Mountains on Neutron Stars: Accreted vs. Non-Accreted crusts

The aim of this paper is to compare the two cases of an isolated neutron star, with a non-accreted crust, and that of an accreting neutron star, with an accreted crust, and try to estimate which one of the two would make a better source of gravitational waves. In order to do this we must evaluate the maximum ``mountain'' that the crust can sustain in these two cases. We first do this using the formalism of Ushomirsky, Cutler and Bildsten (2000) and find that the maximum quadrupole is very similar in the two cases, with the non-accreted crust sustaining a slightly larger mountain. We then develop a perturbation formalism for the problem, that allows us to drop the Cowling approximation and have more control over the boundaries. The use of this formalism confirms that there is not much difference between the two cases, but leads to results approximately one order of magnitude larger than those we obtain with the formalism of Ushomirsky, Cutler and Bildsten (2000).