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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 ofmassive binary neutron stars shows a striking instability as the stars comeclose together: Each star's central density increases by an amount proportionalto 1/(orbital radius). This overwhelms any stabilizing effects of tidalcoupling [which are proportional to 1/(orbital radius)^6] and causes the starsto collapse before they merge. Since the claimed increase of density scaleswith the stars' mass, it should also show up in a perturbation limit where apoint particle of mass $\mu$ orbits a neutron star. We prove analytically thatthis does not happen; the neutron star's central density is unaffected by thecompanion's presence to linear order in $\mu/R$. We show, further, that thedensity increase observed by Wilson et. al. could arise as a consequence of notfaithfully maintaining boundary conditions.Comment: 3 pages, REVTeX, no figures, submitted to Phys Rev D as a Rapid  Communicatio

physical review letters

Central Density of a Neutron Star is Unaffected by a Binary Companion at Linear Order in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">μ</mml:mi><mml:mi>/</mml:mi><mml:mi mathvariant="italic">R</mml:mi></mml:math>

Central Density of a Neutron Star is Unaffected by a Binary Companion at Linear Order inμ/R