Applicability of multi-component study on Bayesian searches for targeted anisotropic stochastic gravitational-wave background

TL;DR

The paper investigates biases in Bayesian searches for anisotropic SGWB when using a single-component sky model and demonstrates that a multi-component framework—combining isotropic and targeted anisotropic components such as Galactic-plane patterns—mitigates these biases. It introduces a Gaussian likelihood for multi-component SGWB inference with a factorized sky model $P_{lm}(f,\vec{\theta})=\epsilon\bar{H}(f,\vec{\theta})\bar{\mathcal{P}}_{lm}$ and precomputable terms $X_{\mu}^i$ and $\Gamma_{\mu\nu}^{ij}$, enabling efficient nested sampling. Through injections of pure isotropic and Galactic-plane patterns, the study shows that two-component recovery precisely retrieves injected parameters for loud signals, while single-component recovery remains biased; probability–probability plots and Bayes factors consistently favor the multi-component model when both components are present. The findings underscore the necessity of multi-template anisotropy analyses in current and future SGWB searches to avoid misinterpretation of sky maps and emphasize that the approach remains robust as long as at least one component has modest signal-to-noise ratio ($\mathrm{SNR} \gtrsim 2$–$3$). This work has practical implications for LVK-era analyses and motivates broader adoption of sky-map separation techniques in stochastic GW searches.

Abstract

Stochastic background gravitational waves have not yet been detected by ground-based laser interferometric detectors, but recent improvements in detector sensitivity have raised considerable expectations for their eventual detection. Previous studies have introduced methods for exploring anisotropic background gravitational waves using Bayesian statistics. These studies represent a groundbreaking approach by offering physically motivated anisotropy mapping that is distinct from the Singular Value Decomposition regularization of the Fisher Information Matrix. However, they are limited by the use of a single model, which can introduce potential bias when dealing with complex data that may consist of a mixture of multiple models. Here, we demonstrate the bias introduced by a single-component model approach in the parametric interpretation of anisotropic stochastic gravitational-wave backgrounds, and we confirm that using multiple-component models can mitigate this bias.

Figures (5)

• Figure 1: An example posterior distribution of two-component recovery against two-component injection test with $\ln{\mathrm{BF}}\sim2.73\times10^4$. The red marker and lines shows the injection parameters for Galactic-plane injection while yellow ones represents those for Isotropic injection.
• Figure 2: An example posterior distribution of single-component recovery against two-component injection test with $\ln{\mathrm{BF}}\sim1.92\times10^4$. The parameters for Galactic-plane model is recovered only. The red marker and lines shows the injection parameters for Galactic-plane injection. The injection parameter for Isotropic injection is not shown in the figure since it is not the target anisotropy to recover for.
• Figure 3: The probability-probability plot for multiple component injection (Isotropic and Galactic-plane). The left plot corresponds to single component (Galactic plane) recovery and the right plot corresponds to multiple component (Isotropic and Galactic-plane) recovery. In the right plot, the index $0$ of $\epsilon$ and $\alpha$ refers to the parameters of Galactic-plane, and index $1$ to that of Isotropic injection. The gray region in both figures is the 2$\sigma$ credible region expected from applying central limit theorem to binomial distribution.
• Figure 4: The two dimensional heat maps for natural logarithm of BF in the case of injecting different sets of amplitude. Left: BF's heat map of multi-component recovery model against noise model. Right: BF's heat map of multi-component recovery model against single component recovery (Galactic-plane) model.
• Figure 5: The histogram of $\ln\mathcal{B}_{\rm N}^{\rm SIG}$ for 500 tests with different noise realization each. The blue, orange, and green correspond to two-component recovery with no injection, single-component and two-component recovery for two-component injections.