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Velocity Dispersions of Massive Quiescent Galaxies from Weak Lensing and Spectroscopy

We use MMT spectroscopy and deep Subaru Hyper Suprime-Cam (HSC) imaging to compare the spectroscopic central stellar velocity dispersion of quiescent galaxies with the effective dispersion of the dark matter halo derived from the stacked lensing signal. The spectroscopic survey (the Smithsonian Hectospec Lensing Survey) provides a sample of 4585 quiescent galaxy lenses with measured line-of-sight central stellar velocity dispersion ($σ_{\rm SHELS}$) that is more than 85% complete for $R < 20.6$, $D_{n}4000> 1.5$ and $M_{\star} > 10^{9.5}{\rm M}_{\odot}$. The median redshift of the sample of lenses is 0.32. We measure the stacked lensing signal from the HSC deep imaging. The central stellar velocity dispersion is directly proportional to the velocity dispersion derived from the lensing $σ_{\rm Lens}$, $σ_{\rm Lens} = (1.05\pm0.15)σ_{\rm SHELS}+(-21.17\pm35.19)$. The independent spectroscopic and weak lensing velocity dispersions probe different scales, $\sim3$kpc and $\gtrsim$ 100 kpc, respectively, and strongly indicate that the observable central stellar velocity dispersion for quiescent galaxies is a good proxy for the velocity dispersion of the dark matter halo. We thus demonstrate the power of combining high-quality imaging and spectroscopy to shed light on the connection between galaxies and their dark matter halos.