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A standard prediction of galaxy formation theory is that the ionizing background suppresses galaxy formation in haloes with peak circular velocities smaller than Vpeak ~ 20 km/s, rendering the majority of haloes below this scale completely dark. We use a suite of cosmological zoom simulations of Milky Way-like haloes that include central Milky Way disk galaxy potentials to investigate the relationship between subhaloes and ultrafaint galaxies. We find that there are far too few subhaloes within 50 kpc of the Milky Way that had Vpeak > 20 km/s to account for the number of ultrafaint galaxies already known within that volume today. In order to match the observed count, we must populate subhaloes down to Vpeak ~ 6 km/s with ultrafaint dwarfs. The required haloes have peak virial temperatures as low as 1,500 K, well below the atomic hydrogen cooling limit of 10^4 K. Allowing for the possibility that the Large Magellanic Cloud contributes several of the satellites within 50 kpc could potentially raise this threshold to 10 km/s (4,000 K), still below the atomic cooling limit and far below the nominal reionization threshold., Comment: 10 pages, 5 figures, 1 table. Submitted to MNRAS

Building upon results of cosmological simulations of ultra-light scalar field dark matter (SFDM), we present a comprehensive model for the density profiles of SFDM haloes as a function of halo virial mass $M_{\rm h}$ and scalar field mass $m$. The central regions of SFDM haloes are dominated by solitons with characteristic densities that increase with increasing halo mass and asymptote to CDM-like profiles at large radii. For scalar field masses $m \sim 10^{-22}$ eV, consistent with large-scale structure observations, $M_{\rm h} \sim 10^{10} \,M_\odot$ haloes have lower core densities than their Cold Dark Matter (CDM) counterparts and this alleviates the Too Big to Fail problem (TBTF) in a regime where feedback is less effective. However, higher-mass SFDM haloes with $M_{\rm h} \sim 10^{11} \,M_\odot$ are denser than their CDM counterparts at small, observationally relevant radii. We use rotation curves of $V \sim 100$ km s$^{-1}$ galaxies from the SPARC database to show that SFDM exacerbates the cusp/core and central density problems seen in CDM at this scale. We conclude that if the conventional cosmological SFDM scaling relations are correct, then baryonic feedback is required to lower densities in SFDM haloes even more so than in CDM. This motivates cosmological and self-consistent hydrodynamic simulations of SFDM to determine whether central soliton structure can be altered by realistic feedback implementations., Comment: 13 pages, 8 figures, submitted to MNRAS

One important result from recent large integral field spectrograph (IFS) surveys is that the intrinsic velocity dispersion of galaxies traced by star-forming gas increases with redshift. Massive, rotation-dominated discs are already in place at z~2, but they are dynamically hotter than spiral galaxies in the local Universe. Although several plausible mechanisms for this elevated velocity dispersion (e.g. star formation feedback, elevated gas supply, or more frequent galaxy interactions) have been proposed, the fundamental driver of the velocity dispersion enhancement at high redshift remains unclear. We investigate the origin of this kinematic evolution using a suite of cosmological simulations from the FIRE (Feedback In Realistic Environments) project. Although IFS surveys generally cover a wider range of stellar masses than in these simulations, the simulated galaxies show trends between intrinsic velocity dispersion, SFR, and redshift in agreement with observations. In both the observed and simulated galaxies, intrinsic velocity dispersion is positively correlated with SFR. Intrinsic velocity dispersion increases with redshift out to z~1 and then flattens beyond that. In the FIRE simulations, intrinsic velocity dispersion can vary significantly on timescales of <100 Myr. These variations closely mirror the time evolution of the SFR and gas inflow rate. By cross-correlating pairs of intrinsic velocity dispersion, gas inflow rate, and SFR, we show that increased gas inflow leads to subsequent enhanced star formation, and enhancements in intrinsic velocity dispersion tend to temporally coincide with increases in gas inflow rate and SFR., Comment: 15 pages, 10 figures; Submitted to MNRAS

