KINEMATICS OF THE OUTFLOW FROM THE YOUNG STAR DG TAU B: ROTATION IN THE VICINITIES OF AN OPTICAL JET

Jets and outflows from young stars play a key role in the star-formation process; however, their nature is still under debate (Arce et al. 2007). The general consensus is that fast protostellar jets are driven and collimated by rotating magnetic fields anchored to the star–disk system (Pudritz et al. 2007; Shang et al. 2007). However, it is not clear where these magnetic fields are anchored to the disk: it could be from the radius at which the stellar magnetosphere truncates the disk (X-wind, Shu et al. 2000) or from an extended region of the disk (disk wind; Königl & Pudritz 2000). Magnetohydrodynamic (MHD) models predict that the jet should inherit a toroidal angular momentum component or, in other words, rotation (Fendt 2011). The magnetic field forces the corotation of the gas up to the Alfvèn radius. Therefore, the magnitude and position of these movements within the outflow would give, in principle, information about their origin on the disk (Anderson et al. 2003). We refer the reader to the introduction of Zapata et al. (2010) for details concerning to the previous studies on jet/outflow rotation based on optical, infrared, and millimeter studies. In this paper (Zapata et al. 2010), the results and limits on previous studies are discussed.

Located at about 150 pc, DG Tau B is a low-luminosity (0.88 L_☉) class I/II young star located about 1' to the SW of the well-known T Tauri star DG Tau (Jones & Cohen 1986; Eislöffel & Mundt 1998; Torres et al. 2009; Luhman et al. 2010; Rodríguez et al. 2012). DG Tau B powers an asymmetric bipolar jet (HH 159) mapped at optical/infrared wavelengths (Eislöffel & Mundt 1998). The red lobe, located to its NW consists of a chain of bright knots extending to about 1' from the source, while the blue lobe located to its SE is much fainter and less collimated, and is detected only up to ∼10'' from the star (Mundt & Fried 1983; Eislöffel & Mundt 1998; Podio et al. 2011). A molecular outflow mapped in carbon monoxide (CO) is observed principally associated with the NW fast optical jet (Mitchell et al. 1997). These authors found that the CO outflow is similar to the optical outflow: the CO redshifted emission extends at least 6000 AU (40'' at the distance of 150 pc) to the NW of the star, while the blueshifted CO emission is confined to a compact region, which is less than 500 AU (about 3''). McGroarty & Ray (2004) proposed that the Herbig–Haro objects 836 and 837, located several arcminutes to the SE of DG Tau B, could be tracing ejecta from this star that took place ∼10⁴ yr ago.

At the base of the outflow emerging from DG Tau B there is a circumstellar disk placed close to edge-on (∼65°; Guilloteau et al. 2011), and detected for the first time in absorption by the broadband imaging of the Hubble Space Telescope (HST; Stapelfeldt et al. 1997). The disk was confirmed by ¹³CO millimeter observations (Padgett et al. 1999). The source position has been determined from 3.5 cm Very Large Array radio continuum observations by Rodriguez et al. (1995), who locate it within the observed dark lane. The position is at α_J2000.0 = 04^h27^m0255, δ_J2000.0 = +26°05'307. The disk has been mapped at millimeter wavelengths using sub-arcsecond resolution with the Plateau de Bure Interferometer (Guilloteau et al. 2011). They found a deconvolved size for the disk of 069 × 034 with a position angle (P.A.) = 26°, and a mass of 0.068 M_☉. Gramajo et al. (2010) modeled the spectral energy distribution of DG Tau B as a young star with a mass of 0.5 M_☉, a temperature of 4000 K and a radius of 2.5 R_☉.

In this paper, we present millimeter line and continuum observations, made with the Submillimeter Array⁶ (SMA), of the young star DG Tau B and its associated outflow. These interferometric observations reveal velocity asymmetries about the flow axis over the entire length of the flow that can be interpreted as outflow rotation. Continuum and line observations of the circumstellar disk associated with DG Tau B are also presented. The paper is organized as follows. In Sections 2 and 3, we discuss the observations and results. In Section 4, we discuss the possible origin of rotating outflows, and, in Section 5, we present the conclusions.

