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

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 $\mathit{\text{Gaia}}$ Early Data Release 3 (EDR3), to build a mass model of the SMC. We test our Jeans mass modelling method ($\text{textsc}Binulator$+$\text{textsc}GravSphere$) 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, ${\rho }_{\mathrm{D}\mathrm{M}}(150\mathrm{p}\mathrm{c})=2.81_{-1.07}^{+0.72}\times {10}^8{M}_{\odot }\mathrm{k}\mathrm{p}{\mathrm{c}}^{-3}$, consistent with a $\mathrm{\Lambda }$ Cold Dark Matter ($\mathrm{\Lambda }$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 ($M_{\mathrm{t}\mathrm{o}\mathrm{t}}\le 3\mathrm{k}\mathrm{p}\mathrm{c})$ 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 $M_{\ast }\mathrm{/}{M}_{200}>{10}^{-2}$. We provide a new, analytic, density profile that reproduces Dark Matter heating behaviour over the range ${10}^{-5}<M_{\ast }\mathrm{/}{M}_{200}<{10}^{-1}$.