Dark matter subhaloes in numerical simulations

We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 1011 to 1014 M⊙ at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation dn/dv = (1/8)(vcmax/vcmax,host)−4. Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for r ≳ 0.3rvir, where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of P ∝ kn, and demonstrate that a steeper spectral index, n, results in significantly less substructur

Dark Matter Subhaloes in Numerical Simulations

We use cosmological LCDM numerical simulations to model the evolution of the substructure population in sixteen dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10^11 to 10^14 Msun at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation: dn/dv=(1/8)(v_cmax/v_cmax,host)^-4. Halo to halo variance in the VDF is a factor of roughly two to four. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for r >~ 0.3r_vir, where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease toward the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias toward more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power law cosmologies of P ~ k^n, and demonstrate that a steeper spectral index, n, results in significantly less substructure.Comment: minor revisions to match accepted version, MNRAS, 359, 135

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, 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 & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the 1010-1011 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 & 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 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorith

Evolution of the density profiles of dark matter haloes

We use numerical simulations in a ΛCDM cosmology to model density profiles in a set of 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 1011-1014 M⊙, down to approximately 0.5 per cent of the virial radius, and from redshift of 5 to the present, covering a larger range in parameter space than previous works. We confirm that the cusp of the density profile is set at redshifts of 2 or greater and remains remarkably stable to the present time, when considered in non-comoving coordinates. Motivated by the diversity and evolution of halo profile shapes, we fit our haloes to the two-parameter profile, ρ ∝ 1/{(cγr/rvir)γ[1 + (cγr/rvir)]3-γ}, where the steepness of the cusp is given by the asymptotic inner slope parameter, γ, and its radial extent is described by the concentration parameter, cγ (with cγ defined as the virial radius divided by the concentration radius). In our simulations, we find γ ≃ 1.4 − 0.08 log10(M/M*) for haloes of 0.01 M*-1000 M*, with a large scatter of Δγ ∼ ±0.3, where M* is the redshift dependent characteristic mass of collapsing haloes; and cγ ≃ 8.(M/M*)−0.15, with a large M/M* dependent scatter roughly equal to ±cγ. Our redshift zero haloes have inner slope parameters ranging approximately from r−1 (Navarro, Frank and White) to r−1.5 (Moore et al.), with a median of roughly r−1.3. This two-parameter profile fit works well for all types of haloes in our simulations, whether or not they show evidence of a steep asymptotic cusp. We also model a cluster in power-law cosmologies of P∝kn, with n = (0, −1, −2, −2.7). Here we find that the concentration radius and the inner cusp slope are both a function of n, with larger concentration radii and shallower cusps for steeper power spectra. We have completed a thorough resolution study and find that the minimum resolved radius is well described by the mean interparticle separation over a range of masses and redshifts. The trend of steeper and more concentrated cusps for smaller M/M* haloes clearly shows that dwarf-sized ΛCDM haloes have, on average, significantly steeper density profiles within the inner few per cent of the virial radius than inferred from recent observations. Code to reproduce this profile can be downloaded from http://www.icc.dur.ac.uk/~reed/profile.htm

Evolution of the Density Profiles of Dark Matter Haloes

We use numerical simulations in a Lambda CDM cosmology to model density profiles in a set of 16 dark matter haloes with resolutions of up to 7 million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 10^11 to 10^14 M_sun, down to approximately 0.5% of the virial radius, and from redshift 5 to the present. The cusp of the density profile is set at redshifts of 2 or greater and remains remarkably stable to the present time, when considered in non-comoving coordinates. We fit our haloes to a 2 parameter profile where the steepness of the asymptotic cusp is given by gamma, and its radial extent is described by the concentration, c_gamma. In our simulations, we find gamma = 1.4 - 0.08Log(M/M_*) for haloes of 0.01M_* to 1000M_*, with a large scatter of gamma ~ +/-0.3$; and c_gamma = 8*M/M_*^{-0.15}, with a large M/M_* dependent scatter roughly equal to +/- c_gamma. Our redshift zero haloes have inner slope parameters ranging approximately from r^{-1} to r^{-1.5}, with a median of roughly r^{-1.3}. This 2 parameter profile fit works well for all our halo types, whether or not they show evidence of a steep asymptotic cusp. We also model a cluster in power law cosmologies of P ~ k^n (n=0,-1,-2,-2.7). We find larger concentration radii and shallower cusps for steeper n. The minimum resolved radius is well described by the mean interparticle separation. The trend of steeper and more concentrated cusps for smaller$M/M_*$ haloes clearly shows that dwarf sized Lambda CDM haloes have, on average, significantly steeper density profiles within the inner few percent of the virial radius than inferred from recent observations. Code to reproduce this profile can be downloaded from http://www.icc.dur.ac.uk/~reed/profile.htmlComment: Code to reproduce this profile can be downloaded from http://www.icc.dur.ac.uk/~reed/profile.html Accepted version, minor changes, MNRAS, 357, 82 (abstract abridged

LEO degradation of graphite and carbon-based composites aboard Space Shuttle Flight STS-46

Six different types of carbon and carbon-boron nitride composites were exposed to low Earth orbit aboard Space Shuttle flight STS-46. The samples received a nominal atomic oxygen fluence of 2.2 x 10(exp 20) atoms/sq cm in 42 hours of exposure. Pyrolytic graphite and highly oriented pyrolytic graphite showed significant degradation, and the measured erosion yield was within a factor of two of published values. The erosion yield of pyrolytic boron nitride was found to be 2.6 x 10(exp 26) cu cm/atom in plasma asher exposure, over 42 times lower than that of pyrolytic graphite. This low erosion yield makes graphite plus boron nitride mixtures quite resistant to low Earth orbit exposure. Evidence suggests that the graphitic component was preferentially etched, leaving the surface boron nitride rich. Degradation resistance increases with boron nitride composition. Carbon fiber/carbon composites degraded in low Earth orbit, and the carbon pitch binder was found to etch more easily than the graphite fibers which have much higher degradation resistance

Evolution of the Mass Function of Dark Matter Haloes

We use a high resolution $\Lambda$CDM 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 $\sigma$ 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} \msun 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 $\simeq$ 6) QSOs, which are thought to be hosted by haloes at 5$\sigma$ 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.Comment: v2: 9 pages, 11 figures, accepted by MNRAS with revisions. Includes additional numerical tests and error discussion, clarifications, and referee suggestion

The Geography of the International System: The CShapes Dataset

We describe CShapes, a new dataset that provides historical maps of state boundaries and capitals in the post-World War II period. The dataset is coded according to both the Correlates of War and the Gleditsch and Ward (1999) state lists, and is therefore compatible with a great number of existing databases in the discipline. Provided in a geographic data format, CShapes can be used directly with standard GIS software, allowing a wide range of spatial computations. In addition, we supply a CShapes package for the R statistical toolkit. This package enables researchers without GIS skills to perform various useful operations on the GIS maps. The paper introduces the CShapes dataset and structure and gives three examples of how to use CShapes in political science research. First, we show how results from quantitative analysis can be depicted intuitively as a map. The second application gives an example of computing indicators on the CShapes maps, which can then be used in statistical tests. Third, we illustrate the use of CShapes for generating different weights matrices in spatial statistical applications. All the examples can be replicated using the freely available R package and do not require specialized GIS skills. The dataset is available for download from the CShapes website (http://nils.weidmann.ws/projects/cshapes). © Taylor & Francis Group, LLC

Experimental assessment of unvalidated assumptions in classical plasticity theory.

This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data, thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model