Density structure of the model starless cores and protostellar envelopes. Subscripts on the curve labels (n30 to n0.03) indicate the model mass M (in M⊙). The dashed vertical line shows the outer boundary radius R = 104 AU for all models. Embedded models are implanted in larger uniform-density clouds with an outer boundary at 3 × 104 AU. The dashed horizontal lines continue the densities of starless cores within the innermost radial zone. The dashed diagonal lines continue the densities of protostellar envelopes towards the radius of the inner dust-free cavity R0, whose size depends on the model temperature profile Td(r) (cf. Fig. 3) and adopted dust sublimation temperature (TS = 103 K). In other words, the dashed diagonal lines visualize the range of densities and radial distances over which the inner boundary R0 is located for L⋆ spanning the entire range 0.03 − 30 L⊙ (see Eq. (1)).
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