Digging into the Interior of Hot Cores with ALMA (DIHCA). I. Dissecting the High-mass Star-forming Core G335.579-0.292 MM1

The single G335–MM1 region identified at 3 mm observations (∼5'' resolution) by Peretto et al. (2013) fragments into at least five continuum sources (Figure 1). These sources were identified by visual inspection. The positions and 1.3 mm fluxes of these sources were derived from a 2D Gaussian fit to the continuum emission and are listed in Table 1. The fit indicates that the sources are elongated with ratios between their axes in the 1.2–2.0 range. The brightest of the five 1.3 mm sources identified by us (ALMA1) matches with the position of one of the two radio continuum sources identified by Avison et al. 2015, MM1a. The second radio source, MM1b, is located in between of two of the 1.3 mm sources (ALMA3 and ALMA4).

Table 1. Continuum Source Properties

ALMA	R.A.	Decl.	Ipeak	Ftotal	Deconvolved Size	vLSR
Source	[h:m:s]	$[^\circ :^{\prime} :^{\prime\prime} ]$	(mJy beam−1)	(mJy)	('')	(km s−1)
1	16:30:58.761	−48:43:54.10	209.8	566 ± 28	0.50 × 0.39	−46.9
2	16:30:58.703	−48:43:52.60	60.2	114 ± 12	0.47 × 0.26	—
3	16:30:58.631	−48:43:51.28	34.1	88 ± 8	0.51 × 0.39	−47.6
4	16:30:58.676	−48:43:51.78	27.8	48 ± 4	0.40 × 0.21	—
5	16:30:58.889	−48:43:55.18	12.6	48 ± 4	0.69 × 0.51	—

Note. Positions in ICRS coordinate standard.

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We have identified two sources potentially associated with MM1b (ALMA3 and ALMA4). Avison et al. (2015) argue that the spectral indices from radio emission for MM1b are consistent with a collimated jet or a compact H ii region. They suggested that this emission is not associated with MM1a, but rather with another source due to the presence of CH₃OH maser emission closer to MM1b. They discarded the jet hypothesis due to the misalignment of MM1b with the HNC emission tracing the molecular outflow associated with MM1a. Given the offset position of MM1b to the ALMA sources, we argue that the radio emission is possibly tracing the lobe of an ionized jet likely associated with the high-mass source ALMA3. However, higher-resolution observations at wavelengths λ ≥ 3 mm are needed to resolve the radio emission and determine its orientation with respect to the ALMA sources.

Line emission is detected mainly toward ALMA1 and ALMA3. Multiple lines are detected toward ALMA1, which is characteristic of young high-mass sources, like hot cores and ultra-compact H ii regions (e.g., Hatchell et al. 1998). A lower number of species is detected toward ALMA3. The lines detected in ALMA3 are weaker than those of ALMA1. We focus our analysis in a handful of lines to explore the kinematics of these two cores. These lines and their properties are summarized in Table 2. The molecular lines detected in other sources correspond to transitions tracing more extended material (e.g., ¹³CO, C¹⁸O), and thus cannot be assigned to one source in particular. The lack of line emission toward the other sources may indicate that they are in an earlier evolutionary stage, likely in the prestellar phase.

Table 2. Summary of Lines Analyzed

Molecule	Transition	Frequency	Eu	Ref.
		(GHz)	(K)
CH3CN	JK = 124–114	220.6792869	183	(1)
CH3CN	JK = 127–117	220.5393235	418	(1)
CH3CN	JK = 128–118	220.4758072	526	(1)
13CO	J = 2 − 1	220.3986842	16	(2)
SiO	J = 5 − 4	217.1049800	31	(2)
H2CO	${J}_{{K}_{a},{K}_{c}}={3}_{\mathrm{0,3}}\mbox{--}{2}_{\mathrm{0,2}}$	218.2221920	21	(2)
HDCO	${J}_{{K}_{a},{K}_{c}}={28}_{\mathrm{5,23}}\mbox{--}{29}_{\mathrm{3,26}}$	220.0294078	1460	(2)
${({\mathrm{CH}}_{3})}_{2}$ CO	${J}_{{K}_{a},{K}_{c}}={54}_{\mathrm{27,28}}\mbox{--}{54}_{\mathrm{26,29}}$ AE	231.6868319	1148	(1)

References. (1) Jet Propulsion Laboratory (Pickett et al. 1998); (2) Cologne Database for Molecular Spectroscopy (Müller et al. 2005).

