3,896 research outputs found
Regularization of the second-order gravitational perturbations produced by a compact object
The equations for the second-order gravitational perturbations produced by a
compact-object have highly singular source terms at the point particle limit.
At this limit the standard retarded solutions to these equations are
ill-defined. Here we construct well-defined and physically meaningful solutions
to these equations. These solutions are important for practical calculations:
the planned gravitational-wave detector LISA requires preparation of waveform
templates for the potential gravitational-waves. Construction of templates with
desired accuracy for extreme mass ratio binaries, in which a compact-object
inspirals towards a supermassive black-hole, requires calculation of the
second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid
Communicatio
Construction of the second-order gravitational perturbations produced by a compact object
Accurate calculation of the gradual inspiral motion in an extreme mass-ratio
binary system, in which a compact-object inspirals towards a supermassive
black-hole requires calculation of the interaction between the compact-object
and the gravitational perturbations that it induces. These metric perturbations
satisfy linear partial differential equations on a curved background spacetime
induced by the supermassive black-hole. At the point particle limit the
second-order perturbations equations have source terms that diverge as
, where is the distance from the particle. This singular behavior
renders the standard retarded solutions of these equations ill-defined. Here we
resolve this problem and construct well-defined and physically meaningful
solutions to these equations. We recently presented an outline of this
resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the
full details of this analysis. These second-order solutions are important for
practical calculations: the planned gravitational-wave detector LISA requires
preparation of waveform templates for the expected gravitational-waves.
Construction of templates with desired accuracy for extreme mass-ratio binaries
requires accurate calculation of the inspiral motion including the interaction
with the second-order gravitational perturbations.Comment: 30 page
The possible statistical relation of Pc1 pulsations to Earthquake occurrence at low latitudes
We examine the association between earthquakes and Pc1 pulsations observed at a low-latitude station in Parkfield, California. The period under examination is ~7.5 years in total, from February 1999 to July 2006, and we use an automatic identification algorithm to extract information on Pc1 pulsations from the magnetometer data. These pulsations are then statistically correlated to earthquakes from the USGS NEIC catalog within a radius of 200 km around the magnetometer, and <I>M</I>&gt;3.0. Results indicate that there is an enhanced occurrence probability of Pc1 pulsations ~5–15 days in advance of the earthquakes, during the daytime. We quantify the statistical significance and show that such an enhancement is unlikely to have occurred due to chance alone. We then examine the effect of declustering our earthquake catalog, and show that even though significance decreases, there is still a statistically significant daytime enhancement prior to the earthquakes. Finally, we select only daytime Pc1 pulsations as the fiducial time of our analysis, and show that earthquakes are ~3–5 times more likely to occur in the week following these pulsations, than normal. Comparing these results to other events, it is preliminarily shown that the normal earthquake probability is unaffected by geomagnetic activity, or a random event sequence
Recovering the stationary phase condition for accurately obtaining scattering and tunneling times
The stationary phase method is often employed for computing tunneling {\em
phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth
step pulses which collide with a potential barrier. The indiscriminate
utilization of this method without considering the barrier boundary effects
leads to some misconceptions in the interpretation of the phase times. After
reexamining the above barrier diffusion problem where we notice the wave packet
collision necessarily leads to the possibility of multiple reflected and
transmitted wave packets, we study the phase times for tunneling/reflecting
particles in a framework where an idea of multiple wave packet decomposition is
recovered. To partially overcome the analytical incongruities which rise up
when tunneling phase time expressions are obtained, we present a theoretical
exercise involving a symmetrical collision between two identical wave packets
and a one dimensional squared potential barrier where the scattered wave
packets can be recomposed by summing the amplitudes of simultaneously reflected
and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl
Celestial mechanics in Kerr spacetime
The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy , the axial component of the
angular momentum, , and Carter's constant . These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies , and associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum , the eccentricity or
the inclination parameter are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra
