The Circumestellar Disk of the B0 Protostar Powering the HH 80-81 Radio Jet

It is well stablished that most low-mass stars develop accreting disks in their earliest stages previous to the pre-main-sequence phase (Adams et al. 1987; Shu et al. 1987; Butner et al. 1991; for the first HST images of disks, see O'dell et al. 1993; O'dell & Wen 1994; Burrows et al. 1996). These disks may be the seed by which planets are formed (see recent reviews by Helled et al. 2014 and Baruteau et al. 2014). The properties of the accretion disks are better studied in the T Tauri stage since the surrounding material has already infallen into the disk-protostar system or has been dispersed by the strong outflow activity (e.g., Hogerheijde et al. 1998; André et al. 2004). Still, recent works have found disks even in the earliest embedded stages of Class 0 protostars (e.g., Tobin et al. 2012; Murillo & Lai 2013; Rao et al. 2014). Class 0 disks are, in general, also smaller in size (≲50 au; e.g., Tobin et al. 2013; Segura-Cox et al. 2016) than T Tauri disks (200–300 au; e.g., Takakuwa et al. 2012; Harsono et al. 2014; Piétu et al. 2014). Disks are usually detected using their (sub)millimeter continuum emission and the emission of major CO isotopes. From the spectral line observations, the kinematical structure of disks around T Tauri protostars is found to be consistent with Keplerian motions (Guilloteau & Dutrey 1998; Guilloteau et al. 1999; Brinch et al. 2007; Lommen et al. 2008; Jørgensen et al. 2009; Schaefer et al. 2009; Takakuwa et al. 2012; Piétu et al. 2014), while it is more difficult to disentangle the kinematic signature of rotation and infalling motions in disks/envelopes of Class 0 protostars (Takakuwa et al. 2007; Brinch et al. 2009; Tobin et al. 2012).

Accretion disks around massive stars are a much rarer phenomenon. This can be explained due to an observational bias: massive young stars dynamically evolve much faster and are located at farther distances. However, it is still a matter of debate whether the most massive stars are ever associated with accretion disks. Most of the reported accretion disks around massive stars are mostly associated with early B-type protostars (Cesaroni et al. 2005; Patel et al. 2005; Franco-Hernández et al. 2009; Fernández-López et al. 2011b; Wang et al. 2012; Sánchez-Monge et al. 2013; Beltrán & de Wit 2016), although there is some evidence of disks around O-type stars (Johnston et al. 2015; Ilee et al. 2016).

The massive star-forming region GGD27 (IRAS 18162−2048) is located at a distance of 1.7 kpc (Gyulbudaghian et al. 1978). It harbors a cluster of IR, millimeter, and centimeter sources tracing young stellar objects in different evolutionary stages (Aspin et al. 1991; Aspin & Geballe 1992; Gomez et al. 1995; Stecklum et al. 1997; Gómez et al. 2003; Qiu et al. 2008; Qiu & Zhang 2009). Some of these sources are associated with molecular outflows and jets. In particular, Fernández-López et al. (2013) find three molecular outflows powered by protostars embedded in MM2; two of them appear to be monopolar. In addition, the main millimeter source, MM1, launches the spectacular (14 pc long) and highly collimated radio jet known as HH 80-81-80N, which is powered by a massive early B-type protostar (Martí et al. 1993, 1995, 1998; Masqué et al. 2012, 2015). The HH 80-81-80N radio jet is the first one in which polarized emission due to relativistic electrons has been detected, indicating the presence of a magnetic field aligned with the jet (Carrasco-González et al. 2010). This is highly indicative that the jet is launched from an accretion disk (Frank et al. 2014). Indeed, recent (sub)millimeter high-angular resolution interferometric observations show evidence of the presence of an accretion disk surrounding the massive protostar (Fernández-López et al. 2011a, 2011b; Carrasco-González et al. 2012, hereafter FL11a, FL11b and CG12): a hot ($T\simeq 150$ K) and very dense ($n({{\rm{H}}}_{2})\simeq {10}^{9}$ cm⁻³) molecular rotating disk-like structure with a radius of $\sim 0\buildrel{\prime\prime}\over{.} 5$ (850 au), with its rotation axes parallel to the radio jet, and surrounding a dusty disk with a radius of $\sim 0\buildrel{\prime\prime}\over{.} 15$ (200 au; FL11a, CG12). The estimated centrifugal radius, $\simeq 650\,\mathrm{au}$ (CG12), suggests that within the uncertainties the observed molecular and dusty rotating structure is an accretion disk. From the available observations, a dynamical mass (disk plus protostar) of $11\mbox{--}15\,{M}_{\odot }$ and an accretion rate $\sim {10}^{-4}\,{{M}}_{\odot }$ yr⁻¹ (FL11b, CG12) have been inferred.

