Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.
We review the quest of modeling rapidly rotating stars during the past 40 years and detail the challenges to be taken up by models facing new data from interferometry, seismology, spectroscopy... We then present the progress of the ESTER project aimed at giving a physically self-consistent model for the structure and evolution of rapidly rotating stars.
We present numerical simulations of gravito-inertial waves propagating in radiative zones of rapidly rotating stars. A first model, using the Boussinesq approximation, allows us to study the oscillations of a quasi-incompressible stratified fluid embedded in a rapidly rotating sphere or spherical shell. In a second step, we investigate the case of a Gamma-Doradus star using the anelastic approximation. Some fascinating features of rapidly rotating fluids, such as wave attractors, appear in both cases.
We present raytracing computations for light emitted from the surface of a rapidly-rotating neutron star in order to construct light curves for X-ray pulsars and bursters. These calculations are for realistic models of rapidly-rotating neutron stars which take into account both the correct exterior metric and the oblate shape of the star. We find that the most important effect arising from rotation comes from the oblate shape of the rotating star. We find that approximating a rotating neutron star as a sphere introduces serious errors in fitted values of the star's radius and mass if the rotat…
We present a self-consistent, relativistic model of rapidly rotating neutron stars describing their exterior gravitational field. This is achieved by matching the new solution of Einstein's field equations found by Manko et al. (2000) and the numerical results for the interior of neutron stars with different equations of state calculated by Cook et al. (1994). This matching process gives constraints for the choice of the five parameters of the vacuum solution. Then we investigate some properties of the gravitational field of rapidly rotating neutron stars with these fixed parameters.
The observational data from some black hole candidates suggest the importance of electromagnetic fields in the vicinity of a black hole. Highly magnetized disk accretion may play an importance rule, and large scale magnetic field may be formed above the disk surface. Then, we expect that the nature of the black hole spacetime would be reveiled by magnetic phenomena near the black hole. We will start to investigate the motion of a charged particle which depends on the initial parameter setting in the black hole dipole magnetic field. Specially, we study the spin effects of a rotating black hole…
We calculate the accretion disc temperature profiles, disc luminosities and boundary layer luminosities for rapidly rotating neutron stars considering the full effect of general relativity. We compare the theoretical values of these quantities with their values inferred from EXOSAT data for four low mass X-ray binary sources: XB 1820-30, GX 17+2, GX 9+1 and GX 349+2 and constrain the values of several properties of these sources. According to our calculations, the neutron stars in GX 9+1 and GX 349+2 are rapidly rotating and stiffer equations of state are unfavoured.
We present a scenario of formation of strange stars due to spin-down of {\it rapidly rotating} neutron stars left after supernova explosions . By assuming a process where the total baryon mass is conserved but the angular momentum is lost due to emission of gravitational waves and/or the magnetic braking, we find that the transition from rapidly rotating neutron stars to slowly rotating strange stars is possible; a large amount of energy $\sim 10^{53} ergs $ could be released. The liberated energy might become a new energy source for a delayed explosion of supernova. Furthermore, our scenario …
We calculate temperature profiles and X-ray spectra of accretion disks around rapidly rotating neutron stars considering the full effect of general relativity. Computed disk temperatures and luminosities are compared with the EXOSAT data to constrain the properties of five low-mass-X-ray-binary sources. We fit our model-spectra with an analytical function, which can in turn be used for routine spectral fitting work. Our equation-of-state dependent spectral model may be useful to constrain the equation-of-state models of neutron stars. We also compare the properties of a rotating neutron star w…
A new non-perturbative method to compute accurate oscillation modes in rapidly rotating stars is presented. In this paper, the effect of the centrifugal force is fully taken into account while the Coriolis force is neglected. This assumption is valid when the time scale of the oscillation is much shorter than the inverse of the rotation rate and is expected to be suitable for high radial order p-modes of $δ$ Scuti stars. Axisymmetric p-modes have been computed in uniformly rotating polytropic models of stars. In the frequency and rotation range considered, we found that as rotation increases (…
