Astron. Astrophys. 343, 251-260 (1999)

2. Equations

We solve the HD and MHD equations expressed in the conservative variables density , momentum vector , and magnetic field . These are given by

We introduced as the total pressure, as the identity tensor, as the external gravitational field, and exploited magnetic units such that the magnetic permeability is unity. We drop the energy equation and assume a polytropic relation connecting the thermal pressure p and the density . For a polytropic index , we thus assume . Hence, we do not address the heat deposition in the corona. Although we solve the time-dependent equations as given above, we will only present steady-state solutions of Eqs. (1)-(3). For stellar wind calculations, we consider a spherically symmetric external gravitational field , where G is the gravitational constant, is the stellar mass, r is the distance to the stellar center, and indicates the radial unit vector.

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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