George Lake

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.

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.

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.

On the survival and destruction of spiral galaxies in clusters

We follow the evolution of disk galaxies within a cluster that forms hierarchically in a cold dark matter N-body simulation. At a redshift z=0.5 we select several dark matter halos that have quiet merger histories and are about to enter the newly forming cluster environment. The halos are replaced with equilibrium high resolution model spirals that are constructed to represent examples of low surface brightness (LSB) and high surface brightness (HSB) galaxies. Varying the disk and halo structural parameters reveals that the response of a spiral galaxy to tidal encounters depends primarily on the potential depth of the mass distribution and the disk scale length. LSB galaxies, characterised by slowly rising rotation curves and large scale lengths, evolve dramatically under the influence of rapid encounters with substructure and strong tidal shocks from the global cluster potential --- galaxy harassment. We find that up to 90% of their stars are tidally stripped and congregate in large diffuse tails that trace the orbital path of the galaxy and form the diffuse intra-cluster light. The bound stellar remnants closely resemble the dwarf spheroidals (dEs) that populate nearby clusters. HSB galaxies are stable to the chaos of cluster formation and tidal encounters. These disks lie well within the tidally limited dark matter halos and their potentials are more concentrated. Although very few stars are stripped, the scale height of the disks increases substantially and no spiral features remain, therefore we speculate that these galaxies would be identified as S0 galaxies in present day clusters.

The Formation of a Realistic Disk Galaxy in Λ-dominated Cosmologies

We simulate the formation of a realistic disk galaxy within the hierarchical scenario of structure formation and study its internal properties to the present epoch. We use a set of smoothed particle hydrodynamic (SPH) simulations, with a high dynamical range and force resolution, that include cooling, star formation, supernovae (SNe) feedback and a redshift-dependent UV background. We compare results from a Λ cold dark matter (ΛCDM) simulation to a Λ warm dark matter (ΛWDM) (2 keV) simulation that forms significantly less small-scale structure. We show how high mass and force resolution in both the gas and dark-matter components play an important role in solving the angular momentum catastrophe claimed from previous simulations of galaxy formation within the hierarchical framework. Hence, a large disk forms without the need of strong energy injection, the z = 0 galaxies lie close to the I band Tully-Fisher relation, and the stellar material in the disk component has a final specific angular momentum equal to 40% and 90% of the dark halo in the ΛCDM and ΛWDM models, respectively. If rescaled to the Milky Way, the ΛCDM galaxy has an overabundance of satellites, with a total mass in the stellar halo 40% of that in the bulge+disk system. The ΛWDM galaxy has a drastically reduced satellite population and a negligible stellar spheroidal component. Encounters with satellites play only a minor role in disturbing the disk. Satellites possess a variety of star formation histories linked to mergers and pericentric passages along their orbit around the primary galaxy. In both cosmologies, the galactic halo retains most of the baryons accreted and builds up a hot gas phase with a substantial X-ray emission. Therefore, while we have been successful in creating a realistic stellar disk in a massive galaxy within the ΛCDM scenario, energy injection emerges as necessary ingredient to reduce the baryon fraction in galactic halos, independent of the cosmology adopted.

Thin, thick and dark discs in ΛCDM

In acold dark matter (� CDM) cosmology, the Milky Way accretes satellites into the stellar disc. We use cosmological simulations to assess the frequency of near disc plane and higher inclination accretion events, and collisionless simulations of satellite mergers to quantify the final state of the accreted material and the effect on the thin disc. On average, a Milky Way-sized galaxy has three subhaloes with vmax > 80 km s −1 ; seven with vmax > 60 km s −1 and 15 with vmax > 40 km s −1 merge at redshift z 1. Assuming isotropic accretion, a third of these merge at an impact angle θ 20 ◦ are twice as likely as low-inclination ones. These lead to structures that closely resemble the recently discovered inner and outer stellar haloes. They also do more damage to the Milky Way stellar disc creating a more pronounced flare, and warp; both long-lived and consistent with current observations. The most massive mergers (vmax 80 km s −1 ) heat the thin disc enough to produce a thick disc. These heated thin-disc stars are essential for obtaining a thick disc as massive as that seen in the Milky Way; they likely comprise some ∼50-90 per cent of the thick disc stars. The Milky Way thin disc must reform from fresh gas after z = 1. Only one in four of our sample Milky Way haloes experiences mergers massive and late enough to fully destroy the thin disc. We conclude that thick, thin and dark discs occur naturally within aCDM cosmology.

Evolution of the mass function of dark matter haloes

We use a high resolutionCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of fifteen, in a 50 h −1 Mpc volume containing 80 million particles. Our low redshift results allow us to probe low σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth and Tormen mass function provides an excellent match to all of our data except for redshifts of ten and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 percent for the 10 10 − 10 11 M⊙ haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth and Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high redshift (z ≃ 6) QSOs, which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50%. We test the sensitivity of our results to force accuracy, starting redshift, and halo finding algorithm.

