357 research outputs found
New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation
We discuss a numerical method to compute the homogeneous solutions of the
Teukolsky equation which is the basic equation of the black hole perturbation
method. We use the formalism developed by Mano, Suzuki and Takasugi, in which
the homogeneous solutions of the radial Teukolsky equation are expressed in
terms of two kinds of series of special functions, and the formulas for the
asymptotic amplitudes are derived explicitly.Although the application of this
method was previously limited to the analytical evaluation of the homogeneous
solutions, we find that it is also useful for numerical computation. We also
find that so-called "renormalized angular momentum parameter", , can be
found only in the limited region of for each if we assume
is real (here, is the angular frequency, and and are degree
and order of the spin-weighted spheroidal harmonics respectively). We also
compute the flux of the gravitational waves induced by a compact star in a
circular orbit on the equatorial plane around a rotating black hole. We find
that the relative error of the energy flux is about which is much
smaller than the one obtained by usual numerical integration methods.Comment: 36 pages,7 figure
An Improved Search Method for Gravitational Ringing of Black Holes
A black hole has characteristic quasi-normal modes that will be excited when
it is formed or when the geometry is perturbed. The state of a black hole when
the quasi-normal modes are excited is called the gravitational ringing, and
detections of it will be a direct confirmation of the existence of black holes.
To detect it, a method based on matched filtering needs to be developed.
Generically, matched filtering requires a large number of templates, because
one has to ensure a proper match of a real gravitational wave with one of
template waveforms to keep the detection efficiency as high as possible. On the
other hand, the number of templates must be kept as small as possible under
limited computational costs. In our previous paper, assuming that the
gravitational ringing is dominated by the least-damped (fundamental) mode with
the least imaginary part of frequency, we constructed an efficient method for
tiling the template space. However, the dependence of the template space metric
on the initial phase of a wave was not taken into account. This dependence
arises because of an unavoidable mismatch between the parameters of a signal
waveform and those given discretely in the template space. In this paper, we
properly take this dependence into account and present an improved, efficient
search method for gravitational ringing of black holes.Comment: 19 pages, 9 figure
Coherent versus coincidence detection of gravitational wave signals from compact inspiraling binaries
We compare two multi-detector detection strategies, namely, the coincidence
and the coherent, for the detection of spinless inspiraling compact binary
gravitational wave signals. The coincident strategy treats the detectors as if
they are isolated - compares individual detector statistics with their
respective thresholds while the coherent strategy combines the detector network
data {\it phase coherently} to obtain a single detection statistic which is
then compared with a single threshold. In the case of geographically separated
detectors, we also consider an {\it enhanced} coincidence strategy because the
usual (naive) coincidence strategy yields poor results for misaligned
detectors. For simplicity, we consider detector pairs having the same power
spectral density of noise, as that of initial LIGO and also assume the noise to
be stationary and Gaussian. We compare the performances of the methods by
plotting the \emph{receiver operating characteristic} (ROC) for the two
strategies. A single astrophysical source as well as a distribution of sources
is considered. We find that the coherent strategy performs better than the two
coincident strategies under the assumptions of stationary Gaussian detector
noise.Comment: Based on the presentation at the 1st Galileo Xu Guangqi conference,
Shanghai
Magnification Probability Distribution Functions of Standard Candles in a Clumpy Universe
Lensing effects on light rays from point light sources, such like Type Ia
supernovae, are simulated in a clumpy universe model. In our universe model, it
is assumed that all matter in the universe takes the form of randomly
distributed objects each of which has finite size and is transparent for light
rays. Monte-Carlo simulations are performed for several lens models, and we
compute probability distribution functions of magnification. In the case of the
lens models that have a smooth density profile or the same degree of density
concentration as the spherical NFW (Navarro-Frenk-White) lens model at the
center, the so-called gamma distributions fit well the magnification
probability distribution functions if the size of lenses is sufficiently larger
than the Einstein radius. In contrast, the gamma distributions do not fit the
magnification probability distribution functions in the case of the SIS
(Singular Isothermal Sphere) lens model. We find, by using the power law cusp
model, that the magnification probability distribution function is fitted well
using the gamma distribution only when the slope of the central density profile
is not very steep. These results suggest that we may obtain information about
the slope of the central density profiles of dark matter halo from the lensing
effect of Type Ia supernovae.Comment: 25 pages, 12 figures, PTP accepted versio
Detecting gravitational waves from precessing binaries of spinning compact objects. II. Search implementation for low-mass binaries
