The dynamics of sinking satellites around disk galaxies: A poor man's alternative to high-resolution numerical simulations

We have developed a simple yet surprisingly accurate analytic scheme for tracking the dynamical evolution of substructure within dark matter halos. The scheme incorporates the effects of dynamical friction, tidal mass loss, and tidal heating via physically motivated approximations. Using our scheme, we can predict the orbital evolution and mass-loss history of individual subhalos in detail. We are also able to determine the impact and importance of the different physical processes on the dynamical evolution of the subhalos. To test and calibrate this model, we compare it with a set of recent high-resolution numerical simulations of mergers between galaxies and small companions. We find that we can reproduce the orbits and mass-loss rates seen in all of these simulations with considerable accuracy, using a single set of values for the three free parameters in our model. Computationally, our scheme is more than 1000 times faster than the simplest of the high-resolution numerical simulations. This means that we can carry out detailed and statistically meaningful investigations into the characteristics of the subhalo population in different cosmologies, the stripping and disruption of the subhalos, and the interactions of the subhalos with other dynamical structures such as a thin disk. This last point is of particular interest given the ubiquity of minor mergers in hierarchical models. In this regard, our method's simplicity and speed makes it particularly attractive for incorporation into semianalytic models of galaxy formation.