STABILITY OF DENSE STELLAR CLUSTERS AGAINST RELATIVISTIC COLLAPSE

Stability of dense stellar clusters against relativistic collapse is investigated by approximate methods, similar to the static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich & Podurets (ZP), have been considered. Three new methods for stability investigation are considered. The first method is based on the choice of the sequence of Maxwellian models with fixed cutoff parameter, in accordance with adiabatic conditions p(cut) is similar to n(c)1/3. The second one is based on the consideration of the sequence of Maxwellian models with the same value of the specific entropy. The third method considers a simple non-Maxwellian distribution function of the clusters, obtained from the Maxwellian distribution by the condition of conservation of adiabatic invariant: f is similar to exp {- [p2c2(n(c0)/n(c))2/3 + m2c4]1/2/T}. The methods considered here give only approximate results about the stability, because adiabatic perturbations of collisionless Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analytically. However, these results are more precise than those of ZP, obtained from consideration of the sequence of Maxwellian models with different temperature. The coincidence of the temperatures in the critical point, T = 0.223 mc2, obtained by two last methods, leads us to believe that these methods, although approximate, provide rather relatively good precision not worse than 10(-3).