Crustal rigidity and rotational deformation of 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 2-D calculations for rotating neutron stars with 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 appearance of hyperons or a phase transition to an exotic state. Results. The values A(M) and B(M) are calculated for 0.2 M⊙ < M < 0.9 Mmax (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⊙ the values of A(M) is nearly EOS independent and are given (within a few percent) by a universal formula A = 3.87 (M/M⊙) 7/3 ×10 erg. We derive the scaling of B with respect to R and M , valid also for a thick crust. We show that B for accreted crust strongly depends on pycnonuclear fusions at ρ > 10 g cm. We point out an error in a recent interpretation of precession of neutron star in an isolated neutron star RX J0720.4-3125. We show that a correct analysis of observations yields an oblateness that can easily be explained in terms of an ordinary neutron star model.