Detecting a stochastic gravitational wave background with space-based interferometers

Abstract

The detection of a stochastic background of gravitational waves could significantly impact our understanding of the physical processes that shaped the early Universe. The challenge lies in separating the cosmological signal from other stochastic processes such as instrument noise and astrophysical foregrounds. One approach is to build two or more detectors and cross correlate their output, thereby enhancing the common gravitational wave signal relative to the uncorrelated instrument noise. When only one detector is available, as will likely be the case with space based gravitational wave astronomy, alternative analysis techniques must be developed. Here we develop an end to end Bayesian analysis technique for detecting a stochastic background with a gigameter Laser Interferometer Space Antenna (LISA) operating with both 6- and 4-links. Our technique requires a detailed understanding of the instrument noise and astrophysical foregrounds. In the millihertz frequency band, the predominate foreground signal will be unresolved white dwarf binaries in the galaxy. We consider how the information from multiple detections can be used to constrain astrophysical population models, and present a method for constraining population models using a Hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We find that a mission that is able to resolve ~ 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%. Having constrained the galaxy shape parameters, we obtain posterior distribution functions for the instrument noise parameters, the galaxy level and modulation parameters, and the stochastic background energy density. We find that we are able to detect a scale-invariant stochastic background with energy density as low as Omega gw= 2x10 -13 for a 6-link interferometer and Omega gw = 5x10 -13 for a 4-link interferometer with one year of data.