Aaron D. Ludlow

The Aquarius project: the subhaloes of galactic haloes

We have performed the largest ever particle simulation of a Milky Way sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of six ultrahighly resolved Milky Way sized haloes, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300 000 gravitationally bound subhaloes within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors of up to 1800 accurately reproduce the largest subhaloes with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhaloes within subhaloes, but contrary to recent claims, we find less substructure in subhaloes than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhaloes than in the main halo. Extrapolating the main halos subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3 per cent within 100 kpc, and to be below 0.1 per cent within the solar circle. The inner density profiles of subhaloes show no sign of converging to a fixed asymptotic slope and are well fitted by gently curving profiles of Einasto form. The mean concentrations of isolated haloes are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km s(-1), an extrapolation over some five orders of magnitude in mass. However, at equal maximum circular velocity, subhaloes are more concentrated than field haloes, with a characteristic density that is typically similar to 2.6 times larger and increases with decreasing distance from halo centre.

The diversity and similarity of simulated cold dark matter haloes

We study the mass, velocity dispersion and anisotropy profiles of Lambda cold dark matter (Lambda CDM) haloes using a suite of N-body simulations of unprecedented numerical resolution. The Aquarius Project follows the formation of six different galaxy-sized haloes simulated several times at varying numerical resolution, allowing numerical convergence to be assessed directly. The highest resolution simulation represents a single dark matter halo using 4.4 billion particles, of which 1.1 billion end up within the virial radius. Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The mass profile of Lambda CDM haloes deviates slightly but systematically from the form proposed by Navarro, Frenk & White. The spherically averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is gamma equivalent to - d ln /d ln r less than or similar to 1. Asymptotic inner slopes as steep as the recently claimed proportional to r-1.2 are clearly ruled out. The radial dependence of gamma is well approximated by a power law, gamma proportional to r alpha (the Einasto profile). The shape parameter, alpha, varies slightly but significantly from halo to halo, implying that the mass profiles of Lambda CDM haloes are not strictly universal: different haloes cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power-law form for the spherically averaged pseudo-phase-space density, /Sigma 3 proportional to r-1.875. The index here is identical to that of Bertschingers similarity solution for self-similar infall on to a point mass from an otherwise uniform Einstein-de Sitter universe. The origin of this striking behaviour is unclear, but its robustness suggests that it reflects a fundamental structural property of Lambda CDM haloes. Our conclusions are reliable down to radii below 0.4 per cent of the virial radius, providing well-defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.

Prospects for detecting supersymmetric dark matter in the Galactic halo.

Dark matter is the dominant form of matter in the Universe, but its nature is unknown. It is plausibly an elementary particle, perhaps the lightest supersymmetric partner of known particle species. In this case, annihilation of dark matter in the halo of the Milky Way should produce γ-rays at a level that may soon be observable. Previous work has argued that the annihilation signal will be dominated by emission from very small clumps (perhaps smaller even than the Earth), which would be most easily detected where they cluster together in the dark matter haloes of dwarf satellite galaxies. Here we report that such small-scale structure will, in fact, have a negligible impact on dark matter detectability. Rather, the dominant and probably most easily detectable signal will be produced by diffuse dark matter in the main halo of the Milky Way. If the main halo is strongly detected, then small dark matter clumps should also be visible, but may well contain no stars, thereby confirming a key prediction of the cold dark matter model.

