Theoretical lower limits on sizes of ultra faint dwarf galaxies from dynamical friction

TL;DR

This paper derives a theoretical lower size limit for ultra faint dwarf galaxies based on dynamical friction timescales, suggesting that smaller dark matter dominated systems would be unstable, challenging the dark matter hypothesis if smaller systems are observed.

Contribution

It introduces a calculation of dynamical friction timescales to establish a lower size limit for dark matter dominated dwarf galaxies, linking stability to observed sizes.

Findings

Ultra faint dwarf spheroidals are close to the stability limit derived.

Dynamical friction timescales become shorter than stellar ages for sizes below 19 pc.

Future smaller systems would challenge the dark matter hypothesis if observed.

Abstract

Dwarf spheroidal galaxies 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 ultra faint dwarfs, puts these systems in the regime where dynamical friction on individual stars starts to become relevant. We calculate the dynamical friction timescales for pressure supported isotropic spherical dark matter dominated stellar systems, yielding $\tau_{DF} =0.93 (r_{h}/10 pc)^{2} (\sigma/ kms^{-1}) Gyr$, { where $r_{h}$ is the half-light radius}. For a stellar velocity dispersion value of $3 km/s$, as typical for the smallest of the recently detected ultra faint dwarf spheroidals, dynamical friction timescales becomes 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 ultra faint 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.