A&A 491, 489-498 (2008)

DOI: 10.1051/0004-6361:200810183

## Deformation and crustal rigidity of rotating neutron stars

**J. L. Zdunik**

^{1}, M. Bejger^{2, 1}, and P. Haensel^{1}^{1}N. Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland

e-mail: [jlz;bejger;haensel]@camk.edu.pl

^{2}LUTH, UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France

Received 13 May 2008 / Accepted 22 August 2008

** Abstract ***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
(where
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
the values of *A*(*M*) are nearly EOS-independent
and are given (within a few percent) by a
universal formula
. 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
.

**Key words:**dense matter

**--**equation of state

**--**stars: neutron

**©**

*ESO 2008*