1.Introduction

The existence of symmetric emitting knots (at similar distances from the outflow source) along some bipolar Herbig-Haro (HH) outflow systems implies highly synchronized jet/counterjet ejections, and therefore a small spatial extent for the jet production region. This was pointed out by ^{Raga et al. (2011a)} in their study of Spitzer Infrared Array Camera (IRAC) images of the HH 34 outflow. In a second paper, ^{Raga et al. (2011b)} developed a ballistic jet model which constrained the ejection asymmetries using the observed jet/counterjet structures, and applied the model to the HH 34 and HH 111 outflows.

These analyses of jet/counterjet asymmetries have been carried out with IR Spitzer images in the 4 IRAC channels (centered at 3.6, 4.5, 5.8 and 8.0 μm). This is because at optical wavelengths, larger jet/counterjet asymmetries are found in the knots close to the outflow source, often with one of the two lobes being undetected because of a large optical extinction (this is the case, e.g., of the HH 34, HH 111 and HH 1/2 outflows). The intrinsic symmetry of the two lobes is then only visible at infrared (IR) wavelengths, as first shown in a quite dramatic way by the H₂ 2.1 μm observations of HH 111 of ^{Gredel & Reipurth (1994)}.

A clear candidate for this kind of study is the HH 212 outflow, which is an impressive “IR jet”, discovered at IR wavelengths by ^{Zinnecker et al. (1998)} and with only very faint optical emission (^{Reipurth et al. 2019}). This outflow lies very close to the plane of the sky (Claussen et al. 1998) and is at a distance of approximately 400 pc (^{Anthony-Twarog 1982}, ^{Kounkel et al. 2017}). Recent proper motion determinations (^{Reipurth et al. 2019}) show that the jet and the counterjet have a velocity of ≈170km s^-1.

H₂ 2.1 μm observations of HH 212 (^{Davis et al. 2000}, ^{Smith et al. 2007}, ^{Correia et al. 2009}) show that this outflow has emitting structures with evident jet/counterjet symmetries. We present Spitzer images in the four IRAC channels (I1-I4, at 3.6, 4.5, 5.8 and 8.0 μm) and an archival VLT 2.1 μm image of HH 212, and determine the positions of knots along the jet and the counterjet.

We then use the knots within 40´´ from the outflow source to calculate jet/counterjet knot position offsets. These offsets (as a function of distance from the outflow source) are then interpreted in terms of the ballistic outflow model of ^{Raga et al. (2011b)} in order to constrain the jet/counterjet asymmetries of the ejection process. We also study the deviations of the knot positions perpendicular to the outflow axis, and interpret them in terms of the “orbiting outflow source” model of ^{Masciadri & Raga (2002)}.

The paper is organized as follows. The observations are discussed in § 2. The measurement of knot intensities and positions (as well as the determinations of jet/counterjet knot offsets) are presented in § 3. § 4 presents interpretations of the HH 212 measurements, including an application of the jet/counterjet asymmetry model of ^{Raga et al. (2011b)}, an application of the “orbiting source jet” model of ^{Masciadri & Raga (2002)}, an evaluation of the difference in extinction towards the jet and the counterjet, and a discussion of the features of the outflow that do not show a clear jet/counterjet symmetry. The results are summarized in § 5.

2.The Observations

The IRAC data were obtained during the Cryo-Spitzer mission, program PID 3315 (PI Noriega-Crespo) on “Emission from H2, PAHs and Warm Dust in Protostellar Jets”. The data were collected in the four IRAC bands using a 30 sec high dynamic range (HDR) frame time and a 12 point medium scale Reuleaux dither pattern. A small 2×1 mosaic with a 260 arcsec stepsize was used to capture the outflow within the field of view (FoV) of the four IRAC (3.6, 4.5, 5.8 and 8.0 μm) channels. The resulting images have a 0.6´´ pixel size.

