Dark matter properties from the Fornax globular cluster timing:
  dynamical friction and cored profiles
  I summarize our recent results to use the orbits of globular clusters (GCs)
in the Fornax dwarf spheroidal (dSph) galaxy to learn more about dark matter
(DM) properties. Our focus is on clarifying how dynamical friction (DF) from
the DM halo is modified from the different microscopic properties of DM, which
may alter $both$ the scattering processes responsible of DF and the DM profiles
(in particular generating a core), which also modifies DF. We consider: $(i)$
fermionic degenerate dark matter (DDM), where Pauli blocking should be taken
into account in the dynamical friction computation; $(ii)$ self-interacting
dark matter (SIDM) and $(iii)$ ultralight dark matter (ULDM), for which this
problem has been addressed by a variety of methods in recent literature. We
derive DF with a Fokker-Planck formalism, reproducing previous results for ULDM
and cold DM, while providing new results for DDM. Furthermore, ULDM, DDM and
SIDM may generate cores in dSphs, which suppress dynamical friction and prolong
GC orbits. We conclude that in all these cases the modifications in the DM
modelling does not easily solve the so-called timing `problem' of Fornax GCs.
We finally study this `problem' in terms of the initial conditions,
demonstrating that the observed orbits of Fornax GCs are consistent with this
expectation of a cuspy DM profile with a mild `fine-tuning' at the level of
$\sim25\%$.
