Dust masses of z > 5 galaxies from SED fitting and ALMA upper limits

We aim at constraining the dust mass in high-z (z greater than or similar to 5) galaxies using the upper limits obtained by Atacama Large Millimetre/submillimetre Array (ALMA) in combination with the rest-frame UV-optical spectral energy distributions (SEDs). For SED fitting, because of degeneracy between dust extinction and stellar age, we focus on two extremes: continuous star formation (Model A) and instantaneous star formation (Model B). We apply these models to Himiko (as a representative UV-bright object) and a composite SED of z > 5 Lyman break galaxies (LBGs). For Himiko, Model A requires a significant dust extinction, which leads to a high dust temperature > 70 K for consistency with the ALMA upper limit. This high dust temperature puts a strong upper limit on the total dust mass M-d less than or similar to 2 x 10(6) M-circle dot, and the dust mass produced per supernova (SN) m(d,SN) less than or similar to 0.1 M-circle dot. Such a low md, SN suggests significant loss of dust by reverse shock destruction or outflow, and implies that SNe are not the dominant source of dust at high z. Model B allows M-d similar to 2 x 10(7) M-circle dot and m(d,SN) similar to 0.3 M-circle dot. We could distinguish between Models A and B if we observe Himiko at wavelength < 1.2 mm by ALMA. For the LBG sample, we obtain M-d less than or similar to 2 x 10(6) M-circle dot for a typical LBG at z > 5, but this only puts an upper limit for m(d,SN) as similar to 2 M-circle dot. This clarifies the importance of observing UV-bright objects (like Himiko) to constrain the dust production by SNe.