Evolution of the black hole – Bulge relationship in QSOs

QSOs allow study of the evolution of the relationship between black holes in galactic nuclei and their host galaxies. The black hole mass MBH can be derived from the widths of the broad emission lines, and the stellar velocity dispersion σ∗ of the host galaxy can be inferred from the narrow emission lines. Results based on [O iii] and [O ii] line widths indicate that the MBH − σ∗ relationship, at redshifts up to z ≈ 2, is consistent with no evolution or an increase of up to ∼0.5 dex in MBH at fixed σ∗. CO line widths offer an estimate of σ∗ for luminous QSOs at high redshifts. The available objects from z ≈ 4–6 have very massive black holes, MBH ∼ 109.5M⊙, but their CO line widths suggest much smaller host galaxies than would be expected by the local MBH − σ∗ relationship. The most massive black holes must continue to reside in comparatively modest galaxies today, because their number density inferred from QSO statistics exceeds the present-day abundance of proportionally massive galaxies.