Quasi-universal Relations Research Articles

On the Maximum Mass and Oblateness of Rotating Neutron Stars with Generic Equations of State

A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than 106 generic EOSs, we assess the validity of quasi-universal relations of neutron-star properties for a broad range of rotation rates, from slow rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modeling of the X-ray emission from the surface of rotating stars.

Unraveling information about supranuclear-dense matter from the complete binary neutron star coalescence process using future gravitational-wave detector networks

Gravitational waves provide us with an extraordinary tool to study the matter inside neutron stars. In particular, the postmerger signal probes an extreme temperature and density regime and will help reveal information about the equation of state of supranuclear-dense matter. Although current detectors are most sensitive to the signal emitted by binary neutron stars before the merger, the upgrades of existing detectors and the construction of the next generation of detectors will make postmerger detections feasible. For this purpose, we present a new analytical, frequency-domain model for the inspiral-merger-postmerger signal emitted by binary neutron star systems. The inspiral and merger parts of the signals are modeled with IMRPhenomD_NRTidalv2, and we describe the main emission peak of the postmerger with a three-parameter Lorentzian, using two different approaches: one in which the Lorentzian parameters are kept free, and one in which we model them via quasiuniversal relations. We test the performance of our new complete waveform model in parameter estimation analyses, studying simulated signals obtained both from our developed model and by injecting numerical relativity waveforms. We investigate the performance of different detector networks to determine the improvement that future detectors will bring to our analysis. We consider Advanced $\mathrm{LIGO}+$ and Advanced $\mathrm{Virgo}+$, KAGRA, and LIGO-India. We also study the possible impact of a detector with high sensitivity in the kilohertz band like NEMO, and finally we compare these results to the ones we obtain with third-generation detectors, the Einstein Telescope and the Cosmic Explorer.

A Bayesian Inference of a Relativistic Mean-field Model of Neutron Star Matter from Observations of NICER and GW170817/AT2017gfo

Observations of optical and near-infrared counterparts of binary neutron star mergers not only enrich our knowledge about the abundance of heavy elements in the universe and help reveal the remnant object just after the merger, which is generally known, but can also effectively constrain the dense properties of the nuclear matter and the equation of state (EOS) in the interior of the merging stars. Following the relativistic mean-field description of nuclear matter, we perform a Bayesian inference of the EOS and the properties of the nuclear matter using the first multi-messenger event GW170817/AT2017gfo, together with the NICER mass–radius measurements of pulsars. The kilonova is described by a radiation-transfer model with the dynamical ejecta, and light curves connect with the EOS through the quasi-universal relations between the properties of the ejecta (the ejected mass, velocity, opacity, or electron fraction) and binary parameters (the mass ratio and reduced tidal deformability). It is found that the posterior distributions of the reduced tidal deformability from the AT2017gfo analysis display a bimodal structure, with the first peak enhanced by the GW170817 data, leading to slightly softened posterior EOSs, while the second peak cannot be achieved by a nuclear EOS with saturation properties in their empirical ranges. The inclusion of NICER data results in a stiffened EOS posterior because of the massive pulsar PSR J0740+6620. We provide the results at nuclear saturation density for the nuclear incompressibility, the symmetry energy, and its slope, as well as the nucleon effective mass, from our analysis of the observational data.

Systematic errors due to quasiuniversal relations in binary neutron stars and their correction for unbiased model selection

Inference of the equation of state (EOS) of dense nuclear matter in neutron-star cores is a principal science goal of x-ray and gravitational-wave observations of neutron stars. In particular, gravitational-wave observations provide an independent probe of the properties of bulk matter in neutron star cores that can then be used to compare with theoretically derived equations of state. In this paper, we quantify the systematic errors arising from the application of EOS-independent quasiuniversal relations in the estimation of neutron star tidal deformabilities and radii from gravitational-wave measurements and introduce a strategy to correct for the systematic biases in the inferred radii. We apply this method to a simulated population of events expected to be observed by future upgrades of current detectors and the next generation of ground-based observatories. We show that our approach can accurately correct for the systematic biases arising from approximate universal relations in the mass-radius curves of neutron stars. Using the posterior distributions of the mass and radius for the simulated population we infer the underlying EOS with a good degree of precision. Our method revives the possibility of using the universal relations for rapid Bayesian model selection of the dense matter EOS in gravitational-wave observations.

Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers

The postmerger gravitational wave (GW) emission from a binary neutron star merger is expected to provide exciting new constraints on the dense-matter equation of state (EoS). Such constraints rely, by and large, on the existence of quasi-universal relations, which relate the peak frequencies of the postmerger GW spectrum to properties of the neutron star structure in a model-independent way. In this work, we report on violations of existing quasi-universal relations between the peak spectral frequency, f 2, and the stellar radius, for EoS models with backwards-bending slopes in their mass–radius relations (such that the radius increases at high masses). The violations are extreme, with variations in f 2 of up to ∼600 Hz between EoSs that predict the same radius for a 1.4 M ⊙ neutron star but that have significantly different radii at higher masses. Quasi-universality can be restored by adding in a second parameter to the fitting formulae that depends on the slope of the mass–radius curve. We further find strong evidence that quasi-universality is better maintained for the radii of very massive stars (with masses 2 M ⊙). Both statements imply that f 2 is mainly sensitive to the high-density EoS. Combined with observations of the binary neutron star inspiral, these generalized quasi-universal relations can be used to simultaneously infer the characteristic radius and slope of the neutron star mass–radius relation.

Prospects for distinguishing dynamical tides in inspiralling binary neutron stars with third generation gravitational-wave detectors

Tidal effects in gravitational-wave (GW) observations from binary neutron star mergers have the potential to probe ultra-dense matter and shed light on the unknown nuclear equation of state of neutron stars. Tidal effects in inspiralling neutron star binaries become relevant at GW frequencies of a few hundred Hz and require detectors with exquisite high-frequency sensitivity. Third generation GW detectors such as the Einstein Telescope or Cosmic Explorer will be particularly sensitive in this high-frequency regime, allowing us to probe neutron star tides beyond the adiabatic approximation. Here we assess whether dynamical tides can be measured from a neutron star inspiral. We find that the measurability of dynamical tides depends strongly on the neutron star mass and equation of state. For a semi-realistic population of 10,000 inspiralling binary neutron stars, we conservatively estimate that on average $\mathcal{O}(50)$ binaries will have measurable dynamical tides. As dynamical tides are characterised not only by the star's tidal deformability but also by its fundamental ($f$-) mode frequency, they present a possibility of probing higher-order tidal effects and test consistency with quasi-universal relations. For a GW170817-like signal in a third generation detector network, we find that the stars' $f$-mode frequencies can be measured to within a few hundred Hz.

Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We treat hadronic matter using a Brueckner-Hartree-Fock quantum many-body approach and modern two-body and three-body nuclear interactions derived within chiral effective field theory. Quark matter is modeled using an extended version of the bag model. We combine these approaches to construct a new finite-temperature composition-dependent equation of state (EOS) with a first-order phase transition between hadrons and deconfined quarks. We perform numerical relativity simulations of BNS mergers with this new EOS and compare results obtained with or without the deconfinment phase transition. We find that deconfined quark production in a neutron star merger results from matter crossing the phase boundary over a wide range of temperatures and densities. The softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasiuniversal relations for the postmerger GW peak frequency. Consequently, the postmerger GW peak frequency alone is not sufficient to conclusively exclude or confirm the presence of a phase transition in a BNS merger. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, $r$-process nucleosynthetic yields and associated electromagnetic counterparts. While there are differences in the electromagnetic counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two, so they are degenerate with other effects. An exception is the nonthermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

Fully general-relativistic simulations of isolated and binary strange quark stars

