A Keplerian Disk around Orion SrCI, a ∼ 15 M_⊙ YSO

We detect the disk in the continuum at 3.2 mm, 1.3 mm, and 0.8 mm (Figure 1 shows the 3.2 and 1.3 mm images⁶ ). At 1.3 mm, where we have enough resolution to clearly distinguish the line-emitting region from the disk midplane, we detect spectral lines only from the surfaces above and below the continuum disk (Figure 2). The nondetection of lines in the disk midplane is a strong indication that the continuum is optically thick, as has previously been noted (e.g., Plambeck & Wright 2016).

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We fit the highest-resolution 1.3 mm and 3.2 mm continuum image with a simple model to determine the basic observational structure. The optimization was performed using a Levenberg–Marquardt fitter (Newville et al. 2014). We used a linear model (i.e., an infinitely thin perfectly edge-on disk) for the disk, with endpoints and amplitude as free parameters. This simple model left significant residuals, so we added a two-dimensional Gaussian smoothing kernel as another three free parameters to obtain a substantially better fit. The models and their residuals are shown in Appendix A.

We determined that the disk is resolved in both directions, with a vertical FWHM height of about 20 au and a length of about 100 au (Table 4). These measurements are close to those published by Plambeck & Wright (2016), though their data only marginally resolved the source at wavelengths 1.3 mm and shorter.

This simple model leaves a significant residual compact source near the center of the disk, which we measured by adding a smeared point source to the model (see Appendix A). We have allowed the source to be smeared only in the direction of the disk's elongation, requiring only two additional free parameters. This source is discussed further in Section 4.6.

Table 4 lists the fitted parameters. It includes measurements of the total integrated intensity recovered in the model and the ratio of the compact central source to the total. We also display fits to the Reid et al. (2007) 7 mm continuum data with the same model; these fits do not contain any absolute astrometry information.

The disk position angle points to within 2° of the Becklin-Neugebauer object (Orion BN); the PA of the vector from SrcI to Source BN is −376, while the measured disk position angle is −36° to −37°. This coincidence was noted by Bally et al. (2011) and Goddi et al. (2011).

The disk has a peak brightness temperature at 1.3 mm of ∼600 K at the position of the compact source and ∼400–500 K at other positions, with a gradual decline from the center to the exterior. These measurements agree with the continuum model of Plambeck & Wright (2016), who inferred the presence of an optically thick T = 500 K surface from the SED. The 3.2 mm continuum has a higher peak brightness temperature at the position of the central compact source, but otherwise is consistent with the 1.3 mm brightness (see Figure 1).

We detect several SiO lines, including the 1 mm ²⁸SiO v = 0 and v = 1 J = 5–4 lines, the 3 mm isotopologue lines ²⁹SiO v = 0 and v = 1 J = 2–1, and the 3 mm ²⁸SiO v = 0 and v = 1 J = 2–1 lines. Several of these transitions are known and well-studied masers. Some images of these data are shown in Appendix B, but because the emphasis of this work is not on the outflow, we do not discuss the SiO further here.

The next brightest line after the masing SiO lines is the H₂O ${5}_{\mathrm{5,0}}\mbox{--}{6}_{\mathrm{4,3}}$ line at 232.68670 GHz, with E_U = 3461.9 K. Hirota et al. (2012) detected this line in 2'' resolution ALMA Science Verification data, but believed it to be masing. We report here that, because it is similar in morphology and excitation level to the 336 GHz vibrationally excited water line reported in Hirota et al. (2014), and it has a peak brightness temperature ∼1500 ± 100 K (in the robust −2 maps; see Figure 2), it is most likely a thermal line.

The water line traces an X-shaped feature above and below the disk, resembling the overall distribution of SiO masers. The water is not directly aligned with the continuum disk (Figures 2 and 19), but it does exhibit emission parallel to the disk at small (<20 au) separation. The morphology of this line confirms that it traces both the disk and the inner rotating outflow discussed by Hirota et al. (2017; see also Kim et al. 2008; Matthews et al. 2010).

Because the water emission is thermal, it exhibits less extreme brightness fluctuations across the image than the SiO masers, allowing us to fit an upper envelope velocity curve in Section 3.5. The kinematics of the water line away from the disk are discussed further in Appendix C.

