Zhi-Yun Li edited initialwindtemperature.tex  about 10 years ago

Commit id: 5c76e79615ab94b8eef93e1df7b153ef5a631bfa

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\end{equation}  The post-shock temperature $T_{\mathrm{post-shock}}$ is now the sum of the value calculated in eqn.~\ref{eqn:T} and $T_0$.  For small radii and large $T_0$ the term in the last square root can become negative. Physically, this corresponds to situations where the thermal pressure is much larger than $P(z)$. The shock front is pushed outwards. Without the thermal pressure $\psi$ is always positive, because the ram pressure approches 0 when the shock front is almost parallel to the flow direction of the wind. In a hot wind, there is no such limit and the thermal pressure can force the shock front below the plane of the disk. However, in CTTS the disk provides a solid barrier and, this close to the star, the magnetic field influences the direction of the flow. To explore what a hot wind would do to the shape of the shock front while avoiding this problem, we start the integration at $\omega_0=1$~AU. Figure~\ref{fig:T_0} shows that a wind with just $T_0=10^5$~K leads to essentially the same shape in the shock front as a cold wind, only the post-shock temperature distribution is slightly shifted (rightmost panel). Even for much higher temperatures around $T_0=10^6$~K the shape does not change dramatically. However, almost the entire emission measure of the wind is now shifted into the temperature regime where we expect X-ray radiation. ({\bf Hans: for the 1MK case, one worry is that the Mach number for the perpendicular component of the pre-shock wind speed may not be greater than 1, in which case a shock may not form at all. We may want to check/comment on the possibility.})