  We investigate the X-ray active galactic nucleus (AGN) properties of
millimeter galaxies in the Great Observatories Origins Deep Survey South
(GOODS-S) field detected with the Atacama Large Millimeter/submillimeter Array
(ALMA), by utilizing the Chandra 7-Ms data, the deepest X-ray survey to date.
Our millimeter galaxy sample comes from the ASAGAO survey covering 26
arcmin$^2$ (12 sources at a 1.2-mm flux-density limit of $\approx$0.6 mJy),
supplemented by the deeper but narrower 1.3-mm survey of a part of the ASAGAO
field by Dunlop et al.\ (2017). Fourteen out of the total 25 millimeter
galaxies have Chandra counterparts. The observed AGN fractions at $z=1.5-3$ is
found to be 90$^{+8}_{-19}$\% and $57^{+23}_{-25}$\% for the ultra/luminous
infrared galaxies with $\log L_{\rm IR}/L_{\odot} = 12-12.8$ and $\log L_{\rm
IR}/L_{\odot} = 11.5-12$, respectively. The majority ($\sim$2/3) of the ALMA
and/or Herschel detected X-ray AGNs at $z=1.5-3$ appear to be star-formation
dominant populations, having $L_{\rm X}$/ $L_{\rm IR}$ ratios smaller than the
"simultaneous evolution" value expected from the local black-hole mass to
stellar mass ($M_{\rm BH}$-$M_*$) relation. On the basis of the $L_{\rm X}$ and
stellar mass relation, we infer that a large fraction of star-forming galaxies
at $z=1.5-3$ have black hole masses smaller than those expected from the local
$M_{\rm BH}$-$M_*$ relation. This is opposite to previous reports on luminous
AGN at same redshifts detected in wider and shallower surveys, which are
subject to selection biases against lower luminosity AGN. Our results are
consistent with an evolutionary scenario that star formation occurs first, and
an AGN-dominant phase follows later, in objects finally evolving into galaxies
with classical bulges.
