arXiv subjects

S. Bonazzola

Publications and source records attributed to S. Bonazzola.

At least 19 recordsLinked to original sources

arXiv2020

General solution for the vacuum electromagnetic field in the surroundings of a rotating star

Aims. Many recent observations of pulsars and magnetars can be interpreted in terms of neutron stars (NS) with multipole electromagnetic fields. As a first approximation, we investigate the multipole magnetic and electric fields in the environment of a rotating star when this environment is deprived of plasma. Methods. We compute a multipole expansion of the electromagnetic field in vacuum for a given magnetic field on the conducting surface of the rotating star. Then, we consider a few consequences of multipole fields of pulsars. Results. We provide an explicit form of the solution. For each spherical harmonic of the magnetic field, the expansion contains a finite number of terms. A multipole magnetic field can provide an explanation for the stable sub-structures of pulses, and they offer a solution to the problem of current closure in pulsar magnetospheres. Conclusions. This computation generalises the widely used model of a rotating star in vacuum with a dipole field. It can be especially useful as a first approximation to the electromagnetic environment of a compact star, for instance a neutron star, with an arbitrarily magnetic field.

astro-ph.HE↗

arXiv2009

Luminosity of a quark star undergoing torsional oscillations and the problem of gamma ray bursts

We discuss whether the winding-up of the magnetic field by differential rotation in a new-born quark star can produce a sufficiently-high, energy, emission rate of sufficiently long duration to explain long gamma-ray bursts. In the context of magnetohydrodynamics, we study the torsional oscillations and energy extraction from a new-born, hot, differentially rotating quark star. The new-born compact star is a rapid rotator that produces a relativistic, leptonic wind. The star's torsional oscillation modulates this wind emission considerably when it is odd and of sufficient amplitude, which is relatively easy to reach. Odd oscillations may occur just after the formation of a quark star. Other asymmetries can cause similar effects. The buoyancy of wound-up magnetic fields is inhibited, or its effects are limited, by a variety of different mechanisms. Direct electromagnetic emission by the torsional oscillation in either an outside vacuum or the leptonic wind surrounding the compact object is found to be insignificant. In contrast, the twist given to the outer magnetic field by an odd torsional oscillation is generally sufficient to open the star's magnetosphere. The Poynting emission of the star in its leptonic environment is then radiated from all of its surface and is enhanced considerably during these open episodes, tapping at the bulk rotational energy of the star. This results in intense energy shedding in the first tens of minutes after the collapse of magnetized quark stars with an initial poloidal field of order of 10**14 Gauss, sufficient to explain long gamma-ray bursts.

astro-ph↗

arXiv2007

MHD of rotating compact stars with spectral methods: description of the algorithm and tests

A flexible spectral code for the study of general relativistic magnetohydrodynamics is presented. Aiming at investigating the physics of slowly rotating magnetized compact stars, this new code makes use of various physically motivated approximations. Among them, the relativistic anelastic approximation is a key ingredient of the current version of the code. In this article, we mainly outline the method, putting emphasis on algorithmic techniques that enable to benefit as much as possible of the non-dissipative character of spectral methods, showing also a potential astrophysical application and providing a few illustrative tests.

gr-qc↗

arXiv2005

Inertial modes in stratified rotating neutron stars : An evolutionary description

With (non-barotropic) equations of state valid even when the neutron, proton and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes are affected by non-barotropicity of the nuclear matter. In our study, the deviation with respect to barotropicity results from the frozen composition of non-superfluid matter composed of neutrons, protons and electrons, when beta equilibrium is broken by millisecond oscillations. We show that already for moderatly fast rotating stars the increasing coupling between polar and axial modes makes those two cases less different than for very slowly rotating stars. In addition, as we directly solve the Euler equations, without coupling only a few number of spherical harmonics, we always found, for the models that we use, a discrete spectrum for the $l = m = 2$ inertial mode. Finally, we find that, for non-barotropic stars, the frequency of this mode, which is our main focus, decreases in a non-negligible way, whereas the time dependence of the energy transfer between polar and axial modes is substantially different due to the existence of low-frequencies gravity modes.