In this paper, we present Submillimeter Array (SMA) observations carried out at 345 GHz at an angular resolution of $0\buildrel{\prime\prime}\over{.} 4$. The observations are briefly described in Section 2 and the molecular line and dust continuum maps are presented in Section 3. An analysis of the kinematic behavior of the rotating disk-like structure from a selected sample of molecular line channel maps is shown in Section 4. In Section 5, we discuss the chemical and physical properties of the molecular gas detected with the SMA. Finally, in Section 6, we draw our main conclusions.

The SMA observations were taken on 2011 July 18 and October 3 in the extended and very extended configurations, respectively. The observations were done using the 345 GHz receivers and the quarter wave plates (QWP). During the observations, the QWP are rotated in order to measure the four circular polarization cross-correlations for each baseline, LL, RR, LR, and RL (R and L stand for right and left circular polarization). Marrone et al. (2006) and Marrone & Rao (2008) describe in detail the SMA polarimeter as well as the polarization calibration strategy. The receiver was tuned to cover the 332.1–336.0 and 344.0–347.9 GHz frequency ranges in the lower (LSB) and upper (USB) sidebands, respectively. The phase center of the telescope was pointing at $\alpha ({\rm{J}}2000.0)={18}^{{\rm{h}}}{19}^{{\rm{m}}}12\buildrel{\rm{s}}\over{.} 10$ and δ(J2000.0) = −20°47'3000. The correlator provided a spectral resolution of about 0.8 MHz (i.e., 0.7 km s⁻¹ at 345 GHz). The gain calibrator was the QSO J1733−130. The bandpass and polarization calibrator was 3c454.3, which was observed in a parallactic angle range of ∼120°. The absolute flux scale was determined from observations of Callisto. The flux uncertainty was estimated to be ∼20%. The instrumental polarization was corrected at an accuracy level of ≃0.1%. The data were reduced using the MIRIAD software package (Wright & Sault 1993). The continuum and line molecular emission were separated in the visibility space using the MIRIAD task uvlin. An iterative process of phase-only self-calibration was performed using the continuum Stokes I data. We started with a time interval of 20 minutes for the gain solutions. Then we decreased the interval in the subsequent steps until we reached an interval of 5 minutes. At the end of the self-calibration the rms noise decreased by about 30%. The derived gain solutions were applied to the molecular line data.

The continuum emission maps were obtained using the whole available bandwidth by setting a robust weighting of 0.5 and selecting the multi-frequency synthesis option in the MIRIAD task invert. The resulting synthesized beam full width at half maximum (FWHM) was $0\buildrel{\prime\prime}\over{.} 48\times 0\buildrel{\prime\prime}\over{.} 35$ with a position angle of $29^\circ$. The achieved rms noise for the Stokes I continuum map was 3.4 mJy beam⁻¹, and for the Stokes Q and U continuum maps was 1.6 mJy beam⁻¹. The larger rms noise of the Stokes I is due to the limited dynamic range of the array. For the molecular line emission, channel maps were done using a robust weighting of 2.0 (equivalent to Natural weighting). This yielded synthesized beams sizes (FWHM, PA) between $0\buildrel{\prime\prime}\over{.} 45\times 0\buildrel{\prime\prime}\over{.} 34$, 31° and $0\buildrel{\prime\prime}\over{.} 47\times 0\buildrel{\prime\prime}\over{.} 35$, 31°, which are the values for the lines with the highest and lowest frequencies, respectively. Figures were created using the GREG package (from the GILDAS⁷ software). The CO 3–2 maps from the observations presented here were already presented in Fernández-López et al. (2013).

