We study a class of Newtonian models for the deformations of non-magnetised neutron stars during their spin-down. All the models have an analytical solution which allows to easily grasp the dependence of the strain on the star’s main physical quantities, such as radius, mass, and crust thickness.
We first use the model proposed by Franco, Link, and Epstein that depicts the star as made of a fluid core and an elastic crust with the same density, to compare the response to a decreasing centrifugal force on stars having different masses and equations of state. We find that the strain angle is peaked at the equator and its maximum value decreases as a function of the mass.
Afterwards, we introduce a second, more refined, model in which the core and the crust have different densities, and the gravitational potential of the deformed body is self-consistently accounted for. The strain angle is still a decreasing function of the stellar mass, but now its maximum value is typically peaked at the poles and is larger (by a factor of four) than the corresponding value in the one-density model.
Finally, within the present analytic approach, we evaluate the impact of the Cowling approximation: when the perturbations of the gravitational potential are neglected, we find an underestimation of the centrifugal effect on the star, since the strain angle is about 40% of the one obtained with the complete model.