James S. Bullock

Profiles of dark haloes. Evolution, scatter, and environment

We study dark-matter halo density profiles in a high-resolution N-body simulation of aCDM cosmology. Our statistical sample contains �5000 haloes in the range 10 11 10 14 h −1 M⊙ and the resolution allows a study of subhaloes inside host haloes. The profiles are parameterized by an NFW form with two parameters, an inner radius rs and a virial radius Rvir, and we define the halo concentration cvirRvir/rs. We find that, for a given halo mass, the redshift dependence of the median concentration is cvir / (1 + z) −1 . This corresponds to rs(z) � constant, and is contrary to earlier suspicions that cvir does not vary much with redshift. The implications are that high- redshift galaxies are predicted to be more extended and dimmer than expected before. Second, we find that the scatter in halo profiles is large, with a 1� �(logcvir) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of �Vmax/Vmax = 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Third, subhaloes and haloes in dense environments tend to be more concentrated than isolated haloes, and show a larger scatter. These results suggest that cvir is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully- Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence, and can thus serve semi-analytic studies of galaxy formation.

Reionization and the abundance of galactic satellites

One of the main challenges facing standard hierarchical structure formation models is that the predicted abundance of Galactic subhalos with circular velocities vc ~ 10-30 km s-1 is an order of magnitude higher than the number of satellites actually observed within the Local Group. Using a simple model for the formation and evolution of dark halos, based on the extended Press-Schechter formalism and tested against N-body results, we show that the theoretical predictions can be reconciled with observations if gas accretion in low-mass halos is suppressed after the epoch of reionization. In this picture, the observed dwarf satellites correspond to the small fraction of halos that accreted substantial amounts of gas before reionization. The photoionization mechanism naturally explains why the discrepancy between predicted halos and observed satellites sets in at vc ~ 30 km s-1, and for reasonable choices of the reionization redshift (zre ~ 5-12) the model can reproduce both the amplitude and shape of the observed velocity function of galactic satellites. If this explanation is correct, then typical bright galaxy halos contain many low-mass dark matter subhalos. These might be detectable through their gravitational lensing effects, through their influence on stellar disks, or as dwarf satellites with very high mass-to-light ratios. This model also predicts a diffuse stellar component produced by large numbers of tidally disrupted dwarfs, perhaps sufficient to account for most of the Milky Ways stellar halo.

Too big to fail? The puzzling darkness of massive Milky Way subhaloes

ABSTRACT We show that dissipationless CDM simulations predict that the majority of themost massive subhalos of the Milky Way are too dense to host any of its brightsatellites (L V > 10 5 L ). These dark subhalos have circular velocities at infall ofV infall = 30 1070kms 1 and infall masses of [0:2 4] 10 M . Unless the Milky Way isa statistical anomaly, this implies that galaxy formation becomes e ectively stochasticat these masses. This is in marked contrast to the well-established monotonic relationbetween galaxy luminosity and halo circular velocity (or halo mass) for more massivehalos. We show that at least two (and typically four) of these massive dark subhalosare expected to produce a larger dark matter annihilation ux than Draco. It maybe possible to circumvent these conclusions if baryonic feedback in dwarf satellites ordi erent dark matter physics can reduce the central densities of massive subhalos byorder unity on a scale of 0.3 { 1 kpc.Key words: Galaxy: halo { galaxies: abundances { dark matter { cosmology: theory

Tracing Galaxy Formation with Stellar Halos. I. Methods

If the favored hierarchical cosmological model is correct, then the Milky Way system should have accreted � 100– 200 luminous satellite galaxies in the past � 12 Gyr. We model this process using a hybrid semianalytic plus N-body approach that distinguishes explicitly between the evolution of light and dark matter in accreted satellites. This distinction is essential to our ability to produce a realistic stellar halo, with mass and density profile much like that of our own Galaxy, and a surviving satellite population that matches the observed number counts and structural parameter distributions of the satellite galaxies of the Milky Way. Our accreted stellar halos have density profiles that typically drop off with radius faster than the dark matter and follow power laws at rk30 kpc with � / r � � , � ’ 3 4. They are well fit by Hernquist profiles over the full radial range. We find that stellar halos are assembled from the inside out, with the majority of mass (� 80%) coming from the � 15 most massive accretion events. The satellites that contributetothestellarhalohavemedianaccretiontimes of � 9Gyrinthepast,whilesurvivingsatellitesystems have median accretion times of � 5 Gyr in the past. This implies that stars associated with the inner halo should be quite differentchemicallyfromstarsinsurvivingsatellitesandalsofromstarsintheouterhaloorthoseliberatedinrecent disruptionevents.Webrieflydiscusstheexpectedspatialstructureandphase-spacestructureforhalosformedinthismanner. Searches for this type of structure offer a direct test of whether cosmology is indeed hierarchical on small scales. Subject headingg dark matter — galaxies: dwarf — galaxies: evolution — galaxies: formation — galaxies: halos — galaxies: kinematics and dynamics — Galaxy: evolution — Galaxy: formation — Galaxy: halo — Galaxy: kinematics and dynamics — Local Group

