Polarization analysis of gravitational-wave backgrounds from the correlation signals of ground-based interferometers: measuring a circular-polarization mode

TL;DR

This work develops a comprehensive framework to measure the circular polarization (Stokes $V$) of a stochastic gravitational-wave background using cross-correlations of ground-based interferometers. It introduces an overlap-function formalism for both unpolarized ($I$) and circularly polarized ($V$) components and analyzes how detector geometry, including optimal configurations and antipodal setups, affects sensitivity. The authors derive broadband SNR expressions and quantify the performance of next-generation networks, showing that a larger network enables simultaneous estimation of $I$ and $V$ with limited statistical loss, thereby enabling tests of parity violation in the early universe. The results provide concrete guidance for detector design and data-analysis strategies to probe fundamental physics via gravitational-wave backgrounds.

Abstract

The Stokes V parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and non-vanishing value of the V parameter yields a circularly polarized signal. Cosmologically, V parameter may be a direct probe for parity violation in the universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently $Ω_{GW}$), the signal analysis including a circular-polarized mode has a rich structure due to the multi-dimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.

Figures (13)

• Figure 1: Detector planes are tangential to a sphere. Two detectors $a$ and $b$ are separated by the angle $\beta$ measured from the center of the sphere. The angles $\sigma_1$ and $\sigma_2$ describe the orientation of bisectors of interferometers in a counter-clockwise manner relative to the great circle joining two sites.
• Figure 2: Type I configuration with a given separation angle $\beta$. Relative to a fixed L-shaped interferometer $a$, the second one must be placed on two great circles shown with long-dashed lines (left panel). We also have four equivalent detector orientations due to mod-$90^\circ$ freedom as shown in the right panel.
• Figure 4: The functions $\Theta_1(f,\beta)$ and $\Theta_2(f,\beta)$ for detectors on the Earth at frequencies $f=10$Hz, 50Hz and 70Hz.
• Figure 6: The function $\Theta_3(f,\beta)$ for detectors on the Earth at frequencies $f=10$Hz, 50Hz and 70Hz.
• Figure 8: The function $|\gamma_V|$ for detectors on the Earth with type III configuration. The solid curve (dotted curve) is the result with $\beta=\pi$ ($\beta=5\pi/6$). The dashed line is result with $\beta_{max}$ for which the function $|\gamma_V|$ becomes maximum with given frequency $f$.