# Astrospheres

##### Shock transition

The left tables below are the more general one and the parameter in these tables are used to estimate the shock parameter using the Rankine Hugonoit equations (see for details). The right table can be used to initialise the left tables using the (observable) parameters from a stellar wind - interstellar medium counterflow situtaion.

It is assumed that the ideal MHD equations are appplicable, and the termination shock (TS) can be calculated by the Parker/Wilkin equations. The stellar wind temperature is assumed to be 1000 [K] at the TS (based on the Voyager data, because this temperature is not observable.

If the choice of the interstellar parameters also allow for a shock, these parameters are also given below

The TS and the possible bow shock (BS) are calulated under the assumption, that the normal vector $$\vec{n}$$ is aligned along the Cartesian x-axis. Thus choosing the right table as input the shock parameter are a sophisticated guess and not derived from a simulation.

The left table contains the values directly in front of a shock, and thus give the correct values for the choosen configuration, where it is always assuemd that the velocity in front of the shock is aligned to the x-axis.

The parameter in the right, if used, needs to be submitted first, and will fill the left table, which then can be submitted. The left table can also be used to study the influence of different parameters, for example the direction of the shock normal $$\vec{n}$$

Parameter in front of the (TS) shock
 Parameter $$\vec{n}$$ $$\vec{B}$$ [$$\mu$$G] $$\vec{u}$$[km/s] $$\rho$$* [cm-3] T[K] γ
Parameter in front the (BS) shock
 Parameter $$\vec{n}$$ $$\vec{B}$$ [$$\mu$$G] $$\vec{u}$$[km/s] $$\rho$$* [cm-3] T[K] γ

Stellar and interstelar parameter from observations
including derived parameter and sophisticated guesses
 Parameter units value $$\dot{M}$$ [$$M_\odot$$ / yr] $$u_{sw}$$ [ km/s] $$T_{sw}(R_{TS})$$ [ K] $$B_\odot$$ [ kG] $$\Omega_\odot$$ [ per day] $$\rho*_{ism}$$ [cm$$^{-3}$$] $$u_{ism}$$ [ km/s] $$B_{ism}$$ [ $$\mu$$G] $$B_{\vartheta}$$ [ deg] $$B_{\varphi}$$ [ deg] $$T_{ism}$$ [ K] $$R_{TS}$$ [ AU ]