build-up of stellar mass in one main system across cosmic time as opposed to reflecting the contributions of many individual star formation histories of merged dwarfs.

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The origin of the diverse morphologies and kinematics of Milky Way-mass galaxies in the FIRE-2 simulations

We use hydrodynamic cosmological zoom-in simulations from the FIRE project to explore the morphologies and kinematics of fifteen Milky Way (MW)-mass galaxies. Our sample ranges from compact, bulge-dominated systems with 90% of their stellar mass within 2.5 kpc to well-ordered disks that reach $\gtrsim15$ kpc. The gas in our galaxies always forms a thin, rotation-supported disk at $z=0$, with sizes primarily determined by the gas mass. For stars, we quantify kinematics and morphology both via the fraction of stars on disk-like orbits and with the radial extent of the stellar disk. In this mass range, stellar morphology and kinematics are poorly correlated with the properties of the halo available from dark matter-only simulations (halo merger history, spin, or formation time). They more strongly correlate with the gaseous histories of the galaxies: those that maintain a high gas mass in the disk after $z\sim1$ develop well-ordered stellar disks. The best predictor of morphology we identify is the spin of the gas in the halo at the time the galaxy formed 1/2 of its stars (i.e. the gas that builds the galaxy). High-$z$ mergers, before a hot halo emerges, produce some of the most massive bulges in the sample (from compact disks in gas-rich mergers), while later-forming bulges typically originate from internal processes, as satellites are stripped of gas before the galaxies merge. Moreover, most stars in $z=0$ MW-mass galaxies (even $z=0$ bulge stars) form in a disk: $\gtrsim$60-90% of stars begin their lives rotationally supported.

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Discrete Effects in Stellar Feedback: Individual Supernovae, Hypernovae, and IMF Sampling in Dwarf Galaxies

Using high-resolution simulations from the FIRE-2 (Feedback In Realistic Environments) project, we study the effects of discreteness in stellar feedback processes on the evolution of galaxies and the properties of the interstellar medium (ISM). We specifically consider the discretization of supernovae (SNe), including hypernovae (HNe), and sampling the initial mass function (IMF). We study these processes in cosmological simulations of dwarf galaxies with $z=0$ stellar masses $M_{\ast}\sim 10^{4}-3\times10^{6}\,M_\odot$ (halo masses $\sim 10^{9}-10^{10}\,M_\odot$). We show that the discrete nature of individual SNe (as opposed to a model in which their energy/momentum deposition is continuous over time, similar to stellar winds) is crucial in generating a reasonable ISM structure and galactic winds and in regulating dwarf stellar masses. However, once SNe are discretized, accounting for the effects of IMF sampling on continuous mechanisms such as radiative feedback and stellar mass-loss (as opposed to adopting IMF-averaged rates) has weak effects on galaxy-scale properties. We also consider the effects of rare HNe events with energies $\sim 10^{53}\,{\rm erg}$. The effects of HNe are similar to the effects of clustered explosions of SNe -- which are already captured in our default simulation setup -- and do not quench star formation (provided that the HNe do not dominate the total SNe energy budget), which suggests that HNe yield products should be observable in ultra-faint dwarfs today.

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A New Public Release of the GIZMO Code

We describe a major update to the public GIZMO code. GIZMO has been used in simulations of cosmology; galaxy and star formation and evolution; black hole accretion and feedback; proto-stellar disk dynamics and planet formation; fluid dynamics and plasma physics; dust-gas dynamics; giant impacts and solid-body interactions; collisionless gravitational dynamics; and more. This release of the public code supports: hydrodynamics (using various mesh-free finite-volume Godunov methods or SPH), ideal and non-ideal MHD, anisotropic conduction and viscosity, radiative cooling and chemistry, star and black hole formation and feedback, sink particles, dust-gas (aero)-dynamics (with or without magnetic fields), elastic/plastic dynamics, arbitrary (gas, stellar, degenerate, solid/liquid material) equations of state, passive scalar/turbulent diffusion, large-eddy and shearing boxes, self-gravity with fully-adaptive force softenings, arbitrary cosmological expansion, and on-the-fly group-finding. It is massively-parallel with hybrid MPI+OpenMP scaling verified up to >1 million threads. The code is extensively documented, with test problems and tutorials provided for these different physics modules.

