The rest-frame optical sizes of massive galaxies with suppressed star formation at $zsim4$

We present the rest-frame optical sizes of massive quiescent galaxies (QGs) at $zsim4$ measured at $K$-band with the Infrared Camera and Spectrograph (IRCS) and AO188 on the Subaru telescope. Based on a deep multi-wavelength catalog in the Subaru XMM-Newton Deep Survey Field (SXDS), covering a wide wavelength range from the $u$-band to the IRAC $8.0mu m$ over 0.7 deg$^2$, we evaluate photometric redshift to identify massive ($M_{star}sim10^{11} M_odot$) galaxies with suppressed star formation. These galaxies show a prominent 4000$rm AA$ break feature at $zsim4$, suggestive of an evolved stellar population. We then conduct follow-up $K$-band imaging with adaptive optics for the five brightest galaxies ($K_{AB,total}=22.5sim23.4$). Compared to lower redshift ones, QGs at $zsim4$ have smaller physical sizes of effective radii $r_{eff}=0.2$ to $1.8$ kpc. The mean size measured by stacking the four brightest objects is $r_{eff}=0.7rm kpc$. This is the first measurement of the rest-frame optical sizes of QGs at $zsim4$. We evaluate the robustness of our size measurements using simulations and find that our size estimates are reasonably accurate with an expected systematic bias of $sim0.2$ kpc. If we account for the stellar mass evolution, massive QGs at $zsim4$ are likely to evolve into the most massive galaxies today. We find their size evolution with cosmic time in a form of $log(r_e/{rm kpc})= -0.44+1.77 log(t/rm Gyr)$. Their size growth is proportional to the square of stellar mass, indicating the size-stellar mass growth driven by minor dry mergers.