Formation and Atmosphere of Complex Organic Molecules of the HH 212 Protostellar Disk

The envelope can now be better studied at higher angular resolutions. As before, HCO⁺ emission is detected near the equatorial plane within ∼3 km s⁻¹ of the systemic velocity. Based on our analysis of the gas kinematics below and later in Section 3.3, the emission there shows an infall motion with some rotation and thus traces a flattened infalling-rotating envelope. In order to see the velocity distribution pictorially, we divide the velocity range into a low velocity range with $| {V}_{\mathrm{off}}| \leqslant 1.5$ km s⁻¹ and a high velocity range with $1.5\leqslant | {V}_{\mathrm{off}}| \,\leqslant 3$ km s⁻¹.

Figure 1(a) shows the HCO⁺ maps at low velocity at 01 resolution. The redshifted and blueshifted emissions near the equatorial plane (indicated by the orange lines) within a radius of ∼2'' of the central source trace the flattened envelope. Figure 1(b) shows the HCO⁺ maps at high velocity at 006 resolution. At high velocity, since the emission structure is more compact, a higher resolution is used. The innermost part of the envelope can be seen at high velocity down to ∼01 of the central source. As can be seen from these two figures, the envelope is flared, with a thickness increasing with increasing distance from the central source. For simplicity, the boundaries of the envelope are assumed to have a parabolic structure, with $z=a+{{bR}}^{2}$ in the cylindrical coordinate system. Here a is the position offset from the central source and b is a constant describing the curvature. Using a rough eye fitting to the redshifted and blueshifted HCO⁺ emission of the envelope at both low velocity (Figures 1(a)) and high velocity (Figure 1(b)), we obtained a = 0.05 and b = 0.45 for the upper boundary and a = −0.05 and b = −0.6 for the lower boundary, as delineated by the dotted parabolic curves. Note that since the boundaries are neither symmetric nor sharply defined, the parabolic curves are mainly to guide the readers.

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At low velocity as shown in Figure 1(a), the blueshifted emission of the envelope is seen across the central source, with the west side brighter than the east side. The redshifted emission is weaker and is seen mainly in the east. As discussed in Lee et al. (2014), this spatial distribution indicates that the envelope has mainly infall motion but some small rotation with the redshifted side in the east and the blueshifted side in the west. The redshifted emission is fainter and even absent in the west, due to a self-absorption in the near side of the infalling envelope (Evans 1999). An emission hole is seen at the center toward the dusty disk in both blueshifted and redshifted maps. This is because the dusty disk is bright and optically thick (Lee et al. 2017); thus, the emission behind it is blocked and the emission in front of it appears absorbed against the bright background. The emission above the upper envelope boundary and below the lower envelope boundary traces the outflow and jetlike emission and will be discussed in a future publication.

At high velocity as shown in Figure 1(b), the redshifted and blueshifted emissions are now seen on the opposite sides within ∼03 of the central source surrounding the dusty disk, indicating that the motion there becomes dominated by the rotation. No emission is detected toward the dusty disk within ∼01 of the center, because the disk continuum emission becomes optically thick there (Lee et al. 2017). The redshifted emission extending slightly to the south from the lower boundary could trace a low-velocity outflow coming out of the envelope. The blueshifted emission above the upper disk surface and below the lower disk surface is from the infalling envelope in the far side that is not blocked by the disk.

Figure 2(a) shows the position–velocity (PV) diagram of the envelope cut along the major axis (equator). It shows a blueshifted triangular structure pointing toward the high blueshifted velocity and a redshifted triangular structure pointing toward the high redshifted velocity, similar to those seen before at a lower resolution of ∼045 (Lee et al. 2014). As discussed by the authors, these features are signatures of infall motion in the envelope, with the blueshifted triangular structure coming from the far side of the envelope and the redshifted structure from the near side. The blueshifted triangular structure shifts slightly to the west because of a small rotation (going from the east to the west in the far side) in the infalling envelope. The base of the redshifted triangular structure near the systemic velocity is absent, due to the self-absorption in the near side, which is infalling toward the central source and thus preferentially absorbs the redshifted part of the emission (Evans 1999). This absorption by the infalling envelope on the near side is the reason why there is little redshifted HCO+ emission on the west side of the central source. At higher angular resolution of ∼01, the high redshifted (≳1.5 km s⁻¹) and high blueshifted (≲−2 km s⁻¹) emissions near the central source are now seen on the opposite sides of the source, confirming that the motion there becomes dominated by the rotation.

