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Deep Absorption Line Studies of Quiescent Galaxies at z~2: The Dynamical Mass-Size Relation, and First Constraints on the Fundamental plane

We present dynamical and structural scaling relations of quiescent galaxies at z=2, including the dynamical mass-size relation and the first constraints on the fundamental plane (FP). The backbone of the analysis is a new, very deep VLT/X-shooter spectrum of a massive, compact, quiescent galaxy at z=2.0389. We detect the continuum between 3700-22000A and several strong absorption features (Balmer series, Ca H+K, G-band), from which we derive a stellar velocity dispersion of 318 +/- 53 km/s. We perform detailed modeling of the continuum emission and line indices and derive strong simultaneous constraints on the age, metallicity, and stellar mass. The galaxy is a dusty (A_V=0.77 (+0.36,-0.32)) solar metallicity (log(Z/Zsun) = 0.02 (+0.20,-0.41)) post starburst galaxy, with a mean luminosity weighted log(age/yr) of 8.9 +/- 0.1. The galaxy formed the majority of its stars at z>3 and currently has little or no ongoing star formation. We compile a sample of three other z~2 quiescent galaxies with measured velocity dispersions, two of which are also post starburst like. Their dynamical mass-size relation is offset significantly less than the stellar mass-size relation from the local early type relations, which we attribute to a lower central dark matter fraction. Recent cosmological merger simulations qualitatively agree with the data, but can not fully account for the evolution in the dark matter fraction. The z~2 FP requires additional evolution beyond passive stellar aging, to be in agreement with the local FP. The structural evolution predicted by the cosmological simulations is insufficient, suggesting that additional, possibly non-homologous structural evolution is needed.