---
author:
- 'L. T. Maud[^1]'
- 'R. Cesaroni'
- 'M. S. N. Kumar'
- 'V. M. Rivilla'
- '[A]{}. Ginsburg and P. D. Klaassen'
- 'D. Harsono'
- '[Á]{}. S[á]{}nchez-Monge'
- 'A. Ahmadi'
- 'V. Allen'
- 'M. T. Beltr[á]{}n'
- 'H. Beuther'
- 'R. Galv[á]{}n-Madrid'
- 'C. Goddi'
- 'M. G. Hoare'
- 'M. R. Hogerheijde'
- 'K. G. Johnston'
- 'R. Kuiper'
- 'L. Moscadelli'
- 'T. Peters'
- 'L. Testi F. F. S. van der Tak'
- 'W. J. de Wit'
date: 'Received April 2019 / Accepted in A&A June 2019'
title: 'Substructures in the Keplerian disc around the O-type (proto)star G17.64$+$0.16 [^2] '
---

Introduction {#intro}
============

Spiral arms or rings and gaps in the discs of solar mass protostars are now common place, detectable at both IR and mm wavelengths [@Alma2015; @Brandt2014; @Andrews2016; @Andrews2018; @Walsh2017; @Monnier2019; @Boer2016]. Ring-gap structures have been explained by planets, zonal-flows, snow-lines, or dust trapping [@Nazari2019; @Isella2018; @Dipierro2015; @Ruge2016; @Zhang2015], while spiral structures could be caused by interactions with planets or stellar binaries, or due to a gravitational instability of the disc itself [@Benisty2017; @Quillen2005; @Meru2017; @Mayer2016]. In the context of massive star formation, there are only a handful of sources that have convincing evidence of disc rotation on sub-1000au scales [e.g. @Johnston2015; @Ilee2016; @Ginsburg2018; @Moscadelli2014; @Moscadelli2019; @Zapata2019]. The detection of discs and rotation can still be somewhat difficult to identify even in the few targets that have been probed at sub-100au resolution. Work by @Beuther2019 indicate a highly fragmented star formation region in G351.77-0.54, with 12 identified structures, and tentative evidence of rotation in a few cores, while @Goddi2018 observed the W51 region and also indicate a highly clustered complex environment with little, if any, evidence for stable discs.

![image](G17_LB_cont_two.ps){width="100.00000%"}

Theoretical works involving the formation of massive stars must invoke accretion discs. Simulations typically result in large-scale (500$-$1000au) spiral-like features or streamers that funnel the accretion flows [@Meyer2018; @Harries2017; @Krumholz2009; @Peters2010b; @Kuiper2011; @Klassen2016; @Rosen2016; @Kuiper2018], which themselves have recently been observed in a few cases [@Maud2017; @Izquierdo2018; @Liu2015; @Cesaroni2014]. Multiple, or binary systems are clearly predicted by those simulations, and the substructures, either spirals, rings or fragmented discs around massive protostars should be possible to image using ALMA [e.g. @Jankovic2019; @Meyer2018].

Studies indicate that over 70% of main-sequence OB stars [@Sana2012; @Moe2017], and 50% of massive young stellar objects [@Pomohaci2019] are known to display binarity or multiplicity. In the deeply embedded star formation stages very high angular resolution ($<$100au scales) sub-mm observations are required to probe the natal environments. There is one recent example of a binary in a proto-O-star system where the secondary, separated by $\sim$1200au, is still within the disc and thought to have formed by disc fragmentation [@Ilee2018]. Furthermore, @Zhang2019 present ALMA long-baseline observations that resolve a high-mass binary system (total-mass$\sim$18M$_{\odot}$) with a physical separation of $\sim$180au.

However, rings, gaps or spiral substructures below 500au spatial scales have not yet been detected in discs around massive-protostars.

