An Improved Model for the Dynamical Evolution of Dark Matter Subhaloes
  Using an analytical model, we study the evolution of subhalo, including its
mass, angular momentum and merging time-scale. This model considers the
dominant processes governing subhalo evolution, such as dynamical friction,
tidal stripping and tidal heating. We find that in order to best match the
evolution of angular momentum measured from N-body simulation, mass stripping
by tidal force should become inefficient after subhalo has experienced a few
passages of pericenter. It is also found that the often used Coulomb logarithm
$\ln M/m$ has to be revised to best fit the merging time-scales from
simulation. Combining the analytical model with the Extended Press-Schechter
(EPS) based merger trees, we study the subhalo mass function, and their spatial
distribution in a Milky-Way (MW) type halo. By tuning the tidal stripping
efficiency, we can gain a better match to the subhalo mass function from
simulation. The predicted distribution of subhaloes is found to agree with the
distribution of MW satellites, but is more concentrated than the simulation
results. The radial distribution of subhaloes depends weakly on subhaloes mass
at both present day and the time of accretion, but strongly on the accretion
time. Using the improved model, we measure the second moment of the subhalo
occupation distribution, and it agrees well with the results of Kravtsov et al.
(2004a) and Zheng et al. (2005).
