Generalized Optimal Statistic for Multiple Cross Correlated Signals

The Optimal Statistic is a frequentist approach within pulsar timing arrays (PTAs) to calculate the amplitude squared of our gravitational wave background (GWB). The expected cross correlations of this signal are quadrupolar and higher order. But monopole and dipole correlated noise may be present within our data.

To better retrieve signals that are present, we present a generalized optimal statistic capable of analyzing multiple cross correlated signals (MCOS) simultaneously. By creating simulations with quadrupole GWB, monopole GWB and a combination of both, we show that the MCOS is able to correctly identify the GWB present within our data.