Discriminating between a stochastic gravitational wave background and instrument noise

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 the Laser Interferometer Space Antenna (LISA), alternative analysis techniques must be developed. Here we show that models of the noise and signal transfer functions can be used to tease apart the gravitational and instrument noise contributions. We discuss the role of gravitational wave insensitive “null channels” formed from particular combinations of the time delay interferometry, and derive a new combination that maintains this insensitivity for unequal arm-length detectors. We show that, in the absence of astrophysical foregrounds, LISA could detect signals with energy densities as low as ${\Omega }_{\mathrm{gw}}=6\times {10}^{-13}$ with just one month of data. We describe an end-to-end Bayesian analysis pipeline that is able to search for, characterize and assign confidence levels for the detection of a stochastic gravitational wave background, and demonstrate the effectiveness of this approach using simulated data from the third round of Mock LISA Data Challenges.

Figure 1

Our model for the noise in the $A$ and $T$ channels compared to smoothed spectra formed from the MLDC training data.

Figure 2

The sensitivity curve for the $A$, $E$ and $T$ channels, showing the insensitivity of the $T$ channel to a gravitational wave signal.

Figure 3

Histograms showing the posterior distribution functions for the position noise levels, scaled by the nominal level. On the left are the sums along each arm, and on the right are the differences. The vertical lines denote the injected values.

Figure 4

Histograms showing the posterior distribution functions for the acceleration noise levels, scaled by the nominal level. On the left are the sums along each arm, and on the right are the differences. The vertical lines denote the injected values.

Figure 5

The posterior distribution for the gravitational wave background level (scaled up by ${10}^{13}$). The vertical line denotes the injected values.

Figure 6

The posterior distribution for the gravitational wave background slope.

Figure 7

Bayes factor showing the detectability versus background level. The line shows the average values of the scattered points.

Figure 8

Bayes factors for the $X$, $Y$, and $Z$ channels

Figure 9

Sensitivity curve for unequal arm LISA. Our new $T$ channel restores the usual low-frequency insensitivity to a stochastic gravitational wave background.

Figure 10

The time-domain $A$-channel response to the full galactic foreground (red, large amplitude variation); the unresolved component of the galactic foreground (green, smaller amplitude variation) and the instrument noise (blue, uniform amplitude). The signals were passband filtered between 0.1–10 mHZ.