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arXiv2004

A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates

We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial hypersurfaces t=const, which corresponds to the asymptotic structure of the physical 3-metric induced by the spacetime metric. Thanks to the joint use of Dirac gauge, maximal slicing and spherical components of tensor fields, the ten Einstein equations are reduced to a system of five quasi-linear elliptic equations (including the Hamiltonian and momentum constraints) coupled to two quasi-linear scalar wave equations. The remaining three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows a direct computation of the spherical components of the conformal metric from the two scalar potentials which obey the wave equations. We present some numerical evolution of 3-D gravitational wave spacetimes which demonstrates the stability of the proposed scheme.

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arXiv2002

Inertial modes in slowly rotating stars : an evolutionary description

We present a new hydro code based on spectral methods using spherical coordinates. The first version of this code aims at studying time evolution of inertial modes in slowly rotating neutron stars. In this article, we introduce the anelastic approximation, developed in atmospheric physics, using the mass conservation equation to discard acoustic waves. We describe our algorithms and some tests of the linear version of the code, and also some preliminary linear results. We show, in the Newtonian framework with differentially rotating background, as in the relativistic case with the strong Cowling approximation, that the main part of the velocity quickly concentrates near the equator of the star. Thus, our time evolution approach gives results analogous to those obtained by Karino {\it et al.} \cite{karino01} within a calculation of eigenvectors. Furthermore, in agreement with the work of Lockitch {\it et al.} \cite{lockandf01}, we found that the velocity seems to always get a non-vanishing polar part.

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arXiv2001

Binary black holes in circular orbits. I. A global spacetime approach

We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of general relativity on a (3-dimensional) spacelike hypersurface, our approach deals with the full (4-dimensional) spacetime. This permits a rigorous definition of the orbital angular velocity. Neglecting the gravitational radiation reaction, we assume that the black holes move on closed circular orbits, which amounts to endowing the spacetime with a helical Killing vector. We discuss the choice of the spacetime manifold, the desired properties of the spacetime metric, as well as the choice of the rotation state for the black holes. As a simplifying assumption, the space 3-metric is approximated by a conformally flat one. The problem is then reduced to solving five of the ten Einstein equations, which are derived here, as well as the boundary conditions on the black hole surfaces and at spatial infinity. We exhibit the remaining five Einstein equations and propose to use them to evaluate the error induced by the conformal flatness approximation. The orbital angular velocity of the system is computed through a requirement which reduces to the classical virial theorem at the Newtonian limit.

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arXiv2001

A multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $Δ\vec{N} + λ\vec{\nabla}(\vec{\nabla}\cdot \vec{N}) = \vec{S}$ with $λ\not= -1$. The source can extend in all the Euclidean space ${\bf R}^3$, provided it decays at least as $r^{-3}$. A multi-domain approach is used, along with spherical coordinates $(r,θ,ϕ)$. In each domain, Chebyshev polynomials (in $r$ or $1/r$) and spherical harmonics (in $θ$ and $ϕ$) expansions are used. If the source decays as $r^{-k}$ the error of the numerical solution is shown to decrease at least as $N^{-2(k-2)}$, where $N$ is the number of Chebyshev coefficients. The error is even evanescent, i.e. decreases as $\exp(-N)$, if the source does not contain any spherical harmonics of index $l\geq k -3$ (scalar case) or $l\geq k-5$ (vectorial case).

gr-qc↗

arXiv2000

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests

We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with gamma=2.

gr-qc↗

arXiv1999

Darwin-Riemann problems in general relativity

A review is given of recent results about the computation of irrotational Darwin-Riemann configurations in general relativity. Such configurations are expected to represent fairly well the late stages of inspiralling binary neutron stars.

gr-qc↗

arXiv1999

Fast rotation of strange stars

Exact models of uniformly rotating strange stars, built of self bound quark matter, are calculated within the framework of general relativity. This is made possible thanks to a new numerical technique capable to handle the strong density discontinuity at the surface of these stars. Numerical calculations are done for a simple MIT bag model equation of state of strange quark matter. Evolutionary sequences of models of rotating strange stars at constant baryon mass are calculated. Maximally rotating configurations of strange stars are determined, assuming that the rotation frequency is limited by the mass shedding and the secular instability with respect to axisymmetric perturbations. Exact formulae which give the dependence of the maximum rotation frequency, and of the maximum mass and corresponding radius of rotating configurations, on the value of the bag constant, are obtained. The values of T/W for rapidly rotating massive strange stars are significantly higher than those for ordinary neutron stars. This might indicate particular susceptibility of rapidly rotating strange stars to triaxial instabilities.

