The kinematics of massive quiescent galaxies at $1.4 < z < 2.1$: dark matter fractions, IMF variation, and the relation to local early-type galaxies.

We study the dynamical properties of massive quiescent galaxies at $1.4 < z < 2.1$ using deep Hubble Space Telescope WFC3/F160W imaging and a combination of literature stellar velocity dispersion measurements and new near-infrared spectra obtained using KMOS on the ESO VLT. We use these data to show that the typical dynamical-to-stellar mass ratio has increased by $\sim$0.2 dex from $z = 2$ to the present day, and investigate this evolution in the context of possible changes in the stellar initial mass function (IMF) and/or fraction of dark matter contained within the galaxy effective radius, $f_\mathrm{DM}$. Comparing our high-redshift sample to their likely descendants at low-redshift, we find that $f_\mathrm{DM}$ has increased by a factor of more than 4 since $z \approx 1.8$, from $f_\mathrm{DM}$ = $6.6\pm1.0$% to $\sim$24%. The observed increase appears robust to changes in the methods used to estimate dynamical masses or match progenitors and descendants. We quantify possible variation of the stellar IMF through the offset parameter $\alpha$, defined as the ratio of dynamical mass in stars to the stellar mass estimated using a Chabrier IMF. We demonstrate that the correlation between stellar velocity dispersion and $\alpha$ reported among quiescent galaxies at low-redshift is already in place at $z = 2$, and argue that subsequent evolution through (mostly minor) merging should act to preserve this relation while contributing significantly to galaxies overall growth in size and stellar mass.