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Galaxy mergers at high redshifts trigger the activity of their centralsupermassive black holes, eventually also leading to their coalescence -- and apotential source of low-frequency gravitational waves detectable by the SKAPulsar Timing Array (PTA). Two key parameters related to the fuelling of blackholes are the Eddington ratio of quasar accretion $\eta_{\rm Edd}$, and theradiative efficiency of the accretion process, $\epsilon$ (which affects theso-called active lifetime of the quasar, $t_{\rm QSO}$). We forecast the regimeof detectability of gravitational wave events with SKA PTA, finding theassociated binaries to have orbital periods on the order of weeks to years,observable through relativistic Doppler velocity boosting and/or opticalvariability of their light curves. Combining the SKA regime of detectabilitywith the latest observational constraints on high-redshift black hole mass andluminosity functions, and theoretically motivated prescriptions for the mergerrates of dark matter haloes, we forecast the number of active counterparts ofSKA PTA events expected as a function of primary black hole mass at $z \gtrsim6$. We find that the quasar counterpart of the most massive black holes will be${uniquely \ localizable}$ within the SKA PTA error ellipse at $z \gtrsim 6$.We also forecast the number of expected counterparts as a function of thequasars' Eddington ratio and active lifetime. Our results show that SKA PTAdetections can place robust constraints on the seeding and growth mechanisms ofthe first supermassive black holes.

Unravelling the formation of the first supermassive black holes with the SKA pulsar timing array