We present a new set of high-resolution hydrodynamic cosmological zoom-in simulations that apply the Feedback In Realistic Environments (FIRE) physics to both Local Group (LG)-like and isolated Milky Way (MW)-like volumes (ten host systems in total with baryonic particle mass $\simeq 3,500-7,000\,M_\odot$). We study the stellar mass functions, circular velocity or mass profiles, and velocity dispersions of the dwarf galaxy populations. The simulations reproduce the stellar mass function and central densities of MW satellite dwarfs for $M_\ast \geq10^{5.5}\,M_\odot$ and predict the existence of $\sim3$ unidentified galaxies with $M_\ast\sim10^5\,M_\odot$ within $300$ kpc of the MW. Overall, we find no evidence for the classical missing satellites or too-big-to-fail (TBTF) problems for satellite galaxies in our sample. Among the satellites, TBTF is resolved primarily by subhalo disruption and overall mass loss; central density profiles of subhalos are of secondary importance. For non-satellite galaxies, our LG-like simulations predict as many as $\sim10$ as-of-yet unseen galaxies at distances $0.3-1$ Mpc from both hosts, with $M_\ast\simeq10^{5-6}\,M_\odot$ (in halos with $V_\mathrm{max}\sim 20~\mathrm{km\,s}^{-1}$), albeit with large halo-to-halo variance. None of our simulations produces a compact, baryon-dominated, high-density dwarf elliptical-type galaxy (with $V_\mathrm{circ} \gtrsim 35~\mathrm{km\,s}^{-1}$ at $r<1\,$kpc), of which six may appear in the LG (but none in the MW). It may therefore remain a challenge to reproduce the full diversity of the dwarf population, including both the highest and lowest density systems., Comment: Main text: 14 pages, 6 figures, 1 table. Appendices: 3 figures, 1 table. Submitted to MNRAS

We use a semi-analytic model for globular cluster (GC) formation built on dark matter merger trees to explore the relative role of formation physics and hierarchical assembly in determining the properties of GC populations. Many previous works have argued that the observed linear relation between total GC mass and halo mass points to a fundamental GC -- dark matter connection or indicates that GCs formed at very high redshift before feedback processes introduced nonlinearity in the baryon-to-dark matter mass relation. We demonstrate that at $M_{\rm vir}(z=0) \gtrsim 10^{11.5} M_{\odot}$, a constant ratio between halo mass and total GC mass is in fact an almost inevitable consequence of hierarchical assembly: by the central limit theorem, it is expected at $z=0$ independent of the GC-to-halo mass relation at the time of GC formation. The GC-to-halo mass relation at $M_{\rm vir}(z=0) < 10^{11.5} M_{\odot}$ is more sensitive to the details of the GC formation process. In our fiducial model, GC formation occurs in galaxies when the gas surface density exceeds a critical value. This model naturally predicts bimodal GC color distributions similar to those observed in nearby galaxies and reproduces the observed relation between GC system metallicity and halo mass. It predicts that the cosmic GC formation rate peaked at $z$ $\sim$ 4, too late for GCs to contribute significantly to the UV luminosity density during reionization., Comment: Accepted to MNRAS. 21 pages, 15 figures, plus appendices

The oldest stars in the Milky Way (MW) bear imprints of the Galaxy's early assembly history. We use FIRE cosmological zoom-in simulations of three MW-mass disk galaxies to study the spatial distribution, chemistry, and kinematics of the oldest surviving stars ($z_{\rm form} \gtrsim 5$) in MW-like galaxies. We predict the oldest stars to be less centrally concentrated at $z=0$ than stars formed at later times as a result of two processes. First, the majority of the oldest stars are not formed $\textit{in situ}$ but are accreted during hierarchical assembly. These $\textit{ex situ}$ stars are deposited on dispersion-supported, halo-like orbits but dominate over old stars formed $\textit{in situ}$ in the solar neighborhood, and in some simulations, even in the galactic center. Secondly, old stars formed $\textit{in situ}$ are driven outwards by bursty star formation and energetic feedback processes that create a time-varying gravitational potential at $z\gtrsim 2$, similar to the process that creates dark matter cores and expands stellar orbits in bursty dwarf galaxies. The total fraction of stars that are ancient is more than an order of magnitude higher for sight lines $\textit{away}$ from the bulge and inner halo than for inward-looking sight lines. Although the task of identifying specific stars as ancient remains challenging, we anticipate that million-star spectral surveys and photometric surveys targeting metal-poor stars already include hundreds of stars formed before $z=5$. We predict most of these targets to have higher metallicity ($-3 < \rm [Fe/H] < -2$) than the most extreme metal-poor stars., Comment: 16 pages, 12 figures, plus appendix. Accepted to MNRAS with minor revisions since v1

