Assessing the Fornax globular cluster timing problem in different models of dark matter

Abstract

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 Lyα limits. If the Ly-α 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 ∼ 25%.

Density Wakes due to Dynamical Friction in Cored Potentials

“…These numerical predictions are compatible with observations of dwarf galaxy globular cluster populations whose DF inspiral times (in the Chandrasekhar picture) are much less than a Hubble time (Tremaine 1976;Durrell et al 1996;Hernandez & Gilmore 1998;Miller et al 1998;Oh et al 2000;Vesperini 2000;Mackey & Gilmore 2003;Lotz et al 2004;Huang & Koposov 2021). Without the possibility of core stalling, the survival of such globular populations is a puzzle sometimes known as the "timing problem," and has even motivated consideration of new physics, such as ultralight dark matter (Hui et al 2017;Bar et al 2021) or modified Newtonian dynamics (Angus & Diaferio 2009). Kaur & Sridhar (2018) investigated the core stalling problem analytically in the TW framework and found that the stalling results from the depletion and weakening of corotating resonances in the inner core of the galaxy.…”

Subsonic accretion and dynamical friction for a black hole moving through a self-interacting scalar dark matter cloud

“…the observed tension in the orbital decay of clusters of stars as seen in the Fornax Dwarf Spheroidal, could be addressed by SFDM models. Indeed, CDM numerical simulations lead to a faster orbital decay, and so a higher dynamical friction, than obtained in observations (e.g., [29,30] as reviews). For FDM, this tension disappears for low DM masses m < 10 −21 eV [21,31,32], but this range of scalar masses is in potential tension with other observables.…”

“…The smaller dynamical friction associated with such self-interacting scalar dark matter might result in a decrease of the dephasing of the emission frequency of gravitational waves as compared to FDM and CDM. Also, SFDM could play a role in the Fornax globular cluster timing problem if dynamical friction is reduced [29]. This is left for future studies.…”

The spatial distribution of globular clusters in dwarf spheroidal galaxies and the timing problem

“…Much effort has been devoted to place constraints on the dark matter density distribution of Fornax dSph galaxy from the present-day distribution of its GCs (Tremaine 1976;Goerdt et al 2006;Sánchez-Salcedo et al 2006;Angus & Diaferio 2009;Inoue 2009;Cole et al 2012;Arca-Sedda & Capuzzo-Dolcetta 2016;Boldrini et al 2019;Leung et al 2020;Meadows et al 2020;Bar et al 2021;Shao et al 2021). A cored dark matter halo could explain the so-called timing problem, that is, why none of the five GCs in Fornax dSph galaxy have been sunk to the centre if the dynamical friction timescale, at least for two of them, is shorter than the age of the GCs.…”