We present an analytical model for the magnetic flux surfaces for rapidly rotating magnetized young stellar objects which is based on ideal, stationary, axisymmetric magnetohydrodynamics. The resulting cold wind solutions reproduce observed wind velocities of a few hundred \kms$ $ and the outer jet radi us for a collimated jet of several thousand stellar radii. The theory of axisymmetric magnetospheres around rapidly rotating stellar sources is outlined including electric fields due to the rapid rotation. Gravity of the central object is consistently built into this theory. A consistent wind t…
Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the…
We study effects of the strange quark mass and of the QCD coupling constant in the MIT bag model of quark matter with lowest order quark-gluon interactions on the rapid rotation of strange stars. The influence of rotation on global parameters of strange stars is greater than in the case of the neutron star models. We show that independently of the strange quark mass and the coupling constans the ratio of the rotational kinetic energy to the absolute value of the gravitational potential energy for rotating strange stars is significantly higher than for ordinary neutron stars. This might indicat…
We present computed spectra, as seen by a distant observer, from the accretion disc around a rapidly rotating neutron star. Our calculations are carried out in a fully general relativistic framework, with exact treatment of rotation. We take into account the Doppler shift, gravitational redshift and light bending effects in order to compute the observed spectrum. We find that light bending significantly modifies the high-energy part of the spectrum. Computed spectra for slowly rotating neutron stars are also presented. These results would be important for modelling the observed X-ray spectra o…
We investigate charge accretion in vicinity of a slowly rotating compact star with a non-stationary electromagnetic field. Exact solutions to the general relativistic Maxwell equations are obtained for a star formed of a highly degenerate plasma with a gravitational field given by the linearized Kerr metric. These solutions are used to formulate and then to study numerically the equations of motion for a charged particle in star's vicinity using the gravitoelectromagnetic force law. The analysis shows that close to the star charge accretion does not always remain ordered. It is found that the …
We use the integrated spectrum of the X-ray background and quasars Spectral Energy Distribution to derive the contribution of quasars to the energy output of the Universe. We find a lower limit for the energy from accretion onto black holes of 6%, of the total luminosity of the Universe and probably more, with 15% quite possible. Comparing these values with the masses of black holes in the center of nearby galaxies we show that the accretion process must be on average very efficient: at least 15% of the accreted mass must be transformed into radiated energy. This further implies that most supe…
Gravitational waves are tiny disturbances in space-time and are a fundamental, although not yet directly confirmed, prediction of General Relativity. Rapidly rotating neutron stars are one of the possible sources of gravitational radiation dependent upon pulsar's rotational frequency, details of the equation of state of stellar matter, and distance to detector. Applying an equation of state with symmetry energy constrained by recent nuclear laboratory data, we set an upper limit on the strain-amplitude of gravitational waves emitted by rapidly rotating neutron stars.
We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $Γ= 2$ and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion (e.g. via a pha…
Accuracies reached in space astrometry now permit the accurate determination of astrometric radial velocities, without any use of spectroscopy. Knowing this true stellar motion, spectral shifts intrinsic to stellar atmospheres can be identified, for instance gravitational redshifts and those caused by velocity fields on stellar surfaces. The astrometric accuracy is independent of any spectral complexity, such as the smeared-out line profiles of rapidly rotating stars. Besides a better determination of stellar velocities, this permits more precise studies of atmospheric dynamics, such as possib…
It has been suggested that the frequency in the co-rotating innermost stable circular orbit (ISCO) about a compact stellar remnant can be determined through X-ray observations of low-mass X-ray binaries, and that its value can be used to constrain the equation of state of ultradense matter. Upon constructing numerical models of rapidly rotating strange (quark) stars in general relativity, we find that for stars rotating at the equatorial mass-shedding limit, the ISCO is indeed above the stellar surface, for a wide range of central energy densities at a height equal to 11% of the circumferentia…
For a new equation of state of strange quark matter, we construct equilibrium sequences of rapidly rotating strange stars in general relativity. The sequences are the normal and supramassive evolutionary sequences of constant rest mass. We also calculate equilibrium sequences for a constant value of $Ω$ corresponding to the most rapidly rotating pulsar PSR 1937 + 21. In addition to this, we calculate the radius of the marginally stable orbit and its dependence on $Ω$, relevant for modeling of kilo-Hertz quasi-periodic oscillations in X-ray binaries.