G17.64$+$0.16 (hereafter G17.64, also AFGL 2136, G017.6380+00.1566, CRL 2136, and IRAS 18196-1331) is a well-known massive young stellar object (MYSO) that we originally targeted with ALMA along with five other luminous O-type (proto)stars in search for evidence of discs [@Cesaroni2017]. Located at 2.2kpc and with a bolometric luminosity of 1$\times$10$^5$L$_{\odot}$[^3] [@Lumsden2013] G17.64 is one of the closest O-type (proto)stars. It is a bright source at near- to mid-IR wavelengths [@Kastner1992; @Holbrook1998; @deWit2009; @Murakawa2013] and is detected through to the cm regime [e.g. @vandertak2000b; @Menten2004; @Lu2014]. It drives an outflow (position-angle $\sim$135$^{\circ}$), illuminates a reflection nebulae, and excites H$_2$O masers [@Menten2004]. Interferometric IR observations indicated G17.64 as a candidate compact ($<$100au) disc source [@Boley2013]. @Maud2018 presented 0.2$''$ resolution ALMA data probing scales down to $\sim$400au. They did not resolve the continuum emission, but marginally resolved the SiO emission that is thought to trace a rotating disc and disc wind. Modelling the position-velocity profile they estimated a central source mass between 20 and 30M$_{\odot}$. In this letter we report on the observations of G17.64 using the ALMA long-baselines at Band 6. Achieving a resolution of 20$\times$15mas (44$\times$33au), ten times higher than our previous study, we now fully resolve the dust and molecular line emission and for the first time uncover clear enhanced substructures in the disc around this massive forming O-star.

. ![image](G17.H2O_mod_4panel.ps){width="95.00000%"}

Observations {#obs}
============

The ALMA 12m observations consist of one execution block (EB) conducted during Cycle 5 on 4 October 2017 (project ID: 2017.1.00098.S - PI: Maud) in configuration C43-10, with 43 antennas. The on-source time was 30.6minutes. The spectral setup covered the frequency range of our previous observations [see also @Cesaroni2017]. To provide maximal sensitivity to the dust continuum, all four spectral-windows (SPWs) were configured with the widest bandwidth of 1.875GHz but covered previously detected lines, e.g. SiO (5$-$4) and H30$\alpha$. The resulting velocity resolution was of the order 1.3kms$^{-1}$, except in the SPW covering SiO which was 0.8kms$^{-1}$. We also covered the H$_2$O 5$_{5,0}-$6$_{4,3}$ line in the same SPW as H30$\alpha$. The maximal angular resolution of 20$\times$15mas at a position-angle (PA) of -88.4$^{\circ}$ in the continuum was achieved using a robust parameter of 0.0 [@Briggs1995]. Data calibration used the [casa]{} pipeline, version 5.1.1 [@McMullin2007], while subsequent imaging and self-calibration used version 5.4.0. As G17.64 is comparably line weak [@Cesaroni2017] all line-free regions were easily identifiable and continuum subtraction was undertaken in the [*u*,v]{} domain. Self-calibration was possible down to a solution time of 6s in phase and 54s for amplitude, improving the dynamic range from 405 to 640. The final continuum noise level achieved was 40.4$\mu$Jybeam$^{-1}$. For the H$_2$O images a robust value of 1.5 was used to boost surface brightness sensitivity. The resulting resolution was 28$\times$23mas at a PA of 65.8$^{\circ}$ and achieved a sensitivity of 0.76mJybm$^{-1}$ch$^{-1}$ (1.3kms$^{-1}$). We detected SiO (5$-$4) and the H30$\alpha$ radio-recombination line which are mentioned in the appendix. During self-calibration we shifted the phase centre of G17.64 to the position of peak emission, J2000 18$^{\rm h}$22$^{\rm m}$26.3862$^{\rm s}$ $-$13$^{\circ}$30$'$11.9717$''$, to centralise our images. All imaging and self-calibration steps were performed with and without shifting the phase centre to ensure the features detected are real and not interferometric side-lobe artefacts, no notable differences were seen in any of our images.

Results {#res}
=======

Continuum emission {#contemm}
------------------

Figure \[fig:fig1\]a shows our image of the continuum emission from G17.64 in a logarithmic colour scaling to highlight the fainter emission. The continuum dust disc is well resolved and has a clear enhanced ring-like structure that is most readily visible to the north and south between 65$-$97au in the radial direction.

Fitting an ellipse to the 50$\sigma$ contour level ($\sim$2.0mJybeam$^{-1}$) we find that the disc measures 93$\times$71mas. Assuming a circular thin-disc where the mm-sized dust grains have settled to the mid-plane [e.g. @Testi2014] we estimate the disc inclination as $\sim$40$\pm$4$^{\circ}$ (where 90$^{\circ}$ is edge-on). The uncertainty propagates from fitting the disc size at the 30$\sigma$ and 70$\sigma$ contours and calculation of the respective inclination angles. The peak flux is 25.12mJybeam$^{-1}$, while the enhanced arc regions peak at between 3$-$4mJybeam$^{-1}$. We recover an integrated flux of 79.14mJy (within a 60mas radius circle) which is entirely consistent with the previous ALMA observations [81.3mJy before free-free subtraction, @Maud2018] and confirms that we are not resolving out any emission and can attribute the total flux entirely to the disc. Using a minimum value of 250m when considering the well sampled short baselines, we note our maximal recoverable scale is at least 0.64$''$, much larger than the dust disc.

