Ben Moore

Dark Matter Substructure within Galactic Halos

We use numerical simulations to examine the substructure within galactic and cluster mass halos that form within a hierarchical universe. Clusters are easily reproduced with a steep mass spectrum of thousands of substructure clumps that closely matches the observations. However, the survival of dark matter substructure also occurs on galactic scales, leading to the remarkable result that galaxy halos appear as scaled versions of galaxy clusters. The model predicts that the virialized extent of the Milky Ways halo should contain about 500 satellites with circular velocities larger than the Draco and Ursa Minor systems, i.e., bound masses 108 M☉ and tidally limited sizes 1 kpc. The substructure clumps are on orbits that take a large fraction of them through the stellar disk, leading to significant resonant and impulsive heating. Their abundance and singular density profiles have important implications for the existence of old thin disks, cold stellar streams, gravitational lensing, and indirect/direct detection experiments.

Galaxy harassment and the evolution of clusters of galaxies

NEARBY clusters of galaxies are filled with red elliptical E and lenticular SO galaxies1, while younger clusters (at redshifts of ≳ 0.4) contain substantial populations of blue spiral galaxies with morphological peculiarities2–7 (see Fig. 1). Thus, within the last 4–5 billion years, galaxies in clusters underwent strong evolution that completely changed their character. By contrast, galaxies that are not associated with clusters show far less morphological evolution8. Here we propose that multiple highspeed encounters between galaxies—galaxy harassment— drives the morphological evolution in clusters. Our simulations show that these encounters are very different from mergers; they transform small disk galaxies into dwarf elliptical or dwarf spheroidal galaxies. Harassment will leave detectable debris arcs and could provide fuel for quasars in sub-luminous host galaxies.

Cold collapse and the core catastrophe

We show that a universe dominated by cold dark matter fails to reproduce the rotation curves of dark matter dominated galaxies, one of the key problems that it was designed to resolve. We perform numerical simulations of the formation of dark matter haloes, each containing ≳106 particles and resolved to 0.003 times the virial radius, allowing an accurate comparison with rotation curve data. A good fit to both Galactic and cluster-sized haloes can be achieved using the density profile ρ(r)∝[(rrs)1.5(1+(rrs)1.5)]−1, where rs is a scale radius. This profile has a steeper asymptotic slope, ρ(r)∝r−1.5, and a sharper turn-over than found by lower resolution studies. The central structure of relaxed haloes that form within a hierarchical universe has a remarkably small scatter. We compare the results with a sample of dark matter dominated, low surface brightness (LSB) galaxies with circular velocities in the range 100–300xa0kmxa0s−1. The rotation curves of discs within cold dark matter haloes rise too steeply to match these data, which require a constant mass density in the central regions. The effects of Ωmass and Λ cannot reconcile the cold dark matter (CDM) model with data – even if we leave the concentration as a free parameter, we are unable to reproduce the observations with such a steep central density profile. It is important to confirm these results using stellar rather than Hxa0i rotation curves for LSB galaxies. We test the effects of introducing a cut-off in the power spectrum that may occur in a universe dominated by warm dark matter. In this case, haloes form by a monolithic collapse but the final density profile barely changes, demonstrating that the merger history does not play a role in determining the halo structure.

Resolving the Structure of Cold Dark Matter Halos

We examine the effects of mass resolution and force softening on the density profiles of cold dark matter halos that form within cosmological N-body simulations. As we increase the mass and force resolution, we resolve progenitor halos that collapse at higher redshifts and have very high densities. At our highest resolution we have nearly 3×106 particles within the virial radius, which is several orders of magnitude more than previously used, and we can resolve more than 1000 surviving dark matter halos within this single virialized system. The halo profiles become steeper in the central regions, and we may not have achieved convergence to a unique slope within the inner 10% of the virialized region. Results from two very high resolution halo simulations yield steep inner density profiles, ρ(r)~r−1.4. The abundance and properties of arcs formed within this potential will be different from calculations based on lower resolution simulations. The kinematics of disks within such a steep potential may prove problematic for the cold dark matter model when compared with the observed properties of halos on galactic scales.

Morphological Transformation from Galaxy Harassment

Galaxy morphologies in clusters have undergone a remarkable transition over the past several billion yr. Distant clusters at z ~ 0.4 are filled with small spiral galaxies, many of which are disturbed and show evidence of multiple bursts of star formation. This population is absent from nearby clusters, where spheroidals comprise the faint end of the luminosity function. Our numerical simulations follow the evolution of disk galaxies in a rich cluster resulting from encounters with brighter galaxies and the clusters tidal field, or galaxy harassment. After a bursting transient phase, they undergo a complete morphological transformation from disks to spheroidals. We examine the remnants and find support for our theory in detailed comparisons of the photometry and kinematics of the spheroidal galaxies in clusters. Our model naturally accounts for the intermediate-age stellar population seen in these spheroidals, as well as for the trend in the dwarf-to-giant ratio with cluster richness. The final shapes are typically prolate and are flattened primarily by velocity anisotropy. Their mass-to-light ratios are in the range 3-8, in good agreement with observations.

