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A&A
Volume 684, April 2024
Article Number A141
Number of page(s) 18
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202346763
Published online 18 April 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Before being confirmed through observations, disks have been expected to surround forming stars of different masses since, under the conversation of angular momentum, the collapsing cloud will flatten perpendicular to the rotation axis. Numerical models (Klassen et al. 2016; Rosen et al. 2016; Harries et al. 2017; Meyer et al. 2018) have also suggested that circumstellar disks can channel material to the central forming star, overcoming the strong feedback from the central protostar that may halt the infall of material (Kahn 1974; Wolfire & Cassinelli 1987). Circumstellar disks around low- (M* < 2 M⊙) and intermediate-mass (2 M⊙ < M* < 8 M⊙) protostars have often been detected (e.g., Ansdell et al. 2016, 2018; Tripathi et al. 2017; Andrews et al. 2018). However, the picture and role of the circumstellar disks around high-mass protostars (M* > 8M⊙) are still unclear. Observational difficulties arise as they are relatively rare, distant (the typical distance is several kpc), and embedded in more crowded environments than their low-mass counterparts. In many cases, complex velocity structures and potential multiplicity can also confuse the detection (e.g., Cesaroni et al. 2017; Ahmadi et al. 2018; Beuther et al. 2018). Additionally, the commonly insufficient angular resolution makes confirming the existence of disks around massive protostars a challenging task.

Searching for disks around massive stars with (sub)mm interferometers can be dated back to the late 1990s (Zhang et al. 1998). Despite the aforementioned limitations, there is accumulating evidence for disks around high-mass protostars (Wang et al. 2012; Sánchez-Monge et al. 2013; Cesaroni et al. 2014; Beltrán et al. 2014; Beltrán & de Wit 2016; Girart et al. 2017), thanks to instrument development. With the advent of the Ata-cama Large Millimeter Array (ALMA), which has sufficiently high angular resolutions (<0.1″, corresponding to ≤ 100 au at a typical distance of a few kpc for high-mass star-forming regions) and a high sensitivity, evidence for Keplerian rotating disks around massive protostars has been found, such as G35.20-0.74N (Sánchez-Monge et al. 2013), G35.03+0.35 (Beltrán et al. 2014), Orion source I (Ginsburg et al. 2018), G17.64+0.16 (Maud et al. 2018), G11.92-0.61 MM1 (Ilee et al. 2018), and MonR2-IRS2 (Jiménez-Serra et al. 2020). Despite the growing observational evidence of Keplerian disks (on the order of 102 ~ 103 au), there are also some studies that found no disks at similar resolutions (Ginsburg et al. 2017; Goddi et al. 2020). Considering the limited sample size of detection and non-detection cases, it is still uncertain whether the disk-mediated accretion scenario is the primary mechanism for high-mass star formation.

With this in mind, we use the Submillimeter Array (SMA) to build a large sample of disk candidates in Cygnus-X at 1.3 mm with multiple configurations. Cygnus-X is the most massive giant molecular cloud within 3 kpc of the Sun (Schneider et al. 2006). It also has a rich collection of HII regions (Wendker et al. 1991) and several OB associations (Uyaniker et al. 2001), making it an active star formation region in the Galaxy. Hundreds of massive dense cores (the size of a few 0.1 pc, masses of tens to hundreds of Solar masses) have been identified in the complex (Motte et al. 2007; Cao et al. 2019). Previous observations (e.g., Bontemps et al. 2010) with high angular resolutions have resolved some of these dense cores into smaller fragments on the order of 1000 au, which are termed condensations. We conducted an SMA survey of dust continuum and molecular line emission in 1.3 mm toward 48 massive dense cores identified in Cygnus-X. With a resolution of 1.8″ (corresponding to ~2000 au at a distance of 1.4 kpc for Cygnus-X), we find a large population of dust condensations. As a part of our project, Surveys of Clumps, CorEs, and CoNdenSations in CygnUS-X (CENSUS, PI: Keping Qiu), this paper focuses on the outflow structures and gas kinematics around the dust condensations. Our SMA survey reveals many CO outflows originating in condensations. High-density tracers (e.g., CH3CN, CH3OH and H2CO lines) have allowed us to further investigate the molecular gas kinematics of the condensations. This paper is structured as follows. Section 2 summarizes the observations and data reduction. Section 3 presents the images of 1.3 mm dust continuum, outflows, and the velocity field traced by selected molecular lines along with the derived gas temperature. In Sect. 4, we provide the detection rate and its implications for high-mass star formation. Summaries are presented in Sect. 5.

