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

Context. Polarized extinction and emission from dust in the interstellar medium (ISM) are hard to interpret, as their dependence on dust optical properties, grain alignment, and magnetic field orientation is complex. This is particularly true in molecular clouds. The aforementioned phenomena are usually considered independently in polarization studies, while it is likely that they all contribute and their effects have yet to be disentangled. Aims. 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 the magnetic field orientation into account. Methods. We focused on the dependence between λmax (the wavelength of maximum polarization in extinction) and other observables such as the extinction polarization, the emission polarization, and the ratio between the two. We set out to reproduce these correlations using Monte Carlo simulations in which we varied the relevant quantities in a dust model, which are grain alignment, size distribution, and magnetic field orientation, to mimic the diverse conditions that are expected inside molecular clouds. Results. None of the quantities we chose can explain the observational data on their 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 a low ratio of polarization in emission to polarization in extinction, are not reproduced by our simulation. Conclusions. 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. Our results also point the way for future and more sophisticated models