Upper limit set by causality on the tidal deformability of a neutron star
Abstract
A principal goal of gravitationalwave astronomy is to constrain the neutron star equation of state (EOS) by measuring the tidal deformability of neutron stars. The tidally induced departure of the waveform from that of a point particle [or a spinless binary black hole (BBH)] increases with the stiffness of the EOS. We show that causality (the requirement that the speed of sound be less than the speed of light for a perfect fluid satisfying a oneparameter equation of state) places an upper bound on tidal deformability as a function of mass. Like the upper mass limit, the limit on deformability is obtained by using an EOS with v_{sound}=c for high densities and matching to a low density (candidate) EOS at a matching density of order nuclear saturation density. We use these results and those of Lackey et al. [Phys. Rev. D 89, 043009 (2014), 10.1103/PhysRevD.89.043009] to estimate the resulting upper limit on the gravitationalwave phase shift of a black holeneutron star (BHNS) binary relative to a BBH. Even for assumptions weak enough to allow a maximum mass of 4 M_{☉} (a match at nuclear saturation density to an unusually stiff lowdensity candidate EOS), the upper limit on dimensionless tidal deformability is stringent. It leads to a still more stringent estimated upper limit on the maximum tidally induced phase shift prior to merger. We comment in an appendix on the relation among causality, the condition v_{sound}<c , and the condition d p /d ∊ <1 for the effective EOS governing the equilibrium star.
 Publication:

Physical Review D
 Pub Date:
 April 2017
 DOI:
 10.1103/PhysRevD.95.083014
 arXiv:
 arXiv:1701.03797
 Bibcode:
 2017PhRvD..95h3014V
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 Nuclear Theory
 EPrint:
 24 pages, 10 figures. Updated to more closely reflect published version