In @Maud2018 we reported that the radio wavelength emission accounts for between 3.57mJy and 29.5mJy when extrapolated to the mm regime. Considering the peak flux is 25.12mJybeam$^{-1}$, this places an upper limit to the free-free contamination in the case that it fully represents the mm emission. In Fig. \[fig:fig1\]b we show the image of G17.64 after the subtraction of a point source, made in the visibility domain, using the upper limit of the free-free contamination. A point source assumption is consistent with the size (29mas at 43GHz) found by @Menten2004 and the reduction in angular size with increasing frequency ($\theta\,\propto\,\nu^{-0.6}$, @Wright1975). Note, the removal of a point-source in the visibility domain can be understood as removing a 2D gaussian with the synthesised beam parameters in the image plane. After the removal of the maximal and minimal free-free components the resulting lower limit optically thin disc mass ranges from 0.6 to 2.6M$_{\odot}$ following @Hildebrand1983 and using dust temperatures of 50K, 100K and 150K consistent with @Maud2018 and Section \[temps\] (see appendix for details).

@Jankovic2019 report that total removal of a central gaussian feature can be a useful technique to highlight residual substructures. It is coincidental that the necessary removal of the free-free contamination from G17.64 has a similar effect. In Fig. \[fig:fig1\]b the brightest structure in the dust disc has a peak flux of 4.4mJybeam$^{-1}$. Although speculative, because the free-free contamination is uncertain, we tentatively reveal an enhanced inner ring or poorly resolved spiral-like structure.

![image](G17.toomre_max4_flat_flip_-0.4.ps){width="95.00000%"}

H$_2$O {#water}
------

Figure \[fig:fig2\] presents the moment-0 and moment-1 maps of the H$_2$O 5$_{5,0}-$6$_{4,3}\,\nu_2=1$ line at 232.68670GHz ($E_u$=3461.9K) in panels (a) and (b) and position-velocity (PV) diagrams over plotted with contours of the data and the best representative model in panels (c) and (d). The extreme excitation energy of this line makes it particularly suited for tracing very inner regions of a molecular disc [@Hirota2014; @Ginsburg2018]. To our sensitivity and resolution limit the H$_2$O emission appears devoid of any structure and does not extend beyond the outer radius of the disc as traced by the dust continuum emission (grey contours Fig.\[fig:fig2\]b). In all velocity channels the peak of emission is away from the centre of the dust disc, while at the highest blue- and red-shifted velocities the H$_2$O emission peaks between the enhanced continuum dust ring and the central location of G17.64. The moment-0 contours in Figure \[fig:fig2\]a shows how the H$_2$O emission could appear like a disc with a central hole, or a single wide ring ranging from approximately half of the beam ($\sim$30au) to 120au in radius, [e.g. like the SO emission in @Yen2014]. The cut for the PV diagram was taken at a position angle of 25.9$^{\circ}$ using a width of 5 pixels to encompass one beam of emission (grey dashed line in Fig.\[fig:fig2\]a,b). The PA was established by fitting a line through the centres of Gaussian fits to independent moment-0 maps of the blue- (3.2$-$21.4kms$^{-1}$) and red-shifted (22.7$-$44.8kms$^{-1}$) emission and the central position of G17.64 from the dust continuum. The PV diagram depicts the clear pattern of Keplerian rotation, particularly the red-shifted emission $>$30kms$^{-1}$ where the highest velocities peak closer towards the central source. The H$_2$O is undoubtedly tracing a rotating disc.

Discussion
==========

Stellar mass {#stelmass}
------------

Based on its luminosity G17.64 is firmly positioned as an O-star [e.g. @Vacca1996]. However, previous estimates of the stellar mass, which are essential for understanding the disc stability, were not well constrained due to poorly resolved kinematics [@Maud2018]. Building from our previous representative models presented in @Maud2018 we match the H$_2$O PV diagram with only very minor changes. We use our ‘disc-only’ model for the H$_2$O emission, as there is no evidence for extended structure, we fix the disc outer radius to 120au as per the dust and H$_2$O maps and also revise the inclination angle to 40$\pm$5$^{\circ}$. Now that the disc is fully resolved we have a measure of the system inclination which was a previously degenerate parameter [@Maud2018]. The inner radius is varied only between 25$-$30au in line with the lack of strong H$_2$O emission at the centre [Fig.2a, see also @Maud2018], and consistent with the potentially ionised inner disc seen in H30$\alpha$ emission (appendix). With these modifications, the modelled central mass must be increased to 45$\pm$10M$_{\odot}$ to best match the observed PV diagram (Fig.\[fig:fig2\]c,d), especially the red-shifted emission at higher velocities. The mass increase compared to @Maud2018 is due to the revised inclination angle as the disc is more face-on. Following @Maud2018, fitting is made by-eye matching equivalent contour levels [see also @Ilee2018].

