To understand the evolution of dust properties in molecular clouds in the course of the star formation process, we constrain the changes in the dust emissivity index from star-forming filaments to prestellar and protostellar cores to T Tauri stars. Using the NIKA2 continuum camera on the IRAM 30~m telescope, we observed the Taurus B211/B213 filament at 1.2,mm and 2,mm with unprecedented sensitivity and used the resulting maps to derive the dust emissivity index . Our sample of 105 objects detected in the map of the B211/B213 filament indicates that, overall, decreases from filament and prestellar cores () to protostellar cores () to T-Tauri protoplanetary disk (). The averaged dust emissivity index across the B211/B213 filament exhibits a flat () profile. This may imply that dust grain sizes are rather homogeneous in the filament, start to grow significantly in size only after the onset of the gravitational contraction/collapse of prestellar cores to protostars, reaching big sizes in T Tauri protoplanetary disks. This evolution from the parent filament to T-Tauri disks happens on a timescale of about 1-2~Myr.

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