A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies

TL;DR

This paper presents a new method to measure the slopes of mass profiles in dwarf spheroidal galaxies using stellar spectroscopic data, without relying on dark matter halo models, and applies it to Fornax and Sculptor.

Contribution

It introduces a statistical approach combining stellar subcomponent analysis and Jeans models to directly estimate mass profile slopes from spectroscopic data.

Findings

Measured slopes suggest cored dark matter profiles in Fornax and Sculptor.

Method rules out cuspy NFW profiles with high statistical significance.

Synthetic tests show the method may underestimate the true slope.

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 halflight radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the halflight radius of a dSph stellar component, and 2) some dSphs have chemo-dynamically distinct stellar \textit{sub}components 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 halflight 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 $\Gamma\equiv \Delta \log M / \Delta \log r=2.61_{-0.37}^{+0.43}$ and $\Gamma=2.95_{-0.39}^{+0.51}$, 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 ($d\log M/d\log r \leq 2$ at all radii) with significance $\ga 96%$ and $\ga 99%$, 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 $\Gamma$ (implying that the stated NFW exclusion levels are conservative).