The hypothesis that strange quark matter is the true ground state of matter has been investigated for almost four decades, but only a few works have explored the dynamics of binary systems of quark stars. This is partly due to the numerical challenges that need to be faced when modelling the large discontinuities at the surface of these stars. We here present a novel technique in which the EOS of a quark star is suitably rescaled to produce a smooth change of the specific enthalpy across a very thin crust. The introduction of the crust has been carefully tested by considering the oscillation properties of isolated quark stars, showing that the response of the simulated quark stars matches accurately the perturbative predictions. Using this technique, we have carried out the first fully general-relativistic simulations of the merger of quark-star binaries finding several important differences between quark-star binaries and hadronic-star binaries with the same mass and comparable tidal deformability. In particular, we find that dynamical mass loss is significantly suppressed in quark-star binaries. In addition, quark-star binaries have merger and post-merger frequencies that obey the same quasi-universal relations derived from hadron stars if expressed in terms of the tidal deformability, but not when expressed in terms of the average stellar compactness. Hence, it may be difficult to distinguish the two classes of stars if no information on the stellar radius is available. Finally, differences are found in the distributions in velocity and entropy of the ejected matter, for which quark-stars have much smaller tails. Whether these differences in the ejected matter will leave an imprint in the electromagnetic counterpart and nucleosynthetic yields remains unclear, calling for the construction of an accurate model for the evaporation of the ejected quarks into nucleons.

Quasiuniversal relations for generalized Skyrme stars

First proposed in 2013 by Yagi and Yunes, the quasi-universal \emph{I-Love-Q relations} consist of a set of relations between the moment of inertia, the spin-induced quadrupole moment and the electric quadrupolar tidal deformability of neutron stars which are independent of the Equation of State (EoS) within an accuracy of $\sim1\%$. In this work, we show that these relations hold for different Skyrme-based nuclear matter EoS and also for the star-like solutions of different Einstein-BPS-Skyrme-models, some of which do not even present a barotropic equation of state. Further, other quasi-universal relations are analyzed, and together with recent GW observations, we use them to select the generalized Skyrme model that better reproduces observations. Our results reaffirm both the universality of the \emph{I-Love-Q} relations and the suitability of generalized Skyrme models to describe nuclear matter inside neutron stars.

Measuring individual masses of binary white dwarfs with space-based gravitational-wave interferometers

ABSTRACT Unlike gravitational waves from merging black holes and neutron stars that chirp significantly over the observational period of ground-based detectors, gravitational waves from binary white dwarfs are almost monochromatic. This makes it extremely challenging to measure their individual masses. Here, we take a novel approach of using finite-size effects and applying certain universal relations to measure individual masses of binary white dwarfs using Laser Interferometer Space Antenna. We found quasi-universal relations among the mass, moment of inertia, and tidal deformability of a white dwarf that do not depend sensitively on the white dwarf composition. These relations allow us to rewrite the moments of inertia and tidal deformabilities in the waveform in terms of the masses. We then carried out a Fisher analysis to estimate how accurately one can measure the individual masses from the chirp mass and finite-size measurements. We found that the individual white dwarf masses can be measured with LISA for a 4-yr observation if the initial frequency is high enough (∼0.02 Hz) and either the binary separation is small (∼1 kpc) or the masses are relatively large (m ≳ 0.8 M⊙). This opens a new possibility of measuring individual masses of binary white dwarfs with space-based interferometers.

New quasi-universal relations for static and rapid rotating neutron stars

In the last few decades, lots of universal relations between different global physical quantities of neutron stars have been proposed to constrain the unobservable or hard to be observed properties of neutron stars. But few of them are related to the gravitational redshift or the gravitational binding energy, especially for the fast rotating neutron stars. Here we will focus on the universal relations related to these two quantities. Based on 11 equations of state (EOSs) from the predictions of microscopic nuclear many-body theories for normal or hybrid neutron stars, we proposed a set of new quasi-universal relations under three rotating cases: static, general rotating and Keplerian rotating. These new quasi-universal relations provide a potential way to constrain or estimate the unobservable or hard to be observed properties of neutron stars.

