A Ringed Pole-on Outflow from DO Tauri Revealed by ALMA

We present ALMA Cycle 4 archive observations (Project 2016.1.01042.S; P.I. Claire Chandler) toward the surroundings of the young stellar object DO Tauri. During the observations carried out on 2016 November 28, 47 antennas (with baselines from 16 to 626 m) were on duty and the weather was good (average precipitable water vapor column 2.05 mm and average system temperature ∼120 K) to operate at Band 6. The array was pointed at α_J2000.0 = 04^h38^m28600, and δ_J2000.0 = 26°10'4920, and the primary beam of the 12 m antennas corresponds to about 26'' at the observing frequency. Time on source was 1.22 minutes.

The correlator setup included eight spectral windows comprising about 6800 MHz, which we used to generate a continuum image after removing the emission from the line channels (mainly from the bright CO(2−1) transition). The spectral windows were centered at 232.366 GHz (spw0), 216.994 GHz (spw1), 231.193 GHz (spw2), 230.703 GHz (spw3), 218.787 GHz (spw4), 219.256 GHz (spw5), 219.725 GHz (spw6), and 220.194 GHz (spw7). For our study, we are particularly interested in spectral window 3, which contains the CO(2−1) emission at a spectral resolution of 0.488 MHz (about 0.63 km s⁻¹ at 230.538 GHz).

The ALMA data were calibrated using the data reduction scripts provided by ALMA for the Common Astronomy Software Applications (CASA) package (McMullin et al. 2007), which we use in its version 4.7.0. The atmospheric phase noise was reduced using radiometer measurements. The quasar J0510 + 1800 was used as bandpass and absolute flux calibrator, assuming a model with a flux density of 2.139 Jy at 232.366 GHz and a millimeter spectral index of −0.393,⁵ produced by the ALMA monitoring of quasars. Typically, the uncertainty in the ALMA flux measurements is estimated to be of the order of ∼10% for Band 6. The quasar J0438 + 3004 was used to track and correct the phase variations.

After the standard calibration, the continuum data was imaged using CASA version 5.4.0. We set the robust parameter to 0.5 and obtained a synthesized beam of 071 × 047 (PA = 149°). We made three iterations of self-calibration, reducing the final rms of the image by 60% (from 0.2 to 0.07 mJy beam⁻¹) and improving the signal-to-noise ratio from 80 to 350. The final solutions found during the continuum self-calibration stage were applied to the CO(2−1) spectral window and a velocity cube was constructed using robust = 0.5. This yielded an image with a synthesized beam of 078 × 053 (PA = 145°) at the native velocity resolution of 0.63 km s⁻¹. The rms of the velocity cube in one channel is about 13 mJy beam⁻¹ (0.72 K).

To better spatially resolve DO Tauri's dusty disk, we construct the final continuum image using a second day of observations within the same ALMA project 2016.1.01042.S, taken on 2017 August 2 with the array in a more extended configuration (with baselines from 32 to 2620 m). These data have higher-angular resolution and, therefore, are not as sensitive as the former observations in tracing the molecular extended emission. In the second track, ALMA had 46 available antennas, and the weather conditions were better, yielding a median system temperature of about 70 K. The correlator setup and the pointing were similar to the first track of observations. J0510+1800 was used as the bandpass calibrator and J0423-0120 as the flux calibrator (assuming it has 0.835 Jy at 223.670 GHz and a millimeter spectral index −0.437, values extracted from the ALMA monitoring of quasars). The phase was corrected using intertwined observations of J0426+2327. The time spent on DO Tauri was 3.7 minutes, and after three rounds of self-calibration, we end up with a signal-to-noise ratio enhancement rising from 85 to more than 400. The synthesized beam of the resulting image is 017 × 012 (PA = 14°) when using robust 0.5, and the final rms noise level is 0.06 mJy beam⁻¹ (or 0.067 K, see Figure 1).

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In the following, we use the high-angular resolution data set for imaging and analyzing the continuum emission due to its finest resolution. For imaging and analyzing the molecular gas emission, we prepared a data set combining both configurations, which yields a synthesized beam of 021 × 016 (PA = 7°) and an rms noise level of 4.6 mJy beam⁻¹ (or 3.1 K) as measured in the empty channels of the velocity cube.

To further investigate the optical jet of DO Tauri, we downloaded the available images of this source in the HST Legacy Archive (P.I. C. Dougados; HST proposal ID8215, New clues to the ejection process in young stars: Forbidden line imaging of TTauri microjets). The data comprises forbidden line observations, in particular, and we took two images. The first one was obtained in a deep (about 2 hr) integration using a narrowband filter (47 Å bandwidth) centered at 6732 Å (the emission of the [S ii] 6717 and 6731 Å lines, characteristic of optical jets, are then included in the imaged wavelength range). The other image was taken with a filter of 483 Å bandwidth centered at 5483 Å, which does not include the characteristic emission lines, and is, thus, useful for mapping the continuum emission. Figure 2 present these HST data from which we could measure the PA of the optical jet.

