On the basis of near-infrared imaging observations, we derived visual extinction (Av) distribution toward ten Bok globules through measurements of both the color excess (E_{H-K}) and the stellar density at J, H, and Ks (star count). Radial column density profiles for each globule were analyzed with the Bonnor-Ebert sphere model. Using the data of our ten globules and four globules in the literature, we investigated the stability of globules on the basis of xi_max, which characterizes the Bonnor-Ebert sphere as well as the stability of the equilibrium state against the gravitational collapse. We found that more than half of starless globules are located near the critical state (xi_max = 6.5 +/- 2). Thus, we suggest that a nearly critical Bonnor-Ebert sphere characterizes the typical density structure of starless globules. Remaining starless globules show clearly unstable states (xi_max > 10). Since unstable equilibrium states are not long maintained, we expect that these globules are on the way to gravitational collapse or that they are stabilized by non-thermal support. It was also found that all the star-forming globules show unstable solutions of xi_max >10, which is consistent with the fact that they have started gravitational collapse. We investigated the evolution of a collapsing gas sphere whose initial condition is a nearly critical Bonnor-Ebert sphere. We found that the column density profiles of the collapsing sphere mimic those of the static Bonnor-Ebert spheres in unstable equilibrium. The collapsing gas sphere resembles marginally unstable Bonnor-Ebert spheres for a long time. We found that the frequency distribution of xi_max for the observed starless globules is consistent with that from model calculations of the collapsing sphere.
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