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 $10^6$ generic EOSs, we asses 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 modelling of the X-ray emission from the surface of rotating stars.
Kilohertz QPOs can be used as a probe of the inner regions of accretion disks in compact stars and hence also of the properties of the central object. Most models of kHz QPOs involve epicyclic frequencies to explain their origin. We compute the epicyclic frequencies of nearly circular orbits around rotating strange quark stars. The MIT bag model is used to model the equation of state of quark matter and the uniformly rotating stellar configurations are computed in full general relativity. The vertical epicyclic frequency and the related nodal precession rate of inclined orbits are very sensiti…
We report on numerical calculations of orbital and epicyclic frequencies in nearly circular orbits around rotating neutron stars and strange quark stars. The FPS equation of state was used to describe the neutron star structure while the MIT bag model was used to model the equation of state of strange quark stars. The uniformly rotating stellar configurations were computed in full general relativity. We find that the vertical epicyclic frequency is very sensitive to the oblateness of the rotating star. For models of rotating neutron stars of moderate mass, as well as for strange quark star mod…
Neutron stars spinning at moderate rates (~300-600Hz) become oblate in shape and acquire a nonzero quadrupole moment. In this paper, we calculate profiles of atomic features from such neutron stars using a ray-tracing algorithm in the Hartle-Thorne approximation. We show that line profiles acquire cores that are much narrower than the widths expected from pure Doppler effects for a large range of observer inclinations. As a result, the effects of both the oblateness and the quadrupole moments of neutron stars need to be taken into account when aiming to measure neutron star radii from rotation…
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 …
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 Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fi…
We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara (2001). Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding (Shibata et al., 2011) obtained in axisymmetric simulations.
$f(R)$ theories of gravity are one of the most popular alternative explanations for dark energy and therefore studying the possible astrophysical implications of these theories is an important task. In the present paper we make a substantial advance in this direction by considering rapidly rotating neutron stars in $R^2$ gravity. The results are obtained numerically and the method we use is non-perturbative and self-consistent. The neutron star properties, such as mass, radius and moment of inertia, are studied in detail and the results show that rotation magnifies the deviations from general …
The opportunity to study physics at supra-nuclear densities through X-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations determines all of the multipole moments of a neutron star just from the first three (the mass monopole, the current dipole and the mass quadrupole moment) approximately independently of the equation of state. These three-hair relations were found to hold in neutron stars that rotate rigidly, as is the case in old pulsars, but neutron …
Recently it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia $I$, their quadrupole moment $Q$, and their tidal deformation Love number $λ$ (the I-Love-Q relations), independently of the equation of state of the compact object. In the present work a similar, more general, universality is shown to hold true for all rotating neutron stars within General Relativity; the first four multipole moments of the neutron star are related in a way independent of the nuclear matter equation of state we assume. By exploiting this relation, we can…
We investigate the dynamical stability of relativistic, differentially rotating, quasi-toroidal models of neutron stars through hydrodynamical simulations in full general relativity. We find that all quasi-toroidal configurations studied in this work are dynamically unstable against the growth of non-axisymmetric modes. Both one-arm and bar mode instabilities grow during their evolution. We find that very high rest mass configurations collapse to form black holes. Our calculations suggest that configurations whose rest mass is less than the binary neutron star threshold mass for prompt collaps…
We present the field equations governing the equilibrium of rapidly rotating neutron stars in scalar-tensor theories of gravity, as well as representative numerical solutions. The conditions for the presence of a nontrivial scalar field and the deviations from the general relativistic solutions are studied. Two examples of scalar-tensor theories are examined - one case that is equivalent to the Brans-Dicke theory and a second case, that is perturbatively equivalent to Einstein's General Relativity in the weak field regime, but can differ significantly for strong fields. Our numerical results s…
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…
Neutron stars provide an excellent laboratory for physics under the most extreme conditions. Up to now, models of axisymmetric, stationary, differentially rotating neutron stars were constructed under the strong assumption of barotropicity, where a one-to-one relation between all thermodynamic quantities exists. This implies that the specific angular momentum of a matter element depends only on its angular velocity. The physical conditions in the early stages of neutron stars, however, are determined by their violent birth processes, typically a supernova or in some cases the merger of two neu…
