Incompressible analytical models for spinning-down pulsars

We study a class of Newtonian models for the deformations of non-magnetized neutron stars duringtheir spin-down. The models have all an analytical solution, and thus allow to understand easily thedependence of the strain on the star’s main physical quantities, such as radius, mass and crust thickness.In the first “historical” model the star is assumed to be comprised of a fluid core and an elastic crustwith the same density. We compare the response of stars with different masses and equations of stateto a decreasing centrifugal force, finding smaller deformations for heavier stars: the strain angle ispeaked at the equator and turns out to be a decreasing function of the mass.We introduce a second,more refined, model in which the core and the crust have different densities and the gravitationalpotential of the deformed body is self-consistently accounted for. Also in this case the strain angle isa decreasing function of the stellar mass, but its maximum value is at the poles and is always largerthan the corresponding one in the one-density model by a factor of two. Finally, within the presentanalytic approach, it is possible to estimate easily the impact of the Cowling approximation: neglectingthe perturbations of the gravitational potential, the strain angle is 40% of the one obtained with thecomplete model.