Unraveling the formation histories of the first supermassive black holes with the Square Kilometre Array's pulsar timing array

Galaxy mergers at high redshifts trigger activity of their central supermassive black holes, eventually also leading to their coalescence as well as a potential source of low-frequency gravitational waves detectable by the Square Kilometre Array's pulsar timing array (SKA PTA). Two key parameters related to the fueling of black holes are the Eddington ratio of quasar accretion, & eta;(Edd), and the radiative efficiency of the accretion process, & epsilon; (which affects the so-called active lifetime of the quasar, t(QSO)). Here, we forecast the regime of detectability of gravitational wave events with SKA PTA. We find the associated binaries to have orbital periods of the order of weeks to years, observable via relativistic Doppler velocity boosting and/or optical variability of their light curves. Combining the SKA regime of detectability with the latest observational constraints on high-redshift black hole mass and luminosity functions, as well as theoretically motivated prescriptions for the merger rates of dark matter halos, we forecast the number of active counterparts of SKA PTA events expected as a function of primary black hole mass at z  & GSIM; 6. We find that the quasar counterpart of the most massive black holes will be uniquely localizable within the SKA PTA error ellipse at z  & GSIM; 6. We also forecast the number of expected counterparts as a function of the quasars' Eddington ratios and active lifetimes. Our results show that SKA PTA detections can place robust constraints on the seeding and growth mechanisms of the first supermassive black holes.