Among the various phenomena observed in star formation regions, jets from Young Stellar Objects (YSOs) are certainly one of the most intriguing. They show chains of aligned knots, almost periodically spaced, and optically emitting mainly in the and lines, over distances from the central source that may reach the parsec scale (see Ray 1997). Furthermore, data on line intensity ratios tell us that these knots are actually shocks with velocities of few tens km s-1, and that show proper motions with pattern speeds that approach the jet speed. Herbig-Haro jets therefore pose two main problems: i) they survive instabilities for distances as large as a thousand jet radii, and ii) the displayed emission knots require interpretation.
The former problem has been investigated, in the 2-D limit, by Massaglia et al. (1996, Paper I) and Rossi et al. (1997, Paper II) who have shown that radiative losses drastically reduce the effect of the nonlinear evolution of Kelvin-Helmholtz instabilities as far as jet momentum transfer from the jet to the ambient medium is concerned, and therefore increase the jet capability to survive instabilities. Stone, Xu & Hardee (1997) have recently addressed the same problem for antisymmetric modes in a slab jet discussing the effects of different cooling functions.
In previous papers on this subject (Bodo et al. 1994, 1995, Papers I and II) we have studied the instability using the so called 'temporal' approach, in which one can follow the system evolution for longer times, as opposed to the 'spatial analysis' (see Hardee & Norman 1988a,b and Stone, Xu & Hardee 1997), in which one is limited by the transit time through the grid. While the temporal analysis is to be preferred when studying the physics of the instability evolution over long time scales, the spatial approach allows for more detailed comparison with observations. Apart from the advantages and disadvantages, the interest of following both approaches lies in the fact that there is a more profound physical difference between the two schemes: in the temporal analysis, when shocks are formed they propagate in a medium that has already been processed more and more by the preceding shocks and therefore has changed its physical conditions; in contrast, in the spatial analysis, the shocks find a medium whose conditions depend solely on the position of every shock in the shock train. Therefore the application of the Taylor's hypothesis to translate time into space in a temporal analysis, as usually done, has to be carried out with a grain of salt. The study of the differences between the two approaches is one of the goals of the paper.
Moreover, before going fully 3-D, it can be useful to gain a general idea of the main characteristics of the instability evolution by comparing the results obtained in the cylindrical and slab geometries, and what happens if radiative losses are included in the picture. Therefore, in summary, the purpose of this paper is to examine the details of the nonlinear evolution of the K-H instabilities looking at the role played by i) geometry, ii) radiative losses, iii) different jet-ambient density ratios, and iv) spatial analysis of modes against the temporal one. The application of the results obtained to the origin of the emission knots in HH jets are argument of the companion paper (Micono et al. 1997, Paper IV).
The plan of the paper is the following: in the next section (Sect. 2), we describe the basic physical problem and the integration method; in Sect. 3 we recall the basic results of previous investigations; the simulations results are discussed in Sect. 4, and the conclusions are given in Sect. 5.
© European Southern Observatory (ESO) 1998
Online publication: April 28, 1998