  According to the hierarchical formation paradigm, galaxies form through
mergers of smaller entities and massive black holes (MBHs), if lurking at their
centers, migrate to the nucleus of the newly formed galaxy, where they form
binary systems. The formation and evolution of MBH binaries, and in particular
their coalescence timescale, is very relevant for current and future facilities
aimed at detecting the gravitational-wave signal produced by the MBH close to
coalescence. While most of the studies targeting this process are based on
hydrodynamic simulations, the high computational cost makes a complete
parameter space exploration prohibitive. Semi-analytic approaches represent a
valid alternative, but they require ad-hoc prescriptions for the mass loss of
the merging galaxies in minor mergers due to tidal stripping, which is not
commonly considered or at most modelled assuming very idealised geometries. In
this work, we propose a novel, effective model for the tidal stripping in
axisymmetric potentials, to be implemented in semi-analytic models. We validate
our semi-analytic approach against N-body simulations considering different
galaxy sizes, inclinations, and eccentricities, finding only a moderate
dependence on the orbit eccentricity. In particular, we find that, for almost
circular orbits, our model mildly overestimates the mass loss, and this is due
to the adjustment of the stellar distribution after the mass is removed.
Nonetheless, the model exhibits a very good agreement with simulations in all
the considered conditions, and thus represents an extremely powerful addition
to semi-analytic calculations.