We used the final reprocessing from the Spitzer Archive with a standard angular resolution of FWHM≈2 arcsec. Figure 1 shows the entire outflow in the four bands. As expected, the HH 212 jet itself is brighter at 4.5 μm, given that some of the bright pure (0-0) rotational lines fall within the IRAC Channel 2 bandpass, i.e. S(9) 4.6947, S(10) 4.4096 and S(11) 4.1810 μm (^{Noriega-Crespo et al 2004a}, ^2004b; ^{Looney et al. 2007}; ^{Tobin et al. 2007}; ^{Ybarra & Lada 2009}; ^{Maret et al. 2009}, ^{Raga et al. 2011a}; ^{Noriega-Crespo & Raga 2012}). The IRAC Channel 2 map could also be brighter because of the CO rovibrational lines that fall in its range. However these lines require high temperatures and densities that do not normally occur in protostellar jets. Nevertheless, the jet is detected in all four bands (Figure 1).

Fig. 1 The HH 212 outow in H2 2.1 μm (left frame) and in the four IRAC channels I1-I4, at 3.6, 4.5, 5.8 and 8.0 μm (four frames towards the right). The orientation and the scale of the images are shown in the left frame. The White cross (in all frames) indicates the position of the outow source. 

We also used a VLT H₂ 2.1 μm image obtained with the High Acuity Wide field K-Band Imager (HAWK-I), as part of its Science Verification program (PI Schneider, “How symmetric is a symmetric flow. A deep H2 image of the Herbig Haro object 212”) observed in Janauary 2018, and enhanced by the ground-layer adaptive optics module (GRAAL) with an image quality of the order 0.2´´. The raw and reduced data are available through the ESO archive. The uncalibrated image has a 0.106´´ pixel size (^{Leibundgut et al. 2018}). This image is shown in the left frames of Figures 1 and 2.

Fig. 2 The central region of the HH 212 outow in in H₂ 2.1 μm (left frame) and in the four IRAC channels (I1-I4, with 3.6, 4.5, 5.8 and 8.0 μm central wavelengths, respectively). The ordinate points to the NNE (at 22:5^o clockwise from N). The circle in the central region of the I4 map is the position of the source. The crosses indicate the positions of knots along the jet/counterjet (see the text). The knot identifications of ^{Lee et al. (2007)} are given on the H₂ 2.1 μm map. The images are displayed with a linear color scale. The color figure can be viewed online. 

3.The Knot Positions and Intensities

Figure 2 shows the H₂ 2.1μm and the I1-I4 IRAC maps (with 3.6, 4.5, 5.8 and 8.0 𝜇m central wavelengths, respectively) of the HH 212 outflow. The images have been rotated 22.5^o clockwise, so that the outflow axis is parallel to the ordinate. The position of the outflow source (for which we have used the position given in § 3.1 of ^{Galván-Madrid et al. 2004}) is shown with a black circle in the central region of the I4 map. On the H₂2,1 μm map we show the identifications given by ^{Lee et al. (2007)} for the H₂ knots.

In order to find the positions of the jet/counterjet knots, we convolved the I1-I4 maps with a “Mexican hat” wavelet with a central peak of radius, which has the effect of isolating well defined emission peaks from the spatially more extended emission. On these convolved maps we searched for peaks along the jet axis with an intensity larger than a cutoff value I_c (for which we have chosen values of 0.03, 0.05, 0.1 and 0.1 mJy/sterad for the I1, I2, I3 and I4 channels, respectively), and carried out paraboloidal fits in 3 x 3 pixel regions (around each of the peaks) to determine the knot positions. This procedure is described in detail by ^{Raga et al. (2017)}.

The H₂ 2.1μm jet/counterjet knot positions were found on a convolution of this image with a central peak of σ=5 pixel radius. We selected peaks with at least 10^-2 times the peak knot intensity (which was found for one of the SB knots of ^{Lee et al. 2007}) in the convolved frame.

The resulting knot positions are shown as black crosses on the H₂ 2.1μm and I1-I4 maps of Figure 2. It is clear that many of the knots along the NE jet (top half of the frames) have corresponding emitting structures in the SW counterjet (bottom half of the frames).

The knot located ≈26´´ to the N of the source (labeled NK7 by ^{Lee et al. 2007}) has no detectable counterpart in the counterjet in the IRAC I1-I4 maps. However, in the H₂ 2.1μm image we do detect a faint counterpart along the counterjet (labeled SK7).