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At high resolution of ∼01, we can study the infall motion directly using the PV diagram of the envelope cut along the minor axis, as shown in Figure 2(b). The PV structure for the faint emission at high velocity with $| {V}_{\mathrm{off}}| \gt 2$ km s⁻¹ should be mainly from the outflow and jetlike emission along the jet axis, as seen in Figure 7(b) in Lee et al. (2014). In addition, the emission on the redshifted side suffers significantly from the self-absorption. Therefore, we only focus on the low-velocity part ($| {V}_{\mathrm{off}}| \,\lt 2$ km s⁻¹) on the blueshifted side as pointed by the arrows, and we model it in Section 3.3 below to see whether the infall velocity increases toward the center.

Line emissions from four COMs and D₂CO are detected toward the center (see Table 5). Figure 3 shows the integrated intensity maps of CH₃OH (methanol, three lines) and CH₂DOH (deuterated methanol, 18 lines at 13 frequencies) lines in various transitions. Since the emission morphology is similar, the maps of the same molecule are stacked together to make a map with a higher signal-to-noise ratio (S/N). Figure 4 shows the stacked maps of CH₃OH and CH₂DOH, along with the maps of three other molecules, CH₃SH (methyl mercaptan), NH₂CHO (formamide), and D₂CO (doubly deuterated formaldehyde), all at ∼004 resolution.

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Unlike HCO⁺, the molecules CH₃OH, CH₂DOH, and CH₃SH are only detected within ∼40 au (01) of the central source, and the molecules NH₂CHO and D₂CO are only detected closer in (within ∼30 au). Notice that CH₂DOH is a D-substituted methanol and CH₃SH is a sulfur analogue of methanol, and they both have the same spatial distribution as the methanol. The emission structures are more extended for CH₃OH, CH₂DOH, and CH₃SH than for NH₂CHO and D₂CO. The A-coefficients of these five molecules can be roughly divided into two groups, one for CH₃OH, CH₂DOH, and CH₃SH having a value of ∼10⁻⁴ s⁻¹, and the other for NH₂CHO and D₂CO having a value of (1−3) × 10⁻³ s⁻¹, as seen in Table 5. Thus, the difference in the spatial distribution of these molecules might be partly due to the different values of their A-coefficients, which could reflect different critical densities. These complex molecules are detected at ∼005 (20 au) above and below the midplane, and thus above the upper dusty disk surface in the north and below the lower dusty disk surface in the south. The observed morphologies are suggestive of the COMs tracing the outer layers (i.e., atmosphere) of the disk, although it is also plausible that they trace the base of a disk wind. We favor the former interpretation over the latter because, as we will show below, the radial component of the velocity for these layers is much smaller than the rotational component. In addition, based on our analysis of the gas kinematics below and later in Section 3.3, the emission there shows a Keplerian rotation and thus indeed traces the atmosphere of a Keplerian rotating disk. Again, no molecular line emission is detected toward the opaque dusty disk. Since the dusty disk is optically thick, we cannot determine whether this is because of an absorption against the bright dust continuum or because of no emission of these molecules in the disk. Since the disk midplane has a temperature of ∼70 K at ∼40 au (Lee et al. 2017), these molecules could also be depleted onto the dust grains near the midplane at the observed radius. The emission is brighter in the south than in the north. This is in opposition to the dust emission, which is brighter in the north. The redshifted emission and blueshifted emission are seen on the opposite sides of the jet axis, confirming that the disk atmosphere traced by the COMs is rotating. Notice that in the south in the methanol and deuterated methanol maps, the blue and red emissions have some overlap at small radii, due to the low velocity resolution and (thermal and possibly turbulent) line broadening, as discussed later. The emission maps show mainly a two-peak structure in the atmosphere, with one peak to the east and the other to the west of the rotational axis, tracing the two limb-brightened edges of a rotating ring there, as discussed later. NH₂CHO and probably D₂CO could trace a rotating ring closer to the rotational axis than CH₃OH, CH₂DOH, and CH₃SH, because their emission peaks are closer in.

