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Register a new userConstraining the Equation of State of Neutron Stars from Binary Mergers
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Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered.
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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.
Determining the differential-rotation law of compact stellar objects produced in binary neutron stars mergers or core-collapse supernovae is an old problem in relativistic astrophysics. Addressing this problem is important because it impacts directly on the maximum mass these objects can attain and hence on the threshold to black-hole formation under realistic conditions. Using the results from a large number of numerical simulations in full general relativity of binary neutron star mergers described with various equations of state and masses, we study the rotational properties of the resulting hypermassive neutron stars. We find that the angular-velocity distribution shows only a modest dependence on the equation of state, thus exhibiting the traits of quasi-universality found in other aspects of compact stars, both isolated and in binary systems. The distributions are characterized by an almost uniformly rotating core and a disk. Such a configuration is significantly different from the $j-{rm constant}$ differential-rotation law that is commonly adopted in equilibrium models of differentially rotating stars. Furthermore, the rest-mass contained in such a disk can be quite large, ranging from $simeq 0.03,M_{odot}$ in the case of high-mass binaries with stiff equations of state, up to $simeq 0.2,M_{odot}$ for low-mass binaries with soft equations of state. We comment on the astrophysical implications of our findings and on the long-term evolutionary scenarios that can be conjectured on the basis of our simulations.
We study the gravitational-wave peak luminosity and radiated energy of quasicircular neutron star mergers using a large sample of numerical relativity simulations with different binary parameters and input physics. The peak luminosity for all the binaries can be described in terms of the mass ratio and of the leading-order post-Newtonian tidal parameter solely. The mergers resulting in a prompt collapse to black hole have largest peak luminosities. However, the largest amount of energy per unit mass is radiated by mergers that produce a hypermassive neutron star or a massive neutron star remnant. We quantify the gravitational-wave luminosity of binary neutron star merger events, and set upper limits on the radiated energy and the remnant angular momentum from these events. We find that there is an empirical universal relation connecting the total gravitational radiation and the angular momentum of the remnant. Our results constrain the final spin of the remnant black-hole and also indicate that stable neutron star remnant forms with super-Keplerian angular momentum.
Extending previous work by a number of authors, we have recently presented a new approach in which the detection of gravitational waves from merging neutron star binaries can be used to determine the equation of state of matter at nuclear density and hence the structure of neutron stars. In particular, after performing a large number of numerical-relativity simulations of binaries with nuclear equations of state, we have found that the post-merger emission is characterized by two distinct and robust spectral features. While the high-frequency peak was already shown to be associated with the oscillations of the hypermassive neutron star produced by the merger and to depend on the equation of state, we have highlighted that the low-frequency peak is related to the merger process and to the total compactness of the stars in the binary. This relation is essentially universal and provides a powerful tool to set tight constraints on the equation of state. We here provide additional information on the extensive analysis performed, illustrating the methods used, the tests considered, as well as the robustness of the results. We also discuss additional relations that can be deduced when exploring the data and how these correlate with various properties of the binary. Finally, we present a simple mechanical toy model that explains the main spectral features of the post-merger signal and can even reproduce analytically the complex waveforms emitted right after the merger.
We present a study of the merger of six different known galactic systems of binary neutron stars (BNS) of unequal mass with a mass ratio between $0.75$ and $0.99$. Specifically, these systems are J1756-2251, J0737-3039A, J1906+0746, B1534+12, J0453+1559 and B1913+16. We follow the dynamics of the merger from the late stage of the inspiral process up to $sim$ 20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH), using a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLy with a thermal component. For the most extreme of these systems ($q=0.75$, J0453+1559), we also investigate the effects of different EOSs: APR4, H4, and MS1. Our numerical simulations are performed using only publicly available open source code such as, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. We show results on the gravitational wave signals, spectrogram and frequencies of the BNS after the merger and the BH properties in the two cases in which the system collapse within the simulated time.
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