$\gamma$-ray and $\nu$ searches for dark matter subhalos in the Milky
  Way with a baryonic potential
  The distribution of dark matter (DM) subhalos in our Galaxy remains disputed,
leading to varying $\gamma$-ray and $\nu$ flux predictions from their
annihilation or decay. In this work, we study how, in the inner Galaxy, subhalo
tidal disruption from the Galactic baryonic potential impacts these signals.
Based on state-of-the art modeling of this effect from numerical simulations
and semi-analytical results, updated subhalo spatial distributions are derived
and included in the CLUMPY code. The latter is used to produce a thousand
realizations of the $\gamma$-ray and $\nu$ sky. Compared to predictions based
on DM only, we conclude a decrease of the flux of the brightest subhalo by a
factor 2 to 7 for annihilating DM and no impact on decaying DM: the discovery
prospects or limits subhalos can set on DM candidates are affected by the same
factor. This study also provides probability density functions for the
distance, mass, and angular distribution of the brightest subhalo, among which
the mass may hint at its nature: it is most likely a dwarf spheroidal galaxy in
the case of strong tidal effects from the baryonic potential, whereas it is
lighter and possibly a dark halo for DM only or less pronounced tidal effects.
