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We present the first stellar velocity dispersion measurement of a massivequenching galaxy at z=4.01. The galaxy is first identified as a massive z>~4galaxy with suppressed star formation from photometric redshifts based on deepmulti-band data in the UKIDSS Ultra Deep Survey field. A follow-upspectroscopic observation with MOSFIRE on Keck revealed strong multipleabsorption features, which are identified as Balmer absorption lines, giving asecure redshift of z=4.01. Thanks to the high S/N of the spectrum, we are ableto estimate the stellar velocity dispersion, sigma=268+/-59 km/s. This velocitydispersion is consistent with that of massive galaxies today, implying nosignificant evolution in stellar velocity dispersion over the last 12 Gyr.Based on an upper limit on its physical size from deep optical images(r_eff<1.3 kpc), we find that its dynamical mass is consistent with the stellarmass inferred from photometry. Furthermore, the galaxy is located on the massfundamental plane extrapolated from lower redshift galaxies. Combining allthese results, we find that the velocity dispersion does not significantlyevolve with redshift, although the size and mass of massive quenched galaxiesdo. This suggests that the mass in the core of massive galaxies does not evolvesignificantly, while most of the mass growth occurs in the outskirts of thegalaxies, which also increases the size. This picture is consistent with atwo-phase formation scenario in which mass and size growth is due to accretionin the outskirts of galaxies via mergers.

Stellar Velocity Dispersion of a Massive Quenching Galaxy at z=4.01