771 research outputs found
The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars
In this work, we present the analytic treatment of the large order Bessel
functions that arise in the Fourier Transform (FT) of the Gravitational Wave
(GW) signal from a pulsar. We outline several strategies which employ
asymptotic expansions in evaluation of such Bessel functions which also happen
to have large argument. Large order Bessel functions also arise in the
Peters-Mathews model of binary inspiralling stars emitting GW and several
problems in potential scattering theory. Other applications also arise in a
variety of problems in Applied Mathematics as well as in the Natural Sciences
and present a challenge for High Performance Computing(HPC).Comment: 8 pages, Uses IEEE style files: Ieee.cls, Ieee.clo and floatsty.sty.
Accepted for publication in High Performance Computing Symposium, May 15-18
(HPCS 2005) Guelph, Ontario, Canad
Implementation of the frequency-modulated sideband search method for gravitational waves from low mass X-ray binaries
We describe the practical implementation of the sideband search, a search for
periodic gravitational waves from neutron stars in binary systems. The orbital
motion of the source in its binary system causes frequency-modulation in the
combination of matched filters known as the -statistic. The
sideband search is based on the incoherent summation of these
frequency-modulated -statistic sidebands. It provides a new
detection statistic for sources in binary systems, called the
-statistic. The search is well suited to low-mass X-ray binaries,
the brightest of which, called Sco X-1, is an ideal target candidate. For
sources like Sco X-1, with well constrained orbital parameters, a slight
variation on the search is possible. The extra orbital information can be used
to approximately demodulate the data from the binary orbital motion in the
coherent stage, before incoherently summing the now reduced number of
sidebands. We investigate this approach and show that it improves the
sensitivity of the standard Sco X-1 directed sideband search. Prior information
on the neutron star inclination and gravitational wave polarization can also be
used to improve upper limit sensitivity. We estimate the sensitivity of a Sco
X-1 directed sideband search on 10 days of LIGO data and show that it can beat
previous upper limits in current LIGO data, with a possibility of constraining
theoretical upper limits using future advanced instruments.Comment: 20 pages, 5 figure
Data analysis of continuous gravitational wave: All sky search and study of templates
We have studied the problem of all sky search in reference to continuous
gravitational wave particularly for such sources whose wave-form are known in
advance. We have made an analysis of the number of templates required for
matched filter analysis as applicable to these sources. We have employed the
concept of {\it fitting factor} {\it (FF)}; treating the source location as the
parameters of the signal manifold and have studied the matching of the signal
with templates corresponding to different source locations. We have
investigated the variation of FF with source location and have noticed a
symmetry in template parameters, and . It has been found
that the two different template values in source location, each in
and , have same {\it FF}. We have also computed the number of templates
required assuming the noise power spectral density to be flat. It is
observed that higher {\it FF} requires exponentially increasing large number of
templates.Comment: Accepted in MNRAS, 14 pages, 5 figure
Data analysis of continuous gravitational wave: Fourier transform-II
In this paper we obtain the Fourier Transform of a continuous gravitational
wave. We have analysed the data set for (i) one year observation time and (ii)
arbitrary observation time, for arbitrary location of detector and source
taking into account the effects arising due to rotational as well as orbital
motion of the earth. As an application of the transform we considered spin down
and N-component signal analysis.Comment: Accepted in MNRAS, 14 pages, 4 figure
Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin
Gravitational wave searches for continuous-wave signals from neutron stars
are especially challenging when the star's spin frequency is unknown a priori
from electromagnetic observations and wanders stochastically under the action
of internal (e.g. superfluid or magnetospheric) or external (e.g. accretion)
torques. It is shown that frequency tracking by hidden Markov model (HMM)
methods can be combined with existing maximum likelihood coherent matched
filters like the F-statistic to surmount some of the challenges raised by spin