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The main focus of this paper is on the study of the large-scale molecular gas emission near DO Tauri, but we also report the characteristics of the disk dust emission, spatially resolved here, and its associated CO(2−1) emission (see also the recently reported ALMA results by Long et al. 2019, analogous to these simultaneously derived here). The disk is detected at 1.3 mm continuum (Figure 1) with an intensity peak of 24.55 ± 0.06 mJy beam⁻¹ and a flux density of 116.8 ± 0.1 mJy, consistent with the 125.4 ± 3.5 mJy reported by Kwon et al. (2015) at a similar frequency. These authors derived a disk mass of 0.014 ± 0.001 M_⊙ by using a sophisticated disk modeling. We have fit DO Tauri's disk emission in the uv-plane after using a 2D-Gaussian model implemented in the task uvmodelfit in CASA. The disk is centered at (α, δ)_J2000 = (04^h38^m285935, 26°10'49272) with a positional uncertainty of 0001. The estimated major and minor axes of the disk are 03447 ± 00004 × 03251 ± 00005 (these are statistical uncertainties). Note that this is roughly a circular disk, with a 47 au radius and the uncertainty of its PA and inclination may be larger than that provided by the statistical procedure. Therefore, we estimate the uncertainty of the disk PA and inclination as the difference with the same quantities derived by Long et al. (2019). For a circular disk, this fit implies an inclination of 19° ± 9° with respect to the plane of the sky. Plus, its derived PA is 150° ± 20°, not exactly perpendicular to the optical jet axis (with PA = 260° ± 1°, see Section 3.2), for it is deviated by about 20° from this configuration. Let us note here that an independent 2D-Gaussian fit to the continuum emission in the image plane, gives a similar result but with a different PA of 175° ± 6°. Taking this latter result and considering the uncertainties, the orientation of the disk is consistent with being perpendicular to the jet direction.

The CO(2−1) molecular image of Figure 1 (left panel) shows the emission integrated in the velocity ranges [0.6, 5.0] km s⁻¹ (blueshifted) and [6.9, 12.7] km s⁻¹ (redshifted) emission. A north–south velocity gradient is evident at the disk position. We measured the PA of the blue-/redshifted velocity gradient in the disk. The PA between the blue- and redshifted peaks of the CO(2−1) emission (which are apart 022, i.e., the size of one beam approximately) is 1° ± 4°. This PA does not coincide with the disk PA derived from the Gaussian fit to the continuum emission implemented in the uv-plane. We note that our PA measurement using the CO emission could be affected by contaminating extended emission most present at blueshifted velocities. In any case, this PA is not exactly perpendicular to the jet axis. If real, the PA discrepancies could be the result of a tilt or warp in the disk but only through new more sensitive and higher-angular-resolution observations can the PA be more accurately measured. Figure 1 (right panel) shows a position–velocity diagram along the velocity gradient of the DO Tauri's CO disk. The molecular emission is separated in two parts by a cloud absorption feature centered at 5.7 km s⁻¹. Close to the central star (zero offset), the emission is at larger absolute velocities, which steeply decreases with the distance to the star. This is suggestive of a Keplerian rotation pattern with a velocity gradient of about 3–4 km s⁻¹ between the red- and blueshifted emission at a fiducial radius of about 03 (about 40 au). The presence of extended emission and the spectral resolution of the current data hampers a more accurate measurement of this gradient, which we very roughly estimate to imply a dynamical mass ranging 1.1–1.9 M_⊙ (M = V${}_{\mathrm{rad}}^{2}$ r/(sin²(i) G, using $i=19^\circ$), see also curves in the position–velocity diagram of Figure 1). At this point, the detection of the disk in the CO images and pv-diagrams is slightly speculative, and it does not merit more sophisticated modeling. Confirming and characterizing the disk will probably require to make isotope ¹³CO and/or C¹⁸O observations that are less confused with outflow emission.

Microjets are usually associated with quite evolved young stars such as Class II objects. From an observational point of view, this implies: (a) a near-infrared jet counterpart is not usually detected (H₂ emission); (b) the jet emission is short as compared with classical optical jets, consisting of just a few knots close to its driving source; (c) the driving source can be detected at optical wavelengths. (b) and (c) cause difficulties to detect microjets, being the dominant problem the pollution of the jet emission by the emission from the star and from the light scattered by the surrounding material. This is especially critical in deep (long time exposure) images, inevitable to detect the jet emission.

Figure 2 shows the [S ii] optical emission from the microjet in the HST images of DO Tauri. Although difficult to visualize due to the contamination from the source emission and the spikes produced by the saturation of the image, the emission from the microjet is clearly distinguished west of the young stellar emission. The maximum of the emission of the jet has a PA of 260° ± 1° with respect to the peak emission toward the central object, and is 19 ± 0.1 (270 au) away from it. In addition, Figure 2 reveals two possible knots further from the protostar due southwest. These two knots are not exactly aligned with the PA of the inner jet (260°), which may suggest it is wiggling. However, a more clear detection of these knots is needed to confirm the hints of wiggling. The measured PA of the inner part of the optical jet is roughly consistent with the previously value of 70° ± 10° (or its corresponding 250° ± 10°) reported by Hirth et al. (1997), but the difference (10°) is of the order of the uncertainty in Hirth's et al. long slit spectra measurements.

In an attempt to look for the counterpart of the microjet, we subtract the continuum emission contribution to the line emission image (right panel in Figure 2). The resulting image still contains remainders of the saturation spikes and the rings of the diffraction pattern. However, it is possible to identify some bright pixels 09 due northeast of the star (PA = 42°) that may belong to the eastern lobe of the jet. The PA between this bright feature and the southwestern jet is 71°, which matches the expected orientation of the jet. The problem is that the line joining both features goes north of the peak emission of the central object. At this moment, we cannot be certain whether this northeast emission is part of the counterjet, and we refrain ourselves from further analyzing it.

3.3.1. Three Sets of CO Rings

Figure 3 shows the velocity cube of the CO(2−1) emission surrounding DO Tauri from 8.2 to −10.2 km s⁻¹. From −10.2 to −12.7 km s⁻¹, the emission is weak (see also figures in the 2.1), and at velocities larger than 8.2 km s⁻¹, there is only emission from the disk. The cloud velocity is centered at 5.7 km s⁻¹, and the corresponding channel shows the typical interferometer emptiness due to the presence of extended emission and some absorption spatially coincident with the disk position (both are seen also in channels at 5.0 and 6.3 km s⁻¹). The redshifted emission spans ∼5 km s⁻¹ while the blueshifted emission spans ∼18 km s⁻¹. This asymmetry in the CO line profile was already noticed by Koerner & Sargent (1995) in a spectrum toward the young stellar disk. The CO emission surrounding the disk shows some elliptical structures of different sizes. To understand these CO structures, we split them in three sets of elliptical rings spanning different velocity ranges.⁶

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A small scale set of 17 rings of average geometrical mean radius 16 (225 au) and width between 06 and 10 (80–140 au) can be identified in velocity channels from −8.3 to 1.9 km s⁻¹. From here on, we refer to these rings as set of Small Blueshifted rings or SB rings. For instance, these rings are prominent in the −3.2 km s⁻¹ channel (the brightest CO structure at this velocity, Figure 4), in which the disk of DO Tauri is outside of the SB ring, although it is close to its easternmost rim. The SB rings are the brightest features seen in CO at blueshifted velocities. Their northeast rim is brighter compared to their southwest rim, which fades (and is undetected) at more blueshifted velocities (v_rad < −2.6 km s⁻¹), making the rings incomplete.

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In channels where v_rad > −2.6 km s⁻¹, we identify a second set of 17 rings, which we name "Medium-size rings" or M rings, hereafter. These rings surround the smaller SB rings from −2.6 to 1.9 km s⁻¹, velocities at which both structures are present simultaneously (see, for instance, channels at 0.6, 1.2 and 1.9 km s⁻¹ in Figure 4). Between 1.9 and 4.4 km s⁻¹, the M rings encompass the emission from the DO Tauri disk and are filled with some extended emission. At redshifted velocities, two simultaneous (and equal) M rings explain the emission distribution morphology better (Figure 4). These two rings spatially coincide with the northeast and northwest arcs observed by Itoh et al. (2008) using NIR and optical images. The M rings have an average geometrical mean radius of 23 (320 au) and a width ranging between 06 and 1.1(80–150 au). In general, M rings are oriented northwest–southeast and show brighter emission toward their northern rim.

Figure 3 also shows a third set of rings that encompass the M and SB sets of rings at larger scales, from −10.8 to 1.9 km s⁻¹. We name them set of Large Blueshifted rings (LB rings). The 23 LB rings have an average geometrical mean radius of 57 (about 800 au) and a width between 08 and 16 (110–220 au). They show stronger emission and are seen as complete rings between 1.2 and −4.5 km s⁻¹. At more blueshifted velocities they fade and only their northeast rims are detected.