In Figure 3 we show the peak intensities of the jet and counterjet knots in the I1-I4 IRAC maps (measured on the convolutions with a σ = 2 pixel radius wavelet) as a function of distance 𝑥 from the outflow source. This distance is measured along the ordinate of Figures 1 and 2, but (as the offsets of the knots along the abscissa are very small). Almost identical values are obtained if one takes the radial source/knot distances.

Fig 3 Fluxes measured for the knots along the jet (blue circles with vertical lines) and counterjet (red circles) as a function of distance 𝑥 along the outflow axis in the I1-I4 IRAC channel maps. The fluxes are given in mJy/sterad. The vertical lines are shown so as to highlight the occurrence of jet/counterjet knot pairs with closely matched positions. The color figure can be viewed online. 

The jet and counterjet knots at similar distances from the source have intensities that differ by factors of ≈ 2. We see that at similar distances from the source:

These trends can be interpreted as the result of a different extinction towards the two outflow lobes, as described in § 4.3.

In the top frame of Figure 4 we show the peak H₂ 2.1μm intensities of the jet and counterjet knots (measured on the convolution with a σ =5 pixel radius wavelet) as a function of distance x from the outflow source. The intensities are given in units of the peak intensity of the SK1 knot (see Figure 2). The jet and counterjet knots at similar distances from the source have intensities that differ by factors of ≈3, except for knots NK7 and SK7 (at ≈26´´ from the source) which have intensities that differ by a factor of ≈10.

Fig. 4 Top frame: Fluxes measured for the knots along the jet (blue circles with vertical lines) and counterjet (red circles) as a function of distance 𝑥 along the outflow axis in the H₂ 2.1𝜇m map. The fluxes are given in units of the flux of the SK1 knot. Bottom frame: jet/counterjet knot offsets Δx(crosses) and the squares (Δx)2 of these values (squares) as a function of distance from the source. The results of the linear (black solid lines) and quadratic fits (black dashed lines) to the Δx and (Δx)2 vs. x dependencies are shown (see the text). The red lines are the corresponding fits to the points with x < 30´´ only. The jet/counterjet knot offsets have measurements errors of ≈0.05´´ (corresponding to ≈1/2 pixel). The color figure can be viewed online. 

We now use the H₂ 2.1μm map (which has a higher angular resolution than the IRAC maps) to define jet/counterjet knot associations with pairs of knots which have values of |x| (the distance to the outflow source) differing by less than 2´´. For these pairs of knots, we calculate the jet−counterjet knot position offsets Δx=xj-xcj as a function of x = x _j In the bottom frame of Figure 4 we show the resulting 𝛥𝑥 (crosses) an(Δx)2d (squares) as a function of x. This plot shows a trend of marginally increasing jet-counterjet knot position offsets with distance from the outflow source.

In Figure 5 we show the (x, y) knot positions of the inner H₂ 2.1μm knots, with x measured along (positive values for the N jet) and 𝑦 across the outflow axis (positive values to the E) from the position of the outflow source. It appears that the knots with |x|<30″ have offsets (with respect to the outflow direction) with a jet/counterjet mirror symmetric pattern. This result is discussed in more detail below.

Fig. 5. Positions of the inner HH 212 knots measured on the H₂ 2.1𝜇m frame. The 𝑥 coordinate lies along (positive 𝑥 to the N), and the 𝑦 coordinate across the outflow axis (positive 𝑦 to the E). The solid curve is a least squares fit to the knots with |𝑥|<30″ of the ballistic “orbiting source jet” of ^{Masciadri & Raga (2002)}, as described in the text. The positions along and across the outflow axis have errors of ≈0.03´´. 

Finally, we used the new H₂2.1μm image (obtained in January 2018) together with the IRAC I1-I4 maps (obtained in February 2005) to estimate the proper motions of the HH 212 knots within 50´´ from the outflow source. This of course gives only rough estimates of the proper motions, since different knot morphologies in the different spectral bands can in principle lead to position offsets that are not due to proper motions.