wandering. Specifically it is found that, for an isolated, biaxial rotor whose
spin frequency walks randomly, HMM tracking of the F-statistic output from
coherent segments with duration T_drift = 10d over a total observation time of
T_obs = 1yr can detect signals with wave strains h0 > 2e-26 at a noise level
characteristic of the Advanced Laser Interferometer Gravitational Wave
Observatory (Advanced LIGO). For a biaxial rotor with randomly walking spin in
a binary orbit, whose orbital period and semi-major axis are known
approximately from electromagnetic observations, HMM tracking of the
Bessel-weighted F-statistic output can detect signals with h0 > 8e-26. An
efficient, recursive, HMM solver based on the Viterbi algorithm is
demonstrated, which requires ~10^3 CPU-hours for a typical, broadband (0.5-kHz)
search for the low-mass X-ray binary Scorpius X-1, including generation of the
relevant F-statistic input. In a "realistic" observational scenario, Viterbi
tracking successfully detects 41 out of 50 synthetic signals without spin
wandering in Stage I of the Scorpius X-1 Mock Data Challenge convened by the
LIGO Scientific Collaboration down to a wave strain of h0 = 1.1e-25, recovering
the frequency with a root-mean-square accuracy of <= 4.3e-3 Hz
A method for narrow-band searches of continuous gravitational wave signals
Targeted searches of continuous waves from spinning neutron stars normally
assume that the frequency of the gravitational wave signal is at a given known
ratio with respect to the rotational frequency of the source, e.g. twice for an
asymmetric neutron star rotating around a principal axis of inertia. In fact
this assumption may well be invalid if, for instance, the gravitational wave
signal is due to a solid core rotating at a slightly different rate with
respect to the star crust. In this paper we present a method for {\it
narrow-band} searches of continuous gravitational wave signals from known
pulsars in the data of interferometric detectors. This method assumes source
position is known to high accuracy, while a small frequency and spin-down range
around the electromagnetic-inferred values is explored. Barycentric and
spin-down corrections are done with an efficient time-domain procedure.
Sensitivity and computational efficiency estimates are given and results of
tests done using simulated data are also discussed.Comment: 13 pages; 6 figures; accepted in PR
Probing for massive stochastic gravitational-wave background with a detector network
In a general metric theory of gravitation in four dimensions, six
polarizations of a gravitational wave are allowed: two scalar and two vector
modes, in addition to two tensor modes in general relativity. Such additional
polarization modes appear due to additional degrees of freedom in modified
gravity theories. Also graviton mass, which could be different in each
polarization, is another characteristic of modification of gravity. Thus,
testing the existence of additional polarization modes and graviton mass can be
a model-independent test of gravity theories. Here we extend the previous
framework of correlation analysis of a gravitational-wave background to the
massive case and show that a ground-based detector network can probe for
massive stochastic gravitational waves with its mass around ~10^{-14} eV. We
also show that more than three detectors can cleanly separate the mixture of
polarization modes in detector outputs and determine the graviton mass.Comment: 13 pages, 6 figure
Observability of Dark Matter Substructure with Pulsar Timing Correlations
Dark matter substructure on small scales is currently weakly constrained, and
its study may shed light on the nature of the dark matter. In this work we
study the gravitational effects of dark matter substructure on measured pulsar
phases in pulsar timing arrays (PTAs). Due to the stability of pulse phases
observed over several years, dark matter substructure around the Earth-pulsar
system can imprint discernible signatures in gravitational Doppler and Shapiro
delays. We compute pulsar phase correlations induced by general dark matter
substructure, and project constraints for a few models such as monochromatic
primordial black holes (PBHs), and Cold Dark Matter (CDM)-like NFW subhalos.
This work extends our previous analysis, which focused on static or single
transiting events, to a stochastic analysis of multiple transiting events. We
find that stochastic correlations, in a PTA similar to the Square Kilometer
Array (SKA), are uniquely powerful to constrain subhalos as light as , with concentrations as low as that predicted by standard
CDM.Comment: 45 pages, 12 figure
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