We aim at constraining the dust mass in high-redshift ( z \gtrsim 5 ) galaxies using the upper limits obtained by 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 _ { \mathrm { d } } \lesssim 2 \times 10 ^ { 6 } M _ { \sun } , and the dust mass produced per supernova ( SN ) m _ { \mathrm { d,SN } } \lesssim 0.1 M _ { \sun } .
Such a low m _ { \mathrm { d,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 _ { \mathrm { d } } \sim 2 \times 10 ^ { 7 } M _ { \sun } and m _ { \mathrm { d,SN } } \sim 0.3 M _ { \sun } .
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 _ { \mathrm { d } } \lesssim 2 \times 10 ^ { 6 } M _ { \sun } for a typical LBG at z > 5 , but this only puts an upper limit for m _ { \mathrm { d,SN } } as \sim 2 M _ { \sun } .
This clarifies the importance of observing UV-bright objects ( like Himiko ) to constrain the dust production by SNe .