We compute spectra from accretion disks around rapidly rotating neutron stars. The full effect of general relativity is considered for the structure calculation of the stars. We take into account the Doppler shift, gravitational redshift and light-bending effects in order to compute the observed spectra. To facilitate direct comparison with observations, a simple empirical function is presented which describes the numerically computed spectra well. This function can in principle be used to distinguish between the Newtonian spectra and the relativistic spectra. We also discuss the possibility o…
We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrarily inclined orbit (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki--Kato formulas. The NS gravitational field is described by the exact s…
The evolution of a nonaxisymmetric bar-mode perturbation of rapidly rotating stars due to a secular instability induced by gravitational wave emission is studied in post-Newtonian simulations taking into account gravitational radiation reaction. A polytropic equation of state with the polytropic index $n=1$ is adopted. The ratio of the rotational kinetic energy to the gravitational potential energy $T/|W|$ is chosen in the range between 0.2 and 0.26. Numerical simulations were performed until the perturbation grows to the nonlinear regime, and illustrate that the outcome after the secular inst…
We present the first tentative detection of spinning dust emission from specific astronomical sources. All other detections in the current literature are statistical. The Green Bank 140 foot telescope was used to observe 10 dust clouds at 5, 8, and 10 GHz. In some cases, the observed emission was consistent with the negative spectral slope expected for free-free emission (thermal bremsstrahlung), but in two cases it was not. One HII region yields a rising spectrum, inconsistent with free-free or synchrotron emission at the 10 sigma level. One dark cloud (L 1622) has a similar spectrum with low…
In the solar convection zone, rotation couples with intensely turbulent convection to drive a strong differential rotation and achieve complex magnetic dynamo action. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the global-scale patterns of convection in such stars and the flows of differential rotation and meridional circulation which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rota…
Relativistic Cowling approximation in which all metric perturbations are omitted is applied to non-axisymmetric infinitesimal oscillations of uniformly rotating general relativistic polytropes. Frequencies of lower order f-modes which are important in analysis of secular instability driven by gravitational radiation are investigated and neutral points of the mode along equilibrium sequences of rotating polytropes are determined. Since this approximation becomes more accurate as stars are more relativistic and/or as they rotates more rapidly, we will be able to analyze how a rotation period of …
Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility in studying the complete problem by including spacetime perturbations. Our study includes both axisymmetric and non-axisymmetric perturbations and provides limits for the onset of the secular bar mode rotational i…
Since the last Amaldi meeting in 1997 we have learned that the r-modes of rapidly rotating neutron stars are unstable to gravitational radiation reaction in astrophysically realistic conditions. Newborn neutron stars rotating more rapidly than about 100Hz may spin down to that frequency during up to one year after the supernova that gives them birth, emitting gravitational waves which might be detectable by the enhanced LIGO interferometers at a distance which includes several supernovae per year. A cosmological background of these events may be detectable by advanced LIGO. The spins (about 30…
To investigate the formation mechanism of relativistic jets in active galactic nuclei and micro-quasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of jet formation in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both co-rotating and counter-rotating with respect to the black hole rotation. In the co-rotating disk case, our results are almost the same as those in Schwarzschild black hole cases: a gas pressure-driven jet is formed by…
The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling an…
Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can …
It has been recently demonstrated that the orbital velocity profile around Kerr black holes in the equatorial plane as observed in the locally non-rotating frame exhibits a non-monotonic radial behaviour. We show here that this unexpected minimum-maximum feature of the orbital velocity remains if the Kerr vacuum is generalized to the Kerr-de Sitter or Kerr-anti-de Sitter metric. This is a new general relativity effect in Kerr spacetimes with non-vanishing cosmological constant. Assuming that the profile of the orbital velocity is known, this effect constrains the spacetime parameters.
We construct models of rotating stars using the perturbative approach introduced by J. Hartle in 1967, and a set of equations of state proposed to model hadronic interactions in the inner core of neutron stars. We integrate the equations of stellar structure to third order in the angular velocity and show, comparing our results to those obtained with fully non linear codes, to what extent third order corrections are needed to accurately reproduce the moment of inertia of a star which rotates at rates comparable to that of the fastest isolated pulsars.
Recent observations of Galactic Black Hole Candidates (BHCs) suggest that those that are superluminal jet sources have more rapid black hole spin rates than otherwise normal BHCs. This provides observational support for models of relativistic jet formation that extract rotational energy of the central black hole. To investigate this mechanism, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of the formation of a relativistic jet in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We assume that t…
We use time-evolutions of the linear perturbation equations to study the oscillations of rapidly rotating neutrons stars. Our models account for the buoyancy due to composition gradients and we study, for the first time, the nature of the resultant g-modes in a fast spinning star. We provide detailed comparisons of non-stratified and stratified models. This leads to an improved understanding of the relationship between the inertial modes of a non-stratified star and the g-modes of a stratified system. In particular, we demonstrate that each g-mode becomes rotation-dominated, i.e. approaches a …
I discuss the range of validity of Detweiler's formula for the resonant frequencies of rapidly rotating Kerr black holes. While his formula is correct for extremal black holes, it has also been commonly accepted that it describes very well the resonant frequencies of near extremal black holes, and that therefore there is a large number of modes clustering on the real axis as the black hole becomes extremal. I will show that this last statement is not only incorrect, but that it also does not follow from Detweiler's formula, provided it is handled with due care. It turns out that only the first…
We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black-hole physical parameters: omega=m Omega-i2 pi T(n+1/2), where T and Omega are the temperature and angular velocity of the black hole, and m is the azimuthal harmonic index of a co-rotating equatorial mode. This formula implies that the relaxation period tau sim 1/Im(omega) of the black hole becomes extremely long as the extremal limit T to 0 is…
