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 3700-22000Å and several strong absorption features ( Balmer series , Ca H+K , G-band ) , from which we derive a stellar velocity dispersion of 318 \pm 53 km s ^ { -1 } .
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 / Z _ { \odot } ) = 0.02 ^ { +0.20 } _ { -0.41 } ) post starburst galaxy , with a mean luminosity weighted log ( age/yr ) of 8.9 \pm 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 \sim 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 \sim 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 .