Constraining neutron star tidal Love numbers with gravitational wave detectors

Abstract

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 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 percent. For an inspiral of two non-spinning 1.4 solar mass neutron stars at a distance of 50 Mpc, LIGO II detectors will be able to constrain lambda to lambda < 2.0 10^{37} g cm^2 s^2 with 90% confidence. Fully relativistic stellar models show that the corresponding constraint on radius R for 1.4 solar mass neutron stars would be R < 13.6 km (15.3 km) for a n=0.5 (n=1.0) polytrope.

Figures (2)

• Figure 1: [Top] The solid lines bracket the range of Love numbers $\lambda$ for fully relativistic polytropic neutron star models of mass $m$ with surface redshift $z=0.35$, assuming a range of $0.3 \leq n \leq 1.2$ for the adiabatic index $n$. The top scale gives the radius $R$ for these relativistic models. The dashed lines are corresponding Newtonian values for stars of radius $R$. [Bottom] Upper bound (horizontal line) on the weighted average ${\tilde{\lambda}}$ of the two Love numbers obtainable with LIGO II for a binary inspiral signal at distance of 50 Mpc, for two non-spinning, $1.4 M_\odot$ neutron stars, using only data in the frequency band $f<400$ Hz. The curved lines are the actual values of $\lambda$ for relativistic polytropes with $n=0.5$ (dashed line) and $n=1.0$ (solid line).
• Figure 2: [Top] Analytic approximation (\ref{['eq:tidal1']}) to the tidal perturbation to the gravitational wave phase for two identical $1.4 M_\odot$ neutron stars of radius $R = 15\,$km, modeled as $n=1.0$ polytropes, as a function of gravitational wave frequency $f$. [Bottom] A comparison of different approximations to the tidal phase perturbation: the numerical solution (lower dashed, green curve) to the system (\ref{['eq:system']}), and the adiabatic analytic approximation (\ref{['eq:tidal0']}) (upper dashed, blue), both in the limit (\ref{['simplify']}) and divided by the leading order approximation (\ref{['eq:tidal1']}).