Phase‐space structure in the local dark matter distribution and its signature in direct detection experiments

We study predictions for dark matter phase-space structure near the Sun based on highresolution simulations of six galaxy halos taken from the Aquarius Project. The local DM density distribution is predicted to be remarkably smooth; the density at the Sun differs from the mean over a best-fit ellipsoidal equidensity contour by less than 15% at the 99.9% confidence level. The local velocity distribution is also very smooth, but it differs systematically from a (multivariate) Gaussian distribution. This is not due to th e presence of individual clumps or streams, but to broad features in the velocity modulus and energy distributions that are stable both in space and time and reflect the detailed assembly histo ry of each halo. These features have a significant impact on the signals predicted for WIMP an d axion searches. For example, WIMP recoil rates can deviate by � 10% from those expected from the best-fit multivariate Gaussian models. The axion spectra in our simulations typically peak at lower frequencies than in the case of multivariate Gaussian velocity distribu tions. Also in this case, the spectra show significant imprints of the formation of the halo. Th is implies that once direct DM detection has become routine, features in the detector sign al will allow us to study the dark matter assembly history of the Milky Way. A new field, “dark ma tter astronomy”, will then emerge.

A UNIVERSAL DENSITY PROFILE FOR DARK AND LUMINOUS MATTER

We explore similarities in the luminosity distribution of early-type galaxies and the mass profiles of ΛCDM halos. The spatial structure of these systems may be accurately described by a simple law in which the logarithmic slope of the density varies as a power of the radius: the Sersic law. We show that this law provides a significantly better fit to a set of high-resolution ΛCDM halos than a three-parameter generalization of the Navarro-Frenk-White profile. We discuss possible reasons why the same law should describe dark and luminous systems that span a range of over 7 decades in mass.

The Unorthodox Orbits of Substructure Halos

We use a suite of cosmological N-body simulations to study the properties of substructure halos (subhalos) in galaxy-sized cold dark matter halos. We extend prior work on the subject by considering the whole population of subhalos physically associated with the main system. These are defined as subhalos that have at some time in the past been within the virial radius of the halos main progenitor and that have survived as self-bound entities to z = 0. We find that this population extends beyond three times the virial radius, and contains objects on extreme orbits, including a few with velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups of subhalos, which results in the ejection of some subhalos along tidal streams. Ejected subhalos are primarily low-mass systems, leading to mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time, the less centrally concentrated and kinematically hotter their descendant population. The bias is strongest among the most massive subhalos, but disappears at the low-mass end: below a certain mass, subhalos behave just like test particles in the potential of the main halo. Overall, our findings imply that subhalos identified within the virial radius represent a rather incomplete census of the substructure physically related to a halo: only about one half of all associated subhalos are found today within the virial radius of a halo, and many relatively isolated halos may have actually been ejected in the past from more massive systems. These results may explain the age dependence of the clustering of low-mass halos reported recently by Gao et al., and has further implications for (1) the interpretation of the structural parameters and assembly histories of halos neighboring massive systems; (2) the existence of low-mass dynamical outliers, such as Leo I and And XII in the Local Group; and (3) the presence of evidence for evolutionary effects, such as tidal truncation or ram-pressure stripping, well outside the traditional virial boundary of a galaxy system.

The Diversity and Similarity of Cold Dark Matter Halos

We study the mass, velocity dispersion and anisotropy profiles of Lambda cold dark matter (Lambda CDM) haloes using a suite of N-body simulations of unprecedented numerical resolution. The Aquarius Project follows the formation of six different galaxy-sized haloes simulated several times at varying numerical resolution, allowing numerical convergence to be assessed directly. The highest resolution simulation represents a single dark matter halo using 4.4 billion particles, of which 1.1 billion end up within the virial radius. Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The mass profile of Lambda CDM haloes deviates slightly but systematically from the form proposed by Navarro, Frenk & White. The spherically averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is gamma equivalent to - d ln /d ln r less than or similar to 1. Asymptotic inner slopes as steep as the recently claimed proportional to r-1.2 are clearly ruled out. The radial dependence of gamma is well approximated by a power law, gamma proportional to r alpha (the Einasto profile). The shape parameter, alpha, varies slightly but significantly from halo to halo, implying that the mass profiles of Lambda CDM haloes are not strictly universal: different haloes cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power-law form for the spherically averaged pseudo-phase-space density, /Sigma 3 proportional to r-1.875. The index here is identical to that of Bertschingers similarity solution for self-similar infall on to a point mass from an otherwise uniform Einstein-de Sitter universe. The origin of this striking behaviour is unclear, but its robustness suggests that it reflects a fundamental structural property of Lambda CDM haloes. Our conclusions are reliable down to radii below 0.4 per cent of the virial radius, providing well-defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.

