Constraining phases of quark matter with studies of r-mode damping in neutron stars

The r-mode instability in rotating compact stars is used to constrain the phase of matter at high density. The color-flavor-locked phase with kaon condensation (CFL-K0) and without (CFL) is considered in the temperature range 10^8K < T <10^{11} K. While the bulk viscosity in either phase is only effective at damping the r-mode at temperatures T > 10^{11} K, the shear viscosity in the CFL-K0 phase is the only effective damping agent all the way down to temperatures T > 10^8 K characteristic of cooling neutron stars. However, it cannot keep the star from becoming unstable to gravitational wave emission for rotation frequencies f ~ 56-11 Hz at T ~ 10^8-10^9 K. Stars composed almost entirely of CFL or CFL-K0 matter are ruled out by observation of rapidly rotating neutron stars, indicating that dissipation at the quark-hadron interface or nuclear crust interface must play a key role in damping the instability.Comment: 8 pages, 2 figure

Innermost stable circular orbits around magnetized rotating massive stars

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.Comment: 8 pages, 3 figure

The runaway instability in general relativistic accretion disks

When an accretion disk falls prey to the runaway instability, a large portion of its mass is devoured by the black hole within a few dynamical times. Despite decades of effort, it is still unclear under what conditions such an instability can occur. The technically most advanced relativistic simulations to date were unable to find a clear sign for the onset of the instability. In this work, we present three-dimensional relativistic hydrodynamics simulations of accretion disks around black holes in dynamical space-time. We focus on the configurations that are expected to be particularly prone to the development of this instability. We demonstrate, for the first time, that the fully self-consistent general relativistic evolution does indeed produce a runaway instability.Comment: 5 pages, 3 figures, minor corrections to match published version in MNRAS, +link to animatio

R-mode oscillations of rapidly rotating barotropic stars in general relativity: Analysis by the relativistic Cowling approximation

We develop a numerical scheme for obtaining the $r$-mode oscillations of rapidly rotating relativistic stars. In the present scheme, we neglect all metric perturbations and only take account of the dynamics of the fluid in the background spacetime of the unperturbed star (the relativistic Cowling approximation). We also assume the star is barotropic, i.e. neutrally stable against convection under the assumption of adiabatic oscillations. Our numerical scheme is based on the Yoshida-Eriguchi formulation for the analysis of the general relativistic f-mode oscillations in the Cowling approximation and a general relativistic generalization of the Karino-Yoshida-Yoshida-Eriguchi's numerical scheme for obtaining oscillations of rapidly rotating Newtonian stars. By this new numerical scheme, frequencies of the $r$-mode oscillations are obtained as functions of the ratio of the rotational energy to the absolute value of the gravitational energy $T/|W|$ along sequences of polytropic equilibrium stars whose ratio of the pressure to the total energy density at the center of the star and the polytropic index are kept constant. It is found that the dimensionless oscillation frequency $\sigma/\Omega$ is a linearly decreasing function of $T/|W|$, where $\sigma$ and $\Omega$ are the oscillation frequency and the angular velocity of the star measured in an inertial frame at spatial infinity. We also find that oscillation frequencies of the $r$-modes are highly dependent on the relativistic factor $M/R$ of the star as already found in previous studies in which the slow rotation approximation has been used. Here $M$ and $R$ denote the mass and radius of the star, respectively.Comment: 9 pages, 6 figure

Quark core formation in spinning-down pulsars

Pulsars spin-down due to magnetic torque reducing its radius and increasing the central energy density. Some pulsar which are born with central densities close to the critical value of quark deconfinement may undergo a phase transition and structural re-arrengement. This process may excite oscillation modes and emmit gravitational waves. We determine the rate of quark core formation in neutron stars using a realistic population synthesis code.Comment: Proceedings of the 2nd International Workshop on Astronomy and Relativistic Astrophysics, to appear in IJMP

Electron-positron energy deposition rate from neutrino pair annihilation in the equatorial plane of rapidly rotating neutron and quark stars

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 relativistic effects, and we obtain the general relativistic corrections to the energy and momentum deposition rates for arbitrary stationary and axisymmetric space-times. We obtain the energy and momentum deposition rates for several classes of rapidly rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the MIT bag model equation of state and in the CFL (Color-Flavor-Locked) phase, respectively. Compared to the Newtonian calculations, rotation and general relativistic effects increase the total annihilation rate measured by an observer at infinity. The differences in the equations of state for neutron and quark matter also have important effects on the spatial distribution of the energy deposition rate by neutrino-antineutrino annihilation.Comment: 29 pages, 6 figures, accepted for publication in MNRA

Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Perturbative approach to the structure of rapidly rotating neutron stars

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.Comment: 17 pages, 5 figures, minor changes to match version accepted by Phys. Rev.