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We estimated the local standard of rest (LSR) velocity (v_LSR) of ALMA1 from the CH₃CN J = 12–11 K = 7 and 8 transitions. For ALMA3, we estimated the v_LSR from the centroid of the K = 7 line, which is equivalent to the velocity at the position of the source from its first moment map. The velocities are listed in Table 1. Figure 2 shows the continuum of ALMA1 and example CH₃CN spectra from two locations marked on the continuum image. The saturated CH₃CN line emission in Figure 2(b) indicates that the lower-K transitions have become optically thick toward the center position of ALMA1. These transitions even show self-absorbed profiles, except for K = 7 and 8, which are optically thinner. The spectrum shown toward the southeast of the peak position of ALMA1 (Figure 2(c)) is typical of optically thin spectra around the central region, displaying Gaussian-like profiles and not self-absorption features. Although the gas traced by high-K-ladder transitions is hotter than low-K transitions and may thus correspond to a different velocity component, the derived LSR velocity is consistent with other species and previous estimations of the source v_LSR at larger scales (v_LSR = −46.6 km s⁻¹; Bronfman et al. 1996). To determine the v_LSR of ALMA1, the lines were fitted with a Gaussian profile, and the adopted velocity corresponds to the average v_LSR of both K = 7 and 8 transitions.

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From the 2D Gaussian fit to the dust continuum image, we estimate the size of the sources. The radius is defined as the geometric mean of the deconvolved semimajor and minor axes (see Table 1). The results are listed in Table 3. All sources are compact (∼400–800 au) with radii typical of inner envelope/disk scales (<5000 au).

Table 3. Source Physical Properties

ALMA	R	T	Md	${N}_{{{\rm{H}}}_{2}}$	${N}_{{\mathrm{CH}}_{3}\mathrm{CN}}$
Source	(au)	(K)	(M☉)	(1024 cm−2)	(cm−2)
1 a	710	100	19	10.4	—
		300	6.2	3.3	—
2 b	570	> 20	< 24	18.7	—
3	730	290	1.0	0.6	1013
4 b	470	> 20	< 10	8.7	—
5 b	960	> 20	< 10	3.9	—

Notes. The radius, R, corresponds to half of the geometric mean of the deconvolved sizes (FWHM) from Table 1.

^a The dust temperatures are an approximation (see Section 3.2). ^b CH₃CN emission is not detected toward these sources; hence, the temperature is a lower limit, and the gas masses and column densities are upper limits.

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To estimate the dust temperature, we attempt to fit the CH₃CN J = 12–11 K = 0–7 transitions toward the continuum peak of the sources with a local thermal equilibrium (LTE) 1D model. However, the line emission toward ALMA1 becomes quickly saturated; hence, we only fit the temperature toward ALMA3. The fit was performed with the Markov Chain Monte Carlo method within XCLASS (Möller et al. 2017). We obtain a gas temperature at the continuum peak of ALMA3 of 290 K. For ALMA1, we estimate a dust mass using a temperature of 100 and 300 K. The former correspond to roughly the brightness temperature at which the lower-K transition lines saturate. As the emission is becoming optically thick, the brightness temperature should converge to the kinetic temperature. However, the beam filling factor is likely less than one (e.g., Su et al. 2009); hence, this provides a temperature lower limit and in turn a dust mass upper limit. The latter temperature is based on the result for ALMA3.

Assuming that the dust and gas temperatures are in equilibrium, we estimate the gas mass as

$$\begin{eqnarray}&&{M}_{d}=\displaystyle \frac{{F}_{\nu }{d}^{2}{R}_{\mathrm{gd}}}{{\kappa }_{\nu }{B}_{\nu }({T}_{d})}\end{eqnarray} \tag{ 1 }$$

with F_{1.3 mm} the flux density from Table 1, d = 3.25 kpc the source distance, the gas-to-dust mass ratio R_gd = 100, the dust opacity κ_{1.3 mm} = 1 cm² gr⁻¹ (Ossenkopf & Henning 1994), and B_ν the Planck blackbody function. The H₂ column density is estimated from the dust emission as

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}=\displaystyle \frac{{I}_{\nu }{R}_{\mathrm{gd}}}{{B}_{\nu }({T}_{d}){\kappa }_{\nu }{\mu }_{{{\rm{H}}}_{2}}{m}_{{\rm{H}}}}\end{eqnarray} \tag{ 2 }$$

with I_{1.3 mm} the peak intensity from Table 1, ${\mu }_{{{\rm{H}}}_{2}}=2.8$ the molecular weight per hydrogen molecule (e.g., Kauffmann et al. 2008), and m_H the atomic hydrogen mass. The results are listed in Table 3. We estimate that the contribution from free–free emission to the 1.3 mm flux densities is less than 5 mJy for ALMA1 and less than 1 mJy for ALMA3 from the fit to the radio centimeter observations in Avison et al. (2015), and is thus negligible.

