We have considered a simple system of second order differential equations that describes the temperature and ionization cross-section of a turbulent mixing layer. Even though these equations are based on a simple, turbulent viscosity approach, they probably describe the properties of a real turbulent flow at least in a qualitative way. We have then carried out integrations of these equations, using the MAPPINGS code to compute the ionization rates and the radiative energy loss term. With the numerical solutions, we confirm the existence of the quasi-isothermal, large h regime which was predicted from the analytic model of Noriega-Crespo et al. (1996) and Raga & Cantó (1997).
From our numerical solutions to the mixing layer equations, we also obtain predictions of the emission line spectrum of the flow. We find that the spectrum has basically fixed characteristics over a wide parameter range. This result is interesting from the point of view of comparisons with low excitation HH objects, which all show very similar line ratios (Raga et al. 1996). The observed invariance of the line ratios would appear to favour a mixing layer interpretation of the emission, as shock wave models predict large line ratio changes as a function of shock velocity (see, e.g., Hartigan et al. 1987).
However, the line ratios that we obtain from our mixing layer models do not agree in detail with the ones observed in low excitation HH objects in general. Therefore, a direct interpretation of the emission from these objects in terms of the present models does not seem to be appropriate.
Interestingly, the line ratios observed in the intermediate velocity component of the micro-jet of DG Tau (which was proposed on kinematical grounds to arise in a mixing layer by Lavalley et al. 1997) seem to agree with the emission predicted from a mixing layer model (Lavalley, personal communication). We conclude that turbulent dissipation in mixing layers may be an important ingredient for interpreting the emission line ratios in T Tauri micro-jets that are or will be measured with the current generation of high resolution instruments.
Finally, we should note that even though the models described in this paper have been computed for parameters appropriate for mixing layers around the beam of HH jets, with similar models one could study other, interesting problems. For example, these models could be applied to the mixing layers formed in wind/clump interactions (Dyson et al. 1995), in two-wind interactions (Raga et al. 1995), or in extragalactic "cooling flows" (Begelman & Fabian 1990). We are in the process of studying some of these applications of our model.
© European Southern Observatory (ESO) 1999
Online publication: May 6, 1999