Gravitational Waves
I have been interested in the theoretical aspects of gravitational
wave detection and observation. The major component of my work is in
the data analysis of gravitational wave signals embedded in the noise
of the detector. The aim is to extract the signal from the noise. Also
I have been interested in theoretically modelling the laser
interferometric detector mainly concerning its optics. Below I describe
briefly some of the work.
- Graviational Wave Data Analysis of Ground Based Detectors:
The recent data analysis work can be divided into two major
parts:
(i) Gravitational wave data analysis of inspiraling
binaries
(ii) Mapping the sky for the
gravitational wave stochastic background
- Inspiraling binaries:
Strategies for
extracting the signals have been proposed using maximum
likelihood methods, matched filtering etc. and have been optimised for
computational costs without sacrificing signal-to-noise. Following the
work by Mohanty & Dhurandhar, Anand Sengupta, Albert Lazzarini and
myself extended the hierarchy to include the time-of-arrival parameter
into the hierarchy thus making it a three dimensional hierarchy: the
two masses and the time-of-arrival. This strategy brings down the
computational costs by a factor of few tens. The other strategy
involved optimally sampling the parameter space by
interpolating between templates. Sanjit Mitra,
myself and Sam Finn employed the Chebyshev polynomials in order to
interpolate and thus cut down by a factor of about 25-30 % per
dimension of the parameter space. This strategy is independent of the
hierarchical strategy and they can be used together to further
improve on the costs. Also the
interpolated search works better in a higher dimensional parameter
space, thus would be useful when the spins of the binary stars are
taken into account. This work was part of the LSC.
- Stochastic background:
The idea is to use a targeted search
for the stochastic background. By using a directed filter for a
fixed direction in the sky with a varying time-delay incorporated into
the cross-correlation of signals between two detectors, the SNR
accumulates over time. This is done for each independent fixed
direction in the sky. We then obtain a map of the sky gravitational
wave stochastic background. The map is not clean because a
point source gets spread into either a eight or a tear drop depending
on the relative latitude - these are the point spread functions for
different directions. Sanjit Mitra and the group has been able to
deconvolve the sky map for injected signals in Gaussian
noise. Work is in progress in order to improve the methodology.
- The Space-based detector LISA:
Here as I have mentioned in the main text my
main contribution has been to show that the laser frequency noise
cancelling data combinations for LISA
form a module over the polynomial ring
of time-delay operators. This is a problem in time-delay
interferometry (TDI). The data combinations
are polynomial vectors where the
polynomials are in the time-delay
operators. Grobner basis methods have been
used to obtain the generators of
the module of syzygies. This module
provides us with an exhaustive set of data
combinations cancelling laser frequency noise. These results can be
used to advantage for making LISA directionally sensitive
and it can be made to follow a given source fixed in the barycentric
frame, thus helping to enhance the signal-to-noise. Thus useful
optimisation problems can be addressed based on this foundation already
given by the module. This work was under IFCPAR with Jean-Yves
Vinet as my collaborator and the follow up work on optimisation with
younger collaborators, R. Nayak and A. Pai.
In order to extend these results to a moving
LISA we examined the stability of the LISA constellation where
each spacecraft moves around the Sun in a geodesic orbit.
We used the Clohessy-Wiltshire (Hill's) equations to study the
stability and proved and improved on previous results on the freely
flying spacecraft comprising LISA. S. Koshti was the additional younger
collaborator.
We now plan to work out the general and
special relativistic effects on the time-delays in LISA and their
further effect and generalisation to next generation TDI variables.