The stacked CH₃OH and CH₂DOH maps have sufficient S/N for kinematic study. Figures 5(a) and (b) show the PV diagrams obtained by cutting their emission across the upper (blue) and lower (red) disk atmospheres parallel to the disk major axis. Here the upper disk atmosphere means the atmosphere in the north above the dusty disk surface, and the lower disk atmosphere means the atmosphere in the south below the dusty disk surface. The PV structure is similar in these two molecules, in agreement with them coming from the same region in the disk atmosphere. In addition, the PV structures in the upper and lower disk atmospheres are also similar, indicating that the atmospheres on both sides of the disk have a similar motion. At low velocity ($| {V}_{\mathrm{off}}| \lesssim 2$ km s⁻¹), linear PV structures are seen across the rotational (jet) axis, as indicated by the solid lines, which are obtained from a single linear fit to the linear PV structures seen in both methanol and deuterated methanol. At the two ends of the linear structures, the velocity becomes differential and increases toward the center. We can map these PV structures using the stacked deuterated methanol map, which has a higher S/N than the stacked methanol map. Figure 6(a) shows the maps for both the linear part (green contours) and the differential part (red and blue contours for redshifted and blueshifted emission, respectively). For the linear part, the map shows a band of emission above the upper dusty disk surface and a band below the lower dusty disk surface. For the differential PV part, both the blueshifted and redshifted emissions are seen on the two edges of the disk atmosphere. In the south, the emissions also extend inward to the rotational axis. As shown by the magenta lines, their scale height decreases as they go closer to the rotational axis, indicating that the disk atmosphere traced by COMs is flared, as discussed below. In addition, their thickness (FWHM) also decreases toward the rotational axis.

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Figure 6(b) shows a cartoon to explain the PV and the emission structures of the line emission, by adding a disk atmosphere (outlined by the curves and lines) on the dusty disk (color disk, with the color changing from blue to orange for the cold to hot disk surface). As mentioned earlier, the disk is almost edge-on, with its near side tilted slightly by 4° to the south. The disk atmosphere is assumed to be flared with the scale height (magenta lines) increasing with the radius, like the dusty disk. As can be seen from the cartoon, we can only detect the outermost ring of the disk atmosphere, which is not blocked by the dusty disk. For the upper disk atmosphere, the front part of the ring is projected onto the dusty disk, due to the tilt, and thus is absorbed against the bright disk continuum emission. Hence, the observed linear PV structure and its associated emission are from the back part of the ring. For the lower disk atmosphere, the back part of the ring is blocked by the disk, and thus the observed linear PV structure and its associated emission are from the front part of the ring. The radial (infall or expansion) motion of the ring can be studied with the PV diagrams of methanol and deuterated methanol along the minor axis, as shown in Figures 5(c) and (d). It it clear from the PV diagrams that the infall velocity there has dropped to zero. It has a small range of velocities, probably due to thermal and turbulent (due to, e.g., shock) broadening in the line emission and the low velocity resolution of ∼0.85 km s⁻¹ in the stacked maps.

Besides the outermost ring, the part of the disk atmosphere along the major axis (magenta lines) can also be detected, as shown in Figure 6(b). This part produces the blue- and redshifted emission in the disk atmosphere extending inward to the rotational axis, with a scale height decreasing toward the center, associated with the differential PV structure. For the upper disk atmosphere, the inner part is not detected because of the absorption against the dusty disk. For the lower disk atmosphere, the inner part can be detected, because the dusty disk, with density decreasing with height (Lee et al. 2017), becomes optically thin at the highest rim. This allows us to see the atmosphere further in, as seen in the observations.