Several unidentified lines are observed in emission at the outer edge of the continuum disk. A table of their approximate rest frequencies is presented in Appendix D. They all share a common morphology, though they vary in strength. The peak signal from these lines appears around the T_B ∼ 150 K contour in the robust −2 weighted 1.3 mm continuum images (Figure 2), and the lines are particularly strong at the endpoints of the disk. Little line emission is detected where the continuum is brightest, T_B ≳ 300 K.

The best explanation for these lines is that they trace the outer surface of a mostly optically thick (in the continuum) disk. In this scenario, the lines have an excitation temperature similar to the brightness temperature of the disk, but have optical depths of order τ ∼ 0.1–1. Directly toward the disk continuum emission peak, since the line excitation temperature is the same as the background continuum temperature, ${T}_{\mathrm{ex}}={T}_{\mathrm{bg}}$, no emission (or absorption) is observed. Just above and below the disk midplane continuum peak, the dust column density (and therefore optical depth) drops rapidly, but the molecular optical depth drops more slowly, so some emission is still observed (${T}_{\mathrm{ex}}\sim 200\mbox{--}500$ K, but ${\tau }_{\mathrm{line}}\sim 0.1\mbox{--}0.5$, resulting in the ${T}_{B,\max }\sim 100$ K observed). At the disk endpoints, the column density of molecular material is higher because we are looking along the tangent of the disk, so the line optical depth and therefore brightness are greater.

Since these lines only appear immediately around the disk, and in particular because they peak just outside of the dust emission along the disk axis, they are the most direct tracers of the disk's kinematics.

The disk appears to exhibit a Keplerian rotation curve, which allows us to use the velocity profile to measure the central mass. Following Seifried et al. (2016), we measure the outer edge of the detected emission in a position–velocity (PV) diagram to define the rotation curve surrounding SrcI. The emission along each line of sight in the PV diagram is followed from its peak down to some emission threshold. We use a threshold of 5-σ, as was done in Seifried et al. (2016), but we also assess the importance of this threshold in Section 3.5.2. Additionally, to facilitate direct comparison with previous works, we use the centroid-of-velocity-channel approach in Appendix E (although Seifried et al. (2016) warn it may underestimate the central mass) and obtain similar results, albeit from different spectral lines.

Of the detected lines, the H₂O line spans the widest range of velocities as a function of radius. As shown in Figure 3, there is H₂O emission spanning at least radii r ≈ 10 to 100 au. Many other molecules, most of which we have not been able to identify, span a range of radii 30–80 au, while SiS spans 30 au to an unconstrained outer radius. The SiO lines span varying radii, but they are predominantly detected far from the disk midplane (however, see Appendix B, in which SiO also exhibits Keplerian velocity curves).

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We find that a 15 ${M}_{\odot }$ edge-on Keplerian rotation curve fits⁷ the outer edge of the H₂O line well (Figure 3). The 15 ${M}_{\odot }$ profile is also an acceptable match to the outer profiles of the unidentified lines described in Section 3.4 and shown in supplemental figures in Appendix F.

A lower-mass central source is consistent with the H₂O data only if we allow for substantial line-broadening driven by turbulence. We estimate an upper limit on the turbulent line-broadening of FWHM ≲ 4 $\mathrm{km}\,{{\rm{s}}}^{-1}$ based on the narrowest features observed in the H₂O and other unknown lines, which results in a one-sided broadening of HWHM < 2 $\mathrm{km}\,{{\rm{s}}}^{-1}$; if such line-broadening is present, the mass may be lower by ∼20%–30%. However, since Flaherty et al. (2017) observed stringent upper limits on turbulence in lower-mass disks, we expect turbulent broadening to be relatively small, and possibly negligible. The upper-limit line-broadening we observe is consistent with line-blending from unresolved kinematics within the beam and is close to the intrinsic velocity resolution of our data.

A substantially smaller mass, such as the 5–10 ${M}_{\odot }$ suggested previously (Hirota et al. 2014; Plambeck & Wright 2016), is inconsistent with the data: for models with such masses, emission is clearly detected outside of the predicted Keplerian curve (see, e.g., the green curve in Figure 3).

3.5.1. Examination of Alternative Velocity Profile Models

To support the argument that the velocity profiles are Keplerian, as opposed to some other power-law profile as has been found for the outer envelopes of several low-mass YSOs (Murillo et al. 2013; Lindberg et al. 2014; Ohashi et al. 2014; Aso et al. 2017; Lee et al. 2017), we show power-law fits to the outer envelope velocity profile of the H₂O line in Figure 4. This figure convincingly demonstrates that a power law α = 1 (e.g., as observed in the outer parts of low-mass YSO disks; Aso et al. 2017) is inconsistent with the data. While the best-fit profile of α ≈ 0.4 is slightly shallower than the Keplerian α = 0.5 curve, both shallow profiles are consistent with the data. The limited spectral resolution of our data is evident in this plot, where there is little separation in velocity from ∼30–50 au; higher spectral resolution observations or more sophisticated modeling may be able to provide a tighter constraint on the power-law slope.

