deletions | additions       diff --git a/Results.tex b/Results.tex  index 0b27f48..32f54f9 100644  --- a/Results.tex  +++ b/Results.tex 
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\citet{2011AN....332..448G} published a grid of X-ray spectra\footnote{Available at http://hdl.handle.net/10904/10202} based on these models with pre-shock velocities between 300 and 1000~km~s$^{-1}$ in increments of 100~km~s$^{-1}$. We integrate all emission between 0.3 and 3~keV for each spectrum. At 300~km~s$^{-1}$ only 2\% of the available energy is emitted between 0.3 and 3~keV (Figure~\ref{fig:fracxray}), so we set the fraction to zero for pre-shock velocities of 0, 100 and 200~km~s$^{-1}$, which are not covered by the model grid. The fraction of energy emitted in X-rays is independent of the density except for a few density-sensitive emission lines with negligible contribution to the integrated flux. The physical size of the post-shock region depends strongly on the density, but total energy available only depends on the pre-shock velocity and the total mass flux. Thus, the X-ray luminosity $L_X$ does not change, if the post-shock region is compressed by some external pressure and the calculated values of $L_X$ are robust.  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. In our fiducial model (Fig.~\ref{fig:result}, solid red line), the pre-shock velocity is $>250$~km~s$^{-1}$ at $z<5$~AU and $z>20$~AU. Given the large solid angle covered by the inner disk rim, the $z<5$~AU region contributes significantly to the total mass flux (compare the red line and the red filled histogram in Figure~\ref{fig:result}, rightmost panel). However, in most YSOs the central object is highly absorbed. Therefore, we calculate all $L_X$ values taking into account only regions with $z>5$~AU. For the fiducial, the high $v_\inf$, $v_\infty$,  the low $\dot M$, and the shallow $P$ model in Figure~\ref{fig:result} the predicted $L_X$ is $3\cdot10^{29}$, $5\cdot10^{30}$, $1\cdot10^{28}$, and $1\cdot10^{31}$~erg~s$^{-1}$, respectively. \citet{2009A&A...493..579G} already showed that in DG~Tau a small fraction, 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. In our fiducial model, this small fraction corresponds to the mass flow close to the jet axis, where the pre-shock velocities are highest.  \subsection{The size of the post-shock zone}  diff --git a/parameters.tex b/parameters.tex  index 9d4263b..a317a81 100644  --- a/parameters.tex  +++ b/parameters.tex 
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\label{sect:parameters}  In this section we discuss observational and theoretical constraints on boundary conditions and input values for the model, most notably $P(z)$, $\dot M$, $v_\infty$, and $\omega(z=0)$. Table~\ref{tab:fiducial} shows the values we adopt as most likely in the following discussion (fiducial model). We vary the parameters individually to show how each of them affects the solution of the ODE.   \begin{table}  \label{tab:fiducial}  \caption{Values \caption{\label{tab:fiducial}Values  for fiducial model and fit to DG Tau} \begin{tabular}{ccc}  \hline\hline  parameter & fiducial & fit to DG~Tau\\  diff --git a/soundspeed.tex b/soundspeed.tex  index 976ad2d..d4f47f8 100644  --- a/soundspeed.tex  +++ b/soundspeed.tex 
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\subsubsection{Sound speed}  Observations of jets and winds from CTTS indicate that typical temperatures are a few thousand K (except in shocked regions) and typical densities are in the range $10^4-10^6 \mathrm{ cm}^{-3}$ in the optically visible component \citep[e.g.][]{2000A&A...356L..41L,2007ApJ...657..897K}. This might not be the same outflow component that our model describes, but it is the best observational estimate. With those numbers the sound speed $c_s$ is  \begin{equation}  c_s = \left(\gamma \sqrt{\gamma  \frac{k T}{m_{\textrm{H}}\right)^{0.5} T}{m_{\textrm{H}}}}  \approx 10 \textrm{ km s}^{-1} \; , \end{equation}  which is low enough that a strong shock forms even for small $\psi$.