Bayesian analysis of the shear modulus in the neutron-star crust

Abstract

The elastic properties of the neutron-star crust are important for the calculations of crustal modes. In particular, the ability of the crust to support shear stresses has been connected to observations of quasi-periodic oscillations and to crust deformations potentially emitting gravitational waves. In this work, we assess the uncertainties in the shear modulus and shear speed in the neutron-star outer and inner crust. To this aim, we performed a Bayesian analysis of the shear properties of the neutron-star crust at zero temperature starting from both a non-informative and a nuclear-physics-informed prior. For the treatment of inhomogeneous matter in the crust, we relied on the one-component plasma approximation, with a (semi-)classical treatment of the ions. We show that the use of a nuclear-physics-informed prior has a non-negligible impact on the prediction of the elastic properties of the crust. The frequency of the fundamental torsional crustal modes we obtain is compatible with the low-frequency range of observed quasi-periodic oscillations, our estimates lying in the interval $\approx 20 - 50$~Hz. Although the different considered priors lead to compatible results, the inclusion of nuclear-physics experimental information in the prior considerably reduces the uncertainties in the prediction of the elastic properties of the crust, potentially constraining the predicted frequency of the crustal modes.