Gravitational wave asteroseismology with fast rotating neutron stars

We investigate damping and growth times of the f-mode for rapidly rotating stars and a variety of different polytropic equations of state in the Cowling approximation. We discuss the differences in the eigenfunctions of co- and counterrotating modes and compute the damping times of the f-mode for several EoS and all rotation rates up to the Kepler-limit. This is the first study of the damping/growth time of this type of oscillations for fast rotating neutron stars in a general relativistic framework. We use these frequencies and damping/growth times to create robust empirical formulae which can be used for gravitational wave asteroseismology. The estimation of the damping/growth time is based on the quadrupole formula and our results agree very well with Newtonian ones in the appropriate limit.Comment: 15 pages, 8 figures, version accepted for publication in PhysRev

An Explanation for the Bimodal Distribution of Gamma-Ray Bursts: Millisecond Pulsars from Accretion-Induced Collapse

Cosmological gamma-ray bursts (GRBs) could be driven by dissipation of pure electromagnetic energy (Poynting flux) extracted from rapidly rotating compact objects with strong magnetic fields. One such possibility is a young millisecond pulsar (MSP) formed from accretion-induced collapse (AIC) of a white dwarf. The combination of an efficient magnetic dynamo, likely operating during the first seconds of the initially hot and turbulent MSP interior, and the subsequent modest beaming of gamma-ray emitting outflows, would easily account for energy constraints. But the remarkable feature of such models is that they may naturally explain the hitherto unexplained bimodal distribution in GRB time durations. The two burst classes could correspond to MSPs that form spinning above and below a gravitationally unstable limit respectively. In the former case, the spin-down time scale is due to gravitational radiation emission ($<1s$) while the spin-down time scale of the latter is due to electromagnetic dipole emission ($\gg 1s$). These two time scales account for the short and long GRB durations, i.e. the observed bimodal GRB duration distribution. A natural prediction is that the short duration GRBs would be accompanied by strong gravitational radiation emission which is absent from the longer class. Both would show millisecond variabilities.Comment: 10 pages, Ap

Tidal torque induced by orbital decay in compact object binaries

As we observe in the moon-earth system, tidal interactions in binary systems can lead to angular momentum exchange. The presence of viscosity is generally regarded as the condition for such transfer to happen. In this paper, we show how the orbital evolution can cause a persistent torque between the binary components, even for inviscid bodies. This preferentially occurs at the final stage of coalescence of compact binaries, when the orbit shrinks successively by gravitational waves and plunging on a timescale shorter than the viscous timescale. The total orbital energy transferred to the secondary by this torque is ~0.01 of its binding energy. We further show that this persistent torque induces a differentially rotating quadrupole perturbation. Specializing to the case of a secondary neutron star, we find that this non equilibrium state has an associated free energy of 10^47-10^48 erg, just prior to coalescence. This energy is likely stored in internal fluid motions, with a sizable amount of differential rotation. By tapping this free energy reservoir, a preexisting weak magnetic field could be amplified up to a strength of ~10^15 Gauss. Such a dynamically driven tidal torque can thus recycle an old neutron star into a highly magnetized neutron star, with possible observational consequences at merger.Comment: 14 pages, 8 figures, new sections added, accepted on Sept.19, published on MNRA

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l the fundamental mode (without radial nodes) has a frequency ~300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies >=20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (have approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.Comment: 15 pages, 3 figures, Accepted for publication in MNRA

Shell sources as a probe of relativistic effects in neutron star models

A perturbing shell is introduced as a device for studying the excitation of fluid motions in relativistic stellar models. We show that this approach allows a reasonably clean separation of radiation from the shell and from fluid motions in the star, and provides broad flexibility in the location and timescale of perturbations driving the fluid motions. With this model we compare the relativistic and Newtonian results for the generation of even parity gravitational waves from constant density models. Our results suggest that relativistic effects will not be important in computations of the gravitational emission except possibly in the case of excitation of the neutron star on very short time scales.Comment: 16 pages LaTeX with 6 eps figures; submitted to Phys. Rev.

On the Shear Instability in Relativistic Neutron Stars

We present new results on instabilities in rapidly and differentially rotating neutron stars. We model the stars in full general relativity and describe the stellar matter adopting a cold realistic equation of state based on the unified SLy prescription. We provide evidence that rapidly and differentially rotating stars that are below the expected threshold for the dynamical bar-mode instability, beta_c = T/|W| ~ 0.25, do nevertheless develop a shear instability on a dynamical timescale and for a wide range of values of beta. This class of instability, which has so far been found only for small values of beta and with very small growth rates, is therefore more generic than previously found and potentially more effective in producing strong sources of gravitational waves. Overall, our findings support the phenomenological predictions made by Watts, Andersson and Jones on the nature of the low-T/|W|.Comment: 20 pages; accepted to the Classical and Quantum Gravity special issue for MICRA200

Gravitational waves from a test particle scattered by a neutron star: Axial mode case

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius $R \lesssim 3M$), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).Comment: 21 pages, revtex, 11 figures are attached with eps files Accepted to Phys. Rev.

Shear Viscosity and Oscillations of Neutron Star Crusts

We calculate the electron shear viscosity (determined by Coulomb electron collisions) for a dense matter in a wide range of parameters typical for white dwarf cores and neutron star crusts. In the density range from ~10^3 g cm^-3 to 10^7-10^10 g cm^-3 we consider the matter composed of widely abundant astrophysical elements, from H to Fe. For higher densities, 10^10-10^14 g cm^-3, we employ the ground-state nuclear composition, taking into account finite sizes of atomic nuclei and the distribution of proton charge over the nucleus. Numerical values of the viscosity are approximated by an analytic expression convenient for applications. Using the approximation of plane-parallel layer we study eigenfrequencies, eigenmodes and viscous damping times of oscillations of high multipolarity, l~500-1000, localized in the outer crust of a neutron star. For instance, at l~500 oscillations have frequencies f >= 40 kHz and are localized not deeper than ~300 m from the surface. When the crust temperature decreases from 10^9 K to 10^7 K, the dissipation time of these oscillations (with a few radial nodes) decreases from ~1 year to 10-15 days.Comment: 23 pages, 13 figure

The nature of low T/|W| dynamical instabilities in differentially rotating stars

Recent numerical simulations indicate the presence of dynamical instabilities of the f-mode in differentially rotating stars even at very low values of T/|W|, the ratio of kinetic to potential energy. In this Letter we argue that these may be shear instabilities that occur when the degree of differential rotation exceeds a critical value and when the f-mode develops a corotation point associated with the presence of a continuous spectrum. Our explanation, which is supported by detailed studies of a simple shell model, offers a straightforward way of understanding all of the key features of these instabilities