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SDSS-IV MaNGA: Constraints on the Conditions for Star Formation in Galaxy Discs

Regions of disc galaxies with widespread star formation tend to be both gravitationally unstable and self-shielded against ionizing radiation, whereas extended outer discs with little or no star formation tend to be stable and unshielded on average. We explore what drives the transition between these two regimes, specifically whether discs first meet the conditions for self-shielding (parameterized by dust optical depth, $τ$) or gravitational instability (parameterized by a modified version of Toomre's instability parameters, $Q_{\rm thermal}$, which quantifies the stability of a gas disc that is thermally supported at $T=10^4$ K). We first introduce a new metric formed by the product of these quantities, $Q_{\rm thermal}τ$, which indicates whether the conditions for disk instability or self-shielding are easier to meet in a given region of a galaxy, and we discuss how $Q_{\rm thermal}τ$ can be constrained even in the absence of direct gas information. We then analyse a sample of 13 galaxies with resolved gas measurements and find that on average galaxies will reach the threshold for disk instabilities ($Q_{\rm thermal}<1$) before reaching the threshold for self-shielding ($τ>1$). Using integral field spectroscopic observations of a sample of 236 galaxies from the MaNGA survey, we find that the value of $Q_{\rm thermal}τ$ in star-forming discs is consistent with similar behavior. These results support a scenario where disc fragmentation and collapse occurs before self-shielding, suggesting that gravitational instabilities are the primary condition for widespread star formation in galaxy discs. Our results support similar conclusions based on recent galaxy simulations.

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Stellar feedback strongly alters the amplification and morphology of galactic magnetic fields

Using high-resolution magnetohydrodynamic simulations of idealized, non-cosmological galaxies, we investigate how cooling, star formation, and stellar feedback affect galactic magnetic fields. We find that the amplification histories, saturation values, and morphologies of the magnetic fields vary considerably depending on the baryonic physics employed, primarily because of differences in the gas density distribution. In particular, adiabatic runs and runs with a sub-grid (effective equation of state) stellar feedback model yield lower saturation values and morphologies that exhibit greater large-scale order compared with runs that adopt explicit stellar feedback and runs with cooling and star formation but no feedback. The discrepancies mostly lie in gas denser than the galactic average, which requires cooling and explicit fragmentation to capture. Independent of the baryonic physics included, the magnetic field strength scales with gas density as $B\propto n^{2/3}$, suggesting isotropic flux freezing or equipartition between the magnetic and gravitational energies during the field amplification. We conclude that accurate treatments of cooling, star formation, and stellar feedback are crucial for obtaining the correct magnetic field strength and morphology in dense gas, which, in turn, is essential for properly modeling other physical processes that depend on the magnetic field, such as cosmic ray feedback.

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FIRE in the Field: Simulating the Threshold of Galaxy Formation

We present a suite of 15 cosmological zoom-in simulations of isolated dark matter halos, all with masses of $M_{\rm halo} \approx 10^{10}\,{\rm M}_\odot$ at $z=0$, in order to understand the relationship between halo assembly, galaxy formation, and feedback's effects on the central density structure in dwarf galaxies. These simulations are part of the Feedback in Realistic Environments (FIRE) project and are performed at extremely high resolution. The resultant galaxies have stellar masses that are consistent with rough abundance matching estimates, coinciding with the faintest galaxies that can be seen beyond the virial radius of the Milky Way ($M_\star/{\rm M}_\odot\approx 10^5-10^7$). This non-negligible spread in stellar mass at $z=0$ in halos within a narrow range of virial masses is strongly correlated with central halo density or maximum circular velocity $V_{\rm max}$. Much of this dependence of $M_\star$ on a second parameter (beyond $M_{\rm halo}$) is a direct consequence of the $M_{\rm halo}\sim10^{10}\,{\rm M}_\odot$ mass scale coinciding with the threshold for strong reionization suppression: the densest, earliest-forming halos remain above the UV-suppression scale throughout their histories while late-forming systems fall below the UV-suppression scale over longer periods and form fewer stars as a result. In fact, the latest-forming, lowest-concentration halo in our suite fails to form any stars. Halos that form galaxies with $M_\star\gtrsim2\times10^{6}\,{\rm M}_\odot$ have reduced central densities relative to dark-matter-only simulations, and the radial extent of the density modifications is well-approximated by the galaxy half-mass radius $r_{1/2}$. This apparent stellar mass threshold of $M_\star \approx 2\times 10^{6} \approx 2\times 10^{-4} \,M_{\rm halo}$ is broadly consistent with previous work and provides a testable prediction of FIRE feedback models in LCDM.