3.1. 880 $\mu m$ Continuum Emission

Figure 1 shows the 880 μm (340.0 GHz) continuum map toward GGD27 obtained with the SMA. This map is in good agreement with the subarcsecond 1.35 mm continuum maps by FL11a, where the sources were detected. Table 1 shows the position, peak intensity, and flux density of the sources. MM1 shows compact emission. A Gaussian fit to this source yielded a deconvolved size of $\simeq 0\buildrel{\prime\prime}\over{.} 17$, indicating that the source radius is ∼150 au, which is coincident with the upper limit found by FL11a. However, the fit cannot constrain whether the source is elongated in a particular direction. MM2(W) and MM2(E) are surrounded by weak emission at a ∼15 mJy beam⁻¹ level extending ∼1''(about 1700 au). No dust continuum emission is detected around the warm molecular core (WMC; Qiu & Zhang 2009).

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Table 1.  880 μm Continuum Emission

	R.A.	Decl.	${I}_{\nu }^{\mathrm{peak}}$	${S}_{\nu }^{\mathrm{int}}$
Source	18h19h	$-20^\circ 47^{\prime}$	(mJy beam−1)	(mJy)
MM1	12098	3102	624 ± 4	732 ± 9
MM2(E)	12515	2750	102 ± 4	350 ± 23a
MM2(W)	12462	2750	33 ± 4	⋯
WMCb	12450	2470	≲16

Notes.

^aTotal flux of MM2(E) and MM2(W). ^bPosition from Qiu & Zhang (2009).

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No continuum polarization is detected above the 3σ level in the Stokes Q and U maps. This yields an upper limit (at 3σ) of polarization of 0.8% and 4.7% for MM1 and MM2(W), respectively. The MM1 upper limit is significantly lower than the typical values found in millimeter interferometric observations of dense cores around low- and high-mass star-forming regions (∼2%–10%, e.g., Girart et al. 1999, 2006, 2009; Lai et al. 2003; Hull et al. 2014; Zhang et al. 2014), but it is not far from the values found in disks around low-mass young stellar objects (Hughes et al. 2013; Rao et al. 2014; Stephens et al. 2014; Kataoka et al. 2016).

3.2. Molecular Emission in MM1

Previous arcsecond observations show that in GGD27 there are three sites with bright molecular emission (e.g., Qiu & Zhang 2009): two of them are sites of massive star formation, GGD27 MM1 and MM2, and the WMC, which does not have clear signs of star formation. The new subarcsecond angular resolution observations over the whole observed spectra (totaling about 7.8 GHz) show very different molecular characteristics in the three molecular sources (see Figure 2). MM2 and WMC present an almost empty spectra, showing no emission lines in the whole spectrum except for the CO 3–2 line, and marginal emission of the SO 9₈–8₇, CH₃OH ${7}_{\mathrm{1,7}}\mbox{--}{6}_{\mathrm{1,6}}$ lines for WMC, and of the H¹³CO⁺ 4–3 line for MM 2. This is different to what has been found previously at both lower angular resolution and lower frequencies, especially toward WMC, where several relatively complex molecules were clearly detected, e.g., CH₃OH, CH₃CN, or HNCO (Qiu & Zhang 2009). MM2 exhibits strong CO emission associated with molecular outflows being powered by embedded protostars (Fernández-López et al. 2013).

