An Episodic Wide-angle Outflow in HH 46/47

To be more quantitative, we fit the morphology and kinematics of the outflow shells with expanding parabolas. Following the method by Lee et al. (2000), the morphology and velocity of a single expanding parabolic shell can be described (in cylindrical coordinates) as

$\begin{eqnarray}&&\left(\displaystyle \frac{z}{{R}_{0}}\right)={\left(\displaystyle \frac{R}{{R}_{0}}\right)}^{2},\quad {v}_{z}=\displaystyle \frac{z}{{t}_{0}},\quad {v}_{R}=\displaystyle \frac{R}{{t}_{0}},\end{eqnarray} \tag{ 1 }$

where the z-axis is along the outflow axis, the R-axis is perpendicular to the z-axis, and v_z and v_R are the velocities in the directions of z and R (i.e., the forward velocity and the expansion velocity), respectively. The free parameters in this model are the inclination i between the outflow axis and the plane of the sky, parameter R₀, which determines the width of the outflow shell, and t₀, which determines the velocity distribution of the outflow shell. Note that the characteristic radius R₀ is just the radius of the shell at z = R, i.e., θ = 45°. Also, t₀ can be considered the dynamical age of the shell. We further define a characteristic velocity v₀ ≡ R₀/t₀, which is the outflowing velocity v_z or expanding velocity v_R at z = R. In such a model, the half-opening angle of the shell at the height of z is $\tan {\theta }_{\mathrm{open}}(z)=\sqrt{{R}_{0}/z}$.

Such a model predicts an elliptical shape of emissions in the channel maps, and as the channel velocity increases the elliptical structure becomes wider and shifts further away from the central source. The model also predicts a parabolic shape in the PV diagram along the outflow axis and elliptical shapes in the PV diagrams perpendicular to the outflow axis. Such behaviors are indeed consistent with our observations. The same model was used to explain the blueshifted lobe in Paper II, in which we did not have enough spatial resolution and sensitivity to detect the multiple shell structures.

We fit the shells Sb1 and Sb2 in the blueshifted lobe and shells Sr1 and Sr2 in the redshifted lobe by comparing the model described above with the observed emission distributions in both channel maps and PV diagrams. Here, we only focus on the location of the emission in space and velocity, and do not attempt to reproduce the intensity distribution. To reduce the number of free parameters, we adopt a constant inclination angle for shells in the same lobe. To perform the fitting, the inclination i is searched within a range 30° ≤ i ≤ 45° with an interval of 5°, the parameter t₀ is searched within a range from 0.05 to 1 arcsec km⁻¹ s with an interval of 0.05 arcsec km⁻¹ s, and the parameter R₀ is searched with an interval of 001 within a range from 1'' to 3''. Furthermore, in fitting the shells Sb1 and Sb2, we assume that the low-velocity walls of these two shells have merged into one structure (labeled as "Sb1L, Sb2L, Sb3L" in Figure 5).

The best-fit models are selected by visually comparing the model curves (which are shown by the red curves in Figures 3 and 4, and the blue and red curves in Figure 5) with the observed distribution of the outflow emission. The parameter values of what we consider the "best-fit" models are listed in Table 1, including the characteristic velocities v₀ = R₀/t₀ and the shell half-opening angles θ_open at z = 15''. The fitted inclinations are i = 40° and i = 35° between the outflow axis and the plane of sky for the blueshifted and redshifted outflows, respectively. These are consistent with the values derived from observations of the optical (blueshifted) jet by Eislöffel & Mundt (1994) and Hartigan et al. (2005), which are 34° ± 3° and 375 ± 25, respectively.

Table 1.  Parameters of the Fitted Parabolic Shells

Shell	ia	R0 (arcsec)	t0 (arcsec km−1 s)	Age (103 yr)b	v0 (km s−1)c	θopen (z = 15'')d
Sb1	40°	2.6	0.55	1.2	4.7	226
Sb2		2.7	0.70	1.5	3.9	230
Sb3		2.8	0.85	1.8	3.3	233
Sr1	35°	1.3	0.15	0.32	8.7	164
Sr2		1.9	0.25	0.53	7.6	196

Notes.

