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-V) and far-infrared dust emissivity (parameterized by the power-law index beta). Starting from the size distribution models proposed by Weingartner & Draine, using the dust absorption and emission properties derived by Laor & Draine for carbonaceous and silicate grains, and by Li & Draine for polycyclic aromatic hydrocarbon grains, we calculate the extinction and compare it with the reddening vector derived by Schlafly et al. An optimizer and an Markov chain Monte Carlo method are used to explore the space of available parameters for the size distributions. We find that larger grains are correlated with high R-V. However, this trend is not enough to explain the emission-extinction correlation observed by Schlafly et al. For the R-V - beta correlation to arise, we need to impose explicit priors for the carbonaceous and silicate volume priors as functions of R-V. The results show that a composition with higher ratio of carbonaceous to silicate grains leads to higher R-V and lower beta. A relation between E(B - V)/tau(353) and R-V is apparent, with possible consequences for the recalibration of emission-based dust maps as a function of R-V.