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In contrast to these two sources, GGD27 MM1 shows many molecular transitions along the observed bandwidth (see Figures 2 and 3). The spectra are dominated by SO₂ and SO isotopologues, as well as by CH₃OH lines. Other lines detected are isotopologues of HCN, HC₃N, and deuterated formaldehyde. The H¹³CO⁺ 4–3 line is marginally detected in absorption toward the dust emission and in emission in an elongated structure east of the MM1 (the spectra of these two features are shown in Figure 4). Table 2 lists the parameters of the lines detected in MM1: line transition, frequency, line strength, energy level, and integrated flux of the detected molecular transitions. The integrated flux was obtained by adding the emission for the channels where the emission is detected and over a region of ∼2 arcsec² on GGD27 MM1.

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Table 2.  Molecular Line Parameters

Molecular	ν	El	${\rm{S}}{\mu }^{2}$	$\int {I}_{\nu }^{\mathrm{MM}1}\,{dv}$
transition	(GHz)	(K)		(Jy km s−1)
SO2
${4}_{\mathrm{3,1}}\mbox{--}{3}_{\mathrm{2,2}}$	332.50524	15.34	6.92	15.56 ± 0.64
${8}_{\mathrm{2,6}}\mbox{--}{7}_{\mathrm{1,7}}$	334.67335	27.08	4.95	13.91 ± 0.59
${13}_{\mathrm{2,12}}\mbox{--}{12}_{\mathrm{1,11}}$ a	345.33854	76.41	13.41	13.82 ± 0.58
${16}_{\mathrm{4,12}}\mbox{--}{16}_{\mathrm{3,13}}$ a	346.52388	147.83	23.10	17.37 ± 1.15
${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{0,18}}$	346.65217	151.50	41.98	21.03 ± 0.58
${21}_{\mathrm{2,20}}\mbox{--}{21}_{\mathrm{1,21}}$	332.09143	203.59	15.20	13.00 ± 0.61
34SO2
${6}_{\mathrm{4,2}}\mbox{--}{6}_{\mathrm{3,3}}$	345.55309	40.66	6.34	3.24 ± 0.60
${7}_{\mathrm{4,4}}\mbox{--}{7}_{\mathrm{3,5}}$ b	345.51966	47.09	8.09	1.44 ± 0.58
${8}_{\mathrm{4,4}}\mbox{--}{8}_{\mathrm{3,5}}$	345.16866	54.46	9.77	4.43 ± 0.73
${9}_{\mathrm{4,6}}\mbox{--}{9}_{\mathrm{3,7}}$	345.28562	62.72	11.41	5.20 ± 0.78
${10}_{\mathrm{4,6}}\mbox{--}{10}_{\mathrm{3,7}}$	344.24535	71.97	13.06	4.82 ± 0.66
${11}_{\mathrm{4,8}}\mbox{--}{11}_{\mathrm{3,9}}$	344.99816	82.05	14.67	3.22 ± 0.69
${13}_{\mathrm{4,10}}\mbox{--}{13}_{\mathrm{3,11}}$	344.80791	105.06	17.92	4.05 ± 0.67
${15}_{\mathrm{4,12}}\mbox{--}{15}_{\mathrm{3,13}}$	344.98758	131.76	21.20	4.92 ± 0.69
${16}_{\mathrm{4,12}}\mbox{--}{16}_{\mathrm{3,13}}$	332.83623	147.14	23.23	4.55 ± 0.62
${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{0,18}}$	344.58104	151.10	42.24	4.91 ± 0.68
${17}_{\mathrm{4,14}}\mbox{--}{17}_{\mathrm{3,15}}$	345.92935	162.14	24.49	2.28 ± 0.57
OS17O
${15}_{\mathrm{4,11}}\mbox{--}{15}_{\mathrm{3,12}}$ b	345.93452	133.72	125.43	2.90 ± 0.53
SO
98–87a	346.52848	62.14	21.52	23.03 ± 1.15
88–77	344.31061	70.96	18.56	15.56 ± 0.20
34SO
78–67	333.90098	63.84	16.24	10.01 ± 0.60
CH3OH
${2}_{\mathrm{2,1}}\mbox{--}{3}_{\mathrm{1,2}}$	335.13369	28.59	0.31	3.12 ± 0.40
${7}_{\mathrm{1,7}}\mbox{--}{6}_{\mathrm{1,6}}$ A+	335.58200	62.87	5.55	11.35 ± 0.44
${5}_{\mathrm{4,2}}\mbox{--}{6}_{\mathrm{3,3}}$	346.20278	98.55	0.496	2.40 ± 0.54
${5}_{\mathrm{4,1}}\mbox{--}{6}_{\mathrm{3,4}}$	346.20437	98.55	0.496	2.40 ± 0.54
${3}_{\mathrm{0,3}}-{2}_{\mathrm{1,2}}$ vt = 1	334.42659	298.42	0.89	1.24 ± 0.44
${16}_{\mathrm{1,15}}\mbox{--}{15}_{\mathrm{2,14}}$	345.90397	316.05	7.13	6.03 ± 0.70
${18}_{\mathrm{2,16}}\mbox{--}{17}_{\mathrm{3,14}}$	344.10913	402.88	5.31	4.13 ± 0.49
${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{2,16}}$	344.44390	434.70	6.00	3.26 ± 0.75
${18}_{-\mathrm{3,16}}\mbox{--}{17}_{-\mathrm{4,14}}$ b	345.91919	442.83	5.61	2.02 ± 0.50
CO 3–2c	345.79599	16.60	0.036
HDCO ${5}_{\mathrm{1,4}}\mbox{--}{4}_{\mathrm{1,3}}$ b	335.09679	40.17	26.05	1.64 ± 0.40
${\mathrm{HC}}_{3}^{15}{\rm{N}}$ 38–37	335.56088	297.98	526.9	2.08 ± 0.37
HC15N 4–3	344.20011	24.78	35.65	4.76 ± 0.63
H13CN 4–3	345.33976	24.86	35.65	a
H13CO+ 4–3d	346.99835	24.98	60.85	−2.22 ± 0.51
SiO 8–7	347.33082	58.35	76.79	2.58 ± 0.77

