25 au Angular Resolution Observations of HH 211 with ALMA: Jet Properties and Shock Structures in SiO, CO, and SO

SiO(J = 8–7), CO(J = 3–2), and SO(N_J = 8₉–7₈) are detected on both sides of the central source, and their emission intensity maps are shown in Figures 1(a)–(c), respectively. As seen before (Lee et al. 2009), the jet in these lines is highly collimated with a small wiggle and consists of a chain of knots, even though the SO emission is relatively weak. Moreover, SiO, SO, and CO emissions trace a bow-shock structure for knot BK3 in the jet (green box in Figure 1).

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In channel maps of these emissions (Figure 2 for SiO, Figure 3 for CO, and Figure 4 for SO), the jet appears increasingly collimated going from low to high velocity. In CO, the jet is seen at high velocity (V_LSR ≤ 0.2 km s⁻¹ and V_LSR ≥ 18.2 km s⁻¹), and outflow shells are seen at low velocity (0.2 km s⁻¹ ≤ V_LSR ≤ 18.2 km s⁻¹), as seen before (Gueth & Guilloteau 1999; Lee et al. 2007). This distribution is also seen in other objects (Santiago-García et al. 2009; Lee et al. 2015). SO traces the jet as SiO and CO does, and shows evidence of shell-like structure at V_LSR = 9.2 km s⁻¹ within 2'' of the central source tracing the base of the outflow. All three lines can also trace bow-shock structures, e.g., at velocity ∼−8.8 and 0.2 km s⁻¹ on the blueshifted side.

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In 2008, we observed HH 211 at a resolution of 025 with the Submillimeter Array (SMA; Lee et al. 2009, Figure 5(c)). Therefore, the proper motion can be estimated by measuring the position shift of the knots from the 2008 SMA observation to the 2016 ALMA observation (Figures 5(a) and (b)). The time interval is 7.72 yr. We first degraded the 2016 ALMA map from 008 to 025 resolution and aligned the maps with the continuum peaks. In these two epochs, eight knots within ∼8'' of the central source, four on each side of the source, are used for proper motion measurement. We measured the peak positions of these knots (Figure 5) and calculated the position shift of the knots. The error bar of position shift is assumed to be one-third of the beam size along the jet axis. The proper motion is then estimated to be ∼0068 ± 001 per year. With the new distance of 321 pc, the transverse velocity is ∼102 ± 16 km s⁻¹. Thus, the inclination angle is refined to be ∼11°, using a mean radial velocity of ∼20 km s⁻¹ estimated in Section 3.5.

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We then compared our result with the previous SMA result reported in Jhan & Lee (2016) for the outer parts of the jet at a distance from 5'' to 16''. We first refined the previous SMA measurements by taking out the 2004-epoch data because its resolution is the lowest (∼12) and the UV coverage is the poorest of those in all epochs. The refined proper motion (triangles in Figure 6) is 30% lower than that measured before, but is closer to our current ALMA measurement for the inner jet, as shown in Figure 6. The figure shows that the velocity of the jet is roughly constant at a distance from 1000 to 5000 au (3''–16'') within the error bar, although there could be a slight decrease in velocity with distance, as shown by the linear fit.

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A reflection-symmetric wiggle has been detected in the jet and was modeled with an orbiting jet source model in Lee et al. (2010). The same model with the same parameters was later used to fit the wiggle in three other epochs (2004, 2010, and 2013) of the SMA data of the SiO line (Jhan & Lee 2016). Now, we can verify whether the model can still fit the same wiggle in our ALMA observation in the inner part of the jet at higher resolution. In our mapped region, the jet shows one to two wiggle cycles, as shown in Figure 5(a). After adjustment for proper motion, the previous best-fit parameters still roughly fit the pattern of the wiggle but with some deviations, especially in the regions, from 3'' to 6'' and from −3'' to −4'' where the peaks of the knots deviate to the north from the model. We discuss the deviations in more detail in Section 4.1.