Galaxies on FIRE (Feedback In Realistic Environments): Stellar feedback explains cosmologically inefficient star formation

We present a series of high-resolution cosmological simulations of galaxy formation to z = 0, spanning halo masses ∼10^8–10^(13) M⊙, and stellar masses ∼10^4–10^(11) M⊙. Our simulations include fully explicit treatment of the multiphase interstellar medium and stellar feedback. The stellar feedback inputs (energy, momentum, mass, and metal fluxes) are taken directly from stellar population models. These sources of feedback, with zero adjusted parameters, reproduce the observed relation between stellar and halo mass up to M_(halo) ∼ 10^(12) M⊙. We predict weak redshift evolution in the M*–M_(halo) relation, consistent with current constraints to z > 6. We find that the M*–M_(halo) relation is insensitive to numerical details, but is sensitive to feedback physics. Simulations with only supernova feedback fail to reproduce observed stellar masses, particularly in dwarf and high-redshift galaxies: radiative feedback (photoheating and radiation pressure) is necessary to destroy giant molecular clouds and enable efficient coupling of later supernovae to the gas. Star formation rates (SFRs) agree well with the observed Kennicutt relation at all redshifts. The galaxy-averaged Kennicutt relation is very different from the numerically imposed law for converting gas into stars, and is determined by self-regulation via stellar feedback. Feedback reduces SFRs and produces reservoirs of gas that lead to rising late-time star formation histories, significantly different from halo accretion histories. Feedback also produces large short-time-scale variability in galactic SFRs, especially in dwarfs. These properties are not captured by common ‘sub-grid’ wind models.

Accurate Masses for Dispersion-supported Galaxies

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analysing resolved line-of-sight velocity data for globular clusters, dwarf galaxies and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the mass enclosed within the 3D deprojected half-light radius r 1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy as long as the projected velocity dispersion profile is fairly flat near the half-light radius, as is typically observed. We find M 1/2 = 3G -1 (σ 2 los )r 1/2 ≃ 4G -1 (σ 2 los )R e , where (σ 2 los ) is the luminosity-weighted square of the line-of-sight velocity dispersion and R e is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of a mass of approximately 3 x 10 9 M ⊙ . assuming a A cold dark matter cosmology. The faintest MW dSphs seem to have formed in dark matter haloes that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity between them. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their dynamical I-band mass-to-light ratios Υ I 1/2 . The Υ I 1/2 versus M 1/2 relation for dispersion-supported galaxies follows a U shape, with a broad minimum near Υ I 1/2 ≃ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to Υ I 1/2 ≃ 3200 for ultra-faint dSphs and a more shallow rise to Υ I 1/2 ≃ 800 for galaxy cluster spheroids.

A Merger-driven Scenario for Cosmological Disk Galaxy Formation

The hierarchical nature of the ?CDM cosmology poses serious difficulties for the formation of disk galaxies. To help resolve these issues, we describe a new, merger-driven scenario for the cosmological formation of disk galaxies at high redshifts that supplements the standard dissipational collapse model. In this picture, large gaseous disks may be produced from high angular momentum mergers of systems that are gas dominated, i.e., Mgas/(Mgas + M) 0.5 at the height of the merger. Pressurization from the multiphase ISM prevents the complete conversion of gas into stars during the merger, and if enough gas remains to form a disk, the remnant eventually resembles a disk galaxy. We perform numerical simulations of galaxy mergers to study how supernovae feedback strength, black hole feedback, progenitor gas fraction, merger mass ratio, and orbital geometry impact the formation of remnant disks. We find that disks can build angular momentum through mergers and the degree of rotational support of the baryons in the remnant is primarily related to feedback processes associated with star formation. Disk-dominated remnants are restricted to form in mergers that are gas dominated at the time of final coalescence. We also show that the formation of rotationally supported stellar systems in mergers is not restricted to idealized orbits, and both gas-rich major and minor mergers can produce disk-dominated stellar remnants. We suggest that the hierarchical nature of the ?CDM cosmology and the physics of the ISM may act together to form spiral galaxies by building the angular momentum of disks through gas-dominated mergers at high redshifts.

