Surviving the waves: evidence for a dark matter cusp in the tidally disrupting Small Magellanic Cloud

Abstract

ABSTRACT We use spectroscopic data for ${\sim }6000$ red giant branch stars in the Small Magellanic Cloud (SMC), together with proper motion data from Gaia Early Data Release 3, to build a mass model of the SMC. We test our Jeans mass modelling method (binulator + gravsphere) on mock data for an SMC-like dwarf undergoing severe tidal disruption, showing that we are able to successfully remove tidally unbound interlopers, recovering the dark matter density and stellar velocity anisotropy profiles within our 95 per cent confidence intervals. We then apply our method to real SMC data, finding that the stars of the cleaned sample are isotropic at all radii (at 95 per cent confidence) and that the inner dark matter density profile is dense, $\rho _{\rm DM}(150\ {\rm pc}) = 1.58_{-0.58}^{+0.80}\times 10^8 \ {\rm M}_{\odot }\, \rm kpc^{-3}$, consistent with a $\Lambda$ cold dark matter cusp. Our model gives a new estimate of the SMC’s total mass within 3 kpc $(M_{\rm tot} \le 3\ {\rm kpc})$ of $2.29\pm 0.46 \times 10^9 \ {\rm M}_{\odot }$. We also derive an astrophysical ‘J-factor’ of $18.99\pm 0.16$ GeV$^2$ cm$^{-5}$ and a ‘D-factor’ of $18.73\pm 0.04$ GeV$^2$ cm$^{-5}$, making the SMC a promising target for dark matter annihilation and decay searches. Finally, we combine our findings with literature measurements to test models in which dark matter is ‘heated up’ by baryonic effects. We find good qualitative agreement with the Di Cintio et al. model but we deviate from the Lazar et al. model at high $M_*/M_{200} > 10^{-2}$. We provide a new, analytical, density profile that reproduces dark matter heating behaviour over the range $10^{-4} < M_*/M_{200} < 10^{-1}$.