deletions | additions       diff --git a/disk_winds.tex b/disk_winds.tex  index 99f54c8..3b85d2a 100644  --- a/disk_winds.tex  +++ b/disk_winds.tex 
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Numerically, the magneto-centrifugally accelerated disk wind is probably the best explored component. Magneto-hydrodynamic (MHD) simulations of the disk wind have been performed in 2D \citep[e.g.][]{2005ApJ...630..945A}, 2.5D \citep[e.g.][]{2011ApJ...728L..11R} or 3D \citep[e.g.][]{2006ApJ...653L..33A}, but typically do not resolve the stellar wind. However, they show that the disk wind is collimated close to the axis and that the densities are largest in this region. Furthermore, the Alfv\'en surface (which separates the magnetically dominated region from the flow-dominated region) is located at many AUs for the inner layers of the jet. This is in contrast with the outer, less collimated layers of the wind, which leave the magnetically dominated region at a few AUs.  \citet{2009A&A...502..217M} present analytical and numerical solutions for several scenarios that mix an inner stellar wind and an outer disk wind \citep[this model has been extended in][]{2012A&A...545A..53M,2014A&A...562A.117T}. In contrast to our approach, they impose a smooth transition between stellar wind and disk wind and they start their simulation at $z=50$~AU instead of at the star. With some time variability in the wind launching their models produce knot features in the jet. In the context of our analysis, we note that the pressure in their models is magnetically dominated and that Kompaneet's approximation does not hold in the disk wind, but that the presure gradient is small on scales of a few AU. The pressure at the jet axis is high in the plane of the disk and drops by one to two orders of magnitude until it reaches a plateau ($P_\infty$). Below we use an exponential $P(z)=P_\infty+P_0\exp\left(-\frac{z}{h}\right)$ to mimic this profile.  Similar profiles for the inner density and pressure are seen in simulations by other groups \citep[e.g.\][]{2005ApJ...630..945A,Li_Krasnopolsky_Blandford_2006,2008ApJ...678.1109M}.  \citep{2006ApJ...653L..33A} \citep[e.g.\][]{2005ApJ...630..945A,2006ApJ...653L..33A,2008ApJ...678.1109M}.  Figure~\ref{fig:p_ext} shows how different pressure profiles influence the shock position. Larger pressures force the shock front onto the symmetry axes for smaller $z$ (top row). If the pressure is constant in the region where the shock front hits the symmetry axis, then the angle between the shock front and the jet axis is large, which causes high post-shock temperatures (solid red line in top row). On the other hand, if there is a pressure gradient when the shock front bends towards the jet axis, then the shock front and the stream lines form a smaller angle and the post-shock temperatures are lower (dotted black line in the top row).