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Astron. Astrophys. 348, 584-593 (1999)

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5. Shocks in the L483 protostellar jet

5.1. H2 excitation in shocks

[FORMULA] can be excited into emission by shock waves generated by the supersonic injection of mass into the ambient medium by the protostellar jet (Draine & McKee, 1993; Hollenbach 1997; Eisloffel, 1997). A bow shock accelerates gas ahead of the jet, and a second shock, the Mach disk, decelerates material in the jet. The bow shock is formed as shocked gas impacts the quiescent ambient material. The Mach disk is formed where the jet impacts previously shocked material. Since the ratios of the emission lines of [FORMULA] are dependent upon the excitation mechanism, this molecule can be used as a diagnostic of the processes happening within the jet (e.g. Hartigan et al. 1996; Burton 1992; Gredel 1996).

In the L483 jet, the emission lines observed at the jet head fall off in strength with increasing v, the v=1-0 lines being the strongest, and the v=3-2 lines much weaker. This is indicative of shock excited [FORMULA]. Processes such as UV fluorescence or [FORMULA] reformation should produce stronger emission from higher v levels (Burton 1992).

[FORMULA] can be excited into emission in two types of shock. A jump, or J-shock takes place where the magnetic field is weak, and the gas properties change suddenly. The bulk motion is dissipated into thermal energy, and the front is followed by a distinct region of cooling. A bow shock may consist of J shocks of decreasing strength with increasing distance from the jet axis. [FORMULA] emission arises from the hot gas inside the wings of the bow shock and Mach disk, where the shock velocity is below the [FORMULA] dissociation velocity (Hartigan et al. 1996). [FORMULA] line emission and molecule dissociation controls the cooling, and the degree of dissociation is dependent upon the shock driving pressure.

In the presence of a strong magnetic field, a continuous, or C-shock takes place. This is a magnetically mediated two fluid shock. The ions are pushed ahead of the shock, and gradually heat and accelerate the predominantly neutral pre-shock material. Planar C-shocks produce a narrow range of [FORMULA] excitation temperatures, whereas for bow C-shocks, the excitation temperature varies along the bow. For both types of shock, the molecules can be dissociated at the tip of the bow shock, where the shock velocity is at a maximum. [FORMULA] emission arises along the wings of the bow shock, where the effective shock velocity is lower. C-shocks produce higher column densities of shocked molecular hydrogen than J-shocks (Smith 1995).

In a slightly weaker magnetic field, a magnetic precursor can form ahead of the shock. Some ions are still accelerated, but are unable to heat the pre-shock material enough to cushion the following shock. In this case, a C-shock forms, and is followed by a J-shock, where the molecules are dissociated. [FORMULA] emission should occur everywhere along the bow shock where the precursor exists (Hartigan et al. 1996).

5.2. Shock analysis at the jet head

The relative strengths of the strongest lines in the spectra can be compared to models of shocks in molecular jets and outflows (e.g. Smith 1995), and give an indication of the type and speed of the shock. A comparison of the L483 shock ratios with the models of Smith (1995) is given in Table 5.


[TABLE]

Table 5. Comparison of line ratios for different types of shocks, with varying speeds (Smith 1995). The type of shock is indicated by the letter, and the speed, in km s-1, is then given. These are compared to the line ratios for different positions along the jet.


The [FORMULA] ratio indicates that either a fast C-shock with speed 40-45 km s-1, or a slow J-shock, with speed 9-11 km s-1, is consistent with the data. The [FORMULA] ratio is indicative of a fast C-shock with speed [FORMULA] 35 km s-1. The value of these shock ratios suggest that the L483 outflow has a leading bow C-shock, where the jet is impacting the ambient medium with a shock speed of 40-45 km s-1. In addition, the curvature in the rotation diagram suggests that the rotation temperature increases with the energy of the vibrational level. This suggests that the leading shock is a bow C-shock (Smith et al. 1991), where different speeds along the bow surface leads to different temperature regions along the bow, and so different excitation regions.

The shock speeds are not constrained by any shift in the wavelength of the H2 lines, which were measured only at low velocity resolution. We calculate a [FORMULA] upper limit of 135 km s-1 on the H2 lines' velocity shifts relative to the rest velocity of the source (Sect. 2); however, this is a limit on the line-of-sight component, whereas in L483 it is clear that the outflow axis is nearly in the plane of the sky (Hatchell et al. 1999), so the velocity would be expected to be dominated by the component perpendicular to the line of sight.

Models (e.g. Hartigan 1989) of Mach disks from stellar jets indicate that the distance between the bow shock and the Mach disk is approximately 500 AU in most cases. As the emission from the bow shock in the L483 jet extends spatially across over 700 AU along the jet, we are unable to discern whether we are seeing emission from the bow shock, Mach disk, or both.

5.3. Shock velocity limit from CO observations

A strict lower limit on the shock speed can be derived from the low velocity CO outflow that surrounds the shocked H2 jet in L483 (Hatchell et al. 1999). In a simple bow shock model, material heated by the bow shock expands sideways, sweeping up the ambient medium to create a CO shell. In the time it has taken the bow shock to travel a distance [FORMULA] along the jet axis to its current position (marked by shocked H2) from a given position in the CO outflow, the outflow has expanded to a radius r at a velocity greater than the observed transverse expansion velocity [FORMULA] (as the shell expansion slows as more material is swept up). From the CO observations, both r and [FORMULA] can be estimated and we can use this to put a lower limit on the speed at which the bow shock progresses, [FORMULA].

