The effect of mass loss on the dynamical evolution of a stellar system - Analytic approximations

If half or more of the mass of a virialized system is lost in less than one dynamical crossing time, the system dissociates. If the mass loss occurs in a collapsing protosystem with uniform density, no angular momentum, and relatively little radiation of energy, the minimum fractional mass loss required for dissociation is reduced to ΔM/M0 = Rc/(2R0). Here Rc is the radius of the system when the mass loss occurs and R0 is the radius it would have attained after virialization if no mass loss had occurred. A situation of this type is expected in a protocluster that forms from a collapsing interstellar cloud. The stars form when the protocluster is near its point of maximum compression. Any newly formed OB stars produce an H II region whose expansion dissipates the residual gas in the protocluster before the system reaches dynamical equilibrium. The angular momentum of the protosystem and any radiative losses from it prior to star formation will tend to stabilize it against mass loss by limiting the compression factor 2R0/Rc. The angular momentum places a lower limit on the radius Rc, and the radiative losses reduce the final equilibrium radius R0. However, observed infantile clusters such as the Trapezium are sufficiently compressed at the present time that a loss of as little as 10% of their mass is sufficient to dissociate them. This may explain why most young stars are not located in gravitationally bound clusters. If the protocluster gas contains an appreciable magnetic field, the compression of this field in the collapsing cloud drains off some of the gravitational energy that otherwise would go into the kinetic energy of collapse. This increases the minimum mass loss required to dissociate the system, but it is still very small for most systems. The mean terminal expansion velocity of an association produced by the breakup of a protocluster is usually comparable to the velocity dispersion in an open cluster and cannot be larger than the expansion velocity of the H II region.