2 Observations and data reduction

We first chose massive dense cores (MDCs) identified by Motte et al. (2007) as the targets of the SMA high-resolution observations. Because the region toward Cygnus OB2 was not covered by Motte et al. (2007), we then added eight dust continuum peaks seen in the JCMT 850 μm maps of the OB2 region (Cao et al. 2019). Since we are searching for disk candidates toward dust condensations in this work, we excluded the SMA data that detected no dust condensations or for which the 1.3 mm continuum emission was heavily contaminated by the free-free emission. In the end, the SMA observations presented in this work were done with 31 single-pointing fields and two mosaic fields, covering 48 MDCs identified by Cao et al. (2021, see Table A.1). It is also worth noting that all these MDCs were included in a VLA study of compact radio sources by Wang et al. (2022), which is also part of the CENSUS project. Detailed information about our SMA observations is presented in Table 1.

We calibrated the raw data with the IDL superset MIR1, and exported the calibrated visibilities into CASA (McMullin et al. 2007) for joint imaging. All images were made using a Briggs weighting of 0.5 (Briggs 1995) to balance resolution and sensitivity. The resulting synthesized beams are ~1.8″ in the final maps. During our observations, the SMA correlator was being upgraded from the ASIC to SWARM. Also considering the archive observations, the data used in this project had total bandwidths ranging from 4 GHz to 16 GHz, and the spectral resolution also varied. However, all the high-density tracers relevant to this work and the outflow tracers, CO (2−1), 13CO (2−1), and SiO (5−4), were all covered by each observation. We also smoothed all the data into a uniform-frequency resolution of 812.5 kHz (~1 km s−1 at 230 GHz) during imaging.

3 Results

3.1 Dust condensations and outflows

The 1.3 mm continuum maps of sources in our sample are shown in Fig. 1 (Figs. A.1 and A.3 show continuum maps of the two mosaic fields). With a typical resolution of ~1.8″ (~2000 au), these massive dense cores (MDCs, ~0.1 pc) are resolved into dust condensations (~0.01 pc). Most fields harbor a few bright and compact condensations, except Field15, which appears to be dominated by a single source. Some fields, such as Field2 and Field17, exhibit high levels of fragmentation. Cao et al. (2021) employed “getsources”2 to identify condensation from these MDCs. Applying the criterion that the emission peak must exceed 5σ of the image noise levels, the robust detections of dust condensations are about 200. The full width at half maximum (FWHM) diameters of these condensations range from 0.008 to 0.05 pc.

To search for disk candidates, first we have to find condensations located at the geometrical center of a bipolar outflow or connected to a unipolar outflow, since accretion disks are expected to be associated with jets or outflows ejected along their rotation axes (Cesaroni et al. 2007). CO emission lines usually trace the molecular outflowing gas. The velocity-integrated intensity maps of 12CO 2−1 toward sources in our sample are shown in Fig. 2 (Figs. A.2 and A.4 show outflow structures of the two mosaic fields). We use red and blue arrows to depict redshifted and blueshifted outflow axes, respectively. SiO 5−4 emission also help us confirm the outflow axis. The details of the SiO 5−4 emission are presented in Yang et al. (2024). In total, we find 49 dust condensations associated with outflows (hereafter “outflow-associated” condensations) and expect to find disk candidates among them.

3.2 High-density tracers

The most reliable criteria of disk identification are based on the velocity field, which requires us to study the kinematics of these 49 outflow-associated condensations. We looked through all the detected molecular line emission from outflow-associated condensations and found that only 27 of these condensations have high-density tracers to investigate the kinematics. These 27 condensations are labeled as “dense-gas-traced”. For the other 22 outflow-associated condensations, we cannot study their kinematics, and therefore we leave them out in the following analyses.

