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We present host stellar velocity dispersion measurements for a sample of 88broad-line quasars at 0.1<z<1 (46 at z>0.6) from the Sloan Digital Sky SurveyReverberation Mapping (SDSS-RM) project. High signal-to-noise ratio coaddedspectra (average S/N~30 per 69 km/s pixel) from SDSS-RM allowed decompositionof the host and quasar spectra, and measurement of the host stellar velocitydispersions and black hole (BH) masses using the single-epoch (SE) virialmethod. The large sample size and dynamic range in luminosity(L5100=10^(43.2-44.7) erg/s) lead to the first clear detection of a correlationbetween SE virial BH mass and host stellar velocity dispersion far beyond thelocal universe. However, the observed correlation is significantly flatter thanthe local relation, suggesting that there are selection biases in high-zluminosity-threshold quasar samples for such studies. Our uniform sample andanalysis enable an investigation of the redshift evolution of the M-sigmarelation free of caveats by comparing different samples/analyses at disjointredshifts. We do not observe evolution of the M-sigma relation in our sample,up to z~1, but there is an indication that the relation flattens towards higherredshifts. Coupled with the increasing threshold luminosity with redshift inour sample, this again suggests certain selection biases are at work, andsimple simulations demonstrate that a constant M-sigma relation is favored toz~1. Our results highlight the scientific potential of deep coaddedspectroscopy from quasar monitoring programs, and offer a new path to probe theco-evolution of BHs and galaxies at earlier times.

The Sloan Digital Sky Survey Reverberation Mapping Project: No Evidence for Evolution in the M-sigma Relation to z~1