Measuring the slopes of mass profiles for dwarf spheroidals in triaxial CDM potentials

TL;DR

This study assesses the reliability of mass slope estimates in dwarf spheroidals using triaxial dark matter haloes, finding that simple mass estimators provide robust lower limits despite halo triaxiality and tracer profile variations.

Contribution

It demonstrates that mass estimators assuming spherical symmetry yield reliable lower bounds for mass profile slopes in triaxial haloes, regardless of tracer density profile shape.

Findings

Halo triaxiality causes an anti-correlation between effective radius and velocity dispersion.

Systematic errors are dominated by overestimation bias for concentrated tracer populations.

Simple mass estimates reliably provide lower limits for the slope of mass profiles.

Abstract

We generate stellar distribution functions (DFs) in triaxial haloes in order to examine the reliability of slopes $\Gamma\equiv \Delta {\rm log} M / \Delta {\rm log} r$ inferred by applying mass estimators of the form $M\propto R_e\sigma^2$ (i.e. assuming spherical symmetry, where $R_e$ and $\sigma$ are luminous effective radius and global velocity dispersion, respectively) to two stellar sub-populations independently tracing the same gravitational potential. The DFs take the form $f(E)$, are dynamically stable, and are generated within triaxial potentials corresponding directly to subhaloes formed in cosmological dark-matter-only simulations of Milky Way and galaxy cluster haloes. Additionally, we consider the effect of different tracer number density profiles (cuspy and cored) on the inferred slopes of mass profiles. For the isotropic DFs considered here, we find that halo triaxiality tends to introduce an anti-correlation between $R_e$ and $\sigma$ when estimated for a variety of viewing angles. The net effect is a negligible contribution to the systematic error associated with the slope of the mass profile, which continues to be dominated by a bias toward greater overestimation of masses for more-concentrated tracer populations. We demonstrate that simple mass estimates for two distinct tracer populations can give reliable (and cosmologically meaningful) lower limits for $\Gamma$, irrespective of the degree of triaxiality or shape of the tracer number density profile.