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

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4. Results

In this section we present the results of the application of the diagnostic technique to the beam section of six Herbig-Haro jets: HH 34, HH 46/47, HH 24G, HH 24C/E, the HL Tau jet and HH 228 (Th 28 jet). Each case is described in detail in the following, while a general discussion, together with two tables summarizing the main results is presented in the next section.

4.1. HH 34

One of the most spectacular examples of a Herbig-Haro jet is the HH 34 outflow, which lies in the L1641 complex, at a distance of [FORMULA] 480 pc (Reipurth et al. 1986, Bührke et al. 1988). South of the source HH 34 IRS lies the blueshifted HH 34 jet, a [FORMULA] long chain of well-aligned bright knots, which is followed by a section where very little emission is seen, and by the large bow shaped feature HH 34S at a distance of [FORMULA] from the source. In the following, we limit ourselves to the study of the beam of the jet, from a few arcseconds to about [FORMULA] from the source. In the beam, which is inclined at roughly [FORMULA] to the plane of the sky, the emitting gas parcels move with a space velocity of [FORMULA] 220 km s-1 (Eislöffel & Mundt 1992, Heathcote & Reipurth 1992). The average radius of the knots is [FORMULA] ([FORMULA] cm at the assumed distance of 480 pc) as derived both from ground based and HST observations (Raga et al. 1991, Ray et al. 1996).

Our results for the HH 34 jet are presented in a column of graphs in Fig. 6. Panel a shows a contour plot of a [SII] image of the object. Intensity tracings along the beam integrated over the line widths of H[FORMULA], [SII] 6716+6731, [NII] 6548+6584, and of the sum of the two [OI] lines at 6300 and 6363 Å, all normalized to the H[FORMULA] peak, are shown in panel b . They provide an overview of the line brightness and the excitation conditions with distance from the source.

[FIGURE] Fig. 6a-f. Physical conditions along the beam of the HH 34 jet. From top to bottom : a  contour plot of a [SII] image of the jet, b  intensity tracings in the various lines normalized to the H[FORMULA] peak (see text), c  electron density derived from the [SII] lines ratio, d  hydrogen ionization fraction [FORMULA] and superimposed recombination curve (see text), e  average excitation temperature of the forbidden line emission region, f  total hydrogen density [FORMULA]

In panel c we plot the electron density as derived from the [SII] line ratio; in the bright part of the beam it is observed to increase progressively to knot J (following the nomenclature by Raga et al. 1991), the second brightest knot in the flow. Beyond knot J the jet apparently flares out and [FORMULA] falls again. Contrary to the electron density, the ionization fraction (panel d ) is found to decrease from [FORMULA] at the beginning of the flow to very low values ([FORMULA]) in the bright portion of the jet. Among the jets of our sample, the HH 34 flow apparently is the most neutral on average: [FORMULA] is lower than 0.05 in the brightest section. At position [FORMULA], coincident with the location between knots B and C, the ionization fraction jumps up to about 0.25 and simultaneously a local enhancement in the electron density is observed. At our spatial resolution we cannot decide if indeed in this region the flow gets reionized, or if this behavior is mimicked by a high measurement error due to the faintness of this part of the jet. Apart from this point, the ionization nicely follows a recombination curve calculated assuming that on average the gas parcels flow in a set of nested cones, whose shape is specified by the initial jet radius and a constant opening angle. Other required input parameters are the average jet speed, the jet distance, an estimate of the inclination angle of the beam with respect to the plane of the sky, and an estimate of the initial electron density. See the Appendix for a description of this model. Our best-fit curve for the HH 34 jet turns out to have a negative opening angle [FORMULA], i.e., the jet is slightly converging. This is in accordance with the behavior of [FORMULA], and with previous investigations by Raga et al. (1991), who measured the jet diameter directly on optical images. Ray et al. (1996), however, find a much more complex structure on high resolution images from HST: at least knots I and J clearly show a bow shape, and an almost perfect anticorrelation between peak intensity and jet width is observed all along the flow.

The average excitation temperature of the forbidden lines emission region also is found to mildly decrease from about 104 K at the beginning of the flow to about 6000 K at the end of the bright section (see panel e ). Then it rises again to [FORMULA] 6500 K in the last two positions, where the faint bow-shaped knot L is located. A small enhancement in the ionization fraction is simultaneously observed. The results for these last two positions may, however, be affected by the faintness of the lines.