We detect a series of molecular lines tracing high-density gas for each dense-gas-traced condensation, including transitions from CH3CN, CH3OH, H2CO, and DCN. The information on these transitions is listed in Table 2. CH3CN lines have proven to be a great dense gas and disk tracer. However, we only detect CH3CN emission in a few sources. Considering the various evolutionary stages and physical and chemical properties of condensations in our sample, it is difficult to find a uniform disk tracer for all the condensations. Consequently, we employed different species to investigate the kinematics in our study. The intensity-weighted mean velocity (first-moment) maps of the representative molecular line toward dense-gas-traced condensations are shown in Fig. 3. We chose the molecular spectral lines to show the dense gas kinematics according to the following criteria: (i) the molecular line should show compact emission around the central source of the outflow, which ensures the emission mainly come from the circumstellar disk or surrounding envelope; (ii) if several dense gas tracers all exhibited a velocity gradient in a similar direction, we chose the molecular line whose emission exhibited the clearest velocity gradient. In most cases, we had seven molecular line emission from five species to investigate the kinematics of these dense-gas-traced condensations. The high-excitation transitions of CH3CN and CH3OH are common dense gas tracers to search for rotating disks or “toroids”. The line emission from low energy levels of some molecular species, DCN and H2CO, can also trace the velocity fields around condensation. In some cases (e.g., Tobin et al. 2020; Cheng et al. 2022, Field8 MM1 in our sample), C18O (2−1) emission can also exhibit a velocity gradient as the result of a rotating disk or envelope.

Table 1

Observational parameters.

3.3 Identification of disk candidates

The rotating disk candidates can be identified by two simple criteria following Cesaroni et al. (2017): (i) the position angle of the observed velocity gradient should be within 20° orthogonal to the CO outflow axis and (ii) the relative velocity with respect to the systemic velocity of the source should increase toward the center in the position-velocity (PV) plots. The position angles of the outflow axis and velocity gradient are given in Table 3. We employ relatively loose constraints (20 degrees) on the relative angles between the outflow axis and velocity gradient for several reasons. First, the position angles of the outflow axis and velocity gradient are generally defined by eyes. The complex velocity fields and asymmetries in the outflow emission can bring large uncertainties to the measurement of the position angles. Second, in some cases the dust condensations are clustered, making it difficult to confirm which one is the central source of the outflow. Among the 27 dense-gas-traced condensations, only nine display velocity gradients roughly perpendicular to the outflow axis. We label these condensations as disk candidates.

To better illustrate the gas kinematics and investigate whether the velocity gradient is consistent with rotation, we checked the PV cuts in the direction of the velocity gradient (see Fig. 4).

The plots of four identified disk candidates (Field3 MM1, Field8 MM1, Field18 MM1, and Field21 MM1) roughly exhibit a butterfly-shaped feature that is characteristic of Keplerian rotation. We overlaid red Keplerian curves on the PV plots of these four sources. It should be noted that these Keplerian curves are shown only for comparison purposes and are not fitting models. Precise mass estimates of the central protostars from the P–V plots still need higher-resolution observations to resolve the “true disks”, and to constrain the inclination of the disk plane. The rest plots show features that more closely resemble rigid-body rotation than Keplerian rotation. These features are also seen in simulations (e.g., Ahmadi et al. 2019) and observational data (e.g., Cesaroni et al. 2017) with comparable resolutions to our SMA observations. This is likely caused by the insufficient resolution. The contributions of unresolved disks and infalling, rotating envelopes are heavily blended, and thus make the Keplerian curve not fit well with the observational data. Higher-resolution observations are needed to separate the contributions of the disk and envelope.

thumbnail Fig. 1

SMA 1.3 mm continuum emission of sources in our sample. The contour levels are (−3, 3, 6, 9, 12, 18, 24, 36, 48, 60)×σ, where σ is the rms of the dust continuum. The synthesized beam of each image is shown in the bottom left. The red plus represents the dust condensation extracted by Cao et al. (2021).
thumbnail Fig. 2

Molecular outflows detected in CO (2−1) in some sources. The blueshifted and redshifted outflows of CO (2−1) are plotted in blue and red contours, respectively. The contour levels are (−3, 3, 6, 9, 12, 15, 18, 24, 36, 48, 60)×σ, where σ is the rms of the integrated CO emission. The blue and red arrows mark the outflow axes identified in the region. The grayscale images and black contours show SMA 1.3 mm continuum emission. The contour levels are the same as in Fig. 1. The extracted dust condensation is marked by a black cross.
thumbnail Fig. 3

Intensity-weighted mean velocity maps of representative molecular line emission toward all dense-gas-traced sources, overlaid with the SMA 1.3 mm continuum emission contours, the same as in Fig. 1. The background color map shows the relative velocity to the systemic velocity of the source. The blue and red arrows represent the blueshifted and redshifted CO outflow axis, respectively. The dashed black lines indicate the velocity gradient orientation inferred from molecular line kinematics. Each panel is labeled with the species name and the excitation energy (in Kelvin) of the upper level of the transition. The label “disk candidate” on the bottom right marks the disk candidates in our sample.

