SENSITIVITY OF THE LASER INTERFEROMETER GRAVITATIONAL-WAVE OBSERVATORY TO A STOCHASTIC BACKGROUND, AND ITS DEPENDENCE ON THE DETECTOR ORIENTATIONS

We analyze the sensitivity of a network of interferometer gravitationa l-wave detectors to the gravitational-wave stochastic background, and derive the dependence of this sensitivity on the orientations of the d etector arms. We build on and extend the recent work of Christensen, b ut our conclusion for the optimal choice of orientations of a pair of detectors differs from his. For a pair of detectors (such as LIGO) tha t subtends an angle at the center of the Earth of less than or similar to 70-degrees, we find that the optimal configuration is for each det ector to have its arms make an angle of 45-degrees (modulo 90-degrees) with the arc of the great circle that joins them. For detectors that are farther separated, each detector should instead have one arm align ed with this arc. We show that the broadband sensitivity to the stocha stic background of a detector pair which are less than or similar to 3 000 km apart is essentially determined by their relative rotation. The ir average rotation with respect to the arc joining them is unimportan t. We also describe in detail the optimal data-analysis algorithm for searching for the stochastic background with a detector network, which is implicit in earlier work of Michelson. The LIGO pair of detectors will be separated by approximately 3000 km. The minimum detectable sto chastic energy density for these detectors with their currently planne d orientations is approximately 3% greater than what it would be if th e orientations were optimal, and approximately 4 times what it would b e if their separation were less than or similar to a few kilometers. ( The detectors are chosen to be far apart so that their sources of nois e will be uncorrelated, and in order to improve the angular resolution of the determinations of positions of burst sources.)