Panel f then presents the total hydrogen density as resulting from [FORMULA]. Since our results are not derived from a shock calculation, we cannot identify a compression factor to be applied to the resulting hydrogen density, as in HMR94. Here we use as total density the ratio between the electron density and ionization fraction (see below). The total density profile along the jet shows a similar behavior as the electron density: after a slight decline prior to [FORMULA] the total density increases from about 4000 cm-3 to 5.8 104 cm-3 near knot J. Then it decreases again to values close to the initial values. No jump in the total density profile is evident at position 5:003, where an abrupt change in the electron density is seen.

From the total density a mean value of [FORMULA] cm-3 along the jet can be deduced. With a mean molecular weight of 1.24 the average mass loss and momentum rates for the HH 34 jet then are [FORMULA] M[FORMULA] yr-1 and [FORMULA] M[FORMULA] yr-1 km s- 1. These values are very close to the values found in BCO95 from a spectrum integrated all along the beam, and a factor 2 larger than those of HMR94, who derive an average ionization half of ours, but then apply a correction factor 0.25 for postshock compression (see below).

4.2. HH 46/47

The HH 46/47 outflow lies at the edge of the Gum nebula at a distance of roughly 450 pc. The jet consists of a long wiggling chain of knots, more pronounced in the first half of the flow and fainter in the second half (see, e.g. Eislöffel & Mundt 1994). The knots at the base of the jet are bright in [SII] and H[FORMULA] and are spatially resolved with an apparent radius of about 0:004 corresponding to about [FORMULA] cm. On HST images the numerous features of the fainter section appear as narrow wisps and filaments (Heathcote et al. 1996); probably they represent shocks resulting from the interaction of the jet with the surrounding medium. The visible jet terminates in an extended bow shock, HH 47A. On HST images HH 47A clearly appears as a clumpy region prominent in [SII] `sandwiched' between the forward bow shock and the Mach disk, both luminous in collisionally excited H[FORMULA]. Recent kinematical studies found an inclination angle of about [FORMULA] of the flow to the plane of the sky and an average velocity of about 300 km s-1 (Eislöffel & Mundt 1994, Morse et al. 1994).

Here, we analyse the north-western part of the flow from its base to HH 47A (Fig. 7, panel a ). The excitation conditions vary considerably along the flow (panel b ). The bright reflection nebula at the base of the jet severely hampers the determination of the physical quantities in this region. Although the reflected light was carefully subtracted larger errors in the resulting values for positions [FORMULA] indicate residual contamination. The electron density (panel c ) steadily decreases from [FORMULA] 1200 cm-3 close to the source to about 100 cm-3 at [FORMULA]. In the following faint section [FORMULA] is very low ([FORMULA] 10-30 cm-3), while it increases again in the working surface, where it reaches its local maximum value ([FORMULA] 350 cm-3) just before the location where the forward shock should be found.

[FIGURE] Fig. 7a-f. Physical conditions along the beam of the HH 46/47 jet. Panel description as in Fig. 6. The values denoted by an asterisk are results for a region where the applicability of our technique becomes critical.

The ionization fraction [FORMULA] also decreases on average along the first section of the flow (panel d ). From the source to [FORMULA] it falls from 0.23 to 0.050, then it rises again to 0.145 at position [FORMULA], and then floats around 0.12 until [FORMULA]. Further out, the ionization degree falls substantially to [FORMULA] = 0.02 at the end of the first bright segment of the jet. After [FORMULA], but before HH 47A, the technique qualitatively indicates that the jet is highly ionized, the resulting [FORMULA] varying between 0.5 and 0.9. This result has to be taken with caution though, because here the extremely low gas density and the high ionization make one to suspect that photoionization effects produced by the shock fronts themselves may not be negligible. In the HH 47A the ionization fraction decreases to about 0.055 and then jumps up again close to the forward shock of the working surface. The recombination curve superimposed along the first [FORMULA] of the jet would correspond to an opening angle of [FORMULA], i.e. a slightly diverging jet.