Disc stability {#temps}
--------------

In discs undergoing Keplerian rotation, local regions may be unstable to axisymmetric perturbations if the Toomre parameter, Q, [@Toomre1964] is:

$$Q = \frac{c_s \kappa}{\pi G \Sigma} < 1,$$

where $c_s$ is the sound speed, $\kappa$ is the epicyclic frequency - orbital velocity $\Omega$ for a Keplerian disc - G is the gravitational constant, and $\Sigma$ is the disc surface density. Figure \[fig:fig3\]a,b show the Toomre Q maps for G17.64 where the minimal and maximal free-free contamination is removed. A deprojection has been applied in the image plane for the minor disc axis after rotation (major axis is north-south). We follow the methods outlined in @Beuther2017a and @Ahmadi2018. Both the mass surface density, calculated from the column density [Eq 2. @Schuller2009] multiplied by the mean molecular weight and mass of the hydrogen atom ($\mu m_{\rm H}$, where $\mu$ = 2.3), and the sound speed use a radial temperature dependence and we directly calculate the orbital velocity from Keplerian rotation. The temperature of the disc is calculated using $T(R)\propto (R/R_0)^{-0.4}$ [@Whitney2003] propagating from the outer radius and temperature of a 45M$_{\odot}$ main-sequence O-star from @Hosokawa2009, where for G17.64 we estimated, $R_0\sim$9.3R$_{\odot}$, $L\sim$1.9$\times$10$^{5}$L$_{\odot}$ and $T\sim$60000K. At radii $<$150au the disk temperature is $>$150K.

The ring-like enhancement between radii 65$-$97au has the lowest Toomre Q values, between 2 and 4. There is little difference between the data with the minimal and maximal free-free contamination removed as the lowest Q regions are away from the central peak where the free-free contamination occurs. There are no current instabilities identified in the substructures (c.f. Fig.\[fig:fig1\]b). If we use a steeper temperature profile [e.g. -0.5, @Brinch2010] the temperature in the disc is below 150K, and the overall cooler disc can become unstable Q$<$1. Additionally, in an optically thick case, suggested by the continuum average brightness temperatures (see the appendix), the surface density will increase when correcting for opacity and Q would decrease. If considering a highly flared disc, the Toomre criterion is met where Q$<$1.7 [@Durisen2007], thus a proxy of the dust and gas disc scale heights and temperature estimation from radiative transfer are required to better constrain the stability. The presented Toomre Q analysis suggests that unless the dust is cold and significantly shielded the disc can remain stable against fragmentation. This does not preclude that the existing substructures may have formed from fragmentation. During formation, a more massive, cooler, and potentially largely flared disc combined with a reduced stellar mass would have yielded conditions where Q&lt;1.7.

Disc enhancements
-----------------

G17.64 is the first massive O-type source in which substructure has been observed in the disc. Interestingly, recent IR interferometry and models by @Frost2019 suggest that the MYSO G305.20+0.21 could be a massive transition disc, with an inner edge at 60au, not dissimilar to the ring-enhancement in G17.64, although there are no high-resolution mm studies. Similar processes, such as radial drifts, could be at work in G17.64 as they are in low-mass sources [@Pinilla2018]. In this case dust grains become trapped in pressure maxima and can grow (see Sec.\[intro\]), however, multi-wavelength observations are required to establish dust grain sizes and confirm the phenomena. Considering that most massive systems exist as binaries, it is plausible that a binary companion is the cause of the ring-like enhancements, much like the 1.8M$_{\odot}$ source HD142527 [@Price2018]. We could interpret the brightest dust peak south-east of G17.64+0.16 as a binary companion, although there is no clearly separated source like in @Ilee2018. The substructures could be spirals caused by instabilities occurring before this ‘stable’ disc phase as these would appear as arc or ring-like enhancements if not fully resolved. Higher-frequency observations may be the only way to probe 10au scales, provided that substructures are still visible with increasing optical depth.

