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-circle dot < M < 0.9 M-max (where M-max 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-circle dot 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-circle dot)(7/3) x 10(53) 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) g cm(-3).