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).