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The mass for the α = 0.5 curve is M = 15 ${M}_{\odot }$. We do not determine masses for the other models, since they are not consistent with a point-like gravitational potential. We show the curves for a central 13–17 ${M}_{\odot }$ source in magenta: since there are many points above the curve, a more massive central source is plausible, while a less massive source is unlikely.

3.5.2. An Estimate of the Error on the Mass Measurement

We assess the uncertainty introduced by the threshold level adopted in the velocity envelope profile measurement. Figure 5 shows the effects of increasing or decreasing the threshold, which also decreases or increases the measured mass, respectively. These figures suggest that our measurement uncertainty with the PV envelope-fitting technique is approximately 2 ${M}_{\odot }$.

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We measure a mass for the object at the center of the disk of M_I = 15 ${M}_{\odot }$, which is higher than most previously reported measurements. Our mass measurement is higher than previous works in part because our spatial resolution is high enough to allow a direct fit of the rotation curve to the outer envelope of an emission line in position–velocity space. Additionally, though, the greater sensitivity of these observations allowed us to detect the outer envelope of the H₂O position–velocity diagram and detect—and resolve—several unknown lines that directly trace the disk. The inconsistency between these new estimates and the lower masses previously derived from SiO measurements hints that, in this system, SiO chemically selects a kinemetically distinct region from the disk.

Even if SrcI consists of an equal-mass binary, this mass measurement confirms that the Orion Molecular Cloud is presently a region with ongoing high-mass star formation.

Since we observe an optically thick surface, we can infer the luminosity required to keep such a surface at the observed ${T}_{B,1.3\mathrm{mm}}\approx 500$ K, assuming it is heated only by radiation. Taking the disk radius to be 50 au, the required central source luminosity is 6500 ${L}_{\odot }$. This estimate should be taken as a lower limit, since the inner disk is likely to be optically thick and capable of shielding the outer disk, thereby keeping the observed τ = 1 surface 1.3 mm cooler than it would be if it were produced by radiative equilibrium with the central star.

Our observations yield disk properties nearly identical to those in Plambeck & Wright (2016), so we do not revisit their disk mass or density estimates. We note, however, that these new observations have sufficient angular resolution to distinguish the molecular lines that trace the outflow from those that directly trace the disk.

Several authors (Gómez et al. 2008; Bally et al. 2011; Goddi et al. 2011) suggested that the high proper motion of SrcI, BN, and SrcN, combined with the observed ${{\rm{H}}}_{2}$ outflow, implied the outflow and the runaway stars were produced in the same single event ∼500 years ago. That event was the dynamical decay of a non-hierarchical multiple system, i.e., it was the interaction of multiple stars at the center of a small cluster. More recent observations by Luhman et al. (2017) have shown that SrcN is unlikely to have participated in this interaction, but instead that SrcX, another star within the same field, has high proper motion that points back to the interaction center (J. Bally et al. 2018, in preparation).

Farias & Tan (2018) report that, while any dynamical decay scenarios involving Sources I, X, and BN that can reproduce the observed proper motions are unlikely, those with a higher mass for SrcI (M_I > 14 ${M}_{\odot }$) are the only ones capable of producing the observed proper motions.⁸ Our observed higher mass for SrcI, M_I ≳ 15 ${M}_{\odot }$, therefore implies that the dynamical interaction scenario remains viable.

Plambeck & Wright (2016) argued that both the mass of SrcI and the presence of the disk rule out the dynamical ejection model of Bally et al. (2011). We have shown that the star is significantly more massive, but what about the disk?

Following Bally et al. (2011), we note that the disk truncates at R < 50 au. At this radius, the orbital timescale is ∼70 years, so gas at the disk's outer radius would have had 5 to 10 dynamical times to relax into a circular disk configuration after the explosive event.

