On the dark matter profile in Sculptor: breaking the β degeneracy with Virial shape parameters

Abstract

We present a new method for studying tracers in gravitational systems where higher moments of the line-of-sight velocity distribution are introduced via Virial equations rather than the Jeans equations. Unlike the fourth order Jeans equations, the fourth order Virial equations can simply be added to the standard second order Jeans equation without introducing a new anisotropy parameter β . We introduce two new global shape parameters ζ A and ζ B which replace the kurtosis as a more statistically robust measure of the shape of the line of sight velocity distribution. We show that in the case of stars in dwarf spheroidal galaxies these new parameters can significantly reduce the range of density profiles that are otherwise consistent with the observed stellar kinematics (a problem sometimes known as the β degeneracy). Specifically, we find that ζ A focuses tightly on a subset of solutions where cusped density profiles are degenerate with more concentrated cored dark matter haloes. If the number density of stars ν(r) is fixed, then introducing ζ B can further reduce the space of solutions by constraining the outer slope of the dark matter density profile. Assuming a Plummer profile for ν(r) we recover the surprising result that the dark matter in Sculptor may be cuspy after all, in contrast to the conclusions of other approaches.

Small-Scale Cosmology “Crisis” and Self-Interacting Right-Handed Neutrino Warm Dark Matter

“…In this respect we mention a new method for estimating the dSph gravitational potential [21], based on exploiting the higher order analogues of the projected Virial Theorem 2K z + W s = 0, which provide global constraints on the moments of the velocity distribution ( v n z ) by effectively integrating the spherical Jeans equations over all radii: second order :…”

“…The quantities (2) carry more or less the same information as the corresponding Jeans equations [21]. Based on such novel approaches, and defining appropriate Virial shape estimators from (2), the authors of Ref.…”

“…Based on such novel approaches, and defining appropriate Virial shape estimators from (2), the authors of Ref. [21] performed an illustrative analysis on the DM profile of the galaxy Sculptor, NGC 253, in the Sculptor group, using phenomenological expressions for ν(r) and the density profile ρ(r), which is taken to be close to the NFW. This galaxy is a good study case, given that it is one of the brightest galaxies in the vicinity of the Milky Way, and is a starburst, that is it undergoes intense star formation, which according to several astronomers it is believed to have been caused by the collision with a dwarf galaxy a few hundred million years ago, disturbing its disc and started the currently observed starburst.…”

Made-to-measure dark matter haloes, elliptical galaxies and dwarf galaxies in action coordinates

“…In the case of dwarf spheroidal galaxies, many studies have been carried out in order to determine the nature of the dark matter density law. Some results favour cores (e.g., Walker & Peñarrubia 2011;Amorisco & Evans 2012;Agnello & Evans 2012), while others offer a different view (e.g., Breddels & Helmi 2013;Strigari et al 2014;Richardson & Fairbairn 2014). As such, it is clear that dynamical models of both cored and cuspy dark matter haloes are required to resolve the controversy.…”

What can Gaia (with Thirty Meter Telescope) say about the Sculptor Dwarf's Core?

“…[22]. Alternately, as this strategy introduces more observables without increasing the number of unknowns, the proper motion measurements may be used to test the consistency of the fourth order equilibrium analysis, which may in turn shed light on Sculptor's formation.…”