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How and when in the star formation sequence do dust grains start to grow into pebbles is a cornerstone question to both star and planet formation. We compute the polarized radiative transfer from a model solar-type protostellar core, using the polaris code, aligning the dust grains with the local magnetic field, following the radiative torques (RATs) theory. We test the dependency of the resulting dust polarized emission with the maximum grain size of the dust size distribution at the envelope scale, from |$a_\mathrm{max}=1\,$| to |$50 \,\hbox{$\mu $m}$|⁠. Our work shows that, in the framework of RAT alignment, large dust grains are required to produce polarized dust emission at levels similar to those currently observed in solar-type protostellar envelopes at millimetre wavelengths. Considering the current theoretical difficulties to align a large fraction of small ISM-like grains in the conditions typical of protostellar envelopes, our results suggest that grain growth (typically |$\gt 10 \,\hbox{$\mu $m}$|⁠) might have already significantly progressed at scales 100–1000 au in the youngest objects, observed less than 105 yr after the onset of collapse. Observations of dust polarized emission might open a new avenue to explore dust pristine properties and describe, for example, the initial conditions for the formation of planetesimals. [ABSTRACT FROM AUTHOR]

Context. Ultraviolet radiation plays a crucial role in molecular clouds. Radiation and matter are tightly coupled and their interplay influences the physical and chemical properties of gas. In particular, modeling the radiation propagation requires calculating column densities, which can be numerically expensive in high-resolution multidimensional simulations. Aims. Developing fast methods for estimating column densities is mandatory if we are interested in the dynamical influence of the radiative transfer. In particular, we focus on the effect of the UV screening on the dynamics and on the statistical properties of molecular clouds. Methods. We have developed a tree-based method for a fast estimate of column densities, implemented in the adaptive mesh refinement code RAMSES.We performed numerical simulations using this method in order to analyze the influence of the screening on the clump formation. Results. We find that the accuracy for the extinction of the tree-based method is better than 10%, while the relative error for the column density can be much more. We describe the implementation of a method based on precalculating the geometrical terms that noticeably reduces the calculation time. To study the influence of the screening on the statistical properties of molecular clouds we present the probability distribution function of gas and the associated temperature per density bin and the mass spectra for different density thresholds. Conclusions. The tree-based method is fast and accurate enough to be used during numerical simulations since no communication is needed between CPUs when using a fully threaded tree. It is then suitable to parallel computing. We show that the screening for far UV radiation mainly affects the dense gas, thereby favoring low temperatures and affecting the fragmentation. We show that when we include the screening, more structures are formed with higher densities in comparison to the case that does not include this effect. We interpret this as the result of the shielding effect of dust, which protects the interiors of clumps from the incoming radiation, thus diminishing the temperature and changing locally the Jeans mass. [ABSTRACT FROM AUTHOR]