Orbital parameters of infalling satellite haloes in the hierarchical
  $\Lambda$CDM model
  We present distributions of orbital parameters of infalling satellites of
$\Lambda$CDM haloes in the mass range $10^{12}-10^{14}$M$_\odot$, which
represent the initial conditions for the subsequent evolution of substructures
within the host halo. We use merger trees constructed in a high resolution
cosmological N-body simulation to trace satellite haloes, and identify the time
of infall. We find signficant trends in the distribution of orbital parameters
with both the host halo mass and the ratio of satellite-to-host halo masses.
For all host halo masses, satellites whose infall mass is a larger fraction of
the host halo mass have more eccentric, radially biased orbits. At fixed
satellite-to-host halo mass ratio, high mass haloes are biased towards
accreting satellites on slightly more radial orbits. To charactise the orbital
distributions fully requires fitting the correlated bivariate distribution of
two chosen orbital parameters (e.g. radial and tangential velocity or energy
and angular momentum). We provide simple fits to one choice of the bivariate
distributions, which when transformed faithfully, captures the behaviour of any
of the projected one-dimensional distributions.