^aInclination angle between the outflow axis and the plane of sky. The same value is used for shells in the same lobe in order to reduced the numbers of free parameters. ^bDynamical age calculated from t₀ assuming a distance of d = 450 pc. ^cCharacteristic velocity of the shell defined as v₀ ≡ R₀/t₀. ^dHalf-opening angle of the fitted shell at a height of z = 15'', $\tan {\theta }_{\mathrm{open}}=\sqrt{{R}_{0}/15^{\prime\prime} }$.

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In the redshifted outflow, the Sr1 and Sr2 shells are fit with t₀ = 0.15 and 0.25 arcsec km⁻¹ s and R₀ = 13 and 19. These models describe the two shells relatively well, especially the Sr1 shell. The model fit to Sr2 is not as good as that of Sr1, especially at higher velocities. This is partly due to the fact that Sr2 is slightly asymmetric with respect to the outflow axis (seen more clearly in the channel maps at v_out = +33 to +45 km s⁻¹ Figure 4). Sr2 also appears tilted (or skewed) in the PV diagrams perpendicular to the outflow axis (panels h and i of Figure 5). These features may be caused by rotation or a slight change in the outflow direction, which the models do not take into account. The fitted values of t₀ of 0.15 and 0.25 arcsec km⁻¹ s correspond to timescales of 3.2 × 10² and 5.3 × 10² yr assuming a source distance of 450 pc, which can be considered the dynamical ages of these two shells, result in an age difference between the Sr1 and Sr2 shells of 2.1 × 10² yr.

In the blueshifted side, the parameters for the best-fit models for shells Sb1 and Sb2 are t₀ = 0.55 and 0.70 arcsec km⁻¹ s and R₀ = 26 and 27. The fitted values of t₀ correspond to timescales of 1.2 × 10³ and 1.5 × 10³ yr, which result in an age difference between the Sb1 and Sb2 shells of 3.2 × 10² yr. If we assume that the time interval between shells Sb1 and Sb2 is the same as the interval between Sb2 and Sb3, then we can estimate a value for t₀ for shell Sb3 of 0.85 arcsec km⁻¹ s (by adding Δt_0,B ≡ t_0,Sb2−t_0,Sb1 to the estimated t₀ for Sb2). With this assumption, we find that using a value of R₀ = 28 results in a model that agrees fairly well to shell Sb3. The widths of the three shells, parameterized by R₀, are slightly different, the fastest shell (Sb1) being the narrowest and the slowest shell (Sb3) being the widest. Varying shell widths are needed for the model to fit the velocity gradient seen at the edge of the blue lobe cavity (e.g., at position offsets of about 6'' on both sides of outflow axis) in the PV diagrams perpendicular to the outflow axis (panels (b)–(e) of Figure 5), where the emission becomes wider at lower outflow velocities.

From the fitted models, it can be seen that the blueshifted shells in general are wider, slower, and much older than the redshifted shells. On each side, the faster, younger shells are also narrower than the slower, older shells. However, in the blueshifted side, the shells have very similar widths (which can also be seen from the half-opening angles listed in Table 1), while on the redshifted side, the two shells have clearly different widths. Furthermore, the three blueshifted shells can be explained by outflow shells of different dynamical ages, with similar age differences among consecutive shells.

The parabolic outflowing shells can be produced by entrainment by a wide-angle wind (Li & Shu 1996; Lee et al. 2000). In such models, the molecular outflow is swept up by a radial wide-angle wind with force distribution ∝1/sin²(θ), where θ is the polar angle relative to the outflow axis. Such a wind interacts with a flattened ambient core with density distribution ∝sin²(θ)/r², and instantaneously mixes with shocked ambient gas. The resultant swept-up outflowing shell is then a radially expanding parabola with a Hubble-law velocity structure.

