Variation of the dust emissivity index β_1−3mm as a function of the physical scale integrated in the protostellar envelope. The thick black line indicates the trend when all directions are considered while the gray line indicates the (log-lin) fit to the trend (see Table 2). The colored lines indicate the trend in various angular bins with respect to the outflow direction. If PA is the position angle with respect to the outflow axis, the red lines indicate the trends for regions located close to the outflow direction (−22.5° < PA < 22.5°). The blue lines indicate the trends for regions located close to the 45° PA (22.5° < PA < 67.5° and −67.5° < PA < 22.5°). The green lines indicate the trends for regions located close to the equatorial plane (67.5° <PA < 122.5°). The orange dotted line indicates the fit to the β_{1−3 mm} values corrected for the central region (see Sect. 4). We do not apply the correctionfor L1448-C, as its 3 mm flux is dominated at most scales by the compact component, with barely any flux coming from the envelope, leading to large uncertainties in the β_{1−3 mm} determination. Finally, the light blue shaded line indicates the position of the CO snow line determined from the N₂ H⁺ and C¹⁸ O observations(Gaudel et al. 2019; Anderl et al. 2016).