The 1.3 mm flux density of G335–MM1 is 1.4 Jy from aperture photometry and 0.9 Jy by summing the values in Table 1. The expected flux at 1.3 mm from the spectral energy distribution in Avison et al. (2015), obtained by interpolating the data points at 870 μm and 3.2 mm, is ∼ 2.1 Jy. On the other hand, the sum of the masses is ∼ 10% of the total mass estimated by Peretto et al. (2013) from 3.2 mm observations. The discrepancy in mass can be explained primarily by the temperature estimates, followed by extended emission not included in the 2D Gaussian fit measurements, and finally emission filtered out by the interferometer.

The mass of the gas reservoir of ALMA3 is 1 M_☉ (Table 3). However this value is likely a lower limit, because cooler regions of the envelope also contribute to the dust emission. Emission from the region may have also been filtered out by the interferometer.

Line emission from CH₃CN transitions, a commonly used tracer of gas rotation, is detected only toward two sources (ALMA1 and ALMA3). In ALMA1, transitions K = 0 to 5 are saturated and blended with other molecular lines (e.g., Figure 2). We therefore calculated the moments 0, 1, and 2 for transition K = 7, which are presented in Figure 3 (line width is displayed instead of velocity dispersion). For ALMA3, the transition K = 4 is used in the moments shown in Figure 4 as there is less contamination from other molecular lines. The first and second moments were calculated only with data over 5σ_rms with σ_rms = 5 mJy beam⁻¹. Line emission from CH₃CN is only detected in ALMA1 and ALMA3 as shown by the contours in Figures 3(a) and 4(a). The deconvolved size of the emission in the contours of Figure 3(a) is 06 (∼2000 au); thus, it is likely tracing the inner region of the circumstellar envelope and/or disk.

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Outflow emission is detected in the ¹³CO J = 2–1 and SiO J = 5–4 transition lines. We separated the red- and blueshifted line components to study the directions of the flows (Figure 5). The blue and red windows are separated ±3.25 km s⁻¹ from the v_LSR and have widths of ∼22.75 and 13 km s⁻¹ for ¹³CO and SiO, respectively. A clear molecular flow is detected toward ALMA1 in the NE–SW direction, consistent with outflow A of Avison et al. (2021). From the blueshifted emission, we estimate a P.A. ∼ 210°. Additionally, the arc-shaped structure observed in the dust emission toward the west of ALMA1 (Figure 2(a)) is likely associated with emission from the base of the outflow cavity as seen in ¹³CO. This may be the result of a wide angle wind interacting with the envelope (e.g., Kuiper et al. 2015), as observed in the diffuse dust emission and outflow emission of G16.64+0.16 (Maud et al. 2018). Toward ALMA3, ¹³CO seems to be tracing the envelope of the source with the blue- and redshifted orientation consistent with the rotation pattern observed in CH₃CN. The redshifted SiO emission toward the NW shows structures that may be associated with ALMA3 (SE–NW direction, P.A. ∼ −45°) and ALMA4 (SW–NE direction, P.A. ∼ 45°). Avison et al. (2021) detected CO outflow emission likely associated with the radio source MM1b roughly in the EW direction. However, the CO outflow lobe is blueshifted rather than redshifted as seen in the SE–NW SiO emission, and the origin of the SiO emission does not coincide with ALMA3. Hence, we cannot rule out that the SiO emission is related to an unresolved source.

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We have identified two lines with upper energy levels higher than 1000 K: HDCO (28_5,23 − 29_3,26) with E_up equal to 1460 K and (CH₃)₂CO (54_27,28 − 54_26,29) AE with E_up equal to 1140 K. Their moment maps are displayed in Figure 6. The emission of these two lines is compact, but resolved toward ALMA1. Both lines are likely tracing the innermost regions of the hot core given the high temperatures required to be excited. The first moment maps of these lines show a consistent velocity gradient with that of CH₃CN, but remarkably, the lines are redshifted rather than blueshifted toward the center of the source.