Because each shell can be well fit with the wide-angle wind entrainment model, it is natural to explain the multiple shell structure as being formed by the entrainment of ambient circumstellar material by multiple outbursts of a wide-angle wind. One outburst of the wide-angle wind may not be able to entrain all the material to clear up the cavity, therefore the later outbursts will continue to entrain material to form subsequent shells. In such a scenario, the time intervals between successive shells, which are 2.1 × 10² yr for the redshifted outflow and 3.2 × 10² yr for the blueshifted outflow, can be considered the time interval between wind outbursts. These estimated outburst intervals are consistent with those seen in the episodic knots of HH 46/47 and in other sources. In the HH 46/47 outflow, an outburst interval of about 300 yr was estimated from the knots observed along the jet (see Paper I). Plunkett et al. (2015) estimated outburst intervals to range from 80 to 540 yr, with a mean value of 310 yr for a young embedded source in the Serpens South protostellar cluster. We thus suggest that in HH 46/47 the multiple shell structures may arise from the same high accretion rate episodes, which is reflected in both the jet and wide-angle wind components of the outflow. In fact, in Paper I, the identified jet knots R1 and R2 are found to have dynamical ages of 360 and 650 yr, close to the ages of shells Sr1 (320 yr) and Sr2 (530 yr), suggesting that the episodicity seen in the jet and the wide-angle outflows may be caused by the same outburst events.

We note that the dynamical ages of these shells estimated here may not accurately reflect their true ages. If the outburst happens in a short time compared to the dynamical timescale of the outflow shell, the shell entrained during such an outburst event will decelerate due to the interaction with the surrounding material. Therefore, it is likely that the estimated dynamical ages are upper limits of their true ages. The time intervals are also likely to be upper limits. Yet, the similarity between the time intervals estimated here and those estimated from the jet supports the scenario that the different observed shell structures are produced in multiple outburst events.

If the wide-angle shells on both sides are caused by the same accretion bursts in the disk, then a shell in the blueshifted side should correspond to a shell in the redshifted side. However, it is difficult to identify such pairs in our data because the entrainment is affected by significantly different environments with which each lobe is interacting. The dynamical ages of the identified shells in the blueshifted lobe are significantly larger than those of the shells in the redshifted lobe and also significantly higher than the time interval between shells (Δt_0,B). It is therefore likely that the Sb1, Sb2, or Sb3 shells on the blueshifted lobe are not caused by the most recent outburst events. There may not be much molecular gas left in the blue lobe cavity in order for the youngest outburst to entrain any material to form a shell detectable in CO (unlike the redshifted lobe, see below), as previous outflow bursts may have cleared the cavity. Observations of the optical jet on the blueshifted side found that the furthermost jet knot (HH 47D) has a dynamical age of 1.3 × 10³ yr (Hartigan et al. 2005), which is similar to the age of shell Sb1, and other knots closer to the protostar have much younger ages. This supports that Sb1, Sb2, and Sb3 shells are not caused by recent, but by relatively old outburst events. It is possible that the Sb4 and Sb5 structures in the blueshifted side are caused by the most recent outburst, but due to the lack of ambient cloud material, the CO emission associated with these shell is only concentrated in the region close to the protostar.

Unlike the shells in the blue lobe, the youngest shell in the red lobe (Sr1) has an age similar to the outburst interval. Hence, the Sr1 shell may be the product of the most recent outburst. The red lobe is immersed in the dense part of the parent core and therefore there is still abundant material inside this cavity. Also, the fact that Sr1 is significantly narrower than shell Sr2, is consistent with the scenario where Sr1 has only formed recently. Because the narrower and newer shells are faster than the older and wider shells (see Section 4.1), they are expected to collide with older shells in the future. Based on the sizes R₀ and velocities (v₀; assumed to be constant), Sb1 will catch up with Sb2 in $({R}_{0,\mathrm{Sb}2}-{R}_{0,\mathrm{Sb}1})/({v}_{0,\mathrm{Sb}1}-{v}_{0,\mathrm{Sb}2})=2.7\times {10}^{2}$ yr, Sb2 will merge with Sb3 in 3.6 × 10² yr, and Sr1 will reach Sr2 in 1.2 × 10³ yr. The real catch-up timescales should be shorter than these, as the outer shells are likely to slow down due to the interaction with the dense ambient material. This may explain why only two or three shells can be detected on both sides, as the shells may only survive for a few outburst periods before they collide with the old shells and form the outflow cavity walls seen in the low-velocity channels.

In order to further explore whether the observed outflow shells are caused by entrainment/interaction with the envelope or are being directly launched from the disk, we estimate the mass and momentum rates of these shells from the ¹²CO (2–1) emission. To obtain the gas mass, we assume optically thin emission and adopt an abundance of ¹²CO of 10⁻⁴ relative to H₂ and a gas mass of 2.34 × 10⁻²⁴ g per H₂ molecule. Following Paper II, we adopt an excitation temperature of T_ex = 15 K. An excitation temperature of 50 K would increase the mass estimate by a factor of 1.5. In each velocity channel, we only include the primary-beam-corrected emission above 3σ and within a primary beam response greater than 0.2 relative to the phase center. We include all the emission associated with the outflow, except the emission at outflow velocities less than 2 km s⁻¹ in order to avoid possibly adding emission from core material to our outflow mass estimate.

