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Numerous observations have shown that almost all galaxies in our Universehost supermassive black holes (SMBHs), but there is still much debate abouttheir formation and evolutionary processes. Recently, gravitational waves (GWs)have been expected to be a new and important informative observation, inparticular, in the low-frequency region by making use of the LaserInterferometer Space Antenna (LISA) and Pulsar Timing Arrays (PTAs). As anevolutionary process of the SMBHs, we revisit a dark matter (DM) halo-SMBHcoevolution model based on the halo merger tree employing an ansatz for themass relation between the DM halos and the SMBHs at $z=6$. In this model, themass of SMBHs grows through their mergers associated with the halo mergers, andhence the evolutionary information must be stored in the GWs emitted at themergers. We investigate the stochastic gravitational background from thecoalescing SMBH binaries, which the PTAs can detect, and also the GW burstsemitted at the mergers, which can be detected by the mHz band observations suchas LISA. We also discuss the possibility of probing the mass relation betweenthe DM halos and the SMBHs at high redshift by future GW observations.

Probing the mass relation between supermassive black holes and dark matter halos at high redshifts by gravitational wave experiments