ALMA Observations of the Very Young Class 0 Protostellar System HH211-mms: A 30 au Dusty Disk with a Disk Wind Traced by SO?

Figure 1(a) shows the continuum map toward the central region at a frequency of ∼350 GHz and resolution of ∼004. A compact and bright disklike structure is seen inside an extended and faint envelope that is elongated roughly perpendicular to the jet axis. The envelope and disk have a total flux density of ∼192 ± 38 mJy, measured within the 5σ contour. Notice that, unlike the previous continuum map shown at ∼02 resolution in Lee et al. (2009), no secondary emission peak is seen here at ∼03 toward the southwest (SW). In order to confirm this, we made a continuum map with a similar resolution to that in Lee et al. (2009) using a taper of 025, but still only observed a smooth extension of the envelope toward the SW to ∼04. Thus, the secondary emission peak seen in Lee et al. (2009) is likely an artifact due to limited UV-coverages of the Submillimeter Array when using the super-uniform weighting on the visibilities. Zooming into the center at a higher resolution of ∼003, we can better resolve the disk structure, as shown in Figure 1(b). Notice that the envelope becomes mostly below 3σ detection due tothe higher noise level in brightness temperature at higher resolution. The disk has an emission peak at the position α₍₂₀₀₀₎ = 3^h43^m568054 and δ₍₂₀₀₀₎ = 32°00'50189, which is considered to be the location of the central protostar in this paper. The disk has a total flux density of ∼83 ± 16 mJy, measured within the ∼5σ contour.

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A two-dimensional Gaussian fit to the disk structure indicates that the disk has a major axis at a position angle of 276 and is thus almost exactly perpendicular to the jet axis. This, together with the known jet orientation, suggests that the disk is close to edge-on, with an inclination angle of ≲6° to the plane of the sky (here 0° for an edge-on disk) and the nearside tilted to the northwest (NW). The disk has a deconvolved size (FWHM) of 0127 (or ∼30 au) along the major axis and 0067 (∼16 au) along the minor axis. The aspect ratio of the disk in the plane of the sky is ∼0.5, larger than that expected for a thin disk with an inclination angle of 6°, which is ∼0.1. Therefore, the disk is geometrically thick, as found in the slightly evolved but vertically resolved edge-on Class 0 disks, e.g., HH 212 (Lee et al. 2017a). This indicates that the (sub)millimeter light-emitting grains have yet to settle to the midplane. This is different from the Class I disk HH 30, which is very thin in the dust continuum image (unresolved vertically; F. Menard et al. 2018, in preparation), or the Class I/II disk HL Tau, which has signs of dust settling from the shape of the gaps (ALMA Partnership et al. 2015). Observations at higher resolution are needed to check in HH 211-mms for a dark lane similar to that seen in HH 212 (Lee et al. 2017a).

An intensity cut along the major axis of the disk shows an intensity jump at the position offsets of ∼±01 from ∼10 K there to ∼90 K at the source position (Figure 1(c)). These position offsets can be considered as the locations where the innermost envelope transitions to the disk, as discussed in HH 212 (Lee et al. 2017a, 2017b). The intensity profile has a FWHM of ∼ 0134, resulting in a deconvolved FWHM of 0127 along the major axis, as found earlier in the two-dimensional Gaussian fit to the disk structure.

We can study the disk properties by estimating the spectral index α (with the flux density F_ν ∝ ν^α) in the spectral energy distribution of the disk emission, using the flux densities of the disk emission at two different frequencies. Previously, the disk has been detected by the VLA at 36.9 GHz at a resolution of ∼007 with a flux density of ∼0.855 mJy (Segura-Cox et al. 2016; Tobin et al. 2016). Part of this flux density is believed to be from free–free emission, because the spectral index between 36.9 and 28.5 GHz is ∼1.65 (Tobin et al. 2016). Recent analysis shows that the dust emission corrected for the free–free emission is ∼0.57 mJy at ∼33 GHz (λ ∼ 9 mm) in Ka-band observations (Tychoniec et al. 2018). Therefore, with the flux density of the disk measured above at 350 GHz, we have α ∼ 2.11 ± 0.2, slightly higher than that for an optically thick thermal dust emission, for which α = 2. Thus, the disk here must be warm and partly optically thick.

