Moircs deep survey. III. Active galactic nuclei in massive galaxies at z = 2-4

We investigate the X-ray properties of the K-band-selected galaxies at redshift 2 < z < 4 by using our deep near-infrared images obtained in the Multi-Object Infrared Camera and Spectrograph Deep Survey project and the published Chandra X-ray source catalog. Sixty-one X-ray sources with the 2-10 keV luminosity L_X = 10⁴²-10⁴⁴ erg s ^-1 are identified with the K-selected galaxies and we found that they are exclusively (90%) associated with the massive objects with a stellar mass larger than 10^10.5 M ₁. Our results are consistent with the idea that the M _BH/M _str ratio of the galaxies at z = 2-4 is similar to the present-day value. On the other hand, the active galactic nucleus (AGN) detection rate among the very massive galaxies with a stellar mass larger than 10¹¹ M ₁ is high, 33% (26/78). They are active objects in the sense that the black hole mass accretion rate is 1%-50% of the Eddington limit if they indeed have similar M _BH/M _str ratio with those observed in the local universe. The active duration in the AGN duty cycle of the high-redshift massive galaxies seems large.