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4.1.1. Large-scale Infall

The velocity field in ALMA1 presents an overall gradient from east to west (Figure 3(a)). However, this gradient is likely masked as a result of a combination of gas motions. Possible reasons that make velocity gradients difficult to identify are (e.g., Silva et al. 2017): (i) CH₃CN is possibly tracing outflowing motions, for instance, from gas removed from a disk surface by stellar winds, together with rotation and infall (e.g., Beuther et al. 2017) making the interpretation of the velocity gradients less straightforward; (ii) the observed velocity field is potentially produced by the combination of gas motions due to the presence of unresolved sources; (iii) the orientation of the protostellar disk is close to face-on; and/or (iv) infall or expansion motions.

The first moment map of the K = 7 transition presented in Figure 3(a) shows a spot of velocities close to zero at the center of the core enclosed mainly by the 80 × σ_rms level of the zeroth moment contour. These velocities are bluer than expected for a smooth transition of velocity from east to west, assuming CH₃CN is tracing the rotation of the core envelope/disk. Henceforth we refer to this region as the blueshifted spot. As shown in Figure 2, the CH₃CN lines up to K = 4 show an absorption feature at the center of the line, resembling the blue-asymmetry characteristic of infall motions (e.g., Zhang et al. 1998) and resulting in the blueshifted spot (e.g., Estalella et al. 2019). This blue-asymmetric profile is not evident in larger, likely optically thinner, K transitions, but the effect of the collapse can still be detected through the first moment map. The first moment map spot of blueshifted velocities (with respect to the v_LSR) is thus likely produced by line profiles that are blue-skewed. To further investigate the infall hypothesis, we search for blueshifted emission coupled with redshifted absorption against the continuum source, also known as an "inverse P-Cygni profile." Such features provide unambiguous evidence for infall toward the central protostar (e.g., Evans et al. 2015).

Among the myriad lines included in the spectral setup, those that trace a more extended gas distribution display absorption against the continuum only at the center position of ALMA1 (and not anywhere else). Figure 7 shows the spectrum of ¹³CO (2–1) and H₂CO (3_0,3–2_0,2) at the peak position of the dust continuum of ALMA1. The ¹³CO displays an absorption against the continuum that is redshifted with respect to the v_LSR of –46.9 km s⁻¹ by 1.7 km s⁻¹. On the other hand, the H₂CO line in Figure 7(b) shows a dip consistent with the source v_LSR. In order to be excited, ¹³CO requires lower densities and temperatures than H₂CO. We therefore suggest that the absorption against the continuum that is redshifted with respect to the v_LSR in the ¹³CO line is tracing a large-scale infall, consistent with the findings at the much lower resolution of 5'' (∼15000 au) by Peretto et al. (2013). This is also supported by the position–velocity (pv) map of ¹³CO in Figure 8, where the morphology of the emission resembles the "C" shape characteristic of infall motions (Zhang & Ho 1997). H₂CO emission may be produced closer to the core center (or in the outflows) making harder the detection of infall signs (although the absorption dip is slightly redshifted with respect to the v_LSR).

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4.1.2. Small-scale Expansion

The spot at the core center in the first moment map (Figure 6) of the hot lines HDCO and (CH₂)₂CO is redshifted with respect to the v_LSR (and not blueshifted as in CH₃CN). Moment maps have so far been made by using windows of ±5.2 and ±6.5 km s⁻¹ symmetric from the v_LSR. The HDCO line profile toward the continuum source position presented in Figure 9 is single peaked with a red wing at higher velocities (shadowed region). In order to discard the red wing as the cause of the redshifted spot, we have derived the velocity structure in ALMA1 by first finding the peak at each pixel (defining a "local" pixel v_LSR) and then assuming different windows to make the first moment. The velocity maps are shown in Figure 10. This approach would be more robust to strong velocity gradients, and we have no need to adopt large windows for making moment maps that can introduce noise or contamination from neighboring spectral lines. Figure 10 shows that HDCO is redshifted toward the center of the continuum source and is increasingly blueshifted farther out, while toward the arc-shaped structure, the emission is blueshifted as observed in CH₃CN. The area of the redshifted region increases when more channels are included and shifts toward the south (see Figures 10(c) and (d)), indicating that the lines to the south are skewed toward the red due to high-velocity line wings. Overall, the velocity gradient is consistent with what is seen in CH₃CN, and as the window for making the moment map increases, the redshifted spot becomes more evident. Applying a similar reasoning to the origin of the blue-asymmetric/skewed lines (e.g., Zhou et al. 1993, see also the expansion line profiles in Keto et al. 2006), this pattern likely indicates gas expansion at the core center. Anglada et al. (1987) noted that an inverted profile to that of blue-asymmetric profiles is expected for expansion motions if the temperature increases toward the central region and the velocities decrease outwards. The first condition is likely satisfied since a high-mass young stellar object may have already been formed and started to ionize the circumstellar gas. They also assumed in their analysis that the Sobolev approximation is valid, but the expansion velocity of HDCO (see Section 4.3) is comparable to the line width. Hence the second condition may not necessarily be satisfied.

