2010MNRAS.406L..35T

We propose a novel method to estimate M_*/M_BH, the ratio of stellar mass (M_*) to black hole mass (M_BH) at various redshifts using two recent observational results: the correlation between the bolometric luminosity of active galactic nuclei (AGN) and the star formation rate (SFR) in their host galaxies, and the correlation between SFR and M_* in star-forming (SF) galaxies. Our analysis is based on M_BH and L_bol measurements in two large samples of type I AGN at z ≃ 1 and 2, and the measurements of M_*/M_BH in 0.05 < z < 0.2 red galaxies. We find that M_*/M_BH depends on M_BH at all redshifts. At z ≃ 2, M_*/M_BH∼ 280 and ∼40 for M_BH= 10⁸ and M_BH= 10⁹M_☉, respectively. M_*/M_BH grows by a factor of ∼4-8 from z ≃ 2 to 0 with extreme cases that are as large as 10-20. The evolution is steeper than reported in other studies, probably because we treat only AGN in SF hosts. We caution that estimates of M_*/M_BH evolution which ignore the dependence of this ratio on M_BH can lead to erroneous conclusions.