deletions | additions       diff --git a/disk_winds.tex b/disk_winds.tex  index 49e01e3..733cc1e 100644  --- a/disk_winds.tex  +++ b/disk_winds.tex 
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\subsection{Disk wind as boundary conditions for a stellar wind}  Different models exist to explain wind launching from the stellar surface \citep{1988ApJ...332L..41K,2005ApJ...632L.135M}, the X-point close to the inner disk edge \citep{1994ApJ...429..781S} and magneto-centrifugal launching from the disk \citep{1982MNRAS.199..883B,2005ApJ...630..945A}. It is likely that more than one mechanism contributes to the total outflow from the system. In this case, we expect a contact discontinuity between the different components. 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{2005ApJ...630..945A}, 2.5D \citep{2011ApJ...728L..11R} or 3D \citep{2006ApJ...653L..33A}, but typically do not resolve the stellar wind, where the magneto-centrifugal launching is not effective. However, they show that the disk wind is collimated close to the axis and that the densities are largest in this region. Furthermore, the inner layers of the outflow close to the jet are within the Alfv\'en Alfven  surface, the boundary between a magnetically dominated flow and a gas-pressure dominated flow, even at distances of several tens of AU from the central star, in contrast to the outer, less collimated layers of the wind, which leave the magnetically dominated region at a few AU. \citet{2009A&A...502..217M} \citet{2009A&A...502..217M}  present analytical and numerical solutions for several scenarios that mix an inner, presumably stellar, wind and an outer disk wind. In contrast to our approach, they impose a smooth transition between stellar wind and disk wind, which allows them to model the entire outflow region numerically. With some time variability in the wind launching their models produce promising knot features in the jet. In the context of our analysis, we note that the presure in their models is magnetically dominated and much higher close to the jet axies than at larger radii in apparent contrast to Kompaneet's approximation. However, the an inner jet component as suggested in this article is so narrow that it essentiall stays confind to the innermost resolution elements. The presure at the jet axis is high initially and reaches a plateau after at $P_\infty$  dropping by one to two orders of magnitude. Below we use simple exponential ($P(z)=P_\infty+P_0\exp\left(-\frac{z}{h}\right)$)  or power-law functions forP(z)  that mimic this behaviour. Similar profiles for the inner density and presure are seen in simulations by competing groups \citep[e.g.]{2005ApJ...630..945A,Li_Krasnopolsky_Blandford_2006,2008ApJ...678.1109M}.  Observations of jets and winds from CTTS indicate that typical temperatures are a few thousand K and typical densities of the range $10^4-10^5 \mathrm{ cm}^{-3}$ \citep[e.g.][]{2000A&A...356L..41L,2007ApJ...657..897K} \citep[e.g.][]{2000A&A...356L..41L,2007ApJ...657..897K} and we chose the paramters of $P(z)$ to reach presure compatible with the observed densities and temperatures.     Figure~\ref{fig:p_ext} shows how different presure profiles influence the shock position. As expected, larger presures force the shock front onto the symetry axes for smaller $z$ (top row). If the presure profile is almost linear in the region where the shock front hits the symetry axis, then the angle between the shock front and the jet axis is large, which causes high post-shock temperatures (dotted black and solid red line in the upper row). In contrast, the presure gradient becomes less steep when the shock front bends towards the jet axis again, then it will approach the axis slower. The shock front and the stream lines form a smaller angle and pre-shock speeds and thus the post-shock temperatures are lower (dashed green line in the top row).     The solutions shown in the bottom row of the figure are for the same scale heights as those in the upper row, but here we use smaller $P_0$ for scenarios with large $h$, so that the shock front reaches the jet axis at approximately the same $z$. Close to the disk plane the pre-shock speeds differ signifcantly, but at large $z$ they reach very similar values. However, the scenerios with the smaller $P_0$ values reach slightly larger radii and the slightly different shape of the shock front leads to more material at high temperature.