Astron. Astrophys. 333, 678-686 (1998)

## 2. Steady shell: physical considerations

What we call a steady shell in this work is a concentration of the expanding stellar wind plasma. This is also called a density fluctuation. The concentration of fluid is formed in the stellar envelope and at a certain distance . The simplest shape for this shell is spherical and the width of it, H, is determined by the inner and outer radii (). The fluid density in the shell region determines the shell mass . The fluid passes through the shell region as it expands and also rotates. A characteristic time period is the time in which a certain fluid element passes through the shell.

Using the single fluid HD theory, it is obvious that in a situation like this there is evidence of deceleration in the stellar envelope. If the deceleration is efficiently strong the conservation of mass leads to an increase in density. So, the fluid must be initially accelerated from low velocities at the stellar surface to higher, then it decelerates and then it accelerates again and escapes to infinitely large distances from the central object. In this way, three domains in the stellar envelope exist: an inner acceleration region, a deceleration region and an outer acceleration region. A schematic view of this case is shown in Fig. 1.

 Fig. 1. Schematic view of a spherical steady shell

The deceleration is due to the gravitational attraction of the central object. The outer acceleration region is probably due to radiative forces since no other mechanism is known to drive the outflow at very large distances. Under discussion is the mechanism that drives the outflow in the inner acceleration region. In this work we adopt a thermal mechanism to drive the outflow in the inner part with a smaller radiative force contributing. We expect the flow in the shell region to be supersonic because in the subsonic region the acceleration must be very high and there is no evidence for deceleration there. The previously described situation is going to be modelled in the next sections. This kind of shell is qualitatively different from dusty shells, from time-dependent travelling shells or from shell-like structures formed by interactions of supernovae progenitor winds with the ambient circumstellar gas. In the first kind the interaction between plasma and grains has to be evaluated while in the other two time-dependent HD must be employed (especially when the structure is formed by an explosion in the star's interior).

© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998