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


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          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, \(\kappa_{\rm UV}\) and \(\kappa_{\rm IR}\), 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 \(\kappa_{\rm UV}=5.0\times10^4\) cm\(^2\) g\(^{-1}\) and \(\kappa_{\rm IR}=30(\lambda/100\mu m)^{-\beta}\) 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 \(\xi_{\rm cl}=0.1\), corresponding to \(\sim10\)\% of the volume filling factor of the clumps in this high-\(z\) galaxy if the clump size is \(\sim10\) pc, similar to that of giant molecular clouds in the local Universe.

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          27 April 2020

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          MNRAS accepted

          Galaxy astrophysics


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