The Sloan Digital Sky Survey Reverberation Mapping Project: No evidence for evolution in the $M_{\bullet }-{\sigma }_{\ast }$ RELATION TO $z\sim 1$

We present host stellar velocity dispersion measurements for a sample of 88 broad-line quasars at $0.1<z<1$ (46 at $z>0.6$) from the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project. High signal-to-noise ratio coadded spectra (average $S/N\approx 30$ per 69 $km{s}^{-1}$ pixel) from SDSS-RM allowed for the decomposition of the host and quasar spectra and for measurements of the host stellar velocity dispersions and black hole (BH) masses using the single-epoch (SE) virial method. The large sample size and dynamic range in luminosity ($L_{5100}={10}^{43.2-44.7}erg{s}^{-1}$) lead to the first clear detection of a correlation between SE virial BH mass and host stellar velocity dispersion far beyond the local universe. However, the observed correlation is significantly flatter than the local relation, suggesting that there are selection biases in high-z luminosity-threshold quasar samples for such studies. Our uniform sample and analysis enable an investigation of the redshift evolution of the $M_{\bullet }-{\sigma }_{\ast }$ relation relatively free of caveats by comparing different samples/analyses at disjoint redshifts. We do not observe evolution of the $M_{\bullet }-{\sigma }_{\ast }$ relation in our sample up to $z\sim 1$, but there is an indication that the relation flattens toward higher redshifts. Coupled with the increasing threshold luminosity with redshift in our sample, this again suggests that certain selection biases are at work, and simple simulations demonstrate that a constant $M_{\bullet }-{\sigma }_{\ast }$ relation is favored to $z\sim 1$. Our results highlight the scientific potential of deep coadded spectroscopy from quasar monitoring programs, and offer a new path to probe the co-evolution of BHs and galaxies at earlier times.