Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session M12: Gravitational Waveforms from Inspiralling Binaries |
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Sponsoring Units: GGR Chair: Shane L. Larson, Weber State University Room: Hyatt Regency Jacksonville Riverfront City Terrace 8 |
Sunday, April 15, 2007 3:15PM - 3:27PM |
M12.00001: Evolution of the Carter constant for inspirals into a black hole: effects of the quadrupole and quadratic in spin Tanja Hinderer, Eanna Flanagan The inspiral of stellar mass compact objects into massive black holes are an important source for future gravitational wave detectors such as LISA and Advanced LIGO. The detection of these sources relies on the accurate modeling of the binary dynamics. Crude approximate waveforms can be computed using post-Newtonian methods. We analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment $Q$ to linear order in $Q$, to the leading post-Newtonian order, and to linear order in the mass ratio. This system admits three constants of the motion in absence of radiation reaction: energy, angular momentum along the symmetry axis, and a third constant analogous to the Carter constant. We compute instantaneous and time-averaged rates of change of the three constants. For a Kerr black hole, the quadrupole is related to the spin parameter $a=S/M^2$ by $Q=-a^2M^3$. Our results, when combined with an interaction quadratic in the spin (the backscattering of the radiation off the piece of spacetime curvature due to the black hole's spin), gives the next to leading order evolution of the Carter constant, the leading order term being linear in the spin was previously computed by Ryan. [Preview Abstract] |
Sunday, April 15, 2007 3:27PM - 3:39PM |
M12.00002: Gravitational radiation reaction for inspiralling binaries - spin-spin effects to 3.5 post-Newtonian order Han Wang, Clifford M. Will Spin may play an important role in the inspiral of compact binary systems and may have observable effects on the gravitational wave signal emitted. Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)5] and O[(v/c)7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that not like the spin-orbit coupling, which has not effect on spin at this order, there is a 3.5PN order spin-spin induced precession to the individual spin. Using the equations of motion and the spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al. [Preview Abstract] |
Sunday, April 15, 2007 3:39PM - 3:51PM |
M12.00003: Spin-orbit Gravitational Radiation Reaction for Two-body Systems Jing Zeng, Clifford Will We study gravitational radiation reaction in the equations of motion for binary systems with spinning bodies up to post$^{7/2}$-Newtonian order. We write down the most general expression for spin-orbit radiation reaction terms in the binary equations of motion and in the spin evolution equations, and use energy and angular momentum balance and the expressions for energy and angular momentum flux in the far-zone to the desired order to fix a set of arbitrary coefficients. We show that the residual freedom in the undetermined coefficients corresponds to the effects of gauge or coordinate freedom at 3.5PN order. [Preview Abstract] |
Sunday, April 15, 2007 3:51PM - 4:03PM |
M12.00004: Mapping spacetime geometry with gravitational wave observatories Chao Li, Geoffrey Lovelace We consider the gravitational waves emitted from an extreme mass ratio inspiral (EMRI) system that consists of a small object (the ``moon") orbiting a massive body whose metric is stationary, axisymmetric, reflectional symmetric and asymptotically flat (SARSAF). Numerical experiments suggest that the moon moves in a multi-periodic orbit; this may be due to the KAM theorem. We show that the emitted waves can be expanded into a discrete Fourier series with three fundamental frequencies that evolve slowly due to radiation reaction. A previous study (\emph{Ryan's theorem} Phys. Rev. D {\bf 52} 5707 (1995)) showed how to extract the spacetime metric from these evolving frequencies, assuming a nearly circular, nearly equatorial orbit. We generalize this theorem in two ways: We show that (i) for nearly circular, nearly equatorial orbits the moon's evolving orbital elements and its tidal coupling to the central body can be extracted along with the metric (joint work with Geoffrey Lovelace), and (ii) if the orbit has substantial eccentricity, the metric can still be extracted. We also argue that generalizing Ryan's theorem to generic orbits will require details of wave generation theory. [Preview Abstract] |
Sunday, April 15, 2007 4:03PM - 4:15PM |
M12.00005: Approximate methods for building extreme mass ratio inspiral waveforms Scott Hughes The ``extreme mass ratio inspiral'' (or EMRI) problem has captured much attention in recent years. This is due to its relevance at describing a potentially important gravitational-wave source, and to the elegance of techniques which are being developed to solve it. A complete, self-consistent solution to this problem will require detailed knowledge of the self-interaction of a small body orbiting a Kerr black hole, taken (at least in part) to second order. This challenge will consume much time and effort. In the meantime, there is an exigent need for waveforms which, though not correct in all details, are sufficiently reliable that they can be used to understand how to measure these waves with space-based gravitational-wave antennae. I will describe in this talk results from a crude but surprisingly effective ``kludge'' approximation. The kludge produces waves which match well with available strong-field results, requiring only a fraction of the computational effort. Motivated by how the kludge operates, I will argue that a good medium between the kludge and the full solution is a ``hybrid'' approach to waveform generation. This hybrid combines the best features of both time and frequency domain approaches to black hole perturbation theory, using them to make EMRI waves that are as accurate as is possible without incorporating self-force information. [Preview Abstract] |
Sunday, April 15, 2007 4:15PM - 4:27PM |
M12.00006: Accurate time--domain gravitational waveforms for extreme-mass-ratio binaries Gaurav Khanna, Lior M. Burko The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in Schwarzschild and Kerr, we find agreement to within 1\% or better, which may be even further improved. This improvement is with respect to previously reported deviations of 10--20\% in the energy flux. We apply our method to orbits for which frequency-domain calculations have a relative disadvantage (namely, summation over very many modes would be required), specifically high-eccentricity (elliptical and parabolic) ``zoom--whirl" orbits, and find the energy fluxes, waveforms, and characteristic strain in gravitational waves. Our calculations maintain the desired accuracy also for orbits in the strong field regime. This proof-of-concept work demonstrates that time-domain generation of waveforms can be accurate and computationally efficient, and can complement frequency-domain calculations where the latter have relative disadvantages, in addition to providing an independent check on them. Further improvements in particle modeling, non-uniform grids (including adaptive mesh refinement), and parallel computation, in addition to grid refinement and enlargement of the computational domain, may improve the accuracy even further. [Preview Abstract] |
Sunday, April 15, 2007 4:27PM - 4:39PM |
M12.00007: Gravitational waves from extreme mass ratio inspirals: A numerical model for the singular source term in the time domain Pranesh Adhyam Sundararajan, Gaurav Khanna Radiation from a point particle orbiting and thus perturbing a massive black hole is a promising source of gravitational waves. The Teukolsky perturbation equation contains the Dirac-delta function and its derivatives when specialized to represent a point particle. We present a model to discretize the delta function (and its derivatives) and thus solve the equation as a (2+1) PDE on a numerical grid in the time domain. The derivation of this model is motivated by preserving the discrete versions of the integral properties of the delta function and its derivatives. We present gravitational waveforms and energy fluxes calculated at a point far from the horizon. Where comparisons are possible, these numerically extracted fluxes are accurate to within 1$\%$ of earlier work. Comparisons with earlier source models show an order of magnitude gain in speed (performance). In the near future, we intend to use this numerical laboratory to study gravitational wave emission from astrophysically realistic binary systems. [Preview Abstract] |
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