The average temperature (panel e ) varies between [FORMULA] and [FORMULA] K along the bright part of the beam. Values as high as 4.5[FORMULA] K are reached in the following faint section, but no strong increase is seen at the location of the Mach disk and the forward shock of HH 47A.

In panel f we show the derived total density [FORMULA]. In the bright part of the flow [FORMULA] varies in the range 1.2-17.0 103 cm-3. Similar to the electron density, [FORMULA] is higher near the first bright knot and in the working surface, while it is very low in the faint section. It increases consistently also at the end of the bright section, due to the extremely low ionization. Taking a mean [FORMULA] cm-3 over the first [FORMULA], a jet speed of 300 km s-1 and a radius of 2.7 1015 cm, we derive mean mass loss and momentum transfer rates of [FORMULA] M[FORMULA] yr-1 and [FORMULA] M[FORMULA] yr- 1 km s-1. These values are about one quarter of those found by HMR94. From their planar shock models these authors found an average ionization fraction of 0.036 (see the discussion in the next section). They adopt as average electron density [FORMULA] 250 cm-3, and then correct their total density estimate for a compression factor 0.2 leading to [FORMULA] cm-3, less than one third of ours. They assumed, however, a mean jet radius of 1:003 arcseconds while we used 0:004 (from HST images).

4.3. HH 24C/E

The HH 24 complex lies in the NGC 2068 nebula at a distance of 480 pc. At least three separate outflows are emanating from this complex (see, e.g. Mundt et al. 1991, hereafter MRR91, Eislöffel & Mundt, 1997). The HH 24C/E jet, described by Solf (1987), spans over [FORMULA] in the sky, and is apparently accelerated by the invisible source SSV 63 (Strom et al. 1976). The HH 24C jet consists of a straight blueshifted chain of knots north-west from the source at a distance of [FORMULA] to [FORMULA]. The counterjet, HH 24E, extends from [FORMULA] to [FORMULA] from the source (see also Eislöffel & Mundt 1997). At [FORMULA] from the source one finds the bright condensation HH 24A, that may, however, be part of a separate outflow, the HH 24MMS jet. Measured radial velocities are -180 km s-1 in the C jet and about 150 km s-1 in the E counterjet (MRR91). Both structures have roughly constant spatial widths in their brightest sections, on average about [FORMULA] for HH 24C and [FORMULA] for HH 24E, which correspond to 8 [FORMULA] and 5 [FORMULA] cm, respectively, at the assumed distance of 480 pc (MRR91).

HH 24C presents conditions of mild excitation (Fig. 8, panel b ). Correspondingly the ionization fraction never falls below 15% in the bright region (panel d ). The ionization data points do not follow a monotonic trend. Instead, [FORMULA] is oscillating around a mean value of [FORMULA] 0.25, with a slight increase in the fainter middle section of the flow, where the gas is apparently reionized: contrary to HH 34 the ionization data points are better fit by two different recombination curves. For this jet no determination of the inclination angle is available, therefore we calculated for each jet section three sets of recombination curves, corresponding to inclination angles to the plane of the sky of [FORMULA], [FORMULA], and [FORMULA]. In any of these cases the best-fit recombination curves for the first jet section correspond to a flow slightly converging by an angle of [FORMULA], while the second beam section is better described assuming an opening angle of [FORMULA]. As the best-fitting inclination angle we find [FORMULA] - [FORMULA]. The electron density (panel c ) decreases on average along the flow, but peaks at the positions of the two brightest knots. At knot C2 (following the denomination of MRR91), at [FORMULA], we find 880 cm-3, and at knot C5, at [FORMULA], we find 470 cm-3. The average excitation temperature starts at 2.0 104 K at the beginning of the flow (panel e ), then falls by 104 K and increases again to reach 2 104 K at position [FORMULA], i.e. at the end of the bright beam section. Apart from position [FORMULA], the behavior of the total density (panel f ) is similar to that of [FORMULA]: they both follow the intensity profile of the lines. The average total density is about 2.1 [FORMULA] cm-3. The fact that both the electron density and the total density are rather low helps to understand how a moderate ionization degree can be maintained over large distances, contrary to, e.g., the HH 34 jet. Under such low density conditions recombination is disfavoured and therefore the ionization degree can be maintained over a relatively long distance. Assuming that the average density is constant on the transverse jet section, and taking a jet velocity of 425 km s-1 and a jet radius of [FORMULA], the average mass loss rate obtained for this jet is [FORMULA] M[FORMULA] yr-1, while the momentum transfer rate is [FORMULA] M[FORMULA] yr- 1 km s-1.

