Surviving the Waves: evidence for a Dark Matter cusp in the tidally disrupting Small Magellanic Cloud

Abstract

We use spectroscopic data for $\sim 6,000$ Red Giant Branch (RGB) stars in the Small Magellanic Cloud (SMC), together with proper motion data from \textit{Gaia} Early Data Release 3 (EDR3), to build a mass model of the SMC. We test our Jeans mass modelling method (\textsc{Binulator}+\textsc{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\% 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\% confidence), and that the inner Dark Matter density profile is dense, $\ddot{I}{}_{\mathrm{DM}}(150\mathrm{pc})=2.81_{-1.07}^{+0.72}\times 10^8{M}_{\odot }\mathrm{kp}{\mathrm{c}}^{-3}$, consistent with a $\hat{I}›$ Cold Dark Matter ($\hat{I}›$CDM) cusp at least down to 400\,pc from the SMC's centre. Our model gives a new estimate of the SMC's total mass within 3\,kpc ($M_{\mathrm{tot}}\le 3\mathrm{kpc})$ of $2.34\pm 0.46\times 10^9{M}_{\odot }$. We also derive an astrophysical \textquote{$J$-factor} of $19.22\pm 0.14$\, GeV${}^2$\,cm${}^{-5}$ and a \textquote{$D$-factor} of $18.80\pm 0.03$\, 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 \textquote{heated up} by baryonic effects. We find good qualitative agreement with the Di Cintio et al. 2014 model but we deviate from the Lazar et al. 2020 model at high $M_{\ast }/M_{200}>10^{-2}$. We provide a new, analytic, density profile that reproduces Dark Matter heating behaviour over the range $10^{-5}<M_{\ast }/M_{200}<10^{-1}$.

Accepted for publication on MNRAS