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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 \left(\gamma  \frac{k T}{m_{\textrm{H}}\right)^{0.5} \approx 10 \textrm{ km s}^{-1} \; , \end{equation}  which is low enough that a strong shock forms even for small $\psi$.