Discriminating between a Stochastic Gravitational Wave Background and Instrument Noise

TL;DR

The paper develops a rigorous, single-detector framework for discriminating a stochastic gravitational-wave background from instrument noise in LISA by modeling the noise and signal transfer in the six cross-spectral TDI channels. It introduces an end-to-end Bayesian pipeline that jointly infers the noise spectra and the stochastic background, validated on Mock LISA Data Challenge data, and demonstrates that a background with $Omega_gw$ around $6\times10^{-13}$ could be detected with one month of data in the absence of a galactic foreground. A key contribution is the analysis of null channels, including a new $T$-channel construction for unequal arm lengths, enabling GW-insensitive tests and robust detector characterization. The work also outlines extensions to include foregrounds, time-frequency structure, and priors from resolved binaries, highlighting practical limits set by astrophysical foregrounds on LISA's stochastic background sensitivity.

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 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 $Ω_{\rm gw} = 6 \times 10^{-13}$ 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.

Figures (10)

• 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. One 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 position noise levels, scaled by the nominal level. One 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.