[EQUATION]

where [FORMULA] and [FORMULA] are the observed maximum red and blue velocities at a position [FORMULA] from the bow shock. For unknown inclination, a strict lower limit on [FORMULA] can be found by putting [FORMULA]. Using the values [FORMULA] and [FORMULA], [FORMULA] and [FORMULA] (Hatchell et al. 1999, Figs. 7 and 9) the lower limit on the shock velocity is [FORMULA]. This is a strict lower limit: firstly because of the inclination angle; secondly because the measured [FORMULA] at [FORMULA] from the bow shock actually corresponds to a annulus of gas that was ejected further from the bow shock and thus has a greater r, a slower [FORMULA] and a longer travel time than the annulus ejected from [FORMULA]; and thirdly because we are measuring the average shock speed over [FORMULA] whereas the shock will travel faster into the lower ambient density further from the star. This lower limit of 30 km s-1 rules out slow J shocks of 9-11 km s-1 as the excitation mechanism.

5.4. Jet density

By considering the transfer of momentum, the ratio of the ambient to jet volume densities can be calculated by balancing the ram pressures in the jet and in the swept up ambient medium (Blondin et al. 1990):

[EQUATION]

where [FORMULA] and [FORMULA] are the jet and shock velocities, respectively, and [FORMULA] and [FORMULA] are the ambient and jet densities, respectively. For the bow shock speed of 40 km s-1 estimated from the line ratios, and assuming a typical jet speed of 200 km s-1, this gives a [FORMULA] ratio of 16. If the jet speed were faster, then this ratio would increase. This suggests that the L483 outflow contains a light jet, which is at least a factor of 10 less dense than the medium into which it is moving.

5.5. Shock analysis at other positions

The [FORMULA] ratios along the jet vary within the range of 6 and 9, consistent with a fast C-shock of speed 40-45 km s-1. However, for positions away from the jet head, these ratios may indicate a slower J-shock, with speed [FORMULA] 11 km s-1. The lower limit to the shock speed found from the CO observations does not apply at these positions, only at the jet head. This implies that the jet could contain a series of internal shocks (Raga & Noriega-Crespo 1992). Fig. 5 suggests that the peaks have a similar temperature, but a lower column density than the jet head, which would support this case. However, there are alternative processes which could produce this pattern of temperatures and column densities. These are explored below.

One possibility is a wandering jet. Some jets have been observed to vary slightly in direction as they propagate from the central object. This could lead to apparent clumps of emission in longslit spectra, as the jet moves in and out of the slit position. However, in this case, we have two parallel slit positions, on and off the jet axis, which show the clumps at the same positions. Also the [FORMULA] image of Fuller et al. (1995) shows that there are clumps in the jet. Therefore, the knots in the spectra of the L483 jet are not due to a wandering jet.

It is possible that the emission peaks are clumps of denser material within the jet (Burton 1992; Richter et al. 1995; Micono et al. 1998). Clumps of emission could be formed locally from ambient molecular gas though hydrodynamic instabilities in the jet flow, such as Kelvin-Helmholtz instabilities. The radiative jets entering cool molecular clouds sweep up molecular gas. The instabilities at the boundary leads to ambient material being dragged into the jet, forming dense clumps. Although the [FORMULA] cooling timescale is [FORMULA] 1 year, an energetic jet could reproduce [FORMULA] clumps at the high excitation temperatures near 2000 K. It is conceivable that these clumps would be produced at similar positions, so that the [FORMULA] maps taken at different times will show a similar spatial distribution of knots (compare Fig. 1, taken in 1995 and Fig. 3a, taken in 1997). It is therefore possible that the clumps are formed through jet instabilities.

An alternative model suggests a continuous jet with sporadic periods of higher or episodic activity (Suttner et al. 1997; Bell 1998), possibly corresponding to some type of FU Ori object outburst. FU Ori objects are T Tauri stars that show a sudden and persistent increase in magnitude. Typically, these outbursts last for between 10 and 100 yr, with between 500 and 10000 yr between outbursts. They are thought to be due to enhanced accretion from the disk. The duration of each outburst for the L483 source implied by the size of the knots, assuming a typical jet speed of 200 km s-1, is [FORMULA] 11 yr, which is in line with the models. However, the inferred time between outbursts in L483 is [FORMULA] 50 yr, which is an order of magnitude too short. As the driving source in L483 is thought to be an extremely young class 0 object, it is possible that the outbursts are more frequent during this early epoch.

Based on these observations, and current models of protostellar jets, it is not possible to distinguish between these possibilities. If the knots are due to intrinsic jet variabilities, then observations of the counter-jet could confirm this alternative, as the counter-jet would be expected to show the same pattern of knots, as does HH212 (Zinnecker et al. 1997). In many other sources, knots as traced by CO bullets are in pairs, which suggest intrinsic variation processes. In addition, proper motion observations of the jet could be undertaken. For intrinsic jet variations, we would expect more coherent proper motions, as the knots travel with the jet.

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© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999
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