The observations were carried out with the SMA on 2011 December and 2012 February, when the array was in its compact and extended configuration, respectively. The independent baselines in these configurations ranged in projected length from 10 to 140 kλ. The phase reference center for the observations was set to α_J2000.0 = 04^h27^m0266, δ_J2000.0 = +26°05'304. Two frequency bands, centered at 230.457 GHz (upper sideband) and 220.457 GHz (lower sideband) were observed simultaneously. We concatenated the two data sets using the task in MIRIAD called "uvcat." The two different observations were identical, and only the antenna configuration of the SMA changed. The primary beam of the SMA at 230 GHz has a FWHM of 57'', and the continuum and line emission arising from DG Tau B fall well within it.

The SMA digital correlator was configured to have 48 spectral windows ("chunks") of 104 MHz and 128 channels each. This provided a spectral resolution of 0.812 MHz (∼1 km s⁻¹) per channel. However, some of these spectral windows included 512 channels (one of these bands included the CO line), providing 0.203 MHz (∼0.26 km s⁻¹) of resolution. This very high spectral resolution allowed a reliable study of the CO kinematics.

Observations of Uranus provided the absolute scale for the flux density calibration. The gain calibrators were the quasars 3C 111 and 3C 84, while 3C 279 was used for bandpass calibration. The uncertainty in the flux scale is estimated to be between 15% and 20%, based on the SMA monitoring of quasars.

The data were calibrated using the IDL superset MIR, originally developed for the Owens Valley Radio Observatory (Scoville et al. 1993) and adapted for the SMA.⁷ The calibrated data were imaged and analyzed in the standard manner using the MIRIAD (Sault et al. 1995) and KARMA (Gooch 1996) softwares.⁸ A 1300 μm continuum image was obtained by averaging line-free channels in the lower sideband with a bandwidth of about 4 GHz. A continuum image using both bands was also obtained; however, similar results were reached. For the line emission, the continuum was also removed. We set the ROBUST parameter of the task INVERT to +2 to obtain a better sensitivity losing some angular resolution. The resulting rms noise for the continuum was about 9 mJy beam⁻¹, at an angular resolution of 187 × 163 with a P.A. = 643. The rms noise in each channel of the spectral line data was about 90 mJy beam⁻¹ at the same angular resolution.

In Figure 1, we present the resulting map of the ¹²CO(2–1) line and 1300 μm continuum observations made with the SMA of DG Tau B. This image is overlaid with HST images obtained with the infrared camera WFPC2 (Stapelfeldt et al. 1997). Figure 1 reveals the innermost parts of the NW monopolar redshifted outflow with the rotated "V" morphology reported for the first time by Mitchell et al. (1997). By contrast, the blueshifted CO emission is confined to a compact region, close to the disk. The spatial correspondence between knots in the optical jet and successive broadenings of the outflow supports the hypothesis that the molecular flow is produced by the action of multiple working surfaces or the entrainment of the ambient gas (Mitchell et al. 1997). In this image, are also seen the optical jet and the infrared nebulosities of scattered light. The 1300 μm emission falls very well within the circumstellar disk imaged in absorption by the broadband imaging of the HST. We conclude that the 1300 μm emission here is tracing the innermost parts of the disk, very close to the young star DG Tau B.

Zoom In Zoom Out Reset image size

For the continuum 1300 μm emission, and using a Gaussian fitting, we found that the flux density and peak intensity values of DG Tau B are 590 ± 30 mJy and 310 ± 20 mJy beam⁻¹, respectively. We also find from this fit that the source has a deconvolved size of 18 ± 05 × 15 ± 06 with a P.A. = +30° ± 5°. Therefore, at the distance of the Taurus molecular cloud complex (150 pc) the size of the continuum source is about 270 × 225 AU.

Following Hildebrand (1983) and assuming optically thin isothermal dust emission, a gas-to-dust ratio of 100, a dust temperature of 30 K, a dust mass opacity κ_1300 μm = 1.1 cm² g⁻¹ (Ossenkopf & Henning 1994), and that this object is located at 150 pc, we estimate the total mass associated with the dust continuum emission to be 0.08 M_☉, this is in very good agreement with the value obtained by Guilloteau et al. (2011). The 1300 μm continuum emission is thus tracing the circumstellar disk surrounding DG Tau B. Furthermore, we remark that the mass obtained here could be partially optically thick, and therefore this is a lower limit.

