Expansion radiale non-stationnaire d'une sphère gazeuse polytropique

Abstract

A bstract. — A non-stationary solution of the hydrodynamical equations for a polytropic gas sphere expanding in its own gravitational field is given. This particular solution is regular at the center (r = 0) of the model [u(r, t) → 0, p(r, t) → pc, m(r, t ) → 0, p(r, t) → pe for r → 0] and tends to the well known static solution of Emden. Far from the center it has the properties of the critical solution given by Parker [5, 6] to explain the stationary expansion of the Solar Wind. The model is externally limited by a progressive shock wave whose position and velocity are discussed. The application to the case of the Sun shows that this hydrodynamical expansion does not change very much the radial distribution of the density and pressure in the inner regions, and, therefore the static models for the internal structure are very good approximations. One shows also that the stationarity of the expansion of the coronal envelop is also a very good approximation in the case of the Sun. These approximations seem also to be justified in the case of M-giant stars ejecting a larger part of their total mass.