677 research outputs found
Geostationary earth climate sensor: Scientific utility and feasibility, phase A
The possibility of accurate broad band radiation budget measurements from a GEO platform will provide a unique opportunity for viewing radiation processes in the atmosphere-ocean system. The CSU/TRW team has prepared a Phase 1 instrument design study demonstrating that measurements of radiation budget are practical from geosynchronous orbit with proven technology. This instrument concept is the Geostationary Earth Climate Sensor (GECS). A range of resolutions down to 20 km at the top of the atmosphere are possible, depending upon the scientific goals of the experiment. These tradeoffs of resolution and measurement repeat cycles are examined for scientific utility. The design of a flexible instrument is shown to be possible to meet the two goals: long-term, systematic monitoring of the diurnal cycles of radiation budget; and high time and space resolution studies of regional radiation features
The Innermost Stable Circular Orbit of Binary Black Holes
We introduce a new method to construct solutions to the constraint equations
of general relativity describing binary black holes in quasicircular orbit.
Black hole pairs with arbitrary momenta can be constructed with a simple method
recently suggested by Brandt and Bruegmann, and quasicircular orbits can then
be found by locating a minimum in the binding energy along sequences of
constant horizon area. This approach produces binary black holes in a
"three-sheeted" manifold structure, as opposed to the "two-sheeted" structure
in the conformal-imaging approach adopted earlier by Cook. We focus on locating
the innermost stable circular orbit and compare with earlier calculations. Our
results confirm those of Cook and imply that the underlying manifold structure
has a very small effect on the location of the innermost stable circular orbit.Comment: 8 pages, 3 figures, RevTex, submitted to PR
Evolution systems for non-linear perturbations of background geometries
The formulation of the initial value problem for the Einstein equations is at
the heart of obtaining interesting new solutions using numerical relativity and
still very much under theoretical and applied scrutiny. We develop a
specialised background geometry approach, for systems where there is
non-trivial a priori knowledge about the spacetime under study. The background
three-geometry and associated connection are used to express the ADM evolution
equations in terms of physical non-linear deviations from that background.
Expressing the equations in first order form leads naturally to a system
closely linked to the Einstein-Christoffel system, introduced by Anderson and
York, and sharing its hyperbolicity properties. We illustrate the drastic
alteration of the source structure of the equations, and discuss why this is
likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in
Physical Review
3D simulations of linearized scalar fields in Kerr spacetime
We investigate the behavior of a dynamical scalar field on a fixed Kerr
background in Kerr-Schild coordinates using a 3+1 dimensional spectral
evolution code, and we measure the power-law tail decay that occurs at late
times. We compare evolutions of initial data proportional to f(r)
Y_lm(theta,phi) where Y_lm is a spherical harmonic and (r,theta,phi) are
Kerr-Schild coordinates, to that of initial data proportional to f(r_BL)
Y_lm(theta_BL,phi), where (r_BL,theta_BL) are Boyer-Lindquist coordinates. We
find that although these two cases are initially almost identical, the
evolution can be quite different at intermediate times; however, at late times
the power-law decay rates are equal.Comment: 12 pages, 9 figures, revtex4. Major revision: added figures, added
subsection on convergence, clarified discussion. To appear in Phys Rev
Einstein boundary conditions for the 3+1 Einstein equations
In the 3+1 framework of the Einstein equations for the case of vanishing
shift vector and arbitrary lapse, we calculate explicitly the four boundary
equations arising from the vanishing of the projection of the Einstein tensor
along the normal to the boundary surface of the initial-boundary value problem.
Such conditions take the form of evolution equations along (as opposed to
across) the boundary for certain components of the extrinsic curvature and for
certain space-derivatives of the intrinsic metric. We argue that, in general,
such boundary conditions do not follow necessarily from the evolution equations
and the initial data, but need to be imposed on the boundary values of the
fundamental variables. Using the Einstein-Christoffel formulation, which is
strongly hyperbolic, we show how three of the boundary equations should be used
to prescribe the values of some incoming characteristic fields. Additionally,
we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to
appear in Phys. Rev.
