231 research outputs found
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
The Effect of the LISA Response Function on Observations of Monochromatic Sources
The Laser Interferometer Space Antenna (LISA) is expected to provide the
largest observational sample of binary systems of faint sub-solar mass compact
objects, in particular white-dwarfs, whose radiation is monochromatic over most
of the LISA observational window. Current astrophysical estimates suggest that
the instrument will be able to resolve about 10000 such systems, with a large
fraction of them at frequencies above 3 mHz, where the wavelength of
gravitational waves becomes comparable to or shorter than the LISA arm-length.
This affects the structure of the so-called LISA transfer function which cannot
be treated as constant in this frequency range: it introduces characteristic
phase and amplitude modulations that depend on the source location in the sky
and the emission frequency. Here we investigate the effect of the LISA transfer
function on detection and parameter estimation for monochromatic sources. For
signal detection we show that filters constructed by approximating the transfer
function as a constant (long wavelength approximation) introduce a negligible
loss of signal-to-noise ratio -- the fitting factor always exceeds 0.97 -- for
f below 10mHz, therefore in a frequency range where one would actually expect
the approximation to fail. For parameter estimation, we conclude that in the
range 3mHz to 30mHz the errors associated with parameter measurements differ
from about 5% up to a factor of 10 (depending on the actual source parameters
and emission frequency) with respect to those computed using the long
wavelength approximation.Comment: replacement version with typos correcte
Relativistic Stellar Pulsations With Near-Zone Boundary Conditions
A new method is presented here for evaluating approximately the pulsation
modes of relativistic stellar models. This approximation relies on the fact
that gravitational radiation influences these modes only on timescales that are
much longer than the basic hydrodynamic timescale of the system. This makes it
possible to impose the boundary conditions on the gravitational potentials at
the surface of the star rather than in the asymptotic wave zone of the
gravitational field. This approximation is tested here by predicting the
frequencies of the outgoing non-radial hydrodynamic modes of non-rotating
stars. The real parts of the frequencies are determined with an accuracy that
is better than our knowledge of the exact frequencies (about 0.01%) except in
the most relativistic models where it decreases to about 0.1%. The imaginary
parts of the frequencies are determined with an accuracy of approximately M/R,
where M is the mass and R is the radius of the star in question.Comment: 10 pages (REVTeX 3.1), 5 figs., 1 table, fixed minor typos, published
in Phys. Rev. D 56, 2118 (1997
Gravitational Waves from coalescing binaries: Estimation of parameters
The paper presents a statistical model which reproduces the results of Monte
Carlo simulations to estimate the parameters of the gravitational wave signal
from a coalesing binary system. The model however is quite general and would be
useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure
Propagation of gravitational waves from slow motion sources in a Coulomb type potential
We consider the propagation of gravitational waves generated by slow motion
sources in Coulomb type potential due to the mass of the source. Then, the
formula for gravitational waveform including tail is obtained in a
straightforward manner by using the spherical Coulomb function. We discuss its
relation with the formula in the previous work.Comment: 13 pages, no figures, to be published in Phys. Rev.
Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies
Post-Newtonian expansions of the binding energy and gravitational wave flux
truncated at the {\it same relative} post-Newtonian order form the basis of the
{\it standard adiabatic} approximation to the phasing of gravitational waves
from inspiralling compact binaries. Viewed in terms of the dynamics of the
binary, the standard approximation is equivalent to neglecting certain
conservative post-Newtonian terms in the acceleration. In an earlier work, we
had proposed a new {\it complete adiabatic} approximant constructed from the
energy and flux functions. At the leading order it employs the 2PN energy
function rather than the 0PN one in the standard approximation, so that,
effectively the approximation corresponds to the dynamics where there are no
missing post-Newtonian terms in the acceleration. In this paper, we compare the
overlaps of the standard and complete adiabatic templates with the exact
waveform in the adiabatic approximation of a test-mass motion in the
Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It
is found that the complete adiabatic approximants lead to a remarkable
improvement in the {\it effectualness} at lower PN ( 3PN) orders, while
standard approximants of order 3PN provide a good lower-bound to the
complete approximants for the construction of effectual templates. {\it
Faithfulness} of complete approximants is better than that of standard
approximants except for a few post-Newtonian orders. Standard and complete
approximants beyond the adiabatic approximation are also studied using the
Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant.
