deletions | additions       diff --git a/our_equations.tex b/our_equations.tex  index be1e2c2..f804b95 100644  --- a/our_equations.tex  +++ b/our_equations.tex 
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In our case we are dealing with an oblique shock (Figure~\ref{fig:sketch}). Equations~\ref{eqn:RH1} to \ref{eqn:RH3} stay valid if only the velocity component perpendicular to the shock front is taken as $v_0$.   We use a cylindrical coordinate system $(z, \omega, \theta)$ with an origin at the central star. We place the $z$-axis along the jet outflow direction and assume rotational symmetry around the jet axis. Thus, the flow can effectively be written in $(z,\omega)$. The symbol $r$ denotes the spherical radius, i.e.\ the distance of any point to the star at the origin of the coordinate system.   \textbf{In this article we adapt the model of  \citet{2012MNRAS.422.2282K} employ to non-relativistic speeds and Figure~1 in their publication shows  thesame  geometry of this model  in a relativistic calculation much detail}  and we refer to their discussion and their figure~1 for a more detailed description. \textbf{Although the basic geometry is the same, we chose to include our Fig.~\ref{fig:sketch} in this work for the benefit of reader who are not familiar with the work of \citet{2012MNRAS.422.2282K} on extra-galactic jets.}  We treat the disk wind as an outer boundary condition with a given pressure profile and concentrate on the description of the stellar wind. To simplify the equations we adopt Kompaneets' approximation \citep{1960SPhD....5...46K} which states that there is no axial pressure gradient so that the pressure profile of the disk wind extends through all layers of the outflow:  \begin{equation}