In this section, we adopt the toy model developed by Sakai et al. (2014), which has been used to reproduce the similar PV structures of the envelope and disk in L1527. In this model, the gas motion in the envelope is approximated by the motion of a particle with conservation of both specific angular momentum and total energy. If the total energy is negligible at large distances and the specific angular momentum l is conserved in the infalling material, then the radial velocity v_r and the rotation velocity v_ϕ (where ϕ is the azimuthal angle) at radius r from the protostar are given by

$$\begin{eqnarray}&&{v}_{r}=-\sqrt{\displaystyle \frac{2{GM}}{r}-\displaystyle \frac{{l}^{2}}{{r}^{2}}}\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{v}_{\phi }=\displaystyle \frac{l}{r},\end{eqnarray} \tag{ 2 }$$

where M is the mass of the central protostar plus disk. The radius at which the gravitational acceleration is balanced by the centrifugal force is given by

$$\begin{eqnarray}&&{r}_{c}=\displaystyle \frac{{l}^{2}}{{GM}}.\end{eqnarray} \tag{ 3 }$$

This is the CR, where the radial velocity is equal to the rotation velocity, both with a magnitude of GM/l. The radius at which all the kinetic energy is converted to the rotational motion is given by

$$\begin{eqnarray}&&{r}_{0}=\displaystyle \frac{{l}^{2}}{2{GM}}.\end{eqnarray} \tag{ 4 }$$

This is the radius of the CB, where ${v}_{\phi }=2{GM}/l$. It is half of the CR. The infalling and rotating gas cannot move inward of the CB, unless it loses kinetic energy and angular momentum. If the gas does lose kinetic energy and angular momentum, then a disk is expected to form with a Keplerian rotation.

The envelope outside the disk is flared with the structure outlined by the dotted parabolic curves in Figure 1(a). For given l and M, we can derive model PV structures for the envelope along the major and minor axis, by calculating the highest and lowest velocities at each position offset from the central source. These model PV structures can then be used to fit the outer boundaries of the observed PV structures. From M, we also can calculate the Keplerian rotation for the disk. Thus, the observed kinematics of the envelope and disk atmosphere can be fitted simultaneously with only two parameters, l and M.

The best-fit parameters to both the envelope and disk kinematics simultaneously are found to be l = 140 ± 30 au km s⁻¹ and M = 0.25 ± 0.05 M_⊙, by matching (1) the outer boundaries of the PV structures of the envelope along the major and minor axis, (2) the maximum velocity in the PV diagram of the envelope along the major axis at the CB, (3) the maximum infall velocity of the envelope at the protostar position, and (4) the differential PV structure seen in the disk. For the envelope, the fit is based more on the blueshifted side, because the redshifted side suffers from self-absorption. As can be seen in Figures 7(a) and (b), the model PV structures delineate the outer boundaries of the observed PV structures reasonably well on the blueshifted side, and they also appear reasonable on the redshifted side. The best-fit parameters result in a CB at ∼011 ± 002 with a maximum velocity of ∼3.2 km s⁻¹, roughly matching that seen in the observed PV structure in Figure 7(a). The maximum infall velocity is ∼1.6 km s⁻¹, similar to that seen at the source position in Figure 7(a) and similar to the maximum velocity in Figure 7(b). For the disk, as marked in the figure, the CB roughly matches the two end positions of the linear PV structures seen in methanol and deuterated methanol, and the Keplerian rotation also roughly matches the differential PV structures on both the redshifted and blueshifted sides. In summary, this simple toy model can broadly reproduce all the important features in the PV diagrams of the envelope and disk. The observed infall velocity indeed increases toward the center, as expected for a gravitational collapse.

