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Gravitational-wave measurements of the tidal deformability in neutron-star binary coalescences can be used to infer the still unknown equation of state (EoS) of dense matter above the nuclear saturation density. By employing a Bayesian-ranking test we quantify the ability of current and future gravitational-wave observations to discriminate among families of realistic EoS which differ in particle content and ab-initio microscopic calculations. While the constraining power of GW170817 is limited, stringent constraints can be placed with approximately 10 coalescences detected by LIGO-Virgo at design sensitivity, but only for relatively stiff EoS which are already marginally in tension with GW170817. However, we show that even just a single detection with a third-generation detector such as the Einstein Telescope or Cosmic Explorer will rule out several families of EoS with very strong statistical significance, and can discriminate among models which feature similar softness, hence constraining the properties of nuclear matter to unprecedented levels.
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Fisher matrix and related studies have suggested that with second-generation gravitational wave detectors, it may be possible to infer the equation of state of neutron stars using tidal effects in binary inspiral. Here we present the first fully Bayesian investigation of this problem. We simulate a realistic data analysis setting by performing a series of numerical experiments of binary neutron star signals hidden in detector noise, assuming the projected final design sensitivity of the Advanced LIGO- Virgo network. With an astrophysical distribution of events (in particular, uniform in co-moving volume), we find that only a few tens of detections will be required to arrive at strong constraints, even for some of the softest equations of state in the literature. Thus, direct gravitational wave detection will provide a unique probe of neutron star structure.
Observations of the properties of multiple coalescing neutron stars will simultaneously provide insight into neutron star mass and spin distribution, the neutron star merger rate, and the nuclear equation of state. Not all merging binaries containing neutron stars are expected to be identical. Plausible sources of diversity in these coalescing binaries can arise from a broad or multi-peaked NS mass distribution; the effect of different and extreme NS natal spins; the possibility of NS-BH mergers; or even the possibility of phase transitions, allowing for NS with similar mass but strongly divergent radius. In this work, we provide a concrete algorithm to combine all information obtained from GW measurements into a joint constraint on the NS merger rate, the distribution of NS properties, and the nuclear equation of state. Using a concrete example, we show how biased mass distribution inferences can significantly impact the recovered equation of state, even in the small-$N$ limit. With the same concrete example, we show how small-$N$ observations could identify a bimodal mass and spin distribution for merging NS simultaneously with the EOS. Our concordance approach can be immediately generalized to incorporate other observational constraints.
Third-generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to both high signal-to-noise ratios and long-duration signals. We demonstrate that current Bayesian inference paradigms can be extended to the analysis of binary neutron star signals without breaking the computational bank. We construct reduced order models for $sim 90,mathrm{minute}$ long gravitational-wave signals, covering the observing band ($5-2048,mathrm{Hz}$), speeding up inference by a factor of $sim 1.3times 10^4$ compared to the calculation times without reduced order models. The reduced order models incorporate key physics including the effects of tidal deformability, amplitude modulation due to the Earths rotation, and spin-induced orbital precession. We show how reduced order modeling can accelerate inference on data containing multiple, overlapping gravitational-wave signals, and determine the speedup as a function of the number of overlapping signals. Thus, we conclude that Bayesian inference is computationally tractable for the long-lived, overlapping, high signal-to-noise-ratio events present in 3G observatories.
Recently exploratory studies were performed on the possibility of constraining the neutron star equation of state (EOS) using signals from coalescing binary neutron stars, or neutron star-black hole systems, as they will be seen in upcoming advanced gravitational wave detectors such as Advanced LIGO and Advanced Virgo. In particular, it was estimated to what extent the combined information from multiple detections would enable one to distinguish between different equations of state through hypothesis ranking or parameter estimation. Under the assumption of zero neutron star spins both in signals and in template waveforms and considering tidal effects to 1 post-Newtonian (1PN) order, it was found that O(20) sources would suffice to distinguish between a hard, moderate, and soft equation of state. Here we revisit these results, this time including neutron star tidal effects to the highest order currently known, termination of gravitational waveforms at the contact frequency, neutron star spins, and the resulting quadrupole-monopole interaction. We also take the masses of neutron stars in simulated sources to be distributed according to a relatively strongly peaked Gaussian, as hinted at by observations, but without assuming that the data analyst will necessarily have accurate knowledge of this distribution for use as a mass prior. We find that especially the effect of the latter is dramatic, necessitating many more detections to distinguish between different EOS and causing systematic biases in parameter estimation, on top of biases due to imperfect understanding of the signal model pointed out in earlier work. This would get mitigated if reliable prior information about the mass distribution could be folded into the analyses.
On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function $p(rho)$ of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as $R_1=10.8^{+2.0}_{-1.7}$ km for the heavier star and $R_2= 10.7^{+2.1}_{-1.5}$ km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than $1.97 ,M_odot$ as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain $R_1= 11.9^{+1.4}_{-1.4}$ km and $R_2= 11.9^{+1.4}_{-1.4}$ km at the 90% credible level. Finally, we obtain constraints on $p(rho)$ at supranuclear densities, with pressure at twice nuclear saturation density measured at $3.5^{+2.7}_{-1.7}times 10^{34} ,mathrm{dyn}/mathrm{cm}^{2}$ at the 90% level.
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