The ALMA view of the high-redshift relation between supermassive black holes and their host galaxies

Abstract: This work aims at studying the $M_{BH}-M_{dyn}$ relation of a sample of $2<z\<7$ quasars by constraining their host galaxy masses through full kinematical modeling of the cold gas kinematics, thus avoiding all possible biases and effects introduced by the rough virial estimates usually adopted so far. For this purpose we retrieved public observations of $72$ quasar host galaxies observed in ${\rm [CII]_{158\mu m}}$ or ${\rm CO}$ transitions with the Atacama Large Millimeter Array (ALMA). We then selected those quasars whose line emission is spatially resolved and performed a kinematic analysis on ALMA observations. We estimated the dynamical mass of the systems by modeling the gas kinematics with a rotating disc taking into account geometrical and instrumental effects. Our dynamical mass estimates, combined with $M_{BH}$ obtained from literature and our own new ${\rm CIV}\lambda1550$ observations, have allowed us to investigate the $ M_{BH}/M_{dyn}$ in the early Universe. Overall we obtained a sample of $10$ quasars at $z\sim2-7$ in which line emission is detected with high S/N ($> 5-10$) and the gas kinematics is spatially resolved and dominated by ordered rotation. The estimated dynamical masses place $6$ out of $10$ quasars above the local relation yielding to a $M_{BH}/M_{dyn}$ ratios $\sim10\times$ higher than those estimated in low-$z$ galaxies. On the other hand, we found that $4$ quasars at $z\sim 4-6$ have dynamical-to-BH mass ratios consistent with what is observed in early-type galaxies in the local Universe.