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With 18 deuterated methanol lines (at 13 frequencies) detected, we can construct a population diagram to estimate the mean excitation temperature and the column density of the molecule in the region traced by the COMs. It is a diagram that plots the column density per statistical weight in the upper energy state in the optically thin limit, ${N}_{u}^{\mathrm{thin}}/{g}_{u}$, versus the upper energy level E_u of the lines. Here ${N}_{u}^{\mathrm{thin}}=(8\pi k{\nu }^{2}/{{hc}}^{3}{A}_{{ul}})W$, where the integrated line intensity $W=\int {T}_{B}{dv}$, with T_B being the brightness temperature.

The integrated line intensity of each transition can be measured toward the lower disk atmosphere, where the emission is better detected, using the total intensity map (integrated over velocity, as shown in Figure 3) with a 2σ cutoff. The resulting population diagram is shown in Figure 8. Fitting the data points of deuterated methanol, we estimate a mean excitation temperature of 165 ± 85 K and a mean column density of (9.2 ± 2.0) × 10¹⁶ cm⁻². Since the data points are scattered as a result of the low S/N, the fitting results have a big uncertainty in excitation temperature. Nevertheless, the inferred excitation temperature is consistent with the temperature at peak abundance for (deuterated) methanol in warm-up models of hot cores, which is estimated to be ∼120 K (Garrod & Widicus Weaver 2013) or ∼130 K (Müller et al. 2016). This broad consistency supports the notion that the observed (deuterated) methanol is produced by warming of icy grains in the disk atmosphere. If this is indeed the case, the COM-producing icy grains should stay high up in the disk atmosphere, with interesting implications for grain growth and settling that should be explored with detailed modeling in future investigations.

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We also measure the integrated line intensity of the methanol lines. Since only three lines are detected and the data points are scattered, we cannot estimate the temperature and column density reliably for methanol. Since the methanol has a similar spatial distribution to the deuterated methanol, we assume the same temperature for the methanol and then estimate the column density. Based on the two lines with an upper energy level ${E}_{u}\gt 300\,{\rm{K}}$, which are less optically thick (with a peak brightness temperature close to 80 K), we can scale down the data points of methanol by 7.4 to roughly match the best-fit solid line of the deuterated methanol. This implies a column density of ≳(3.4 ± 1.0) × 10¹⁷ cm⁻² for methanol and thus an abundance ratio of [CH₂DOH]/[CH₃OH] ≲ 0.27.

Methanol lines have been detected before at ∼055 resolution toward the center in 19 transitions, including the one here at 345.9039 GHz, with the upper energy level reaching 750 K (Leurini et al. 2016). The excitation temperature of the methanol was estimated to be ∼295 K. Thus, the temperature estimated here could be underestimated by a factor of ∼2.

The integrated line intensity of CH₃SH is ∼88 K km s⁻¹ toward the disk atmosphere in the southern hemisphere. Assuming the same excitation temperature of 165 K for CH₃SH, the column density is found to be ∼1.0 × 10¹⁷ cm⁻², using the rotation partition function in Xu et al. (2012). Thus, [CH₃OH]/[CH₃SH] ∼ 3.4. The integrated line intensity is ∼70 K km s⁻¹ for NH₂CHO and 77 K km s⁻¹ for D₂CO. The excitation temperature of NH₂CHO and D₂CO is unknown. If we assume the same excitation temperature, then the column density is ∼1.6 × 10¹⁵ cm⁻² for NH₂CHO and ∼3.2 × 10¹⁵ cm⁻² for D₂CO.

