Probing circular polarization in stochastic gravitational wave background with pulsar timing arrays

We study the detectability of circular polarization in a stochastic gravitational wave background from various sources such as supermassive black hole binaries, cosmic strings, and inflation in the early universe with pulsar timing arrays. We calculate generalized overlap reduction functions for the circularly polarized stochastic gravitational wave background. We find that the circular polarization cannot be detected for an isotropic background. However, there is a chance to observe the circular polarization for an anisotropic gravitational wave background. We also show how to separate polarized gravitational waves from unpolarized gravitational waves.

Figure 1

Plots of the generalized ORFs ${\mathrm{\Gamma }}_{lm}^V$ as a function of the angular separation between the two pulsars $\xi$. In Fig. 1, we find the ORF for the monopole ($\mathrm{l}=0$) is trivial. In Fig. 1, the ORFs for the dipole ($\mathrm{l}=1$) are shown. In Fig. 1, the ORFs for the quadrupole ($\mathrm{l}=2$) are depicted. In Fig. 1, the ORFs for the octupole ($\mathrm{l}=3$) are plotted. The black solid curve, the blue dashed curve, the red dotted curve, the dark-red space-dotted curve, and the green long-dashed curve represent $m=0$, $m=\pm 1$, $m=+2$, $m=-2$, $m=\pm 3$, respectively.

Figure 2

Density plots of the network ORFs ${\mathrm{\Gamma }}_{12:34}^I$ (left panels) and ${\mathrm{\Gamma }}_{12:34}^V$ (right panels) as a function of the two angular separations $\xi$, $\zeta$ for two pulsar pairs, respectively. For simplicity, we assumed $c_{10}^I/c_{00}^I=c_{11}^I/c_{00}^I=c_{1-1}^I/c_{00}^I=1$.

Figure 3

Plots the generalized ORFs ${\mathrm{\Gamma }}_{lm}^I$ as a function of the angular separation between the two pulsars $\xi$. Figure 3 shows monopole ($\mathrm{l}=0$), Fig. 3 shows dipole ($\mathrm{l}=1$), Fig. 3 shows quadrupole ($\mathrm{l}=2$), and Fig. 3 shows octupole ($\mathrm{l}=3$). The black solid curve, the blue dashed curve, the dark-blue dash-dotted curve, the red dotted curve, the green long-dashed curve, the dark-green space-dashed curve represent $m=0$, $m=+1$, $m=-1$, $m=\pm 2$, $m=+3$, $m=-3$, respectively.