Assessing the Fornax globular cluster timing problem in different models
  of dark matter
  We investigate what the orbits of globular clusters (GCs) in the Fornax dwarf
spheroidal (dSph) galaxy can teach us about dark matter (DM). This problem was
recently studied for ultralight dark matter (ULDM). We consider two additional
models: (i) fermionic degenerate dark matter (DDM), where Pauli blocking should
be taken into account in the dynamical friction computation; and (ii)
self-interacting dark matter (SIDM). We give a simple and direct Fokker-Planck
derivation of dynamical friction, new in the case of DDM and reproducing
previous results in the literature for ULDM and cold DM. ULDM, DDM and SIDM
were considered in the past as leading to cores in dSphs, a feature that acts
to suppress dynamical friction and prolong GC orbits. For DDM we derive a
version of the cosmological free streaming limit that is independent of the DM
production mechanism, finding that DDM cannot produce an appreciable core in
Fornax without violating Ly-$\alpha$ limits. If the Ly-$\alpha$ limit is
discounted for some reason, then stellar kinematics data does allow a DDM core
which could prolong GC orbits. For SIDM we find that significant prolongation
of GC orbits could be obtained for values of the self-interaction cross section
considered in previous works. In addition to reassessing the inspiral time
using updated observational data, we give a new perspective on the so-called GC
timing problem, demonstrating that for a cuspy cold DM profile dynamical
friction predicts a $z=0$ radial distribution for the innermost GCs that is
independent of initial conditions. The observed orbits of Fornax GCs are
consistent with this expectation with a mild apparent fine-tuning at the level
of $\sim25\%$.