Notes.

^aSO₂ ${13}_{\mathrm{2,12}}\mbox{--}{12}_{\mathrm{1,11}}$ and H¹³CN 4–3 are blended. The same holds for SO 9₈–8₇ and SO₂ ${16}_{\mathrm{4,12}}\mbox{--}{16}_{\mathrm{3,13}}$. Therefore, their estimated line intensities are possibly not well determined and the quoted uncertainties come just from the fitting procedure. ^bTentative detection. ^cVery broad line; the cloud velocities are strongly affected by missing flux. ^dTentative detection seen in absorption.

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In order to better study and characterize the morphology and the kinematics of the detected molecular lines toward MM1, we present here channel maps of representative molecular lines (Figure 3), the zero- and first-order moment maps (integrated emission and velocity field weighted by intensity, respectively; Figure 5), and the position–velocity cuts along the major and minor axes of the molecular emission ($\mathrm{PA}=111^\circ$ and 21°, respectively; Figure 6). For three high-excitation CH₃OH lines (${16}_{\mathrm{1,15}}\mbox{--}{15}_{\mathrm{2,14}}$, ${18}_{\mathrm{2,16}}\mbox{--}{17}_{\mathrm{3,14}}$, and ${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{2,16}}$) and most of the detected ³⁴SO lines (see the caption of Figure 3 for more details), the maps were combined in order to increase their signal-to-noise ratio. The three figures show that there is a distinctive velocity gradient along the major axis of the molecular disk-like structure (blueshifted and redshifted gas to the east and west, respectively). This velocity gradient is along the major axis of the molecular emission and perpendicular to the HH 80-81-80N radio jet. These properties are more clearly seen in the SO₂, ³⁴SO₂, and ³⁴SO lines. Indeed, the first-order moment maps of these lines are in agreement with those previously reported (FL11b, CG12), but the maps presented here resolve significantly better the velocity gradient. The emission along the major axis extends $\sim 1\buildrel{\prime\prime}\over{.} 4$ or 2400 au. The position–velocity cuts along the major axis also show a clear linear velocity gradient. The different lines of the SO₂ main isotopologues show the same gradient within the uncertainties. However, the combination of ³⁴SO₂ lines show a steeper gradient and more compact emission. The peak emission also appears at higher velocities. The steeper velocity gradient is also seen in the ³⁴SO line. The position–velocity cuts along the minor axis present a broaden of the velocity range at the center for all the cases. All these features suggest that the emission traces a rotating molecular disk around the massive star, as previously suggested in FL11b and CG12.

