Recent observational progress has challenged the dust grain-alignment theories used to explain the polarized dust emission routinely observed in star-forming cores. In an effort to improve our understanding of the dust grain alignment mechanism(s), we have gathered a dozen ALMA maps of (sub)millimeter-wavelength polarized dust emission from Class 0 protostars, and carried out a comprehensive statistical analysis of dust polarization quantities. We analyze the statistical properties of the polarization fraction P_frac and dispersion of polarization position angles S. More specifically, we investigate the relationship between S and P_frac as well as the evolution of the product S*P_frac as a function of the column density of the gas in the protostellar envelopes. We find a significant correlation in the polarized dust emission from protostellar envelopes seen with ALMA; the power-law index differs significantly from the one observed by Planck in star-forming clouds. The product S*P_frac, which is sensitive to the dust grain alignment efficiency, is approximately constant across three orders of magnitude in envelope column density. This suggests that the grain alignment mechanism producing the bulk of the polarized dust emission in star-forming cores may not depend systematically on the local conditions such as local gas density. Ultimately, our results suggest dust alignment mechanism(s) are efficient at producing dust polarized emission in the various local conditions typical of Class 0 protostars. The grain alignment efficiency found in these objects seems to be higher than the efficiency produced by the standard RAT alignment of paramagnetic grains. Further study will be needed to understand how more efficient grain alignment via, e.g., different irradiation conditions, dust grain characteristics, or additional grain alignment mechanisms can reproduce the observations.
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