Radiative equilibrium estimates of dust temperature and mass in high-redshift galaxies

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, κ_UV and κ_IR, 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 κ_UV = 5.0 × 10⁴ and κ_IR = 30(λ/100 μm)^−β cm² g⁻¹ with β = 2.0, we obtain dust temperatures of 38–70 K and masses of 10^6.5–7.3 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 ξ_cl = 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.