A Foundation for Gravitational-Wave Population Inference within the LISA Global Fit

Abstract

Population inference in gravitational-wave astronomy allows us to connect individual detections to the astrophysics of compact objects and their environments. Current approaches employed for population inference with LIGO-Virgo-KAGRA data approximate evaluation of the hierarchical population likelihood via post-processing of individual-event posteriors. However, the case of the Laser Interferometer Space Antenna (LISA) will be more complex for two main reasons: the transdimensional "global fit" approach to LISA data analysis which models all signals and noise simultaneously, and the presence of both individually-resolved signals and the unresolved stochastic ``Galactic foreground" arising from the Galactic binary population, which induces a circular dependence between the resolved and unresolved systems and our ability to detect the former. These challenges are not without opportunity; LISA's data will contain every mHz compact binary in the Milky Way -- either individually or within the Galactic foreground -- with great potential for Galactic and stellar astrophysics. We therefore propose an alternative approach: direct evaluation of the full hierarchical population likelihood within the LISA global fit. We develop a statistical formalism for joint inference of individually-resolved gravitational-wave sources, an unresolved stochastic foreground, and a shared, underlying astrophysical population, present PELARGIR, a prototype GPU-accelerated population inference module for the LISA global fit, demonstrate the formalism and PELARGIR via a toy model analysis, and lay out a roadmap towards an astrophysically-motivated LISA global fit with embedded population inference. While we apply the formalism here to the population of LISA Galactic binaries, it is applicable across the gravitational-wave spectrum with use cases in pulsar timing and next-generation terrestrial observatories.

Figures (7)

• Figure 1: Result of the thresholding algorithm as applied to the fiducial population synthesis catalogue of thiele_applying_2023 at a frequency resolution of $\Delta f = 10^{-5}$ Hz, representative of the resolution of short-time Fourier transform based approaches. PELARGIR finds $N_{\rm res}=8,091$ resolved systems, depicted in black.
• Figure 2: Corner plot showing the hyperparameter posteriors from the toy model population analysis. Contours shown are the 68%, 95%, and 99.7% credible levels. The quoted constraints are the means and 95% credible intervals. The dashed lines indicate the simulated values. We include all walkers of the zero-temperature chain and remove the first 2,500 samples from each walker's chain to account for burn-in.
• Figure 3: Recovered population distributions, plotted against the (density-normalized) histograms of both the full simulated GB population and the resolved GBs from that population. The inferred distributions are shown as 95% credible intervals. The recovered distributions follow the full population. The differences between the resolved and unresolved subpopulations can be clearly seen; as would be expected, the resolved systems have higher masses and frequencies but sit at lower distances than their unresolved counterparts. The inferred distance distribution is strongly peaked at the Galactic center due to $r_{\rm bulge}$ being unconstrained; we cut off the top of the distribution for improved visibility of the histograms.
• Figure 4: The population-derived prior on the number of resolved binaries.
• Figure 5: Posterior distribution of the total PSD spectrum, i.e. the sum of the instrumental noise and Galactic foreground contribution, for the toy model population analysis. The population-informed prior on the spectrum is strongly-informative without biasing the spectral posterior. While in principle a by-product of the population inference formalism, this indicates potential for this approach to produce a population-driven, astrophysically informed spectral model for the LISA Galactic foreground.