4 Discussion

In recent years, many disk candidates around massive protostars have been detected (Beltrán & de Wit 2016). The resolution of these observations is typically on the order of 1000 au or coarser, comparable to our SMA observations. However, it is worth noting that these disk-like structures are more likely infalling, rotating envelopes or “toroids” (Cesaroni et al. 2007; Beltrán & de Wit 2016), rather than true accretion disks on a smaller scale. The true accretion disks should generally have sizes on the order of 100 au, as revealed by recent ALMA observations (e.g., Maud et al. 2018; Ilee et al. 2018; Ginsburg et al. 2018; Jiménez-Serra et al. 2020). Since circumstellar disks are usually believed to mediate material onto protostars from the rotating envelopes, the detection of the rotating structures suggests the existence of embedded circumstellar disks.

With high-resolution SMA observations (~1.8″), we built up a unique sample consisting of 49 dust condensations associated with molecular outflows. Considering the well-established disk-outflow association in various environments (Cesaroni et al. 2007), we expected to find evidence of a rotating disk or envelope in each outflow-associated condensation. However, only 27 condensations were detected in high-density tracers, and these dense-gas-traced condensations are our targets in searching for rotating evidence. Among the dense-gas-traced condensations, nine condensations show velocity gradients perpendicular to the outflow axis, indicating that these sources may host rotating envelopes or toroids with circumstellar disks embedded in them. The properties of these identified disk candidates are discussed in Sect. 4.1. The other dense-gas-traced condensations have no clear velocity gradients or show velocity gradients parallel to the CO outflow axis, which is against the disk hypothesis. The missing rotation signs in these sources are discussed in Sect. 4.2. For the rest of the outflow-associated condensations, we do not detect appropriate molecular line emission for studying the kinematics of dense gas around these sources. More sensitive observations are needed to confirm whether these sources are disk candidates.

Table 2

Information on the spectral lines.

thumbnail Fig. 4

PV diagram of spectral lines toward the disk candidates, cut along the dashed black lines shown in Fig. 3. The dashed red lines show the Keplerian rotation curves for central masses labeled in the upper left. The black contours correspond to 3, 5, 7, 9,11, and 13 σ levels. The vertical line marks the reference point. The horizontal line indicates the systemic velocity.

4.1 Properties of identified disk candidates

Cao et al. (2021) determined the dust temperature of identified dust condensations (refer to their Appendix B) through a combination of two results: the large-scale (~36″) dust temperature map from SED fitting results of Herschel data and a power law radial temperature profile T(r)∝r−0.4L*0.2$T\left( r \right) \propto {r^{ - 0.4}}L_*^{0.2}$ obtained from an approximate radiative transfer model, where L* represents the luminosity of the central heating source (protostars). The results are listed in Table 3. It is important to note that since the Herschel data cannot resolve the MDCs, the derived dust temperature can be used as a lower limit when a central heating source is lacking. Additionally, CH3CN and H2CO lines have been detected in certain sources, and we employed the XCLASS (eXtend CASA Line Analysis Software Suite tool, Möller et al. 2017) to estimate the molecular gas temperature of these sources. Detailed information on the molecular gas temperature calculation can be found in Appendix B.

For the gas mass estimates, Cao et al. (2021) assumed optically thin dust emission and adopted the equation: Mgas=gFvD2Bv(T)κv,${M_{{\rm{gas}}}} = {{g{F_v}{D^2}} \over {{B_v}(T){\kappa _v}}},$(1)

where Mgas is the gas mass of the condensation, g is the gas-to-dust mass ratio, Fv the dust flux density at frequency, ν, D the source distance that is set to 1.4 kpc, BV(T) the Planck function at dust temperature, T, and κν the dust opacity coefficient. They adopted a gas-to-dust mass ratio of 100 and a dust opacity, κν = 10(v/1THz)β in cm2 g−1, following the HOBYS consortium3 (e.g., Tigé et al. 2017). The dust opacity power law index β used here is two. The gas mass of disk candidates ranges from 4M⊙ to 80 M⊙.

4.2 Why don’t all outflow sources show evidence of rotation?

Given that accretion disks are physically connected to outflows, we expected to detect evidence of rotating disks in all outflow-associated condensations. For sources without the emission of dense gas tracers, we cannot determine their kinematics. These sources were excluded from our analyses. So, our analysis focused on the 27 dense-gas-traced condensations. The disk candidate detection rate in the dense-gas-traced group is only 9/27=33.3%, and the question is why only one third of outflow sources show evidence of disks.

