An extensive study of dynamical friction in dwarf galaxies: the role of stars, dark matter, halo profiles and MOND

We investigate the in-spiralling time-scales of globular clusters (GCs) in dwarf spheroidal (dSph) and dwarf elliptical (dE) galaxies, due to dynamical friction (DF). We address the problem of these time-scales having been variously estimated in the literature as much shorter than a Hubble time. Using self-consistent two-component (dark matter and stars) models, we explore mechanisms which may yield extended DF time-scales in such systems in order to explain why dwarf galaxies often show GC systems. As a general rule, dark matter and stars both give a comparable contribution to the dynamical drag. By exploring various possibilities for their gravitational make-up, it is shown that these studies help to constrain the parameters of the dark matter haloes in these galaxies, as well as to test alternatives to dark matter. Under the assumption of a dark halo having a central density core with a typical King core radius somewhat larger than the observed stellar core radius, DF time-scales are naturally extended upwards of a Hubble time. Cuspy dark haloes yield time-scales ≲4.5 Gyr, for any dark halo parameters in accordance with observations of stellar line-of-sight velocity dispersion in dSph galaxies. We confirm, after a detailed formulation of the DF problem under the alternative hypothesis of modified Newtonian dynamics (MOND) and in the lack of any dark matter, that due to the enhanced dynamical drag of the stars, the DF time-scales in MOND would be extremely short. Taking the well-measured structural parameters of the Fornax dSph and its GC system as a case study, we conclude that requiring DF time-scales comparable to the Hubble time strongly favours dark haloes with a central core.