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

Abstract

Estimating the temperature and mass of dust in high-$z$ galaxies is essential for discussions of the origin of dust in the early Universe. However, this suffers from 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 effects of the mass absorption coefficients of dust at ultraviolet and infrared wavelengths, ${\kappa }_{\mathrm{UV}}$ and ${\kappa }_{\mathrm{IR}}$, 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 ${\kappa }_{\mathrm{UV}}=5.0\times 10^4$ cm${}^2$ g${}^{-1}$ and ${\kappa }_{\mathrm{IR}}=30(\lambda /100\mu m{)}^{-\beta }$ cm${}^2$ g${}^{-1}$ with $\beta =2.0$, we obtain dust temperatures of 38--70~K and masses of $10^{6.5-7.3}$ M${}_{\odot }$ for the three geometries considered. We obtain similar temperatures and masses from just a single data point in the dust continuum, suggesting the usefulness of the algorithm for high-$z$ galaxies with limited infrared observations. In the clumpy-sphere case, 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-fit clumpiness parameter is ${\xi }_{\mathrm{cl}}=0.1$, corresponding to $\sim 10$\% of the volume filling factor of the clumps in this high-$z$ galaxy if the clump size is $\sim 10$ pc, similar to that of giant molecular clouds in the local Universe.

MNRAS accepted

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