2016MNRAS.462.2734H

Dwarf spheroidal galaxies (dSphs) are the smallest known stellar systems where under Newtonian interpretations, a significant amount of dark matter is required to explain observed kinematics. In fact, they are, in this sense, the most heavily dark matter-dominated objects known. That, plus the increasingly small sizes of the newly discovered ultrafaint dwarfs, puts these systems in the regime where dynamical friction on individual stars starts to become relevant. We calculate the dynamical friction time-scales for pressure-supported isotropic spherical dark matter-dominated stellar systems, yielding τ_DF = 0.93(r_h/10 pc)²(σ/km s^–1) Gyr, where r_h is the half-light radius. For a stellar velocity dispersion value of 3 km s^–1, as typical for the smallest of the recently detected ultrafaint dwarf spheroidals, dynamical friction time-scales become smaller than the 10 Gyr typical of the stellar ages for these systems, for r_h < 19 pc. Thus, this becomes a theoretical lower limit below which dark matter-dominated stellar systems become unstable to dynamical friction. We present a comparison with structural parameters of the smallest ultrafaint dwarf spheroidals known, showing that these are already close to the stability limit derived, any future detection of yet smaller such systems would be inconsistent with a particle dark matter hypothesis.