Panel a: gas densities along the trajectory of a parcel of gas gradually infalling through the envelopes of Sgr B2(N2-N5). The quasi-static contraction phase is characterized by the density increasing over time at a constant radius (Fig. F.4a). The subsequent free-fall collapse phase assumes a density distribution propotional to r^−1.5. Panel b: visual extinction calculated as a function of the density along the trajectory of a parcel of gas gradually infalling through the envelope. The quasi-static contraction phase is characterized by the extinction increasing over time at a constant radius (Fig. F.4b). During the free-fall collapse phase the extinction increases with the density (Eq. (16)) until A_v-max = 500 mag. Panel c: temperature evolution along the trajectory of a parcel of gas gradually infalling through the envelope (see also Fig. F.6). The evolution of the temperature during the quasi-static contraction phase is shown for a minimum temperature T_min = 15 K (see Fig. 4).