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*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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