3.3.2. Ring-fitting Procedure

3.3.3. Ring Properties as a Function of Radial Velocity

The ring fits show some general characteristic trends (some of them as a function of radial velocity) that are shown in Figure 5. First, let us notice that the centers of the elliptical rings with respect to the position of the disk peak continuum emission (we will refer to these as centers or ring centers from now on for simplicity) are linearly aligned with the position of DO Tauri (top left panel in Figure 5). A linear fit to the ring centers (taking only those rings with radial velocity lower than 5.7 km s⁻¹) gives a PA of 2536 ± 0.1 and an alignment better than 01 with the DO Tauri's disk position. This PA matches the orientation of the optical jet reported by Hirth et al. (1997). In addition to this trend, the centers of the SB and M rings are closer to the young stellar disk than those of the LB rings.

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Second, the positions of the ring centers are also correlated with their corresponding radial velocities. The top right panel in Figure 5 shows that the larger the distance between the ring center and the young star, the bluer (the larger, or more negative) its velocity. Moreover, while a linear trend makes a reasonable fit for the LB data, the trends for the SB and M rings are not just linear correspondences. A closer look into these data shows that the velocity increases roughly exponentially with distance from the source, although more points (higher spectral resolution) would be needed to better sample these trends. For now, we can confidently say that the radial velocity increases with the distance from the young star and the increment is steeper further away from the star.

In third place, the bottom left panel in Figure 5 shows the geometrical mean radius of the rings as a function of the radial velocity. The three sets of rings are clearly segregated from each other. SB rings are below 19 (260 au), M rings are between 19 and 3'' (560 au), and LB rings are larger than 4''. Despite the fact that the size of the rings within each set does not change much, the M rings slightly decrease their size monotonically toward bluer velocities, and the LB rings monotonically decrease their radii from 6'' to 4'' and then increase them again monotonically up to more than 6''.

The fourth plot (bottom right panel) in Figure 5 shows the change on the ring orientations as a function of radial velocity. Most of the PAs of the SB rings are in a range of 40° around PA = 140° (note that a quarter of these rings are quite circular and just a few of them are closer to PA = 25°), while those of the M rings seem to linearly vary from 120° (blueshifted velocities) to 180°. The orientation of the LB rings is more uncertain since these rings are quite round; in any case, their PAs do not change more than 20° overall.

CO is known to be a good outflow tracer in star-formation regions, although it can be also encountered as part of the disk, the envelope, and the parental cloud. In DO Tauri, however, the CO(2−1) emission is both spatially extended (spreading much further than the size of the disk) and extended in velocity (over about 20 km s⁻¹), so it seems at least plausible that the SB, M, and LB rings seen in the vicinity of DO Tauri are part of the material dragged by the high-velocity jet reported in the literature (Hirth et al. 1994) and detected in the HST images presented here. Indeed, the sets of elliptical rings seen in CO have their centers aligned with the position of DO Tauri (with the smaller rings closer to the young star than the larger ones) and the PA of the optical jet (260° ± 1°) roughly coincides the PA of the aligned ring centers (2536 ± 0.1).

Usually, outflows show a parabolic biconical shape because they are seen close to the plane of the sky, but in the case of DO Tauri, we do not see this parabola. We interpret the three families of elliptical rings as three different shells of entrained material seen at different radial velocities. In this scenario, we see the outflow from an almost pole-on perspective. Indeed, if the jet and outflow are launched perpendicular to the circumstellar disk plane, the inclination of the jet with respect to the line of sight would be the same as that of the disk, i = 19°. From now on, we will assume this is the case, and we use this inclination to correct for the estimated physical properties when adequate. Taking this inclination into account, the dimensions of the outflow would be 4070 au × 1960 au from the young star to the further ring detected by the ALMA observations. This implies an opening angle of 27° (a collimation factor of 2.1). The size of the CO structure, its opening angle, and the radial velocity extent all agree with the usual measures of CO outflows from protostars and young stars (from a few thousands au to a few pc in length, opening angles typically between 20° and 60° and radial velocity spreads between 10 and 100 km s⁻¹; Arce & Sargent 2006; Bally 2016). When compared with one of the most recent paradigmatic outflows from Class 0 objects such as HH 46/47 (about 60,000 au long and more than 10,000 au in width Arce et al. 2013), this one would be a small (young?) outflow, but in the event that we are only detecting the inner shells of the DO Tauri outflow, then the sizes match better, as the outflow from DO Tauri is still more collimated; for HH 46/47, the inner shells fit in a box of about 5000 au side (Zhang et al. 2016, 2019). If compared with another classical outflow from a Class I/II young star, DG Tau B (see, e.g., Zapata et al. 2015), both have sizes of the same order of magnitude (DG Tau B's is 2550 au long and about 1400 au wide). It is also significant that the outflow from DO Tauri would not have a clear redshifted lobe. This is not a huge obstacle for the outflow hypothesis since other monopolar outflows (probably due to environmental inhomogeneities) have been reported in regions such as GGD 27 or HH 30 (Fernández-López et al. 2013; Louvet et al. 2018).