To study the jet kinematics perpendicular to the jet axis, we present the position–velocity (PV) diagrams along cuts perpendicular to the jet axis in SiO and CO emissions (Figures 7–8) centered at the SiO emission peaks, which have a distance of 05–2'' from the central source. We identified three velocity components in the diagrams, marked by boxes of different colors in the figures: a low-velocity component in red boxes with a wide spatial range, a medium-velocity triangular component in green boxes, and a high-velocity linear component in blue boxes. The low-velocity component is seen mainly in CO, tracing the outflow shell as discussed in Section 3.1. The medium-velocity triangular structure appears in CO and SiO. The high-velocity linear structure is also seen in CO and SiO with almost the same velocity range in these two lines. This high-velocity structure traces the jet itself, as seen in the channel maps. However, the highest velocity of the jet gradually slows down with increasing distances (as can be seen in blue boxes at different distance, or see Figure 8 in Lee & Sahai 2004), and then the high-velocity parts merge with the triangular components in some of the diagrams at large distances.

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The first pair of knots (knots BK0 and RK0) in SiO (Figure 1(a)) appears within 01 of the source and is separated from the other knots downstream. Figure 9 shows the PV diagrams along cuts perpendicular to the jet axis in SiO, CO, and SO. The SiO and CO emission appears roughly in the same velocity range, but the SO emission appears only at low velocity within ∼10 km s⁻¹ of the systemic velocity. Therefore, a slow component is defined with the SO emission using the SO velocity range (from ∼1 to 20 km s⁻¹ in the blueshifted knot and from ∼−4 to 23 km s⁻¹ in the redshifted knot). This slow component in SO has been reported in Lee et al. (2018). At higher angular resolution in SO, this slow outflow was found to be rotating, with a velocity gradient across the jet axis centered at the systemic velocity (see Figure 4 in Lee et al. 2018), and thus it can trace a disk wind. This velocity gradient can also be roughly seen here in SO.

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In addition, SiO and CO also trace a fast component (∼−15 to 0 km s⁻¹ in the blueshifted knot and ∼24 to 42 km s⁻¹ in the redshifted knot), allowing us to search for jet rotation. This fast component, with the central velocity close to the velocity of the jet (as discussed in Section 3.5), traces the jet itself. However, no clear velocity gradient can be seen in these knots at our current resolution.

To study the kinematics along the jet axis, we present PV diagrams cut along the jet axis in CO and SiO (Figure 10). The PV structures in CO and SiO are roughly the same. In addition, the PV structures on the blue- and redshifted side are also roughly the same. Note that in Figure 10(a), the roughly linear structure seen in CO (red contours) on the right side of the jet (roughly at x offsets from −26 to −40) that appears on the other side of the main wiggle is the outflow structure around the jet.

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The knotty structures (knots BK1a, BK2, and BK3) on the blueshifted side are clear. Previously, Jhan & Lee (2016) derived the distance for an internal shock to fully form, which is $\sim {v}_{j}\cdot \tfrac{{v}_{j}}{{\rm{\Delta }}v/(P/2)}\sim$ 26 updated for the new proper motion measurement, where v_j ∼ 102 km s⁻¹ is the jet velocity, Δv ∼ 30 km s⁻¹ is the amplitude of the velocity variation (based on the velocity range of knot BK1), and P ∼ 20 yr is the period of the velocity variation (based on the mean interknot spacing and the proper motion). Thus, these knot structures should be produced by fully formed internal shocks. Their PV structures are all linear with the slow material ahead of the fast material. This indicates that when the fast material catches up with the slow material, it will form an internal working surface between them (see Figure 1 in Suttner et al. 1997). Figure 12 shows that the PV structure of the knot BK3 shows several peaks. As discussed below, these peaks likely point out the positions of the backward (peaks at higher velocity) and forward (peaks at lower velocity) shock, and the internal working surface (point at medium velocity) formed in the knot (Raga et al. 1990; Stone & Norman 1993; Suttner et al. 1997; Lee & Sahai 2004; Jhan & Lee 2016).

