Abstract Evidence for dust around supermassive black holes (SMBHs) in the early universe is strongly suggested by recent observations. However, the accretion mechanism of SMBHs in dusty gas is not well understood yet. We investigate the growth of intermediate-mass black holes (IMBHs) of in dusty clouds by using one-dimensional radiative-hydrodynamics simulations. We find that the accretion of dusty gas onto IMBHs proceeds gently with small fluctuations of the accretion rate, whereas that of pristine gas causes more violent periodic bursts. At dust-to-gas mass ratios similar to the solar neighborhood, the time-averaged luminosity becomes smaller than that for primordial gas by one order of magnitude and the time-averaged Eddington ratio ranges from to in clouds with initial gas densities of . Our calculations show that the effect of dust opacity alone is secondary compared to the radiation pressure on dust in regulating the BH growth. We also derive spectral energy distributions at IR bands by calculating dust thermal emission and show that the flux ratio between and is closely related to the Eddington ratio. Thermal emission from hot dust near the BH dominates only during the phase of high accretion, producing higher flux density at . Therefore, we suggest that a combination of mid-IR observations by the James Webb Space Telescope and far-IR observations by ALMA or Spitzer can be used to estimate the Eddington ratio of massive BHs. We also extend our simple modeling to SMBHs of and show that ALMA can detect SMBHs of at .
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