Finally, let us show a reconstruction of a spatial cut parallel to the outflow major axis based on this scenario (Figure 6). First, we rotate the (R.A., decl.) coordinates of the ring centers into the (x, z') plane, where the projected z' axis is oriented with the outflow axis taking positive values southwest of the young star. We used an outflow PA of 2536 to rotate the coordinates. Second, we correct for the inclination of the outflow with respect to the line of sight, considering it as perpendicular to the disk, to get the unprojected coordinates along the z-axis. After this, we assume that the rings are perfect circumferences with radii equal to the semimajor axis of the fitted ellipses. That is how we build the left panel of Figure 6. The morphology outlined by the points in this figure reminds the shape of protostellar outflows. In the left panel two cylinder-like structures are outlined: one with smaller radius composed of the SB and M rings extending up to ∼1200 au, and a second one with a larger radius that doubles this size reaching ∼4000 au (lower sideband (LSB) rings). The right panel of Figure 6 has a further step in the reconstruction, by forcing the position of the rings to lie in the z-axis (i.e., we force them to be at x = 0). This way, we remove any wiggling of the outflow or errors in measuring the ring center positions. The result is a symmetric outflow, but here, we can notice additional interesting details. On one side, the inner part of the outflow (<1200 au) comprises two concentric structures: one with a roughly constant width (mostly formed by the SB rings) and a wider one whose width seems to decrease smoothly with the distance to the star (the M rings). In contrast, the widest LSB shell (>1200 au) smoothly decreases its aperture up to 3000 au from the star and from this point increases it again.

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In Figure 5, each set of rings shows a different velocity gradient (SB, M, and LB). These velocity gradients show an increase in velocity with distance, sometimes steeper than a simple linear trend. Although the gradients are not linear, they show a similar trend to the Hubble-law behavior found in the cavity walls of some molecular outflows (see for instance Zhang et al. 2016, 2019). Radial wide-angle winds can account for such Hubble-laws provided they have an angular dependent force (e.g., ∝1/sin²(θ), where θ is the polar angle and θ = 0°/180° correspond to the direction perpendicular to the disk plane) and sweep-up gas in a medium with a specific density structure (e.g., ∝ sin²(θ)/r²). Under this model, the resulting outflow walls have a roughly parabolic morphology that expands radially with a constant speed, independent of the outflow shell size. The velocity V(θ) is different for each direction θ, but constant in time. As a result, at any given age t_dyn, the shell shows an apparent Hubble-law, with patches of the shell closer to the source being slower than further ones with V(θ) = R(θ)/t_dyn(Shu et al. 1991, 2000; Li & Shu 1996; Lee et al. 2000).

Assuming the wide-angle wind model, we estimate the dynamical age of each shell by computing the dynamical time of each ring composing it as t_dyn = R/V, where R is the deprojected distance from the young star to the edge of a ring ($R=\sqrt{{z}^{2}+{B}_{\mathrm{maj}}^{2}}$; where z is the distance from the star to the center of the ring, and B_maj is the ring's major axis) and V is an averaged value of the deprojected velocity of the molecular gas of the rings, respectively. We take $V\sim {V}_{\mathrm{radial}}/\cos i$ (i = 19° is the inclination of the outflow) as the averaged value of the deprojected velocity of the gas in an individual ring.⁹ Figure 7 shows graphically the spatial distribution of dynamical times along each shell surface in the reconstructed sketch of the outflow (see also Figure 6). There is a notorious dynamical age segregation between the SB and LB outflow shells (see right panel on Figure 8), indicating that there are at least two different events of outflow entrainment (Zhang et al. 2019). We also consider the M rings as a third outflow shell that partly encompasses the SB shell.

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While the dynamical ages of the rings composing the LB and SB shells are mostly distributed in a 300 yr lapse, the dynamical ages of the M rings are quite spread (due to low velocities and relatively larger sizes). Among them, the more well-delineated M rings between −1.9 and 1.2 km s⁻¹ have dynamical ages ranging 600–1100 yr (700 ± 100 yr on average). These M rings comprise a shell that surrounds part of the the SB outflow shell, which appears ∼300 yr younger. In contrast, the M rings closer to the cloud velocity and those that are redshifted show extended emission inside¹⁰ and have dynamical ages from 600 to 5000 yr, with deprojected gas-velocities as low as 1.3 km s⁻¹ with respect to the cloud velocity. These rings subtend the largest angles from DO Tauri in projection.

