Constraining neutron-star tidal Love numbers with gravitational-wave detectors

Ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, low frequency portion of the signal of detected neutron star--neutron star inspirals. In this early adiabatic regime, the influence of a neutron star's internal structure on the phase of the waveform depends only on a single parameter $\ensuremath{\lambda}$ of the star related to its tidal Love number, namely, the ratio of the induced quadrupole moment to the perturbing tidal gravitational field. We analyze the information obtainable from gravitational wave frequencies smaller than a cutoff frequency of 400 Hz, where corrections to the internal-structure signal are less than 10%. For an inspiral of two nonspinning $1.4{M}_{\ensuremath{\bigodot}}$ neutron stars at a distance of 50 Megaparsecs, LIGO II detectors will be able to constrain $\ensuremath{\lambda}$ to $\ensuremath{\lambda}\ensuremath{\le}2.0\ifmmode\times\else\texttimes\fi{}{10}^{37}\text{ }\text{ }\mathrm{g}\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{s}}^{2}$ with 90% confidence. Fully relativistic stellar models show that the corresponding constraint on radius $R$ for $1.4{M}_{\ensuremath{\bigodot}}$ neutron stars would be $R\ensuremath{\le}13.6\text{ }\text{ }\mathrm{km}$ (15.3 km) for a $n=0.5$ ($n=1.0$) polytrope with equation of state $p\ensuremath{\propto}{\ensuremath{\rho}}^{1+1/n}$.

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