Probing the Growth of Massive Black Holes with Black Hole-Host Galaxy Spin Correlations

Supermassive black holes (SMBHs) are commonly found at the centers of their host galaxies, but their formation still remains an open question. In light of the tight correlation between the BH mass and the velocity dispersions of the bulge component of the host galaxy, a BH-host galaxy coevolution scenario has been established. Such description however still contains many theoretical uncertainties, including the puzzels about the formation of BH seeds at high redshifts and the growth channel fueling these seeds. In this work, we systematically analyze the signatures of different growth channels on MBH spins. We show that different growth channels can be partially distinguished with the magnitudes of MBH spins infered from extreme-mass-ratio-inspirals detected by the Laser Interferometer Space Antenna. In addition, we propose to measure the correlation between the directions of MBH spins and their host galaxy spins, which is possible for extreme mass-ratio inspirals happening in low-redshift galaxies ($z \le 0.3$). With the inclusion of spin direction correlation different formation channels shall be significantly better constrained.