arXiv subjects

Joachim Stadel

Publications and source records attributed to Joachim Stadel.

117 records · Page 7Linked to original sources

arXiv1998

Substructure in Dark Halos: Orbital Eccentricities and Dynamical Friction

We examine the distributions of eccentricities of orbits within mass distributions like 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. 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, but the dependence is weaker than previously suggested. 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. Finally, we discuss a number of applications. We find that the distribution of orbital eccentricities of the globular clusters in the Milky Way is consistent with a close to isotropic velocity distribution. The limited data on the galactic system of satellites, however, appears to be different and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure.

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arXiv1998

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 (dE's) 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.

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arXiv1998

N-point correlations in CDM and $Ω$CDM Simulations

Higher order statistics are investigated in ($Ω$)CDM universes by analyzing $500\mpc$ high resolution tree N-body simulations with both $Ω= 1$, and $Ω< 1$. The amplitudes of the N-point correlation functions are calculated from moments of counts-in-cells determined by a pair of new algorithms especially developed for large simulations. This approach enables massive oversampling with $\simeq 10^{9-14}$ cells for accurate determination of factorial moments from up to 47 million particles in the scale range of $8 \kpc - 125\mpc$. Thorough investigation shows that there are three scale ranges in the simulations: $\ge 8\mpc$, weakly non-linear regime, where perturbation theory applies with utmost precision, $1\mpc - 8\mpc$, the non-linear plateau, and finally $\le 1\mpc$, a regime where dynamical discreteness effects dominate the higher order statistics. In the physically relevant range of $1\mpc-125\mpc$ the results i) confirm the validity of perturbation theory in the weakly non-linear regime, ii) establish the existence of a plateau in the highly non-linear regime similar to the one observed in scale free simulations iii) show extended perturbation theory to be an excellent approximation for the non-linear regime iv) find the time dependence of the $S_N$'s to be negligible in both regimes v) in comparison with similar measurements in the EDSGC survey, strongly support $Ω< 1$ with no biasing vi) show that the formulae of Szapudi & Colombi (1996) provide a good approximation for errors on higher order statistics measured in N-body simulations.

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arXiv1998

Dark Matter Halos within Clusters

We examine the properties of dark matter halos within a rich galaxy cluster using a high resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 halos with circular velocities larger than 80 kms within the cluster's virial radius of 2 Mpc. This enables an unprecedented study of the statistical properties of a large sample of dark matter halos evolving in a dense environment. The cumulative fraction of mass attached to these halos varies from 0% at 200 kpc, to 13% at the virial radius. Even at this resolution the overmerging problem persists; halos that pass within 200 kpc of the cluster center are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor halos. The median ratio of apocentric to pericentric radii is 6:1; the orbital distribution is close to isotropic, circular orbits are rare, radial orbits are common. The orbits of halos are unbiased with respect to both position within the cluster and with the orbits of the smooth dark matter background and no velocity bias is detected. The tidal radii of surviving halos are generally well-fit using the simple analytic prediction applied to their orbital pericenters. Halos within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other halos that cause significant mass loss - ``galaxy harassment''. Mergers between halos do not occur inside the clusters virial radius.

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arXiv1998

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 million particles within the virial radius, several orders of magnitude more than previously used and we can resolve more than one thousand surviving dark matter halos within this single virialised 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 virialised region. Results from two very high resolution halo simulations yield steep inner density profiles, $ρ(r)\sim r^{-1.4}$. 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 CDM model when compared with the observed properties of halos on galactic scales.

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arXiv1997

The Structure and Dynamics of Cold Dark Matter Halos

We investigate the internal structure of cold dark matter halos using high resolution N-body simulations. As the mass and force resolution are increased, halo density profiles become steeper, asymptoting to a slope of $\sim -4/3$ in the central regions and may not have converged to a unique result. At our highest resolution we have nearly 3 million particles within the virial radius, $R_{200}$, and force softening that is $\sim 0.2% R_{200}$. This resolution has also allowed us to resolve a large part of the overmerging problem - we find over 1000 surviving dark halos orbiting within a single cluster potential. These data have given us unprecedented insights into the dynamics and structure of ``halos within halos'', allowing us for the first time, to compare the distribution of dark matter with observations of galaxies in clusters.

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arXiv1997

Time stepping N-body simulations

Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps for each particle in large N-body simulations. Tests with single particles in fixed potentials show that it behaves as a symplectic integrator. We then examine the results of both standard leapfrog and our temporally adaptive leapfrog on full N-body integrations of clusters and large scale structure establishing accuracy criteria for both methods. The adaptive method shows significant speed-ups over single step integrations---but the integrator no longer appears to be symplectic or, in the case of large scale structure simulations, accurate. This loss of accuracy appears to be caused by the way that the timestep is chosen, not by the integrator itself. We present a related integration technique that does retain sufficient accuracy. Although it is not symplectic, it is apparently better than previous implementations and is our current integrator of choice for large astrophysical simulations. We also note that the standard leapfrog difference equations used in cosmological N-body integrations in comoving coordinates are not symplectic. We derive an implementation of leapfrog that is in comoving canonical coordinates to correct for this deficiency.

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arXiv1996

Prospects for Cosmology with Cluster Mass Profiles

We test the precision with which weak lensing data can provide characteristic cluster mass profiles within Cold Dark Matter scenarios. Using a parallel treecode to simulate volumes as large as 500h-1 Mpc with good resolution, we generate samples of large clusters within a standard CDM model and an open CDM model with Omega_o=0.3. We mock high-quality lensing data by including realistic errors, selecting cluster samples based on velocity dispersion, and fitting profiles within a realistic range in radius. We find that a sample of ten clusters can determine logarithmic profile slopes with 1 sigma errors of about 7%. Increasing the sample size to twenty brings this error down to less than 5%, but this is still insufficient to distinguish the two models. However, measures of cluster profiles obtained with weak lensing do place strong constraints for general CDM--like models of structure formation, and we discuss the optimal strategy for obtaining data samples to use for this purpose.

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arXiv1996

A parallel integration method for solar system dynamics

We describe how long-term solar system orbit integration could be implemented on a parallel computer. The interesting feature of our algorithm is that each processor is assigned not to a planet or a pair of planets but to a time-interval. Thus, the 1st week, 2nd week,..., 1000th week of an orbit are computed concurrently. The problem of matching the input to the (n+1)-st processor with the output of the n-th processor can be solved efficiently by an iterative procedure. Our work is related to the so-called waveform relaxation methods in the computational mathematics literature, but is specialized to the Hamiltonian and nearly integrable nature of solar system orbits. Simulations on serial machines suggest that, for the reasonable accuracy requirement of 1" per century, our preliminary parallel algorithm running on a 1000-processor machine would be about 50 times faster than the fastest available serial algorithm, and we have suggestions for further improvements in speed.

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