Gra
Components of the gravitational force in the field of a gravitational wave
Gravitational waves bring about the relative motion of free test masses. The
detailed knowledge of this motion is important conceptually and practically,
because the mirrors of laser interferometric detectors of gravitational waves
are essentially free test masses. There exists an analogy between the motion of
free masses in the field of a gravitational wave and the motion of free charges
in the field of an electromagnetic wave. In particular, a gravitational wave
drives the masses in the plane of the wave-front and also, to a smaller extent,
back and forth in the direction of the wave's propagation. To describe this
motion, we introduce the notion of `electric' and `magnetic' components of the
gravitational force. This analogy is not perfect, but it reflects some
important features of the phenomenon. Using different methods, we demonstrate
the presence and importance of what we call the `magnetic' component of motion
of free masses. It contributes to the variation of distance between a pair of
particles. We explicitely derive the full response function of a 2-arm laser
interferometer to a gravitational wave of arbitrary polarization. We give a
convenient description of the response function in terms of the spin-weighted
spherical harmonics. We show that the previously ignored `magnetic' component
may provide a correction of up to 10 %, or so, to the usual `electric'
component of the response function. The `magnetic' contribution must be taken
into account in the data analysis, if the parameters of the radiating system
are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional
explanations and references in response to referee's comments, to be
published in Class. Quant. Gra
Angular Resolution of the LISA Gravitational Wave Detector
We calculate the angular resolution of the planned LISA detector, a
space-based laser interferometer for measuring low-frequency gravitational
waves from galactic and extragalactic sources. LISA is not a pointed
instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will
measure simultaneously both polarization components of incoming gravitational
waves, so the data will consist of two time series. All physical properties of
the source, including its position, must be extracted from these time series.
LISA's angular resolution is therefore not a fixed quantity, but rather depends
on the type of signal and on how much other information must be extracted.
Information about the source position will be encoded in the measured signal in
three ways: 1) through the relative amplitudes and phases of the two
polarization components, 2) through the periodic Doppler shift imposed on the
signal by the detector's motion around the Sun, and 3) through the further
modulation of the signal caused by the detector's time-varying orientation. We
derive the basic formulae required to calculate the LISA's angular resolution
for a given source. We then evaluate for
two sources of particular interest: monchromatic sources and mergers of
supermassive black holes. For these two types of sources, we calculate (in the
high signal-to-noise approximation) the full variance-covariance matrix, which
gives the accuracy to which all source parameters can be measured. Since our
results on LISA's angular resolution depend mainly on gross features of the
detector geometry, orbit, and noise curve, we expect these results to be fairly
insensitive to modest changes in detector design that may occur between now and
launch. We also expect that our calculations could be easily modified to apply
to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil
The Cosmological Constant and Advanced Gravitational Wave Detectors
Interferometric gravitational wave detectors could measure the frequency
sweep of a binary inspiral [characterized by its chirp mass] to high accuracy.
The observed chirp mass is the intrinsic chirp mass of the binary source
multiplied by , where is the redshift of the source. Assuming a
non-zero cosmological constant, we compute the expected redshift distribution
of observed events for an advanced LIGO detector. We find that the redshift
distribution has a robust and sizable dependence on the cosmological constant;
the data from advanced LIGO detectors could provide an independent measurement
of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear
in Phys. Rev.
Gravitational Radiation Instability in Hot Young Neutron Stars
We show that gravitational radiation drives an instability in hot young
rapidly rotating neutron stars. This instability occurs primarily in the l=2
r-mode and will carry away most of the angular momentum of a rapidly rotating
star by gravitational radiation. On the timescale needed to cool a young
neutron star to about T=10^9 K (about one year) this instability can reduce the
rotation rate of a rapidly rotating star to about 0.076\Omega_K, where \Omega_K
is the Keplerian angular velocity where mass shedding occurs. In older colder
neutron stars this instability is suppressed by viscous effects, allowing older
stars to be spun up by accretion to larger angular velocities.Comment: 4 Pages, 2 Figure
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