  Using a set of high-resolution N-body simulations, we extend the unified
distribution model of cold dark matter (CDM) subhaloes to the warm dark
matter(WDM) case. The same model framework combining the unevolved mass
function, unevolved radial distribution, and tidal stripping can predict the
mass function and spatial distribution of subhaloes in both CDM and WDM
simulations. The dependence of the model on the DM particle property is
universally parameterized through the half-mode mass of the initial power
spectrum. Compared with the CDM model, the WDM model differs most notably in
two aspects. 1) In contrast to the power-law form in CDM, the unevolved subhalo
mass function for WDM is scale-dependent at the low mass end due to the cut-off
in the initial power spectrum. 2) WDM subhaloes are more vulnerable to tidal
stripping and disruption due to their lower concentrations at accretion time.
Their survival rate is also found to depend on the infall mass. Accounting for
these differences, the model predicts a final WDM subhalo mass function that is
also proportional to the unevolved subhalo mass function. The radial
distribution of WDM subhaloes is predicted to be mass-dependent. For low mass
subhaloes, the radial distribution is flatter in the inner halo and steeper in
the outer halo compared to the CDM counterpart, due to the scale-dependent
unevolved mass function and the enhanced tidal stripping. The code for sampling
subhaloes according to our generalized model is available at
https://github.com/fhtouma/subgen2 .
