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Constraint on dust evolution processes in normal galaxies at $z>6$ detected by ALMA

Recent ALMA observations of high-redshift normal galaxies have been providing a great opportunity to clarify the general origin of dust in the Universe, not biased to very bright special objects even at $z>6$. To clarify what constraint we can get for the dust enrichment in normal galaxies detected by ALMA, we use a theoretical model that includes major processes driving dust evolution in a galaxy; that is, dust condensation in stellar ejecta, dust growth by the accretion of gas-phase metals, and supernova destruction. Using the dust emission fluxes detected in two normal galaxies at $z>6$ by ALMA as a constraint, we can get the range of the time-scales (or efficiencies) of the above mentioned processes. We find that if we assume extremely high condensation efficiency in stellar ejecta ($f_{\mathrm{in}} \ga 0.5$), rapid dust enrichment by stellar sources in the early phase may be enough to explain the observed ALMA flux, unless dust destruction by supernovae in those galaxies is stronger than that in nearby galaxies. If we assume a condensation efficiency expected from theoretical calculations ($f_{\mathrm{in}} \la 0.1$), strong dust growth (even stronger than assumed for nearby galaxies if they are metal-poor galaxies) is required. These results indicate that the normal galaxies detected by ALMA at $z>6$ are biased to objects (i) with high dust condensation efficiency in stellar ejecta, (ii) with strong dust growth in very dense molecular clouds, or (iii) with efficient dust growth because of fast metal enrichment up to solar metallicity. A measurement of metallicity is crucial to distinguish among these possibilities.