Analyzing intermittent stochastic gravitational wave background I:Effect of detector response

Abstract

With the growing number of gravitational-wave detections, particularly from binary black hole mergers, there is increasing anticipation that an astrophysical background, formed by an ensemble of faint, high-redshift events, will be observed in the near future by the ground-based detector network. This background is anticipated to exhibit non-Gaussian statistical properties. To develop a robust method for detecting such a non-Gaussian gravitational-wave background, we revisit optimal detection strategies based on the Gaussian-mixture likelihood model. In this work, we demonstrate that properly accounting for the detector antenna pattern is essential. Current approaches typically rely on the overlap reduction function averaged over the sky. Through simulations, we show that using such an averaged response introduces significant biases in parameter estimation. In addition, we propose a computationally feasible method that incorporates second-order corrections as an approximation of the full integral over the source distribution. Our results indicate that this approach effectively eliminates these biases. We also show that our method remains robust even when considering anisotropic backgrounds.

Figures (9)

• Figure 1: Schematic representation of the deformation in the GWB distribution after projection onto the detector $H_1$. The grey and green histograms show the distribution of $\Re\tilde{h}_+$ (Gaussian) and the received signal by the detector $\Re\sf_{H_1}$, respectively. Solid curves indicate three different theoretical predictions: the blue curve ($\mathcal{G}_I$) shows the fully integrated model calculated as in Eq. (\ref{['eq:cov']}), the red curve ($\mathcal{G}_C$) depicts the Gaussian distribution corrected by the second-order covariance matrix $\Gamma_{ab}$ as in Eq. (\ref{['eq_Taylor_L']}), and the black curve ($\mathcal{G}$) represents the leading-order Gaussian approximation.
• Figure 2: Distributions of the quantities related to the GW detector projection vector $\vec{y}=(|\gamma_1|^2,|\gamma_2|^2,\Re\gamma_{12},\Im\gamma_{12})$ for isotropic source distribution. The gray color represents the detector pair LIGO-Livingston vs. LIGO-Hanford, while the blue color represents the detector pair LIGO-Livingston vs. Virgo. The left and right panels correspond to $10$Hz and $100$Hz, respectively.
• Figure 3: Frequency dependence of the mean and the second-order covariance matrix elements of $\vec{y}$ for an isotropic source distribution. Left panel: The sky-averaged overlap reduction function of $\langle \gamma_{IJ}(f, \hat{\Omega}_i) \rangle_{\hat{\Omega}_i}$, which is related to the standard overlap reduction function by $\langle \gamma_{IJ}(f, \hat{\Omega}_i) \rangle_{\hat{\Omega}_i} = 2 \bar{\gamma}_{12}(f)/5$. Right panel: The second-order covariance matrix elements $\Gamma_{ab}$, with different colors representing different components. Solid lines correspond to the LIGO-Livingston vs. LIGO-Hanford detector pair, while dashed lines represent the LIGO-Livingston vs. Virgo pair. Note that the lines corresponding to the (1,3) and (2,3) elements are overlapping.
• Figure 4: A sky map illustrating the distribution of the toy-model anisotropic GWB. The top panel corresponds to the $a_1$ model, characterized by a non-uniform distribution with $\sigma^2_\Omega = 0.06$, while the bottom panel shows the $a_2$ model with $\sigma^2_\Omega = 0.25$.
• Figure 5: Distributions of $\vec{y}=(|\gamma_1|^2,|\gamma_2|^2,\Re\gamma_{12},\Im\gamma_{12})$, comparing the cases of isotropic and anisotropic source distributions. Grey indicates the isotropic distribution, red corresponds to the anisotropic distribution with $\sigma^2_\Omega = 0.25$, and green corresponds to the anisotropic distribution with $\sigma^2_\Omega = 0.06$. The detector pair assumed is LIGO-Livingston vs. LIGO-Hanford. The left and right panels show the results at $10$Hz and $100$Hz, respectively.