Table 3

Information on the dust condensations associated with outflow in our SMA observations.

thumbnail Fig. 5

Schematic diagram of our envelope-disk model. The outflow axis is aligned with the ζ axis. The inner part of the Keplerian disk starts from the inner boundary, rin = 10 au, and extends to the centrifugal barrier, rCB = 100 au. The outer envelope ranges from the centrifugal barrier, rCB, to the outer boundary, rout = 2000 au.

4.2.1 Non-detection of rotating structures

There are several explanations for the lack of a velocity gradient toward some dense-gas-traced condensations. First, in contrast to the simplified classic paradigm of a stable disk-jet system, many simulations (Myers et al. 2013; Seifried et al. 2015; Rosen et al. 2016) predict that protostellar cores may accrete material through asymmetrical filaments without a large, stable Keplerian disk, and some recent ALMA observations support this scenario (e.g., Goddi et al. 2020). However, it needs higher-spatial-resolution observations to confirm whether these sources without rotating structures in our sample actually accrete material through filamentary flows. Second, several condensations, for example Field4 MM3 and Field 10 MM3, are located in complex regions. The emission from adjacent energetic events (e.g., accretion flow or jets and outflows) may confuse the velocity field around these condensations and make it difficult to distinguish the rotating structures or toroids. On the other hand, relatively isolated sources, forming in an environment away from other energetic events, have a higher chance of showing detectable rotating structures (e.g., Field9 MM1, Fieldl6 MM1 in this work and G17.64+0.16 in Maud et al. 2018).

The inclination of the disk plane with respect to the line of sight may also affect the observational evidence of a rotating disk. We made a simple simulation following Zhang et al. (2019) to investigate the influence of inclination on disk identification.

Figure 5 shows the schematic view of an inner Keplerian-rotating disk embedded in a larger-scale infalling and rotating envelope. The masses of the central protostar, accretion disk, and envelope are 10 M⊙, 3 M⊙, and 5 M⊙, respectively. We assumed an opening angle of 150° for the outflow cavity. The flattened envelope has a radial free-fall velocity. Its rotation velocity can be described as νφ ∝ r−l. The inner disk is assumed to be in Keplerian rotation (vrot ∝ r−1/2). We used open-source software, RADMC-3D (Dullemond et al. 2012), and the CASA simulator task simobserve to generate synthetic SMA observations for the model with different inclination angles. The settings for the synthetic observation are the same as for our SMA observations, with an angular resolution of ~1.8″ and a velocity resolution of 1 km s−1. Figure 6 shows the first-moment map of CH3CN (123− 113) for the synthetic observation. The simulation indicates that only when the rotation axis is extremely inclined to the line of sight (incl ≤10°) can the velocity structure of the disk and envelope not be revealed by our SMA observation, meaning the effect of the inclination angles is not the prominent cause of the non-detection of a rotating structure.

However, it is worth noting that the orientation of the velocity gradient slightly changes with the inclination. When the disk plane is nearly edge-on (incl ≥80°), the velocity gradient is almost perpendicular to the outflow axis. As the inclination angle decreases, the orientation of the velocity gradient slightly shifts toward the outflow axis. This phenomena is also seen in other simulations (e.g., Ahmadi et al. 2019). We speculate that it may be because the envelope and disk contributions are strongly blended under poor resolutions. The velocity gradients seen at a low inclination angle (including ≤30°) are mainly contributed by the infalling-rotating envelope since the line-of-sight velocity component in the disk is very small. The disk contributions become increasingly important as the structures get more inclined. Detailed kinematic analyses using high-resolution simulations and more sophisticated models are necessary to investigate the direction of the velocity gradient changes with the inclination and to what extent this could affect the detection of a rotating disk, which is beyond the scope of this work.

thumbnail Fig. 6

Synthetic SMA observations made with the CASA task “simobserve” from the outputs of radiative transfer calculations of the envelope-disk model shown in Fig. 5. From left to right, the inclination angle of the rotation axis with respect to the line of sight changes from 10° to 80 °. The color scale shows the CH3CN (123−113) first-moment map. The red and blue arrows represent redshifted and blueshifted outflows, respectively. The bottom left of each panel shows the synthesized beam.

4.2.2 Comparisons between disk candidates and others

Except for the examples mentioned above, we compared the properties of disk candidates and non-disk dense-gas-traced condensations to further explore the detectability of rotating structures around protostars.

