Inferring the population properties of galactic binaries from LISA's stochastic foreground

Abstract

Galactic binaries are expected to be the most numerous LISA sources and to produce a stochastic gravitational-wave foreground whose spectral shape encodes information about the underlying population. Extracting this information with standard hierarchical methods is challenging due to the high dimensionality of the problem and the computational cost of global-fit analyses. We present a simulation-based inference framework to measure the population properties of galactic binaries directly from the reconstructed foreground. Adopting an astrophysically agnostic parametrization in the observable space -- defined by signal amplitude, frequency, and frequency derivative -- we generate synthetic catalogs and foreground spectra using a global-fit-inspired subtraction algorithm. We then train a neural posterior estimator to map spectra to population parameters. We validate our method on simulated data and recover population parameters with good accuracy, including the total number of binaries. As a by-product, we present a GPU-accelerated version of the subtraction algorithm, which delivers a ~100X speed-up compared to previous implementations in the literature. Our results demonstrate that LISA's stochastic foreground alone carries significant information about the Galactic binary population and provide a practical step toward joint inference from resolved and unresolved sources.

Figures (15)

• Figure 1: Comparison between the astrophysical catalog of Ref. Lamberts:2019nyk (red) and a simulated catalog (blue) generated by our population model assuming $\boldsymbol{\Lambda} = \{\alpha_\text{PL} = -2.9, \alpha_\Gamma = 1.96, \mu_\Gamma = -21, \beta_\Gamma = 1.8, \mu = -22, \sigma = 0.18, \varrho = 0.99, N_\text{b} = 7.5\times10^6\}$.
• Figure 2: Characteristic strain sensitivity as a function of selected population parameters. We show the predicted mean for the A channel assuming $\alpha_\Gamma=2.5$, $\beta_\Gamma=2$, $\mu_\Gamma=-20.5$, $\mu=-22$, $\sigma=0.3$, and $\varrho=0.85$. In the left panel, we vary the spectral index of the frequency distribution $\alpha_\text{PL}$ while fixing $N_{\rm b}=5\times10^{6}$. In the right panel, we vary the total number of binaries $N_{\rm b}$ while fixing $\alpha_\text{PL}=-3.8$.
• Figure 3: Flowchart of our inference pipeline. The left column (blue) depicts the data generation and processing in the training of the normalizing flow. The right column (teal) shows the inference phase, where we perform inference over a set of PSD reconstructions $\{\boldsymbol{S}_n\}$, which can be obtained with different methods (e.g. GPR or MCMC).
• Figure 4: Left. Comparison between the signal $S_n^\text{A}(f)$ obtained from the subtraction algorithm (red) and the corresponding GPR prediction (blue) for $\boldsymbol{\Lambda} = \{\alpha_\text{PL} = -3.82, \alpha_\Gamma = 2.5, \mu_\Gamma = -20.5, \beta_\Gamma = 2, \mu = -21.8, \sigma = 0.24, \varrho = 0.85, N_\text{b} = 15\times10^6 \}$. Right. MCMC reconstructions of the galactic foreground from the same test simulation using the base model (red) and the splines (blue). The solid lines are given by averaging over posterior draws, while the uncertainity (shaded area) is computed as the $1\sigma$ over the same draws times a factor 100 (10) for the base (spline) model for visualization purposes.
• Figure 5: Training (blue) and validation (red) losses as a function of the epoch number (left $y$-axis). The dashed line indicates the learning rate $\eta$ (right $y$-axis).