Within a distance of 26, subknots of knots BK1 and RK1 can be seen on the blue- and redshifted sides in the intensity maps (Figure 10(a)). Although they are hard to identify in the PV diagrams, we can still see four to five cycles of velocity variations, with a variation range of about 25–30 km s⁻¹ for these subknots, consistent with the result in Lee et al. (2009).

Figure 10(c) zooms into the continuous structures, showing the subknot structures in them. The distance between two subknots is about 03, thus the period of the subknot ejection is about 4.5 yr, using a jet velocity of 102 km s⁻¹. Therefore, using the same formula, the distance for an internal shock to fully form in the subknots is ∼06. This is consistent with our observations, which show CO but no SiO emission between 01 to 05 and −01 to −05 because the shocks have not formed yet, and thus no SiO emission can be detected. This result is also aligned with a previous simulation that suggested that a velocity variation with a shorter period is needed to produce the bright emission in the continuous SiO structure near the source (Moraghan et al. 2016). In summary, the PV diagrams suggest at least two different variation periods: one to form the subknot regions near the central source, and the other to form the knotty structure farther downstream the jet.

The column density of knot BK3 can be estimated from the CO emission. Assuming that the CO emission is in local thermal equilibrium and optically thin, and the abundance of CO relative to H₂ is ∼4 × 10⁻⁴, as if the CO gas is formed via gas-phase reactions in an initially atomic jet (Glassgold et al. 1991), the column density of the knot in H₂ is N ∼ 5.6 × 10²⁰ cm⁻². Because the brightness temperature is ∼90 K, we assume the excitation temperature to be 200 K, as adopted in Lee et al. (2010). This excitation temperature is slightly lower than the kinetic temperature derived from the CO emission in much higher transitions in the far-infrared, which was found to be ≳250 K (Giannini et al. 2001). Then, the (two-sided) mass-loss rate of the jet can be given by ${\dot{M}}_{j}\sim 2{v}_{j}{m}_{{{\rm{H}}}_{2}}{Nb}$ ∼ 1.13 × 10⁻⁶ M_⊙ yr⁻¹, where N, ${m}_{{{\rm{H}}}_{2}}$, and b are the column density of the jet, the mass of the H₂ molecule, and the beam size perpendicular to the jet axis (assuming that the size of the jet beam is ∼04, ∼128 au, discussed in Section 4.2), respectively. This mass-loss rate is consistent with the previous measurement (Lee et al. 2010) after adjustment for the new proper motion.

The SiO and SO abundances in knot BK3 can be derived from their column densities and that of H₂. The kinetic temperature was found to be 300−500 K in knots BK1 and RK1 (Hirano et al. 2006). Because knot BK3 is farther away and expands, its excitation temperature should be lower and is thus assumed to be 300 K. This excitation temperature of SiO and SO is higher than that of CO because both emissions seem to trace stronger shocks than the CO emission does. When we assume that both emissions are optically thin, the SiO and SO column density are ∼7.9 × 10¹⁴ cm⁻² and ∼1.0 × 10¹⁴ cm⁻², resulting in SiO and SO abundances of ∼1.4 × 10⁻⁶ and ∼1.8 × 10⁻⁷, respectively. Note that the abundance of SiO in quiescent molecular clouds is ≤1 × 10⁻¹¹ (Ziurys et al. 1989), and the abundance of SO in cold quiescent clouds (cores) is ∼5 × 10⁻⁹ (Ohishi & Kaifu 1998). This means that both SiO and SO are highly enhanced by shocks in the knot.

