An optimum time-stepping scheme for N-body simulations

We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than previous time-stepping criteria used in N-body simulations. Furthermore, it requires far fewer force evaluations in low density regions of the simulation and has no dependence on artificial parameters such as, for example, the softening length. This can be orders of magnitude faster than conventional ad-hoc methods that employ combinations of acceleration and softening and is ideally suited for hard problems, such as obtaining the correct dynamics in the very central regions of dark matter haloes. We also derive an eccentricity correction for a general leapfrog integration scheme that can follow gravitational scattering events for orbits with eccentricity e -> 1 with high precision. These new approaches allow us to study a range of problems in collisionless and collisional dynamics from few body problems to cosmological structure formation. We present tests of the time-stepping scheme in N-body simulations of 2-body orbits with eccentricity e -> 1 (elliptic and hyperbolic), equilibrium haloes and a hierarchical cosmological structure formation run.Comment: 15 pages, 10 figures, replaced with version that matches published versio

Analysis of galactic tides and stars on CDM microhalos

A special purpose N-body simulation has been built to understand the tidal heating of the smallest dark matter substructures (10^{-6}\msun and 0.01pc) from the grainy potential of the Milky Way due to individual stars in the disk and the bulge. To test the method we first run simulations of single encounters of microhalos with an isolated star, and compare with analytical predictions of the dark particle bound fraction as a function of impact parameter. We then follow the orbits of a set of microhalos in a realistic flattened Milky Way potential. We concentrate on (detectable) microhalos passing near the Sun with a range of pericenter and apocenter. Stellar perturbers near the orbital path of a microhalo would exert stochachstic impulses, which we apply in a Monte Carlo fashion according to the Besancon model for the distribution of stars of different masses and ages in our Galaxy. Also incorporated are the usual pericenter tidal heating and disk-shocking heating. We give a detailed diagnosis of typical microhalos and find microhalos with internal tangential anisotropy are slightly more robust than the ones with radial anisotropy. In addition, the dark particles generally go through of a random walk in velocity space and diffuse out of the microhalos. We show that the typical destruction time scales are strongly correlated with the stellar density averaged along a microhalo's orbit over the age of the stellar disk. We also present the morphology of a microhalo at several epochs which may hold the key to dark matter detections.Comment: 15 pages, 12 figure

Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology

We use a combination of three large N-body simulations to investigate the dependence of dark matter halo concentrations on halo mass and redshift in the WMAP year 5 cosmology. The median relation between concentration and mass is adequately described by a power-law for halo masses in the range 10^11 - 10^15 Msol/h and redshifts z < 2, regardless of whether the halo density profiles are fit using NFW or Einasto profiles. Compared with recent analyses of the Millennium Simulation, which uses a value of sigma_8 that is higher than allowed by WMAP5, z = 0 halo concentrations are reduced by factors ranging from 23 per cent at 10^11 Msol/h to 16 per cent at 10^14 Msol/h. The predicted concentrations are much lower than inferred from X-ray observations of groups and clusters.Comment: 6 pages, 4 figures, Accepted by MNRAS letters. Version 4: Typo fixe

Sex Commonalities and Differences in Obesity-Related Alterations in Intrinsic Brain Activity and Connectivity.

OBJECTIVE:This study aimed to characterize obesity-related sex differences in the intrinsic activity and connectivity of the brain's reward networks. METHODS:Eighty-six women (n = 43) and men (n = 43) completed a 10-minute resting functional magnetic resonance imaging scan. Sex differences and commonalities in BMI-related frequency power distribution and reward seed-based connectivity were investigated by using partial least squares analysis. RESULTS:For whole-brain activity in both men and women, increased BMI was associated with increased slow-5 activity in the left globus pallidus (GP) and substantia nigra. In women only, increased BMI was associated with increased slow-4 activity in the right GP and bilateral putamen. For seed-based connectivity in women, increased BMI was associated with reduced slow-5 connectivity between the left GP and putamen and the emotion and cortical regulation regions, but in men, increased BMI was associated with increased connectivity with the medial frontal cortex. In both men and women, increased BMI was associated with increased slow-4 connectivity between the right GP and bilateral putamen and the emotion regulation and sensorimotor-related regions. CONCLUSIONS:The stronger relationship between increased BMI and decreased connectivity of core reward network components with cortical and emotion regulation regions in women may be related to the greater prevalence of emotional eating. The present findings suggest the importance of personalized treatments for obesity that consider the sex of the affected individual

Halo model description of the non-linear dark matter power spectrum at k≫1k \gg 1 Mpc−1^{-1}

Accurate knowledge of the non-linear dark-matter power spectrum is important for understanding the large-scale structure of the Universe, the statistics of dark-matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark-matter power spectrum and its cross-power spectrum with dark-matter haloes. Our model extends the halo-model formalism, including realistic substructure population within individual dark-matter haloes and the scatter of the concentration parameter at fixed halo mass. We consider three prescriptions for the mass-concentration relation and two for the substructure distribution in dark-matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales, and is crucial for proper modeling the cosmological weak-lensing signal due to low-mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from n-body simulations.Comment: Accepted for publication in MNRAS - minor change

Quantifying the heart of darkness with GHALO - a multi-billion particle simulation of our galactic halo

