Heating and Ionization of X-Winds

In order to compare the x-wind with observations, one needs to be able to calculate its thermal and ionization properties. We formulate the physical basis for the streamline-by-streamline integration of the ionization and heat equations of the steady x-wind. In addition to the well-known processes associated with the interaction of stellar and accretion-funnel hot-spot radiation with the wind, we include X-ray heating and ionization, mechanical heating, and a revised calculation of ambipolar diffusion heating. The mechanical heating arises from fluctuations produced by star-disk interactions of the time dependent x-wind that are carried by the wind to large distances where they are dissipated in shocks, MHD waves, and turbulent cascades. We model the time-averaged heating by the scale-free volumetric heating rate, $\Gamma_{\rm mech} = \alpha \rho v^3 s^{-1}$, where $\rho$ and $v$ are the local mass density and wind speed, respectively, $s$ is the distance from the origin, and $\alpha$ is a phenomenological constant. When we consider a partially-revealed but active young stellar object, we find that choosing $\alpha \sim 10^{-3}$ in our numerical calculations produces temperatures and electron fractions that are high enough for the x-wind jet to radiate in the optical forbidden lines at the level and on the spatial scales that are observed. We also discuss a variety of applications of our thermal-chemical calculations that can lead to further observational checks of x-wind theory.