Kentaro Takami

Constraining the Equation of State of Neutron Stars from Binary Mergers

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.

Spectral properties of the post-merger gravitational-wave signal from binary neutron stars

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.

Gravitational-wave signal from binary neutron stars: a systematic analysis of the spectral properties

A number of works have shown that important information on the equation of state of matter at nuclear density can be extracted from the gravitational waves emitted by merging neutron-star binaries. We present a comprehensive analysis of the gravitational-wave signal emitted during the inspiral, merger and post-merger of 56 neutron-star binaries. This sample of binaries, arguably the largest studied to date with realistic equations of state, spans across six different nuclear-physics equations of state and ten masses, allowing us to sharpen a number of results recently obtained on the spectral properties of the gravitational-wave signal. Overall we find that: (i) for binaries with masses differing no more than

A quasi-radial stability criterion for rotating relativistic stars

20\%

Black-hole production from ultrarelativistic collisions

, the frequency at gravitational-wave amplitudes maximum is related quasi-universally with the tidal deformability of the two stars; (ii) the spectral properties vary during the post-merger phase, with a transient phase lasting a few millisecond after the merger and followed by a quasi-stationary phase; (iii) when distinguishing the spectral peaks between these two phases, a number of ambiguities in the identification of the peaks disappear, leaving a simple and robust picture; (iv) using properly identified frequencies, quasi-universal relations are found between the spectral features and the properties of the neutron stars; (v) for the most salient peaks analytic fitting functions can be obtained in terms of the stellar tidal deformability or compactness. Altogether, these results support the idea that the equation of state of nuclear matter can be constrained tightly when a signal in gravitational waves from binary neutron stars is detected.

Source Redshifts from Gravitational-Wave Observations of Binary Neutron Star Mergers

The stability properties of relativistic stars against gravitational collapse to black holes is a classical problem in general relativity. In 1988, a sufficient criterion for secular instability was established by Friedman, Ipser & Sorkin, who proved that a sequence of uniformly rotating barotropic stars are secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full general relativity the F-mode frequency for a large number of rotating stars, we show that the neutral-stability point, that is, where the frequency becomes zero, differs from the turning point for rotating stars. Using numerical simulations, we validate that the new criterion can be used to assess the dynamical stability of relativistic rotating stars.

Concluding Remarks: Connecting Relativistic Heavy Ion Collisions and Neutron Star Mergers by the Equation of State of Dense Hadron- and Quark Matter as signalled by Gravitational Waves

Determining the conditions under which a black hole can be produced is a long-standing and fundamental problem in general relativity. We use numerical simulations of colliding self-gravitating fluid objects to study the conditions of black-hole formation when the objects are boosted to ultrarelativistic speeds. Expanding on the previous work, we show that the collision is characterized by a type-I critical behaviour, with a black hole being produced for masses above a critical value, Mc, and a partially bound object for masses below the critical one. More importantly, we show for the first time that the critical mass varies with the initial effective Lorentz factor � γ � following a simple scaling of the type Mc ∼ K� γ � −1.0 , thus indicating that a black hole of infinitesimal mass is produced in the limit of a diverging Lorentz factor. Furthermore, because a scaling is present also in terms of the initial stellar compactness, we provide a condition for black-hole formation in the spirit of the hoop conjecture.

Extracting Information on the Equation of State from Binary Neutron Stars

Inspiraling compact binaries as standard sirens will become an invaluable tool for cosmology when we enter the gravitational-wave detection era. However, a degeneracy in the information carried by gravitational waves between the total rest-frame mass M and the redshift z of the source implies that neither can be directly extracted from the signal; only the combination M(1+z), the redshifted mass, can be directly extracted from the signal. Recent work has shown that for third-generation detectors, a tidal correction to the gravitational-wave phase in the late-inspiral signal of binary neutron star systems can be used to break the mass-redshift degeneracy. Here, we propose to use the signature encoded in the postmerger signal allowing the accurate extraction of the intrinsic rest-frame mass of the source, in turn permitting the determination of source redshift and luminosity distance. The entirety of this analysis method and any subsequent cosmological inference derived from it would be obtained solely from gravitational-wave observations and, hence, would be independent of the cosmological distance ladder. Using numerical simulations of binary neutron star mergers of different mass, we model gravitational-wave signals at different redshifts and use a Bayesian parameter estimation to determine the accuracy with which the redshift and mass can be extracted. We find that for a known illustrative neutron star equation of state and using the Einstein telescope, the median of the 1σ confidence regions in redshift corresponds to ∼10%–20% uncertainties at redshifts of z<0.04.

Rotational properties of hypermassive neutron stars from binary mergers

The underlying open questions in the fields of general relativistic astrophysics and elementary particle and nuclear physics are strongly connected and their results are interdependent. Although the physical systems are quite different, the 4D-simulation of a merger of a binary system of two neutron stars and the properties of the hot and dense matter created in high energy heavy ion collisions, strongly depend on the equation of state of fundamental elementary matter. Neutron star mergers represent optimal astrophysical laboratories to investigate the QCD phase structure using a spectrogram of the post-merger phase of the emitted gravitational waves. These studies can be supplemented by observations from heavy ion collisions to possibly reach a conclusive picture on the QCD phase structure at high density and temperature. As gravitational waves (GWs) emitted from merging neutron star binaries are on the verge of their first detection, it is important to understand the main characteristics of the underlying merging system in order to predict the expected GW signal. Based on numerical-relativity simulations of merging neutron star binaries, the emitted GW and the interior structure of the generated hypermassive neutron stars (HMNS) have been analyzed in detail. This article will focus on the internal and rotational HMNS properties and their connection with the emitted GW signal. Especially, the appearance of the hadon-quark phase transition in the interior region of the HMNS and its conjunction with the spectral properties of the emitted GW will be addressed and confronted with the simulation results of high energy heavy ion collisions.

Neutron-star Radius from a Population of Binary Neutron Star Mergers

Recently Bauswein and Janka [6, 7] found that the typical frequency of a hypermassive neutron star, which is called \(f_2\) in this paper, is a simple function of the average rest-mass density, essentially independently of the equation of state considered. While expected, this result is very important to decide the system mass from observed gravitational waves. However in their simulations, the Einstein equations were solved by assuming conformal flatness and employing a gravitational radiation-reaction scheme within a post-Newtonian framework. Besides this mathematical approximation, there is also a numerical one in the use of smooth-particle hydrodynamics code, which is well-know to be particularly dissipative and that rapidly suppresses the amplitude of the bar-mode deformation and rapidly yields to an almost axisymmetric system. Therefore we have reinvestigated the calculations in their work improving on the two approximations discussed above (i.e., conformal flatness and smooth-particle hydrodynamics) to obtain an accurate description both during the inspiral and after the merger. Then we have found another typical frequency with a clear peak, which is called \(f_\mathrm {LI}\) in this paper. Finally we show the relations between the initial masses and the \(f_\mathrm {LI}\) and \(f_2\) frequencies of the gravitational waves emission from a hypermassive neutron stars.