Gravitational Radiation Back Reaction Research Articles

Gravitational radiation back-reaction from f-modes on neutron stars

ABSTRACT The problem of the gravitational radiation damping of neutron star fundamental (f) mode oscillations has received considerable attention. Many studies have looked at the stability of such oscillations in rapidly rotating stars, calculating the growth or decay rate of the mode amplitude. In this paper, we look at the relatively neglected problem of the radiation reaction on the spin of the star. We specialize greatly to the so-called Kelvin modes: the modes of oscillation of (initially) non-rotating incompressible stars. We find the unexpected result that the excitation of a mode of angular momentum δJ on an initially non-rotating star ends up radiating an angular momentum 2δJ to infinity, leaving the star itself with a bulk angular momentum of −δJ. This result is interesting in itself, and also will have implications for the angular momentum budgets of spinning down neutron stars, should such modes be excited.

Gravitational wave from GRB center: A black hole-torus system

We discuss a possible gravitational wave radiation from a center of GRB, which consists of a rotating black hole and a torus. The gravitational waves can be generated by the precession as well as the local intrinsic inhomogeneity of the torus. Using the typical values relevant to GRB center, one can expect gravitational wave production with frequencies roughly in the range of 10 2 up to 10 3 Hz, which correspond basically to the Lense-Thirring frequency and the Keplerian frequency, respectively. For a rigid precession, the amplitude is found to be not smaller than the recent estimation for a precessing neutron star. For a Lense-Thirring precession, the line-broadening in the observed spectrum is expected due to the modulation of the torus orientation to the line of sight. The effect of the back reaction of gravitational radiation is estimated to be not so significant for long-duration GRBs.

Newtonian hydrodynamics of the coalescence of black holes with neutron stars - IV. Irrotational binaries with a soft equation of state

We present the results of three-dimensional hydrodynamical simulations of the final stages of in-spiral in a black hole–neutron star binary, when the separation is comparable to the stellar radius. We use a Newtonian smooth particle hydrodynamics (SPH) code to model the evolution of the system, and take the neutron star to be a polytrope with a soft (adiabatic indices and equation of state and the black hole to be a Newtonian point mass. The only non-Newtonian effect we include is a gravitational radiation back reaction force, computed in the quadrupole approximation for point masses. We use irrotational binaries as initial conditions for our dynamical simulations, which are begun when the system is on the verge of initiating mass transfer and followed for approximately 23 ms. For all the cases studied we find that the star is disrupted on a dynamical time-scale, and forms a massive accretion torus around the spinning (Kerr) black hole. The rotation axis is clear of baryons (less than 10−5 M⊙ within 10°) to an extent that would not preclude the formation of a relativistic fireball capable of powering a cosmological gamma-ray burst. Some mass (the specific amount is sensitive to the stiffness of the equation of state) may be dynamically ejected from the system during the coalescence and could undergo r-process nucleosynthesis. We calculate the waveforms, luminosities and energy spectra of the gravitational radiation signal, and show how they reflect the global outcome of the coalescence process.

Spin effects in gravitational radiation back reaction. III. Compact binaries with two spinning components

The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of the spin and orbital angular momenta reveal a speed-up effect due to the eccentricity. The dissipative evolutions of the relevant dynamical and angular variables is presented in the form of a closed system of differential equations.

Spin effects in gravitational radiation back reaction. II. Finite mass effects

A convenient formalism for averaging the losses produced by gravitational radiation backreaction over one orbital period was developed in an earlier paper. In the present paper we generalize this formalism to include the case of a closed system composed from two bodies of comparable masses, one of them having the spin S. We employ the equations of motion given by Barker and O'Connell, where terms up to linear order in the spin (the spin-orbit interaction terms) are kept. To obtain the radiative losses up to terms linear in the spin, the equations of motion are taken to the same order. Then the magnitude L of the angular momentum L, the angle kappa subtended by S and L and the energy E are conserved. The analysis of the radial motion leads to a new parametrization of the orbit. From the instantaneous gravitational radiation losses computed by Kidder the leading terms and the spin-orbit terms are taken. Following Apostolatos, Cutler, Sussman and Thorne, the evolution of the vectors S and L in the momentary plane spanned by these vectors is separated from the evolution of the plane in space. The radiation-induced change in the spin is smaller than the leading-order spin terms in the momentary angular momentum loss. This enables us to compute the averaged losses in the constants of motion E, L and L_S=L cos kappa. In the latter, the radiative spin loss terms average to zero. An alternative description using the orbital elements a,e and kappa is given. The finite mass effects contribute terms, comparable in magnitude, to the basic, test-particle spin terms in the averaged losses.

Spin effects in gravitational radiation back reaction. I. The Lense-Thirring approximation

The gravitational radiation backreaction effects are considered in the Lense-Thirring approximation. New methods for parameterizing the orbit and for averaging the instantaneous radiative losses are developed. To first order in the spin S of the black hole, both in the absence and in the presence of gravitational radiation, a complete description of the test-particle orbit is given. This is achieved by two improvements over the existing descriptions. First, by introducing new angle variables with a straightforward geometrical meaning. Second, by finding a new parametrization of a generic orbit, which assures that the integration over a radial period can be done in an especially simple way, by applying the residue theorem. The instantaneous radiation losses of the system are computed using the formulation of Blanchet, Damour and Iyer(1989). All losses are given both in terms of the dynamical constants of motion and the properly defined orbital elements $a,e,\iota$ and $\Psi_0$. The radiative losses of the constants characterizing the Lense-Thirring motion, when suitably converted, are in agreement with earlier results of Kidder, Will and Wiseman(1993), Ryan(1996) and Shibata(1994). In addition, the radiative losses of two slowly changing orbital elements $\Psi_0,\Phi_0$ are given in order to complete the characterization of the orbit.

Radiative back reaction on global strings.

We consider radiative back reaction for global strings using the Kalb-Ramond formalism. In analogy with the point electron in classical electrodynamics we show how local radiative corrections to the equations of motion allow one to remove the divergence in the self-field and calculate a first-order approximation to the radiation back reaction force. The effects of this back reaction force are studied numerically by resubstituting the equations of motion to suppress exponentially growing solutions. By direct comparison with numerical field theory simulations and analytic radiation calculations we establish that the ``local back reaction approximation'' provides a satisfactory quantitative description of radiative damping for a wide variety of string configurations. Finally, we discuss the relevance of this work to the evolution of a network of global strings and their possible cosmological consequences. These methods can also be applied to describe the effects of gravitational radiation back reaction on local strings, electromagnetic radiation back reaction on superconducting strings, and other forms of string radiative back reaction. \textcopyright{} 1996 The American Physical Society.

Small-scale structure on a cosmic-string network.

We construct an analytic model of the accumulation of small-scale structure on a cosmic-string network in an expanding universe. The structure is composed of kinks which form when the string segments cross and intercommute, and then decay from stretching and gravitational radiation back reaction. We calculate the linear density of kinks, $K(t)$, for a general power-law expansion $a(t)={(\frac{t}{{t}_{0}})}^{p}$; after a period of rapid initial growth, the linear density approaches scaling $K(t)\ensuremath{\propto}{t}^{\ensuremath{-}1}$. We also examine the transition from the radiation- to matter-dominated eras; after the transition between eras, $K(t)$ drops before settling once more into scaling. Because of the slow decay of kinks, we find that the kink density is many orders of magnitude larger than one might expect. The predictions of our model are in good quantitative agreement with the kink density observed in the numerical simulations. Our model may explain the observed lack of scaling behavior in the small-scale structure and in the formation of loops observed in numerical simulations.