Astron. Astrophys. 342, 717-735 (1999)

1. Introduction

Bipolar collimated mass flows associated with young stellar objects (YSOs) have widely been recognized as an essential ingredient of the star formation process. Here, we focus on the highly-collimated optical Herbig-Haro (HH) jets (e.g. Eislöffel 1996, Ray 1996). They manifest themselves as highly supersonic (Mach number 20-30) atomic flows, very well collimated over distances ranging from a few AU to several parsecs. They generally consist of a chain of bright and quasi-periodically spaced knots ("the beam") followed by an invisible section, and one or more bow-shaped features aligned with the linear section. Although HH jets were first found about one and a half decade ago (Mundt & Fried 1983), many of their features remain largely unexplained. For example, the excitation of the optical emission in the beam is generally attributed to the presence of shocks that locally heat the gas. These shocks may be formed by hydrodynamical Kelvin-Helmholtz instabilities arising in the interaction with the surrounding medium (see, e.g., Bodo et al. 1994, Stone et al. 1997, Hardee & Stone 1997), or alternatively by velocity variability in the outflow ejection (see, e.g., Stone & Norman 1993, Falle & Raga 1993, 1995). Recent Hubble Space Telescope (HST) observations (Ray et al. 1996, Heathcote et al. 1996, Reipurth et al. 1997) show that all the extended jets observed so far (HH 34, HH 46/47, and HH 111) present morphological characteristics that support the idea of velocity variations in the outflow. In particular, the HST images show that many jet knots can be resolved in bow shocks with the bows pointing away from the source. Such structures can be explained by velocity variations of the flow in the presence of a boundary layer. Furthermore, the capability of the narrow central jet to drive a slower but much more massive molecular outflow, although probable, is not yet firmly established, nor has it been definitely proven that outflows can provide a mechanism to remove excess angular momentum from the disk or star, thereby preventing the accreting star from spinning up to break-up velocity. In order to establish if a reliable dynamical interaction exists between optical and molecular flows, and between mass accretion and ejection, the mass loss and momentum transfer rates of the flows should be known. However, for optical jets large uncertainties affect these estimates, which vary by orders of magnitude, depending on the model assumed.

It becomes clear that a crucial physical parameter for any jet model is the hydrogen total density of the flow, which is poorly known for HH jets. The total density in a jet cannot be measured directly, contrary to the electron density , which is easily found from the ratio of the [SII] lines at 6716 Å and 6731 Å (see, e.g. Osterbrock 1989). Hartigan et al. (1994, hereafter HMR94) discussed two principal ways to determine the total density in such objects. The first involves the determination of the luminosity in one forbidden line (Edwards et al. 1987, Cabrit et al. 1990), from which the number of the emitting atoms in the aperture can be deduced. The assumption of a given abundance of the emitting species with respect to hydrogen together with an estimate of the flow radius would then yield the total density in the gas. Spectrophotometric measurements are rare, however, because of the lack of reliable reddening estimates. In addition, the fractional ionization of the emitting species, the excitation temperature and the local filling factor should be known a priori to estimate the average total number density. The second method involves the determination of the hydrogen ionization fraction of the emitting gas. In order to estimate , HMR94 constructed a grid of planar shock models, and compared the model line ratios with the observed ones. A selected shock model then gives the average ionization fraction in the post shock region, and the total density is derived taking into account that there the gas is more compressed than on average. The results are largely model-dependent: they are greatly affected by the assumed pre-shock conditions and the presence of (unknown) magnetic fields, that may alter the properties of the shocks. Moreover, the assumption of a planar shock geometry is likely a simplification with respect to the actual situation, in which the front may have a curved shape.

Recently, Bacciotti et al. (1995, hereafter called BCO95) developed a spectroscopic diagnostic technique that allows one to find the ionization fraction in the jet beam in a model-independent way. The technique, which used ratios of easy to observe forbidden lines together with H, exploited the fact that in the low excitation conditions in the beam of many HH jets the ionization state of oxygen and nitrogen is dominated by charge exchange with hydrogen atoms. A first application of the procedure to spectra of HH 34 and HH 111 integrated along the beam provided values of of about 0.07 and 0.1, respectively, and an average total hydrogen density of about cm^-3 for both jets.

As demonstrated by HMR94, weak shocks in the beams of HH jets are usually not capable of producing in situ an ionization degree larger than a few per cent. On the other hand, BCO95 pointed out that the typical recombination time of the jet gas is of the order of the travel time of the bright jet section, so that if the ionization of the jet is initially produced in the acceleration region (for example by means of a strong steady shock heavily shielded from view) the recombination is sufficiently slow to leave the jet gas considerably ionized even at large distances from the star. If the BCO95 interpretation is correct, the ionization fraction should be observed to gently decrease along the jet axis on spatial scales determined by the product of recombination time and the flow velocity. This prediction is not affected by the presence of weak shocks that may form in the beam, if these contribute to the ionization of the gas at a very low level.

The observational confirmation of such a picture can come from the analysis of spectra spatially resolved along the jet axis. As a first attempt, Bacciotti et al. (1996, hereafter BHN96) examined the optical outflow from RW Aurigae. The results confirmed the suggestion by BCO95: the ionization fraction decreases along the beam according to a well-defined recombination law, from near the star to about 0.02 at a distance of ,( 1000 AU). In RW Aur the total density is again of the order of 10⁴ cm^-3. It is therefore of great interest to investigate further typical jets in order to obtain a model-independent determination of their fundamental physical parameters, and to establish if the agreement between the "slow recombination" model and the observed trends is confirmed on a larger statistical basis.

Motivated by these ideas we here present the results for a number of outflows: HH 34, HH 46/47, HH 24G, HH 24C/E, HL Tau jet, HH 228 (Th 28). In this way we want to give useful constraints to the models of jet formation and propagation, and possibly to shed light on the dynamical relationships between optical and molecular outflows. In Sect. 2 we describe the observations and the data reduction. Sect. 3 summarizes the physical assumptions underlying the adopted diagnostic technique, and illustrates recent improvements that eliminate possible misinterpretations of the conditions of the emitting gas. In Sect. 4 we describe the results obtained for the "beam" section of the analysed Herbig-Haro jets. A general discussion is presented in Sect. 5, where we summarize our findings and illustrate several interesting physical implications. The main conclusions are given in Sect. 6.

© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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