Searching for isotropic stochastic gravitational-wave background in the international pulsar timing array second data release

We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and further this process has scalar transverse (ST) correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is 30 +/- 2. The median and the 90% equal-tail amplitudes of ST mode are A(ST) = 1.29(-0.44)(+0.51) x 10(-15), or equivalently the energy density parameter per logarithm frequency is Omega(ST)(GW) = 2.31(-1.30)(+2.19) x 10(-9), at frequency of 1 year(-1). However, we do not find any statistically significant evidence for the tensor transverse (TT) mode and then place the 95% upper limits as A(TT) < 3.95 x 10(-15), or equivalently Omega(TT)(GW) < 2.16 x 10(-9), at frequency of 1 year(-1).