Table 3 lists the parameters of the condensations. To better illustrate the temperature difference between disk and non-disk groups, Fig. 7 shows the distribution of dust temperatures for all dense-gas-traced condensations. Most disk candidates, except for Field9 MM1 and Fieldl8 MM1, have dust temperatures exceeding 30 K, with a median temperature of 34 K. On the other hand, the non-disk dense-gas-traced condensations generally have lower dust temperatures, with a median value of 22.5 K. The 1-σ uncertainty of the dust temperature is σT = 4 K. The difference between the median temperature of disk candidate and non-disk dense-gas-traced sources is about three times the temperature uncertainty. We ran a Kolmogorov-Smirnow test (K-S test) to investigate how significant the temperature difference is between the disk candidate and non-disk dense-gas-traced sources. A ρ value of ≈0.01 was obtained for testing the null hypothesis that the two distributions are identical, indicating a statistically significant difference in dust temperature between the two groups. Even though the dust temperature is derived from the Herschel data with a coarser resolution, considering that the temperatures were uniformly derived for all the sources in our sample, we took it into account in checking the evolutionary stages of the sources. The increasing trend in the dust temperature from disk candidates to non-disk dense-gas-traced condensations suggests disk candidates are more evolved.

The brightness of radio continuum emission can also to some extent probe the evolution of high-mass star formation. Wang et al. (2022) have made a systematic study of the radio properties of the condensations in our sample with high-angular-resolution VLA observations. They find that the detection rate of radio sources, either in the form of radio jets or wind, or UC/HC HII, increases as the protostellar object evolves. This trend is consistent with that in Rosero et al. (2016). It may come from this that, at a very early stage, the star formation activities are not strong enough to produce detectable radio emission. For example, Tanaka et al. (2016) modeled the evolution of a massive protostar and its associated jet as it is being photoionized by the protostar. In this outflow-confined HII region model, at a very early stage, the ionizing photon luminosity is too low to ionize the outflow, and thus does not produce free-free emission. As a result, the sources without detectable radio emission are more likely at an earlier stage than the sources with radio emission. We cross-checked 49 outflow-associated condensations with their identified radio sources and found that the radio detection rate of disk candidates is 100%, substantially higher than the detection rate of non-disk dense-gas-traced sources, which stands at 9/18 = 50%. Consequently, disk candidates are generally more evolved than non-disk dense-gas-traced sources, which is consistent with the speculation from the above comparison of dust temperatures.

To further check the evolutionary stages of the sources, we conducted a cross-correlation analysis between the 49 outflow-associated condensations and the mid-infrared sources from the Cygnus-X Archive catalog4. By applying a spatial constraint of 2″, approximately the mean size of the condensation, we found that 23 condensations coincide with Spitzer sources (see Table 4). In a previous study, Kryukova et al. (2014) systemically surveyed protostars in the Cygnus-X region using Spitzer IRAC and 24 μm photometry. They estimated the spectral index, α = δ log(λFλ)/δ log(λ) in wavelength ranges from 3.6 μm to 24 μm. Based on their estimated spectral index, α, these sources are identified as Class 0/I (α > 0.3), flat spectrum (−0.3 < α < 0.3), and Class II (using criteria of Gutermuth et al. 2009) young stellar objects (YSOs). We note that Kryukova et al. (2014) classified these protostar candidates only depending on their mid-infrared color, without considering their masses. Therefore, it is important to clarify that a condensation classified as Class 0/I/II or flat spectrum only reflects its IR color and does not mean that it is a low-mass protostar or young star. We used this information to constrain the evolutionary stages of these sources. Apparently, a source dark all the way from 3.6 μm to 24 μm is cold and at an earlier evolutionary stage compared to a source that is detected in several Spitzer bands and that could be classified as Class 0/I/II or flat spectrum by Kryukova et al. (2014). Some of the brightest sources in our sample are saturated (e.g., Field7 MM2) or unresolved (e.g., Field2 MM2) at 24 μm, and thus it is not possible to do 24 μm photometry. Kryukova et al. (2014) excluded these sources in their classification catalog, while we notice that these sources always have bright emission at 3.6 μm to 8.0 μm . Therefore, it is reasonable to assume that the sources that are saturated or unresolved at 24 μm are also relatively more evolved. Eventually, we found that more than half of the non-disk (11/18 = 61.1%) dense-gas-traced condensations are dark in 3.6 μm to 24 μm, while 8/9 = 88.9% of the disk candidates have bright emission in 3.6 μm to 24 μm. This again suggests that disk candidates are relatively more evolved than non-disk dense-gas-traced sources.