Substructure in Dark Halos: Orbital Eccentricities and Dynamical Friction

The virialized regions of galaxies and clusters contain significant amounts of substructure; clusters have hundreds to thousands of galaxies, and satellite systems and globular clusters orbit the halos of individual galaxies. These orbits can decay owing to dynamical friction. Depending on their orbits and their masses, the substructures either merge, are disrupted, or survive to the present day. We examine the distributions of eccentricities of orbits within mass distributions similar to those we see for galaxies and clusters. A comprehensive understanding of these orbital properties is essential to calculate the rates of physical processes relevant to the formation and evolution of galaxies and clusters. We derive the orbital eccentricity distributions for a number of spherical potentials. These distributions depend strongly on the velocity anisotropy, but only slightly on the shape of the potential. The eccentricity distributions in the case of an isotropic distribution function are strongly skewed toward high eccentricities, with a median value of typically ~0.6, corresponding to an apocenter-to-pericenter ratio of 4.0. We also present high-resolution N-body simulations of the orbital decay of satellite systems on eccentric orbits in an isothermal halo. The dynamical friction timescales are found to decrease with increasing orbital eccentricity because of the dominating deceleration at the orbits pericenter. The orbital eccentricity stays remarkably constant throughout the decay; although the eccentricity decreases near pericenter, it increases again near apocenter, such that there is no net circularization. We briefly discuss several applications for our derived distributions of orbital eccentricities and the resulting decay rates from dynamical friction. We compare the theoretical eccentricity distributions to those of globular clusters and galactic satellites for which all six phase-space coordinates (and therewith their orbits) have been determined. We find that the globular clusters are consistent with a close-to-isotropic velocity distribution, and they show large orbital eccentricities because of this (not in spite of this, as has been previously asserted). In addition, we find that the limited data on the Galactic system of satellites appears to be different and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure.

The effect of non-gravitational gas heating in groups and clusters of galaxies

We present a detailed study of a set of gas-dynamical simulations of galaxy groups and clusters in a flat, �CDM model with m = 0.3, aimed at exploring the effect of non– gravitational heating on the observable properties of the intracluster medium (ICM). We use GASOLINE, a version of the code PKDGRAV that includes an SPH description of hydrodynamics to simulate the formation of four cosmic halos with virial temperatures in the range 0.5∼ T ∼ 8 keV. These simulations resolve the structure and properties of the intra–cluster medium (ICM) down to a small fraction of the virial radius, Rvir. At our resolution X–ray luminosities, (LX), of runs with gravitational heating only are in good agreement, over almost two orders of magnitude in mass, with analytical predictions, that assume a universal profile for CDM halos. For each simulated structure, non–gravitational heating of the ICM is implemented in two different ways: (1) by imposing a minimum entropy floor, Sfl, at a given redshift, that we take in the range 16 z 65; (2) by gradually heating gas within collapsed regions, proportionally to the supernova rate expected from semi–analytical modeling of galaxy formation in halos having mass equal to that of the simulated systems. Our main results are the following. (a) An extra heating energy Eh∼ 1 keV per gas particle within Rvir at z = 0 is required to reproduce the observed LX–T relation, independent of whether it is provided in an impulsive way to create an entropy floor Sfl = 50–100 keV cm 2 , or is modulated in redshift according to the star formation rate; our SN feedback recipe provides at most Eh ≃ 1/3 keV/part and, therefore, its effect on the LX–T relation is too small to account for the observed LX–T relation. (b) The required heating implies, in small groups with T ∼ 0.5 keV, a baryon fraction as low as ∼ 40% of the cosmic value at Rvir/2; this fraction increases to about 80% for a T ≃ 3 keV cluster. (c) Temperature profiles are almost scale free across the whole explored mass range, with T decreasing by a factor of three at the virial radius. (d) The mass–temperature relation is almost unaffected by non–gravitational heating and follows quite closely the M ∝ T 3/2 scaling; however, when compared with data on the M500–Tew relation, it has a ∼ 40% higher normalization. This discrepancy is independent of the heating scheme adopted. The inclusion of cooling in a run of a small group steepens the central profile of the potential well while removing gas from the diffuse phase. This has the effects of increasing Tew by ∼ 30%, possibly reconciling the simulated and the observed M500–Tew relations, and of decreasing LX by ∼ 40%. However, in spite of the inclusion of SN feedback energy, almost 40% of the gas drops out from the hot diffuse phase, in excess of current observational estimates of the amount of cold baryons in galaxy systems. Likely, only a combination of different heating sources (SNe and AGNs) and cooling will be able to reproduce both the LX–Tew and M500–Tew relations, as observed in groups and clusters, while balancing the cooling runaway.