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Astron. Astrophys. 346, 260-266 (1999)

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1. Introduction

Meaburn & Dyson (1987) and Solf (1987) suggested that at least part of the atomic/ionic emission observed in Herbig-Haro (HH) objects could arise in turbulent mixing layers, rather than in shock waves. This idea was further explored by Raymond et al. (1994).

It is not so clear what exactly the difference is between "standard" shock wave heating (i. e., heating and/or ionization due to the passage of a single, well defined shock wave), and the heating that takes place in a compressible, turbulent mixing layer. In particular, it is not entirely clear whether such a turbulent layer actually generates a number of weak shock waves, or whether it has a turbulent cascade ending in turbulent dissipation without the appearance of shock waves.

The initial work on the theory of astrophysical turbulent mixing layers was presented by Kahn (1980), who studied the linear and quadratic perturbation theory of the interface at the edge of a jet flow. The linear theory was studied in considerable detail in the context of extragalactic jets by a number of authors in both the gas dynamic and magnetohydrodynamic contexts (see, e. g., the review of Bodo 1998). For the radiative HH jet case, numerical simulations have recently been carried out, e. g., by Rossi et al. (1997) and by Stone et al. (1997).

Analytic models based on the standard "turbulent viscosity" approach (with a turbulent viscosity parametrized with a simple, "mixing length" approximation) were computed by Cantó & Raga (1991) and Noriega-Crespo et al. (1996). Also, Dyson et al. (1995), Lizano & Giovanardi (1995) and Taylor & Raga (1995) computed models which included more or less detailed treatments of the chemistry associated with mixing layers. However, non of these models include a proper calculation of the ionization state and emission of the ionized regions of these flows.

In the present paper, we compute models of atomic/ionic turbulent mixing layers for jet velocities in the [FORMULA]-500 km s-1 range. For computing these models, we consider rate equations for a series of (up to four times ionized) ions. These models, which have a similar degree of sophistication to currently existing shock wave models, allow us to make predictions of the line ratios that would be observed in the spectrum produced by mixing layer flows.

The paper is organized as follows. The equations describing a turbulent mixing layer are discussed in Sect. 2. The results obtained from numerical integrations of the energy and ionization rate equations are described in Sect. 3. The line ratios predicted from these models are discussed in Sect. 4, in the context of observations of HH objects and microjets from T Tauri jets.

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© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999