[FIGURE] Fig. 8a-f. Physical conditions along the beam of the HH 24C jet. Panel description as in Fig. 6. The superimposed recombination curves are calculated for a jet inclination angle of [FORMULA] (dashed lines), [FORMULA] (solid lines) and [FORMULA] (dash-dotted lines). The source is located to the left.

In HH 24E, moderately low excitation conditions are present along the jet. In HH 24E the ionization degree (Fig. 9, panel d ) shows two pronounced jumps at positions [FORMULA], i.e. just after knot E, and [FORMULA], i.e. at the beginning of the bright condensation HH 24A. The ionization fraction decreases smoothly within each of the three sections, albeit along three different recombination curves. On average, it becomes progressively higher from one section to the next: [FORMULA] varies from [FORMULA] 0.15 to [FORMULA] 0.06 in the first section, from [FORMULA] 0.36 to 0.17 in the second, and from 0.38 to [FORMULA] 0.3 in the third section. As in HH 24C, the jet inclination angle is unknown, so that for each different jet section we calculated three sets of tentative curves corresponding to [FORMULA], [FORMULA], and [FORMULA]. The best fit in each jet section is obtained for opening angles of [FORMULA], [FORMULA], and [FORMULA], respectively. Interestingly enough, the data points in HH 24A are best reproduced assuming an inclination angle of only [FORMULA], which is quite lower than the [FORMULA] - [FORMULA] inclination angle that describes the first two sections of HH 24E and HH 24C. This could be evidence that HH 24A may indeed belong to the nearby HH 24MMS jet, and not to the HH 24E jet. The average excitation temperature (panel e ) decreases from 1.5 104 K to 1.0-1.1 104 K near knot A. An isolated marked decay at 5400 K is observed at position [FORMULA], where, however, the jet is very faint. In knot A the electron density increases from [FORMULA] 350 to [FORMULA] 1400 cm-3, while no apparent enhancement is seen near the first jump at [FORMULA]. On the other hand, the derived total density (panel f ) is higher in the first section of the flow than in knot A (if allowance is made for the large errors in the first positions). As a mean along the flow one can take [FORMULA] cm-3, which, together with an assumed [FORMULA] inclination angle, 2.5 [FORMULA] cm radius and 150 km s-1 radial velocity of the jet, yields a total mass loss rate of [FORMULA] M[FORMULA] yr-1 and a total momentum supply rate [FORMULA] M[FORMULA] yr- 1 km s-1.

[FIGURE] Fig. 9a-f. Physical conditions along the beam of the HH 24E counter jet. Panel description as in Figs. 6 and 8. Note marked enhancements in the ionization fraction at positions [FORMULA] and [FORMULA] and the subsequent decline in the direction away from the source (see text).

4.4. HH 24G

The HH 24G outflow is apparently emanating from the IR source SSV63 NE, which lies [FORMULA] to the south-west of this jet (MRR91). It consists of two separate condensations which are rather diffuse in appearance, followed by a small clump at the end of the flow. The jet is blueshifted and has a radial velocity of -130 km s-1. Its average width in the brightest region is [FORMULA] corresponding approximately to a diameter of 3.6 1016 cm.

