Stability of starless cores. Top: ratio of gravitational potential to thermal kinetic energy vs. total gas mass (1.36 × M_H), both integrated within the N₂ column density contours (Table 5). The lower dashed horizontal line marks the bounding limit of − E_grav/E_therm = 1, while the upper line marks the state of virialization at − E_grav/E_therm = 2. Bottom: estimated central density (see Sect. 5.5) vs. total gas mass for the same starless cores. The dashed line marks the maximum stable density of a pressure-supported, self-gravitating modified (nonisothermal) BES (with photelectric heating at the core boundary taken into account) as calculated by Keto & Caselli (2008, their Fig. 14). Typical estimated uncertainties on the source parameters are indicated as Y error bars on CB 4. The uncertainty in mass corresponds to the size of the label.