The correlation of black hole mass with metallicity index of host spheroid

We investigate the correlation between the mass of the supermassive black holes (SMBHs) and metal abundance, using existing data sets. The SMBH mass $M_{bh}$ is well correlated with integrated stellar feature of Mgb. For 28 galaxies, the best-fit $M_{bh}$-Mgb relation has a small scatter, which is an equivalent level with other well-known relation, such as a correlation between the stellar velocity dispersion and the mass. An averaged iron index $<$Fe$>$ also positively correlates with $M_{bh}$, but the best-fit $M_{bh}$-$<$Fe$>$ relation has a larger scatter. The difference comes from the synthesis and evolution mechanisms, and may be important for the SMBH and star formation history in the host spheroid.