A Bayesian approach to the follow-up of candidate gravitational wave signals
Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo
and Tama-300) have now reached high sensitivity and duty cycle. We present a
Bayesian evidence-based approach to the search for gravitational waves, in
particular aimed at the followup of candidate events generated by the analysis
pipeline. We introduce and demonstrate an efficient method to compute the
evidence and odds ratio between different models, and illustrate this approach
using the specific case of the gravitational wave signal generated during the
inspiral phase of binary systems, modelled at the leading quadrupole Newtonian
order, in synthetic noise. We show that the method is effective in detecting
signals at the detection threshold and it is robust against (some types of)
instrumental artefacts. The computational efficiency of this method makes it
scalable to the analysis of all the triggers generated by the analysis
pipelines to search for coalescing binaries in surveys with ground-based
interferometers, and to a whole variety of signal waveforms, characterised by a
larger number of parameters.Comment: 9 page
Radiative multipole moments of integer-spin fields in curved spacetime
Radiative multipole moments of scalar, electromagnetic, and linearized
gravitational fields in Schwarzschild spacetime are computed to third order in
v in a weak-field, slow-motion approximation, where v is a characteristic
velocity associated with the motion of the source. To zeroth order in v, a
radiative moment of order l is given by the corresponding source moment
differentiated l times with respect to retarded time. At second order in v,
additional terms appear inside the spatial integrals. These are near-zone
corrections which depend on the detailed behavior of the source. At third order
in v, the correction terms occur outside the spatial integrals, so that they do
not depend on the detailed behavior of the source. These are wave-propagation
corrections which are heuristically understood as arising from the scattering
of the radiation by the spacetime curvature surrounding the source. Our
calculations show that the wave-propagation corrections take a universal form
which is independent of multipole order and field type. We also show that in
general relativity, temporal and spatial curvatures contribute equally to the
wave-propagation corrections.Comment: 34 pages, ReVTe
Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates
We ascertain the effectiveness of the second post-Newtonian approximation to
the gravitational waves emitted during the adiabatic inspiral of a compact
binary system as templates for signal searches with kilometer-scale
interferometric detectors. The reference signal is obtained by solving the
Teukolsky equation for a small mass moving on a circular orbit around a large
nonrotating black hole. Fitting factors computed from this signal and these
templates, for various types of binary systems, are all above the 90% mark.
According to Apostolatos' criterion, second post-Newtonian waveforms should
make acceptably effective search templates.Comment: LaTeX, one eps figure. Hires and color versions are available from
http://jovian.physics.uoguelph.ca/~droz/uni/papers/search.htm
Colliding Black Holes: The Close Limit
The problem of the mutual attraction and joining of two black holes is of
importance as both a source of gravitational waves and as a testbed of
numerical relativity. If the holes start out close enough that they are
initially surrounded by a common horizon, the problem can be viewed as a
perturbation of a single black hole. We take initial data due to Misner for
close black holes, apply perturbation theory and evolve the data with the
Zerilli equation. The computed gravitational radiation agrees with and extends
the results of full numerical computations.Comment: 4 pages, Revtex, 3 postscript figures included, CGPG-94/2-
Expanding the Capability of Satellite Operations using a Global Federated Ground Station Network
Small-scale spaceflight programs such as those found at universities and start-up companies may operate satellites from a single ground station. This station’s location may not be optimal for radio communications, and a single station limits the contact time available to conduct operations. The idea of a global federated ground station network (FGN) has been theorized in the past, and with today’s wide-spread internet connectivity it is now possible for such a network to exist. One example of an FGN that is functioning today is an open-source project called SatNOGS. The Michigan eXploration Laboratory (MXL) at the University of Michigan has applied the benefits of this network to enhance operations of their Tandem Beacon Experiment (TBEx) CubeSat mission by gathering 2.2x the beacons gathered by their home station alone. 93% of those additional beacons were collected by six SatNOGS stations. Augmenting MXL’s home station with these six stations increases access time to the TBEx satellites by a factor of 5 to15. This increased temporal coverage also enabled MXL operators to identify their spacecraft after deployment and correct an error causing the TBEx radios to function intermittently, saving the mission in its earliest days
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