We study the impact of a warm dark matter (WDM) cosmology on dwarf galaxy formation through a suite of cosmological hydrodynamical zoom-in simulations of $M_{\rm halo} \approx10^{10}\,M_{\odot}$ dark matter halos as part of the Feedback in Realistic Environments (FIRE) project. A main focus of this paper is to evaluate the combined effects of dark matter physics and stellar feedback on the well-known small-scale issues found in cold dark matter (CDM) models. We find that the $z=0$ stellar mass of a galaxy is strongly correlated with the central density of its host dark matter halo at the time of formation, $z_{\rm f}$, in both CDM and WDM models. WDM halos follow the same $M_{\star}(z=0)-V_{\rm max}(z_{\rm f})$ relation as in CDM, but they form later, are less centrally dense, and therefore contain galaxies that are less massive than their CDM counterparts. As a result, the impact of baryonic effects on the central gravitational potential is typically diminished relative to CDM. However, the combination of delayed formation in WDM and energy input from stellar feedback results in dark matter profiles with lower overall densities. The WDM galaxies studied here have a wider diversity of star formation histories (SFHs) than the same systems simulated in CDM, and the two lowest $M_{\star}$ WDM galaxies form all of their stars at late times. The discovery of young ultra-faint dwarf galaxies with no ancient star formation -- which do not exist in our CDM simulations -- would therefore provide evidence in support of WDM., Comment: 15 pages, 8 figures, 1 table; submitted to MNRAS

We present the reconstructed evolution of rest-frame ultra-violet (UV) luminosities of the most massive Milky Way dwarf spheroidal satellite galaxy, Fornax, and its five globular clusters (GCs) across redshift, based on analysis of the stellar fossil record and stellar population synthesis modeling. We find that (1) Fornax's (proto-)GCs can generate $10-100$ times more UV flux than the field population, despite comprising $<\sim 5\%$ of the stellar mass at the relevant redshifts; (2) due to their respective surface brightnesses, it is more likely that faint, compact sources in the Hubble Frontier Fields (HFFs) are GCs hosted by faint galaxies, than faint galaxies themselves. This may significantly complicate the construction of a galaxy UV luminosity function at $z>3$. (3) GC formation can introduce order-of-magnitude errors in abundance matching. We also find that some compact HFF objects are consistent with the reconstructed properties of Fornax's GCs at the same redshifts (e.g., surface brightness, star formation rate), suggesting we may already have detected proto-GCs in the early Universe. Finally, we discuss the prospects for improving the connections between local GCs and proto-GCs detected in the early Universe., Comment: 13 pages, 6 figures, submitted to MNRAS

In the local Universe, there is a strong division in the star-forming properties of low-mass galaxies, with star formation largely ubiquitous amongst the field population while satellite systems are predominantly quenched. This dichotomy implies that environmental processes play the dominant role in suppressing star formation within this low-mass regime (${M}_{\star} \sim 10^{5.5-8}~{\rm M}_{\odot}$). As shown by observations of the Local Volume, however, there is a non-negligible population of passive systems in the field, which challenges our understanding of quenching at low masses. By applying the satellite quenching models of Fillingham et al. (2015) to subhalo populations in the Exploring the Local Volume In Simulations (ELVIS) suite, we investigate the role of environmental processes in quenching star formation within the nearby field. Using model parameters that reproduce the satellite quenched fraction in the Local Group, we predict a quenched fraction -- due solely to environmental effects -- of $\sim 0.52 \pm 0.26$ within $1< R/R_{\rm vir} < 2$ of the Milky Way and M31. This is in good agreement with current observations of the Local Volume and suggests that the majority of the passive field systems observed at these distances are quenched via environmental mechanisms. Beyond $2~R_{\rm vir}$, however, dwarf galaxy quenching becomes difficult to explain through an interaction with either the Milky Way or M31, such that more isolated, field dwarfs may be self-quenched as a result of star-formation feedback., Comment: 9 pages, 4 figures, MNRAS accepted version, comments welcome - RIP Ducky...gone but never forgotten

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., Comment: 14 pages, 12 figures; submitted to MNRAS on 12/28/17