Following Zapata et al. (2014), assuming local thermodynamic equilibrium, and that the ¹²CO(2–1) molecular emission is optically thin, we estimate the outflow mass using the following equation.

$$\begin{eqnarray*} \frac{M(\hbox{H}_2)}{M_\odot }&=&6.3 \times 10^{-20} m({\rm H_2}) X_\frac{{\rm H_2}}{{\rm CO}}\\ &&\times \left(\frac{c^2 d^2}{2k\nu ^2} \right) \frac{ \exp \left(\frac{5.5}{T_{{\rm ex}}} \right) \int S_{\nu } dv \Delta \Omega }{ \left(1 - \exp \left[\frac{-11.0}{T_{{\rm ex}}} \right] \right) }, \end{eqnarray*}$$

where all units are in cgs, m(H₂) is the mass of the molecular hydrogen, X $_{({{\rm H_2}}/{{\rm CO}})}$ is the fractional abundance between the carbon monoxide and the molecular hydrogen (10⁴), c is the speed of light, k is the Boltzmann constant, ν is the rest frequency of the CO line in Hz, d is distance (150 pc), S_ν is the flux density of the CO (Jansky), dv is the velocity range in cm s⁻¹, ΔΩ is the solid angle of the source in steradians, and T_ex is excitation temperature taken to be 50 K. We then estimate a mass for the outflow powered by DG Tau B of 3×10⁻³ M_☉. This value is consistent with the mass of other molecular outflows powered by young low-mass protostars; see Wu et al. (2004). The mass estimated here is only a lower limit because the CO emission is likely to be optically thick.

In Figure 2, we present two position–velocity diagrams or cuts obtained across the redshifted side of the outflow, named C1 and C2; see Figure 1. These diagrams reveal the spatial structure of the gas across the flow as a function of the radial velocities and at distances far from DG Tau B (∼1400 AU for the case of C1 and 1900 AU for C2). In both cuts velocity gradients across the outflow with an amplitude of about 2 km s⁻¹ are revealed. In the cut C1, the gradient is somewhat larger than 2 km s⁻¹. This gradient is also confirmed by the spectra obtained in both sides of the flow as shown in Figure 2 in the lower panels. Both cuts were intentionally made over two optical bullets in order to reveal their dynamics (see Figure 1); however, only the bullet associated with the cut called C2 has a clear molecular counterpart. This is located in the middle of the borders of the molecular flow. This molecular emission associated with the optical bullet is too compact to reveal any velocity gradient.

Zoom In Zoom Out Reset image size

Figure 3 presents the first moment or the intensity weighted velocity of the ¹²CO(2–1) emission from the inner part of the outflow overlaid on the HST infrared image (using the spectral filter F675w) and with the SMA 1300 μm continuum image. The image reveals the dynamics of the CO gas in the innermost parts of the flow and in the vicinity of the optical jet. Here, the blue colors represent blueshifted emission, while the red colors, redshifted emission. The velocity gradient across the outflow is also revealed in this figure; it is more evident in its blueshifted side and close to DG Tau B. A possibility of why the rotation is diluted farther from DG Tau B could come from the fact that the flow is not exactly on the plane of the sky, and far from the source the poloidal velocities dominate.

Zoom In Zoom Out Reset image size

In Figure 3, in the lower panels, we also show two position–velocity diagrams we made to reveal the kinematics of the molecular gas close to the circumstellar disk related with DG Tau B. In the position–velocity diagrams called D1 and D2 (at a distance from DG Tau B of about 220 AU), an asymmetric "V"-shaped (or, perhaps, a triangular shape) velocity pattern is revealed. The diagrams are made at a distance of about 250 AU from the source. These velocity patterns have been attributed to outflow rotation (Lee et al. 2008; Zapata et al. 2010; Pech et al. 2012; Peters et al. 2014). These patterns are formed because the low-velocity gas far from the outflow axis has a velocity gradient (i.e., rotation), while the gas in the jet and close to the axis seems to be only accelerated in direction of the flow. If the low-velocity gas were parallel to the direction of the outflow (i.e., no rotation), one would expect these V shapes to be symmetric with respect to the axis of the flow. The amplitude of such velocity asymmetries is about 4 km s⁻¹. We noted that this gradient is larger to that observed far from the source, perhaps due to the conservation of angular momentum.

From ¹²CO (and ¹³CO) observations, one can obtain the disk mass and kinematics (T. Bourke et al. in preparation). The disk mass is ∼0.1 M_☉. Position–velocity diagrams of both isotopes show disk rotation in the same sense as the observed outflow rotation. These diagrams can be fitted by Keplerian curves that give the central stellar mass as a function of inclination angle. The best fit gives M_* ∼ 0.5 M_☉ for an inclination angle of 65°.