Within the individual shells, not all of the rings have the same dynamical time, unlike one would expect in the wind-driven model (Lee et al. 2000). These differences can be accounted for if there are any inhomogeneities in the ambient cloud that may decelerate the outflow material at different rates in different directions θ. Moreover, deviations from the model are also expected if the outflow is not steady (Lee et al. 2001) as is the case for DO Tauri, where multiple shells are observed.

An interesting alternative scenario for the DO Tauri outflowing shells is that they are generated by successive jet-driven bowshocks (Ostriker et al. 2001). In this model, a narrow jet produces an expanding bowshock when bumping into the ambient medium. The velocity of the outflow thus created increases as a power law with increasing distance to the source. This model implies shorter dynamical times at larger distances from the source, which is the trend observed along the LB and SB shells (Figure 7). The rings with the largest dynamical times in these shells show the largest opening angles too and have gas with lower projected velocities (Figure 6).

Finally, from the left panel of Figure 8, it can be inferred that within each shell, the dynamical times increase very steeply at lower velocities. This strongly suggests a slowing down of the shells close to the star where a more dense ambient material is expected. In particular, it should be noted that due to possible outflow deceleration, the measured dynamical times are upper limits to the true age. Hence, the best estimate of each shell age is obtained by measuring the dynamical time at large distances, where t_dyn is almost constant and the deceleration does not seem to be too severe. We, therefore, estimate the dynamical age of the observed outflow in 1090 ± 90 yr, considering the dynamical time of the furthermost LB shell. The mean averaged dynamical times of the three shells are gathered in Table 1 (error bars for these values are derived from rms times).

Table 1.  Physical Properties of the Three Sets of Rings

	SB	Ma	LB	Total
Mean geometrical radius (au)	195–240	280–350	640–850	⋯
Distance from DO Tauri (au)b	530–1025	190–910	1140–3680	⋯
Tdyn (yr)	460 ± 70	700 ± 100	1090 ± 90	1090 ± 90
M (10−5 M⊙)	2.6	4.0	5.9	12.5
P (10−4 M⊙ km s−1)	2.1	2.5	6.5	11.1
E (1040 erg)	1.8	1.6	7.6	10.9
$\dot{M}$(10−8 M⊙ yr−1)	5.6	5.7	5.4	11.4
$\dot{P}$(10−7 M⊙ km s−1 yr−1)	4.6	3.6	6.0	10.2
γ	3.2 ± 0.3	2.2 ± 0.4	3.9 ± 0.7	⋯

Notes.

^aMagnitudes for the M shell are estimated taking into account only emission with V_outf < −4 km s⁻¹. ^bCorrected by outflow inclination ($z={d}_{\mathrm{observed}}/\sin (i)$).

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Measuring gas masses using CO(2−1) has several problems (Arce & Goodman 2001; Dunham et al. 2014; Zhang et al. 2016) because this molecule is sometimes contaminated with emission from the disk and the natal cloud and can be optically thick. Here, we make an attempt to estimate the mass, linear momentum, and kinetic energy of the molecular ringed structure found in DO Tauri, to compare these quantities with those of young stellar outflows.

Since we do not possess observations of any optically thick tracer, we assume an excitation temperature of 25 K as a proxy for the mass, momentum and energy estimates. Similar values have been used for outflows of other Class II young stars (usually T_ex < 30 K, see, e.g., CB 26 and HH 30, Launhardt et al. 2009; Louvet et al. 2018). Using this T_ex, we found that some channels are optically thick at the peak emission. This choice sets a lower limit to the mass derived from now on.

Despite the existence of CO(2−1) optically thick emission at the brightest parts of the rings in several velocity channels (mainly in the SB and M rings), large areas have brightness temperatures between 3 and 8 K, which translate into optical depths ranging between 0.2 and 0.5. Therefore, we can just make a crude estimate of the mass, momentum, and energy of the outflow by assuming local thermodynamic equilibrium and optically thin CO emission. Note, in addition, that it is also possible that the ALMA observations are filtering out part of the extended material of the outflow. With these caveats in mind, we estimate first column densities as well as the shell masses, momenta, and kinetic energy, using an analog procedure to that in Pineda et al. (2008) and Zhang et al. (2016), with expressions adapted to the CO(2−1) transition following Mangum & Shirley (2015). In particular, we use the following equation to derive the column density for the optically thin case:

$$\begin{eqnarray*}\begin{array}{rcl}{N}_{\mathrm{tot}}(\mathrm{CO}) & = & \displaystyle \frac{3h}{8{\pi }^{3}{\mu }^{2}S}\cdot \displaystyle \frac{{Q}_{\mathrm{rot}}}{g}\displaystyle \frac{\,{e}^{{E}_{u}/{{kT}}_{\mathrm{ex}}}}{{e}^{h\nu /{{kT}}_{\mathrm{ex}}}-1}\\ & & \cdot \displaystyle \frac{\displaystyle \int {T}_{B}{dv}}{[{J}_{\nu }({T}_{\mathrm{ex}})-{J}_{\nu }({T}_{\mathrm{bg}})]}\\ & = & \displaystyle \frac{3h}{8{\pi }^{3}{\mu }^{2}J}\cdot \displaystyle \frac{{Q}_{\mathrm{rot}}\,{e}^{{E}_{u}/{{kT}}_{\mathrm{ex}}}}{{e}^{h\nu /{{kT}}_{\mathrm{ex}}}-1}\cdot \displaystyle \frac{\displaystyle \int {T}_{B}{dv}}{[{J}_{\nu }({T}_{\mathrm{ex}})-{J}_{\nu }({T}_{\mathrm{bg}})]},\end{array}\end{eqnarray*}$$

which, for the particular transition CO(2−1), can be expressed as

$$\begin{eqnarray*}\begin{array}{rcl}{N}_{\mathrm{tot}}(\mathrm{CO}) & = & \displaystyle \frac{1.196\times {10}^{14}\,({T}_{\mathrm{ex}}+0.921)\,{e}^{16.596/{T}_{\mathrm{ex}}}}{{e}^{11.065/{T}_{\mathrm{ex}}}-1}\\ & & \cdot \displaystyle \frac{{T}_{B}{\rm{\Delta }}v}{[{J}_{\nu }({T}_{\mathrm{ex}})-{J}_{\nu }({T}_{\mathrm{bg}})]}.\end{array}\end{eqnarray*}$$

To obtain the latter expression, we used the line strength S = J/(2J + 1) = 2/5, the dipole moment μ = 1.1011 × 10⁻¹⁹ StatC cm, the partition function ${Q}_{\mathrm{rot}}={{kT}}_{\mathrm{ex}}/({{hB}}_{0})+1/3$ with a rigid rotor rotation constant B₀ = 57.635968 GHz, the degeneracy g = 2J + 1 = 5, the T_B in K, and the Δv velocity interval in km s⁻¹. From this, we estimate the mass by doing $M\,=\mu {m}_{h}{\rm{\Omega }}{N}_{\mathrm{tot}}/{X}_{\mathrm{CO}}$, using a mean molecular weight μ = 2.8 times the atomic hydrogen mass and a CO abundance of X_CO = 10⁻⁴ (Ω is the area of the rings). We further correct the momenta and kinetic energy by the adopted outflow inclination (we use i = 19° in ${v}_{\mathrm{outflow}}={v}_{\mathrm{rad}}/\cos (i)$, where v_rad is the line-of-sight or radial velocity). The results for each of the three outflow shells are summarized in Table 1, considering the M shell as the part with V < −4 km s⁻¹, thus excluding the redshifted emission and the emission close to the cloud velocity contaminated by the DO Tauri circumstellar disk. The LB shell has approximately twice the mass of the SB shells. The three shells carry out a comparable amount of energy and momentum. Globally, the lower limits for the total mass of the blueshifted outflow, the total linear momentum, and the total kinetic energy are 1.3 × 10⁻⁴ M_⊙, 1.1 × 10⁻³ M_⊙ km s⁻¹, and 1.1 × 10⁴¹ erg, respectively.

Moreover, with the mass and the dynamical age of the blueshifted lobe of the outflow, we can now derive an estimate (lower limits due to possible optically thick CO emission, T_ex uncertainty and t_dyn being an upper limit of the outflow age) of its average mass-load rate (1.1 × 10⁻⁷ M_⊙ yr⁻¹) and its average rate of linear momentum injected by the wind/jet into the CO outflow (1.0 × 10⁻⁶ M_⊙ km s⁻¹ yr⁻¹). Table 1 contains these quantities estimated for the three individual shells. There is a striking good agreement of the $\dot{M}$ and the $\dot{P}$ among the three shells, with average values ${\dot{M}}_{\mathrm{shells}}=5.5\times {10}^{-8}$ M_⊙ yr⁻¹ and ${\dot{P}}_{\mathrm{shells}}=4.7\times {10}^{-7}$ M_⊙ km s⁻¹ yr⁻¹. These values may be compared with the mass-loss rate and its associated momentum rate extracted from the optical observations of the jet. Observing forbidden lines and assuming a projected plane of the sky velocity (150 km s⁻¹) and length (125), Hartigan et al. (1995) derived a jet mass-loss rate of 3.1 × 10⁻⁸ M_⊙ yr⁻¹. We can update this value using the inclination of the outflow (i = 19°), the line-of-sight blueshifted jet velocity of 95 km s⁻¹ (taking into account the cloud velocity and the observations of Hirth et al. (1994)), the blueshifted jet length from the HST observations (∼2'') and the equation A10 from Appendix A.1 in Hartigan et al. (1995). This way we obtain a jet mass-loss rate ${\dot{M}}_{\mathrm{jet}}=4.3\times {10}^{-9}$ M_⊙ yr⁻¹. We can also make a rough estimate of the jet mass-loss rate assuming that it is a fraction of the accretion rate of the disk (${\dot{M}}_{\mathrm{jet}}\simeq 0.1{\dot{M}}_{\mathrm{acc}}$, see, e.g., Pudritz & Banerjee 2005). ${\dot{M}}_{\mathrm{acc}}$ has been estimated as 1.4 × 10⁻⁷ M_⊙ yr⁻¹ and 3.0 × 10⁻⁸ M_⊙ yr⁻¹ (Gullbring et al. 1998; Alonso-Martínez et al. 2017), yielding jet mass-loss rates ranging 3 × 10⁻⁹–10⁻⁸ M_⊙ yr⁻¹, in good agreement with our new estimate for the Hartigan et al. observations. In summary, the average mass-load rate from the outflow shells is a factor 5–20 larger than the jet mass-loss rate. In the meantime, its rate of injected momentum is comparable to that of the optical jet (4×10⁻⁷ M_⊙ km s⁻¹ yr⁻¹). This may suggest that the outflow shells mainly comprise swept-up gas from the original envelope/cloud, with only a small fraction of material incorporated from the wind directly launched from the disk. The momentum of this wind is apparently conserved when sweeping up the CO shells.