We estimate a total mass of 5.6 × 10⁻³ and 1.0 × 10⁻² M_⊙ and momentum of 4.4 × 10⁻² and 8.7 × 10⁻² M_⊙ km s⁻¹ in the shells of the blue and redshifted outflow lobes, respectively. Here, in calculating the total momenta, we use the velocity of each channel and multiply by the outflow mass of that channel. These are very likely lower limits due to the optically thin assumption, uncounted low-velocity outflowing material, and possible higher excitation temperatures (e.g., Dunham et al. 2014). Using the estimated ages of the oldest shells on both sides (1.8 × 10³ yr for Sb3 and 5.3 × 10² yr for Sr2), the time-averaged mass outflow rates are 3.1 × 10⁻⁶ and 1.8 × 10⁻⁵ M_⊙ yr⁻¹ for the blueshifted and redshifted outflow lobes, respectively. And the time-averaged momentum injection rates are 2.4 × 10⁻⁵ and 1.6 × 10⁻⁴ M_⊙ yr⁻¹ km s⁻¹ for the blueshifted and redshifted outflow lobes, respectively. Note that these rates are averaged over the outflow age, and the mass loss and momentum injection rates during each outburst are expected to be significantly higher than these values.

The above estimates for the mass outflow rates are one to two orders of magnitude larger (or even larger given that the values quoted above are lower limits) than most estimates of the mass-loss rate for the HH 46/47 protostellar jet using optical and IR atomic line emission, which range between 0.3 and 5 × 10⁻⁷ M_⊙ yr⁻¹ (e.g., Hartigan et al. 1994; Antoniucci et al. 2008; Garcia Lopez et al. 2010; Mottram et al. 2017).¹² Moreover, if we assume a mass-loss rate of ∼10⁻⁷ M_⊙ yr⁻¹ and a velocity of about 100 km s⁻¹ (e.g., Morse et al. 1994; Hartigan et al. 2005) for the wind launched by the disk, this then leads to a momentum injection rate of approximately 10⁻⁵ M_⊙ yr⁻¹. These results show that the observed ¹²CO (2–1) shells have mass-loading rates that are one to two orders of magnitudes higher than the mass-loss rates of the jet (or wind) launched from the disk, but have momentum injection rates similar to the jet/winds directly launched from the disk. This is consistent with the scenario in which the observed ¹²CO (2–1) shells are mostly made of ambient material that was entrained by the wind launched from the disk, in a momentum-conserving interaction, and not of material that was directly launched from the disk. This is also consistent with theoretical simulations that show that only 25%–30% of the mass in a molecular outflow is directly launched from the disk and the rest of the mass is entrained material (e.g., Offner & Chaban 2017).

As discussed above, the observed shells are consistent with wide-angle wind entrainment with multiple outburst events. Although the same episodicity is also seen in the jet, we think these shells are unlikely to be formed by jet entrainment. In fact, multiple layer structures were identified in the extended redshifted lobe of the HH 46/47 molecular outflow observed in ¹²CO (1–0), which were identified to be associated with several jet–bow-shock events (see Paper II). Those structures are at much lower velocities (v_out < 10 km s⁻¹), have a different morphology, and are found at much larger distances from the source (>50'') compared to the shells reported here. Thus, they are unlikely associated with the high-velocity shells discussed in this paper. In some cases, shells at the base of the outflow cavities indeed are found to be connected to the jet–bow shocks far away from the central sources (e.g., Lee et al. 2015). However, it is unclear whether the morphology and kinematics of the shells observed here (which are consistent with those expected for radially expanding parabolic shells), can be also explained by jet–bow-shock entrainment. More theoretical simulations and models are needed to test whether such shells can be formed solely by jet–bow-shock entrainment.