4.1. Outflow Rotation

4.2. On the Origin of the Molecular Flow Rotation

From Figures 2 and 3, the observed CO outflow has a radial velocity of v_r ∼ 3 km s⁻¹ (subtracting the LSR velocity of central source), and a rotation speed v_φ ∼ 1 km s⁻¹ at a distance from the jet axis R ∼ 150 AU. As discussed above, the outflow rotation is in the same direction as the rotation of the Keplerian disk around the central star. Also, given the inclination angle of the jet axis with respect to the line of sight θ_i ∼ 65^o (Eislöffel & Mundt 1998), the corrected poloidal speed is v_p = v_r/cos (θ_i) ∼ 7.1 km s⁻¹.

What is the origin of this rotating molecular flow? One possibility is that the observed molecular flow is infalling rotating gas from the parent molecular core. In particular, one can test the collapse flow solution of a rotating isothermal core by Terebey et al. (1984, hereafter TSC). This flow will collapse to the midplane and will form a disk with a size given by the centrifugal radius, $r_c = \Omega _c^2 G^3 M_*^3 / 16 a^8$, where Ω_c is the rotation rate of the core, G is the gravitational constant, a is the sound speed, and M_* is the mass of the central star. Figure 4 shows the rotation velocity of the collapsing flow as a function of the distance to the rotation axis along cuts parallel to the disk midplane, at different heights from the disk: z = r_c, 3r_c, 5r_c, where we assumed a centrifugal radius r_c = 100 AU. This figure shows that for all the curves the rotation velocity of the collapsing gas is smaller than the observed rotation speed v_φ ∼ 1 km s⁻¹. In fact, for the cut at z = 5 r_c = 500 AU, the rotational speed of the infalling gas is v_ϕ < 0.2 km s⁻¹; this velocity decreases even more for cuts further up from the disk midplane. Therefore, the observed rotating flow cannot correspond to infalling material from this type of rotating envelope.

Zoom In Zoom Out Reset image size

Another possibility is that the rotating molecular flow corresponds to a slow wind ejected from the Keplerian disk. We now examine two types of disk winds: magneto-centrifugal winds and photoevaporated winds.

For a magneto-centrifugal wind, the poloidal v_p and rotation v_ϕ velocities at a distance R from the rotation axis, can be related to the Keplerian rotation rate at the footpoint r₀ on the disk, $\Omega _{K0} = (G M_* / r_0^3)^{1/2}$, by a cubic equation (Equation (4) of Anderson et al. 2003). For a central star with a mass M_* = 0.5 M_☉, this equation gives an footpoint r₀ ∼ 11 AU. One can also obtain the parameter $\lambda _\phi = R v_\phi / (r_0^2 \Omega _{K0}) \sim 2.1$, which is the ratio of the specific angular momentum at R to the specific angular momentum at the footpoint r₀. When the jets reach high Alfvénic Mach numbers and large radii, λ_ϕ should be equal to the lever arm, λ = (r_A/r₀)², where r_A is the Alfvén radius where the flow reaches the Alfvén speed (e.g., Ferreira et al. 2006). The lever arm of the flow can be estimated in the asymptotic regime from the ratio of the poloidal speed to the Keplerian speed at the footpoint, r_A/r₀ ∼ vp/2^1/2v_K(r₀) ∼ 0.8. Then, the implied values of λ_ϕ and λ are very small, with values of ∼1–2, providing very little poloidal acceleration. Furthermore, since the lever arm relates the wind mass-loss rate with the disk accretion rate, $\dot{M}_{w} \sim \dot{M}_{\rm acc}/\lambda$, these low values of λ imply a very high efficiency of mass ejection. In contrast, values of λ ∼ 10 are expected for MHD disk winds models such that the wind carries away one tenth of the mass accretion rate (e.g., Königl & Pudritz 2000). In summary, because the molecular flow has a poloidal velocity comparable to the rotation speed, its interpretation as a magneto-centrifugal disk wind poses severe problems of mass ejection.

