We used near-infrared 2MASS data to construct visual extinction maps of a sample of Southern Bok globules utilizing the NICE method. We derived radial extinction profiles of dense cores identified in the globules and analyzed their stability against gravitational collapse with isothermal Bonnor-Ebert spheres. The frequency distribution of the stability parameter xi_max of these cores shows that a large number of them are located in stable states, followed by an abrupt decrease of cores in unstable states. This decrease is steeper for globules with associated IRAS point sources than for starless globules. Moreover, globules in stable states have a Bonnor-Ebert temperature of T = 15 +- 6 K, while the group of critical plus unstable globules has a different temperature of T = 10 +- 3 K. Distances were estimated to all the globules studied in this work and the spectral class of the IRAS sources was calculated. No variations were found in the stability parameters of the cores and the spectral class of their associated IRAS sources. On the basis of 13CO J = 1-0 molecular line observations, we identified and modeled a blue-assymetric line profile toward a globule of the sample, obtaining an upper limit infall speed of 0.25 km/s.

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