Assuming that the disk emission is optically thin, the (gas and dust) mass of the disk can be roughly estimated using the formula

$$\begin{eqnarray}&&{M}_{\mathrm{disk}}\,\sim \,\displaystyle \frac{{D}^{2}{F}_{\nu }}{{B}_{\nu }({T}_{\mathrm{dust}}){\kappa }_{\nu }}\end{eqnarray} \tag{ 1 }$$

where D is the distance to the source, B_ν is the blackbody intensity at the dust temperature T_dust, F_ν is the observed flux density, and κ_ν is the mass opacity per gram of gas and dust mass. As discussed earlier, the observed brightness temperature reaches 90 K, thus we assume T_dust = 100 K. Since the mass opacity is uncertain, we assume two different mass opacities for two different phases of star formation. One is the empirical opacity derived from T-Tauri disks in the late phase of star formation, which is ${\kappa }_{\nu }=0.1{(\nu /{10}^{3}\mathrm{GHz})}^{\beta }$ cm² g⁻¹ (Beckwith et al. 1990), and the other is the mass opacity of protostellar cores in the early phase (Ossenkopf & Henning 1994), which is ${\kappa }_{\nu }=0.00899{(\nu /231\mathrm{GHz})}^{\beta }$ cm² g⁻¹ (Tychoniec et al. 2018), where β is the dust opacity index. The actual opacity of the HH 211 protostellar disk can be in between the two. We assume β = 1, as usually assumed for protostellar disks (Andrews et al. 2009). The resulting disk masses are ∼1.8 M_Jup and ∼4.6 M_Jup, respectively. Since the emission is at least partially optically thick, the masses estimated here are only lower limits.

We can compare the disk masses estimated above with that derived from the emission at 33 GHz, which is more optically thin. At that frequency, the mass opacity is an extrapolation from the above mass opacities (which were derived for the wavelength λ ≲ 1.3 mm) and is thus more uncertain. Adopting a flux density of 0.57 mJy at 33 GHz (Tychoniec et al. 2018), the resulting disk masses are ∼14 M_Jup and 35 M_Jup, respectively, for the two different mass opacities, and thus are much higher than those estimated above. Previously with the same formula, Tychoniec et al. (2018) has derived a disk mass of ∼120 M_Jup, assuming a dust temperature of 30 K and a mass opacity of protostellar cores. As discussed above, a dust temperature of ∼100 K is more reasonable. Thus the disk mass should be revised to be ∼35 M_Jup. Since the mass opacity is so uncertain and the continuum at lower frequency can probe further in where the temperature is higher, further work is needed to check the disk masses derived here at 33 GHz.

SO N_J = 8₉ − 7₈ emission is detected within ∼013 (30 au) of the central source, as shown in Figure 2(a). It traces a compact bipolar outflow, consisting of a SE component and a NW component, extending out from the disk surfaces surrounding the jet axis. The outflow width reaches ∼02 (46 au) at a height of ∼01 (23 au). Note that faint SO emission is also detected along the jet axis at a distance >1'' from the central source, tracing the knots in the jet as seen before in Lee et al. (2010), but it is too faint to be discussed here meaningfully. Almost no SO emission is detected along the major axis of the dusty disk, likely because the dust emission there is optically thick and bright, as seen in HH 212 (Lee et al. 2017b). As shown in Figure 2(b), the spectrum averaged over the emitting region shows that most emission is within ∼±10 km s⁻¹ of the systemic velocity. The spectrum profile is asymmetric about the systemic velocity, with less emission in the blue.

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The structure of the SO emission can be better seen in the channel maps shown in Figure 3. The SE and NW outflow components are seen in both redshifted and blueshifted velocities, with the SE component extending to higher blueshifted velocities and the NW component extending to higher redshifted velocities. This is expected because the outflow must have similar inclination to the jet and is thus almost in the plane of the sky, with the SE component tilted slightly toward us and the NW component tilted slightly away from us. At low velocities with $| {V}_{\mathrm{off}}| \lesssim 4.5$ km s⁻¹, the SO emission on the dusty disk surfaces forms flattened structures aligned with the dusty disk surfaces (see Figures 3(c)–(f)), and thus actually traces the disk atmosphere, as seen in HH 212. The disk atmosphere can be clearly seen at the lowest velocities, as indicated in Figures 3(d) and (e), with its radius estimated to be ∼005 or 12 au, using a 4σ detection level. Above the disk surfaces, the SO emission forms shell-like structures around the jet axis opening to the SE and NW from the inner disk (see Figures 3(c)–(f)), tracing the outflow shells. Going from the blueshifted to redshifted velocity, the emission of the shell moves from the SW to the northeast (NE) of the jet axis. This velocity sense is the same as that seen before in the HCO⁺ rotating flattened envelope (Lee et al. 2009), implying that the shell is rotating with the same velocity sense as the flattened envelope. At higher velocity with $| {V}_{\mathrm{off}}| \gt 4.5$ km s⁻¹, the emission is seen along the jet axis, probably tracing the front and back walls of the outflow shells projected along the jet axis.