Constructing Love-Q relations with gravitational wave detections

Quasi-universal relations connecting the tidal deformability and the quadrupole moment of individual neutron stars are predicted by theoretical computations, but have not been measured experimentally. However, such relations are employed during the interpretation of gravitational waves and, therefore, have a direct impact on the interpretation of real data. In this work, we study how quasi-universal relations can be tested and measured from gravitational wave signals connected to binary neutron star coalescences. We study a population of $120$ binary neutron star systems and find that Advanced LIGO and Advanced Virgo at design sensitivity could find possible deviations of predicted relations if the observed neutron stars are highly spinning. In the future, a network of third generation (3G) detectors will be able to even allow a measurement of quasi-universal relations. Thus, the outlined approach provides a new test of general relativity and nuclear physics predictions.

Kilohertz gravitational waves from binary neutron star remnants: Time-domain model and constraints on extreme matter

The remnant star of a neutron star merger is an anticipated loud source of kiloHertz gravitational waves that conveys unique information on the equation of state of hot matter at extreme densities. Observations of such signals are hampered by the photon shot noise of ground-based interferometers and pose a challenge for gravitational-wave astronomy. We develop an analytical time-domain waveform model for postmerger signals informed by numerical relativity simulations. The model completes effective-one-body waveforms for quasi-circular nonspinning binaries in the kiloHertz regime. We show that a template-based analysis can detect postmerger signals with a minimal signal-to-noise ratios (SNR) of 8, corresponding to GW170817-like events for third-generation interferometers. Using Bayesian model selection and the complete inspiral-merger-postmerger waveform model it is possible to infer whether the merger outcome is a prompt collapse to a black hole or a remnant star. In the latter case, the radius of the maximum mass (most compact) nonrotating neutron star can be determined to kilometer precision. We demonstrate the feasibility of inferring the stiffness of the equation of state at extreme densities using the quasiuniversal relations deduced from numerical-relativity simulations.

Simulating Binary Neutron Stars with Hybrid Equation of States: Gravitational Waves, Electromagnetic Signatures and Challenges for Numerical Relativity

The gravitational wave and electromagnetic signatures connected to the merger of two neutron stars allow us to test the nature of matter at supranuclear densities. Since the Equation of State governing the interior of neutron stars is only loosely constrained, there is even the possibility that strange quark matter exists inside the core of neutron stars. We investigate how strange quark matter cores affect the binary neutron star coalescence by performing numerical relativity simulations. Interestingly, the strong phase transition can cause a reduction of the convergence order of the numerical schemes to first order if the numerical resolution is not high enough. Therefore, an additional challenge is added in producing high-quality gravitational wave templates for Equation of States with a strong phase transition. Focusing on one particular configuration of an equal mass configuration consistent with GW170817, we compute and discuss the associated gravitational wave signal and some of the electromagnetic counterparts connected to the merger of the two stars. We find that existing waveform approximants employed for the analysis of GW170817 allow describing this kind of systems within the numerical uncertainties, which, however, are several times larger than for pure hadronic Equation of States, which means that even higher resolutions have been employed for an accurate gravitational wave model comparison. We also show that for the chosen Equation of State, quasi-universal relations describing the gravitational wave emission after the moment of merger seem to hold and that the electromagnetic signatures connected to our chosen setup would not be bright enough to explain the kilonova associated to GW170817.

Effective field theory with genuine many‐body forces and tidal effects on neutron stars

Neutron stars are characterized by their masses, radii, spinning speeds (associated with their moments of inertia), and degree of deformation. Under the action of an external static tidal quadrupole field ℰij, the neutron star undergoes a deformation measured in terms of the ratio between the quadrupole moment induced in the star and the field ℰij, which defines, in turn, the tidal deformability parameter. In this contribution, we combine our recent predictions for the neutron stars' tidal parameter with recent gravitational wave observations of merging the binary system GW170817 with quasiuniversal relations between the maximum mass of rotating and nonrotating neutron stars. Our results indicate that predictions of the tidal parameter represent a useful constraint of the Equation of State (EoS) of neutron stars.

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

We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realistic, and with none of the sources located within 100Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies, we utilize analytical fits to postmerger numerical relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasiuniversal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300Mpc, so long as the equation of state is not too soft or the binaries are not too heavy. We also give error estimates for the Einstein Telescope.

Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars

Abstract Combining the GW observations of merging systems of binary neutron stars and quasi-universal relations, we set constraints on the maximum mass that can be attained by nonrotating stellar models of neutron stars. More specifically, exploiting the recent observation of the GW event GW170817 and drawing from basic arguments on kilonova modeling of GRB 170817A together with the quasi-universal relation between the maximum mass of nonrotating stellar models and the maximum mass supported through uniform rotation , we set limits for the maximum mass to be , where the lower limit in this range comes from pulsar observations. Our estimate, which follows a very simple line of arguments and does not rely on the modeling of the electromagnetic signal in terms of numerical simulations, can be further refined as new detections become available. We briefly discuss the impact that our conclusions have on the equation of state of nuclear matter.

Quasiuniversal Properties of Neutron Star Mergers

Binary neutron star mergers are studied using nonlinear $3+1$ numerical relativity simulations and the analytical effective-one-body model. The effective-one-body model predicts quasiuniversal relations between the mass-rescaled gravitational wave frequency and the binding energy at the moment of merger and certain dimensionless binary tidal coupling constants depending on the stars' Love numbers, compactnesses, and the binary mass ratio. These relations are quasiuniversal in the sense that, for a given value of the tidal coupling constant, they depend significantly neither on the equation of state nor on the mass ratio, though they do depend on stars spins. The spin dependence is approximately linear for small spins aligned with the orbital angular momentum. The quasiuniversality is a property of the conservative dynamics; nontrivial relations emerge as the binary interaction becomes tidally dominated. This analytical prediction is qualitatively consistent with new, multiorbit numerical relativity results for the relevant case of equal-mass irrotational binaries. Universal relations are, thus, expected to characterize neutron star mergers dynamics. In the context of gravitational wave astronomy, these universal relations may be used to constrain the neutron star equation of state using waveforms that model the merger accurately.

Regime theories in gravel‐bed rivers: models, controlling variables, and applications in disturbed Italian rivers

AbstractDownstream hydraulic geometry relationships describe the shape of alluvial channels in terms of bankfull width, flow depth, flow velocity, and channel slope. Recent investigations have stressed the difference in spatial scales associated with these variables and thus the time span required for their adjustment after a disturbance. The aim of this study is to explore the consequences in regime models considering the hypothesis that while channel width and depth adjust quickly to changes in water and sediment supply, reach slope requires a longer time span. Three theoretical models were applied. One model incorporates an extremal hypothesis (Millar RG. 2005. Theoretical regime equations for mobile gravel‐bed rivers with stable banks. Geomorphology 64: 207–220), and the other two are fully physically based (Ikeda S, Parker G, Kimura Y. 1988. Stable width and depth of straight gravel rivers with heterogeneous bed materials. Water Resources Research 24: 713–722; Parker G, Wilcock PR, Paola C, Dietrich W, Pitlick J. 2007. Physical basis for quasi universal relations describing bankfull hydraulic geometry of single‐thread gravel‐bed rivers. Journal of Geophysical Research 112, DOI: 10.1029/2006JF000549). In order to evaluate the performance of models introducing the slope as an independent variable, we propose two modifications to previous models.The performance of regime models was tested against published data from 142 river reaches and new hydraulic geometry data from gravel‐bed rivers in Patagonia (Argentina) and north‐eastern Italy.Models that assume slope as a control (Ikeda et al., 1988; or Millar, 2005) predict channel depth and width reasonably well. Parker et al.'s (2007) model improved predictions because it filters the scatter in slope data with a relation slope–discharge. The extremal hypothesis model of Millar (2005) predicts comparably to the other physically based models.Millar's model was chosen to describe the recent changes in the Piave and Brenta rivers due to human intervention – mainly in‐channel gravel mining. The change in sediment supply and recovery was estimated for these rivers. This study supports the interpretation that sediment supply is the key factor guiding morphological changes in these rivers. Copyright © 2013 John Wiley & Sons, Ltd.