A new calibration method of sub-halo orbital evolution for semi-analytic
  models
  Understanding the non-linear dynamics of satellite halos (a.k.a. "sub-halos")
is important for predicting the abundance and distribution of dark matter
substructures and satellite galaxies, and for distinguishing among
microphysical dark matter models using observations. Typically, modeling these
dynamics requires large N-body simulations with high resolution. Semi-analytic
models can provide a more efficient way to describe the key physical processes
such as dynamical friction, tidal mass loss, and tidal heating, with only a few
free parameters. In this work, we present a fast Monte Carlo Markov Chain
fitting approach to explore the parameter space of such a sub-halo non-linear
evolution model. We use the dynamical models described in an earlier work and
calibrate the models to two sets of high-resolution cold dark matter N-body
simulations, ELVIS and Caterpillar. Compared to previous calibrations that used
manual parameter tuning, our approach provides a more robust way to determine
the best-fit parameters and their posterior probabilities. We find that jointly
fitting for the sub-halo mass and maximum velocity functions can break the
degeneracy between tidal stripping and tidal heating parameters, as well as
providing better constraints on the strength of dynamical friction. We show
that our semi-analytic simulation can accurately reproduce N-body simulations
statistics, and that the calibration results for the two sets of N-body
simulations agree at 95% confidence level. Dynamical models calibrated in this
work will be important for future dark matter substructure studies.
