End-point of the rp process and periodic gravitational wave emission

Abstract

The general end-point of the rp process in rapidly accreting neutron stars is believed to be a surface distribution of matter whose nuclear composition may depend on position. Its evolution during compression beyond the neutron-drip threshold density is determined by the presence of nuclear formation enthalpy minima at the proton closed shells. At threshold, a sequence of weak interactions with capture or emission of neutron pairs rapidly transform nuclei to the most accessible proton closed shell. Therefore, angular asymmetries in nuclear composition present in accreted matter at neutron drip are preserved during further compression to higher densities provided transition rates between closed shells are negligible. Although it has been confirmed that this condition is satisfied for predicted internal temperatures and for the formation enthalpy distribution used in this work, it would not be so if the true enthalpy differences between maxima and minima in the distribution were a factor of two smaller. For this reason, it does not appear possible to assert with any confidence that position-dependent surface composition can lead to significant angle-dependence of the equation of state and to potentially observable gravitational radiation. The effect of non-radial internal temperature gradients on angle-dependency of the equation of state is also not quantifiable.