Prospects for Direct Detection of the Circular Polarization of the Gravitational-Wave Background

We discuss the prospects for directly detecting a circular polarization signal of the gravitational-wave background. We find it is generally difficult to probe the monopole mode of the signal due to the broad directivity of the gravitational-wave detectors. But the dipole ($l=1$) and octupole ($l=3$) modes of the signal can be measured in a simple manner by combining outputs of two unaligned detectors, and we can dig them deeply under confusion and detector noises. Around $f\sim 0.1\mathrm{mHz}$ the Laser Interferometer Space Antenna will provide ideal data streams to detect these patterns whose magnitudes are as small as $\sim 1$ percent of the detector noise level in terms of the nondimensional energy density ${\Omega }_{\mathrm{GW}}(f)$.

Figure 1

The effective two-arm interferometers corresponding to the TDI modes $A$ and $E$. The three spacecraft of LISA are shown with circles on the $XY$ plane. The beam pattern functions for the $T$ mode are given with three unit vectors ${\mathit{m}}_i$ as $F_T^P=\sum _{i=1}^3({\mathit{m}}_i·{\mathit{e}}^P·{\mathit{m}}_i)({\mathit{m}}_i·\mathit{n})$.