The conformal flatness approximation to the Einstein equations has been successfully used in many astrophysical applications such as initial data constructions and dynamical simulations. Although it has been shown that full general relativistic strongly differentially rotating equilibrium models deviate by at most a few percent from their conformally flat counterparts, whether those conformally flat solutions remain stable has not been fully addressed. To further understand the limitations of the conformal flatness approximation, in this work, we construct spatially-conformally-flat hot hypermassive neutron stars with post-merger-like rotation laws, and perform conformally flat evolutions and analysis over dynamical timescales. We find that enforcing conformally-flat spacetime could change the equilibrium of quasi-toroidal models with high angular momentum for $J \gtrsim 9 ~G M_{\odot}^2 / c$ compared to fully general relativistic cases. In contrast, all the quasi-spherical models considered in this work remain stable even with high angular momentum $J=9~G M_{\odot}^2 / c$. Our investigation suggests that the quasi-spherical models are suitable initial data for long-lived hypermassive neutron star modeling in conformally flat spacetime.
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.
The stability properties of rotating relativistic stars against prompt gravitational collapse to a black hole are rather well understood for uniformly rotating models. This is not the case for differentially rotating neutron stars, which are expected to be produced in catastrophic events such as the merger of binary system of neutron stars or the collapse of a massive stellar core. We consider sequences of differentially rotating equilibrium models using the $j$-constant law and by combining them with their dynamical evolution, we show that a sufficient stability criterion for differentially r…
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 …
Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events, according to both numerical simulations and the multi-messenger observation of GW170817. The lifetime and evolution of such a differentially rotating star, is tightly related to the observations in the post-merger phase. Various studies on the maximum mass of differentially rotating neutron stars have been done in the past, most of which assume the so-called $j$-const law as the rotation profile inside the star and consider only neutron star equations of state. In this paper, we ex…
A binary neutron star merger produces a rapidly and differentially rotating compact remnant whose lifespan heavily affects the electromagnetic and gravitational emissions. Its stability depends on both the equation of state (EOS) and the rotation law and it is usually investigated through numerical simulations. Nevertheless, by means of a sufficient criterion for secular instability, equilibrium sequences can be used as a computationally inexpensive way to estimate the onset of dynamical instability, which, in general, is close to the secular one. This method works well for uniform rotation an…
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…
We investigate the nature of low T/W dynamical instabilities in various ranges of the stiffness of the equation of state in differentially rotating stars. Here T is the rotational kinetic energy, while W the gravitational binding energy. We analyze these instabilities in both a linear perturbation analysis and a three-dimensional hydrodynamical simulation. An unstable normal mode of a differentially rotating star is detected by solving an eigenvalue problem along the equatorial plane of the star. The physical mechanism of low T/W dynamical instabilities is also qualitatively confirmed by a sca…
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…
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 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…
We determine the accuracy of the conformal flatness (IWM-CFC) approximation for the case of single, but strongly differentially rotating relativistic stars. We find that for the fastest rotating and most relativistic polytropic models, the deviation from full general relativity is below 5% for integrated quantities and below 10% for local quantities, such as the angular velocity. Furthermore, we study the deviation of the IWM-CFC approximation from full general relativity by evaluating and comparing different error indicators. We find that for the models that are not near the maximum mass, a s…
We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum J/M^2, where J and M are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with J/M^2<1, i.e., "sub-Kerr" models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves rese…
We present the first fully relativistic numerical calculations of differentially rotating Strange Quark Stars models for broad ranges of the maximum density and of the degree of differential rotation. Our simulations are performed with the very accurate and stable multi-domain spectral code FlatStar and use the MIT Bag model for describing strange quark matter. Our calculations based on a thorough exploration of the solution space show that the maximum mass of strange stars depends on both the degree of differential rotation and a type of solution, similarly to neutron stars described by a pol…
(Abridged.) The mean-square current quadrupole moment associated with vorticity fluctuations in high-Reynolds-number turbulence in a differentially rotating neutron star is calculated analytically, as are the amplitude and decoherence time of the resulting, stochastic gravitational wave signal. The calculation resolves the subtle question of whether the signal is dominated by the smallest or largest turbulent eddies: for the Kolmogorov-like power spectrum observed in superfluid spherical Couette simulations, the wave strain is controlled by the largest eddies, and the decoherence time approxim…
We study the main astrophysical properties of differentially rotating neutron stars described as stationary and axisymmetric configurations of a moderately stiff $Γ=2$ polytropic fluid. The high level of accuracy and of stability of our relativistic multidomain pseudo-spectral code enables us to explore the whole solution space for broad ranges of the degree of differential rotation, but also of the stellar density and oblateness. Staying within an astrophysicaly motivated range of rotation profiles, we investigate the characteristics of neutron stars with maximal mass for all types of familie…
Outcomes of numerical relativity simulations of massive core collapses or binary neutron star mergers with moderate masses suggest formations of rapidly and differentially rotating neutron stars. Subsequent fall back accretion may also amplify the degree of differential rotations. We propose new formulations for modeling differential rotations of those compact stars, and present selected solutions of differentially rotating, stationary, and axisymmetric compact stars in equilibriums. For the cases when rotating stars reach break-up velocities, the maximum masses of such rotating models are obt…
