Gravitational Wave Emission by Cataclysmic Variables: numerical models of semi-detached binaries

Gravitational wave emission is considered to be the driving force for the evolution of short-period cataclysmic binary stars, making them a potential test for the validity of General Relativity. In spite of continuous refinements of the physical description, a 10% mismatch exists between the theoretical minimum period ($P_{\rm turn} \simeq 70$ min) and the short-period cut-off ($P_{\rm min} \simeq 80$ min) observed in the period distribution for cataclysmic variable binaries. A possible explanation for this mismatch was associated with the use of the Roche model. We here present a systematic comparison between self-consistent, numerically constructed sequences of hydrostatic models of binary stars and Roche models of semi-detached binaries. On the basis of our approach, we also derive a value for the minimum period of cataclysmic variable binaries. The results obtained through the comparison indicate that the Roche model is indeed very good, with deviations from the numerical solution which are of a few percent at most. Our results therefore suggest that additional sources of angular momentum loss or alternative explanations need to be considered in order to justify the mismatch.Comment: 7pages, 4figures. To appear in MNRA

Differentially-rotating neutron star models with a parametrized rotation profile

We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best describe the binary neutron star remnants cannot produce equilibrium configurations with values of T/|W| that exceed 0.14, the criterion for the onset of the secular instability.Comment: Submitted to A&A, 6 pages, 3 figure

Oscillations of vertically integrated relativistic tori -II. Axisymmetric modes in a Kerr spacetime

This is the second of a series of papers investigating the oscillation properties of relativistic, non-selfgravitating tori orbiting around black holes. Extending the work done in a Schwarzschild background, we here consider the axisymmetric oscillations of vertically integrated tori in a Kerr spacetime. The tori are modeled with a number of different non-Keplerian distributions of specific angular momentum and we discuss how the oscillation properties depend on these and on the rotation of the central black hole. We first consider a local analysis to highlight the relations between acoustic and epicyclic oscillations in a Kerr spacetime and subsequently perform a global eigenmode analysis to compute the axisymmetric p modes. In analogy with what found in a Schwarzschild background, these modes behave as sound waves that are modified by rotation and are globally trapped in the torus. For constant distributions of specific angular momentum, the eigenfrequencies appear in a sequence 2:3:4:... which is essentially independent of the size of the disc and of the black hole rotation. For non-constant distributions of angular momentum, on the other hand, the sequence depends on the properties of the disc and on the spin of the black hole, becoming harmonic for sufficiently large tori. We also comment on how p modes could explain the high frequency quasi-periodic oscillations observed in low-mass X-ray binaries with a black hole candidate and the properties of an equivalent model in Newtonian physics.Comment: 13 pages, MNRAS, in pres