The shape of a galaxy's spatially unresolved, globally integrated 21-cm emission line depends on its internal gas kinematics: galaxies with rotation-supported gas disks produce double-horned profiles with steep wings, while galaxies with dispersion-supported gas produce Gaussian-like profiles with sloped wings. Using mock observations of simulated galaxies from the FIRE project, we show that one can therefore constrain a galaxy's gas kinematics from its unresolved 21-cm line profile. In particular, we find that the kurtosis of the 21-cm line increases with decreasing $V/\sigma$, and that this trend is robust across a wide range of masses, signal-to-noise ratios, and inclinations. We then quantify the shapes of 21-cm line profiles from a morphologically unbiased sample of $\sim$2000 low-redshift, HI-detected galaxies with $M_{\rm star} = 10^{7-11} M_{\odot}$ and compare to the simulated galaxies. At $M_{\rm star} \gtrsim 10^{10} M_{\odot}$, both the observed and simulated galaxies produce double-horned profiles with low kurtosis and steep wings, consistent with rotation-supported disks. Both the observed and simulated line profiles become more Gaussian-like (higher kurtosis and less-steep wings) at lower masses, indicating increased dispersion support. However, the simulated galaxies transition from rotation to dispersion support more strongly: at $M_{\rm star} = 10^{8-10}M_{\odot}$, most of the simulations produce more Gaussian-like profiles than typical observed galaxies with similar mass, indicating that gas in the low-mass simulated galaxies is, on average, overly dispersion-supported. Most of the lower-mass simulated galaxies also have somewhat lower gas fractions than the median of the observed population. The simulations nevertheless reproduce the observed line-width baryonic Tully-Fisher relation, which is insensitive to rotation vs. dispersion support., Comment: 10 pages, 5 figures, plus appendices. Accepted to MNRAS with minor revisions since v1

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., Comment: Submitted to MNRAS; comments welcome. 24 pages, 17 figures (including several full page), 1 table, and 3 appendices

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., Comment: 9 pages, 4 figures

We contrast predictions for the high-redshift galaxy population and reionization history between cold dark matter (CDM) and an alternative self-interacting dark matter model based on the recently developed ETHOS framework that alleviates the small-scale CDM challenges within the Local Group. We perform the highest resolution hydrodynamical cosmological simulations (a 36~Mpc$^3$ volume with gas cell mass of $\sim10^5\mathrm{M}_{\odot}$ and minimum gas softening of $\sim180$~pc) within ETHOS to date -- plus a CDM counterpart -- to quantify the abundance of galaxies at high redshift and their impact on reionization. We find that ETHOS predicts galaxies with higher ultraviolet (UV) luminosities than their CDM counterparts and a faster build-up of the faint end of the UV luminosity function. These effects, however, make the optical depth to reionization less sensitive to the power spectrum cut-off: the ETHOS model differs from the CDM $\tau$ value by only 10 per cent and is consistent with Planck limits if the effective escape fraction of UV photons is 0.1-0.5. We conclude that current observations of high-redshift luminosity functions cannot differentiate between ETHOS and CDM models, but deep JWST surveys of strongly-lensed, inherently faint galaxies have the potential to test non-CDM models that offer attractive solutions to CDM's Local Group problems., Comment: 14 pages, 8 figures, version accepted for MNRAS publication. Please contact lovell@hi.is with any comments

Metal-poor globular clusters (GCs) are both numerous and ancient, which indicates that they may be important contributors to ionizing radiation in the reionization era. Starting from the observed number density and stellar mass function of old GCs at $z=0$, I compute the contribution of GCs to ultraviolet luminosity functions (UVLFs) in the high-redshift Universe ($10 \gtrsim z \gtrsim 4$). Even under absolutely minimal assumptions - no disruption of GCs and no reduction in GC stellar mass from early times to the present - GC star formation contributes non-negligibly to the UVLF at luminosities that are accessible to the Hubble Space Telescope (HST; $M_{1500} \approx -17$). If the stellar masses of GCs were significantly higher in the past, as is predicted by most models explaining GC chemical anomalies, then GCs dominate the UV emission from many galaxies in existing deep-field observations. On the other hand, it is difficult to reconcile observed UVLFS with models requiring stellar masses at birth that exceed present-day stellar masses by more than a factor of 10. The James Webb Space Telescope will be able to directly detect individual GCs at $z \sim 6$ in essentially all bright galaxies, and many galaxies below the knee of the UVLF, for most of the scenarios considered here. The properties of a subset of high-$z$ galaxies with $-19 \lesssim M_{1500} \lesssim -14$ in HST lensing fields indicate that they may actually be GCs in formation., Comment: 9 pages, 7 figures; MNRAS (accepted). V2: minor revisions and clarifications; conclusions unchanged

