Isothermal distributions in MONDian gravity as a simple unifying explanation for the ubiquitous $ρ\propto r^{-3}$ density profiles in tenuous stellar halos

That the stellar halo of the Milky Way has a density profile which to first approximation satisfies $\rho \propto r^{-3}$ has been known for a long time. More recently, it has become clear that M31 also has such an extended stellar halo, which approximately follows the same radial scaling. Studies of distant galaxies have revealed the same phenomenology. Also, we now know that the density profiles of the globular cluster systems of our Galaxy and Andromeda to first approximation follow $\rho \propto r^{-3}$, $\Sigma \propto R^{-2}$ in projection. Recently, diffuse populations of stars have been detected spherically surrounding a number of Galactic globular clusters, extending much beyond the Newtonian tidal radii, often without showing any evidence of tidal features. Within the standard Newtonian and GR scenario, numerous and diverse particular explanations have been suggested, individually tailored to each of the different classes of systems described above. Here we show that in a MONDian gravity scenario, any isothermal tenuous halo of tracer particles forming a small perturbation surrounding a spherically symmetric mass distribution, will have an equilibrium configuration which to first approximation satisfies a $\rho \propto r^{-3}$ scaling.