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Figure 4 shows the position–velocity (PV) diagrams across the jet axis at increasing distance from the central source. The kinematics of the disk atmosphere can be studied with the PV diagrams at the disk surfaces in Figures 4(a) and (d). As mentioned above, the disk atmosphere is traced by the emission on the disk surfaces with $| {V}_{\mathrm{off}}| \lesssim 4.5$ km s⁻¹. There the redshifted emission is seen in the NE and the blueshifted in the SW (see Figures 4(a) and (d)), the same as those seen in the HCO⁺ rotating flattened envelope. Notice that in Figure 4(d), the emission at V_off ∼ −0.5 km s⁻¹ and 012 is a separate component not associated with the disk atmosphere in the NW, and further observations are needed to determine its origin. In addition, the outer boundaries of the PV structures can be roughly outlined by the magenta curves, which are the Keplerian rotation curves due to a protostellar mass of 50 M_Jup, suggesting that the central protostar has a mass of ≲50 M_Jup. For the disk atmosphere in the SE, a linear PV structure (as delineated by the green line in Figure 4(a)) is seen, revealing a rotating ring in the atmosphere. For the disk atmosphere in the NW, a roughly elliptical-like PV structure (as delineated by the tilted green ellipse in Figure 4(d)) can be seen, revealing a rotating and expanding ring in the atmosphere. This indicates that the atmosphere there has been significantly affected by the outflow, as seen in HH 212 (Lee et al. 2018). Notice that the center of the PV structure (bracketed by the Keplerian curves) has a velocity shift of ∼−0.5 km s⁻¹ in the SE atmosphere and ∼0.5 km s⁻¹ in the NW atmosphere. This implies that the atmosphere also has a small outflow velocity of ∼5 km s⁻¹, assuming an inclination angle of 6°. However, since the velocity shift is small, further observations are needed to confirm the outflow velocity of the atmosphere.

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The kinematics of the bipolar rotating outflow can be studied with the PV diagrams above the disk surfaces in Figures 4(b)–(c) and (e)–(f). For the SE outflow component, the blueshifted and redshifted emission are seen on the opposite sides of the jet axis (Figures 4(b) and (c)), as discussed above. The specific angular momentum of the outflow is estimated to be ≲20 au km s⁻¹, with the largest possible value marked by the linear line in the diagrams. For the NW outflow component (Figures 4(e) and (f)), as shown by the tilted green ellipse, the emission structure could form a tilted elliptical PV structure, as seen before in the rotating outflow in Orion BN/KL Source I (Hirota et al. 2017) and HH 212 (Lee et al. 2018). From these elliptical PV structures, we estimated a similar specific angular momentum of ∼20 au km s⁻¹, with an expansion velocity of 6–7 km s⁻¹. On the other hand, we cannot identify any elliptical PV structure in Figures 4(b) and (c), and hence cannot estimate the expansion velocity for the SE outflow component.

Figure 5 shows the PV diagram cut along the jet axis. Most of the emission is associated with the disk atmosphere with position offsets of ∼±006. Not much emission is seen from the outflow along the jet axis. Future observations are needed to resolve the PV structure of the disk atmosphere along the jet axis.

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As seen in Figure 2(a), the SO emission has a mean intensity of 300 ± 60 K km s⁻¹. Assuming an optically thin emission in local thermodynamic equilibrium and an excitation temperature of ∼100 K as in HH 212 (Lee et al. 2018), the mean SO column density is estimated to be ∼4.4 ± 0.9 × 10¹⁵ cm⁻². Assuming an SO abundance of 2 × 10⁻⁶ as found in the jet (Lee et al. 2010), the molecular hydrogen column density is ∼2.2 ± 0.4 × 10²¹ cm⁻². This SO abundance in the jet was derived previously by dividing the SO column density by the H₂ column density (derived from CO emission) in the jet (Lee et al. 2010). Given that the shell thickness is ≲005 or 12 au, the mean density in the shell is ≳1.2 × 10⁷ cm⁻³, which is close to the critical density of the SO line. The total flux of the SO emission is ∼0.87 Jy km s⁻¹. Thus, the total mass in the atmosphere and rotating outflow is ∼1.3 × 10⁻³ M_Jup.

