Michael S. Warren

Toward a halo mass function for precision cosmology: The Limits of universality

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at -->z 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at -->z = 0 for virial masses in the range -->1011 h−1 M☉ ≤ M≤ 1015 h−1 M☉ to 5%, improving on previous results by a factor of 2-3. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at -->z = 0 and earlier epochs. Earlier studies have sought to calibrate a universal mass function, in the sense that the same functional form and parameters can be used for different cosmologies and redshifts when expressed in appropriate variables. In addition to our fitting formulae, our main finding is that the mass function cannot be represented by a universal function at this level or accuracy. The amplitude of the universal function decreases monotonically by 20%-50%, depending on the mass definition, from -->z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.

Dark halos formed via dissipationless collapse. I - Shapes and alignment of angular momentum

We use N-body simulations on highly parallel supercomputers to study the structure of Galactic dark matter halos. The systems form by gravitational collapse from scale-free and more general Gaussian initial density perturbations in an expanding 400 Mpc 3 spherical slice of an Einstein-deSitter universe. We use N∼10 6 and a force softening e=5 kpc in most of our models. We analyze the structure and kinematics of the ∼10 2 largest relaxed halos in each of 10 separate simulations

A parallel hashed oct-tree N-body algorithm

The authors report on an efficient adaptive N-body method which we have recently designed and implemented. The algorithm computes the forces on an arbitrary distribution of bodies in a time which scales as N log N with the particle number. The accuracy of the force calculations is analytically bounded, and can be adjusted via a user defined parameter between a few percent relative accuracy, down to machine arithmetic accuracy. Instead of using pointers to indicate the topology of the tree, the authors identify each possible cell with a key. The mapping of keys into memory locations is achieved via a hash table. This allows the program to access data in an efficient manner across multiple processors. Performance of the parallel program is measured on the 512 processor Intel Touchstone Delta system. Comments on a number of wide-ranging applications which can benefit from application of this type of algorithm are included.

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including smoothed particle hydrodynamics (SPH) and grid methods with fixed, deformable, or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gasdynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be nonradiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying, although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of 2. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to within about 10%, and the ratio of specific dark matter kinetic to gas thermal energies agree to within about 5%. Various factors, including differences in the internal timing of the simulations, contribute to the spread in calculated cluster properties. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modeled.

The large-scale bias of dark matter halos: numerical calibration and model tests

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flatCDM cosmology. Halos are identified using the spherical over density algorithm, which finds the mass around isolated peaks in the density field such that the m ean density istimes the background. We calibrate fitting functions for the large scale bias that are adaptable to any value ofwe examine. We find a � 6% scatter about our best fit bias relation. Our fitting functi ons couple to the halo mass functions of Tinker et. al. (2008) such that bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellip soidal collapse model of Sheth, Mo, & Tormen (2001), and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking l ength 0.2 are systematically lower than for halos with the canonical � = 200 overdensity by � 10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak- background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but � 20% residuals remain, both at high and low masses. Subject headings:cosmology:theory — methods:numerical — large scale structure of the universe

Percolation Galaxy Groups and Clusters in the SDSS Redshift Survey: Identification, Catalogs, and the Multiplicity Function

We identify galaxy groups and clusters in volume-limited samples of the Sloan Digital Sky Survey (SDSS) redshift survey, using a redshift-space friends-of-friends algorithm. We optimize the friends-of-friends linking lengths to recover galaxy systems that occupy the same dark matter halos, using a set of mock catalogs created by populating halos of N-body simulations with galaxies. Extensive tests with these mock catalogs show that no combination of perpendicular and line-of-sight linking lengths is able to yield groups and clusters that simultaneously recover the true halo multiplicity function, projected size distribution, and velocity dispersion. We adopt a linking length combination that yields, for galaxy groups with 10 or more members: a group multiplicity function that is unbiased with respect to the true halo multiplicity function; an unbiased median relation between the multiplicities of groups and their associated halos; a spurious group fraction of less than ~1%; a halo completeness of more than ~97%; the correct projected size distribution as a function of multiplicity; and a velocity dispersion distribution that is ~20% too low at all multiplicities. These results hold over a range of mock catalogs that use different input recipes of populating halos with galaxies. We apply our group-finding algorithm to the SDSS data and obtain three group and cluster catalogs for three volume-limited samples that cover 3495.1 deg2 on the sky, go out to redshifts of 0.1, 0.068, and 0.045, and contain 57,138, 37,820, and 18,895 galaxies, respectively. We correct for incompleteness caused by fiber collisions and survey edges and obtain measurements of the group multiplicity function, with errors calculated from realistic mock catalogs. These multiplicity function measurements provide a key constraint on the relation between galaxy populations and dark matter halos.

