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

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2. Equations

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

[EQUATION]

[EQUATION]

[EQUATION]

We introduced [FORMULA] as the total pressure, [FORMULA] as the identity tensor, [FORMULA] 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 [FORMULA]. For a polytropic index [FORMULA], we thus assume [FORMULA]. 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 [FORMULA] solutions of Eqs. (1)-(3). For stellar wind calculations, we consider a spherically symmetric external gravitational field [FORMULA], where G is the gravitational constant, [FORMULA] is the stellar mass, r is the distance to the stellar center, and [FORMULA] indicates the radial unit vector.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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