As mentioned in Section 3.3, the orbiting jet source model could still fit our current observation with some deviations. Because this model can also fit the wiggle structure farther out in another three epochs over a period of 9 yr, we believe that the model is roughly correct but needs some refinement. Comparing our observational results in Figure 5(b) to 2008 SMA observations in Figure 5(c) at the same resolution, we found that the peaks of the knots (knot BK1a, BK2, and BK3) in our ALMA observations deviate to the north from the model, with little flux detected in the south. This deviation does not appear in the SMA observations, in which the peaks of the knots are aligned with the model.

One possible reason is that our ALMA observation results might miss some flux, so that some flux of the knots is missing. The maximum recoverable size is ∼075, and the size of the knots is ∼1'', so the structures of the knots may not be fully observed. Therefore the apparent peaks of the knots may deviate to the north from the model, but we are not sure how and to what extent the missing flux affects our results. Observations with more complete UV coverage are needed to confirm this possibility.

It is also possible that the structures of the knots do deviate to the north from the model. In the orbiting jet source model (Lee et al. 2010), the orbit of the jet source was assumed to be circular. However, because this reflection-symmetric wiggle is likely due to an orbital motion of the jet source in a binary system (Lee et al. 2010), it is possible that the orbit is not perfectly circular. It may be elliptical so that the model may under- or overestimate the trajectories at different distances (González & Raga 2004). In the high-resolution observation, the peak positions of the knots therefore cannot be fitted exactly by the model. Nonetheless, because the binary separation in this model is ∼4.6 au (Lee et al. 2010), further observations at higher resolution are also needed to confirm or refute whether a binary system exists.

As mentioned in Section 3.5, it takes time (or distance as the jet propagates) to fully form internal shocks in knots and subknots, and the corresponding distances in our case are about 26 and 06, respectively. Therefore we expect to see shock structures, including backward and forward shocks and sideways ejection in the knots and subknots, after these distances. Because subknots are not spatially resolved, we focus on the knots here.

Figure 11 summarizes the forward and backward shocks, internal working surface, sideways ejection, and their PV structures in schematic diagrams (Raga et al. 1990; Stone & Norman 1993; Suttner et al. 1997; Lee & Sahai 2004; Jhan & Lee 2016). When we use the cut perpendicular to the jet axis (Figure 11(b)), we can see a hollow elliptical PV structure that is due to the expanding bow-shock structure. At the center of this elliptical PV structure, we can see a filled elliptical PV structure that arises from the jet beam with sideways ejection. In the cut along the jet axis (Figure 11(c)), we can see a zig-zag PV structure containing a forward shock (low velocity), a backward shock (high velocity), an internal working surface (in the middle; Lee & Sahai 2004), and an elliptical PV structure for the sideways ejection extents in the middle.

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Knot BK3 appears to be a bow-like structure and is at a greater distance than 26. It can therefore be used to study the shock structure. Figure 12(a) shows a SiO PV diagram of knot BK3 cut along the jet axis through the peak position. We can see a zig-zag PV structure consisting of forward (low-velocity) and backward (high-velocity) shock and internal working surface (in the middle), as discussed above. There are other components in the area of the internal working surface (circled by a red ellipse and labeled "sideways ejection"), and these components may be due to sideways ejection. To make it clearer, Figure 12(b) is a SiO PV diagram of knot BK3 along a cut perpendicular to the jet axis through the peak position, and it shows an elliptical PV structure that can be attributed to a bow-shock structure produced by sideways ejection. Comparing Figures 12(a) and (b) (cut through the same reference central point, but different directions), we conclude that the additional PV component (circled in Figure 12(a)) corresponds to the PV structure of the sideways ejection. Furthermore, the emission inside the elliptical PV structure in Figure 12(b) is the PV structure of the internal working surface (in the jet beam itself), as discussed above. We also calculated that the PV structure of the sideways ejection along the jet axis would be $W\cdot \sin (i)$ ∼ 02 in extent, where the width of the knot W ∼ 1'' and the inclination angle i ∼ 11°. This extent agrees with that seen in Figure 12(a) for the region labeled "sideways ejection". In our case, the knot can therefore be resolved into backward and forward shocks plus sideways ejection. A model illustration of these shock structures is given in the next section.