We present equilibrium sequences of rotating relativistic stars, constructed with a new rotation law that was proposed by Uryu et al. (2017). We choose rotational parameters motivated by simulations of binary neutron star merger remnants, but otherwise adopt a cold, relativistic N=1 polytropic EOS, in order to perform a detailed comparison to published equilibrium sequences that used the Komatsu, Eriguchi and Hachisu (1989) rotation law. We find a small influence of the choice of rotation law on the mass of the equilibrium models and a somewhat larger influence on their radius. The versatility…
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…
Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the "low-T/|W| instability"), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magneti…
Besides being among the most promising sources of gravitational waves, merging neutron star binaries also represent a leading scenario to explain the phenomenology of short gamma-ray bursts (SGRBs). Recent observations have revealed a large subclass of SGRBs with roughly constant luminosity in their X-ray afterglows, lasting $10\!-\!10^4$ s. These features are generally taken as evidence of a long-lived central engine powered by the magnetic spin-down of a uniformly rotating, magnetized object. We propose a different scenario in which the central engine powering the X-ray emission is a differe…
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…
Low-$T/|W|$ instabilities in differentially rotating neutron stars resembling merger remnants
Heidelberger Institut für Theoretische Studien（海德堡理论研究所）；GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Department of Physics, University of Trieste（的里雅斯特大学物理系）；INFN, Sezione di Trieste（意大利国家核物理研究院的里雅斯特分部）；Helmholtz Research Academy Hesse for FAIR (HFHF)（黑森FAIR亥姆霍兹研究学院）；Department of Physics, Aristotle University of Thessaloniki（萨洛尼卡亚里士多德大学物理系）
The observed sub-class of "superluminous" Type Ia supernovae lacks a convincing theoretical explanation. If the emission of such objects were powered exclusively by radioactive decay of 56Ni formed in the explosion, a progenitor mass close to or even above the Chandrasekhar limit for a non-rotating white dwarf star would be required. Masses significantly exceeding this limit can be supported by differential rotation. We, therefore, explore explosions and predict observables for various scenarios resulting from differentially rotating carbon-oxygen white dwarfs close to their respective limit o…
We propose a mechanism to produce fluctuations in the viscosity parameter ($α$) in differetially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background $α$ was treated as a passive/slave variable in the sense of dynamical system theory. We demonstrate a complete physical picture of growth, saturation and final degradation of the perturbation as a result of the nonlinear nature of coupled system of equations. The strong dependence of this fluctuation on the radial location in the accretion disc and the base angular momentum dist…
We introduce our approaches, in particular the modifications of the primitive recovery procedure, to handle bare quark stars in numerical relativity simulations. Reliability and convergence of our implementation are demonstrated by evolving two triaxially rotating quark star models with different mass as well as a differentially rotating quark star model which has sufficiently large kinetic energy to be dynamically unstable. These simulations allow us to verify that our method is capable of resolving the evolution of the discontinuous surface of quark stars and possible mass ejection from them…
A global mode is shown to be unstable to non-axisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic field where local standard MRI becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global do…
We find a class of twisted and differentially rotating neutron star magnetospheres that do not have a light cylinder, generate no wind and thus do not spin-down. The magnetosphere is composed of embedded differentially rotating flux surfaces, with the angular velocity decreasing as $Ω\propto 1/r$ (equivalently, becoming smaller at the foot-points closer to the axis of rotation). For each given North-South self-similar twist profile there is a set of self-similar angular velocity profiles (limited from above) with a "smooth", dipolar-like magnetic field structure extending to infinity. For spin…
The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of $10^{15-16}$G. How such a strong magnetic field can originate during the formation of a neutron star is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical c…
Hydrodynamic turbulence driven by crust-core differential rotation imposes a fundamental noise floor on gravitational wave observations of neutron stars. The gravitational wave emission peaks at the Kolmogorov decoherence frequency which, for reasonable values of the crust-core shear, ΔΩ, occurs near the most sensitive part of the frequency band for ground-based, long-baseline interferometers. We calculate the energy density spectrum of the stochastic gravitational wave background from a cosmological population of turbulent neutron stars generalising previous calculations for individual source…
We investigate the nature of so-called low $T/W$ dynamical instability in a differentially rotating star by focusing on the role played by the corotation radius of the unstable oscillation modes. An one dimensional model of linear perturbation, which neglects dependence of variables on the coordinate along the rotational axis of the star, is solved to obtain stable and unstable eigenmodes. A linear eigenmode having a corotation radius, at which azimuthal pattern speed of the mode coincides with the stellar angular velocity, is categorized to either a complex (growing or damping) mode or a pure…
We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code and those computed by the full theory. Entire sequences of the low order counter-rotating f-modes are …
Most viable models of Type Ia supernovae (SN~Ia) require the thermonuclear explosion of a carbon/oxygen white dwarf that has evolved in a binary system. Rotation could be an important aspect of any model for SN~Ia, whether single or double degenerate, with the white dwarf mass at, below, or above the Chandrasekhar limit. {\sl Differential rotation} is specifically invoked in attempts to account for the apparent excess mass in the super--Chandrasekhar events. Some earlier work has suggested that only uniform rotation is consistent with the expected mechanisms of angular momentum transport in wh…
Asteroseismology has revealed small core-to-surface rotation contrasts in stars in the whole HR diagram. This is the signature of strong transport of angular momentum (AM) in stellar interiors. One of the plausible candidates to efficiently carry AM is magnetic fields with various topologies that could be present in stellar radiative zones. Among them, strong axisymmetric azimuthal magnetic fields have received a lot of interest. Indeed, if they are subject to the so-called Tayler instability, the accompanying triggered Maxwell stresses can transport AM efficiently. In addition, the electromot…
