A framework for LISA population inference

TL;DR

This paper addresses how to infer astrophysical population properties from LISA data when the Global Fit includes both a sea of overlapping signals and individually resolvable sources. It introduces a general hierarchical Bayesian framework that jointly models resolved sources and the stochastic foreground, using a resolvability function $\alpha(\theta,\Lambda)$ to partition contributions and a mapping $p(\Sigma|\Lambda)$ linking foreground properties to population hyperparameters. A key result is a general population likelihood that reduces to standard LVK forms in appropriate limits, demonstrated via a toy Global Fit analyzed with RJMCMC, revealing how analysis choices such as SNR thresholds influence inference. This approach provides a practical foundation for LISA population inference, enabling simultaneous constraints on source populations, foreground properties, and the total event rate, with implications for future detectors and data-product design.

Abstract

The Laser Interferometer Space Antenna (LISA) is expected to have a source rich data stream containing signals from large numbers of many different types of source. This will include both individually resolvable signals and overlapping stochastic backgrounds, a regime intermediate between current ground-based detectors and pulsar timing arrays. The resolved sources and backgrounds will be fitted together in a high dimensional Global Fit. To extract information about the astrophysical populations to which the sources belong, we need to decode the information in the Global Fit, which requires new methodology that has not been required for the analysis of current gravitational wave detectors. Here, we %start that development, presenting present a hierarchical Bayesian framework to infer the properties of astrophysical populations directly from the output of a LISA Global Fit, consistently accounting for information encoded in both the resolved sources and the unresolved background. Using a simplified model of the Global Fit, we illustrate how the interplay between resolved and unresolved components affects population inference and highlight the impact of data analysis choices, such as the signal-to-noise threshold for resolved sources, on the results. Our approach provides a practical foundation for population inference using LISA data.

Figures (4)

• Figure 1: The upper panel shows the reconstruction of the total noise ($90\%$ confidence interval) and the lower panel the corresponding distribution on the number of resolved sources for different choices of the lower threshold on the SNR. Grey points show the data in all the bins, the black dashed line shows the theoretical expectation for the noise, given in Eq \ref{['eq:sigma_foreground_th']}, and the dotted one the amplitude of a single source. Increasing $\rho_{\rm min}$ decreases the number of resolved sources and pushes the background contribution to extend to higher frequency.
• Figure 2: Posterior distribution of the noise parameters in the $\rho_{\rm min}=10$ (blue) and $50$ (red) cases. $A_0$ is the amplitude of the foreground in the first bin. We did not normalise the distributions of $f_{{\rm res},F}$ to the same binning scheme given their disjoint support in order to make the fine features more apparent.
• Figure 3: Probability of resolvability of a source as a function their estimated SNR (left) and frequency (right). In the latter case we also show in coloured bands the $90\%$ confidence interval on $\alpha(f,f_{{\rm res}},s_{{\rm res}})$ defined in Eq. \ref{['eq:res_func']}.
• Figure 4: Posterior on the population hyperparameters for the different choices of $\rho_{\rm min}$ considered in this work. We show with a black line the true value of hyperparameters. For $f_{{\rm res},P}$ and $s_{{\rm res},P}$ there is no true value as they are fitted to optimise our description of the data as a stochastic and a resolvable component.