  We show that the anisotropies of the astrophysical stochastic gravitational
wave background in the mHz band have a strong dependence on the modelling of
galactic and sub-galactic physics. We explore a wide range of self-consistent
astrophysical models for stellar evolution and for the distribution of orbital
parameters, all calibrated such that they predict the same number of resolved
mergers to fit the number of detections during LIGO/Virgo O1+O2 observations
runs. We show that different physical choices for the process of black hole
collapse and cut-off in the black hole mass distribution give fractional
differences in the angular power spectrum of anisotropies up to 50\% on all
angular scales. We also point out that the astrophysical information which can
be extracted from anisotropies is complementary to the isotropic background and
individual mergers. These results underline the interest in the anisotropies of
the stochastic gravitational wave background as a new and potentially rich
field of research, at the cross-road between astrophysics and cosmology.
