We present deep, near-infrared HST/WFC3 grism spectroscopy and imaging for a sample of 14 galaxies at z~2 selected from a mass-complete photometric catalog in the COSMOS field. By combining the grism observations with photometry in 30 bands, we derive accurate constraints on their redshifts, stellar masses, ages, dust extinction and formation redshifts. We show that the slope and scatter of the z~2 mass-size relation of quiescent galaxies is consistent with the local relation, and confirm previous findings that the sizes for a given mass are smaller by a factor of two to three. Finally, we show that the observed evolution of the mass-size relation of quiescent galaxies between z=2 and 0 can be explained by quenching of increasingly larger star-forming galaxies, at a rate dictated by the increase in the number density of quiescent galaxies with decreasing redshift. However, we find that the scatter in the mass-size relation should increase in the quenching-driven scenario in contrast to what is seen in the data. This suggests that merging is not needed to explain the evolution of the median mass-size relation of massive galaxies, but may still be required to tighten its scatter, and explain the size growth of individual z=2 galaxies quiescent galaxies.
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