We proceeded as follows. For the knots that are present in all the I1-I4 IRAC maps, we first calculate the average positions (along and across the outflow axis), and the standard deviations of these positions. We then use these I1-I4 “first epoch” average knot positions to calculate the knot proper motions together with their corresponding positions in the H₂2.1μm “second epoch” map. The proper motion velocities calculated from these knot offsets (assuming a distance of 400 pc to HH 212) are given in Table 1.

This table gives the knot identifications (shown in the left frame of Figure 2), the positions 𝑥 along the outflow axis (measured in the H₂2.1 μm map, with positive 𝑥 pointing along the N jet), and the proper motion velocities along (positive values to the N) and across (positive values to the W) the outflow axis with their errors (in parentheses). Even though the errors shown are quite small for most of the knots, it is likely that there are larger systematic errors due to the fact that we compare images with different emission features.

The determined proper motion velocities are well aligned with the directions of the jet and the counterjet axes, except for knot NB3. This knot has a motion directed to the NW, which could indicate that it does not belong to the HH 212 outflow or that it has a substantially different morphology in H₂2.1 μm than in the other spectral bands.

Most of the knots have axial velocities in the range from ≈ 50 to 170 km s^-1, which is roughly consistent with the previously determined proper motions of the HH 212 knots 115 ± 50: km s^-1 by ^{Lee et al. (2015)} and somewhat higher velocities by ^{Reipurth et al. (2019)}. If one compares our results (shown in Table 1) with Table 2 of ^{Reipurth et al. (2019)}, one finds quite good agreements for the motions of most of the knots present in both tables (note that the knot that we have labeled NB3 does not correspond to the knot with the same denomination in ^{Reipurth et al. 2019}).

4.Interpretation of the Results

4.3.The Jet/Counterjet Extinction

As discussed in § 3, the jet knots (blue points) in the IRAC channel maps are generally brighter than the counterjet knots (red points, see Figure 3) at the same distances from the outflow source, especially for the shorter wavelengths channels (I1 and I2). In order to quantify this effect, we calculate the I_j/I_cj jet-to-counterjet knot intensity ratios for the three knots at distances x=5→15″(from the outflow source), and use these ratios to calculate a mean ratio ⟨Ij/Icj⟩ for each of the four IRAC channels. Figure 6 shows the resulting mean jet-to-counterjet ⟨Ij/Icj⟩ ratios (shown as magnitudes) as a function of λ (where λ is the central wavelength of the four IRAC channels). In this figure we also show the jet-to-counterjet intensity ratio of the knots seen in the 2.1μm map.

Fig. 6 Mean values of the jet/counterjet intensity ratio (calculated with the three knot pairs at x = 5 → 15´´, see the text) as a function of central wavelength of the IRAC channels and of the VLT H₂ map. The intensity ratios are shown as a magnitude, and as a function of the central wavelength. The solid line shows a least squares fit to the observed line ratios of a linearly transformed R= 5extinction curve. The fit to the data gives a higher absorption towards the counterjet of A_v = 16.9 ± 2.3. The dashed line shows a fit to the intensity ratios with λ >3μm. 

We carried out a weighted least squares fits with a linear transformation of the R=Av/E(B-V)=5 extinction curve (appropriate for star formation regions) of ^{Fitzpatrick (1999)}, and we show the results in Figure 6. We show two fits:

• a fit to the jet-to-counterjet intensity ratios measured in the IRAC maps (dashed curve in Figure 6). The fit gives a visual extinction to the counterjet larger by Av=16.9±2.3 than the extinction towards the jet,

• a fit to the jet-to-counterjet intensity ratios measured in the IRAC maps and in the 2.1 μm map (solid curve in Figure 6). The fit gives a visual extinction to the counterjet larger by Av=7.2±1.3 than the extinction towards the jet.

These of course are estimates only of the difference between the jet and counterjet extinction, and not a determination of the value of the total extinction to the HH 212 outflow.

The measured I_j/I_cj jet-to-counterjet knot intensity ratios shown in Figure 6 have quite large deviations from the extinction curves. This indicates that the jet and counterjet knots at similar distances from the source have relatively large intrinsic intensity differences, not attributable in a direct way to a difference in the extinction.

