A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies
Abstract
We introduce a method for measuring the slopes of mass profiles within dwarf spheroidal (dSph) galaxies directly from stellar spectroscopic data and without adopting a dark matter halo model. Our method combines two recent results: (1) spherically symmetric, equilibrium Jeans models imply that the product of half-light radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the half-light radius of a dSph stellar component, and (2) some dSphs have chemodynamically distinct stellar subcomponents that independently trace the same gravitational potential. We devise a statistical method that uses measurements of stellar positions, velocities, and spectral indices to distinguish two dSph stellar subcomponents and to estimate their individual half-light radii and velocity dispersions. For a dSph with two detected stellar subcomponents, we obtain estimates of masses enclosed at two discrete points in the same mass profile, immediately defining a slope. Applied to published spectroscopic data, our method distinguishes stellar subcomponents in the Fornax and Sculptor dSphs, for which we measure slopes Γ ≡ Δlog M/Δlog r = 2.61+0.43 -0.37 and Γ = 2.95+0.51 -0.39, respectively. These values are consistent with "cores" of constant density within the central few hundred parsecs of each galaxy and rule out "cuspy" Navarro-Frenk-White (NFW) profiles (dlog M/dlog r <= 2 at all radii) with a significance >~ 96% and >~ 99%, respectively. Tests with synthetic data indicate that our method tends systematically to overestimate the mass of the inner stellar subcomponent to a greater degree than that of the outer stellar subcomponent, and therefore to underestimate the slope Γ (implying that the stated NFW exclusion levels are conservative).
- Publication:
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The Astrophysical Journal
- Pub Date:
- November 2011
- DOI:
- 10.1088/0004-637X/742/1/20
- arXiv:
- arXiv:1108.2404
- Bibcode:
- 2011ApJ...742...20W
- Keywords:
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- dark matter;
- galaxies: dwarf;
- galaxies: fundamental parameters;
- galaxies: kinematics and dynamics;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- Accepted for publication in The Astrophysical Journal (added references)