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Astron. Astrophys. 328, 121-129 (1997)

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5. Comparison of 3D numerical simulations with Sedov solution

In order to evaluate the fragmentation criteria (3) and (7) to derive the instability time [FORMULA], and [FORMULA] from the fragmentation integral [FORMULA] according to the equation (8), we have to estimate the value of the sound speed within the shell c which we assume to be constant over a reasonable fraction of the expansion. As long as the cold and thin shell keeps its low temperature, the reverse shock increases the thickness of the shell keeping the volume density inside the shell constant, which results in a constant sound speed. We take arbitrarily the value [FORMULA] km/s, which is probably the lower (and therefore the most suitable) limit.

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 [FORMULA] and [FORMULA] are proportional to [FORMULA] and that [FORMULA] is fairly independent of it. The slightly lower expansion velocities at [FORMULA] 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 [FORMULA] are also evaluated. We can conclude that the value of [FORMULA] 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 [FORMULA] we can also check the expansion velocity [FORMULA]:

[EQUATION]

The value of [FORMULA] is in all the cases examined less than 10 km/s: [FORMULA], which is in very good correspondence with the observed values of random motions in the interstellar medium.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998

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