Precessing supermassive black hole binaries and dark energy measurements with LISA

Spin induced precessional modulations of gravitational wave signals from supermassive black hole binaries can improve the estimation of luminosity distance to the source by space based gravitational wave missions like the Laser Interferometer Space Antenna (LISA). We study how this impacts the ablity of LISA to do cosmology, specifically, to measure the dark energy equation of state (EOS) parameter $w$. Using the $\Lambda$CDM model of cosmology, we show that observations of precessing binaries by LISA, combined with a redshift measurement, can improve the determination of $w$ up to an order of magnitude with respect to the non precessing case depending on the masses, mass ratio and the redshift.Comment: 4 pages, 4 figures, version accepted to PR

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

Non radial oscillations of slowly ratating relativistic stars

This PhD thesis is devoted to the study of the non-radial oscillations of slowly rotating neutron stars, in the framework of General Relativity. We studied these oscillations using the linear perturbation theory. At first we constructed the background stellar model. Then we introduced small perturbations, linearized the Einstein equations and studied the response of the perturbed system by solving the equations describing it, as an initial value problem or as it is usually said by many authors, in the time domain. The basic assumptions that we made in this study are the following, ² The star is a perfect fluid and has zero temperature, ² The star is rotating uniformly with angular velocity ­ and this rotation is a considered as perturbation of the non-rotating stellar model, ² The magnetic field of the star is negligible. All the above assumptions follow from observational facts. Subsequently we introduced small perturbations on this stellar model both on the fluid of the star and the spacetime around it. The perturbation functions are assumed to be of small order ± and in general are function of all the variables of the problem, i.e. t, r, µ, A. We then splitted the perturbation functions into radial and angular parts using spherical harmonics. This is allowed because of the spherical symmetry of the background. We also introduced a dimensionless parameter " = ­=­K, that is the ratio of the angular velocity of the star, over the angular velocity at the mass shedding limit. By assuming that this parameter is small " << 1, i.e. the star is rotating slowly, we calculated the Einstein equations (3.33) and the equations of motion of the fluid (3.38) and linearized them to both parameters " and ±. By integrating the above equations over solid angles we eliminated the angular dependence of the perturbation functions. This way we arrived to a system of partial differential equations (PDEs) of time t and space r that describes the small non-radial perturbations of a slowly rotating neutron star. Having the above system of equations in hand, we tried to solve it numerically and calculate the eigenfrequencies of the system. In order to understand them better we have splitted them into two basic parts, as is common in the bibliography. The part that describes the fluid perturbations and the part that describes the spacetime perturbations. In the literature is common to use the term “Cowling Approximation” when the spacetime perturbations are neglected, and the term “Inverse Cowling Approximation (ICA)” when the perturbations of the stellar fluid are neglected. The first step was to study the part that describes the fluid perturbations, and extract the stellar oscillation modes. By studying this part of the problem we have gained useful information about f, p and r modes of slowly rotating neutron stars. We also studied a interesting phenomenon that appears in this level of approximation, i.e. existence of a continuous spectrum. The continuous spectrum has significant influence on the appearance and the life of the normal modes of the star, for different spherical harmonic indices l. As a second step we have re-written the equations that describe the perturbations of a slowly rotating neutron star, in a new gauge, that has been used up to now only for non-rotating stars. The motivation was that the already existing equations were not very well posed for numerical evolution, due to the existence of mixed second order spatial and temporal derivatives of the perturbation functions. Indeed the equations that we produced in the new gauge seemed more appropriate for numerical evolutions, and they could be rather easily transformed into a first order system. Subsequently we have turned to the old system of equations in the widely used Regge-Wheeler gauge. By redefinition of new variables and lengthy calculations we have managed to re-write it in first order form of evolution equations. As a test for the numerical stability of this system we evolved the part that describes the spacetime perturbations and showed that is numerically stable. For the first time we also calculated frequencies of w-modes for both polytropic and uniform density equations of state. Finally, in order to check the limits of our linear slow rotation approximation for the fluid modes, we added to the perturbed equations of motion of the fluid (3.38) the second order terms in rotation O("2). We then studied the improvement of the accuracy in the calculation of the background model i.e. the mass and the radius. We concluded our study by examining the way the eigenfrequencies of the various oscillation modes is influenced by the inclusion of the second order terms

Bounding the mass of the graviton with gravitational waves: Effect of spin precessions in massive black hole binaries

International audienceObservations of gravitational waves from massive binary black-hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precessions of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation based on the method of matched filtering of gravitational-wave signals vs theoretical template waveforms. For the proposed Laser Interferometer Space Antenna, we show that precessions, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black-hole systems of equal masses 106M⊙ at 3 Gpc, the lower bounds on the graviton Compton wavelength achievable are of the order of 5×1016km

Nonradial oscillations of slowly and differentially rotating compact stars

The equations describing nonradial adiabatic oscillations of differentially rotating relativistic stars are derived in relativistic slow rotation approximation. The differentially rotating configuration is described by a perturbative version of the relativistic j-constant rotation law. Focusing on the oscillation properties of the stellar fluid, the adiabatic nonradial perturbations are studied in the Cowling approximation with a system of five partial differential equations. In these equations, differential rotation introduces new coupling terms between the perturbative quantities with respect to the uniformly rotating stars. In particular, we investigate the axisymmetric and barotropic oscillations and compare their spectral properties with those obtained in nonlinear hydrodynamical studies. The perturbative description of the differentially rotating background and the oscillation spectrum agree within a few percent with those of the nonlinear studies

Non-axisymmetric oscillations of differentially rotating relativistic stars

Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness M/R, the degree of differential rotation A and the number of maximun couplings [script-I]max. It is shown that the rotational splitting of the non-axisymmetric modes is strongly enhached by increasing the compactness of the star and the degree of differential rotation. Finally, we investigate the relation between the fundamental quadrupole mode and the corotation band of differentially rotating stars