Astrophysical N-body simulations using hierarchical tree data structures

The authors report on recent large astrophysical N-body simulations executed on the Intel Touchstone Delta system. They review the astrophysical motivation and the numerical techniques and discuss steps taken to parallelize these simulations. The methods scale as O(N log N), for large values of N, and also scale linearly with the number of processors. The performance sustained for a duration of 67 h, was between 5.1 and 5.4 Gflop/s on a 512-processor system.<<ETX>>

A portable parallel particle program

We describe our implementation of the parallel hashed oct-tree (HOT) code, and in particular its application to neighbor finding in a smoothed particle hydrodynamics (SPH) code. We also review the error bounds on the multipole approximations involved in treecodes, and extend them to include general cell-cell interactions. Performance of the program on a variety of problems (including gravity, SPH, vortex method and panel method) is measured on several parallel and sequential machines.

Large-scale bias and stochasticity of haloes and dark matter

On large scales, galaxies and their haloes are usually assumed to trace the dark matter with a constant bias and dark matter is assumed to trace the linear density field. We test these assumption using several large N-body simulations with 384 3 ‐1024 3 particles and box sizes of 96‐1152 h −1 Mpc, which can both resolve the small galactic-size haloes and sample the large-scale fluctuations. We explore the average halo bias relation as a function of halo mass and show that existing fitting formulae overestimate the halo bias by up to 20 per cent in the regime just below the non-linear mass. We propose a new expression that fits our simulations well. We find that the halo bias is nearly constant, b ∼ 0.65‐0.7, for masses below one-tenth of the non-linear mass. We next explore the relation between the initial and final dark matter in individual Fourier modes and show that there are significant fluctuations in their ratio, ranging from 10 per cent rms at k ∼ 0.03 h Mpc −1 to 50 per cent rms at k ∼ 0.1 h Mpc −1 .W e a rgue that these large fluctuations are caused by perturbative effects beyond the linear theory, which are dominated by long-wavelength modes with large random fluctuations. Similar or larger fluctuations exist between haloes and dark matter and between haloes of different mass. These fluctuations must be included in attempts to determine the relative bias of two populations from their maps, which would otherwise be immune to sampling variance. Ke yw ords: cosmology: theory ‐ dark matter ‐ large-scale structure of Universe.

The Collapse of Rotating Massive Stars in Three Dimensions

Most simulations of the core collapse of massive stars have focused on the collapse of spherically symmetric objects. If these stars are rotating, this symmetry is broken, opening up a number of effects that are just now being studied. The list of proposed effects spans a range of extremes: from fragmentation of the collapsed iron core to modifications of the convective instabilities above the core; from the generation of strong magnetic fields that then drive the supernova explosion to the late-time formation of magnetic fields to produce magnetars after the launch of the supernova explosion. The list of the observational effects of rotation ranges from modifications in the gamma-ray line spectra, nucleosynthetic yields, and shape of supernova remnants caused by rotation-induced asymmetric explosions to strong pulsar radiation, the emission of gravitational waves, and altered r-process nucleosynthetic yields caused by rapidly rotating stars. In this paper we present the results of three-dimensional collapse simulations of rotating stars for a range of stellar progenitors. We find that for the most rapidly spinning stars, rotation does indeed modify the convection above the proto-neutron star, but it is not fast enough to cause core fragmentation. Similarly, although strong magnetic fields can be produced once the proto-neutron star cools and contracts, the proto-neutron star does not spin fast enough to generate strong magnetic fields quickly after collapse, and, for our simulations, magnetic fields will not dominate the supernova explosion mechanism. Even so, the resulting pulsars for our most rapidly rotating models may emit enough energy to dominate the total explosion energy of the supernova. However, more recent stellar models predict rotation rates that are much too slow to affect the explosion, but these models are not sophisticated enough to determine whether the most recent or past stellar rotation rates are more likely. Thus, we must rely on observational constraints to determine the true rotation rates of stellar cores just before collapse. We conclude with a discussion of the possible constraints on stellar rotation that we can derive from core-collapse supernovae.In this paper, we present the results of 3-dimensional collapse simulations of rotating stars for a range of stellar progenitors. We find that for the fastest spinning stars, rotation does indeed modify the convection above the proto-neutron star, but it is not fast enough to cause core fragmentation. Similarly, although strong magnetic fields can be produced once the proto-neutron star cools and contracts, the proto-neutron star is not spinning fast enough to generate strong magnetic fields quickly after collapse and, for our simulations, magnetic fields will not dominate the supernova explosion mechanism. Even so, the resulting pulsars for our fastest rotating models may emit enough energy to dominate the total explosion energy of the supernova. However, more recent stellar models predict rotation rates that are much too slow to affect the explosion, but these models are not sophisticated enough to determine whether the most recent, or past, stellar rotation rates are most likely. Thus, we must rely upon observational constraints to determine the true rotation rates of stellar cores just before collapse. We conclude with a discussion of the possible constraints on stellar rotation which we can derive from core-collapse supernovae.