Torsional oscillations of dark matter admixed neutron stars

As neutron stars cool, the nuclei in their outer layers crystallize, forming a solid crust that can sustain elastic vibrations known as torsional shear modes. Quasiperiodic oscillations detected after giant flares in magnetars including SGR 1900+14 and SGR 1806+20 have frequencies consistent with these crustal modes. Could these observations be used to constrain the presence of dark matter within neutron stars? To answer this question, we study the torsional oscillations of dark matter admixed neutron stars using the relativistic Cowling approximation. The stellar structure is modeled with a two fluid framework where baryonic matter and dark matter interact only through gravity. We adopt the NL3ωρL55 crust-core unified equation of state for the baryonic component and a self interacting fermionic equation of state for the dark component of the fluid. By solving the Tolman–Oppenheimer–Volkoff equations, we examine how the crust thickness changes because of the presence of dark matter. We then solve the equation that describes the crustal torsional oscillations, and examine how dark matter modifies these oscillation frequencies compared to ordinary neutron stars.