The opening angle of protostellar outflows appears to increase with the source's age; the outflow cavity gradually widens as the source evolves (e.g., Arce & Sargent 2006; Seale & Looney 2008; Velusamy et al. 2014; Hsieh et al. 2017). Outflows are therefore thought to be able to disperse the parent core, terminate the accretion phase, and regulate the core-to-star formation efficiency (e.g., Machida & Hosokawa 2013; Offner & Arce 2014; Offner & Chaban 2017). There are several ways that an outflow can widen as it evolves. In one scenario the outflow cavity widens as the envelope material is continuously entrained by the protostellar jet and/or wide-angle disk wind. In this model one would expect the recently accelerated material to be inside the older, previously entrained material. The newest and faster shell will soon reach the outer, slower shells and transfer momentum to them and the outflow cavity walls. This way, in general, the outflow cavity opening angle will be increasing with time. The observed multiple shell structure in HH 46/47 appears to be consistent with this picture.

In the second scenario the observed outflow is mostly composed of material that is directly launched from the disk (e.g., Machida & Hosokawa 2013). In this model, the disk slowly grows in size, and with it the launching region, at the base of the outflow, slowly widens. This in turn produces the outflow cavity that gradually becomes less collimated. In this scenario at least a part of the recently launched material is expected to be outside of the previously launched material, which is launched from the new outer regions of the disk. Such a model, however, is not consistent with the observations presented here, in which the molecular outflow is made of entrained material and the material entrained by the most recent outflow episode is inside of the older shells. However, we note that these two scenarios are not mutually exclusive.

It is also possible that the outflow cavity widens as the outflow changes direction over time (e.g., Offner et al. 2016; Lee et al. 2017b), which can be caused by a change in the angular momentum direction of the accretion flow, binary interaction, and/or jet precession. However, in the case of HH 46/47, despite the existence of a binary system at the center, the main outflow appears to be symmetric and not affected by a secondary outflow (Papers I and II). Also the precession of the jet appears to be much smaller than the opening angle of the outflow cavity (Paper I), which also indicates that a changing outflow direction may not be the dominant cause of the widening of the outflow in HH 46/47.

The spatial resolution of our current observation is too low to resolve the launching region of the wide-angle wind that entrained the observed molecular outflow. However, the highly coherent properties of the observed outflow shells can provide some constraints on the wind-launching mechanism. In the outflow entrainment scenario, in order to form such a coherent shell structure in each outburst, the wind launched from the disk toward different polar angles needs to be well coordinated. Such coordination can be naturally understood if the launching area in each outburst is a narrow region on the disk. It is very likely that the duration of each outburst is significantly shorter than the interval between outburst events, given that the observed outflow shell from each outburst is very well-defined. We therefore assume the duration of each outburst Δt_outburst is ∼20%–30% of the outburst intervals or about 60 yr (see Section 4.1). If we use the sound speed c_s as the characteristic speed of accreting material in the disk moving inward, we obtain a length scale of ${\rm{\Delta }}R={c}_{s}{\rm{\Delta }}{t}_{\mathrm{outburst}}=(6\,{\rm{au}})\sqrt{T/40\,{\rm{K}}}$, which we can use as a proxy for the width of the launching region on the disk. If the width of the outflow-launching region is much larger than this, it would then be hard for the wind launching at different stellocentric radii to be coordinated enough to form such coherent shells. This estimate of the size for the outflow-launching region is consistent with recent observational studies that deduce a relatively narrow range of radii for the outflow-launching regions (e.g., Bjerkeli et al. 2016; Hirota et al. 2017; Zhang et al. 2018). Note that this is different from the classical picture of a disk wind that is launched over a wide range of stellocentric radii (e.g., Blandord & Payne 1982).

Because accretion variability is believed to be caused by various instabilities in the accretion disk, it is possible that such instabilities can affect particular regions on the disk to enhance the mass or momentum of the launched wind during the outburst. We can further use the outburst interval of 200–300 yr to obtain a characteristic radius by comparing the outburst interval with the Keplerian orbital timescales. The resultant radius is 10–13 au, assuming a mass of 0.3 M_⊙ for the central object (see Paper II). This can be used as a characteristic radius for the disk instability and outflow-launching zone. Note that this source contains a protobinary system with a separation of 026 (120 au) at the center, therefore the estimated characteristic radius of 10–13 au indicates that the outflow-launching region is likely on a circumstellar disk around the primary.