Manuel Tessmer

Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling

This paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by Koenigsdoerffer and Gopakumar [Phys. Rev. D 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasicircular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.

Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin?orbit and leading order in spin(1)?spin(2) and spin-squared couplings

A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next- to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin-orbit and 1PN spin-spin contributions, whereby the spins are assumed to be of 0PN order.

Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders

In this paper, the quasi-Keplerian parameterization for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin–orbit, next-to-next-to-leading order spin(1)–spin(2) and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity-type variable x.

Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy

The article provides full-analytical gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. We avoid, for the first time, the semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic. The article is a completion of a previous article (Tessmer and Schafer, 2010. arXiv:1006.3714) to second post-Newtonian (2PN) order in the harmonic GW amplitude and conservative orbital dynamics. The GW amplitudes are given in spherical tensor components. A fully analytical inversion formula of the Kepler equation in harmonic coordinates is provided, as well as the analytic time Fourier expansion of trigonometric functions of the eccentric anomaly in terms of sines and cosines of the mean anomaly. Copyright line will be provided by the publisher

Accurate and efficient gravitational waveforms for certain galactic compact binaries

Stellar-mass compact binaries in eccentric orbits are almost guaranteed sources of gravitational waves for the Laser Interferometer Space Antenna. We present a prescription to compute accurate and efficient gravitational-wave polarizations associated with bound compact binaries of arbitrary eccentricity and mass ratio moving in slowly precessing orbits. We compare our approach with those existing in the literature and present its advantages.

Full-analytic frequency-domain first-post-Newtonian-accurate gravitational wave forms from eccentric compact binaries

The post-Newtonian (pN) description of the dynamics of compact binary systems is the topic of actual research. Due to the strong nonspherically symmetric gravitational interactions, those objects are supposed to be “secure” sources for the detection of gravitational waves. Currently, LIGO, VIRGO, and GEO600 search for the last seconds or minutes in the life of those sources when the gravitational wave (GW) emission frequency enters the bandwith of the mentioned detectors. The computer resources – in contrast – are currently unable to create numerical GW templates for the early stage of the binary inspiral (this case is important for LISA), where hundreds or even thousands of GW cycles have to be simulated which makes it necessary to propose an analytical prescription of the orbital evolution, and in the case of spinning compact binaries, the spin evolution as well. An equally essential ingredient of the GW data analysis is the transformation of the GW signal into the frequency domain. There exist numerous more or less optimized numerical routines to convert the time domain signal into the frequency or Fourier domain. To economize on computer resources, it is also reasonable and desirable to provide analytical Fourier domain wave forms for the data analysis community. Numerous authors have investigated the performance of circular inspiral templates and their analytical Fourier-domain pendant, which have been set up to a certain standard in the literature thanks to the work of Damour, Blanchet and Iyer to compute higher pN order corrections to the GW energy loss [1–4].

Gravitational waves from compact binaries inspiralling along post-Newtonian accurate eccentric orbits: Data analysis implications

Compact binaries inspiralling along eccentric orbits are plausible gravitational-wave (GW) sources for the ground-based laser interferometers. We explore the losses in the event rates incurred when searching for GWs from compact binaries inspiralling along post-Newtonian accurate eccentric orbits with certain obvious nonoptimal search templates. For the present analysis, GW signals having 2.5 post-Newtonian (PN) accurate orbital evolution are modeled following the phasing formalism, presented by T. Damour, A. Gopakumar, and B. R. Iyer [Phys. Rev. D 70, 064028 (2004)]. We demonstrate that the search templates that model in a gauge-invariant manner GWs from compact binaries inspiralling under quadrupolar radiation reaction along 2PN accurate circular orbits are very efficient in capturing our somewhat realistic GW signals. However, three types of search templates based on the adiabatic, complete adiabatic, and gauge-dependent complete nonadiabatic approximants, detailed in P. Ajith, B. R. Iyer, C. A. K. Robinson, and B. S. Sathyaprakash, Phys. Rev. D 71, 044029 (2005), relevant for the circular inspiral under the quadrupolar radiation reaction were found to be inefficient in capturing the above-mentioned eccentric signal. We conclude that further investigations will be required to probe the ability of various types of PN accurate circular templates, employed to analyze the LIGO/VIRGO data, to capture GWs from compact binaries having tiny orbital eccentricities.

Generalized propagation of light through optical systems. I. Mathematical basics.

The propagation of an input field through tilted and curved surfaces is presented and applied for a field tracing routine. This routine employs a ray tracing method for optimal coordinate customization, which is done due to the strong linear phase terms that arise because of tilted coordinates on one hand and the possibility of an application of fast numerical routines on the other. Several methods are proposed on how to optimize the field sampling during the propagation process, as for the astigmatic phase front problem and the curvature of the surface itself. Two solution methods are given to propagate from the curved surface through the homogeneous space to another two-dimensional submanifold. The approach is fully vectorial, Maxwell exact excluding only surface curvature terms for the Fresnel coefficients. A simple numerical propagation example is given.

Eccentric motion of spinning compact binaries

The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theory easily treatable.

Generalized propagation of light through optical systems. II. Numerical implications.

We present an algorithm implemented in a MATLAB toolbox that is able to compute the wave propagation of coherent visible light through macroscopic lenses. The mathematical operations that complete the status at the end of the first paper of this sequence, where only limited configurations of the propagation direction were allowed toward arbitrarily directed input beam computations, are provided. With their help, high numerical aperture (NA) field tracing is made possible that is based on fast Fourier routines and is Maxwell exact in the limit of macroscopic structures and large curvature radii, including reflection and transmission. Whereas the curvature-dependent terms in the Helmholtz equation are under analytical control through the first perturbation order in the curvature, they are only included in the propagation distance in the current investigation for the sake of reasonable time consumption. We give a number of examples that demonstrate the strengths of our approach, describe essential differences from other approaches that were not obvious when Paper 1 was written, and list a number of drawbacks and possible simplifications to overcome them.