Probing z ≳ 6 massive black holes with gravitational waves

We investigate the coalescence of massive black hole (M-BH greater than or similar to 10(6) M-circle dot) binaries (MBHBs) at 6 < z < 10 by adopting a suite of cosmological hydrodynamical simulations of galaxy formation, zoomed-in on biased (> 3 s) overdense re gions (M-h similar to 10 (12) M-circle dot dark matter haloes at z = 6) of the Universe. We first analyse the impact of different resolutions and AGN feedback prescriptions on the merger rate, assuming instantaneous mergers. Then, we compute the halo bias correction factor due to the o v erdense simulated region. Our simulations predict merger rates that range between 3 and 15 yr (-1) at z similar to 6, depending on the run considered, and after correcting for a bias factor of similar to 20-30. For our fiducial model, we further consider the effect of delay in the MBHB coalescence due to dynamical friction. We find that 83 per cent of MBHBs will merge within the Hubble time, and 21 per cent within 1 Gyr, namely the age of the Universe at z > 6. We finally compute the expected properties of the gravitational wave (GW) signals and find the fraction of LISA detectable events with high signal-to-noise ratio (SNR > 5) to range between 66 per cent and 69 per cent. Ho we ver, identifying the electro-magnetic counterpart of these events remains challenging due to the poor LISA sky localization that, for the loudest signals (M-c similar to 10(6) M-c at z = 6), is around 10 deg(2).