Our toy model here is adopted from Sakai et al. (2014), and it can be considered as a modified version of our previous model. In our previous model, the infalling envelope was assumed to have a freefall motion produced by the gravity of the central source (protostar plus disk) and a small rotation with conservation of specific angular momentum (Lee et al. 2014). Here the infall motion is no longer a pure freefall, but a freefall reduced by the rotational energy according to the conservation of total energy. In this case, both the infall and rotation motions produce constraints on the mass of the central source. In addition, the infall velocity reaches a maximum value at the CR and then decreases to zero at the CB, providing a transition region for a disk to form. As a result, the disk does not form immediately at the CR as we assumed before, but it can form interior to the CB. In our best-fit model, the specific angular momentum is ∼140 au km s⁻¹, the same as before. However, the mass of the central source is ∼0.25 M_⊙, higher than before, which was ∼0.18 M_⊙. As discussed earlier, this is because the mass here gives rise to both the rotation and infall motions, instead of only the infall motion as assumed in our previous model. Hence, the resulting CR is ∼88 au (022), smaller than that estimated before, which was ∼120 au (03).

From the model results, we can investigate in detail the forming process of a rotationally supported Keplerian disk in an infalling-rotating envelope in the star formation. Figure 9 shows a schematic diagram of the envelope and disk within ∼500 au of the central source in HH 212. In our best-fit model to the gas kinematics in HCO⁺ and the COMs, the CR is ∼88 ± 18 au and the CB is at ∼44 ± 9 au. This indicates that HCO⁺ traces the infalling-rotating envelope extending down to ∼44 au and the COMs trace the atmosphere of a Keplerian rotating disk with a radius of ∼44 au. In addition, the innermost envelope in between the CR and the CB can be considered as a transition region, where the infall velocity decreases rapidly to zero so that the envelope can transform into a Keplerian disk. In the schematic diagram, the envelope structure is derived from the HCO⁺ envelope, as described in Section 3.1. The disk is composed of two components: one is the dusty disk seen in continuum in Lee et al. (2017), and the other is the disk atmosphere (surface) seen here in COMs. The dusty disk has an outer radius of ∼68 au (017). However, based on our model result, only the inner part within ∼44 au can be the Keplerian rotating disk, while the outer part of the dusty disk is in the transition region.

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In the dusty disk, the continuum emission is found to become optically thick at r ∼ 40 au, due to a rapid increase in density (Lee et al. 2017). Interestingly, this radius is similar to the radius of the CB, suggesting that the increase in density is caused by the rapid decrease of the infall velocity in the transition region, which is expected in our model. Since the infall velocity decreases to zero at the CB, the material there should be almost stagnated, causing the material to accumulate locally and the disk to become optically thick. Also due to this rapid decrease in the infall velocity, the rotation becomes larger than the infall motion in the transition region, causing the blueshifted emission and redshifted emission there to be seen on the opposite sides of the central source, as shown in Figure 1(b). In the transition region, the dust continuum emission is only detected in the midplane, as shown in the schematic model in Figure 9(b), suggesting that the envelope is denser near the midplane. This could be due to a magnetic effect. If the infalling material is magnetized with an hourglass magnetic field morphology, the material would be falling toward the midplane, as expected for a pseudodisk (Allen et al. 2003).

The dusty disk is flared and in vertical hydrostatic equilibrium (Lee et al. 2017), as expected for an accretion disk. More importantly, its scale height reaches the maximum value of ∼12 au at r ∼ 36 au near the CB, where the peaks of the methanol, deuterated methanol, and methyl mercaptan emissions are detected. As discussed earlier, these emission peaks trace a warm ring in the disk atmosphere with a temperature of 165–295 K. This ring of warm emission could trace a weak shock, e.g., an accretion shock, produced by the rapid decrease of the infall velocity near the CB. Similar weak shocks have been detected in SO in other protostellar systems L1527 (Sakai et al. 2017) and HH 111 (Lee et al. 2016), marking the transition from an infalling envelope to a Keplerian rotating disk. The infall velocity there is almost zero (see Figures 5(c) and (d)), and the rotation velocity interior to that radius can be roughly fitted with a Keplerian rotation (see Figures 7(c) and (d)), indeed supporting that a Keplerian disk has formed there.

