TIDAL AND TIDAL-RESONANT EFFECTS IN COALESCING BINARIES

Tidal and tidal-resonant effects in coalescing compact binary systems are investigated by direct numerical integration of the equations of motion. For the stars polytropic models are used. The tidal effects are found to be dominated by the (non-resonant) $f$-modes. The effect of the $g$-mode-tidal resonances is obtained. The tidal interaction is shown to be of interest especially for low-mass binaries. There exists a characteristic final plunge orbit beyond which the system cannot remain stable even if radiation reaction is not taken into account; in agreement with results obtained by Lai et al. \shortcite{Lai93}. The importance of the investigated effects for the observation of gravitational waves on Earth is discussed.Comment: 17 pages, latex (mn.sty), 5 figures, M.N.R.A.S. in pres

A Semi-analytic Study of Axial Perturbations of Ultra Compact Stars

Compact object perturbations, at linear order, often lead in solving one or more coupled wave equations. The study of these equations was typically done by numerical or semi-analytical methods. The WKB method and the associated Bohr-Sommerfeld rule have been proved extremely useful tools in the study of black-hole perturbations and the estimation of the related quasi-normal modes. Here we present an extension of the aforementioned semi-analytic methods in the study of perturbations of ultra-compact stars and gravastars.Comment: Accepted for publication in CQG, 13 pages, 3 figures, 5 table

The stochastic background of gravitational waves due to the f-mode instability in neutron stars

This paper presents an estimate for the spectral properties of the stochastic background of gravitational waves emitted by a population of hot, young, rapidly rotating neutron stars throughout the Universe undergoing $f$-mode instabilities, formed through either core-collapse supernova explosions or the merger of binary neutron star systems. Their formation rate, from which the gravitational wave event rate is obtained, is deduced from observation-based determinations of the cosmic star formation rate. The gravitational wave emission occurs during the spin-down phase of the $f$-mode instability. For low magnetized neutron stars and assuming 10\% of supernova events lead to $f$-mode unstable neutron stars, the background from supernova-derived neutron stars peaks at $\Omega_{\text{gw}} \sim 10^{-9}$ for the $l=m=2$ $f$-mode, which should be detectable by cross-correlating a pair of second generation interferometers (e.g. Advanced LIGO/Virgo) with an upper estimate for the signal-to-noise ratio of $\approx$ 9.8. The background from supramassive neutron stars formed from binary mergers peaks at $\Omega_{\text{gw}} \sim 10^{-10}$ and should not be detectable, even with third generation interferometers (e.g. Einstein Telescope)

Compactness of neutron stars and Tolman VII solutions in scalar-tensor gravity

We systematically examine the compactness of neutron stars as Tolman VII solutions in scalar-tensor theory of gravity. As a result, when the coupling constant is confined to values provided by astronomical observations we show that the maximum compactness of neutron stars in general relativity is higher than that in scalar-tensor gravity. In addition, we show that although ultra-compact stars, with radius smaller than the Regge-Wheeler potential peak, can exist in general relativity (e.g., Tolman VII solution), their scalarized counterparts cannot {be constructed} even in the limiting case of uniform density stars.Comment: accepted for publication in PR

On the saturation amplitude of the f-mode instability

We investigate strong nonlinear damping effects which occur during high amplitude oscillations of neutron stars, and the gravitational waves they produce. For this, we use a general relativistic nonlinear hydrodynamics code in conjunction with a fixed spacetime (Cowling approximation) and a polytropic equation of state (EOS). Gravitational waves are estimated using the quadrupole formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar, Friedman, Schutz) instability, but we also investigate axisymmetric and quasiradial modes. We study various models to determine the influence of rotation rate and EOS. We find that axisymmetric oscillations at high amplitudes are predominantly damped by shock formation, while the nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly rotating models, coupling to nonaxisymmetric inertial modes. From the observed nonlinear damping, we derive upper limits for the saturation amplitude of CFS-unstable f modes. Finally, we estimate that the corresponding gravitational waves for an oscillation amplitude at the upper limit should be detectable with the advanced LIGO and VIRGO interferometers at distances above 10 MPc. This strongly depends on the stellar model, in particular on the mode frequency.Comment: 24 pages, 31 figures, 6 tables. Updated article to published version. Fixed a typo in Eq. 3