Probing <i>z</i> ≳ six massive black holes with gravitational waves

We investigate the coalescence of massive black hole ($M_{\rm BH}\gtrsim 10^{6}~\rm M_{\odot}$) binaries (MBHBs) at $63 \sigma$) overdense regions ($M_h\sim 10^{12}~\rm M_{\odot}$ dark matter halos $z = 6$) Universe. first analyse impact different resolutions and AGN feedback prescriptions merger rate, assuming instantaneous mergers. Then, we compute halo bias correction factor due to simulated region. Our predict rates that range between 3 - 15 $\rm yr^{-1}$ $z\sim 6$, depending run considered, after correcting for $\sim 20-30$. For our fiducial model, further consider effect delay in MBHB dynamical friction. find 83 per cent MBHBs will merge within Hubble time, 21 1 Gyr, namely age Universe > 6$. finally expected properties gravitational wave (GW) signals fraction LISA detectable events with high signal-to-noise ratio (SNR $>$ 5) 66-69 cent. However, identifying electro-magnetic counterpart these remains challenging poor sky localization that, loudest ($\mathcal M_c\sim 10^6~\rm $z=6$), is around 10 deg^2$.