It is well known that the equation of state (EoS) of compact objects like neutron and quark stars is not determined despite there are several sophisticated models to describe it. From the electromagnetic observations, summarized in \cite{Lattimer01}, and the recent observation of gravitational waves from binary neutron star inspiral GW170817 \cite{Abbott2017_etal} and GW190425 \cite{Abbott2019}, it is possible to make an estimation of the range of masses and so constraint the mass of the neutron and quark stars, determining not only the best approximation for the EoS, but which kind of stars we would be observing. In this paper we explore several configurations of neutron stars assuming a simple polytropic equation of state, using a single layer model without crust. In particular, when the EoS depends on the mass rest density, $p=K ρ_{0}^Γ$, and when it depends on the energy density $p=K ρ^Γ$, considerable differences in the mass-radius relationships are found. On the other hand, we also explore quark stars models using the MIT bag EoS for different values of the vacuum energy density $B$.
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 prov…
Bayesian hierarchical inference of phenomenological parameterized neutron star equations of state (EoS) from multiple gravitational wave observations of binary neutron star mergers is of fundamental importance in improving our understanding of neutron star structure, the general properties of matter at supra nuclear densities and the strong nuclear force. However, such an analysis is computationally costly as it is unable to re-use single-event EoS agnostic parameter estimation runs that are carried out regardless for generating gravitational wave transient catalogs. With the number of events …
Binary neutron star mergers provide a unique probe of the dense-matter equation of state (EoS) across a wide range of parameter space, from the zero-temperature EoS during the inspiral to the high-temperature EoS following the merger. In this paper, we implement a new model for calculating parametrized finite-temperature EoS effects into numerical relativity simulations. This "M* model" is based on a two-parameter approximation of the particle effective mass and includes the leading-order effects of degeneracy in the thermal pressure and energy. We test our numerical implementation by performi…
The merger dynamics of a black hole-neutron star (BHNS) binary is influenced by the neutron star equation of state (EoS) through the latter's effect on the neutron star's radius and on the character of the mass transfer onto the black hole. We study these effects by simulating a number of BHNS binaries in full general relativity using a mixed pseudospectral/finite difference code. We consider several models of the neutron star matter EoS, including Gamma=2 and Gamma=2.75 polytropes and the nuclear-theory based Shen EoS. For models using the Shen EoS, we consider two limits for the evolution of…
Recently, an instability due to the nonlinear coupling of p-modes to g-modes in tidally deformed neutron stars in coalescing binaries has been studied in some detail. The result is significant because it could influence the inspiral and leave an imprint on the gravitational wave signal that depends on the neutron star equation of state (EOS). Because of its potential importance, the details of the instability should be further elucidated and its sensitivity to the EOS should be investigated. To this end, we carry out a numerical analysis with six representative EOSs for both static and non-sta…
We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), …
Viscosity driven bar mode secular instabilities of rapidly rotating neutron stars are studied using LORENE/Nrotstar code. These instabilities set a more rigorous limit to the rotation frequency of neutron star than the Kepler frequency/mass shedding limit. The procedure employed in the code comprises of perturbing an axisymmetric and stationary configuration of a neutron star and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. Symmetry breaking point was found out for Polytropic as well as 10 realistic Equations of states (EOS) from the CompOSE dat…
We show how observations of gravitational waves from binary neutron star (BNS) mergers over the next few years can be combined with insights from nuclear physics to obtain useful constraints on the equation of state (EoS) of dense matter, in particular, constraining the neutron-matter EoS to within 20% between one and two times the nuclear saturation density $n_0\approx 0.16\ {\text{fm}^{-3}}$. Using Fisher information methods, we combine observational constraints from simulated BNS merger events drawn from various population models with independent measurements of the neutron star radii expec…
Rotation causes an increase in a neutron star's mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOS to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for n…
The first binary neutron star merger has already been detected in gravitational waves. The signal was accompanied by an electromagnetic counterpart including a kilonova component powered by the decay of radioactive nuclei, as well as a short $γ$-ray burst. In order to understand the radioactively-powered signal, it is necessary to simulate the outflows and their nucleosynthesis from the post-merger disk. Simulating the disk and predicting the composition of the outflows requires general relativistic magnetohydrodynamical (GRMHD) simulations that include a realistic, finite-temperature equation…
The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter Lambda, describing its deformability, can be extracted from the late inspiral, m…
Latest general relativistic simulations for merger of binary neutron stars with realistic equations of state (EOSs) show that a hypermassive neutron star of an ellipsoidal figure is formed after the merger if the total mass is smaller than a threshold value which depends on the EOSs. The effective amplitude of quasiperiodic gravitational waves from such hypermassive neutron stars is $\sim 6$--$7 \times 10^{-21}$ at a distance of 50 Mpc, which may be large enough for detection by advanced laser interferometric gravitational wave detectors although the frequency is high $\sim 3$ kHz. We point ou…
Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations, to derive joint constraints on the equation of state (EoS) of matter at supranuclear density. In our analysis we use two sets of data: (i) the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo; (ii) the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass X-ray binaries. Using two different parametrizations of the equation of state, we compute the …
Gravitational waves from binary neutron star (BNS) mergers can constrain nuclear matter models predicting the neutron star's equation of state (EOS). Matter effects on the inspiral-merger signal are encoded in the multipolar tidal polarizability parameters, whose leading order combination is sufficient to capture to high accuracy the key features of the merger waveform (e.g.~the merger frequency). Similar EOS-insensitive relations exist for the post-merger signal and can be used to model the emission from the remnant. Several works suggested that the appearance of new degrees of freedom or pha…
Neutron stars (NSs) are excellent natural laboratories to constrain gravity on strong field regime and nuclear matter in extreme conditions. Motivated by the recent discovery of a compact object with $2.59^{+0.08}_{-0.09} M_\odot$ in the binary merger GW190814, if this object was a NS, it serves as a strong constraint on the NS equation of state (EoS), ruling out several soft EoSs favored by GW170817 event. In this work, we revisit the question of the maximum mass of NSs considering a chameleon screening (thin-shell effect) on the NS mass-radius relation, where the microscopic physics inside t…
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 nuclear-physics based EoS which differ in particle content and ab-initio microscopic calculations. While the constraining power of GW170817 is limited, we show that even twenty coalescences detected by LIGO-Virgo at design sensitivity are …
In recent years, a lot of work was done that has revealed some very interesting properties of neutron stars. One can relate the first few multipole moments of a neutron star, or quantities that can be derived from them, with relations that are independent of the equation of state (EoS). This is a very significant result that has great implications for the description of neutron stars and in particular for the description of the spacetime around them. Additionally, it was recently shown that there is a four parameter analytic spacetime, known as the two-soliton spacetime, which can accurately c…
We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses…
Exploiting a very large library of physically plausible equations of state (EOSs) containing more than $10^{7}$ members and yielding more than $10^{9}$ stellar models, we conduct a survey of the impact that a neutron-star radius measurement via electromagnetic observations can have on the EOS of nuclear matter. Such measurements are soon to be expected from the ongoing \textit{Neutron Star Interior Composition Explorer} mission and will complement the constraints on the EOS from gravitational-wave detections. Thanks to the large statistical range of our EOS library, we can obtain a first quant…
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We fi…
The frequencies and damping times of neutron star (and quark star) oscillations have been computed using the most recent equations of state available in the literature. We find that some of the empirical relations that connect the frequencies and damping times of the modes to the mass and radius of the star, and that were previously derived in the literature need to be modified.
Observations of gravitational-wave signals from binary neutron-star mergers, like GW170817, can be used to constrain the neutron-star equation of state (EoS). One method involves modeling the EoS and measuring the model parameters through Bayesian inference. A previous study has demonstrated the effectiveness of using a phenomenologically parameterized piecewise polytrope to extract constraining information from a simulated population of binary neutron-star mergers. Despite its advantages compared to more traditional methods of measuring the tidal deformability of neutron stars, notable defici…
It has been conjectured that in head-on collisions of neutron stars (NSs), the merged object would not collapse promptly even if the total mass is higher than the maximum stable mass of a cold NS. In this paper, we show that the reverse is true: even if the total mass is {\it less} than the maximum stable mass, the merged object can collapse promptly. We demonstrate this for the case of NSs with a realistic equation of state (the Lattimer-Swesty EOS) in head-on {\it and} near head-on collisions. We propose a ``Prompt Collapse Conjecture'' for a generic NS EOS for head on and near head-on colli…
Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $\sim 2 ~ {\rm M}_\odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest …
Gravitational-wave observations of inspiralling binary neutron star systems can be used to measure the neutron-star equation of state (EOS) through the tidally induced shift in the waveform phase that depends on the tidal deformability parameter $λ$. Previous work has shown that $λ$, a function of the neutron-star EOS and mass, is measurable by Advanced LIGO for a single event when including tidal information up to the merger frequency. In this work, we describe a method for stacking measurements of $λ$ from multiple inspiral events to measure the EOS. We use Markov chain Monte Carlo simulatio…
The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imp…
Neutron star crust, formed via accretion of matter from a companion in a low-mass X-ray binary (LMXB), has an equation of state (EOS) stiffer than that of catalyzed matter. At a given neutron star mass, M, the radius of a star with an accreted crust is therefore larger, by DR(M), than for usually considered star built of catalyzed matter. Using a compressible liquid drop model of nuclei, we calculate, within the one-component plasma approximation, the EOSs corresponding to different nuclear compositions of ashes of X-ray bursts in LMXB. These EOSs are then applied for studying the effect of di…