The Dependence of Halo Clustering on Halo Formation History, Concentration, and Occupation

We investigate the dependence of dark matter halo clustering on halo formation time, density profile concentration, and subhalo occupation number, using high-resolution numerical simulations of a ?CDM cosmology. We confirm results that halo clustering is a function of halo formation time at fixed mass and that this trend depends on halo mass. For the first time, we show unequivocally that halo clustering is a function of halo concentration and show that the dependence of halo bias on concentration, mass, and redshift can be accurately parameterized in a simple way: b(M,c|z) = b(M|z)b(c|M/M). Interestingly, the scaling between bias and concentration changes sign with the value of M/M: high-concentration (early forming) objects cluster more strongly for M M, while low-concentration (late forming) objects cluster more strongly for rare high-mass halos, M M. We show the first explicit demonstration that host dark halo clustering depends on the halo occupation number (of dark matter subhalos) at fixed mass and discuss implications for halo model calculations of dark matter power spectra and galaxy clustering statistics. The effect of these halo properties on clustering is strongest for early-forming dwarf-mass halos, which are significantly more clustered than typical halos of their mass. Our results suggest that isolated low-mass galaxies (e.g., low surface brightness dwarfs) should have more slowly rising rotation curves than their more clustered counterparts and may have consequences for the dearth of dwarf galaxies in voids. They also imply that self-calibrating richness-selected cluster samples with their clustering properties might overestimate cluster masses and bias cosmological parameter estimation.

Multiphase galaxy formation: high-velocity clouds and the missing baryon problem

The standard treatment of cooling in Cold Dark Matter halos assumes that all of the gas within a “cooling radius” cools and contracts monolithically to fuel galaxy formation. Here we take into account the expectation that the hot gas in galactic halos is thermally unstable and prone to fragmentation during cooling and show that the implications are more far-reaching than previously expected: allowing multi-phase cooling fundamentally alters expectations about gas infall in galactic halos and naturally gives rise to a characteristic upper-limit on the masses of galaxies, as observed. Specifically, we argue that cooling should proceed via the formation of high-density, � 10 4 K clouds, pressure-confined within a hot gas background. The background medium that emerges has a low density, and can survive as a hydrostatically stable corona with a long cooling time. The fraction of halo baryons contained in the residual hot core component grows with halo mass because the cooling density increases with gas temperature, and this leads to an upper-mass limit in quiescent, non-merged galaxies of � 10 11 M⊙. In this scenario, galaxy formation is fueled by the infall of pressure-supported clouds. For Milky-Way-size systems, clouds of mass � 5 × 10 6 M⊙ that formed or merged within the last several Gyrs should still exist as a residual population in the halo, with a total mass in clouds of � 2 × 10 10 M⊙. The baryonic mass of the Milky Way galaxy is explained naturally in this model, and is a factor of two smaller than would result in the standard treatment without feedback. We expect clouds in galactic halos to be � 1kpc in size and to extend � 150kpc from galactic centers. The predicted properties of Milky Way clouds match well the observed radial velocity distribution, angular sizes, column densities, and velocity widths of High Velocity Clouds around our Galaxy. The clouds we predict are also of the type needed to explain high-ion absorption systems at z < 1, and the predicted covering factor around external galaxies is consistent with observations.

The Accretion Origin of the Milky Way's Stellar Halo

We have used data from the Sloan Digital Sky Survey (SDSS) Data Release 5 to explore the overall structure and substructure of the stellar halo of the Milky Way using ~4 million color-selected main-sequence turnoff stars with -->0.2 18.5 ? r 0.5 3.7 ? 1.2 ? 108 M?. The density profile of the stellar halo is approximately -->? r??, where ? -->2 > ? > ? 4. Yet, we found that all smooth and symmetric models were very poor fits to the distribution of stellar halo stars because the data exhibit a great deal of spatial substructure. We quantified deviations from a smooth oblate/triaxial model using the rms of the data around the model profile on scales 100 pc, after accounting for the (known) contribution of Poisson uncertainties. Within the DR5 area of the SDSS, the fractional rms deviation ?/total of the actual stellar distribution from any smooth, parameterized halo model is 40%: hence, the stellar halo is highly structured. We compared the observations with simulations of galactic stellar halos formed entirely from the accretion of satellites in a cosmological context by analyzing the simulations in the same way as the SDSS data. While the masses, overall profiles, and degree of substructure in the simulated stellar halos show considerable scatter, the properties and degree of substructure in the Milky Ways halo match well the properties of a typical stellar halo built exclusively out of the debris from disrupted satellite galaxies. Our results therefore point toward a picture in which an important fraction of the stellar halo of the Milky Way has been accreted from satellite galaxies.