The apparent anti-correlation between the mass opacity of interstellar dust and the surface-density of interstellar gas

Recent analyses of ${\it Herschel}$ observations suggest that in nearby disc galaxies the dust mass opacity at $500 \, {\rm \mu m}$, $\kappa_{500}$, decreases with increasing gas surface density, $\Sigma_{\rm ISM}$ (Clark et al. 2019). This apparent anti-correlation between $\kappa_{500}$ and $\Sigma_{\rm ISM}$ is opposite to the behaviour expected from theoretical dust evolution models; in such models, dust in denser, cooler regions (i.e. regions of increased $\Sigma_{\rm ISM}$) tends to grow and therefore to have increased $\kappa_{500}$. We show, using a toy model, that the presence of a range of dust temperatures along the line of sight can lead to spuriously low estimated values of $\kappa_{500}$. If in regions of higher $\Sigma_{\rm ISM}$ the range of dust temperatures extends to lower values (as seems likely), the magnitude of this effect may be sufficient to explain the apparent anti-correlation between $\kappa_{500}$ and $\Sigma_{\rm ISM}$. Therefore there may not be any need for spatial variation in the intrinsic dust properties that run counter to theoretical expectations.