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\subsection{X-ray luminosities}  \label{sect:LX}  The post-shock plasma is less dense than the typical stellar corona and can thus be treated in the so-called coronal approximation, meaning that the plasma is optically thin and line ratios for prominent X-ray lines are in the low-density limit. We use the shock models of \citet{2007A&A...466.1111G} to predict the fraction of the total pre-shock kinetic energy that will be emitted in the X-ray range.\citet{2011AN....332..448G} published a grid of X-ray spectra\footnote{Available at http://hdl.handle.net/10904/10202} 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 refer to that publication  for each spectrum. At 300~km~s$^{-1}$ only 2\% of details on  the available energy is emitted between 0.3 and 3~keV, so we set shock models. In summary,  the fraction to zero for pre-shock velocities models simulate radiative cooling  of 0, 100 optically thin plasma in a two-fluid approximation, where electron and  and 200~km~s$^{-1}$, which ions  are not covered by the model grid. The fraction of energy emitted in X-rays is independent of the density except for described with  a few density-sensitive emission lines Maxwellian velocity distribution, each  with negligible contribution to the integrated flux. a different temperature.  The physical size of the post-shock region depends strongly on the density, ionization and recombinations rates are calculated explicitly,  but total energy available even for densities as low as $10^5$~cm${-3}$  only depends on the pre-shock velocity and density. Thus, the X-ray luminosity $L_X$ does not change, if a small fraction of  the post-shock region cooling zone  is compressed by some external pressure and significantly different from  the calculated values of $L_X$ is robust. ionization equilibrium.  \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 density. 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 $L_X$ is 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 $L_X$. However, in most YSOs the central object is highly absorbed. Therefore, all $L_X$ values are calculated taking into account only regions with $z>5$~AU. For the ``fiducial'', the ``high $v_\inf$'', $v_\infreplace_content#x27;',  the ``low $\dot M$'', Mreplace_content#x27;',  and the ``shallow $P$'' $Preplace_content#x27;'  model in Figure~\ref{fig:results} the predicted $L_X$ is $3\cdot10^{29}$, $5\cdot10^{30}$, $1\cdot10^{28}$, and $1\cdot10^{31}$~erg~$^{-1}$, 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} 
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\left(\frac{10^5\mathrm{ cm}^{-3}}{n_0}\right)  \left(\frac{v_{\mathrm{shock}}}{500\mathrm{ km s}^{-1}}\right)^{4.5}\ .  \end{equation}  The derivation for this formula assumes a cylindrical cooling flow. In contrast, in our model the external pressure willcontinue to  compress the post-shock  gas, as it starts cooling. Since denser gas emits more radiation and thus cools faster, $d_{\mathrm{cool}}$ is only an upper limit. With this in mind, figure~\ref{fig:rhocool} (lower panel) indicates that the cooling lengths for our fiducial model is consistent with the X-ray observations that do not resolve the wind shock \citep{2008A&A...488L..13S}.Since only a very small fraction of the stellar mass loss is heated to X-ray emitting temperatures (Fig.~\ref{fig:result}, rightmost panel) the low-mass loss scenario also does not provide enough X-ray luminosity to explain the observations (paper~I).  Significantly higher pressures require unrealistically fast outflows to push the shock front out to 40~AU and lower pressures do not allow a mass flux high enough to power the X-ray luminosity.