## 5. Comparison of 3D numerical simulations with Sedov solutionIn order to evaluate the fragmentation criteria (3) and (7) to
derive the instability time , and
from the fragmentation integral
according to the equation (8), we have to
estimate the value of the sound speed within the shell The results from the computer simulations are compared to formulae (13), (14) and (15) from the Sedov solution in Fig. 1. There is very close agreement between all the predicted and computed values. The 3D simulations confirm that and are proportional to and that is fairly independent of it. The slightly lower expansion velocities at from simulations reflect the fact that the Sedov solution omits the pressure of the ambient medium and that it does not take into account the work done by bubble expansion. The fragmentation integrals and are also evaluated. We can conclude that the value of from simulations is always in the interval (2.01, 2.03), which is rather close to 2.03 derived from the solution of Eq. (17). Knowing we can also check the expansion velocity : The value of is in all the cases examined less than 10 km/s: , which is in very good correspondence with the observed values of random motions in the interstellar medium. © European Southern Observatory (ESO) 1997 Online publication: March 24, 1998 |