Measuring the slopes of mass profiles for dwarf spheroidals in triaxial cold dark matter potentials
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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.