On the anti-correlation between pericentric distance and inner dark matter density of Milky Way's dwarf spheroidal galaxies

An anti-correlation between the central density of the dark matter halo ($\rho_{150,\ {\rm DM}}$) and the pericentric distances ($r_{p}$) of the Milky Way's (MW's) dwarf spheroidal galaxies (dSphs) has been reported in the literature. The existence and origin of such anti-correlation is however controversial, one possibility being that only the densest dSphs can survive the tidal field towards the centre of our Galaxy. In this work, we place particular emphasis on quantifying the statistical significance of such anti-correlation, by using available literature data in order to explore its robustness under different assumptions on the MW gravitational potential, and for various derivations of $\rho_{150}$ and $r_{p}$. We consider models in which the MW is isolated and has a low ($8.8\times10^{11}\,M_{\odot}$) and high ($1.6\times10^{12}\, M_{\odot}$) halo mass, respectively, as well as configurations in which the MW's potential is perturbed by a Large Magellanic Cloud (LMC) infall. We find that, while data generally support models in which the dSphs' central DM density decreases as a function of their pericentric radius, this anti-correlation is statistically significant at $3\sigma$ level only in $\sim$12$\%$ of the combinations of $\rho_{150}$ and $r_{p}$ explored. Moreover, including the impact of the LMC's infall onto the MW weakens or even washes away this anti-correlation, with respect to models in which the MW is isolated. Our results suggest that the strength and existence of such anti-correlation is still debatable: exploring it with high-resolution simulations including baryonic physics and different DM flavours will help us to understand its emergence.