A Universal Mass Profile for Dwarf Spheroidal Galaxies?

Abstract

We apply the Jeans equation to estimate masses for eight of the brightest dwarf spheroidal (dSph) galaxies. For Fornax, the dSph with the largest kinematic data set, we obtain a model-independent constraint on the maximum-circular velocity, V max = 18 +5 −3 km s −1 . Although we obtain only lowerlimits of V max 10 km s −1 for the remaining dSphs, we find that in all cases the enclosed mass at the projected half-light radius is well constrained and robust to a wide range of halo models and velocity anisotropies. We derive a simple analytic formula that estimates M (r half ) accurately with respect to results from the full Jeans analysis. Applying this formula to the entire population of Local Group dSphs with published kinematic data, we demonstrate a correlation such that M (r half ) ∝ r 1.4±0.4 half , or in terms of the mean density interior to the half-light radius, ρ ∝ r −1.6±0.4half . This relation is driven by the fact that the dSph data exhibit a correlation between global velocity dispersion and half-light radius. We argue that tidal forces are unlikely to have introduced this relation, but tides may have increased the scatter and/or altered the slope. While the data are well described by mass profiles ranging over a factor of 2 in normalization (V max ∼ 10 − 20 km s −1 ), we consider the hypothesis that all dSphs are embedded within a "universal" dark matter halo. We show that in addition to the power law M ∝ r 1.4 , viable candidates include a cuspy "NFW" halo with V max ∼ 15 km s −1 and scale radius r 0 ∼ 800 pc, as well as a cored halo with V max ∼ 13 km s −1 and r 0 ∼ 150 pc. Finally, assuming that their measured velocity dispersions accurately reflect their masses, the smallest dSphs now allow us to resolve dSph densities at radii as small as a few tens of pc. At these small scales we find mean densities as large as ρ 5M ⊙ pc −3 ( 200GeV cm −3 ).

The orbital PDF: general inference of the gravitational potential from steady-state tracers

“…The existence of a best-constrained mass despite the parameter degeneracy is broadly in line with empirical results on the robustness of the mass constraint inside the half-light radius from Jeans equation modelling of dwarf galaxies (Walker et al 2009;Wolf et al 2010). The existence of such a characteristic point in the Jeans analysis is further proved by Wolf et al (2010).…”

VLT/FLAMES spectroscopy of red giant branch stars in the Carina dwarf spheroidal galaxy

“…This physical process mainly depends on the supernovae rate and on the binding energy of the galaxy. Therefore, it is likely to be a critically important factor driving the evolution of low mass galaxies (e.g., Dekel & Silk, 1986;Mac Low & Ferrara, 1999;Ferrara & Tolstoy , 2000;Salvadori et al, 2008) like the Carina dSph, with M tot = 6.1 ± 2.3 × 10 6 M ⊙ within the half radius 241 ± 23kpc (Walker et al, 2009). If the bursts of star formation observed in Carina are part of an ongoing cycle of heating and cooling of an initial gas reservoir (e.g., Stinson et al, 2007;Valcke et al, 2008), there should be a clear evolutionary path in the observed abundances, showing the influence of SNe Ia enrichment at increasing [Fe/H] values.…”

The new Milky Way satellites: alignment with the VPOS and predictions for proper motions and velocity dispersions

“…The results depend strongly on which dynamical model (Newtonian dynamics or Modified Newtonian Dynamics, MOND, Milgrom 1983) or which dark matter halo scaling relation is assumed (McGaugh et al 2007;Walker et al 2009). We will provide predictions for all these different cases.…”