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Stacked star formation rate profiles of bursty galaxies exhibit 'coherent' star formation

In a recent work based on 3200 stacked H$α$ maps of galaxies at $z \sim 1$, Nelson et al.~find evidence for `coherent star formation': the stacked SFR profiles of galaxies above (below) the 'star formation main sequence' (MS) are above (below) that of galaxies on the MS at all radii. One might interpret this result as inconsistent with highly bursty star formation and evidence that galaxies evolve smoothly along the MS rather than crossing it many times. We analyze six simulated galaxies at $z\sim1$ from the Feedback in Realistic Environments (FIRE) project in a manner analogous to the observations to test whether the above interpretations are correct. The trends in stacked SFR profiles are qualitatively consistent with those observed. However, SFR profiles of individual galaxies are much more complex than the stacked profiles: the former can be flat or even peak at large radii because of the highly clustered nature of star formation in the simulations. Moreover, the SFR profiles of individual galaxies above (below) the MS are not systematically above (below) those of MS galaxies at all radii. We conclude that the time-averaged coherent star formation evident stacks of observed galaxies is consistent with highly bursty, clumpy star formation of individual galaxies and is not evidence that galaxies evolve smoothly along the MS.

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Gas kinematics, morphology, and angular momentum in the FIRE simulations

We study the z=0 gas kinematics, morphology, and angular momentum content of isolated galaxies in a suite of cosmological zoom-in simulations from the FIRE project spanning $M_{\star}=10^{6-11}M_{\odot}$. Gas becomes increasingly rotationally supported with increasing galaxy mass. In the lowest-mass galaxies ($M_{\star}<10^{8}M_{\odot}$), gas fails to form a morphological disk and is primarily dispersion and pressure supported. At intermediate masses ($M_{\star}=10^{8-10}M_{\odot}$), galaxies display a wide range of gas kinematics and morphologies, from thin, rotating disks, to irregular spheroids with negligible net rotation. All the high-mass ($M_{\star}=10^{10-11}M_{\odot}$) galaxies form rotationally supported gas disks. Many of the halos whose galaxies fail to form disks harbor high angular momentum gas in their circumgalactic medium. The ratio of the specific angular momentum of gas in the central galaxy to that of the dark-matter halo increases significantly with galaxy mass, from $j_{\rm gas}/j_{\rm DM}\sim0.1$ at $M_{\star}=10^{6-7}M_{\odot}$ to $j_{\rm gas}/j_{\rm DM}\sim2$ at $M_{\star}=10^{10-11}M_{\odot}$. The reduced rotational support in the lowest-mass galaxies owes to (a) stellar feedback and the UV background suppressing the accretion of high-angular momentum gas at late times, and (b) stellar feedback driving large non-circular gas motions. We broadly reproduce the observed scaling relations between galaxy mass, gas rotation velocity, size, and angular momentum, but may somewhat underpredict the incidence of disky, high-angular momentum galaxies at the lowest observed masses ($M_{\star}=(10^{6}-2\times10^{7})M_{\odot}$). In our simulations, stars are uniformly less rotationally supported than gas. The common assumption that stars follow the same rotation curve as gas thus substantially overestimates galaxies' stellar angular momentum, particularly at low masses.

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Testing the Recovery of Intrinsic Galaxy Sizes and Masses of z~2 Massive Galaxies Using Cosmological Simulations

Accurate measurements of galaxy masses and sizes are key to tracing galaxy evolution over time. Cosmological zoom-in simulations provide an ideal test bed for assessing the recovery of galaxy properties from observations. Here, we utilize galaxies with $M_*\sim10^{10}-10^{11.5}M_{\odot}$ at z~1.7-2 from the MassiveFIRE cosmological simulation suite, part of the Feedback in Realistic Environments (FIRE) project. Using mock multi-band images, we compare intrinsic galaxy masses and sizes to observational estimates. We find that observations accurately recover stellar masses, with a slight average underestimate of ~0.06 dex and a ~0.15 dex scatter. Recovered half-light radii agree well with intrinsic half-mass radii when averaged over all viewing angles, with a systematic offset of ~0.1 dex (with the half-light radii being larger) and a scatter of ~0.2 dex. When using color gradients to account for mass-to-light variations, recovered half-mass radii also exceed the intrinsic half-mass radii by ~0.1 dex. However, if not properly accounted for, aperture effects can bias size estimates by ~0.1 dex. No differences are found between the mass and size offsets for star-forming and quiescent galaxies. Variations in viewing angle are responsible for ~25% of the scatter in the recovered masses and sizes. Our results thus suggest that the intrinsic scatter in the mass-size relation may have previously been overestimated by ~25%. Moreover, orientation-driven scatter causes the number density of very massive galaxies to be overestimated by ~0.5 dex at $M_*\sim10^{11.5}M_{\odot}$.