A fundamental prediction of the cold dark matter cosmology is the existence of a large number of dark subhalos around galaxies, most of which should be entirely devoid of stars. Confirming the existence of dark substructures stands among the most important empirical challenges in modern cosmology: if they are found and quantified with the mass spectrum expected, then this would close the door on a vast array of competing theories. But in order for observational programs of this kind to reach fruition, we need robust predictions. Here we explore substructure predictions for lensing using galaxy lens-like hosts at z=0.2 from the Illustris simulations both in full hydrodynamics and dark matter only. We quantify substructures more massive than ~ 10^9 M_sun, comparable to current lensing detections derived from HST, Keck, and ALMA. The addition of full hydrodynamics reduces the overall subhalo mass function by about a factor of two. Even for the dark matter only runs, most (~ 85%) lines of sight through projected cylinders of size close to an Einstein radius contain no substructures larger than 10^9 M_sun. The fraction of empty sight lines rises to ~ 95% in full physics simulations. This suggests we will likely need hundreds of strong lensing systems suitable for substructure studies, as well as predictions that include the effects of baryon physics on substructure, to properly constrain cosmological models. Fortunately, the field is poised to fulfill these requirements., Comment: 11 pages, 9 figures

We present a census of variable stars in six M31 dwarf spheroidal satellites observed with the Hubble Space Telescope. We detect 870 RR Lyrae (RRL) stars in the fields of And I (296), II (251), III (111), XV (117), XVI (8), XXVIII (87). We also detect a total of 15 Anomalous Cepheids, three Eclipsing Binaries, and seven field RRL stars compatible with being members of the M31 halo or the Giant Stellar Stream. We derive robust and homogeneous distances to the six galaxies using different methods based on the properties of the RRL stars. Working with the up-to-date set of Period-Wesenheit ($I$, $B$ - $I$) relations published by Marconi et al., we obtain distance moduli of $\mu_0$ = [24.49, 24.16, 24.36, 24.42, 23.70, 24.43] mag (respectively), with systematic uncertainties of 0.08 mag and statistical uncertainties $<$ 0.11 mag. We have considered an enlarged sample of sixteen M31 satellites with published variability studies, and compared their pulsational observables (e.g., periods, amplitudes), with those of fifteen Milky Way satellites for which similar data are available. The properties of the (strictly old) RRL in both satellite systems do not show any significant difference. In particular, we found a strikingly similar correlation between the mean period distribution of the fundamental RRL pulsators (RRab) and the mean metallicities of the galaxies. This indicates that the old RRL progenitors were similar at the early stage in the two environments, suggesting very similar characteristics for the earliest stages of evolution of both satellite systems., Comment: 37 pages, 15 figures (some degraded), 29 tables, in emulateapj format. Accepted for publication in ApJ

We study the morphologies and sizes of galaxies at z>5 using high-resolution cosmological zoom-in simulations from the Feedback In Realistic Environments project. The galaxies show a variety of morphologies, from compact to clumpy to irregular. The simulated galaxies have more extended morphologies and larger sizes when measured using rest-frame optical B-band light than rest-frame UV light; sizes measured from stellar mass surface density are even larger. The UV morphologies are usually dominated by several small, bright young stellar clumps that are not always associated with significant stellar mass. The B-band light traces stellar mass better than the UV, but it can also be biased by the bright clumps. At all redshifts, galaxy size correlates with stellar mass/luminosity with large scatter. The half-light radii range from 0.01 to 0.2 arcsec (0.05-1 kpc physical) at fixed magnitude. At z>5, the size of galaxies at fixed stellar mass/luminosity evolves as (1+z)^{-m}, with m~1-2. For galaxies less massive than M_star~10^8 M_sun, the ratio of the half-mass radius to the halo virial radius is ~10% and does not evolve significantly at z=5-10; this ratio is typically 1-5% for more massive galaxies. A galaxy's "observed" size decreases dramatically at shallower surface brightness limits. This effect may account for the extremely small sizes of z>5 galaxies measured in the Hubble Frontier Fields. We provide predictions for the cumulative light distribution as a function of surface brightness for typical galaxies at z=6., Comment: 11 pages, 11 figures, resubmitted to MNRAS after revision for referee's comments

