A new calibration method of sub-halo orbital evolution for semi-analytic models

Understanding the non-linear dynamics of satellite haloes (a.k.a. 'sub-haloes') is important for predicting the abundance and distribution of dark matter sub-structures and satellite galaxies, and for distinguishing among microphysical dark matter models using observations. Typically, modelling 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 Markov chain Monte Carlo 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-fitting 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 per cent confidence level. Dynamical models calibrated in this work will be important for future dark matter sub-structure studies.