We perform the first magnetohydrodynamic simulations in full general relativity of self-consistent rotating neutron stars (NSs) with ultrastrong mixed poloidal and toroidal magnetic fields. The initial uniformly rotating NS models are computed assuming perfect conductivity, stationarity, and axisymmetry. Although the specific geometry of the mixed field configuration can delay or accelerate the development of various instabilities known from analytic perturbative studies, all our models finally succumb to them. Differential rotation is developed spontaneously in the cores of our magnetars whic…
We investigate the Keplerian (mass-shedding) sequence of rotating neutron stars. Twelve different equations of state are used to describe the nuclear structure. We find four fitting relations which connect the rotating frequency, mass and radius of stars in the mass-shedding limit to the mass and radius of stars in the static sequence. We show the breakdown of approximate relation for the Keplerian frequency derived by Lattimer and Prakash [Science, 304, 536, (2004)] and then we present a new, EOS-independent and more accurate relation. This relation fits the Keplerian frequency of rotating ne…
In the present paper we investigate self-consistently slowly rotating neutron and strange stars in R-squared gravity. For this purpose we first derive the equations describing the structure of the slowly rotating compact stars in $f(R)$-gravity and then simultaneously solve the exterior and the interior problem. The structure of the slowly rotating neutron stars is studied for two different hadronic equations of state and a strange matter equation of state. The moment of inertia and its dependence on the stellar mass and the $R$-squared gravity parameter $a$ is also examined in details. We fin…
Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lin…
We study the solution space of general relativistic, axisymmetric, equilibria of differentially rotating neutron stars with realistic, nuclear equations of state. We find that different types of stars, which were identified by earlier works for polytropic equations of state, arise for realistic equations of state, too. Scanning the solution space for the sample of realistic equations of state we treat, we find lower limits on the maximum rest masses supported by cold, differentially rotating stars for each type of stars. We often discover equilibrium configurations that can support more than 2…
Numerical simulations of oscillating and differentially rotating neutron stars
Université de Strasbourg（斯特拉斯堡大学）；CNRS（法国国家科学研究中心）；Observatoire astronomique de Strasbourg（斯特拉斯堡天文台）；Sorbonne Université（索邦大学）；Observatoire de Paris（巴黎天文台）；PSL（巴黎文理研究大学）；LUX, CNRS UMR 8262（LUX，法国国家科学研究中心联合研究实验室8262）
We present the first numerical models of differentially rotating stars in alternative theories of gravity. We chose a particular class of scalar-tensor theories of gravity that is indistinguishable from GR in the weak field regime but can lead to significant deviations when strong fields are considered. We show that the maximum mass that a differentially rotating neutron star can sustain increases significantly for scalarized solutions and such stars can reach larger angular momenta. In addition, the presence of a nontrivial scalar field has the effect of increasing the required axis ratio for…
General-relativistic resistive-magnetohydrodynamics simulations of self-consistent magnetized rotating neutron stars
University of New Hampshire（新罕布什尔大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校超级计算应用国家中心）；Academy of Athens（雅典科学院）；Universitat de Valéncia（瓦伦西亚大学）；Niels Bohr International Academy, Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；The Chinese University of Hong Kong（香港中文大学）；University of the Ryukyus（冲绳大学）
In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by Belvedere et al. (2012, 2014). We demonstrate how to conduct numerical integration of these equations for different central densities ${\it ρ}_c$ and angular velocities $Ω$ and compute the static $M^{stat}$ and rotating $M^{rot}$ masses, polar $R_p$ and equatorial $R_{\rm eq}$ radii, eccentricity $ε$, moment of inertia $I$, angular momentum $J$, as well as t…
This note describes fitting formulae for the gravitational waveforms generated by a rapidly rotating neutron star (e.g., newly-formed in the core collapse of a supernova) as it evolves from an initial axisymmetric configuration toward a triaxial ellipsoid.
Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. While the simultaneously measurements of mass and radius of non-rotating neutron stars may impose constraints on the properties of the dense nuclear matter, the observation and study of maximally-rotating ones, close to the mass-shedding limit, may lead to significantly further constraints. Theoretical predictions allow neutron stars to rotate extremely fast (even more than $2000 \ {\rm Hz}$). However, until this moment, the fastest observed rotating puls…
Using a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions, the dynamics of magnetized, rigidly rotating neutron stars are studied. Beginning with fully consistent initial data constructed with Magstar, part of the Lorene project, we study the dynamics and stability of rotating, magnetized polytropic stars as models of neutron stars. Evolutions suggest that some of these rotating, magnetized stars may be minimally unstable occurring at the threshold of black hole formation.