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically-clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that arbitrary initial profiles will tend to converge to a universal profile under hierarchical merging, owing to phase-space mixing obeying certain conservation constraints. We perform $N$-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically-clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we provide physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This has important implications for the structure of nascent globular clusters., Comment: 16 pages, 10 figures

We study the implementation of mechanical feedback from supernovae (SNe) and stellar mass loss in galaxy simulations, within the Feedback In Realistic Environments (FIRE) project. We present the FIRE-2 algorithm for coupling mechanical feedback, which can be applied to any hydrodynamics method (e.g. fixed-grid, moving-mesh, and mesh-less methods), and black hole as well as stellar feedback. This algorithm ensures manifest conservation of mass, energy, and momentum, and avoids imprinting 'preferred directions' on the ejecta. We show that it is critical to incorporate both momentum and thermal energy of mechanical ejecta in a self-consistent manner, accounting for SNe cooling radii when they are not resolved. Using idealized simulations of single SN explosions, we show that the FIRE-2 algorithm, independent of resolution, reproduces converged solutions in both energy and momentum. In contrast, common 'fully-thermal' (energy-dump) or 'fully-kinetic' (particle-kicking) schemes in the literature depend strongly on resolution: when applied at mass resolution >100 solar masses, they diverge by orders-of-magnitude from the converged solution. In galaxy-formation simulations, this divergence leads to orders-of-magnitude differences in galaxy properties, unless those models are adjusted in a resolution-dependent way. We show that all models that individually time-resolve SNe converge to the FIRE-2 solution at sufficiently high resolution. However, in both idealized single-SN simulations and cosmological galaxy-formation simulations, the FIRE-2 algorithm converges much faster than other sub-grid models without re-tuning parameters., Comment: 18 pages, 9 figures (+8 pages, 6 figures in appendices). MNRAS (updated to match published version)

The dark energy plus cold dark matter ($\Lambda$CDM) cosmological model has been a demonstrably successful framework for predicting and explaining the large-scale structure of Universe and its evolution with time. Yet on length scales smaller than $\sim 1$ Mpc and mass scales smaller than $\sim 10^{11} M_{\odot}$, the theory faces a number of challenges. For example, the observed cores of many dark-matter dominated galaxies are both less dense and less cuspy than naively predicted in $\Lambda$CDM. The number of small galaxies and dwarf satellites in the Local Group is also far below the predicted count of low-mass dark matter halos and subhalos within similar volumes. These issues underlie the most well-documented problems with $\Lambda$CDM: Cusp/Core, Missing Satellites, and Too-Big-to-Fail. The key question is whether a better understanding of baryon physics, dark matter physics, or both will be required to meet these challenges. Other anomalies, including the observed planar and orbital configurations of Local Group satellites and the tight baryonic/dark matter scaling relations obeyed by the galaxy population, have been less thoroughly explored in the context of $\Lambda$CDM theory. Future surveys to discover faint, distant dwarf galaxies and to precisely measure their masses and density structure hold promising avenues for testing possible solutions to the small-scale challenges going forward. Observational programs to constrain or discover and characterize the number of truly dark low-mass halos are among the most important, and achievable, goals in this field over then next decade. These efforts will either further verify the $\Lambda$CDM paradigm or demand a substantial revision in our understanding of the nature of dark matter., Comment: 47 pages, 15 figures. Draft of a review to appear in ARAA, volume 55. See http://www.annualreviews.org/doi/10.1146/annurev-astro-091916-055313 for updated version. Final online publication date: August 18, 2017. v2: corrected coefficients for Eqs. 8-10

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision., Comment: http://theia.phyip3.dur.ac.uk

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 $\sigma/m= 1\, cm^2/g$ 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 ($\alpha=d\log \rho / d\log r$) in the central $250-500$ pc remains steeper than $\alpha= -0.8$ 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 $\alpha >-0.4$. 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., Comment: 10 Pages, 7 figures, submitted to MNRAS

