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.