Prospects for a precise equation of state measurement from Advanced LIGO and Cosmic Explorer

Daniel Finstad, Laurel V. White, Duncan A. Brown

Submitted on 2 November 2022


Gravitational-wave observations of neutron star mergers can probe the nuclear equation of state by measuring the imprint of the neutron star's tidal deformability on the signal. We investigate the ability of future gravitational-wave observations to produce a precise measurement of the equation of state from binary neutron star inspirals. Since measurability of the tidal effect depends on the equation of state, we explore several equations of state that span current observational constraints. We generate a population of binary neutron stars as seen by a simulated Advanced LIGO-Virgo network, as well as by a planned Cosmic Explorer observatory. We perform Bayesian inference to measure the parameters of each signal, and we combine measurements across each population to determine R1.4, the radius of a 1.4M neutron star. We find that with 321 signals the LIGO-Virgo network is able to measure R1.4 to better than 2% precision for all equations of state we consider, however we find that achieving this precision could take decades of observation, depending on the equation of state and the merger rate. On the other hand we find that with one year of observation, Cosmic Explorer will measure R1.4 to better than 0.6% precision. In both cases we find that systematic biases, such as from an incorrect mass prior, can significantly impact measurement accuracy and efforts will be required to mitigate these effects.


Comment: 11 pages, 6 figures

Subjects: Astrophysics - High Energy Astrophysical Phenomena; General Relativity and Quantum Cosmology


Match between gravitational waveforms for equal mass binaries with and without tidal deformability included. The match is calculated as the noise-weighted overlap between the two waveforms in the frequency range $20-2048$ Hz using the Advanced LIGO design sensitivity noise curve. Waveforms are generated using masses ranging from $1-2$\msun, and for the waveform including tidal deformability we use values of $\tilde\Lambda=\Lambda_{1}=\Lambda_{2}$ that span the range of plausible values between the soft (blue, lower curve) and stiff (green, upper curve) equations of state selected for our analysis.