Forecasts on the Dark Matter Density Profiles of Dwarf Spheroidal Galaxies with Current and Future Kinematic Observations

TL;DR

This paper forecasts how well current and future stellar kinematic data can constrain dark matter density profiles in dwarf spheroidal galaxies, highlighting the observational requirements for distinguishing core versus cusp profiles.

Contribution

It introduces a Fisher matrix-based method to predict density profile uncertainties from kinematic data, validated against full likelihood analyses, and discusses the impact of observational errors and priors.

Findings

Radial velocity measurements of 1000 stars constrain mass within effective radius to 5%.

Distinguishing core vs. cusp profiles requires large samples of proper motions and radial velocities.

Improving observational errors beyond a certain point yields diminishing returns in profile uncertainty reduction.

Abstract

We forecast parameter uncertainties on the mass profile of a typical Milky Way dwarf spheroidal (dSph) galaxy using the spherical Jeans Equation and Fisher matrix formalism. We show that radial velocity measurements for 1000 individual stars can constrain the mass contained within the effective radius of a dSph to within 5%. This is consistent with constraints extracted from current observational data. We demonstrate that a minimum sample of 100,000 (10,000) stars with both radial and proper motions measurements is required to distinguish between a cusped or cored inner slope at the 2-sigma (1-sigma) level. If using the log-slope measured at the half-light radius as a proxy for differentiating between a core or cusp slope, only 1000 line-of-sight and proper motions measurements are required, however, we show this choice of radius does not always unambiguously differentiate between core and cusped profiles. Once observational errors are below half the value of the intrinsic dispersion, improving the observational precision yields little change in the density profile uncertainties. The choice of priors in our profile shape analysis plays a crucial role when the number of stars in a system is less than 100, but does not affect the resulting uncertainties for larger kinematic samples. Our predicted 2D confidence regions agree well with those from a full likelihood analysis run on a mock kinematic dataset taken from the Gaia Challenge, validating our Fisher predictions. Our methodology is flexible, allowing us to predict density profile uncertainties for a wide range of current and future kinematic datasets.