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Not so lumpy after all: modeling the depletion of dark matter subhalos by Milky Way-like galaxies

Among the most important goals in cosmology is detecting and quantifying small ($M_{\rm halo}\simeq10^{6-9}~\mathrm{M}_\odot$) dark matter (DM) subhalos. Current probes around the Milky Way (MW) are most sensitive to such substructure within $\sim20$ kpc of the halo center, where the galaxy contributes significantly to the potential. We explore the effects of baryons on subhalo populations in $Λ$CDM using cosmological zoom-in baryonic simulations of MW-mass halos from the Latte simulation suite, part of the Feedback In Realistic Environments (FIRE) project. Specifically, we compare simulations of the same two halos run using (1) DM-only (DMO), (2) full baryonic physics, and (3) DM with an embedded disk potential grown to match the FIRE simulation. Relative to baryonic simulations, DMO simulations contain $\sim2\times$ as many subhalos within 100 kpc of the halo center; this excess is $\gtrsim5\times$ within 25 kpc. At $z=0$, the baryonic simulations are completely devoid of subhalos down to $3\times10^6~\mathrm{M}_\odot$ within $15$ kpc of the MW-mass galaxy, and fewer than 20 surviving subhalos have orbital pericenters <20 kpc. Despite the complexities of baryonic physics, the simple addition of an embedded central disk potential to DMO simulations reproduces this subhalo depletion, including trends with radius, remarkably well. Thus, the additional tidal field from the central galaxy is the primary cause of subhalo depletion. Subhalos on radial orbits that pass close to the central galaxy are preferentially destroyed, causing the surviving subhalo population to have tangentially biased orbits compared to DMO predictions. Our method of embedding a disk potential in DMO simulations provides a fast and accurate alternative to full baryonic simulations, thus enabling suites of cosmological simulations that can provide accurate and statistical predictions of substructure populations.

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Comparing Models for IMF Variation Across Cosmological Time in Milky Way-like Galaxies

One of the key observations regarding the stellar initial mass function (IMF) is its near-universality in the Milky Way (MW), which provides a powerful way to constrain different star formation models that predict the IMF. However, those models are almost universally "cloud-scale" or smaller -- they take as input or simulate single molecular clouds (GMCs), clumps, or cores, and predict the resulting IMF as a function of the cloud properties. Without a model for the progenitor properties of all clouds which formed the stars at different locations in the MW (including ancient stellar populations formed in high-redshift, likely gas-rich dwarf progenitor galaxies that looked little like the Galaxy today), the predictions cannot be fully explored, nor safely applied to "live" cosmological calculations of the IMF in different galaxies at different cosmological times. We therefore combine a suite of high-resolution cosmological simulations (from the Feedback In Realistic Environments project), which form MW-like galaxies with reasonable star formation properties and explicitly resolve massive GMCs, with various proposed cloud-scale IMF models. We apply the models independently to every star particle formed in the simulations to synthesize the predicted IMF in the present-day galaxy. We explore models where the IMF depends on Jeans mass, sonic or turbulent Bonner-Ebert mass, fragmentation with a polytropic equation-of-state, or where it is self-regulated by protostellar feedback. We show that all of these models, except the feedback-regulated ones, predict far more variation ($\sim 0.6-1$ dex $1\,σ$ scatter in the IMF turnover mass) in the simulations than is observed in the MW.

