Spin effects in gravitational radiation backreaction 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.Comment: 12 pages, 1 figure, Phys.Rev.D15, March, 199

Spin effects in gravitational radiation backreaction 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.Comment: 10 pages, 1 figur

Spin-spin effects in radiating compact binaries

The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum $\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of $\bar{L}$ and other constants of the motion. Among them, self-interaction spin effects are found, representing the second post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring approximation.Comment: 12 pages, to appear in Phys. Rev.

Transition from inspiral to plunge for eccentric equatorial Kerr orbits

Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the implications for observations are no better: if the massive body is $M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at distance $d$ from LISA, then $S/N \lesssim (m/10 M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with $S/N>5$ during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce $S/N>5$ transition events during LISA's lifetime.Comment: Submitted to PR

Post-Newtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Up to O(v8)O(v^8) beyond the quadrupole formula

Extending a method developed by Sasaki in the Schwarzschild case and by Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the post-Newtonian expansion of the gravitational wave luminosities from a test particle in circular orbit around a rotating black hole up to $O(v^8)$ beyond the quadrupole formula. The orbit of a test particle is restricted on the equatorial plane. We find that spin dependent terms appear in each post-Newtonian order, and that at $O(v^6)$ they have a significant effect on the orbital phase evolution of coalescing compact binaries. By comparing the post-Newtonian formula of the luminosity with numerical results we find that, for $30M\lesssim r \lesssim 100M$, the spin dependent terms at $O(v^6)$ and $O(v^7)$ improve the accuracy of the post-Newtonian formula significantly, but those at $O(v^8)$ do not improve.Comment: 27 pages, revtex, 6 figures, submitted to Physical Review

The Statistical Mechanics of Horizons and Black Hole Thermodynamics

Although we know that black holes are characterized by a temperature and an entropy, we do not yet have a satisfactory microscopic ``statistical mechanical'' explanation for black hole thermodynamics. I describe a new approach that attributes the thermodynamic properties to ``would-be gauge'' degrees of freedom that become dynamical on the horizon. For the (2+1)-dimensional black hole, this approach gives the correct entropy. (Talk given at the Pacific Conference on Gravitation and Cosmology, Seoul, February 1996.)Comment: 11 pages, LaTe

Searching for Gravitational Waves from the Inspiral of Precessing Binary Systems: Astrophysical Expectations and Detection Efficiency of "Spiky'' Templates

Relativistic spin-orbit and spin-spin couplings has been shown to modify the gravitational waveforms expected from inspiraling binaries with a black hole and a neutron star. As a result inspiral signals may be missed due to significant losses in signal-to-noise ratio, if precession effects are ignored in gravitational-wave searches. We examine the sensitivity of the anticipated loss of signal-to-noise ratio on two factors: the accuracy of the precessing waveforms adopted as the true signals and the expected distributions of spin-orbit tilt angles, given the current understanding of their physical origin. We find that the results obtained using signals generated by approximate techniques are in good agreement with the ones obtained by integrating the 2PN equations. This shows that a complete account of all high-order post-Newtonian effects is usually not necessary for the determination of detection efficiencies. Based on our current astrophysical expectations, large tilt angles are not favored and as a result the decrease in detection rate varies rather slowly with respect to the black hole spin magnitude and is within 20--30% of the maximum possible values.Comment: 7 fig., accepted by Phys. Rev. D Minor modification

Bounding the mass of the graviton using gravitional-wave observations of inspiralling compact binaries

If gravitation is propagated by a massive field, then the velocity of gravitational waves (gravitons) will depend upon their frequency and the effective Newtonian potential will have a Yukawa form. In the case of inspiralling compact binaries, gravitational waves emitted at low frequency early in the inspiral will travel slightly slower than those emitted at high frequency later, modifying the phase evolution of the observed inspiral gravitational waveform, similar to that caused by post-Newtonian corrections to quadrupole phasing. Matched filtering of the waveforms can bound such frequency-dependent variations in propagation speed, and thereby bound the graviton mass. The bound depends on the mass of the source and on noise characteristics of the detector, but is independent of the distance to the source, except for weak cosmological redshift effects. For observations of stellar-mass compact inspiral using ground-based interferometers of the LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa modifications of Newtonian gravity. For observations of super-massive black hole binary inspiral at cosmological distances using the proposed laser interferometer space antenna (LISA), the bound can be as large as $6 \times 10^{16}$ km. This is three orders of magnitude weaker than model-dependent bounds from galactic cluster dynamics.Comment: 8 pages, RevTeX, submitted to Phys. Rev.

Gravitational waves from coalescing binaries and Doppler experiments

Doppler tracking of interplanetary spacecraft provides the only method presently available for broad-band searches of low frequency gravitational waves. The instruments have a peak sensitivity around the reciprocal of the round-trip light-time T of the radio link connecting the Earth to the space-probe and therefore are particularly suitable to search for coalescing binaries containing massive black holes in galactic nuclei. A number of Doppler experiments -- the most recent involving the probes ULYSSES, GALILEO and MARS OBSERVER -- have been carried out so far; moreover, in 2002-2004 the CASSINI spacecraft will perform three 40 days data acquisition runs with expected sensitivity about twenty times better than that achieved so far. Central aims of this paper are: (i) to explore, as a function of the relevant instrumental and astrophysical parameters, the Doppler output produced by in-spiral signals -- sinusoids of increasing frequency and amplitude (the so-called chirp); (ii) to identify the most important parameter regions where to concentrate intense and dedicated data analysis; (iii) to analyze the all-sky and all-frequency sensitivity of the CASSINI's experiments, with particular emphasis on possible astrophysical targets, such as our Galactic Centre and the Virgo Cluster.Comment: 52 pages, LaTeX, 19 Postscript Figures, submitted to Phys. Rev.

c-Myc regulates transcriptional pause release

Recruitment of the RNA polymerase II (Pol II) transcription initiation apparatus to promoters by specific DNA-binding transcription factors is well recognized as a key regulatory step in gene expression. We report here that promoter-proximal pausing is a general feature of transcription by Pol II in mammalian cells and thus an additional step where regulation of gene expression occurs. This suggests that some transcription factors recruit the transcription apparatus to promoters, whereas others effect promoter-proximal pause release. Indeed, we find that the transcription factor c-Myc, a key regulator of cellular proliferation, plays a major role in Pol II pause release rather than Pol II recruitment at its target genes. We discuss the implications of these results for the role of c-Myc amplification in human cancer.National Institutes of Health (U.S.) (Grant number RO1-HG002668)National Institutes of Health (U.S.) (Grant number RO1-GM34277)National Institutes of Health (U.S.) (Grant number RO1-CA133404)National Cancer Institute (U.S.) (Grant Number PO1- CA42063)National Cancer Institute (U.S.) Cancer Center Support Grant (Grant Number P30-CA14051)National Institutes of Health (U.S.) Postdoctoral Fellowship (5-F32-HD051190