Deformation and crustal rigidity of rotating neutron stars

Aims. We calculate parameters A and B of the Baym-Pines model of the hydro-elastic equilibrium of rotating neutron stars. Parameter A determines the energy increase of a non-rotating star due to a quadrupolar deformation of its shape. Parameter B determines residual quadrupolar deformation due to the crustal shear strain in a neutron star that spun down to a non-rotating state. Methods. The calculations of ${A}$ are based on precise numerical 2D calculations for rotating neutron stars with the realistic equations of state (EOSs) of dense matter. An approximate, but quite precise, formula for B is used, which allows us to separate the contribution of the crust from the dependence on the stellar mass M and radius R. The elastic shear strain distribution within the crust is modeled following Cutler et al. (2003). Realistic EOSs of neutron star cores are used, some of them with high-density softening due to the appearance of hyperons or a phase transition to an exotic state. Results. The values $A(M)$ and $B(M)$ were calculated for $0.2\;M _\odot<M<0.9\;M_{\rm max}$ (where Mmax is the maximum allowable mass) for seven EOSs of neutron star core, combined with several crust models. A standard formula based on the incompressible fluid model is shown to severely underestimate the value of A. For $M<0.7\;M_\odot$ the values of $A(M)$ are nearly EOS-independent and are given (within a few percent) by a universal formula $A=3.87\;(M/M_\odot)^{7/3}\;\times 10^{53}~{\rm erg}$. We derive the scaling of B with respect to R and M, also valid for a thick crust. We show that B for accreted crust strongly depends on pycnonuclear fusions at $\rho>10^{12}~\rm g~cm^{-3}$