Detecting a Stochastic Gravitational Wave Background in the presence of a Galactic Foreground and Instrument Noise

TL;DR

The paper tackles detecting an isotropic stochastic gravitational wave background in the milliHertz band with a space-based detector like LISA, accounting for a Galactic white-dwarf foreground and instrument noise. It develops a complete forward model combining a full transfer-function detector response, a WD foreground with annual modulation, and a stochastic background with flexible spectral shapes, analyzed via Bayesian inference across 50 yearly segments. The key finding is that a scale-invariant background with $\Omega_{gw}$ on the order of a few $\times10^{-13}$ can be detected for both 6-link and 4-link configurations, even when the Galactic foreground is included, and that the modulation and spectral separation are the primary discriminants. This work provides a practical framework for isolating extragalactic backgrounds in LISA data and informs design choices for multi- versus few-link configurations.

Abstract

Detecting a stochastic gravitational wave background requires that we first understand and model any astrophysical foregrounds. In the millihertz frequency band, the predominate foreground signal will be from unresolved white dwarf binaries in the galaxy. We build on our previous work to show that a stochastic gravitational wave background can be detected in the presence of both instrument noise and a galactic confusion foreground. The key to our approach is accurately modeling the spectra for each of the various signal components. We simulate data for a gigameter Laser Interferometer Space Antenna (LISA) operating in the mHz frequency band detector operating with both 6- and 4-links. 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 = 2e-13 for a 6-link interferometer and Omega_gw = 5e-13 for a 4-link interferometer with one year of data.

Figures (13)

• Figure 1: The time domain noise, galaxy, and stochastic background signal components for the X-channel. They have been bandpass filtered between 0.1 and 4 mHz. We show that we are able to detect a scale invariant background with $\Omega_{gw} = 5 \cdot 10^{-13}$, which is well below the instrument noise and galaxy levels.
• Figure 2: Several galaxy realizations showing the scatter in the modulation levels throughout the year compared to the galaxy used in our simulations. The points are scaled by the first Fourier coefficient, $C_0$.
• Figure 3: Several galaxy realizations showing the scatter in the Fourier coefficients for different galaxy realizations. The $\pm 3\sigma$ upper and lower bounds are used as the prior range on the Fourier coefficients in our analysis.
• Figure 4: Our smoothed, simulated data with the model overlaid in black (solid).
• Figure 5: The PDFs for the 6 constrained noise parameter combinations for the AET channels. The position noise parameters are on the left and the acceleration noise parameters on the right. The black (solid) vertical lines show the injected values. The blue (dashed) PDFs included slope fitting and the red (solid) PDFs did not.