On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
We discuss the analytical determination of the location of the Last Stable
Orbit (LSO) in circular general relativistic orbits of two point masses. We use
several different ``resummation methods'' (including new ones) based on the
consideration of gauge-invariant functions, and compare the results they give
at the third post-Newtonian (3PN) approximation of general relativity. Our
treatment is based on the 3PN Hamiltonian of Jaranowski and Sch\"afer. One of
the new methods we introduce is based on the consideration of the (invariant)
function linking the angular momentum and the angular frequency. We also
generalize the ``effective one-body'' approach of Buonanno and Damour by
introducing a non-minimal (i.e. ``non-geodesic'') effective dynamics at the 3PN
level. We find that the location of the LSO sensitively depends on the
(currently unknown) value of the dimensionless quantity \oms which
parametrizes a certain regularization ambiguity of the 3PN dynamics. We find,
however, that all the analytical methods we use numerically agree between
themselves if the value of this parameter is \oms\simeq-9. This suggests that
the correct value of \oms is near -9 (the precise value
\oms^*\equiv-{47/3}+{41/64}\pi^2=-9.3439... seems to play a special role). If
this is the case, we then show how to further improve the analytical
determination of various LSO quantities by using a ``Shanks'' transformation to
accelerate the convergence of the successive (already resummed) PN estimates.Comment: REVTeX, 25 pages, 3 figures, submitted to Phys. Rev.
Ruling Out Chaos in Compact Binary Systems
We investigate the orbits of compact binary systems during the final inspiral
period before coalescence by integrating numerically the second-order
post-Newtonian equations of motion. We include spin-orbit and spin-spin
coupling terms, which, according to a recent study by Levin [J. Levin, Phys.
Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine
this claim, we study the divergence of initially nearby phase-space
trajectories and attempt to measure the Lyapunov exponent gamma. Even for
systems with maximally spinning objects and large spin-orbit misalignment
angles, we find no chaotic behavior. For all the systems we consider, we can
place a strict lower limit on the divergence time t_L=1/gamma that is many
times greater than the typical inspiral time, suggesting that chaos should not
adversely affect the detection of inspiral events by upcoming
gravitational-wave detectors.Comment: 8 pages, 4 figures, submitted to Phys. Rev. Let
Innermost Stable Circular Orbit of a Spinning Particle in Kerr Spacetime
We study stability of a circular orbit of a spinning test particle in a Kerr
spacetime. We find that some of the circular orbits become unstable in the
direction perpendicular to the equatorial plane, although the orbits are still
stable in the radial direction. Then for the large spin case ($S < \sim O(1)),
the innermost stable circular orbit (ISCO) appears before the minimum of the
effective potential in the equatorial plane disappears. This changes the radius
of ISCO and then the frequency of the last circular orbit.Comment: 25 pages including 8 figure
Non-precessional spin-orbit effects on gravitational waves from inspiraling compact binaries to second post-Newtonian order
We derive all second post-Newtonian (2PN), non-precessional effects of spin-
orbit coupling on the gravitational wave forms emitted by an inspiraling binary
composed of spinning, compact bodies in a quasicircular orbit. Previous post-
Newtonian calculations of spin-orbit effects (at 1.5PN order) relied on a fluid
description of the spinning bodies. We simplify the calculations by introducing
into post-Newtonian theory a delta-function description of the influence of the
spins on the bodies' energy-momentum tensor. This description was recently used
by Mino, Shibata, and Tanaka (MST) in Teukolsky-formalism analyses of particles
orbiting massive black holes, and is based on prior work by Dixon. We compute
the 2PN contributions to the wave forms by combining the MST energy-momentum
tensor with the formalism of Blanchet, Damour, and Iyer for evaluating the
binary's radiative multipoles, and with the well-known 1.5PN order equations of
motion for the binary. Our results contribute at 2PN order only to the
amplitudes of the wave forms. The secular evolution of the wave forms' phase,
the quantity most accurately measurable by LIGO, is not affected by our results
until 2.5PN order, at which point other spin-orbit effects also come into play.
We plan to evaluate the entire 2.5PN spin-orbit contribution to the secular
phase evolution in a future paper, using the techniques of this paper.Comment: 11 pages, submitted to Phys. Rev.
- …