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Using centimeter observations, Avison et al. (2015) determined that an HC H ii region, unresolved at their 15 resolution observations, is located a the position of ALMA1. The HC H ii region is an important evolutionary stage in the life of high-mass stars. HC H ii regions tend to be smaller than 0.03 pc (6000 au), and the likely culprit of the ionized flow is the photoevaporation of an accretion disk surface (Kurtz 2005). While in this stage, it has been suggested that the star can continue growing into earlier types by nonspherical accretion flows (Keto 2007). Eventually it is believed that HC H ii regions will expand into ultra-compact (UC) H ii regions and then into classical H ii regions. We suggest that in ALMA1, we are witnessing the early expansion of the ionized gas that is pushing outward the hot molecular gas. The effect of the expansion is more clear in the transitions tracing the hot, inner molecular core (e.g., HDCO). The picture we propose for ALMA1 and its immediate surroundings is sketched in Figure 11. The spatial distribution of the emission from the hot transition lines (Figure 6(a)) is closer to perpendicular to the outflow (P. A. = 210°), with P.A.s between 125° and 130° as measured from a 2D Gaussian fitted to the zeroth-order moments. Hence, it is likely coming from molecular gas in a putative disk surface.

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The K = 4 transition first moment map in Figure 4(a) shows clear signs of rotation toward source ALMA3. We estimate an average P.A. of the rotation axis from the velocity gradient within a region of radius 016 (i.e., one beam) centered on the source of P. A. _rot = 292° ± 8° from the first moment map of the K = 4 transition. A similar value is obtained from the K = 7 transition but with a slightly higher error due to its smaller angular extent (P. A. _rot = 290° ± 9°). We estimate the kinetic mass of source ALMA3 from the velocity extremes from the rotation axis. Assuming that the source is edge-on, the source mass is in the 10–30 M_☉ range (hereafter kinetic mass). Lower inclination angles, i.e., toward a face-on configuration, would imply an even larger mass. This is one order of magnitude larger than the 1 M_☉ derived from the dust emission (Table 3). Note that the kinetic mass includes the contribution of the central (proto)star, which may not contribute to the dust emission, and the circumstellar gas. On the other hand, the dust temperature estimation assumes an isothermal column of gas in LTE with the dust passing through the central (hotter) region. Given that the temperature can have a decreasing temperature profile with radius, the contribution of colder dust in the outer layers may be underestimated by these assumptions. The temperature can reach values of roughly 30 K at clump scales (>0.1 pc; e.g., Faúndez et al. 2004); hence, a lower average temperature than our estimation could explain discrepancies of less than one order of magnitude (assuming dust emission in the Rayleigh–Jeans regime: ${M}_{d}\propto {T}_{d}^{-1}$). Different dust opacity laws would explain discrepancies of a factor ∼2. The lower number of lines detected and lack of radio emission suggest that this source is younger than ALMA1 and still deeply embedded.