We present a suite of cosmological zoom-in simulations at z>5 from the Feedback In Realistic Environments project, spanning a halo mass range M_halo~10^8-10^12 M_sun at z=5. We predict the stellar mass-halo mass relation, stellar mass function, and luminosity function in several bands from z=5-12. The median stellar mass-halo mass relation does not evolve strongly at z=5-12. The faint-end slope of the luminosity function steepens with increasing redshift, as inherited from the halo mass function at these redshifts. Below z~6, the stellar mass function and ultraviolet (UV) luminosity function slightly flatten below M_star~10^4.5 M_sun (fainter than M_1500~-12), owing to the fact that star formation in low-mass halos is suppressed by the ionizing background by the end of reionization. Such flattening does not appear at higher redshifts. We provide redshift-dependent fitting functions for the SFR-M_halo, SFR-M_star, and broad-band magnitude-stellar mass relations. We derive the star formation rate density and stellar mass density at z=5-12 and show that the contribution from very faint galaxies becomes more important at z>8. Furthermore, we find that the decline in the z~6 UV luminosity function brighter than M_1500~-20 is largely due to dust attenuation. Approximately 37% (54%) of the UV luminosity from galaxies brighter than M_1500=-13 (-17) is obscured by dust at z~6. Our results broadly agree with current data and can be tested by future observations., Comment: 23 pages, 17 figures, resubmitted to MNRAS after minor revision. The predicted stellar mass functions and luminosity functions are made publicly available (see Appendix C for details)

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 S\'ersic 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., Comment: Submitted to MNRAS. 11 pages, 12 figures, comments welcome

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., Comment: 24 pages, 16 figures. Accepted to MNRAS with some changes since v1. Figure 10 is new

We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schr\"odinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic $r^{-3}$ NFW-like profile. We find a fundamental relation of the core=to-halo mass with the dimensionless invariant $\Xi \equiv \lvert E \rvert/M^3/(Gm/\hbar)^2$ or $M_{\rm c}/M \simeq 2.6 \Xi^{1/3}$, linking the soliton to global halo properties. For $r \geq 3.5 \,r_{\rm c}$ core radii, we find equipartition between potential, classical kinetic, and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behavior driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a $k^{-1.1}$ power-law. This suggests the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a $k^{-5/3}$ Kolmogorov power-law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying the soliton-sized granules carry most of the turbulent energy in BECDM haloes., Comment: 14 pages, 7 figures, MNRAS accepted; a movie rendering of Figure 1 can be found here: https://youtu.be/UBf9ghy2lPI

I present a simple phenomenological model for the observed linear scaling of the stellar mass in old globular clusters (GCs) with $z=0$ halo mass in which the stellar mass in GCs scales linearly with progenitor halo mass at $z=6$ above a minimum halo mass for GC formation. This model reproduces the observed $M_{\rm GCs}-M_{\rm halo}$ relation at $z=0$ and results in a prediction for the minimum halo mass at $z=6$ required for hosting one GC: $M_{\rm min}(z=6)=1.07 \times 10^9\,M_{\odot}$. Translated to $z=0$, the mean threshold mass is $M_{\rm halo}(z=0) \approx 2\times 10^{10}\,M_{\odot}$. I explore the observability of GCs in the reionization era and their contribution to cosmic reionization, both of which depend sensitively on the (unknown) ratio of GC birth mass to present-day stellar mass, $\xi$. Based on current detections of $z \gtrsim 6$ objects with $M_{1500} < -17$, values of $\xi > 10$ are strongly disfavored; this, in turn, has potentially important implications for GC formation scenarios. Even for low values of $\xi$, some observed high-$z$ galaxies may actually be GCs, complicating estimates of reionization-era galaxy ultraviolet luminosity functions and constraints on dark matter models. GCs are likely important reionization sources if $5 \lesssim \xi \lesssim 10$. I also explore predictions for the fraction of accreted versus in situ GCs in the local Universe and for descendants of systems at the halo mass threshold of GC formation (dwarf galaxies). An appealing feature of the model presented here is the ability to make predictions for GC properties based solely on dark matter halo merger trees., Comment: 11 pages, 7 figures; matches version published in MNRAS (minor modifications from v1)

