Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as in the Cowling approximation. We also investigate non-linear harmonics of the linear modes and notice that rotation changes the pulsation frequencies in a way that would allow for various parametric instabilities between two or three modes to take place. We assess the detectability of each obtained mode by current gravitational wave detectors and outline how the empirical relations that have been constructed for gravitational wave asteroseismology could be extended to include the effects of rotation.Comment: 24 pages, 20 figures; minor corrections, added extended discussion and one figure in one subsectio

Analytic description of the r-mode instability in uniform density stars

We present an analytic description of the $r$-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The $l=m=2$ current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the $r$-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formaulae enables a quick check of such effects on the development of the instability.Comment: 7 pages, 2 figure

Keplerian frequencies and innermost stable circular orbits of rapidly rotating strange stars

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 circumferential stellar radius, which scales inversely with the square root of the energy density, of self-bound quark matter at zero presure. In contrast to static stars, the ISCO frequencies of rapidly rotating strange stars can be as low as 0.9 kHz for a 1.3 solar mass strange star. Hence, the presence of strange stars in low-mass X-ray binaries cannot be excluded on the basis of the currently observed frequencies of kHz QPOs, such as the cut-off frequency of 1066 Hz in 4U 1820-30.Comment: 5 pg., 4 fig

Torsional Oscillations of Relativistic Stars with Dipole Magnetic Fields

We present the formalism and numerical results for torsional oscillations of relativistic stars endowed with a strong dipole magnetic field. We do a systematic search of parameter space by computing torsional mode frequencies for various values of the harmonic index $\ell$ and for various overtones, using an extended sample of models of compact stars, varying in mass, high-density equation of state and crust model. We show that torsional mode frequencies are sensitive to the crust model if the high-density equation of state is very stiff. In addition, torsional mode frequencies are drastically affected by a dipole magnetic field, if the latter has a strength exceeding roughly $10^{15}$G and we find that the magnetic field effects are sensitive to the adopted crust model. Using our extended numerical results we derive empirical relations for the effect of the magnetic field on torsional modes as well as for the crust thickness. We compare our numerical results to observed frequencies in SGRs and find that certain high-density EoS and mass values are favored over others in the non-magnetized limit. On the other hand, if the magnetic field is strong, then its effect has to be taken into account in attempts to formulate a theory of asteroseismology for magnetars.Comment: 17 pages, 5 figure

Revealing the high-density equation of state through binary neutron star mergers

We present a novel method for revealing the equation of state of high-density neutron star matter through gravitational waves emitted during the postmerger phase of a binary neutron star system. The method relies on a small number of detections of the peak frequency in the postmerger phase for binaries of different (relatively low) masses, in the most likely range of expected detections. From such observations, one can construct the derivative of the peak frequency versus the binary mass, in this mass range. Through a detailed study of binary neutron star mergers for a large sample of equations of state, we show that one can extrapolate the above information to the highest possible mass (the threshold mass for black hole formation in a binary neutron star merger). In turn, this allows for an empirical determination of the maximum mass of cold, nonrotating neutron stars to within 0.1 M_sun, while the corresponding radius is determined to within a few percent. Combining this with the determination of the radius of cold, nonrotating neutron stars of 1.6 M_sun (to within a few percent, as was demonstrated in Bauswein et al., PRD, 86, 063001, 2012), allows for a clear distinction of a particular candidate equation of state among a large set of other candidates. Our method is particularly appealing because it reveals simultaneously the moderate and very high-density parts of the equation of state, enabling the distinction of mass-radius relations even if they are similar at typical neutron star masses. Furthermore, our method also allows to deduce the maximum central energy density and maximum central rest-mass density of cold, nonrotating neutron stars with an accuracy of a few per cent.Comment: 14 pages, 12 figures, 2 tables, accepted for publication in Phys. Rev.

Analytic description of the r-mode instability in uniform density stars.

We present an analytic description of the r-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The l=m=2 current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the r-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formulae enable a quick check of such effects on the development of the instability

Axisymmetric Modes of Rotating Relativistic Stars in the Cowling Approximation

Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, nonlinear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l=0,1,2 and 3, for a sequence of rotating stars from the non-rotating limit to the mass-shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50% of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions.Comment: 11 pages, 10 figures, to appear in MNRA

Bridging the gap by shaking superfluid matter

In cold compact stars, Cooper pairing between fermions in dense matter leads to the formation of a gap in their excitation spectrum and typically exponentially suppresses transport properties. However, we show here that weak Urca reactions become strongly enhanced and approach their ungapped level when the star undergoes density oscillations of sufficiently large amplitude. We study both the neutrino emissivity and the bulk viscosity due to direct Urca processes in hadronic, hyperonic and quark matter and discuss different superfluid and superconducting pairing patterns.Comment: 5 pages, 4 figure