Resolving Structure in the Stochastic Gravitational-Wave Power Spectrum with LISA Using Non-parametric Methods

The Laser Interferometer Space Antenna (LISA) is an upcoming space-based detector designed to study gravitational waves (GWs) in the millihertz frequency range. A particularly numerous source of GWs at these frequencies are Galactic compact binaries, especially binaries with one or two white dwarf stars. While a small percentage of such binaries will be individually resolved by LISA, the GWs from most of them will form a stochastic foreground that will be loud and detectable. In this study, we develop Bayesian non-parametric methods based on autoregressive (AR) processes to map the power spectrum of the GW foreground from Galactic Double White Dwarfs (DWDs) and Cataclysmic Variables (CVs). We validate the non-parametric AR model through a series of simulations and analyses, including the recovery of GW foregrounds from simulated DWD and CV populations. We hierarchically inferred the parameters of the AR model using a Bayesian inference pipeline for LISA (BLIP). The flexibility of the AR process will allow us to probe complex structures in the spectrum that deviate from simple power law models. Non-parametric methods will be crucial for studying the stochastic foreground from a combination of source categories and extracting population properties of Galactic compact objects.