The disk mass integrating from r ∼ 36 au toward the center is ∼0.03 M_⊙, using the disk density profile derived from modeling the disk continuum emission in Lee et al. (2017), assuming that the continuum emission is the dust thermal emission. As discussed by the authors, this mass is an upper limit because significant continuum emission could come from dust scattering of the disk thermal emission. Thus, the mass of the central protostar is >0.22 M_⊙. As a result, the disk mass within ∼36 au of the central protostar is <13% of the protostellar mass, further supporting that the Keplerian disk indeed can form with a radius of ∼36 au.

As discussed earlier, the infalling material has to lose a fraction of the kinetic energy and angular momentum in order to form a Keplerian disk. In our observations, the ring of warm molecular gas detected near the CB supports that a fraction of the kinetic energy has indeed been converted to thermal energy through the shock, if the ring is heated by a shock. In the transition region, a low-velocity outflow or wind is seen in HCO⁺ extending out from the lower surface in the east (see Figure 1(b)), which may carry away a fraction of the angular momentum. This low-velocity outflow may in turn be due to the magnetic braking (Allen et al. 2003). Further observations are needed to check whether such an outflow is also seen from other surfaces in the transition region.

Similar envelope kinematics and disk formation have been suggested in another Class 0 system, L1527 (Sakai et al. 2014, 2017). In that system, a geometrically thin infalling envelope is seen in molecular gas traced by CCH. It broadens up in the transition region before joining the Keplerian rotating disk, probably because an accretion shock heats up the material there (Sakai et al. 2017). A similar broadening behavior is also seen here in the transition region in dust continuum, although not in molecular gas traced by HCO⁺ (see Figure 9(b)). In L1527, the central mass is ∼0.18 M_⊙, the specific angular momentum in the envelope is ∼180 au km s⁻¹, and thus the CB is at ∼100 au, about twice as large as in HH 212. A likely Keplerian rotating disk is also detected interior to the CB, with a radius of ∼100 au. Similar disk radius has also been claimed in other Class 0 systems (Lee et al. 2009; Murillo et al. 2013; Yen et al. 2017).

A few Class I Keplerian disks have been claimed in Taurus (Harsono et al. 2014), with a radius of ≲100 au, similar to that found in the Class 0 disks. According to Equation (4) in our model, the CB and thus the disk radius are proportional to the square of the specific angular momentum in the infalling envelope. Therefore, the small radius of those disks could be due to the low specific angular momentum of ≲200 au km s⁻¹ in their infalling envelopes, as in the Class 0 sources. Recently, a small Class I Keplerian disk with a slightly larger radius of ∼100–200 au has also been detected in HH 111 in Orion (Lee et al. 2016). However, unlike the Class I sources in Taurus, HH 111 has a much larger specific angular momentum of ∼1550 au km s⁻¹ in its envelope. Its Keplerian disk is not much bigger than those in the Class 0 sources because a large fraction of the specific angular momentum is lost, probably due to magnetic braking (Lee et al. 2016). Thus, the disk radius could be affected significantly by other effects and hence becomes much smaller than the CB.

Unlike HCO⁺, the COMs are only detected interior to the CB within ∼40 au of the central protostar in the atmosphere of the flared disk. Their emission can be detected down to ∼10 au of the central protostar. No emission is detected further in because the disk is bright and optically thick in dust continuum, and thus the emission is either blocked or absorbed against it. The emission of the methanol, deuterated methanol, and methyl mercaptan peaks near the CB and thus could be caused by a shock interaction in that region, as discussed earlier. On the other hand, since the disk is flared and thus exposed to the radiation of the central protostar, stellar radiative heating and/or mechanical heating (by a stellar or inner-disk wind) could play a role in warming the region where these molecules are detected. This is especially true for the molecules detected at small radii inside the CB, which is less affected by the envelope–disk transition, if at all. Formamide and deuterated formaldehyde are detected closer in, and thus their emission is more likely caused by the radiation heating of the protostar as well. No emission of these COMs is detected beyond 40 au, where the dusty disk is thinning out and thus could be self-shielded from the radiation (or outflow) of the protostar.