In some early models of magnetized core collapse, magnetic braking can prevent a Keplerian rotating disk from forming around a central protostar in the earliest phase of star formation (e.g., Allen et al. 2003; Mellon & Li 2008). However, recent works have shown that, in addition to misaligned magnetic fields (Hennebelle & Ciardi 2009), non-ideal magnetohydrodynamic effects, e.g., Ohmic dissipation and ambipolar diffusion, can enable formation of Keplerian rotating disks (Dapp & Basu 2010; Machida & Matsumoto 2011; Masson et al. 2016; Zhao et al. 2018). Recent ALMA observations at unprecedented angular resolution have also shown that a Keplerian disk can form in ∼5 × 10⁴ yr old Class 0 system HH 212 (Lee et al. 2017a, 2017b). In that system, a dusty disk with a radius of ∼60 au is detected with an intensity jump of ∼10 from the envelope to the disk in the continuum emission at 350 GHz. This intensity jump is believed to trace a density jump produced by an accretion shock around the disk and the envelope transforms to a Keplerian disk after passing through the shock. Indeed, a Keplerian disk with a smaller radius of ∼44 au, which is about two-thirds of the dusty disk radius, was subsequently confirmed from a kinematic study in molecular lines (Lee et al. 2017b).

HH 211-mms is younger than HH 212. Interestingly, a similar intensity jump of ∼9 is also seen in the continuum emission at 350 GHz at a radius of ∼15 au (see Section 3.2). Since this intensity jump can also trace a density jump produced by an accretion shock, a Keplerian disk might have formed with a smaller radius of ∼10 au, roughly in agreement with the radius of the rotating disk atmosphere detected in SO. A similar disk radius was also estimated at 36.9 GHz (or 8.1 mm) (Segura-Cox et al. 2016). In this system, the rotation axis of the disk must be aligned with the jet axis, because the disk is almost exactly perpendicular to the jet. Since the magnetic field in the cloud core is mostly N–S oriented (Matthews et al. 2009; Hull et al. 2014), a large misalignment of ∼60° exists between the magnetic field axis in the cloud core and the rotation axis of the disk. Hence, it is possible that the magnetic braking here is not efficient enough to prevent a disk from forming. Previous dust polarization observations toward the inner envelope of HH 211-mms showed a hint of a toroidal magnetic field wrapping around the disk, further supporting this possibility (Lee et al. 2014). The disk here is small, likely because the specific angular momentum in the envelope is small, roughly estimated to be ∼35 au km s⁻¹ from the HCO⁺ envelope in Lee et al. (2009). This value is much smaller than that in HH 212, which is ∼140 au km s⁻¹, and L1527 (54 au disk), which is ∼130 au km s⁻¹ (Ohashi et al. 2014). In addition, HH 211-mms is much younger than HH 212 and L1527, and thus it is likely that only the inner cloud core with smaller angular momentum has collapsed into the center. As discussed in Tanner & Arce (2011), the radius of the dynamical collapse in HH 211-mms could be only ∼870 au, adjusted to the new distance of 235 pc. As shown in their Figure 11, this is the radius where the specific angular momentum of the extended ammonia envelope decreases to roughly the same as that of the inner HCO⁺ envelope.

