MAGAZ3NE: High Stellar Velocity Dispersions for Ultra-Massive Quiescent Galaxies at $z\gtrsim3$

In this work we publish stellar velocity dispersions, sizes, and dynamical masses for 8 ultra-massive galaxies (UMGs; log($M$/M$_\odot>11$, $z\gtrsim3$) from the Massive Ancient Galaxies At $z>3$ NEar-infrared (MAGAZ3NE) Survey, more than doubling the number of such galaxies with velocity dispersion measurements at this epoch. Using the deep Keck/MOSFIRE and Keck/NIRES spectroscopy of these objects in the $H$- and $K$-bandpasses, we obtain large velocity dispersions of $\sim400$ km s$^{-1}$ for most of the objects, which are some of the highest stellar velocity dispersions measured, and $\sim40$\% larger than those measured for galaxies of similar mass at $z\sim1.7$. The sizes of these objects are also smaller by a factor of 1.5-3 compared to this same $z\sim1.7$ sample. We combine these large velocity dispersions and small sizes to obtain dynamical masses. The dynamical masses are similar to the stellar masses of these galaxies, consistent with a Chabrier initial mass function (IMF). Considered alongside previous studies of massive quiescent galaxies across $0.2<z<4.0$, there is evidence for an evolution in the relation between the dynamical mass - stellar mass ratio and velocity dispersion as a function of redshift. This implies an IMF with fewer low mass stars (e.g., Chabrier IMF) for massive quiescent galaxies at higher redshifts in conflict with the bottom-heavy IMF (e.g., Salpeter IMF) found in their likely $z\sim0$ descendants, though a number of alternative explanations such as a different dynamical structure or significant rotation are not ruled out. Similar to data at lower redshifts, we see evidence for an increase of IMF normalization with velocity dispersion, though the $z\gtrsim3$ trend is steeper than that for $z\sim0.2$ early-type galaxies and offset to lower dynamical-to-stellar mass ratios.