Our observations show the first spatially resolved detection of these COMs in the gas phase in the disk atmosphere in the Class 0 phase of star formation, opening up a window to study their formation mechanism. Methanol is known to be formed efficiently in the ice mantle of dust grains (Herbst & van Dishoeck 2009). Here the abundance ratio of [CH₂DOH]/[CH₃OH] (≲0.27) is about 4 orders of magnitude higher than the cosmic abundance of deuterium of D/H ∼ 10⁻⁵. This high degree of deuteration strongly supports the formation of methanol and deuterated methanol in the ice mantle on the dust grains (Ceccarelli et al. 2001; Parise et al. 2006). We detect these molecules in the gas phase because they are desorbed (evaporated) from the dust grains, due to the heating by a shock and/or the radiation/outflow of the protostar. This scenario is supported by the fact that the excitation temperature inferred from the energy diagram for deuterated methanol is consistent with the temperature at peak abundance in models for producing this gas-phase molecule from warming of icy grains (see Section 3.4). Methyl mercaptan has the same spatial distribution as the methanol and thus could be formed on the dust grains as well. Recently, methyl mercaptan has been detected toward another low-mass star-forming region, IRAS 16293–2422, and argued to be formed in the ice mantle on the dust grains and then desorbed (Majumdar et al. 2016). Detection of doubly deuterated formaldehyde (D₂CO) is also an indicator of active grain surface chemistry (Ceccarelli et al. 2001). Formamide has been detected in both high-mass star-forming regions (Adande et al. 2013) and low-mass star-forming regions (Kahane et al. 2013; López-Sepulcre et al. 2015). It could be formed through the interaction between H₂CO and NH₂ or ${\mathrm{NH}}_{4}^{+}$ in the gas phase (López-Sepulcre et al. 2015). The spatial distribution is similar to that of D₂CO and thus the implied H₂CO, supporting this formation mechanism. However, this molecule could also be formed on icy grain mantles, e.g., via hydrogenation of HNCO (Mendoza et al. 2014; López-Sepulcre et al. 2015). It is detected closer to the protostar than the methanol, which is somewhat surprising in this scenario because, in the standard warm-up models of hot cores, its temperature at peak abundance (∼120 K) is very similar to that for methanol (and deuterated methanol), which is estimated to be ∼120 K (Garrod & Widicus Weaver 2013) or ∼130 K (Müller et al. 2016). The temperature at peak abundance for CH₃SH is similar to that of NH₂CHO (∼120 K), which is much higher than that of D₂CO (∼40 K; R. Garrod 2017, private communication).

As a result, all of our detected COMs could be formed in the ice mantle on the dust grains, either in the envelope or in the disk. Recently, methanol has been detected in the gas phase in a protoplanetary disk (TW Hya) in the T Tauri phase of star formation, with its formation in the disk (Walsh et al. 2016). Here, our detected COMs are also more likely to be formed in the disk, either on the surface or in the midplane, and then brought to the surface by turbulence (Furuya & Aikawa 2014). This is because the COMs detected here are associated with the warm atmosphere of the disk rather than a rapidly infalling inner envelope that is warmed up by stellar radiation or some other means. This is important because icy grains can in principle stay longer in the rotationally supported disk than in the free-falling envelope, which would allow more time for the COMs to form (e.g., Jørgensen et al. 2005). On the other hand, if there is rapid grain growth, large grains may settle quickly toward the midplane, where the temperature may be too low to efficiently produce COMs. Our vertically resolved observations provide strong constraints for models of COM formation and transport.

Methanol has been proposed as a building block for more complex species of fundamental prebiotic importance, like amino acid compounds (Walsh et al. 2016). Formamide has also been proposed as a prebiotic precursor because it could lead to the synthesis of biomolecules, e.g., amino acids and amino sugars, which are the main components for the onset of both (pre)genetic and (pre)metabolic processes, respectively (Saladino et al. 2012). Therefore, the COMs have started to form on disks in the earliest phase of star formation and may play a crucial role in producing the rich organic chemistry needed for life.