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Dust Emissivity Background
Paradis et al. (2012) explained a possible origin of dark gas through $A_V$ observations is formation of dust aggregates, inducing a higher dust emissivity. This can be tested using extinction data, since dust aggregates are expected to have a higher FIR emissivity than isolated grains, but mostly unaffected optical properties in the visible and ultra-violet. Therefore, no substantial $A_V$ excess relative to the gas column density should be observed in that case. The dust emissivity should therefore increase with $A_V$ if dust is aggregating in dense regions.
Figures 1 and 2 show the dust emissivity and dust temperature maps from Planck of the Taurus-California-Perseus (TCP) region.
The average $\beta$ for diffuse lines of sight in the entire sky is $1.55$ (Planck et al. 2014). The median values of $\beta$ for the three clouds are all $1.7$. This is consistent with dust aggregating in these clouds.
Figure 3 shows the 2MASS-derived $A_V$ and $\beta$ relationship. Taurus and California show increasing $\beta$ in increasingly dense regions, consistent with dust aggregation. We can see that $\beta$ is negatively proportional to $A_V$ for Perseus however. This means that for denser regions, the emissivity index decreases.
Dust emissivity index of TCP region with $A_V$ contour at 3 mag.
Dust temperature of TCP region with $A_V$ contour at 3 mag.
$\beta$ vs. 2MASS-derived $A_V$. The increasing $\beta$ with $A_V$ in Taurus and California is consistent with dust aggregation in dense regions.