Improving the Radiometric Search of Stochastic Gravitational Wave Background with a Natural Set of Basis Functions

Abstract

The analysis of stochastic gravitational wave background involves the cross-correlation of signals detected by the two detectors at short time intervals augmented by a filter to optimize the signal to noise ratio. The rotation of Earth leads to a change in the baseline with respect to the signal coming from a particular direction in the sky which causes interference which is used to sample the Gravitational Wave Background. This however leads to a point spread function which means that the contribution from a single source spreads across the sky-sphere. The statistic that is obtained from this analysis shows that the contribution at each point is a weighted sum from the sources over the entire sky.If the sky is divide into n pixels, the weights form a $n \times n$ matrix dubbed the beam pattern matrix. The power is now obtained by solving n linear algebraic equations in power. This process is called deconvolution. The aim of this project is to get a basis to represent the beam pattern matrix and do away with the need to deconvolve the map which is a cumbersome process. The basis being optimized to the problem might also provide some new insight into the problem.