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Published February 15, 2008 | public
Journal Article Open

Gravitational wave radiometry: Mapping a stochastic gravitational wave background


The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either cosmological or astrophysical, bears a strong semblance to the analysis of the cosmic microwave background (CMB) anisotropy and polarization, which too is a stochastic field, statistically described in terms of its correlation properties. An astrophysical gravitational wave background (AGWB) will likely arise from an incoherent superposition of unmodelled and/or unresolved sources and cosmological gravitational wave backgrounds (CGWB) are also predicted in certain scenarios. The basic statistic we use is the cross correlation between the data from a pair of detectors. In order to "point" the pair of detectors at different locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We first present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map using the conjugate gradient method that has been successfully used in the broadly similar, well-studied CMB map-making problem. We numerically implement and demonstrate the method on signal generated by simulated (unpolarized) SGWB for the GW radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include "realistic" additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.

Additional Information

©2008 The American Physical Society. (Received 21 August 2007; published 14 February 2008) S. Mitra would like to acknowledge the Council of Scientific and Industrial Research (India) and Centre National d'Etudes Spatiales (France) for supporting his research and Caltech for supporting his visit to LIGO Laboratory, Caltech in 2006, where part of this work was done. He further thanks Stuart Anderson for helpful suggestions and Kent Blackburn and Patrick Sutton for providing useful help with the software computing facilities. Some of the results in this paper have been derived using the HEALPix [55] package, the Planck Simulator [53], and FTOOLS [56] and some of the plots were made using a colormap, specifically designed for compatibility with grayscale printing, included in the GNUPLOT package [57]. The LIGO Data Analysis System (LDAS) at Caltech and the High Performance Computing (HPC) facility at IUCAA were used for the numerical implementation. This work was supported in part by the Department of Science and Technology Grant No. DST/INT/(US-RP077)/2001 and the National Science Foundation Grants No. INT-01-38459, No. PHY-0630121, and No. PHY-0239735, and the NSF LIGO Laboratory Cooperative Agreement No. PHY-0107417. This paper has LIGO Document No. LIGO-P070033-Z.


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August 22, 2023
August 22, 2023