2017/01/31 by Eric D. Van Oeveren, John L. Friedman
Earth and Planetary Sciences · Physics and Astronomy · #Astrophysics #Dimensionless quantity #Equation of state #Gamma-ray bursts and supernovae #Geophysics and Gravity Measurements #Gravitational wave #Mathematical analysis #Neutron star #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Speed of sound #Upper and lower bounds #astro-ph.HE #gr-qc #nucl-th
paper · pdf · doi:10.1103/physrevd.95.083014
published as Phys. Rev. D 95, 083014 (2017) · 24 pages, 10 figures. Updated to more closely reflect published version
openalex created_date 2017/01/26 · openalex publication_date 2017/04/27 · arxiv created 2017/05/03 · arxiv updated 2017/05/05 · openalex updated_date 2026/08/06
A principal goal of gravitational-wave 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 one-parameter 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 vsound=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)] to estimate the resulting upper limit on the gravitational-wave phase shift of a black hole--neutron star (BHNS) binary relative to a BBH. Even for assumptions weak enough to allow a maximum mass of 4 M_\ensuremath\bigodot (a match at nuclear saturation density to an unusually stiff low-density 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 vsound<c, and the condition dp/d\ensuremathε<1 for the effective EOS governing the equilibrium star.