Interplay of dust alignment, grain growth and magnetic fields in polarization: lessons from the emission-to-extinction ratio

Polarized extinction and emission from dust in the interstellar medium (ISM) are hard to interpret, as they have a complex dependence on dust optical properties, grain alignment and magnetic field orientation. This is particularly true in molecular clouds. The data available today are not yet used to their full potential. The combination of emission and extinction, in particular, provides information not available from either of them alone. We combine data from the scientific literature on polarized dust extinction with Planck data on polarized emission and we use them to constrain the possible variations in dust and environmental conditions inside molecular clouds, and especially translucent lines of sight, taking into account magnetic field orientation. We focus on the dependence between \lambda_max -- the wavelength of maximum polarization in extinction -- and other observables such as the extinction polarization, the emission polarization and the ratio of the two. We set out to reproduce these correlations using Monte-Carlo simulations where the relevant quantities in a dust model -- grain alignment, size distribution and magnetic field orientation -- vary to mimic the diverse conditions expected inside molecular clouds. None of the quantities chosen can explain the observational data on its own: the best results are obtained when all quantities vary significantly across and within clouds. However, some of the data -- most notably the stars with low emission-to-extinction polarization ratio -- are not reproduced by our simulation. Our results suggest not only that dust evolution is necessary to explain polarization in molecular clouds, but that a simple change in size distribution is not sufficient to explain the data, and point the way for future and more sophisticated models.