5,358 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
Compression of Martian atmosphere for production of oxygen
The compression of CO2 from the Martian atmosphere for production of O2 via an electrochemical cell is addressed. Design specifications call for an oxygen production rate of 10 kg per day and for compression of 50 times that mass of CO2. Those specifications require a compression rate of over 770 cfm at standard Martian temperature and pressure (SMTP). Much of the CO2 being compressed represents waste, unless it can be recycled. Recycling can reduce the volume of gas that must be compressed to 40 cfm at SMTP. That volume reduction represents significant mass savings in the compressor, heating equipment, filters, and energy source. Successful recycle of the gas requires separation of CO (produced in the electrochemical cell) from CO2, N2, and Ar found in the Martian atmosphere. That aspect was the focus of this work
Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling
Accurate calculation of the motion of a compact object in a background
spacetime induced by a supermassive black hole is required for the future
detection of such binary systems by the gravitational-wave detector LISA.
Reaching the desired accuracy requires calculation of the second-order
gravitational perturbations produced by the compact object. At the point
particle limit the second-order gravitational perturbation equations turn out
to have highly singular source terms, for which the standard retarded solutions
diverge. Here we study a simplified scalar toy-model in which a point particle
induces a nonlinear scalar field in a given curved spacetime. The corresponding
second-order scalar perturbation equation in this model is found to have a
similar singular source term, and therefore its standard retarded solutions
diverge. We develop a regularization method for constructing well-defined
causal solutions for this equation. Notably these solutions differ from the
standard retarded solutions, which are ill-defined in this case.Comment: 14 page
Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion
A particle of mass moves on a circular orbit around a nonrotating black
hole of mass . Under the assumption the gravitational waves
emitted by such a binary system can be calculated exactly numerically using
black-hole perturbation theory. If, further, the particle is slowly moving,
then the waves can be calculated approximately analytically, and expressed in
the form of a post-Newtonian expansion. We determine the accuracy of this
expansion in a quantitative way by calculating the reduction in signal-to-noise
ratio incurred when matched filtering the exact signal with a nonoptimal,
post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in
the computer code used to generate the results presented in the paper. The
corrected results are presented in an Erratum, which also incorporates new
results, obtained using the recently improved post-Newtonian calculations of
Tanaka, Tagoshi, and Sasak
Improved filters for gravitational waves from inspiralling compact binaries
The order of the post-Newtonian expansion needed, to extract in a reliable
and accurate manner the fully general relativistic gravitational wave signal
from inspiralling compact binaries, is explored. A class of approximate wave
forms, called P-approximants, is constructed based on the following two inputs:
(a) The introduction of two new energy-type and flux-type functions e(v) and
f(v), respectively, (b) the systematic use of Pade approximation for
constructing successive approximants of e(v) and f(v). The new P-approximants
are not only more effectual (larger overlaps) and more faithful (smaller
biases) than the standard Taylor approximants, but also converge faster and
monotonically. The presently available O(v/c)^5-accurate post-Newtonian results
can be used to construct P-approximate wave forms that provide overlaps with
the exact wave form larger than 96.5% implying that more than 90% of potential
events can be detected with the aid of P-approximants as opposed to a mere
10-15 % that would be detectable using standard post-Newtonian approximants.Comment: Latex ([prd,aps,eqsecnum,epsf]{revtex}), 40 pages including 12
encapsulated figures. (The paper, together with all the figures and tables is
available from ftp://carina.astro.cf.ac.uk/pub/incoming/sathya/dis97.uu
Measuring black-hole parameters and testing general relativity using gravitational-wave data from space-based interferometers
Among the expected sources of gravitational waves for the Laser
Interferometer Space Antenna (LISA) is the capture of solar-mass compact stars
by massive black holes residing in galactic centers. We construct a simple
model for such a capture, in which the compact star moves freely on a circular
orbit in the equatorial plane of the massive black hole. We consider the
gravitational waves emitted during the late stages of orbital evolution,
shortly before the orbiting mass reaches the innermost stable circular orbit.
We construct a simple model for the gravitational-wave signal, in which the
phasing of the waves plays the dominant role. The signal's behavior depends on
a number of parameters, including , the mass of the orbiting star, ,
the mass of the central black hole, and , the black hole's angular momentum.
We calculate, using our simplified model, and in the limit of large
signal-to-noise ratio, the accuracy with which these quantities can be
estimated during a gravitational-wave measurement. Our simplified model also
suggests a method for experimentally testing the strong-field predictions of
general relativity.Comment: ReVTeX, 16 pages, 5 postscript figure
Testing Alternative Theories of Gravity using LISA
We investigate the possible bounds which could be placed on alternative
theories of gravity using gravitational wave detection from inspiralling
compact binaries with the proposed LISA space interferometer. Specifically, we
estimate lower bounds on the coupling parameter \omega of scalar-tensor
theories of the Brans-Dicke type and on the Compton wavelength of the graviton
\lambda_g in hypothetical massive graviton theories. In these theories,
modifications of the gravitational radiation damping formulae or of the
propagation of the waves translate into a change in the phase evolution of the
observed gravitational waveform. We obtain the bounds through the technique of
matched filtering, employing the LISA Sensitivity Curve Generator (SCG),
available online. For a neutron star inspiralling into a 10^3 M_sun black hole
in the Virgo Cluster, in a two-year integration, we find a lower bound \omega >
3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6.
The bound is independent of LISA arm length, but is inversely proportional to
the LISA position noise error. Lower bounds on the graviton Compton wavelength
ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year
observations of massive binary black hole inspirals at cosmological distances
(3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass
systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and
to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent
of these parameters because of the dominance of white-dwarf confusion noise in
the relevant part of the frequency spectrum. These bounds improve and extend
earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit
LISA Response Function and Parameter Estimation
We investigate the response function of LISA and consider the adequacy of its
commonly used approximation in the high-frequency range of the observational
band. We concentrate on monochromatic binary systems, such as white dwarf
binaries. We find that above a few mHz the approxmation starts becoming
increasingly inaccurate. The transfer function introduces additional amplitude
and phase modulations in the measured signal that influence parameter estmation
and, if not properly accounted for, lead to losses of signal-to-noise ratio.Comment: 4 pages, 2 figures, amaldi 5 conference proceeding
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-
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