The crust of dark-matter admixed neutron stars: bulk properties and torsional oscillations

We study how dark matter (DM) impacts the crust and the spectrum of torsional crust oscillations of dark-matter-admixed neutron stars (DANSs). We construct two-fluid equilibrium solutions wherein baryonic and DM interact gravitationally only, adopting a unified nuclear equation of state for the former and a fermionic equation of state with repulsive self-interaction for the latter. At fixed total gravitational mass and DM mass fraction, we find that DM reduces the crust thickness in comparison to pure baryonic-matter neutron stars (NSs). The thinning of the crust is negligible when most of the DM distribution extends beyond the star's baryonic surface. However, the crust thickness can decrease by as much as 12% when the DM distribution is within the star's baryonic surface, i.e., when the star has a "dark core." We support these results by deriving approximate analytical formulas for the crust thickness that agree with our numerical calculations at the sub-percent level in best case scenarios. Next, we derive the equation that describes crustal torsional modes of DANSs in the relativistic Cowling approximation. We find that the oscillation frequencies are in general higher than those of a comparable pure baryonic-matter NS, with the largest frequency shifts happening in the same parameter space where the crust thickness decreases the most. Moreover, we study the degeneracy between DM and baryonic-crustal microphysics effects on these modes. As an example, we study electron screening, which softens the crust's shear modulus, thus decreasing the frequencies. We find that the degeneracy between the competing effects of DM and electron screening can be broken in some regions of the parameter space we explored. Should they be measured, our results suggest that torsional oscillations could be used to infer the existence of a DM core within massive NSs. (Abridged)