Assembly history and structure of galactic cold dark matter haloes

We use the Aquarius simulation series to study the imprint of assembly history on the structure of Galaxy-mass cold dark matter haloes. Our results confirm earlier work regarding the influence of mergers on the mass density profile and the inside-out growth of haloes. The inner regions that contain the visible galaxies are stable since early times and are significantly affected only by major mergers. Particles accreted diffusely or in minor mergers are found predominantly in the outskirts of haloes. Our analysis reveals trends that run counter to current perceptions of hierarchical halo assembly. For example, major mergers (i.e. those with progenitor mass ratios greater than 1:10) contribute little to the total mass growth of a halo, on average less than 20 per cent for our six Aquarius haloes. The bulk is contributed roughly equally by minor mergers and by ‘diffuse’ material which is not resolved into individual objects. This is consistent with modelling based on excursion-set theory which suggests that about half of this diffuse material should not be part of a halo of any scale. The simulations themselves suggest that a significant fraction is not truly diffuse, since it was ejected from earlier haloes by mergers prior to their joining the main system. The Aquarius simulations resolve haloes to much lower mass scales than are expected to retain gas or form stars. Thus, the fraction of diffuse dark matter accreted by haloes represents a lower limit to the fraction of diffuse baryons accreted by galaxies. Our results thus confirm that most of the baryons from which visible galaxies form are accreted diffusely, rather than through mergers, and they suggest that only relatively rare major mergers will affect galaxy structure at later times.

The mass profile and accretion history of cold dark matter haloes

We use the Millennium Simulation series to investigate the relation between the accretion history and mass profile of cold dark matter (CDM) haloes. We find that the mean inner density within the scale radius, r(-2) (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the virial mass of the main progenitor equals the mass enclosed within r(-2). Scaled to these characteristic values of mass and density, the average mass accretion history, expressed in terms of the critical density of the Universe, M((crit)(z)), resembles that of the enclosed density profile, M( >), at z = 0. Both follow closely the Navarro, Frenk & White (NFW) profile, which suggests that the similarity of halo mass profiles originates from the mass-independence of halo accretion histories. Support for this interpretation is provided by outlier haloes whose accretion histories deviate from the NFW shape; their mass profiles show correlated deviations from NFW and are better approximated by Einasto profiles. Fitting both M( >) and M((crit)) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work that has linked the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only haloes whose accretion histories differ greatly from the NFW shape show notable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter haloes, which do not form hierarchically, and for fluctuation power spectra other than CDM. Our findings, however, predict a subtle but systematic dependence of mass profile shape on accretion history which, if confirmed, would provide strong support for the link between accretion history and halo structure we propose here.

The Dynamical State and Mass-Concentration Relation of Galaxy Clusters

We use the Millennium Simulation series to study how the dynamical state of dark matter haloes affects the relation between mass and concentration. We find that a large fraction of massive systems are identified when they are substantially out of equilibrium and in a particular phase of their dynamical evolution: the more massive the halo, the more likely it is found at a transient stage of high concentration. This state reflects the recent assembly of massive haloes and corresponds to the first pericentric passage of recently accreted material when, before virialization, the kinetic and potential energies reach maximum and minimum values, respectively. This result explains the puzzling upturn in the mass-concentration relation reported in recent work for massive haloes; indeed, the upturn disappears when only dynamically relaxed systems are considered in the analysis. Our results warn against applying simple equilibrium models to describe the structure of rare, massive galaxy clusters and urge caution when extrapolating scaling laws calibrated on lower mass systems, where such deviations from equilibrium are less common. The evolving dynamical state of galaxy clusters ought to be carefully taken into account if cluster studies are to provide precise cosmological constraints.