The second type of disk winds are photoevaporated winds that arise because the gas at the disk surface is heated by high energy photons from the central star and is able to escape from the local gravitational potential well. Models of these winds from disks around low-mass stars include mainly heating by FUV and X-rays (e.g., Font et al. 2004; Gorti & Hollenbach 2009; Owen et al. 2011). These flows have low poloidal speeds v_p ∼ few × a, where the thermal speed is a ∼ 2 km s⁻¹(T/10³K)^1/2(μ/2)^−1/2, where T is the gas temperature, and μ is the mean mass per particle in units of the hydrogen mass m_H (e.g., Lugo et al. 2004). A characteristic boundary where a photoevaporated wind can escape is given by the gravitational radius r_g = GM_*/a², although pressure gradients can allow photoevaporation from smaller radii, r ∼ r_g/3 − r_g/2. This radius can be written as r_g ∼ 108 (T/10³K)⁻¹(μ/2)(M_*/0.5 M_☉) AU. Photoevaporated winds are thermal winds and evolve conserving the specific angular momentum injected at the disk footpoint, i.e., $r_0^2 \Omega _{K0}= R v_{\varphi }$. For the observed specific angular momentum, this relation gives an ejection point r₀ ∼ 51 AU ∼r_g/2.

On the other hand, we will now show that magneto-centrifugal and photoevaporated slow disk winds do not have enough linear or angular momentum to account for the observed rates in the molecular outflow. The observed molecular flow has a mass $M_{{\rm H_2}} \sim 10^{-3} {\, M_\odot }$, and the associated dynamical time is t_dyn = 1000 AU/v_p ∼ 880 yr. Then, the molecular outflow mass-loss rate is $\dot{M}_{\rm outflow} \sim 1.1 \times 10^{-6} {\, M_\odot }\, {\rm yr^{-1}}$, its momentum rate is $\dot{P}_{\rm outflow} =\dot{M}_{\rm outflow} v_p \sim 6 \times 10^{-6} {\, M_\odot }\, {\rm yr^{-1}}\, {{\rm km\, s^{-1}}}$, and its angular momentum rate is $\dot{L}_{\rm outflow} = \dot{M}_{\rm outflow} R v_\phi \sim 1.65 \times 10^{-4} \,{\, M_\odot }\, {{\rm AU}}\, {{\rm km\, s^{-1}}}$. This linear momentum rate is similar to the rate measured by Mitchell et al. (1994) and, correcting for partial ionization, is consistent to the momentum rate of the high-velocity atomic jet (Podio et al. 2011). Instead, for the slow disk winds considered here, assuming a mass-loss rates similar to that of the central atomic jet $\dot{M}_w \sim 10^{-8} {\, M_\odot }\, {\rm yr^{-1}}$, the linear momentum rate is $\dot{P}_w = \dot{M}_w \, v_p \sim 5.5 \times 10^{-8} {\, M_\odot }\, {\rm yr^{-1}}\, {{\rm km\, s^{-1}}}$, and the angular momentum rate is $\dot{L}_w = \dot{M}_{w} r_0 v_{K0} \lambda _\phi = \dot{M}_w r v_\phi = 1.5 \times 10^{-6} {\, M_\odot }\, {{\rm AU}}\, {\rm yr^{-1}}\, {{\rm km\, s^{-1}}}$. Both rates are smaller than the molecular outflow rates by the factor $\dot{M}_{\rm outflow}/\dot{M}_w \sim 100$.

This large discrepancy between the slow disk wind rates and the outflow rates indicates that the molecular outflow is probably material from a rotating parent cloud entrained by a fast wind (even though the TSC infalling envelope has rotational speeds smaller than the observed v_ϕ). It would be important to show that such entrainment process is capable of carrying also the observed angular momentum (e.g., Canto et al. 1996). A detailed modeling of this process is a very interesting problem but is out of the scope of this paper.

We have reported ¹²CO(2–1) line observations of DG Tau B, and discovered velocity asymmetries about the flow axis with amplitudes roughly on the order of 2 km s⁻¹ far from its exciting source and about 4 km s⁻¹ close to it. This difference in velocities might be due to the conservation of the angular momentum. Similar velocity asymmetries are found on both sides of the outflow, and we interpret them as evidence for outflow rotation. The outflow rotation sense is identical to that revealed in the circumstellar disk. We show that slow disk winds ejected at distances of tens of AU from the star would have the observed poloidal and rotation velocities. Nevertheless, the observed linear and angular momentum rates of the outflow are too large compared to the rates of these slow disk winds and indicate that the molecular rotating flow is probably entrained material from the parent core. DG Tau B appears to be a promising laboratory for future studies of this entrainment process.

L.A.Z, S.L., L.F.R., L.L., and D.T. acknowledge financial support from DGAPA, UNAM, and CONACyT, México. M.F.L. acknowledges financial support from the University of Illinois and the hospitality of the CRyA (UNAM). We thank the anonymous referee for detailed comments that improved our study.

Facility: SMA - SubMillimeter Array