Consistent Dynamical and Stellar Masses with Potential Light IMF in Massive Quiescent Galaxies at 3 < z < 4 Using Velocity Dispersions Measurements with MOSFIRE

We present the velocity dispersion measurements of four massive $\sim10^{11}M_\odot$ quiescent galaxies at $3.2 4$. Investigating the evolution at constant velocity dispersion between $z\sim3.5$ and $z\sim2$, we find a large increase in effective radius $0.35\pm0.12$ dex and in dynamical-to-stellar mass ratio $ $ of 0.33$\pm0.08$ dex, with low expected contribution from dark matter. The dynamical masses for our $z\sim3.5$ sample are consistent with the stellar masses for a Chabrier initial mass function (IMF), with the ratio $ $ = -0.13$\pm$0.10 dex suggesting an IMF lighter than Salpeter may be common for massive quiescent galaxies at $z>3$. This is surprising in light of the Salpeter or heavier IMFs found for high velocity dispersion galaxies at $z\sim2$ and cores of present-day ellipticals, which these galaxies are thought to evolve into. Future imaging and spectroscopic observations with resolved kinematics using the upcoming James Webb Space Telescope could rule out potential systematics from rotation, and confirm these results.