The estimation of the temperature and mass of dust in high-redshift galaxies is essential for discussions of the origin of dust in the early Universe. However, this is made difficult by limited sampling of the infrared spectral-energy distribution. Here, we present an algorithm for deriving the temperature and mass of dust in a galaxy, assuming dust to be in radiative equilibrium. We formulate the algorithm for three geometries: a thin spherical shell, a homogeneous sphere and a clumpy sphere. We also discuss the effects of the mass absorption coefficients of dust at ultraviolet and infrared wavelengths, κUV and κIR, respectively. As an example, we apply the algorithm to a normal, dusty star-forming galaxy at z = 7.5, A1689zD1, for which three data points in the dust continuum are available. Using κUV = 5.0 × 104 and κIR = 30(λ/100 μm)−β cm2 g−1 with β = 2.0, we obtain dust temperatures of 38–70 K and masses of 106.5–7.3 M☉ for the three geometries considered. We obtain similar temperatures and masses from just a single data point in the dust continuum, suggesting that the algorithm is useful for high-redshift galaxies with limited infrared observations. In the case of the clumpy sphere, the temperature becomes equal to that of the usual modified black-body fit, because an additional parameter describing the clumpiness works as an adjuster. The best-fitting clumpiness parameter is ξcl = 0.1, corresponding to ∼10 per cent of the volume filling factor of the clumps in this high-redshift galaxy if the clump size is ∼10 pc, similar to that of giant molecular clouds in the local Universe.
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