Search for the non-linearities of gravitational wave background in NANOGrav 15-year data set

The recently reported signal of common red noise between pulsars by several pulsar timing array collaborations has been thought as evidence of the stochastic gravitational wave background (SGWB) due to the Helling-Downs correlation. In this Letter, we search for the non-Gaussianity of SGWB through its non-linear effect on the overlap reduction function in NANOGrav 15-year data set. In particular, we focus on a folded component to SGWB whose amplitude is quantified with a single parameter $\alpha$ in the unpolarized case. The resulting Bayes factor of $1.68 \pm 0.01$ ($1.78 \pm 0.01$ in the case of signals from SMBHBs) indicates that there is no evidence of such a non-Gaussianity of SGWB in the NANOGrav 15-year data yet. If it is detected in future PTA experiments, it will impact our understanding on the origin of the detected SGWB.