Chinese Acad Sci, Inst High Energy Phys, High Energy Astrophys Lab, Beijing 100039, Peoples R China
; Beijing Univ, Beijing Astrophys Ctr, Beijing 100871, Peoples R China
The strong correlation between the mass of the central supermassive black hole (SMBH) and the bulge in some galaxies and quasars implies that the formation of the black hole is somehow linked to the bulge. The measurement of metallicity by NV/CIV or NV/HeII in quasars allows to discuss a possible way of formation of the black hole. In this letter we trace the metallicity along the possible routes in Rees' diagram in order to test the ways by which SMBHs can form. We derive a relation between the metallicity and the mass of the SMBH as Z proportional to M-BH based on the numerical simulation of the evolution of star clusters. It is in good agreement with the relation determined by the metallicity measured by NV/CIV or NV/HeII in Hamann & Ferland's sample. This lends observational support to the formation of SMBHs via routes R4 or R5, namely, the evolution of dense star clusters.