Implications of Grain Size Distribution and Composition for the Correlation Between Dust Extinction and Emissivity

We study the effect of variations in dust size distribution and composition on the correlation between the spectral shape of extinction (parameterized by $R_{\textrm{V}}$) and far-infrared dust emissivity (parameterized by the power-law index $\beta$). Starting from the size distribution models proposed by Weingartner & Draine (2001), using the dust absorption and emission properties derived by Laor & Draine (1993) for carbonaceous and silicate grains, and by Li & Draine (2001) for PAH grains, we calculate the extinction and compare it with the reddening vector derived by Schlafly et al. (2016). An optimizer and an MCMC are used to explore the space of available parameters for the size distributions. We find that larger grains are correlated with high $R_{\textrm{V}}$. However, this trend is not enough to explain the emission-extinction correlation observed by Schlafly et al. (2016). For the $R_{\textrm{V}}-\beta$ correlation to arise, we need to impose explicit priors for the carbonaceous and silicate volume priors as functions of $R_{\textrm{V}}$. The results show that a composition with higher ratio of carbonaceous to silicate grains leads to higher $R_{\textrm{V}}$ and lower $\beta$. A relation between $E(\textrm{B}-\textrm{V})/\tau_{353}$ and $R_{\textrm{V}}$ is apparent, with possible consequences for the recalibration of emission-based dust maps as a function of $R_{\textrm{V}}$.