In this section, we provide additional support for the interpretation of the moment maps by comparing qualitatively the data with simple LTE radiative transfer models. In these models, the molecular line emission arises from a spherically symmetric core with a radius of a = 2000 au, comparable to the extent of source ALMA1 shown in Figures 3, 6, and 10. We assume that this core is characterized by a density ρ(r) ∝ r^−3/2, and a thermal gradient with temperature T(r) ∝ r^−0.5, characteristic of radiative equilibrium under optically thin dust conditions (Adams & Shu 1985). We calculated models with solid body rotation at each radius combined with infall or expansion motions. The azimuthal velocity fields of the core vary as V_ϕ ∝ r^−1/2. The radial velocities are proportional to ± r^−1/2, with positive velocities for expansion motions and vice versa. This model is a simplified version of a pressure-less free-falling core solution dominated by the gravity of a central object (Ulrich 1976; Mendoza et al. 2004, 2009). Note that the models do not combine infall and expansion motions; thus, they can only explain the features of one line at a time. To fit the observations, we optimize numerically the central v_LSR and the line width. The remaining parameters are fine-tuned by visual inspection. The blue asymmetry, characteristic of infalling motions, requires a combination of partially optically thick emission and internal heating. Figures 12(a) and (b) shows the first moment map of the CH₃CN J = 12–11 K = 4 line toward ALMA1 and the one derived from the model, respectively. We assume that the rotation axis of the core is inclined with respect to the line of sight by i = 45°, and it forms a P.A. = 5°, as indicated by the approximate direction of the velocity gradient. Note that the angular velocity of the core and the inclination angle are degenerate parameters. We are able to reproduce the main features observed in ALMA1 with an infall velocity at the external radius a of V_in(a) = −1.15 km s⁻¹, an angular velocity ${\rm{\Omega }}(a)\sin (i)=3.34\times {10}^{-11}$ s⁻¹, a temperature T(a) = 33 K, and a line absorption coefficient given by κ_v (a) = 3.21 × 10⁻¹⁷ ϕ_v cm⁻¹. The line profile ϕ_v is assumed to be Gaussian with an FWHM of Δv = 2 km s⁻¹. We note that, in agreement with infall, the rotation of the core is not enough to maintain the core in equilibrium at the assumed inclination. The gas mass within a radius R from the model is given by

$$\begin{eqnarray}&&M(\lt R)=\displaystyle \frac{8\pi }{3}\rho (a){\left(\mathrm{Ra}\right)}^{3/2}.\end{eqnarray} \tag{ 3 }$$

From the line absorption coefficient and assuming a CH₃CN abundance of 10⁻⁸ (e.g., Hernández-Hernández et al. 2014), we obtain ρ(a) = 2.9 × 10⁻¹⁶ g cm⁻³. The gas mass of the model at R = 710 au (same size derived from the dust continuum, see Table 3) is M(<710 au) = 6.8 M_☉. We note however that the abundance of CH₃CN is very uncertain and can vary by one order of magnitude (Hernández-Hernández et al. 2014), precluding a direct comparison with the mass derived from dust continuum emission.

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Figures 12(c) and (d) show the maps of the HDCO velocity at peak line intensity obtained from the observations and a rotating and expanding core model. The expansion velocity is ${V}_{\exp }(a)=+0.5$ km s⁻¹. Two features describe the shape of the HDCO line profile: (1) a relatively slow expansion that redshifts the line peak in ≲1 km s⁻¹ in the directions of highest opacity, that is, toward the center of the core (see Figure 10(a)); (2) a distinct redshifted wing, typical of outflows (see Figure 9). A combination of these two effects produce the redshifted velocities shown in the first moment map (Figure 10(d)). We find that a model with an absorption coefficient four times less than that of CH₃CN and a line width Δv = 2.5 km s⁻¹ is able to reproduce fairly well these features of the HDCO line, particularly the redshifting of the peak toward the center of the core. This rotation-expansion model also has a different P.A. = 20° compared to the CH₃CN model, which is suggested by the velocity gradient shown in Figure 10. Models with the same P.A. produce fits that are not significantly worse.

As discussed in Section 4.1, the expansion of the gas is likely caused by the expansion of the HC H ii (see Figure 11). This may have already grown beyond the gravitational radius of the young star (Sartorio et al. 2019), which is 54 au for a 10 M_☉ HMYSO, in the innermost regions of the hot core. Note that the lower opacity associated with the HDCO model implies that the lines of sight associated with τ = 1 cross the core much closer to its center compared to those of CH₃CN. Indeed, while for CH₃CN, the lines of sight with impact parameter of 130 au are optically thick, for HDCO, optically thick lines of sight are those that pass within 30 au of the center. This difference in opacities explains why we are not able to see the expansion signature in the CH₃CN profiles and why we cannot discern the infall signature in the HDCO line. In the former case, the expansion is hidden within a very small radius associated with a large opacity. On the other hand, HDCO emission from gas in expansion is associated with optically thin emission, and therefore the blue asymmetry does not arise.