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 R _e in the rest-frame far-infrared (FIR) wavelength {R}_{{e}({FIR})} obtained from 1627 Atacama Large Millimeter/submillimeter Array (ALMA) 1 mm band maps that become public by 2017 July. Our ALMA sample consists of 1034 sources with the star formation rate ∼ 100{--}1000 {M}_⊙ {{yr}}^-1 and the stellar mass ∼ {10}¹⁰{--}{10}^11.5 {M}_⊙ at z = 0-6. We homogeneously derive {R}_{{e}({FIR})} and FIR luminosity L _FIR of our ALMA sources via the uv-visibility method with the exponential disk model, carefully evaluating selection and measurement incompletenesses by realistic Monte-Carlo simulations. We find that there is a positive correlation between {R}_{{e}({FIR})} and L _FIR at the >99% significance level. The best-fit power-law function, {R}_{{e}({FIR})}\propto {L}_{FIR}^α , provides α =0.28+/- 0.07, and shows that {R}_{{e}({FIR})} at a fixed L _FIR decreases toward high redshifts. The best-fit α and the redshift evolution of {R}_{{e}({FIR})} are similar to those of R _e in the rest-frame UV (optical) wavelength {R}_{{e}({UV})} ({R}_{{e}({Opt}.)}) revealed by Hubble Space Telescope (HST) studies. We identify that our ALMA sources have significant trends of {R}_{{e}({FIR})}≲ {R}_{{e}({UV})} and {R}_{{e}({Opt}.)}, which suggests that the dusty starbursts take place in compact regions. Moreover, {R}_{{e}({FIR})} of our ALMA sources is comparable to {R}_{{e}({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 by not only the major mergers but also the other mechanism(s).