Detection template families (DTFs) are built to capture the essential
features of true gravitational waveforms using a small set of phenomenological
waveform parameters. Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025
(2003)] proposed the ``BCV2'' DTF to perform computationally efficient searches
for signals from precessing binaries of compact stellar objects. Here we test
the signal-matching performance of the BCV2 DTF for asymmetric--mass-ratio
binaries, and specifically for double--black-hole binaries with component
masses (m1,m2): (6~12Msun, 1~3Msun), and for black-hole--neutron-star binaries
with component masses (m1,m2) = (10Msun, 1.4Msun); we take all black holes to
be maximally spinning. We find a satisfactory signal-matching performance, with
fitting factors averaging between 0.94 and 0.98. We also scope out the region
of BCV2 parameters needed for a template-based search, we evaluate the template
match metric, we discuss a template-placement strategy, and we estimate the
number of templates needed for searches at the LIGO design sensitivity. In
addition, after gaining more insight in the dynamics of spin--orbit precession,
we propose a modification of the BCV2 DTF that is parametrized by physical
(rather than phenomenological) parameters. We test this modified ``BCV2P'' DTF
for the (10Msun, 1.4Msun) black-hole--neutron-star system, finding a
signal-matching performance comparable to the BCV2 DTF, and a reliable
parameter-estimation capability for target-binary quantities such as the chirp
mass and the opening angle (the angle between the black-hole spin and the
orbital angular momentum).Comment: 18 pages, 15 figure
Multipole particle in relativity
We discuss the motion of extended objects in a spacetime by considering a
gravitational field created by these objects. We define multipole moments of
the objects as a classification by Lie group SO(3). Then, we construct an
energy-momentum tensor for the objects and derive equations of motion from it.
As a result, we reproduce the Papapetrou equations for a spinning particle.
Furthermore, we will show that we can obtain more simple equations than the
Papapetrou equations by changing the center-of-mass.Comment: 22 pages, 2 figures. Accepted for publication in Phys. Rev.
Gravitational waves from inspiralling compact binaries with magnetic dipole moments
We investigate the effects of the magnetic dipole-dipole coupling and the
electromagnetic radiation on the frequency evolution of gravitational waves
from inspiralling binary neutron stars with magnetic dipole moments. This study
is motivated by the discovery of the superstrongly magnetized neutron stars,
i.e., magnetar. We derive the contributions of the magnetic fields to the
accumulated cycles in gravitational waves as , where denotes the strength of the polar magnetic
fields of each neutron star in the binary system. It is found that the effects
of the magnetic fields will be negligible for the detection and the parameter
estimation of gravitational waves, if the upper limit for magnetic fields of
neutron stars are less than G, which is the maximum magnetic
field observed in the soft gamma repeaters and the anomalous X-ray pulsars up
to date. We also discuss the implications of electromagnetic radiation from the
inspiralling binary neutron stars for the precursory X-ray emission prior to
the gamma ray burst observed by the Ginga satellite.Comment: 15 pages, no figures, accepted for publication in Ap
Gravitational radiation from infall into a black hole: Regularization of the Teukolsky equation
The Teukolsky equation has long been known to lead to divergent integrals
when it is used to calculate the gravitational radiation emitted when a test
mass falls into a black hole from infinity. Two methods have been used in the
past to remove those divergent integrals. In the first, integrations by parts
are carried out, and the infinite boundary terms are simply discarded. In the
second, the Teukolsky equation is transformed into another equation which does
not lead to divergent integrals. The purpose of this paper is to show that
there is nothing intrinsically wrong with the Teukolsky equation when dealing
with non-compact source terms, and that the divergent integrals result simply
from an incorrect choice of Green's function. In this paper, regularization of
the Teukolsky equation is carried out in an entirely natural way which does not
involve modifying the equation.Comment: ReVTeX, 23 page
Gravitational Waves from a Particle Orbiting Around a Rotating Black Holes: Post-Newtonian Expansion
Using the Teukolsky and Sasaki-Nakamura equations for the gravitational
perturbation of the Kerr spacetime, we calculate the post-Newtonian expansion
of the energy and angular momentum luminosities of gravitational waves from a
test particle orbiting around a rotating black hole up through
order beyond the quadrupole formula. We apply a method recently developed by
Sasaki to the case of a rotating black hole. We take into account a small
inclination of the orbital plane to the lowest order of the Carter constant.
The result to P^{3/2}N} order is in agreement with a similar calculation by
Poisson as well as with the standard post-Newtonian calculation by Kidder et
al. Using our result, we calculate the integrated phase of gravitational waves
from a neutron star-neutron star binary and a black hole-neutron star binary
during their inspiral stage. We find that, in both cases, spin-dependent terms
in the PN and PN corrections are important to construct effective
template waveforms which will be used for future laser-interferometric
gravitational wave detectors.Comment: phyzzx 41 page
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