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Note that the PV structure of the sideways ejection at different inclinations can be different due to the projection effect. For example, the IRAS 04166+2706 jet has a high inclination angle of ∼52°, and the PV structure becomes a sawtooth pattern (Santiago-García et al. 2009; Tafalla et al. 2017), whereas HH 212 has a very low inclination angle of ∼4°, and the PV structure becomes arc-like (Lee et al. 2015).

4.2.1. Illustrative Model for Shock Structures in Knot BK3

Here we presented a simple kinematic model to illustrate the shock structures in knot BK3 in more detail. As shown in Figure 11, this model has two components, a jet beam and a bow-shock structure. This jet beam consists of an unshocked jet beam (UJB), a backward shock (BS), an internal working surface (IWS), and a forward shock (FS), mimicking an internal shock produced in pulsed-jet simulations (Raga et al. 1990; Suttner et al. 1997; Lee & Sahai 2004). The velocity structure in the jet beam has two components; one is along the jet axis, and the other is perpendicular to the jet axis for the sideways ejection (see Figure 16). The velocity gradients along the jet axis are therefore assumed to roughly match the observation. These velocity gradients are also expected for an internal shock produced in pulsed-jet simulations (Raga et al. 1990; Suttner et al. 1997; Lee & Sahai 2004). On the other hand, the velocity structure in the bow-shock structure (see Figure 17) is adopted from the jet-driven bow-shock model (Ostriker et al. 2001). The resulting PV diagrams are presented in Figure 13. In the PV diagram cut along the jet axis (Figure 13(a)), we see four linear structures as marked by the white lines, arising from the unshocked jet beam, the backward shock, the internal working surface, and the forward shock, respectively. They are roughly consistent with the observation. The sideways ejections are mostly from the internal working surface, causing a spread in velocity there, as marked by the red ellipse in Figure 13(a). The PV structures marked by the white ellipses are from the bow-shock structure, with the upper (more blueshifted) one from the near side and the lower (less blueshifted) one from the far side. They are also roughly similar to those seen in the observation. Their intensity peaks are also at roughly the same locations as those seen in the observations. In the PV diagram, two components lie along a cut perpendicular to the jet axis (Figure 13(b)): one is an elliptical PV structure from the expanding bow-shock structure, and the other is a filled ellipse (marked by the red ellipse) from the jet beam that has a sideways ejection. These features are also similar to those seen in the observation.

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Figure 14 shows the PV diagrams in SiO, CO, and SO of the fully formed knot BK3. The CO and SO PV structures are roughly the same, as shown in Figures 14(b) and (d). However, the PV structures of the CO emission in Figures 14(a) and (c) only show a part of the PV structure of the SiO emission. These missing parts of the CO PV structures could be due to different emission lines tracing different layers. According to Figure 14(c), PV structures of CO emission do not show the redshifted part of elliptical PV structures (due to the expanding shell produced by the sideways ejection). This could be explained if the SiO layer in the bow shock (as shown in the dark gray layer in Figure 15(a)) extends farther out than the CO layer (as shown in the light gray layer in Figure 15(a)). Therefore, the cut inclined to the jet axis by 79 (=90 − 11) degree used in our PV diagrams does not go through the expanding CO shells (see the dotted curve in Figure 15(a)) on the far side of the knot (closer to the central source). This phenomenon may be due to these two lines tracing different densities. The critical density of the SiO(J = 8–7) transition is ∼10⁸ cm⁻³ (Lee et al. 2009), and that of CO(J = 3–2) is ∼10⁵ cm⁻³. So CO may trace the low-density part of the bow shock (Figure 15(b)), and the SiO layer traces the higher density and outer bow shock (see the dark gray layer in Figure 15(a)). This phenomenon also appears in HH 212 (Lee et al. 2015), but we do not see a clear extension of SiO and CO in our emission maps (higher resolution observations are needed to distinguish it).

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