We perform a series of simulations of a Galactic mass dark matter halo at different resolutions, our largest uses over three billion particles and has a mass resolution of 1000 M_sun. We quantify the structural properties of the inner dark matter distribution and study how they depend on numerical resolution. We can measure the density profile to a distance of 120 pc (0.05% of R_vir) where the logarithmic slope is -0.8 and -1.4 at (0.5% of R_vir). We propose a new two parameter fitting function that has a linearly varying logarithmic density gradient which fits the GHALO and VL2 density profiles extremely well. Convergence in the density profile and the halo shape scales as N^(-1/3), but the shape converges at a radius three times larger at which point the halo becomes more spherical due to numerical resolution. The six dimensional phase-space profile is dominated by the presence of the substructures and does not follow a power law, except in the smooth under-resolved inner few kpc.Comment: 6 pages, 4 figures, submitted to MNRAS Letters, for full sized images, see http://www.itp.uzh.ch/news.htm

Baryonic Pinching of Galactic Dark Matter Halos

High resolution cosmological N-body simulations of four galaxy-scale dark matter halos are compared to corresponding N-body/hydrodynamical simulations containing dark matter, stars and gas. The simulations without baryons share features with others described in the literature in that the dark matter density slope continuously decreases towards the center, with a density \rho~r^{-1.3+/-0.2}, at about 1% of the virial radius for our Milky Way sized galaxies. The central cusps in the simulations which also contain baryons steepen significantly, to \rho~r^{-1.9+/-0.2}, with an indication of the inner logarithmic slope converging. Models of adiabatic contraction of dark matter halos due to the central build-up of stellar/gaseous galaxies are examined. The simplest and most commonly used model, by Blumenthal et al., is shown to overestimate the central dark matter density considerably. A modified model proposed by Gnedin et al. is shown to be a considerable improvement, but not perfect. Moreover it is found that the contraction parameters not only depend on the orbital structure of the dark-matter-only halos but also on the stellar feedback prescription which is most relevant for the baryonic distribution. Implications for dark matter annihilation at the galactic center are discussed and it is found that although our simulations show a considerable reduced halo contraction as compared to the Blumenthal et al. model, the fluxes from dark matter annihilation is still expected to be enhanced by at least a factor of a hundred as compared to dark-matter-only halos. Finally, it is shown that while dark-matter-only halos are typically prolate, the dark matter halos containing baryons are mildly oblate with minor-to-major axis ratios of c/a=0.73+/-0.11, with their flattening aligned with the central baryonic disks.Comment: 16 pages, 14 figures and 8 tables. Minor text improvements, typo corrections and an updated reference list to match the published versio

Cusps in CDM halos

We resolve the inner region of a massive cluster forming in a cosmological LCDM simulation with a mass resolution of 2*10^6 Msun and before z=4.4 even 3*10^5 Msun. This is a billion times less than the clusters final virial mass and a substantial increase over current LCDM simulations. We achieve this resolution using a new multi-mass refinement procedure and are now able to probe a dark matter halo density profile down to 0.1 percent of the virial radius. The inner density profile of this cluster halo is well fitted by a power-law rho ~ r^-gamma down to the smallest resolved scale. An inner region with roughly constant logarithmic slope is now resolved, which suggests that cuspy profiles describe the inner profile better than recently proposed profiles with a core. The cluster studied here is one out of a sample of six high resolution cluster simulations of Diemand et al. (2004) and it's inner slope of gamma = 1.2 lies close to the sample average.Comment: 10 pages,10 figures. Matches version in press. Added Figure 7 and section 3.3. about upper limits of inner slopes, text (incl, title and abstract) revised, conclusions unchange

The templated growth of a chiral transition metal chalcogenide

We demonstrate that an intrinsically chiral, high Miller index surface of an achiral metal can be used to template the enantioselective growth of chiral transition metal chalcogenide films. Specifically, Cu(643)R can be used as a template for the enantioselective growth of a chiral copper telluride alloy surface. Beyond a critical alloy thickness the chiral influence of the Cu(643)R surface diminishes and an achiral surface forms. Our work demonstrates a new method of producing chiral transition metal chalcogenide surfaces, with potential applications in the study of structurally chiral topological insulators

Galactic halo cusp-core: tidal compression in mergers

We explain in simple terms how the buildup of dark haloes by merging compact satellites, as in the CDM cosmology, inevitably leads to an inner cusp of density profile $\rho \propto r^{-\alpha}$ with \alpha \gsim 1, as seen in cosmological N-body simulations. A flatter halo core with $\alpha <1$ exerts on the satellites tidal compression in all directions, which prevents deposit of stripped satellite material in the core region. This makes the satellite orbits decay from the radius where $\alpha \sim 1$ to the halo centre with no local tidal mass transfer and thus causes a rapid steepening of the inner profile to $\alpha >1$. These tidal effects, the resultant steepening of the profile to a cusp, and the stability of this cusp to tandem mergers with compact satellites, are demonstrated using N-body simulations. The transition at $\alpha \sim 1$ is then addressed using toy models in the limiting cases of impulse and adiabatic approximations and using tidal radii for satellites on radial and circular orbits. In an associated paper we address the subsequent slow convergence from either side to an asymptotic stable cusp with \alpha \gsim 1. Our analysis thus implies that an inner cusp is enforced when small haloes are typically more compact than larger haloes, as in the CDM scenario, such that enough satellite material makes it intact into the inner halo and is deposited there. We conclude that a necessary condition for maintaining a flat core, as indicated by observations, is that the inner regions of the CDM satellite haloes be puffed up by about 50% such that when they merge into a bigger halo they would be disrupted outside the halo core. This puffing up could be due to baryonic feedback processes in small haloes, which may be stimulated by the tidal compression in the halo cores.Comment: 19 pages, Latex, mn2e.cls, some revisions, MNRAS in pres