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Assuming that, for a given source of gravitational waves (GWs), we know itssky position, as is the case of GW events with an electromagnetic counterpartsuch as GW170817, we discuss a null stream method to probe GW polarizationsincluding spin-0 (scalar) GW modes and spin-1 (vector) modes, especially withan expected network of Advanced LIGO, Advanced Virgo and KAGRA. For twoindependent null streams for four non-co-aligned GW detectors, we study alocation on the sky, exactly at which the spin-0 modes of GWs vanish in anynull stream for the GW detector network, though the strain output at a detectormay contain the spin-0 modes. Our numerical calculations show that there existseventy sky positions that satisfy this condition of killing the spin-0 modesin the null streams. If a GW source with an electromagnetic counterpart isfound in one of the seventy sky positions, the spin-1 modes will be testableseparately from the spin-0 modes by the null stream method. In addition, westudy a superposition of the two null streams to show that any one of the threemodes (one combined spin-0 and two spin-1 modes) can be eliminated by suitablyadjusting a weighted superposition of the null streams and thereby a set of theremaining polarization modes can be experimentally tested.

Probing gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA