The first year of LISA Galactic foreground

TL;DR

The paper addresses the challenge of extracting the LISA Galactic foreground (GF) from unresolved white-dwarf binaries within the first year of observations using a time–frequency global-fit with the bahamas framework. It introduces a STFT-based representation and two local likelihoods ($\mathcal{L}^{\mathrm{chunk}}_W$ and $\mathcal{L}^{\mathrm{chunk}}_G$) to model a PSD composed of a cyclostationary GF, instrumental noise, and a potential extragalactic foreground (EF), with a parametric GF spectrum $S^{\mathrm{GF}}(f)$ and time-dependent modulation captured by the LISA response. The main contributions show strong evidence for a cyclostationary GF within months, demonstrate substantial computational gains (roughly a factor of $30$) when using the Gamma likelihood with averaged periodograms and NUTS sampling, and establish robustness to data gaps and to an EF component, including validation on the Yorsh data challenge. This framework enables robust, scalable global fits for LISA data, informing Galactic structure inference while accommodating realistic data conditions, and provides open data and code to support reuse and extension.

Abstract

Galactic white-dwarf binaries play a central role in the inference model for the Laser Interferometer Space Antenna. In this manuscript, we employ the $\texttt{bahamas}$ codebase to characterize, in a global-fit fashion, the reconstruction of the Galactic foreground during the first year of observation. To account for its statistical properties, we represent the data in time--frequency domain, and characterize the effectiveness of multiple approaches, e.g. statistically viable likelihoods, sampling schemes, segmentation widths, and gaps density. Our analysis yields consistent results across, with overwhelming evidence in favor of a non-stationary model in less than a month of data. Moreover, we show robustness against the presence of additional extragalactic foregrounds, and test the suitability of our approximations on the more complex simulated data in the $\textit{Yorsh}$ data challenge.

Figures (13)

• Figure 1: (Top left) Evolution of the Galactic foreground spectrum across different time chunks, with the corresponding modulation amplitudes shown in the bottom subplot as colored crosses. The spectrum level is obtained for a fixed total observation time $T_{\rm obs}=1 {\rm yr}$. (Top right) Evolution of the spectrum as the observation time increases. By contrast to the left panel, the modulation amplitude is fixed to that of the first chunk, shown in the bottom subplot as colored dark blue circle. The overall effect on the spectrum is a shift toward lower frequencies. (Bottom) The modulation squared amplitude, highlighting the corresponding reference times as cross and circle markers. For simplicity, all quantities refer to the A channel.
• Figure 2: Data acquisitions and analysis schemes considered in this work. (Left panel) Sequential analysis scheme: data segments are generated and cumulatively analyzed over time. Results from this approach are shown in \ref{['fig:bayes_fac', 'fig:ridgeline', 'fig:ridgeline2', 'fig:corner_chunk2']}. (Right panel) Differential analysis scheme: 2 weeks-long data segments are analyzed independently, and the modulation is reconstructed from in-segment PSD evolution, i.e. across first and second week. Results from this approach are shown in \ref{['fig:evidence_envelope', 'fig:corner_chunk']}.
• Figure 3: Ridgeline plot of the posterior distributions of Galactic foreground parameters obtained from a sequential analysis over one year of observation, using the Gamma likelihood and two-weeks-long segments. Posteriors are centered on the injected values, indicating unbiased reconstructions. From top to bottom, posterior distributions narrow down as more data are accumulated. The Galactic modulation parameters become increasingly well-constrained by leveraging consistency across different segments, up to and including the packet shown on the leftmost column. To help visualization, we scale axis ranges in the bottom panel to the typical posterior widths over the second half year.
• Figure 4: Jensen–Shannon divergence between the marginal posterior distributions on the modulation parameters, as inferred from the Gamma and Whittle likelihoods, and as a function of observation time. Each value remains well below 0.02 $\rm{nat}$ (black dashed line), a rough threshold to establish indistinguishability between one-dimensional distributions.
• Figure 5: Computational gain factor across different setup configurations available in bahamas, as a function of data length. Markers denote the ratio of CPU time required to obtain one posterior sample in two competing configurations: circles denote the ratio of Whittle over Gamma likelihoods, while diamonds denote the ratio of NS over NUTS samplers. Each marker is colored according to the total observation time considered, matching those in \ref{['fig:ridgeline']}. While the Gamma likelihood is approximately 15 times faster than Whittle, NUTS yields samples twice as fast as NS. The latter is furthermore expected to yield even larger speedups once deployed on GPU.