Demonstrating A New Census of INfrared Galaxies with ALMA (DANCING-ALMA). I. FIR Size and Luminosity Relation at z = 0-6 Revealed with 1034 ALMA Sources

We present the large statistics of the galaxy effective radius in the rest-frame far-infrared (FIR) wavelength Re(FIR) obtained from 1627 deep ALMA 1-mm band maps that become public by 2017 July. Our ALMA sample consists of 1034 sources at z=0-6 that typically have the star-formation rate of ~100-1000 M$_{\odot}$/yr and the stellar mass of ~10$^{10}$-10$^{11.5}$ M$_{\odot}$. We homogeneously derive Re(FIR) and FIR luminosity L_FIR of our ALMA sources via the same uv-visibility method with the exponential disk fitting, carefully evaluating the selection and measurement incompletenesses by realistic Monte-Carlo simulations. We find that there is a positive correlation between Re(FIR) and L_FIR at the >99% significance level. The best-fit power-law function, Re(FIR) $\propto$ L_FIR$^{\alpha}$, provides $\alpha=0.28+/-0.07$, and shows that the average Re(FIR) at a fixed L_FIR decreases toward high redshifts. The best-fit $\alpha$ and the redshift evolution of Re(FIR) are similar to those of the galaxy effective radius in the rest-frame UV (optical) wavelength Re(UV) (Re(Opt.)) revealed by Hubble Space Telescope (HST) studies. We identify that our ALMA sources have significant trends of Re(FIR) <~ Re(UV) and Re(Opt.), suggesting that dusty starbursts take place in a compact region. Moreover, Re(FIR) of our ALMA sources is comparable to Re(Opt.) of quiescent galaxies at z~1-3 as a function of stellar mass, supporting the evolutionary connection between these two galaxy populations. We also investigate rest-frame UV and optical morphologies of our ALMA sources with deep HST images, and find that ~30-40% of our ALMA sources are classified as major mergers. This indicates that dusty starbursts are triggered not only by the major mergers but also the other mechanism(s).