The growth of Keplerian disk radius from Class 0 to I phase has been studied by Yen et al. (2017). Figure 6 shows their plot after adding our measurement of HH 211-mms and the new measurement of HH 212 in Lee et al. (2017b). Previously, the trend of the disk growth with the protostellar mass in the early Class 0 phase could not be determined because no disk measurement was confirmed for the protostellar mass less than 0.2 M_⊙. In particular, the two small disk radii with protostellar mass <0.04 M_⊙ (the two leftmost open squares) were inferred from the observations at a resolution of ∼100 au and thus are quite uncertain. For B335, which has a protostellar mass of ≲0.05 M_⊙, a disk radius of ∼3 au was inferred from an observation at ∼50 au resolution, and thus is also very uncertain. In addition, the very small disk radius of B335 could result from magnetic braking (Yen et al. 2015). Now with our measurement of HH 211-mms, we can see more clearly that the disk radius is large enough to be measured with a current instrument (ALMA) in the earliest phase of star formation. The significance of this radius measurement can be gauged from Figure 6, where we present the expectations for two competing scenarios of protostellar disk growth. The first is based on the classic picture of Terebey et al. (1984), who considered the growth of a disk in the collapse of a singular isothermal sphere (SIS) with a solid-body rotation. In this case, the disk radius stays small initially, but grows rapidly with stellar mass at later times, as ${R}_{d}\propto {M}_{* }^{3}$. The reason for such a steep dependence is that the materials at small radii of the SIS rotate very slowly and, when they collapse, they form a very small disk initially. The disk size grows rapidly at later times, as the materials at larger radii of the SIS with much larger specific angular momenta collapse to the central region. The coefficient in front of the ${M}_{* }^{3}$ scaling depends on the isothermal sound speed and especially the initial rotation rate of the SIS, which is uncertain. In Figure 6, there are two dashed (cyan) lines for two coefficients chosen to roughly bracket the currently available data on late Class 0 and early Class I sources. Extension of these lines to earlier times when the protostellar mass is smaller represents the expectation of this "slow-start, rapid-growth" scenario for the youngest Class 0 disks based on the current data. The upper limit inferred for the disk radius for B335 and the lower limit inferred for its stellar mass appear to provide some support for this scenario. However, this support is rather weak, because the disk in B335 has never been detected. Without detecting the disk, it would be difficult to infer the stellar mass or put a strong upper limit on it.

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An alternative scaling was advocated by Basu (1998), based on the asymptotic state of the pre-stellar evolution of a rotating, magnetized dense core, which is expected to have a power-law distribution for both the column density Σ ∝ r⁻¹ and the angular speed ${\rm{\Omega }}\propto {r}^{-1}$ right before the formation of a central stellar object. Compared to the SIS rotating as a solid body in the first scenario, the materials at small radii rotate much faster; they collapse to form a much larger disk compared to the first scenario. Such a disk grows more slowly with the stellar mass at later times, as R_d ∝ M_*, because the specific angular momentum in the pre-collapse configuration increases with radius more slowly compared to the first scenario. The coefficient in front of the linear scaling depends on the sound speed, magnetic field strength, and the rotation rate, and can be different for different sources. In Figure 6, two (green) dot-dashed lines with different coefficients are plotted to roughly bracket the current data for the late Class 0 and early Class I sources. Extension of these lines to earlier times represents the expectation of this "early-start, slow-growth" scenario for the youngest Class 0 disks. Our measurement of the radius of HH 211-mms disk and estimate for its mass lie in the expected region, which provides support for this scenario; they are not consistent with the expectation of the "slow-start, rapid-growth" scenario based on Terebey et al. (1984). Indeed, the trend of linear growth of disk radius with protostellar mass appears to extend to the late Class I phase. However, the disk growth in this phase could be modified by magnetic braking, as suggested by our previous observation of HH 111 (Lee et al. 2016).

In SO, a disk atmosphere is seen on the dusty disk surfaces and a bipolar rotating molecular outflow is seen coming out from the inner disk, as in HH 212 (Lee et al. 2017b). The disk atmosphere has a radius of ∼12 au, similar to the expected radius of a Keplerian disk around the central protostar. The SO emission also shows a warm ring in the disk atmosphere. Such a warm SO ring has been detected before in other protostellar systems, e.g., HH 111 (Lee et al. 2016) and L1527 (Sakai et al. 2017), probably tracing an accretion shock created by a rapid decrease of the infall velocity near the centrifugal barrier where a Keplerian disk is formed. The warm ring in the NW is also expanding, and thus can also be produced or affected by an interaction with the rotating molecular outflow.

The rotating molecular outflow extends out to ∼30 au (∼013) from the inner disk, with its width increasing with distance. The width reaches ∼46 au (02) at a height of ∼23 au (01). The outflow shell can trace back down to the innermost part of the disk to within a few au of the protostar. The outflow has an expansion velocity of ∼6 km s⁻¹ and a specific angular momentum of ≲20 au km s⁻¹, although further observations with a better sensitivity are needed to confirm these values. As in HH 212 and others, more work is needed to confirm if the bipolar outflow really traces the wind from the disk or merely disk material pushed away further by a wide-angle wind (Lee et al. 2010). In addition, for a disk wind, we expect to see nested shells coming out from different radii of the disk. Thus, further observations are also needed to check if outflow shells coming out from different radii can be detected in different density tracers.