...$T_{\rm d}$

The parameters directly derived from fitting the radial distribution of dust emission with an isothermal model (including an on-the-fly simulation) are the King radius $r_{\rm K} = \sqrt{9\sigma^2/4\pi G \rho_0}$ (from the shape of the profile) and the central emissivity $j_\nu = \kappa_\nu \rho_0 B(T_{\rm d})$(from the intensity scale), where $\rho_0$ is the central density and $T_{\rm d}$ the dust temperature. Substituting $\rho_0$ from the second equation into the first one, we obtain $\sigma \sqrt{\kappa_\nu \; B(T_{\rm d})}$.

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