We contribute a publicly available set of tables and code to provide Equations of State (EoS) for matter at neutron star densities. Our EoSes are constrained only by input from hadron physics and fundamental principles, without feedback from neutron star observations, and so without relying on General Relativity. They can therefore be used to test General Relativity itself, as well as modified gravity theories, with neutron star observables, without logical circularity. We have adapted state of the art results from NN chiral potentials for the low--density limit, pQCD results for the asymptoti…
We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate …
The effect of the hyperon softening of the equation of state (EOS) of dense matter on the spin evolution of isolated neutron stars is studied for a broad set of hyperonic EOSs. We use a multidomain 2-D code based on a spectral method, and show how important the precision of solving the equations of stationary motion is for the stability analysis. For some EOSs, the hyperon softening leads to spin-up by the angular momentum loss, in the form of the back bending phenomenon, for a rather broad range of stellar baryon mass. We show that large segments of the evolutionary tracks exhibiting the back…
We present calculations of quasiequilibrium sequences of irrotational binary neutron stars based on realistic equations of state (EOS) for the whole neutron star interior. Three realistic nuclear EOSs of various softness and based on different microscopic models have been joined with a recent realistic EOS of the crust, giving in this way three different EOSs of neutron-star interior. Computations of quasiequilibrium sequences are performed within the Isenberg-Wilson-Mathews approximation to general relativity. For all evolutionary sequences, the innermost stable circular orbit (ISCO) is found…
Fully general-relativistic binary-neutron-star (BNS) merger simulations with quark-hadron crossover (QHC) equations of state (EOSs) are studied for the first time. In contrast to EOSs with purely hadronic matter or with a first-order quark-hadron phase transition (1PT), in the transition region QHC EOSs show a peak in sound speed, and thus a stiffening. We study the effects of such stiffening in the merger and post-merger gravitational (GW) signals. Through simulations in the binary-mass range $2.5 < M/M_{\odot} < 2.75$, characteristic differences due to different EOSs appear in the frequency …
We found type I critical collapses of compact objects modeled by a polytropic equation of state (EOS) with polytropic index $Γ=2$ without the ultra-relativistic assumption. The object is formed in head-on collisions of neutron stars. Further we showed that the critical collapse can occur due to a change of the EOS, without fine tuning of initial data. This opens the possibility that a neutron star like compact object, not just those formed in a collision, may undergo a critical collapse in processes which slowly change the EOS, such as cooling.
We simulate the merger of binary neutron stars and analyze the spectral properties of their gravitational waveforms. For the stars we construct hybrid equations of state (EoSs) with a standard nuclear matter EoS at low densities, transitioning to a state-of-the-art holographic EoS in the otherwise intractable high density regime. Depending on the transition density the characteristic frequencies in the spectrum produced from the hybrid EoSs are shifted to significantly lower values as compared to the pure nuclear matter EoS. The highest rest-mass density reached outside a possible black hole h…
We develop a method for implementing a proposal on utilizing knowledge of neutron star (NS) equation of state (EoS) for inferring the Hubble constant from a population of binary neutron star (BNS) mergers. This method is useful in exploiting BNSs as standard sirens when their redshifts are not available. Gravitational wave (GW) signals from compact object binaries provide a direct measurement of their luminosity distances, but not their redshifts. Unlike in the past, here we employ a realistic EoS parametrization in a Bayesian framework to simultaneously measure the Hubble constant and refine …
We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M$_\odot$ star criterion. We solve the Sturm-Liouville problem to compute 20 lowest radial oscillation modes and their eigenfunctions for neutron star modelled with eight selected unified EoSs from distinct Skyrme-Hartree Fock, Relativistic Mean-Field and quarkyonic models. We compare the behavior of the computed eigenfrequency for NS modelled with hadronic to that with quarkyonic EoSs while varying central densities. The lowest order, f-mode frequency varies sub…
We perform neutrino radiation-hydrodynamics simulations for the merger of asymmetric binary neutron stars in numerical relativity. Neutron stars are modeled by soft and moderately stiff finite-temperature equations of state (EOS). We find that the properties of the dynamical ejecta such as the total mass, neutron richness profile, and specific entropy profile depend on the mass ratio of the binary systems for a given EOS in a unique manner. For the soft EOS (SFHo), the total ejecta mass depends weakly on the mass ratio, but the average of electron number per baryon ($Y_e$) and specific entropy…
Neutron stars and their mergers provide the highest-density regime in which Einstein's equations in full (with a matter source) can be tested against modified theories of gravity. But doing so requires a priori knowledge of the Equation of State from nuclear and hadron physics, where no contamination from computations of astrophysics observables within General Relativity has been built in. We extend the nEoS uncertainty bands, useful for this very purpose, to finite (but small) temperatures up to 30 MeV, given that the necessary computations in ChPT and in pQCD at already available in the lite…
We introduce a parameterized high-density equation of state (EOS) in order to systematize the study of constraints placed by astrophysical observations on the nature of neutron-star matter. To obtain useful constraints, the number of parameters should be smaller than the number of neutron-star properties that have been measured or will have been measured in the next several years. And the set must be large enough to accurately approximate the large set of candidate EOSs. We find that a parameterized EOS based on piecewise polytropes with 3 free parameters matches to about 4% rms error an exten…