Dwarf galaxies are known to have remarkably low star formation efficiency due to strong feedback. Adopting the dwarf galaxies of the Milky Way as a laboratory, we explore a flexible semi-analytic galaxy formation model to understand how the feedback processes shape the satellite galaxies of the Milky Way. Using Markov-Chain Monte-Carlo, we exhaustively search a large parameter space of the model and rigorously show that the general wisdom of strong outflows as the primary feedback mechanism cannot simultaneously explain the stellar mass function and the mass--metallicity relation of the Milky Way satellites. An extended model that assumes that a fraction of baryons is prevented from collapsing into low-mass halos in the first place can be accurately constrained to simultaneously reproduce those observations. The inference suggests that two different physical mechanisms are needed to explain the two different data sets. In particular, moderate outflows with weak halo mass dependence are needed to explain the mass--metallicity relation, and prevention of baryons falling into shallow gravitational potentials of low-mass halos (e.g. "pre-heating") is needed to explain the low stellar mass fraction for a given subhalo mass., Comment: 14 pages, 4 figures, accepted for publication in ApJ

We present the rest-1500\AA\ UV luminosity functions (LF) for star-forming galaxies during the cosmic \textit{high noon} -- the peak of cosmic star formation rate at $1.5

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., Comment: 64 pages, 40 figures. Simulation animations and visualizations available at http://www.tapir.caltech.edu/~phopkins/Site/animations and http://fire.northwestern.edu . Paper includes complete FIRE algorithms and public ICs (http://www.tapir.caltech.edu/~phopkins/publicICs). Updated to match published version

Motivated by the stellar fossil record of Local Group (LG) dwarf galaxies, we show that the star-forming ancestors of the faintest ultra-faint dwarf galaxies (UFDs; ${\rm M}_{\rm V}$ $\sim -2$ or ${\rm M}_{\star}$ $\sim 10^{2}$ at $z=0$) had ultra-violet (UV) luminosities of ${\rm M}_{\rm UV}$ $\sim -3$ to $-6$ during reionization ($z\sim6-10$). The existence of such faint galaxies has substantial implications for early epochs of galaxy formation and reionization. If the faint-end slopes of the UV luminosity functions (UVLFs) during reionization are steep ($\alpha\lesssim-2$) to ${\rm M}_{\rm UV}$ $\sim -3$, then: (i) the ancestors of UFDs produced $>50$% of UV flux from galaxies; (ii) galaxies can maintain reionization with escape fractions that are $>$2 times lower than currently-adopted values; (iii) direct HST and JWST observations may detect only $\sim10-50$% of the UV light from galaxies; (iv) the cosmic star formation history increases by $\gtrsim4-6$ at $z\gtrsim6$. Significant flux from UFDs, and resultant tensions with LG dwarf galaxy counts, are reduced if the high-redshift UVLF turns over. Independent of the UVLF shape, the existence of a large population of UFDs requires a non-zero luminosity function to ${\rm M}_{\rm UV}$ $\sim -3$ during reionization., Comment: 6 pages, 4 Figures. Submitted to MNRAS. Comments welcome

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 $\Lambda$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., Comment: 20 pages, 10 figures, 2 tables. Accepted into MNRAS

We present a proper motion measurement for the halo globular cluster Pyxis, using HST/ACS data as the first epoch, and GeMS/GSAOI Adaptive Optics data as the second, separated by a baseline of about 5 years. This is both the first measurement of the proper motion of Pyxis and the first calibration and use of Multi-Conjugate Adaptive Optics data to measure an absolute proper motion for a faint, distant halo object. Consequently, we present our analysis of the Adaptive Optics data in detail. We obtain a proper motion of mu_alpha cos(delta)=1.09+/-0.31 mas/yr and mu_delta=0.68+/-0.29 mas/yr. From the proper motion and the line-of-sight velocity we find the orbit of Pyxis is rather eccentric with its apocenter at more than 100 kpc and its pericenter at about 30 kpc. We also investigate two literature-proposed associations for Pyxis with the recently discovered ATLAS stream and the Magellanic system. Combining our measurements with dynamical modeling and cosmological numerical simulations we find it unlikely Pyxis is associated with either system. We examine other Milky Way satellites for possible association using the orbit, eccentricity, metallicity, and age as constraints and find no likely matches in satellites down to the mass of Leo II. We propose that Pyxis probably originated in an unknown galaxy, which today is fully disrupted. Assuming that Pyxis is bound and not on a first approach, we derive a 68% lower limit on the mass of the Milky Way of 0.95*10^12 M_sun., Comment: 31 pages, 17 figures, 4 tables, accepted for publication by ApJ

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., Comment: 16 pages, 16 figures; matches version published in MNRAS