We present stellar velocity dispersion measurements in the host galaxies of 10 luminous quasars (M_V < -23) using the Ca H&K lines in off-nuclear spectra. We combine these data with effective radii and magnitudes from the literature to place the host galaxies on the Fundamental Plane (FP) where their properties are compared to other types of galaxies. We find that the radio-loud (RL) QSO hosts have similar properties to massive elliptical galaxies, while the radio-quiet (RQ) hosts are more similar to intermediate mass galaxies. The RL hosts lie at the upper extreme of the FP due to their large velocity dispersions (<sigma_*> = 321 km s^-1), low surface brightness (<mu_e(r)> = 20.8 mag arcsec^-2), and large effective radii (<R_e> = 11.4 kpc), and have <M_*> = 1.5 x 10^12 M_sun and <M/L> = 12.4. In contrast, properties of the RQ hosts are <sigma_*> = 241 km s^-1, <M_*> ~ 4.4 x 10^11 M_sun, and <M/L> ~ 5.3. The distinction between these galaxies occurs at sigma_* ~ 300 km s^-1, R_e ~ 6 kpc, and corresponding M_* ~ 5.9 +/- 3.5 x 10^11 M_sun. Our data support previous results that PG QSOs are related to gas-rich galaxy mergers that form intermediate-mass galaxies, while RL QSOs reside in massive early-type galaxies, most of which also show signs of recent mergers or interactions. Most previous work has drawn these conclusions by using estimates of the black hole mass and inferring host galaxy properties from that, while here we have relied purely on directly measured host galaxy properties.
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