Constraining velocity-dependent self-interacting dark matter with the Milky Way's dwarf spheroidal galaxies

The observed anticorrelation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericentre distances poses a potential signature of self-interacting dark matter (SIDM). In this work, we investigate this possibility by analysing the range of SIDM scattering cross-section per unit mass, sigma/m(chi), able to explain such anticorrelation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of subhalo density profiles is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on sigma/m(chi). We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed sigma/m(chi) ranging between 30 and 50cm(2)g(-1), whereas other dSphs prefer larger values ranging between 70 and 100cm(2)g(-1). These cross-sections correlate with the average collision velocity of DM particles within each subhalo's core, so that systems modelled with large cross-sections have lower collision velocities. We fit the cross-section-velocity correlation with a SIDM particle model, where a DM particle of mass m(chi) = 53.93 +/- 9.81GeV interacts under the exchange of a light mediator of mass m(phi) = 6.6 +/- 0.43MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross-section-velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.

Automated summary

The study investigates the potential signature of self-interacting dark matter (SIDM) based on the observed anticorrelation between central dark matter (DM) densities of bright Milky Way dwarf spheroidal galaxies (dSphs) and their orbital pericentre distances. By analyzing the range of SIDM scattering cross-section per unit mass, the research finds that different dSph models require varying values of sigma/m(chi) to reproduce the observed central DM densities. Larger cross-sections are correlated with lower collision velocities of DM particles within each subhalo's core, leading to a proposed SIDM particle model involving a DM particle with a mass m(chi) = 53.93 +/- 9.81 GeV interacting through a light mediator of mass m(phi) = 6.6 +/- 0.43 MeV. This cross-section-velocity relation explains the diverse DM profiles of MW dSph satellites and matches observational constraints on larger scales.