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Register a new userEquation-of-state-independent relations in neutron stars
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Neutron stars are extremely relativistic objects which abound in our universe and yet are poorly understood, due to the high uncertainty on how matter behaves in the extreme conditions which prevail in the stellar core. It has recently been pointed out that the moment of inertia I, the Love number lambda and the spin-induced quadrupole moment Q of an isolated neutron star, are related through functions which are practically independent of the equation of state. These surprising universal I-lambda-Q relations pave the way for a better understanding of neutron stars, most notably via gravitational-wave emission. Gravitational-wave observations will probe highly-dynamical binaries and it is important to understand whether the universality of the I-lambda-Q relations survives strong-field and finite-size effects. We apply a Post-Newtonian-Affine approach to model tidal deformations in compact binaries and show that the I-lambda relation depends on the inspiral frequency, but is insensitive to the equation of state. We provide a fit for the universal relation, which is valid up to a gravitational wave frequency of ~900 Hz and accurate to within a few percent. Our results strengthen the universality of I-lambda-Q relations, and are relevant for gravitational-wave observations with advanced ground-based interferometers. We also discuss the possibility of using the Love-compactness relation to measure the neutron-star radius with an uncertainty of about 10% or smaller from gravitational-wave observations.
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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.
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.
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.
We study the Starobinsky or $R^2$ model of $f(R)=R+alpha R^2$ for neutron stars with the structure equations represented by the coupled differential equations and the emph{polytropic} type of the matter equation of state. The junction conditions of $f(R)$ gravity are used as the boundary conditions to match the Schwarschild solution at the surface of the star. Based on these the conditions, we demonstrate that the coupled differential equations can be solved emph{directly}. In particular, from the dimensionless equation of state $bar{rho} = bar{k}, bar{p}^{,gamma}$ with $bar{k}sim5.0$ and $gammasim0.75$ and the constraint of $alphalesssim {1.47722}times 10^{7}, text{m}^2$, we obtain the emph{minimal} mass of the NS to be around 1.44 $M_{odot}$. In addition, if $bar{k}$ is larger than 5.0, the mass and radius of the NS would be smaller.
Modern multi-messenger astronomical observations and heavy ion experiments provide new insights into the structure of compact objects. Nevertheless, much ambiguity remains when it comes to super dense matter above the nuclear saturation density such as that found within neutron stars. This work explores equation of state (EOS)-independent universal relations between the physical parameters of static neutron stars at the maximum-mass point, previously proven for General Relativity (GR) and used to constraint EOS candidates within the GR framework. We explore 53 different EOS candidates and prove that these relations hold for scalarized neutron stars in massive scalar-tensor theories, exploring also the effect of non-baryonic EOS. We further show that the relations fit parameters are highly dependent on the theorys parameters. On the basis of these relations multiple constraints on the EOS can be derived and it turns out that they can be significantly different than the GR ones. This demonstrates the importance of taking into account the modified gravity effects even when imposing constraints on the EOS.
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