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Polarizing efficiency as a guide of grain growth and interstellar magnetic field properties

We interpret the relation between the polarizing efficiency $P_{\max}/E(B-V)$ and the wavelength of the maximum polarization $λ_{\max}$ observed for 17 objects (including 243 stars) separated into two groups: "dark clouds" and "open clusters". The objects are assigned to one of the groups according to the distribution of the parameter $λ_{\max}$. We use the model of homogeneous silicate and carbonaceous spheroidal particles with the imperfect alignment and a time-evolving size distribution. The polarization is assumed to be mainly produced by large silicate particles with the sizes $r_{V} \ga r_{V,\rm cut}$. The models with the initial size distribution reproducing the average curve of the interstellar extinction fail to explain the values of $λ_{\max} \ga 0.65\,\mkm$ observed for several dark clouds. We assume that the grain size distribution is modified due to accretion and coagulation, according to the model of Hirashita \& Voshchinnikov (2014). After including the evolutionary effects, $λ_{\max}$ shifts to longer wavelengths on time-scales $\sim 20 (n_\mathrm{H}/10^3 \mathrm{cm}^{-3})^{-1}$ Myr where $n_\mathrm{H}$ is the hydrogen density in molecular clouds where dust processing occurs. The ratio $P_{\max}/E(B-V)$ goes down dramatically when the size of polarizing grains grows. The variations of the degree and direction of particle orientation influence this ratio only moderately. We have also found that the aspect ratio of prolate grains does not affect significantly the polarizing efficiency. For oblate particles, the shape effect is stronger but in most cases the polarization curves produced are too narrow in comparison with the observed ones.