astro-ph↗

arXiv1999

Evolutionary sequences of irrotational binary neutron stars

We present results of numerical computations of quasiequilibrium sequences of binary neutron stars with zero vorticity, in the general relativistic framework. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The evolution of the central density of each star is monitored as the orbit shrinks in response to gravitational wave emission. For a compactification ratio M/R=0.14, the central density remains rather constant (with a slight increase, below 0.1%) before decreasing. For a higher compactification ratio M/R=0.17 (i.e. stars closer to the maximum mass configuration), a very small density increase (at most 0.3%) is observed before the decrease. This effect remains within the error induced by the conformally flat approximation. It can be thus concluded that no substantial compression of the stars is found, which would have indicated a tendency to individually collapse to black hole prior to merger. Moreover, no turning point has been found in the binding energy or angular momentum along evolutionary sequences, which may indicate that these systems do not have any innermost stable circular orbit (ISCO).

gr-qc↗

arXiv1998

Numerical models of irrotational binary neutron stars in general relativity

We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.

gr-qc↗

arXiv1998

Spectral methods in general relativistic astrophysics

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.

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arXiv1998

Numerical approach for high precision 3-D relativistic star models

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error reveals to be of the order of $10^{-10}$. This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.

astro-ph↗

arXiv1998

Strategy to detect the gravitational radiation counterpart of gamma-ray bursts

Both observational and theoretical rates of binary neutron star coalescence give low prospects for detection of a single event by the initial LIGO/VIRGO interferometers. However, by utilizing at the best all the a priori information on the expected signal, a positive detection can be achieved. This relies on the hypothesis that $γ$-ray bursts are the electromagnetic signature of neutron star coalescences. The information about the direction of the source can then be used to add in phase the signals from different detectors in order (i) to increase the signal-to-noise ratio and (ii) to make the noise more Gaussian. Besides, the information about the time of arrival can be used to drastically decrease the observation time and thereby the false alarm rate. Moreover the fluence of the $γ$-ray emission gives some information about the amplitude of the gravitational signal. One can then add the signals from $\sim 10^4$ observation boxes ($\sim$ number of $γ$-ray bursts during 10 years) to yield a positive detection. Such a detection, based on the Maximum a Posteriori Probability Criterium, is a minimal one, in the sense that no information on the position and time of the events, nor on any parameter of the model, is collected. The advantage is that this detection requires an improvement of the detector sensitivity by a factor of only $\sim 1.5$ with respect to the initial LIGO/VIRGO interferometers, and that, if positive, it will confirm the $γ$-ray burst model.

astro-ph↗

arXiv1997

Spontaneous symmetry breaking of rapidly rotating stars in general relativity: influence of the 3D-shift vector

An analytical scheme and a numerical method in order to study the effects of general relativity on the viscosity driven secular bar mode instability of rapidly rotating stars are presented. The approach consists in perturbing an axisymmetric and stationary configuration and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. These are obtained by solution of an approximate set of field equations where only the dominant non-axisymmetric terms are taken into account. The progress with respect to our former investigation consists in a higher relativistic order of the non-axisymmetric terms included into the computation, namely the fully three-dimensional treatment of the vector part of the space-time metric tensor as opposed to the scalar part, solely, in the former case. The scheme is applied to rotating stars built on a polytropic equation of state and compared to our previous results. The 3D-vector part turns out to inhibit the symmetry breaking efficiently. Nevertheless, the bar mode instability is still possible for an astrophysically relevant mass of M_ns=1.4 M_sun when a stiff polytropic equation of state with an adiabatic index of gamma=2.5 is employed. Triaxial neutron stars may be efficient emitters of gravitational waves and are thus potentially interesting sources for the forthcoming laser interferometric gravitational wave detectors such as LIGO, VIRGO and GEO600. From a numerical point of view, the solution of the three-dimensional minimal-distortion shift vector equation in spherical coordinates is an important achievement of our code.

gr-qc↗

arXiv1997

A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries

A general relativistic version of the Euler equation for perfect fluid hydrodynamics is applied to a system of two neutron stars orbiting each other. In the quasi-equilibrium phase of the evolution of this system, a first integral of motion can be derived for certain velocity fields of the neutron star fluid including the (academic) case of co-rotation with respect to the orbital motion (synchronized binaries) and the realistic case of counter-rotation with respect to the orbital motion. The velocity field leading to this latter configuration can be computed by solving three-dimensional vector and scalar Poisson equations.

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