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

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.

Structural Parameters and Possible Association of the Ultra-faint Dwarfs Pegasus III and Pisces II from Deep Hubble Space Telescope Photometry

“…A limiting factor for observational constraints is that we are often restricted to line-of-sight (LOS) velocity data of the stars residing in dwarf galaxies, and with no information on the tangential velocity components, we suffer from the massanisotropy degeneracy. It will thus take more information, such as the shape of the velocity distribution or galactic internal proper motions (PMs), in addition to radial velocities to be able to distinguish a dark-matter central core or cusp (e.g., Strigari et al 2007;Guerra et al 2021;Read et al 2021). Once we have full kinematic information, current virial mass estimators can be extended to further constrain UFD dark-matter halo properties (Errani et al 2018).…”

Snowmass2021 Cosmic Frontier White Paper: Observational Facilities to Study Dark Matter

“…In much lower-mass galaxies such as the Milky Way satellites, stellar feedback should not be strong enough to grossly affect the density profile. Unfortunately, the most recent modeling indicates that clearly distinguishing central dark matter cusps from cores in Milky Way satellites cannot be achieved with radial velocity measurements alone [183]. As originally suggested by [206], though, combining proper motion measurements of dwarf galaxy stars with radial velocities will break the degeneracies that have plagued previous studies.…”

“…The central densities of the smallest luminous dark matter halos (10 8 − 10 9 M ). In small dwarf galaxies, the measured stellar velocity dispersion translates directly to the mean density of dark matter in the innermost ∼ 100 pc of the galaxy [e.g., 182,183]. For the closest Milky Way satellites, these stellar kinematics can be obtained with existing instruments, but for more distant systems that have not been altered by interactions with a massive host galaxy, ELTs will be needed.…”

“…Robust measurements of the density profiles in the most dark matter-dominated dwarf galaxies are a highly-anticipated goal of next-generation facilities. Two observational approaches are possible: radial velocities for ∼ 10 4 stars per dwarf galaxy from wide-field spectroscopic facilities, or proper motions for ∼ 10 3 stars per dwarf from ELTs [183].…”

Structural parameters and possible association of the Ultra-Faint Dwarfs Pegasus III and Pisces II from deep Hubble Space Telescope photometry

“…A limiting factor for observational constraints is that we are often restricted to line-of-sight (LOS) velocity data of the stars residing in dwarf galaxies, and with no information on the tangential velocity components, we suffer from the mass-anisotropy degeneracy. It will thus take more information, such as the shape of the velocity distribution or galactic internal proper motions (PMs), in addition to radial velocities to be able to distinguish a dark matter central core or cusp (e.g., Strigari et al 2007;Read et al 2021;Guerra et al 2021). Once we have full kinematic information, current virial mass estimators can be extended to further constrain UFD dark matter halo properties (Errani et al 2018).…”