We present rapidly rotating neutron stars featuring wormholes in their centers. They arise in general relativity in the presence of a ghost scalar field. The nuclear matter is described by a polytropic equation of state, yielding realistic masses and radii for the neutron stars. The wormholes possess small circumferential radii of size up to 3 km. With increasing wormhole size, the masses and radii of the stars decrease, while the domain of existence of these rotating mixed neutron-star-plus-wormhole systems retains the characteristic properties of a rotating neutron star domain. The question …
Employing a simplified version of the Israel-Stewart formalism for general-relativistic shear-viscous hydrodynamics, we perform axisymmetric general-relativistic simulations for a rotating neutron star surrounded by a massive torus, which can be formed from differentially rotating stars. We show that with our choice of a shear-viscous hydrodynamics formalism, the simulations can be stably performed for a long time scale. We also demonstrate that with a possibly high shear-viscous coefficient, not only viscous angular momentum transport works but also an outflow could be driven from a hot envel…
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift an…
We investigate equilibrium configurations of uniformly rotating neutron stars in $R^2$ gravity with axion scalar field for GM1 equation of state (EoS) for nuclear matter. The mass-radius diagram, mass-central energy density are presented for some frequencies in comparison with static stars. We also compute equatorial and polar radii and moment of inertia for stars. For axion field $ϕ$ the coupling in the form $\sim R^2ϕ$ is assumed. Several interesting results follow from our consideration. Maximal possible star mass with given EoS increases due to the contribution of coupling term. We discove…
In the present paper we examine gravitational wave asteroseismology relations for f-modes of rapidly rotating neutron stars. An approach different to the previous studies is employed - first, the moment of inertia is used instead of the stellar radius, and second, the normalization of the oscillation frequencies and damping times is different. It was shown that in the non-rotating case this can lead to a much stronger equation of state independence and our goal is to generalize the static relations to the rapidly rotating case and values of the spherical mode number $l\ge2$. We employ realisti…
We compute the binding energy and angular momentum of a test-particle at the last stable circular orbit (LSO) on the equatorial plane around a general relativistic, rotating neutron star (NS). We present simple, analytic, but accurate formulas for these quantities that fit the numerical results and which can be used in several astrophysical applications. We demonstrate the accuracy of these formulas for three different equations of state (EOS) based on nuclear relativistic mean-field theory models and argue that they should remain still valid for any NS EOS that satisfy current astrophysical c…
Neutron stars are attractive places to look for dark matter because their high densities allow repeated interactions. Weakly interacting massive particles (WIMPs) may scatter efficiently in the core or in the crust of a neutron star. In this paper we focus on WIMP contributions to transport properties, such as shear viscosity or thermal conductivity, because these can be greatly enhanced by long mean free paths. We speculate that WIMPs increase the shear viscosity of neutron star matter and help stabilize r-mode oscillations. These are collective oscillations where the restoring force is the C…
We construct sequences of rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear matter. We analyze the dependence of the physical properties of these neutron stars on the Gauss-Bonnet coupling strength. For a given equation of state we determine the physically relevant domain of rapidly rotating neutron stars, which is delimited by the set of neutron stars rotating at the Kepler limit, the set of neutron stars along the secular instability line, and the set of static neutron stars. As compared to Einstein gravity, the presenc…
In this work we provide a framework that connects the co-rotating and counter rotating $f$-mode frequencies of rotating neutron stars with their stellar structure. The accurate computation of these modes for realistic equations of state has been presented recently and they are here used as input for a Bayesian analysis of the inverse problem. This allows to quantitatively reconstruct basic neutron star parameters, such as the mass, radius, rotation rate or universal scaling parameters. We find that future observations of both $f$-mode frequencies, in combination with a Bayesian analysis, would…
We investigate the effects ultralight bosonic field dark matter may have on the dynamics of unstable differentially-rotating neutron stars prone to the bar-mode instability. To this aim we perform numerical simulations in general relativity of rotating neutron stars accreting an initial spherically symmetric bosonic field cloud, solving the Einstein-(complex, massive) Klein-Gordon-Euler and the Einstein-(complex) Proca-Euler systems. We find that the presence of the bosonic field can critically modify the development of the bar-mode instability of neutron stars, depending on the total mass of …
In this review article, we present the main results from our most recent research concerning the oscillations of fast rotating neutron stars. We derive a set of time evolution equations for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full general relativity, taking into account the contribution of a dynamic spacetime. Using our code, which features high accuracy at comparably low computational expense, we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit. We propose various u…
The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that …
We study the evolution of magnetized and rigidly rotating neutron stars within a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions. The stars are modeled as rotating, magnetized polytropic stars and we examine diverse scenarios to study their dynamics and stability properties. In particular we concentrate on the stability of the stars and possible critical behavior. In addition to their intrinsic physical significance, we use these evolutions as further tests of our implementation which incorporates new developments t…
The neutrino-antineutrino annihilation into electron-positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyze the influence of general rela…
We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the…
The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short $γ$-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modelling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium …
Within the framework of $f(R,T)$ theories of gravity, we investigate the hydrostatic equilibrium of anisotropic neutron stars with a physically relevant equation of state (EoS) for the radial pressure. In particular, we focus on the $f(R,T) = R+ 2βT$ model, where $β$ is a minimal coupling constant. In the slowly rotating approximation, we derive the modified TOV equations and the expression for the relativistic moment of inertia. The main properties of neutron stars, such as radius, mass and moment of inertia, are studied in detail. Our results revel that the main consequence of the $2βT$ term…
