Relation between the dust emissivity index β_1−3mm and the observed spectral index α_1−3mm-2. The dashed line represents the 1:1 relation, while the plain line represents the polynomial regression to the data (β_1−3mm = −0.07 (α_1−3mm − 2)² + 1.12 (α_1−3mm − 2) + 0.10). Each symbol represents a different protostellar envelope and symbols are color coded with respect to our modeled dust temperature.