Hans Moritz Günther edited Results.tex  almost 10 years ago

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\section{Results}  \label{sect:results}  The last section already showed that for all parameters consistent with the theoretical and observational constraints the stellar wind is enclosed in a finite region by a shock front. This shock front generally reaches a maximum cylindrical radius of only several AUs, but a much larger height above the accretion disk for external pressure profiles with high pressure in the plane of the disk and a large pressure gradient (fiducial model in Fig.~\ref{fig:result}). A shallower pressure profile leads to a stellar wind region that is wider.So wider. So  far, no stellar wind zone is resolved within the more massive and wider disk wind in any CTTS imaging, limiting the maximal size of the stellar wind region to a few AU. Our calculations show that this scenario is compatible with the known properties of the stellar wind. The biggest uncertainty is probably the value of the external pressure. As discussed above, different simulations in the literature predict similar pressure profiles, but the normalization of the pressure depends to a large degree on the disk magnetic field, which is only poorly constrained. In our calculation, we have scaled the pressure such that the post-shock densities are compatible with observations of the jet and we find a fiducial model that is compatible with the X-ray emission from the jet that we set out to explain. However, the magnitude of the pressure is a free parameter in our model and if it could be determined more accurately, that will confirm or rule-out the scenario we suggest in this article. The highest post-shock temperatures are generally reached at the base of the jet when the stellar wind encounters the inner disk rim or at large $z$ when the shock front intersects the jet axis. Thus, the position of the hottest post-shock cooling plasma must be very close to the jet axis. In our fiducial model (Fig.~\ref{fig:result}, solid red line), the temperature is just sufficient to produce X-ray emission. Paper~I showed that in DG~Tau a small faction, about $10^{-3}$, of the total mass loss rate in the outflow is enough to power the observed X-ray emission at the base of the jet. Figure~\ref{fig:rhocool} shows the pre-shock number densities $n_0$ for the four models from Fig.~\ref{fig:result}. A detailed treatment of the post-shock region is beyond the scope of this paper, but an upper limit on the post-shock cooling length $d_{\mathrm{cool}}$ can be derived according to \citet{2002ApJ...576L.149R}:  \begin{equation}