The central density of a neutron star is unaffected by a binary companion at linear order in $\mu/R$

TL;DR

This paper analytically demonstrates that a neutron star's central density remains unchanged at linear order in the mass ratio when in a binary system, challenging previous numerical findings of density increase.

Contribution

It provides an analytical proof that the neutron star's central density is unaffected by a binary companion at linear order, clarifying discrepancies with prior numerical results.

Findings

Central density unaffected at linear order in mass ratio.

Previous observed density increase may be due to boundary condition issues.

Analytical approach clarifies stability behavior in binary neutron stars.

Abstract

Recent numerical work by Wilson, Mathews, and Marronetti [J. R. Wilson, G. J. Mathews and P. Marronetti, Phys. Rev. D 54, 1317 (1996)] on the coalescence of massive binary neutron stars shows a striking instability as the stars come close together: Each star's central density increases by an amount proportional to 1/(orbital radius). This overwhelms any stabilizing effects of tidal coupling [which are proportional to 1/(orbital radius)^6] and causes the stars to collapse before they merge. Since the claimed increase of density scales with the stars' mass, it should also show up in a perturbation limit where a point particle of mass $\mu$ orbits a neutron star. We prove analytically that this does not happen; the neutron star's central density is unaffected by the companion's presence to linear order in $\mu/R$. We show, further, that the density increase observed by Wilson et. al. could arise as a consequence of not faithfully maintaining boundary conditions.