Combining a theoretical model of mass accretion onto a galactic center with a high-resolution N -body/SPH simulation , we investigate the formation of an intermediate massive black hole ( IMBH ) during the hierarchical formation of a small spiral galaxy ( with a total mass of 10 ^ { 10 } M _ { \odot } ) in the high- z universe .
We found that the rate of average mass accretion to the nucleus due to the radiation drag exerted by newly formed stars in the forming galaxy is \approx 10 ^ { -5 } M _ { \odot } yr ^ { -1 } .
As a result of this accretion , an IMBH with \approx 10 ^ { 4 } M _ { \odot } can be formed in the center of the spiral galaxy at z \sim 4 .
We found that a central BH coevolves with the dark matter halo from z \sim 15 to z \sim 2 .
The mass ratio of the BH to the dark matter halo is nearly constant \approx ( 1 - 3 ) \times 10 ^ { -6 } from z \sim 10 to z \sim 2 .
This is because that change in the dark matter potential enhances star formation in the central part of the galaxy , and as a result the BH evolves due to mass accretion via the radiation drag .
Therefore , our model naturally predicts a correlation between massive BHs and dark matter halos .
Moreover , it is found that the final BH-to-bulge mass ratio ( \approx 5 \times 10 ^ { -5 } ) in a small spiral galaxy at high- z is much smaller than that in the large galaxies ( \approx 10 ^ { -3 } ) .
Our results also suggest that the scatter in the observed scaling relations between the bulge mass and black hole mass are caused by a time lag between BH growth and growth of bulge .
We also predict that the X-ray luminosity of AGN is positively correlated with the CO luminosity in the central region .
By comparing our results with the properties of Lyman break galaxies ( LBGs ) , it is predicted that some LBGs have massive BHs of \approx 10 ^ { 6 } -10 ^ { 7 } M _ { \odot } .