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The methanol emission appears to partially depart from the rotating disk pattern, which is clearly shown in the integrated emission and the velocity field of the CH₃OH ${7}_{\mathrm{1,7}}\mbox{--}{6}_{\mathrm{1,6}}$ A⁺ (Figure 5). The position–velocity cut along the major axis shows that whereas part of the emission arises from the rotating disk, there is a clear redshifted knot (peaking at  ${v}_{\mathrm{LSR}}$ = 16.0 km s⁻¹) in the blueshifted side of the rotating disk (see Figure 6). Furthermore, the central channels of the CH₃OH ${7}_{\mathrm{1,7}}\mbox{--}{6}_{\mathrm{1,6}}$ A⁺ line shows that the emission is elongated along the jet axis ( ${v}_{\mathrm{LSR}}$ = 14.0 and 16.0 km s⁻¹ channels in Figure 3). This suggests that not all the methanol emission is associated with the rotating disk, so some may arise from the walls of the cavity excavated by the outflow. The SO 8₈–7₇ line seems to be tracing both features, the rotating disk and the walls of the cavity. Finally, the HC¹⁵N 4–3 line does not clearly show the velocity gradient (see Figure 3), though this could be due to the low signal-to-noise ratio of the emission of this line.

The SO₂ and SO lines appear to show a clear velocity gradient along the major axis of the disk, suggestive of rotation, as observed previously at lower angular resolution (FL11b). To better constrain the kinematics of the disk, we modeled the emission with a rotating, geometrically thin disk, using the SO₂ transitions ${4}_{\mathrm{3,1}}\mbox{--}{3}_{\mathrm{2,2}}$, ${8}_{\mathrm{2,6}}\mbox{--}{7}_{\mathrm{1,7}}$, ${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{0,18}}$, and ${21}_{\mathrm{2,20}}\mbox{--}{21}_{\mathrm{1,21}};$ the ³⁴SO 7₈–6₇ transition; and a sum of ³⁴SO₂ transitions for improving the signal-to-noise ratio.

The position angle of the projection of the disk axis on the plane of the sky (minor axis position angle) was fixed to 21°, which is the position angle of the radio jet (Martí et al. 1993). The inclination of the disk, i, was defined as the angle between the disk axis and the line of sight ($i=0^\circ$ for a face-on disk). We considered a rotation velocity given by a power law of the radius, ${v}_{r}{(r/{r}_{0})}^{{q}_{r}}$, where r₀ is an arbitrary reference radius (${r}_{0}=1^{\prime\prime}$) and v_r is the rotation velocity at the reference radius. We assumed that the molecular emission arises from an area of the disk between an inner radius r_i and an outer radius r_o.

We computed, for each point of a regular grid on the plane of the sky, the projection of the rotation velocity of the corresponding point of the disk along the line of sight v_z. A Gaussian line profile of width ${\rm{\Delta }}v$ and centered on v_z was added to the channels associated with the grid point. The intensity of the Gaussian was taken to follow a power-law dependence on the disk radius, r^q_d. Finally, each channel map was convolved spatially with a Gaussian beam of width ${\rm{\Delta }}s$. However, the intensity scale of the channel maps is arbitrary. A scaling factor, the same for all channel maps, was obtained by minimizing the sum of the squared differences between the data channel maps and the synthetic channel maps. The model depends on a total of 11 parameters, namely the beamwidth, ${\rm{\Delta }}s;$ the linewidth, ${\rm{\Delta }}v;$ the disk center position, $({x}_{0},{y}_{0});$ the disk systemic velocity, v₀; the disk inner and outer radii, r_i and r_o; the radial dependence power-law index of the intensity, q_d; the projection of the disk rotation velocity at the reference radius, ${v}_{r}\sin i;$ the radial dependence power-law index of the rotation velocity, q_r; and the disk inclination angle, i.