According to its [SII]/H[FORMULA] ratio (Fig. 10, panel b ) the HH 24G jet appears to be of low excitation. The average ionization (panel d ), however, turns out to be higher in the second portion of the flow. As in HH 24E, re-ionization episodes appear to be present along the beam, the first one being at [FORMULA], in the faint bridge between the diffuse knots, while a second one at [FORMULA] is related to the intensity maximum in HH 24G2 (nomenclature as in MRR91). At the same position also the electron density peaks ([FORMULA] 600 cm-3), while the temperature reaches its maximum value in the faint bridge ([FORMULA] 1.14 104 K at position [FORMULA]). Another jump might occur at [FORMULA], but our measurement accuracy is not sufficient to ascertain its presence. Therefore, we tentatively superimposed three sets of recombination curves to the [FORMULA] data points, calculated assuming inclination angles of [FORMULA], [FORMULA], and [FORMULA], as for HH 24C/E. The results are better reproduced assuming an inclination angle to the plane of the sky of about [FORMULA] in this jet. The best-fit opening angles are, however, larger than in the previous cases: in the first section the jet apparently opens up at [FORMULA], after the bridge it seems to reconverge following cones with an angle of [FORMULA] and it finally opens up again with [FORMULA]. As in HH 24E, the smooth recombination decreases are observed on the far side of the jump with respect to the source (i.e. downstream), and each subsequent event puts the jet gas to a slightly higher degree of ionization. Notably, the second recombination section is associated with an increase in both the electron and total density from the bridge to the end of the flow.

[FIGURE] Fig. 10a-f. Physical conditions along the beam of the HH 24G jet. Panel description as in Fig. 6. The superimposed recombination curves are calculated for a jet inclination angle of [FORMULA] (dashed line), [FORMULA] (solid line) and [FORMULA] (dash-dotted line). The source is on the left.

Finally, we note that as in HH 24C/E a moderately high degree of ionization is associated with low [FORMULA] and [FORMULA]. The electron density is 200-300 cm-3 for a large portion of the flow while the total density scatters around 1400 cm-3: apparently the jet is lighter in the first section and denser in the second. Because of its rather large average radius, the mass loss and momentum transfer rates in HH 24G are not smaller than those of the other jets. Assuming a constant density in the jet section and an inclination angle of [FORMULA] yields [FORMULA] M[FORMULA] yr-1 and [FORMULA] M[FORMULA] yr- 1 km s-1. These large values could, however, easily be reduced by an order of magnitude, since this flow appears to be rather clumpy 005 we used. (MRR91) so that the effective jet radius may be much smaller than the 2:

4.5. HL Tau jet

North-east of HL Tau, there is a long jet of at least [FORMULA] with a fainter counterjet on the opposite side of HL Tau, only seen in [SII] images. HL Tau is surrounded by a diffuse nebulosity which is bright in H[FORMULA], and which did not allow us a reliable application of the technique in the proximity of the source. We studied, however, the physical properties of the bright, [FORMULA] long structure north-east of HL Tau beyond [FORMULA] from the star to the condensation at [FORMULA] from HL Tau (knot HL-E in Mundt et al. 1990).

The HL Tau jet is blue-shifted with a velocity of about -180 km s-1. The width measured from H[FORMULA] images ranges from [FORMULA] to [FORMULA] and is larger than the corresponding width in [SII] by more than 50% (Mundt et al. 1990). On the basis of the broad H[FORMULA] and narrow [SII] line profile, the authors interpreted the larger jet width in H[FORMULA] in terms of turbulent entrainment of ambient gas at the boundary of the flow. Possible terminal working surfaces have been found recently by Lopéz et al. (1995).

The jet seems to be rather diffuse: in accordance with the estimate by Mundt et al. (1990) the electron density is low everywhere, varying around 300 cm-3 on average (see Fig. 11, panel c ). [FORMULA] stays almost constant along the beam of the HL Tau jet, while it decreases in the HL-E knot. Apart from the first position, that could be affected by the faintness of the [SII] lines, in the bright section of the flow [FORMULA] steadily increases from about 0.14 to about 0.36 (panel d ). This behaviour is opposite to that of the other jets examined so far. The ionization, however, can be produced in the turbulent boundary layer whose presence has been suggested on the basis of the H[FORMULA] line profile, instead of by a violent event at the base of the jet (Mundt et al. 1990). If this is the case, the ionization fraction could be `pumped' all along the length of the flow. As a consequence, no recombination curve can be drawn for this jet. After position z[FORMULA] the emission is very faint again: here, the ionization degree varies between 0.07 and 0.23 without any definite trend. Neglecting the uncertain results for [FORMULA], the average total density is about 1700 cm-3. Assuming a mean radius of [FORMULA], a tentative inclination angle of [FORMULA] and that the system is at a distance of 150 pc, mass loss and momentum transfer rates would be [FORMULA]M [FORMULA] yr-1 and [FORMULA] M[FORMULA] yr- 1 km s-1. This mass loss rate is two orders of magnitude larger than the value estimated by Mundt at al. (1990). The reason for this is that they used the pre-shock density calculated from [FORMULA] on the basis of planar shock models as total density, and in that way obtained [FORMULA] (pre-shock) [FORMULA] 10 cm-3. As stated above, the ionization in this jet could result from turbulent entrainment of ambient material, and not from the jet properties themselves. Therefore, it seems difficult to draw firm conclusions from the results obtained for this jet.