The alignment of SrcI's disk with the I-BN vector is consistent with a dynamical interaction between these sources. If the ejection resulted in SrcI and BN being launched in nearly opposite directions from their center of mass (which must have been moving in the rest-frame of the Orion nebula; J. Bally et al. 2018, in preparation), any material around SrcI that remained bound would be dragged in the direction of SrcI, and would therefore have a resulting angular momentum vector orthogonal to the direction of motion. Any material with velocity relative to SrcI,

$$\begin{eqnarray*}&&v\lt {v}_{\mathrm{esc}}=23\,\mathrm{km}\,{{\rm{s}}}^{-1}{({M}_{I}/15{M}_{\odot })}^{1/2}{(r/50\mathrm{au})}^{-1/2},\end{eqnarray*}$$

would remain bound. Assuming SrcI's present-day proper motion of 11.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ reflects its velocity at the time of ejection, less than half of the original disk mass would have been lost, while the rest would remain bound (material moving in the direction directly opposite of SrcI's ejection direction would have a net velocity relative to SrcI high enough to escape; the greatest mass-loss would occur if the disk was already in the direction of SrcI's eventual launch). Material outside R ≳ 200 au (where v_I = 11.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ > v_esc) would likely all have become unbound, while other material would be retained in a disk parallel to Source I's proper motion.

We have detected a compact (but marginally resolved) source near the center of the disk at both 3.2 and 1.3 mm. The source has a spectral energy distribution that is shallow from 3.2 to 1.3 mm (α ≈ 1.1). Since the source is nearly coincident with an edge-on disk that we show is optically thick at 1.3 mm, it is likely that the source is thermal but is significantly attenuated by the disk at 1.3 mm and seen with less attenuation at 3.2 mm.

Reid et al. (2007) used comparable-resolution 7 mm VLA data to infer the presence of a 2.2 mJy source at the center of the SrcI disk. The compact-source-to-disk flux ratio at 7 mm was ∼30%, substantially higher than what we observe at 1.3 mm and somewhat higher than what we observe at 3.2 mm (Table 4). The spectral index of this compact source from 7 to 3.2 mm is α = 1.6, approaching that of an optically thick blackbody.

The central source has a surface temperature T ≥ 1250 K, the brightness temperature of a 2.2 mJy source within a 41 × 28 milliarcsecond beam at 7 mm. If the source is a 5000 K spherical blackbody (e.g., Testi et al. 2010), it must have a radius R = 7.5 au. Such a gigantic star is implausible, as it would produce a luminosity of 1.5 × 10⁶ ${L}_{\odot }$, several orders of magnitude higher than the total luminosity in the region. We therefore argue that this emission source is not a star.

What is the emission mechanism from this central source? It could simply be hot, optically thick dust that is partly obscured by the cooler disk at higher frequencies. The extension of this "source" along the disk direction (Appendix A, Figure 6) suggests that we are seeing the hot inner disk. As pointed out by Plambeck & Wright (2016), it is quite unlikely to be classical free–free emission from protons and electrons, since there are no detected recombination lines. However, it is still plausible that the emission is produced by brehmsstrahlung emission from H i and ${{\rm{H}}}_{2}$ (Reid et al. 2007; Báez-Rubio et al. 2018).

The source is slightly offset from the center of the disk by 5.8 ± 1.5 au in projection.⁹ This offset, combined with the source's extent, implies that it is not a single central source, but instead is a hot region of the inner disk. Such an asymmetry in the disk could be driven either by instability in the disk, or if the central star is a binary, by the proximity of the more luminous companion.

If this source is an inner edge of the disk, it may imply the presence of a binary that has cleared the area within r < 6–10 au. Since a tight binary is one of the expected outcomes of the dynamical interaction scenario (Goddi et al. 2011), this detection of the inner region in dust emission provides additional circumstantial evidence for that scenario.

If SrcI's central source is a binary, and the measured offset of ∼5 au between the disk midpoint and the central emission source is real, we can guess that the binary's orbit is ≲5 au. For such an orbital radius, the orbital timescale is only ∼3 years. It will therefore be productive to re-observe SrcI over the next several years to see if the hot spot moves on such a timescale.

Figure 17 shows an example of how the centroid-of-velocity approach produces lower-mass fits for some lines, particularly H₂O and SiO. The figure shows both the optically thin edge-on disk model and the midplane-extracted position–velocity diagram with overlaid centroid fits. The centroid fits notably do not extend nearly as far as emission is visible. This discrepancy results from the midplane emission being much fainter than some of the off-plane emission.

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By contrast, a similar side-by-side comparison of the edge-on optically thin model with the U232.511 line reveals a better match. In Figure 18, the overall structure of the observed position–velocity diagram is well-matched to the model.

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