The mass of dusty clumps with temperature and density structure

TL;DR

This paper investigates how temperature and density gradients in dusty clumps influence observed flux and mass estimates, providing approximate formulas and demonstrating their impact on stability assessments.

Contribution

It introduces analytical expressions relating flux density and mass considering gradients, improving accuracy over traditional methods.

Findings

Gradients significantly affect mass estimates from flux measurements.

Approximate formulas are reliable in optically thin and thick regimes.

Applying corrections alters conclusions about clump stability.

Abstract

We consider a dusty clump in the two cases of spherical and cylindrical symmetry to investigate the effect of temperature and density gradients on the observed flux density. Conversely, we evaluate how the presence of such gradients affects the calculation of the clump mass from the observed flux. We provide the reader with approximate expressions relating flux density and mass in the optically thick and thin limits, in the Rayleigh-Jeans regime, and discuss the reliability of these expressions by comparing them to the outcome of a numerical code. Finally, we present an application of our calculations to three examples taken from the literature, which shows how the correction introduced after taking into account temperature and density gradients may affect our conclusions on the stability of the clumps.