Cosmic Evolution of Black Holes and Spheroids. I. The M BH ‐σ Relation at z = 0.36

Abstract

We test the evolution of the correlation between black hole mass and bulge velocity dispersion (M$_{\rm BH}-\sigma$), using a carefully selected sample of 14 Seyfert 1 galaxies at $z=0.36\pm0.01$. We measure velocity dispersion from stellar absorption lines around Mgb (5175\AA) and Fe (5270\AA) using high S/N Keck spectra, and estimate black hole mass from the H$\beta$ line width and the optical luminosity at 5100\AA, based on the empirically calibrated photo-ionization method. We find a significant offset from the local relation, in the sense that velocity dispersions were smaller for given black hole masses at $z=0.36$ than locally. We investigate various sources of systematic uncertainties and find that those cannot account for the observed offset. The measured offset is $\Delta \log M_{\rm BH}=0.62 \pm 0.10 \pm 0.25$, i.e. $\Delta \log \sigma=0.15 \pm 0.03 \pm 0.06$, where the error bars include a random component and an upper limit to the systematics. At face value, this result implies a substantial growth of bulges in the last 4 Gyr, assuming that the local M$_{\rm BH}-\sigma$ relation is the universal evolutionary end-point. Along with two samples of active galaxies with consistently determined black hole mass and stellar velocity dispersion taken from the literature, we quantify the observed evolution with the best fit linear relation, $\Delta \log M_{\rm BH} = (1.66\pm0.43)z + (0.04\pm0.09)$ with respect to the local relationship of Tremaine et al. (2002), and $\Delta \log M_{\rm BH} = (1.55\pm0.46)z + (0.01\pm0.12)$ with respect to that of Ferrarese (2002). This result is consistent with the growth of black holes predating the final growth of bulges at these mass scales ($ $=170 km s$^{-1}$).