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Black Holes on FIRE: Stellar Feedback Limits Early Feeding of Galactic Nuclei

We introduce massive black holes (BHs) in the Feedback In Realistic Environments project and perform high-resolution cosmological hydrodynamic simulations of quasar-mass halos ($M_{\rm halo}(z=2) \approx 10^{12.5}\,\rm{M}_{\odot}$) down to $z=1$. These simulations model stellar feedback by supernovae, stellar winds, and radiation, and BH growth using a gravitational torque-based prescription tied to resolved properties of galactic nuclei. We do not include BH feedback. We show that early BH growth occurs through short ($\lesssim 1\,$Myr) accretion episodes that can reach or even exceed the Eddington rate. In this regime, BH growth is limited by bursty stellar feedback continuously evacuating gas from galactic nuclei, and BHs remain under-massive relative to the local $M_{\rm BH}$-$M_{\rm bulge}$ relation. BH growth is more efficient at later times, when the nuclear stellar potential retains a significant gas reservoir, star formation becomes less bursty, and galaxies settle into a more ordered state, with BHs rapidly converging onto the scaling relation when the host reaches $M_{\rm bulge} \sim 10^{10}\,\rm{M}_{\odot}$. Our results are not sensitive to the details of the accretion model so long as BH growth is tied to the gas content within $\sim 100\,$pc of the BH. Our simulations imply that bursty stellar feedback has strong implications for BH and AGN demographics, especially in the early Universe and for low-mass galaxies.

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A Constrained-Gradient Method to Control Divergence Errors in Numerical MHD

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining zero magnetic field-divergence (div-B). Constrained transport (CT) schemes can achieve this at high accuracy, but have generally been restricted to very specific methods. For more general (meshless, moving-mesh, or ALE) methods, 'divergence-cleaning' schemes reduce the div-B errors, however they can still be significant, especially at discontinuities, and can lead to systematic deviations from correct solutions which converge away very slowly. Here we propose a new constrained gradient (CG) scheme which augments these with a hybrid projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. We emphasize that, unlike 'locally divergence free' methods, this actually minimizes the numerically unstable div-B terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare a wide range of test problems. Compared to state-of-the-art cleaning schemes, our CG method reduces the maximum div-B errors in each problem by 1-3 orders of magnitude (2-5 dex below the typical errors if no div-B cleaning is used). By preventing large div-B even at unresolved discontinuities, the method eliminates systematic errors at jumps. In every problem, the accuracy of our CG results is comparable to CT methods. The cost is modest, ~30% of the hydro algorithm, and the CG correction can be easily implemented in a wide range of different numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a wide range of problems where using only the simplest Powell or '8-wave' cleaning can produce systematic, order-of-magnitude errors.

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The Dynamics of Charged Dust in Magnetized Molecular Clouds

We study the dynamics of large, charged dust grains in turbulent giant molecular clouds (GMCs). Massive dust grains behave as aerodynamic particles in primarily neutral dense gas, and thus are able to produce dramatic small-scale fluctuations in the dust-to-gas ratio. Hopkins & Lee (2016) directly simulated the dynamics of neutral dust grains in super-sonic MHD turbulence, typical of GMCs, and showed that the dust-to-gas fluctuations can exceed factor ~1000 on small scales, with important implications for star formation, stellar abundances, and dust behavior and growth. However, even in primarily neutral gas in GMCs, dust grains are negatively charged and Lorentz forces are non-negligible. Therefore, we extend our previous study by including the effects of Lorentz forces on charged grains (in addition to drag). For small charged grains (sizes <0.1 micron), Lorentz forces suppress dust-to-gas ratio fluctuations, while for large grains (sizes >1 micron), Lorentz forces have essentially no effect, trends that are well explained with a simple theory of dust magnetization. In some special intermediate cases, Lorentz forces can enhance dust-gas segregation. Regardless, for the physically expected scaling of dust charge with grain size, we find the most important effects depend on grain size (via the drag equation) with Lorentz forces/charge as a second-order correction. We show that the dynamics we consider are determined by three dimensionless numbers in the limit of weak background magnetic fields: the turbulent Mach number, a dust drag parameter (proportional to grain size) and a dust Lorentz parameter (proportional to grain charge); these allow us to generalize our simulations to a wide range of conditions.

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Feedback first: the surprisingly weak effects of magnetic fields, viscosity, conduction, and metal diffusion on galaxy formation