Some of the parameters are known beforehand, such as ${\rm{\Delta }}s$, the synthesized beamwidth for every transition. Some others were taken as fixed: the rotation power-law index was taken as that of a Keplerian rotation, ${q}_{r}=-0.5;$ and the intensity power-law index, which takes into account the radial dependence of density and temperature, was taken as ${q}_{d}=-1$.

The fitting procedure was the sampling of the multidimensional parameter space, using the same procedure as that described in Girart et al. (2014) and Estalella (2017). The parameter space was searched for the minimum value of the rms fit residual. Once a minimum of the rms fit residual was found, the uncertainty in the parameters fitted was found as the increment of each of the parameters of the fit necessary to increase the rms fit residual a factor of ${[1+{\rm{\Delta }}(m,\alpha )/(n-m)]}^{1/2}$, where n is the number of data points fitted, m is the number of parameters fitted, and ${\rm{\Delta }}(m,\alpha )$ is the value of ${\chi }^{2}$ for m degrees of freedom (the number of free parameters) and α is the significance level ($\alpha =0.68$ for 1σ uncertainties).

The fit was performed in two steps. In a first run, the eight free parameters (${\rm{\Delta }}v$, x₀, y₀, v₀, r_i, r_o, ${v}_{r}\sin i$, and i) were fitted simultaneously for the six transitions. From this run, we obtained the weighted average of the best-fit values for the parameters that do not depend on the transition, ${\rm{\Delta }}v$, x₀, y₀, v₀, ${v}_{r}\sin i$, and i (see Table 3). The value obtained for the disk inclination was $i=47^\circ \pm 8^\circ$. The projection of the rotation velocity at ${r}_{0}=1^{\prime\prime}$ obtained is ${v}_{r}\sin i=-2.5\pm 0.5$ km s⁻¹, corresponding to a deprojected rotation velocity ${v}_{r}=-3.4\pm 0.8$ km s⁻¹.

Table 3.  Thin-Disk Model: Weighted Average of Best-fit Parameters for All Transitions

Parameter	Units	Value
Linewidth ${\rm{\Delta }}v$	(km s−1)	3.3 ± 0.3
Disk center x0	(arcsec)	−0.13 ± 0.05
Disk center y0	(arcsec)	−0.40 ± 0.04
Disk central v0	(km s−1)	12.4 ± 0.2
Rotation vel. ${v}_{r}\sin i$ a	(km s−1)	−2.5 ± 0.5
Disk inclination i	(degrees)	47 ± 8

Note.

^aAt the reference radius ${r}_{0}=1^{\prime\prime}$.

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In a second run, we set as constant the eight parameters obtained from the first fit and we fitted the inner and outer radii of the disk for every transition. The results obtained are shown in Table 4. The inner radius obtained for all the transitions was ${r}_{i}\lt 0\buildrel{\prime\prime}\over{.} 1$. The outer radius for the SO₂ transitions is ${r}_{o}\simeq 0\buildrel{\prime\prime}\over{.} 75$, while for the ³⁴SO and ³⁴SO₂ transitions it is smaller, ${r}_{o}\simeq 0\buildrel{\prime\prime}\over{.} 55$. Figure 7 shows, as an example of the obtained fits, the channel maps for the SO₂ ${4}_{\mathrm{3,1}}\mbox{--}{3}_{\mathrm{2,2}}$ and ${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{0,18}}$ transition data and their best-fit model. Figure 8 shows the position–velocity cut of the SO₂ ${4}_{\mathrm{3,1}}\mbox{--}{3}_{\mathrm{2,2}}$ line and the best-fit model along the major axis.

