Abstract
Abstract We generate stellar distribution functions (DFs) in triaxial haloes in order to examine the reliability of slopes Γ ≡ Δlog M/Δlog r inferred by applying mass estimators of the form M∝Reσ2 (i.e. assuming spherical symmetry, where Re and σ are luminous effective radius and global velocity dispersion, respectively) to two stellar subpopulations 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 anticorrelation between Re and σ 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 towards greater overestimation of masses for more concentrated tracer populations. We demonstrate that simple mass estimates for two distinct tracer populations can give reliable lower limits for Γ, irrespective of the degree of triaxiality or shape of the tracer number density profile.
Highlights
The Milky Way’s dwarf spheroidal satellites include the most dark-matter-dominated galaxies known, with dynamical mass-to-light ratios ranging from order ∼ 10 to several hundreds in solar units (Mateo 1998)
This makes dwarf spheroidal (dSph) objects of prime interest for studying the distribution of dark matter in galaxies. dSphs lack atomic hydrogen; methods for measuring dSph masses must rely on the kinematics of their pressure-supported stellar populations
Many techniques have been developed with the goal of determining the internal mass distributions of dSphs: spherical Jeans modelling (Lokas & Mamon 2001; Strigari et al 2006, 2008; Koch et al 2007; Battaglia et al 2008; Walker et al 2009; Wolf et al 2010), phase-space modelling (Wilkinson et al 2002; Amorisco & Evans 2011), the multiple stellar populations method (Walker & Penarrubia 2011), the use of the virial theorem for spherical and constant flattened systems (Agnello & Evans 2012) as well as axisymmetric Jeans modc 2011 RAS
Summary
The Milky Way’s dwarf spheroidal (dSph) satellites include the most dark-matter-dominated galaxies known, with dynamical mass-to-light ratios ranging from order ∼ 10 to several hundreds in solar units (Mateo 1998). WP11 tested their method against spherical dynamical models with various degrees of anisotropy and found that mass estimators of the form M (Re) ∝ Reσ systematically overestimate the enclosed mass more strongly for tracers that are more deeply embedded (i.e., more concentrated) in their host haloes. This bias implies that slopes Γ ≡ logM/∆logr tend to be systematically underestimated, such that WP11’s claim of their quoted levels of NFW exlcusion were conservative.
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