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 $\sim25\%$.