[FIGURE] Fig. 11a-f. Physical conditions along the beam of the HL Tau jet. Distances are measured from HL Tau which was on in the long slit. The last five points refer to the HL-E knot. Panel description as in Fig. 6.

4.6. A peculiar case: Th 28 jet (HH 228)

This flow consists of two oppositely directed jet-like structures, each about [FORMULA] long, emanating from the unusual emission-line star Th 28, located in the Lupus T-association at a distance of about 130 pc. Several HH objects are located on both sides on the jet axis (Krautter 1986, Graham & Heyer 1988). On the western side one finds Th 28-HHW, at a distance of about [FORMULA] from the source, while on the eastern side two regions of faint H[FORMULA] emission, Th 28-HHE1 and Th 28-HHE2 are located at [FORMULA] and [FORMULA], respectively. The average radial velocity of the western components of the flow are [FORMULA] km s-1 for the jet and +33 km s-1 for Th 28-HHW, while in the eastern lobe one derives -78 km s-1 for the jet, -67 km s-1 for HHE1, and -87 km s-1 for HHE2 (Graham & Heyer, 1988). Proper motion measurements (Krautter 1986) of the HHE1 knot indicate a tangential velocity of about 320 km s-1. Under the assumption that this knot is a working surface, one derives an inclination angle of this system with respect to the plane of the sky of about [FORMULA]. The spectrum of the source reveals a very active region, with many lines typical of a HH object, superposed on a strong continuum indicating the presence of an underlying star (Krautter et al. 1984).

Our analysis is limited to the western receding lobe, since the emission from the short eastern jet is heavily confused with the lines from the central region, and the knots HHE1 and HHE2 are not detectable in our spectra in the sulphur and oxygen emission lines. Furthermore, in the examined region the validity of the diagnostic is limited by the fact that the system of HH objects appears to be of high excitation. Moreover, quite unusually for HH objects, the [OI] lines are stronger than the [SII] lines over the first 4:005 of the jet. For these reasons, the application of the diagnostic technique to this object has a qualitative character, especially for the jet section.

The electron density [FORMULA] decreases along the flow in the beam, from about 2500 cm-3 to about 800 cm-3, and in the HH object from [FORMULA] 1200 cm-3 to about 170 cm-3 (Fig. 12, panels c ). A steep gradient of [FORMULA] along the flow was already seen by Krautter (1986). The ionization fraction in the jet appears to be rather high, except for the first position, where the [NII] emission is blended with very strong H[FORMULA]; qualitatively, [FORMULA] scatters around 0.5 (left panel d ). In knot HHW [FORMULA] decreases steadily from about 0.4 to [FORMULA] 0.04 (right panel d ). Neither in the beam section nor in the terminal knot were we able to fit the ionization data with a reliable recombination curve. The average temperature decreases from 2.5 104 K to 1.5 104 K in the jet, while it increases from about 1.3 104 K to 1.7 104 K in HHW. In the jet section the total hydrogen density decreases from about 3.3 104 cm-3 to about 1500 cm-3, following the behavior of [FORMULA]; a less steep decay in [FORMULA] is derived in HHW, where it decreases from 3000 cm-3 to about 2500 cm-3. Given the qualitative character of these results, we refrain from estimating the mass loss and momentum transfer rate for the Th 28 jet.

[FIGURE] Fig. 12a-f. Physical conditions along the beam of the red lobe of the HH 228 (Th 28) jet. The left and right columns of graphs illustrate the results for the jet and for the HH object Th 28-HHW, respectively. Panels a are contour plots of a H[FORMULA] image. The following panels are as in Fig. 6. In neither case does a reliable recombination curve fit the data points.

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Online publication: February 23, 1999
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