Several studies (e.g., Arce & Sargent 2006; Qiu et al. 2019; Vazzano et al. 2021; Heimsoth et al. 2022) have found that the outflow opening angles increase as the outflow central sources evolve. Within our sample, we notice that the outflows emanating from disk candidates tend to have wide-angle morphology (e.g., Field8 MM1) or irregular shapes (e.g., the blueshifted lobe associated with Field7 MM2), while the outflows originating in non-disk sources always appear to be collimated (e.g., Field1 MM1). This provides another piece of evidence that disk candidates are generally more evolved.

From all the perspectives discussed above, dust condensations with rotating disks or toroids are generally more evolved than other sources. The apparent lack of rotating structures at relatively early evolutionary stages might be due to the outflow-envelope interactions proposed by Arce & Sargent (2006). Table 3 shows that some non-disk dense-gas-traced condensations display velocity gradients rougly parallel to the axis of outflow (e.g., Field1 MM2). For those dense-gas-traced condensations without a clear velocity gradient, their dense gas emission always appear to be elongated along the outflow axis. Since the spatial resolution of our SMA observations is insufficient to resolve the true accretion disk (on the order of 102 au) that is embedded within the envelope, the high-density tracers mainly come from the contribution of the high-density envelope (on the order of 103 au). In young, deeply embedded sources, the powerful outflow entrains and pushes gas into the envelope, causing the elongated distribution of the dense gas along the outflow axis. As the protostar evolves, the outflow cavities tend to widen. Most of the remaining circumstellar gas is concentrated in the flattened envelope perpendicular to the outflow axis, which is consistent with the model from Zhang et al. (2019). At this stage, it is more common to detect rotating structures or toroids with dense gas tracers.

thumbnail Fig. 7

Dust temperature distribution of all dense-gas-traced condensations in relation of gas mass. Red and blue dots represent disk candidates and non-disk dense-gas-traced condensations, respectively. The dashed red line shows the median temperature of the disk candidates, 34 K. The dashed black line shows the median temperature of the non-disk dense-gas-traced condensations, 22.5 K. In the lower right corner, the vertical and horizontal black error bar indicates the uncertainties of the dust temperature (σT = 4 K) and the gas mass (~0.26 dex) from Cao et al. (2021), respectively.
Table 4

Infrared properties of outflow-associated condensations.

5 Summary

We have shown the results of SMA observations of continuum and molecular line emission toward 31 single-pointing fields and two mosaic fields, covering 48 MDCs in Cygnus-X. The highresolution observations resolve these MDCs into about 200 dust condensations with sizes of order 0.01 pc, 49 of which are found to be associated with CO outflows. The velocity fields for 27 of these outflow-associated condensations are revealed by high-density tracers (e.g., CH3CN and CH3OH lines). Eventually, nine dust condensations are recognized to be rotating, as is evidenced by them showing a velocity gradient perpendicular to the outflow axis. The detected rotating condensations are more likely “toroids” or envelopes with radii on the order of 1000 au, enclosing smaller disks. Further investigations of the P–V diagrams along the velocity gradient reveal cases with butterfly-shaped patterns, indicative of Keplerian-like rotation.

We generated synthetic SMA observations of a disk-envelope model at varying inclination angles with RADMC-3D. Even though the model is simplified, the simulation suggests that inclination can hinder the detection of rotating envelopes or toroids only when the rotation axis is largely inclined to the line of sight.

By comparing disk candidates and non-disk dense-gas-traced condensations, we conclude that the disk candidate detection rate could be sensitive to protostellar evolution. In young, deeply embedded sources, the powerful outflows may dominate the kinematics of the envelopes. As the protostar evolves, the outflows carve a wide-angle cavity, resulting in a flattened rotating envelope that is easier to detect. The insufficient angular resolution of our SMA observations makes it difficult to reveal the deeply embedded “true disk” that has a small size. Observations with a higher resolution and sensitivity are required to figure out whether these disk candidates actually host small-scale Keplerian-like disks and the reason why other dense-gas-traced and outflow-associated condensations do not show evidence of rotating structures.

Acknowledgements

This work is supported by National Key R&D Program of China, nos. 2022YFA1603100, 2017YFA0402604, the National Natural Science Foundation of China (NSFC) grant U1731237, and the science research grant from the China Manned Space Project with no. CMS-CSST-2021-B06.