5. Conclusions

We present Spitzer (IRAC) observations and an H₂2.1μm image of the HH 212 outflow. In these maps, the general structure of the two outflow lobes is seen (see Figure 1).

For the inner ≈1´ of the outflow, we determine the positions of knots along the NE jet and SW counterjet (see Figure 2), and find that they mostly fall into “jet/counterjet knot pairs” (with distances from the source differing by at most ≈ 1.2´´). We then calculate the jet/counterjet knot offsets Δx as a function of distance x from the outflow source (see Figure 4). We carry out the analysis of knot position offsets with the 2.1 μm map, which has higher angular resolution than the IRAC maps.

We interpret the observed jet/counterjet position offsets with the quasi-symmetric ballistic ejection model of ^{Raga et al. (2011}b). Through this exercise we determine that the knot pairs are ejected with time-differences Δτ0≈6 yr and velocity differences Δv0≈2 km s^-1. These results are similar to the ones obtained for HH 34 by ^{Raga et al. (2011b)}. Clearly, an appropriate ejection model should have this degree of jet/counterjet coordination.

One can in principle use the determined jet/counterjet ejection coordination to estimate a physical size for the jet production region. In the cool, magnetized ejection mechanisms appropriate for low mass young stars, the signal transmission velocity (which could be either the Alfvén or the sound speed) is expected to lie in the vs≈0.1→10 km s^-1 range. We would then predict a size of L=Δτ0vs≈0.1→10 AU for the jet production region. The lower limit of this size range is in agreement with the estimation of ^{Lee et al. (2017)} of a ≈ 0.1 AU size for the HH 212 outflow collimation region.

We use the knot positions measured on the H₂2.1 μm image together with the IRAC maps (which were obtained ≈13 yr earlier) to determine proper motions of the knots along the jet and the counterjet. We find generally good agreement with the proper motions obtained by ^{Reipurth et al. (2019)} with two H₂2.1 μm epochs covering an ≈8 yr time-interval.

We also analyze the deviations of the knot positions perpendicular to the mean axis of the outflow. These deviations show a mirror symmetric jet/counterjet pattern, which can be interpreted in terms of a ballistic outflow from a source in an orbit around a binary companion. We fit the model of an outflow source in a circular orbit of ^{Masciadri & Raga (2002)} to the observed deviations (see Figure 5). From the model fit we deduce an (80 ± 30) AU binary separation and a (0.67±0.27) M⊙ mass for the outflow source (assuming that the binary companion has the same mass as the outflow source). This estimate for the separation between the binary components coincides with the ≈ 90 AU radius of the disk around the HH 212 source observed by ^{Codella et al. (2014)}. Our estimated mass is somewhat larger than the ≈0.15 M⊙ mass estimated by ^{Lee et al. (2006}, from observations of an infalling envelope) and the ≈0.3 M⊙ mass estimated by ^{Codella et al. (2014}, from the rotation of the disk) for the HH 212 outflow source.

The general structure of HH 212 has an important asymmetry in that the NK7 knot (at ≈ 25´´ along the NE jet, see Figures 2 and 3) does not have a comparably bright counterpart along the counterjet. This asymmetry is observed at all wavelengths at which the HH 212 outflow has been observed (see ^{Lee et al. 2007}), and therefore cannot be accounted for by differential extinction (see § 4.3 and § 4.4). We suggest that the asymmetric knot NK7 could be interpreted as a true ejection asymmetry, or as a recent brightening of the knot due to the merger of two “outflow events”. If this latter explanation is correct, we might expect a future brightening of a counterjet knot at a comparable distance to the outflow source.

Finally, we use the wavelength dependence of the jet/counterjet intensity ratio (measured in the four IRAC channels) to determine the difference in the extinction to the HH 212 jet and counterjet. We conclude that the extinction towards the counterjet is larger (than the one towards the jet) by A _v ≈ 10 magnitudes. This result is similar to the one found by ^{Raga et al. (2019)} for the HH 34 outflow. However, we find large deviations between the extinction curve and the jet/counterjet intensity ratios (as a function of wavelength). This indicates that the jet and counterjet knots at similar distance from the outflow source have relatively large intrinsic intensity differences.