Synergy between ground and space based gravitational wave detectors. Part II: Localisation

We study the advantage of combining measurements from future ground and space based gravitational wave detectors in estimating the parameters of a black-hole binary coalescence. This is an extension of our previous work (Prog. Theor. Exp. Phys. 2016} (2016) 053E01}) where we used pattern averaged waveform to study non-spinning binaries. In this work we study the localisation and binary plane orientation, including the (non-precessing) spin of binaries. We focus on the third generation terrestrial detector 'Einstein telescope' and a proposed space based detector 'Deci-Hertz Interferometer Gravitational wave Observatory' (DECIGO). We consider two possible orbits for DECIGO, a helio-centric orbit and a Sun-synchronous geo-centric orbit. We demonstrate that one can obtain order of magnitude improvement in the localisation from the space-ground combined measurements, even with a precursor-DECIGO mission (B-DECIGO). This is especially important for the future of gravitational wave astronomy as improving the localisation accuracy further improves our chances of identifying the host galaxies of these binary systems.