Conclusions {#conc}
===========

In this letter we present ALMA long baseline observations that reveal the disc in the proto-O-star G17.64$+$0.16. Through the PV analysis of the H$_2$O emission using our disc model we confirm Keplerian rotation about a central mass of 45$\pm$10M$_{\odot}$. We find that the continuum emission has a significant enhancement of dust emission in a ring-like, or possibly underlying spiral structure. The disc is found to be locally stable through a Toomre Q analysis in the optically thin case when disc temperature are $>$150K.

The authors thank the referee for their detailed comments that helped to improve this manuscript. MSNK acknowledges the support from Fundação para a Ciência e Tecnologia through Investigador contracts and exploratory project IF/00956/2015/CP1273/CT0002 HB and AA acknowledge support from the European Research Council under the European Community’s Horizon 2020 framework program (2014-2020) via the ERC Consolidator Grant ‘From Cloud to Star Formation (CSF)’ (project number 648505). RGM acknowledges support from UNAM-PAPIIT Programme IN104319. RK acknowledges financial support via the Emmy Noether Research Group funded by the German Research Foundation (DFG) under grant no. KU 2849/3-1 and KU 2849/3-2. VMR thanks the funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 664931. This paper makes use of the least-squares fitting by @HammelLS. This paper makes use of the following ALMA data: ADS/JAO.ALMA\#2017.1.00098.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.

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Disc mass and other lines {#AppendixA}
=========================

![image](G17.SIO_H30a.ps){width="95.00000%"}

Disc Mass {#disc-mass .unnumbered}
---------

The disc mass is estimated in the standard fashion : $$M = \frac{g S_\nu d^2}{\kappa_\nu B_\nu(T_d)},$$

where $S_\nu$ is the source flux, g is the gas-to-dust ratio = 100, $B_\nu(T_d)$ is the Planck function for a temperature, $T_d$, $d$ is the source distance, and $\kappa_\nu$ is the dust opacity coefficient. At 1.3mm (220GHz) we use $\kappa_\nu$ = 1.0 cm$^2$g$^{-1}$ as suggested for dust with thin ice mantles at densities of 10$^6-$10$^8$cm$^{-3}$ [@Ossenkopf1994]. As noted we use temperatures, $T_d$, between 50-150K. Even when using temperatures lower than the disc average continuum brightness temperature, 193K and 138K dependent on the free-free subtraction, or those found by scaling from the source temperature (where the inner radii are slightly hotter) the disc mass should be considered as a lower limit if we are in the optically thick regime. An optical depth of $\tau$=1 would account for a disc mass increase by a factor of 1.6, to between 1.0 and 4.2M$_{\odot}$

Other Lines {#other .unnumbered}
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We detected the previously known, strong SiO (5$-$4) molecular line emission and the H30$\alpha$ radio-recombination line. The PV diagrams for these lines are shown in Fig.\[fig:figA1\]. The SiO also well traces the disc structure following the H$_2$O emission at disc radii of $<$120au, however, at low velocities closer to the source V$_{\rm LSR}$ the SiO is significantly more extended reaching out to at least 250au in radius before the surface brightness sensitivity is too low. The map was made with robust 1.5, the resolution is 30$\times$24mas at a PA of 64.9$^{\circ}$ and the sensitivity is 1.02mJybeam$^{-1}$ per 0.8kms$^{-1}$ channel. The extended emission was seen previously in our lower-resolution ALMA observations [@Maud2018] and is thought to be tracing outflowing material in a disc wind.

The H30$\alpha$ emission appears unresolved per channel in the image cube and traces only the very central region of G17.64, although there is a marginal shift in spatial position from blue- to red-shifted velocities. We imaged using a robust 0.0 to provide the highest resolution (20$\times$18mas, PA=-88.4$^{\circ}$). The resulting sensitivity is 1.11mJybeam$^{-1}$ per 1.3kms$^{-1}$ channel. In the PV diagram, Fig.\[fig:figA1\]b, the slight shift in position with change in velocity is clearer, and is in the same rotation sense as the H$_2$O and SiO emission. The H30$\alpha$ could be tracing a hot inner rotating structure inward of the molecular line region. We note that the total spectral coverage of our data are, SPW0: 216.746-218.621GHz, SPW1: 218.854-220.746GHz, SPW2: 230.938-232.812GHz, SPW3: 233.048-234.94GHz.

[^1]: E-mail:lmaud@eso.org

[^2]: The data presented in this article are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

[^3]: Red MSX Survey: http://rms.leeds.ac.uk/cgi-bin/public/RMS\_DATABASE.cgi