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Table 4.  Thin-disk Model: Disk Inner and Outer Radii Fitted for Every Transition

	Inner Radius	Outer Radius
Transition	(arcsec)	(arcsec)
SO2 ${4}_{\mathrm{3,1}}\mbox{--}{3}_{\mathrm{2,2}}$	0.04 ± 0.01	0.74 ± 0.01
SO2 ${8}_{\mathrm{2,6}}\mbox{--}{7}_{\mathrm{1,7}}$	0.04 ± 0.01	0.75 ± 0.01
SO2 ${19}_{\mathrm{1,19}}\mbox{--}{18}_{\mathrm{0,18}}$	0.04 ± 0.01	0.82 ± 0.01
SO2 ${21}_{\mathrm{2,20}}\mbox{--}{21}_{\mathrm{1,21}}$	0.09 ± 0.01	0.69 ± 0.01
34SO 78–67	0.03 ± 0.01	0.54 ± 0.01
34SO2	0.00 ± 0.01	0.59 ± 0.01

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5.1. Rotating Disk-like Structure and the Stellar Mass

5.2. Chemical Composition of the MM1 Rotating Disk-like Structure

5.3. The Outflow Cavity Walls

5.4. The Lack of Molecular Emission Associated with MM2 and WMC

We present subarcsecond angular resolution observations carried out with the SMA at 880 μm toward the GGD27 system. We do not detect any polarized continuum emission and place upper limits for the polarized intensity on GGD27 MM1 (≲0.8%) and GGD27 MM2 ($\lesssim 4.7 \%$). The MM1 spectrum is dominated by the presence of several sulfur-bearing species tracing the disk-like structure (SO and SO₂ isotopologues mainly), but it also shows HCN-bearing and CH₃OH lines. The CH₃OH and SO emission is in part tracing the disk rotation, but also comes from the cavity walls of the outflow excavated by the jet. H¹³CO⁺ is seen in absorption against the MM1 continuum emission. We discuss that the abundance of sulfurated lines in the spectrum (which is not common in other massive hot cores) could indicate the presence of shocked gas at the disk's centrifugal barrier or that MM1 is a hot core at an evolved stage.

The $0\buildrel{\prime\prime}\over{.} 4$ SMA resolution allows us to clearly resolve the SO₂ disk's kinematics. MM1 shows a velocity gradient along the disk's major axis, which is steeper for the ³⁴SO₂ and ³⁴SO lines, since their emission is more compact than for the SO₂ lines. We make a fit to the SMA observations using a thin-disk Keplerian model, which fully characterizes the geometry of the disk. The results of our fit give an inclination of 47°, an inner radius of $\lesssim 0\buildrel{\prime\prime}\over{.} 1$ ($\lesssim 170$ au) and an outer radius between $0\buildrel{\prime\prime}\over{.} 55$ (950 au) and $0\buildrel{\prime\prime}\over{.} 75$ (1300 au), depending on the molecular tracer. We also constrain the radial velocity at a putative radius of 1700 au in 3.4 km s⁻¹. Using these results, the estimated protostellar dynamical mass of MM1 is 4–18 ${M}_{\odot }$.

Finally, we also detect molecular emission from the MM2 and WMC cores (MM2 is also resolved in continuum emission). They show in comparison with MM1 an almost empty spectra suggesting that they are associated with extended emission (detected in previous low-angular resolution observations), and therefore indicating the presence of a very young system (MM2), still in a very early stage of accretion, or/and the presence of a less massive object (WMC).

We thank all members of the SMA staff that made these observations possible. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics, and is funded by the Smithsonian Institution and the Academia Sinica. J.M.G., R.E., G.B., and C.J. are supported by the MINECO (Spain) AYA2014-57369-C3-grant. S.C. acknowledges support from DGAPA, UNAM, and CONACyT, México.