Using high-resolution simulations with explicit treatment of stellar feedback physics based on the FIRE (Feedback in Realistic Environments) project, we study how galaxy formation and the interstellar medium (ISM) are affected by magnetic fields, anisotropic Spitzer-Braginskii conduction and viscosity, and sub-grid metal diffusion from unresolved turbulence. We consider controlled simulations of isolated (non-cosmological) galaxies but also a limited set of cosmological "zoom-in" simulations. Although simulations have shown significant effects from these physics with weak or absent stellar feedback, the effects are much weaker than those of stellar feedback when the latter is modeled explicitly. The additional physics have no systematic effect on galactic star formation rates (SFRs) . In contrast, removing stellar feedback leads to SFRs being over-predicted by factors of $\sim 10 -100$. Without feedback, neither galactic winds nor volume filling hot-phase gas exist, and discs tend to runaway collapse to ultra-thin scale-heights with unphysically dense clumps congregating at the galactic center. With stellar feedback, a multi-phase, turbulent medium with galactic fountains and winds is established. At currently achievable resolutions and for the investigated halo mass range $10^{10}-10^{13} M_{\odot}$, the additional physics investigated here (MHD, conduction, viscosity, metal diffusion) have only weak ($\sim10\%$-level) effects on regulating SFR and altering the balance of phases, outflows, or the energy in ISM turbulence, consistent with simple equipartition arguments. We conclude that galactic star formation and the ISM are primarily governed by a combination of turbulence, gravitational instabilities, and feedback. We add the caveat that AGN feedback is not included in the present work.

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SIDM on FIRE: Hydrodynamical Self-Interacting Dark Matter simulations of low-mass dwarf galaxies

We compare a suite of four simulated dwarf galaxies formed in 10$^{10} M_{\odot}$ haloes of collisionless Cold Dark Matter (CDM) with galaxies simulated in the same haloes with an identical galaxy formation model but a non-zero cross-section for dark matter self-interactions. These cosmological zoom-in simulations are part of the Feedback In Realistic Environments (FIRE) project and utilize the FIRE-2 model for hydrodynamics and galaxy formation physics. We find the stellar masses of the galaxies formed in Self-Interacting Dark Matter (SIDM) with $σ/m= 1\, cm^2/g$ are very similar to those in CDM (spanning $M_{\star} \approx 10^{5.7 - 7.0} M_{\odot}$) and all runs lie on a similar stellar mass -- size relation. The logarithmic dark matter density slope ($α=d\log ρ/ d\log r$) in the central $250-500$ pc remains steeper than $α= -0.8$ for the CDM-Hydro simulations with stellar mass $M_{\star} \sim 10^{6.6} M_{\odot}$ and core-like in the most massive galaxy. In contrast, every SIDM hydrodynamic simulation yields a flatter profile, with $α>-0.4$. Moreover, the central density profiles predicted in SIDM runs without baryons are similar to the SIDM runs that include FIRE-2 baryonic physics. Thus, SIDM appears to be much more robust to the inclusion of (potentially uncertain) baryonic physics than CDM on this mass scale, suggesting SIDM will be easier to falsify than CDM using low-mass galaxies. Our FIRE simulations predict that galaxies less massive than $M_{\star} < 3 \times 10^6 M_{\odot}$ provide potentially ideal targets for discriminating models, with SIDM producing substantial cores in such tiny galaxies and CDM producing cusps.

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Dwarf Galaxy Mass Estimators vs. Cosmological Simulations

We use a suite of high-resolution cosmological dwarf galaxy simulations to test the accuracy of commonly-used mass estimators from Walker et al.(2009) and Wolf et al.(2010), both of which depend on the observed line-of-sight velocity dispersion and the 2D half-light radius of the galaxy, $Re$. The simulations are part of the the Feedback in Realistic Environments (FIRE) project and include twelve systems with stellar masses spanning $10^{5} - 10^{7} M_{\odot}$ that have structural and kinematic properties similar to those of observed dispersion-supported dwarfs. Both estimators are found to be quite accurate: $M_{Wolf}/M_{true} = 0.98^{+0.19}_{-0.12}$ and $M_{Walker}/M_{true} =1.07^{+0.21}_{-0.15}$, with errors reflecting the 68% range over all simulations. The excellent performance of these estimators is remarkable given that they each assume spherical symmetry, a supposition that is broken in our simulated galaxies. Though our dwarfs have negligible rotation support, their 3D stellar distributions are flattened, with short-to-long axis ratios $ c/a \simeq 0.4-0.7$. The accuracy of the estimators shows no trend with asphericity. Our simulated galaxies have sphericalized stellar profiles in 3D that follow a nearly universal form, one that transitions from a core at small radius to a steep fall-off $\propto r^{-4.2}$ at large $r$, they are well fit by Sérsic profiles in projection. We find that the most important empirical quantity affecting mass estimator accuracy is $Re$ . Determining $Re$ by an analytic fit to the surface density profile produces a better estimated mass than if the half-light radius is determined via direct summation.

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