In this paper we study a key phase in the formation of massive galaxies : the transition of star forming galaxies into massive ( M _ { stars } \sim 10 ^ { 11 } M _ { \odot } ) , compact ( r _ { e } \sim 1 kpc ) quiescent galaxies , which takes place from z \sim 3 to z \sim 1.5 .
We use HST grism redshifts and extensive photometry in all five 3D-HST/CANDELS fields , more than doubling the area used previously for such studies , and combine these data with Keck MOSFIRE and NIRSPEC spectroscopy .
We first confirm that a population of massive , compact , star forming galaxies exists at z \gtrsim 2 , using K -band spectroscopy of 25 of these objects at 2.0 < z < 2.5 .
They have a median [ N ii ] /H \alpha ratio of 0.6 , are highly obscured with SFR ( tot ) /SFR ( H \alpha ) \sim 10 , and have a large range of observed line widths .
We infer from the kinematics and spatial distribution of H \alpha that the galaxies have rotating disks of ionized gas that are a factor of \sim 2 more extended than the stellar distribution .
By combining measurements of individual galaxies , we find that the kinematics are consistent with a nearly Keplerian fall-off from V _ { rot } \sim 500 km s ^ { -1 } at 1 kpc to V _ { rot } \sim 250 km s ^ { -1 } at 7 kpc , and that the total mass out to this radius is dominated by the dense stellar component .
Next , we study the size and mass evolution of the progenitors of compact massive galaxies .
Even though individual galaxies may have had complex histories with periods of compaction and mergers , we show that the population of progenitors likely followed a simple inside-out growth track in the size-mass plane of \Delta \log r _ { e } \sim 0.3 \Delta \log M _ { stars } .
This mode of growth gradually increases the stellar mass within a fixed physical radius , and galaxies quench when they reach a stellar density or velocity dispersion threshold .
As shown in other studies , the mode of growth changes after quenching , as dry mergers take the galaxies on a relatively steep track in the size-mass plane .