S. D. M. White — Page 7

arXiv1995

On the Dynamics of the Sagittarius Dwarf Galaxy

We use numerical simulations to test the feasibility of the suggestion by Ibata et al. (1994) that the excess population of stars which they discovered in the Sagittarius region may be the disrupted remains of a dwarf spheroidal galaxy. We find that a Fornax-like model for the pre-disruption system can indeed reproduce the data. However, the galaxy must be on a relatively short period orbit with a pericentre of about $10$ kpc and an apocentre of about $52$ kpc, giving a current transverse velocity of $255$ km/s and a period of $\sim 760$ Myr. Furthermore, disruption must have occurred predominantly on the last pericentric passage rather than on the present one. The data are consistent with transverse motion either towards or away from the Galactic Plane. These results depend primarily on the rotation curve of the Galaxy and are insensitive to the mass distribution in its outer halo or to the mass of its disk.

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arXiv1994

An analytic model for the gravitational clustering of dark matter haloes

We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the Press-Schechter formalism. Gravitational clustering is treated by a spherical model which describes the concentration of dark haloes in collapsing regions. We test this model against results from a variety of N-body simulations. The autocorrelation function of dark haloes in such simulations depends significantly on how haloes are identified. Our predictions agree well with results based on algorithms which break clusters into subgroups more efficiently than the standard friends-of-friends algorithm. The agreement is better than that found by assuming haloes to lie at the present positions of peaks of the linear density field. We use these techniques to study how the distribution of haloes is biased with respect to that of the mass. The initial (Lagrangian) positions of haloes identified at a given redshift and having circular velocities $v_c=v_c^*(z)$ (i.e. mass equal to the characteristic nonlinear mass $M^*$ at that redshift) are very weakly correlated with the linear density field or among themselves. As a result of dynamical evolution, however, the present-day correlations of these haloes are similar to those of the mass. Haloes with lower $v_c$ are biased toward regions with negative overdensity, while those with higher $v_c$ are biased toward regions with positive overdensity. Among the haloes identified at any given epoch, those with higher circular velocities are more strongly correlated today. Among the haloes of given circular velocity, those at higher redshifts are also more strongly clustered today. In the ``standard CDM'' model, haloes with

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