Density Profiles and Substructure of Dark Matter Halos: Converging Results at Ultra-High Numerical Resolution

Can dissipationless N-body simulations be used to reliably determine the structural and substructure properties of dark matter halos? A large simulation of a galaxy cluster in a cold dark matter universe is used to increase the force and mass resolution of current high-resolution simulations by almost an order of magnitude to examine the convergence of the important physical quantities. The cluster contains ~5 million particles within the final virial radius, Rvir 2 Mpc (with H0 = 50 km s-1 Mpc-1), and is simulated using a force resolution of 1.0 kpc (≡0.05% of Rvir); the final virial mass is 4.3 × 1014 M☉, equivalent to a circular velocity of vcirc ≡ (GM/R)1/2 1000 km s-1 at the virial radius. The central density profile has a logarithmic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution have converged to the physical limit down to scales of a few kpc (~0.2% of Rvir). In addition, the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small to large galaxy scales (vcirc > 100 km s-1, m > 1011 M☉), the circular velocity function and the mass function of substructures can be approximated by power laws with slopes of ~-4 and ~-2, respectively. At the current resolution, overmerging (a numerical effect that leads to structureless virialized halos in low-resolution N-body simulations) seems to be globally unimportant for substructure halos with circular velocities of vcirc > 100 km s-1 (~10% of the clusters vcirc). We can identify subhalos orbiting in the very central region of the cluster (R 100 kpc), and we can trace most of the cluster progenitors from high redshift to the present. The object at the cluster center (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with vcirc 300 km s-1. Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by ≈20% over a 5 billion yr period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within 10%, but the halos are spatially antibiased, and in the very central region of the cluster (R/Rvir < 0.3) they show positive velocity bias (bv ≡ σv3D,halos/σv3D,DM 1.2-1.3); however, this effect appears to depend on numerical resolution.

Ram pressure stripping of spiral galaxies in clusters

We use three-dimensional SPH/N-body simulations to study ram pressure stripping of gas from spiral galaxies orbiting in clusters. We find that the analytic expectation of Gunn & Gott, relating the gravitational restoring force provided by the disc to the ram pressure force, provides a good approximation to the radius at which gas will be stripped from a galaxy. However, at small radii it is also important to consider the potential provided by the bulge component. A spiral galaxy passing through the core of a rich cluster, such as Coma, will have its gaseous disc truncated to ∼4xa0kpc, thus losing ∼80xa0per cent of its diffuse gas mass. The time-scale for this to occur is a fraction of a crossing time ∼107xa0yr. Galaxies orbiting within poorer clusters, or inclined to the direction of motion through the intracluster medium, will lose significantly less gas. We conclude that ram pressure alone is insufficient to account for the rapid and widespread truncation of star formation observed in cluster galaxies, or the morphological transformation of Sabs to S0s that is necessary to explain the Butcher–Oemler effect.

Gone with the Wind: The Origin of S0 Galaxies in Clusters

We present three-dimensional, high-resolution hydrodynamical simulations of the interaction between the hot ionized intracluster medium and the cold interstellar medium of spiral galaxies. Ram pressure and turbulent/viscous stripping remove 100% of the atomic hydrogen content of luminous galaxies like the Milky Way within 100 million years. These mechanisms naturally account for the morphology of S0 galaxies and the rapid truncation of star formation implied by spectroscopic observations, as well as a host of observational data on the neutral hydrogen (HI) morphology of galaxies in clusters.

Dark matter haloes within clusters

We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 kmxa0s−1 within the cluster virial radius of 2 Mpc (with Hubble constant H0xa0=xa050xa0kmxa0s−1xa0Mpc−1). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —‘galaxy harassment’. Mergers between haloes do not occur inside the cluster virial radius.

The Metamorphosis of Tidally Stirred Dwarf Galaxies

We present results from high-resolution N-body/SPH (smoothed particle hydrodynamic) simulations of rotationally supported dwarf irregular galaxies moving on bound orbits in the massive dark matter halo of the Milky Way. The dwarf models span a range in disk surface density and the masses and sizes of their dark halos are consistent with the predictions of cold dark matter cosmogonies. We show that the strong tidal field of the Milky Way determines severe mass loss in their halos and disks and induces bar and bending instabilities that transform low surface brightness dwarfs (LSBs) into dwarf spheroidals (dSphs) and high surface brightness dwarfs (HSBs) into dwarf ellipticals (dEs) in less than 10 Gyr. The final central velocity dispersions of the remnants are in the range 8-30 km s-1 and their final v/? falls to values less than 0.5, matching well the kinematics of early-type dwarfs. The transformation requires the orbital time of the dwarf to be 3-4 Gyr, which implies a halo as massive and extended as predicted by hierarchical models of galaxy formation to explain the origin of even the farthest dSph satellites of the Milky Way, Leo I, and Leo II. We show that only dwarfs with central dark matter densities as high as those of Draco and Ursa Minor can survive for 10 Gyr in the proximity of the Milky Way. A correlation between the central density and the distance of the dwarfs from the primary galaxy is indeed expected in hierarchical models, in which the densest objects should have small orbital times because of their early formation epochs. Part of the gas is stripped and part is funneled to the center because of the bar, generating one strong burst of star formation in HSBs and smaller, multiple bursts in LSBs. Therefore, the large variety of star formation histories observed in Local Group dSphs arises because different types of dIrr progenitors respond differently to the external perturbation of the Milky Way. Our evolutionary model naturally explains the morphology-density relation observed in the Local Group and in other nearby loose groups. Extended low surface brightness stellar and gaseous streams originate from LSBs and follow the orbit of the dwarfs for several gigayears. Because of their high velocities, unbound stars projected along the line of sight can lead to overestimating the mass-to-light ratio of the bound remnant by a factor 2, but this does not eliminate the need of extremely high dark matter contents in some of the dSphs.