"Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole

One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such "extreme mass ratio inspiral" systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such "kludge" waveforms and describe ways to generate them. We assess performance of the introduced approximations by comparing "kludge" waveforms to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs.Comment: 29 pages, 11 figures, requires subeqnarray; v2 contains minor changes for consistency with published versio

Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential

We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful to study the inner properties of disk not confined to the equatorial plane where general relativistic effect is indispensable. Therefore, we incorporate the essential properties of the metric at the inner radii through the pseudo-Newtonian potential derived from the general Kerr spacetime. The potential, reproducing most of the salient features of the general-relativity, is valid for entire regime of Kerr parameter. It reproduces the last stable circular orbit exactly as that in the Kerr geometry. It also reproduces last bound orbit and energy at last stable circular orbit with a maximum error ~7% and ~15% respectively upto an orbital inclination 30 degree.Comment: 22 AASTeX pages including 5 postscript figures; Accepted for publication in The Astrophysical Journa

Constructing Gravitational Waves from Generic Spin-Precessing Compact Binary Inspirals

The coalescence of compact objects is one of the most promising sources of gravitational waves for ground-based interferometric detectors, such as advanced LIGO and Virgo. Generically, com- pact objects in binaries are expected to be spinning with spin angular momenta misaligned with the orbital angular momentum, causing the orbital plane to precess. This precession adds rich structure to the gravitational waves, introducing such complexity that an analytic closed-form description has been unavailable until now. We here construct the first closed-form frequency- domain gravitational waveforms that are valid for generic spin-precessing quasicircular compact binary inspirals. We first construct time-domain gravitational waves by solving the post-Newtonian precession equations of motion with radiation reaction through multiple scale analysis. We then Fourier transform these time-domain waveforms with the method of shifted uniform asymptotics to obtain closed-form expressions for frequency-domain waveforms. We study the accuracy of these analytic, frequency-domain waveforms relative to waveforms obtained by numerically evolving the post-Newtonian equations of motion and find that they are suitable for unbiased parameter estimation for 99.2%(94.6%) of the binary configurations we studied at a signal-to-noise ratio of 10(25). These new frequency-domain waveforms could be used for detection and parameter estimation studies due to their accuracy and low computational cost.Comment: 21 pages, final published versio

Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects

The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent theoretical challenges facing GW astronomy. This article briefly reviews the phenomenology of generic-binary dynamics and waveforms, and recent advances in modelling them.Comment: Invited review for General Relativity and Gravitatio

Emergence of macroscopic directed motion in populations of motile colloids

From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales populations of motile organisms display coherent collective motion. This consistent behavior strongly contrasts with the difference in communication abilities between the individuals. Guided by this universal feature, physicists have proposed that solely alignment rules at the individual level could account for the emergence of unidirectional motion at the group level. This hypothesis has been supported by agent-based simulations. However, more complex collective behaviors have been systematically found in experiments including the formation of vortices, fluctuating swarms, clustering and swirling. All these model systems predominantly rely on actual collisions to display collective motion. As a result, the potential local alignment rules are entangled with more complex, often unknown, interactions. The large-scale behavior of the populations therefore depends on these uncontrolled microscopic couplings. Here, we demonstrate a new phase of active matter. We reveal that dilute populations of millions of colloidal rollers self-organize to achieve coherent motion along a unique direction, with very few density and velocity fluctuations. Identifying the microscopic interactions between the rollers allows a theoretical description of this polar-liquid state. Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic flock at low densities, or in that of a homogenous polar phase at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations. Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion

Effects of Transport Delays of Manual Control System Performance

Throughput or transport delays in manual control systems can cause degraded performance and lead to potentially unstable operation. With the expanding use of digital processors, throughput delays can occur in manual control systems in a variety of ways such as in digital flight control systems in real aircraft, and in equation of motion computers and computer generated images in simulators. Research has shown the degrading effect of throughput delays on subjective opinion and system performance and dynamic response. A generic manual control system model is used to provide a relatively simple analysis of and explanation for the effects of various types of delays. The consequence of throughput delays of some simple system architectures is also discussed

On-orbit assembly using superquadric potential fields

The autonomous on-orbit assembly of a large space structure is presented using a method based on superquadric artificial potential fields. The final configuration of the elements which form the structure is represented as the minimum of some attractive potential field. Each element of the structure is then considered as presenting an obstacle to the others using a superquadric potential field attached to the body axes of the element. A controller is developed which ensures that the global potential field decreases monotonically during the assembly process. An error quaternion representation is used to define both the attractive and superquadric obstacle potentials allowing the final configuration of the elements to be defined through both relative position and orientation. Through the use of superquadric potentials, a wide range of geometric objects can be represented using a common formalism, while collision avoidance can make use of both translational and rotation maneuvers to reduce total maneuver cost for the assembly process