Figure 9 shows the mass distribution dm/dV within the shells as a function of velocity corrected by the outflow inclination. Symbols with three different colors designate the three outflow shells. A usual analysis of a mass spectrum diagram, such as this, consists of performing power-law fits of the form v_outflow ∝ v^−γ. We make individual fits to each of the three shells, using only masses corresponding to larger outflow velocities that show a clear power-law behavior. Table 1 collects the resulting slopes for each of the three fits. In the case of ambient shells driven by wide-angle winds, the expected slope of the mass–velocity relationship is about 2 (e.g., Masson & Chernin 1992; Li & Shu 1996; Matzner & McKee 1999). Inclination effects (e.g., Lee et al. 2001) and, most importantly, deviations from the canonical angle dependence on the wind thrust and the ambient density distribution (Matzner & McKee 1999) can modify these values. In the case of DO Tauri's outflow, the slopes of the LB and SB shells are steeper than the slope of the M shell. The overall shape of the mass–velocity relations for the three shells matches quite well the expectations for the wide-angle wind scenario (which are not very different from those of the jet-driven bowshock model, Zhang & Zheng 1997; Downes & Cabrit 2003).

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The resulting mass, momentum, and energy of the blueshifted lobe of the DO Tauri outflow are, in general, lower than those derived for some Class 0 or Class I molecular outflows (∼10⁻³ M_⊙, ${10}^{-3}\mbox{--}0.1$ M_⊙ km s⁻¹, 10⁴¹–10⁴³ erg, Arce 2003; Arce & Sargent 2004; Kwon et al. 2006; Lumbreras & Zapata 2014; Zapata et al. 2014, 2015; Zhang et al. 2016). However, they agree better with the characteristics of the outflow from the Class II HH 30 (M = 1.7 × 10⁻⁵ M_⊙, $\dot{M}=8.9\times {10}^{-8}$ M_⊙ yr⁻¹, Louvet et al. 2018). Thus, DO Tauri's outflow mass and energetics roughly lie within the range of other young stellar outflow values, supporting the outflow interpretation for the nested ringed structures in the surroundings of DO Tauri.

The three CO shells of dragged gas have remarkably coherent and regular shapes several hundreds of au far away from the central source. In order to form structures with this degree of cohesion and shape, the launching zone of the outbursting wind or jet entraining these shells should be causally connected during the outburst period. Following Zhang et al. (2019), we constrain the dimensions of the launching area of the outbursts that entrained the outflow shells. We estimate the interval between the production of the SB and LB outflow shells in ∼600 yr. Part of the M shell was intertwined between these two so we choose a shell interval time of 300 yr. Assuming that the ejection outburst lasts for just a fraction of the interval between the dynamical age of the shells (consider ${t}_{\mathrm{outburst}}\simeq (0.2\mbox{--}0.3)\times {\rm{\Delta }}{t}_{\mathrm{shell}}$ as an upper limit to produce a coherent shell), we derive a length scale ${c}_{s}\cdot {\rm{\Delta }}{t}_{\mathrm{outburst}}$ using the disk sound speed ${c}_{s}=0.24\sqrt{T/10}$ expressed in km s⁻¹. Although this procedure is very approximate, by taking a temperature of 100 K appropriate for the inner part of the disk, we obtain an upper limit for the size of the wind/jet outburst launching region of <10–15 au.