Appendix A Dust continuum and CO outflow maps

Table A.1

Physical parameters of the MDCs

thumbnail Fig. A.1

SMA 1.3 mm continuum map of DR15. Similar to Fig. 1
thumbnail Fig. A.2

SMA CO outflow maps of DR15. Similar to Fig. 2
thumbnail Fig. A.3

SMA 1.3 mm continuum map of DR21OH. Similar to Fig. 1
thumbnail Fig. A.4

SMA CO outflow maps of DR21OH. Similar to Fig. 2

Appendix B Gas temperature

We detected several components of CH3CN(12k − 11k) k-ladder (listed in Table 2) in a few sources in our sample. The CH3CN(12k − 11k) level is helpful in temperature estimates. The three transitions of H2CO with rest frequencies of 218.222,218.475, and 218.760 GHz can also used for estimations of temperature since they are strong and can be fitted simultaneously within a single spectral window in our SMA observations. We have carefully checked the potential influence of absorption and outflow on temperature estimates with H2CO emission. We used the XCLASS (eXtend CASA Line Analysis Software Suite) tool (Möller et al. 2017) to fit the lines for temperature estimates. The myXCLASS function in XCLASS models a spectrum by solving the radiative transfer equation for an isothermal object in one dimension. For example, Fig. B.1 shows the fitting results of CH3CN(12k − 11k) and H2CO in Field5 MM1. The derived gas temperatures are listed in Table B.1. Sources that have H2CO emission affected by outflows are marked by asterisks. It is worth noting that the gas temperatures estimated from transitions of CH3CN and H2CO are higher than the dust temperature from Cao et al. (2021). Because of our coarse resolution, the emission of dense gas tracers, especially CH3CN, probably mainly comes from the inner, unresolved structure surrounding the protostar, which is denser and hotter. It could make the gas temperatures derived from these dense gas tracers much higher than the dust temperatures.

Table B.1 also includes NH3 gas temperatures from Zhang et al. (2024). Their VLA 1.3 cm observations on Cygnus-X cover some MDCs in our SMA observations. They used the lowest NH3 transitions, NH3 (1, 1) and (2, 2), to estimate the rotational temperature. Their angular resolution was sufficient (about 3″) to distinguish two individual condensations.

It is important to note that only a few condensations associated with outflow possess multiple transitions of CH3CN and H2CO for the temperature estimate and many sources have no NH3 gas temperature from Zhang et al. (2024). Consequently, a comprehensive comparison of gas temperatures between disks and non-disks, like what we did with dust temperature, cannot be achieved.

thumbnail Fig. B.1

XCLASS fitting results of CH3CN and H2CO toward Field5 MM1. The black lines represent line emission averaged in the FWHM of the condensation. The red lines are the fitting results from XCLASS. The derived gas temperature from XCLASS is labeled in the map.
Table B.1

Estimation of molecular gas temperature

Notes. (a) Gas temperature derived by XCLASS. (b) Ammonia temperature from Zhang et al. (2024).(*) H2CO emission affected by outflows.

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2

A powerful multi-scale, multi-wavelength source extraction algorithm (Men’shchikov et al. 2012). “getsources” is designed for extracting dense structures in star-forming regions, decomposing images into components and measuring their properties by removing the large-scale background.

3

The Herschel imaging survey of OB young stellar objects. http://www.herschel.fr/cea/hobys/en/index.php

All Tables

Table 1

Observational parameters.

In the text
Table 2

Information on the spectral lines.

In the text
Table 3

Information on the dust condensations associated with outflow in our SMA observations.

In the text
Table 4

Infrared properties of outflow-associated condensations.

In the text
Table A.1

Physical parameters of the MDCs

In the text
Table B.1

Estimation of molecular gas temperature

In the text

All Figures

thumbnail Fig. 1

SMA 1.3 mm continuum emission of sources in our sample. The contour levels are (−3, 3, 6, 9, 12, 18, 24, 36, 48, 60)×σ, where σ is the rms of the dust continuum. The synthesized beam of each image is shown in the bottom left. The red plus represents the dust condensation extracted by Cao et al. (2021).
In the text
thumbnail Fig. 2

Molecular outflows detected in CO (2−1) in some sources. The blueshifted and redshifted outflows of CO (2−1) are plotted in blue and red contours, respectively. The contour levels are (−3, 3, 6, 9, 12, 15, 18, 24, 36, 48, 60)×σ, where σ is the rms of the integrated CO emission. The blue and red arrows mark the outflow axes identified in the region. The grayscale images and black contours show SMA 1.3 mm continuum emission. The contour levels are the same as in Fig. 1. The extracted dust condensation is marked by a black cross.
In the text
thumbnail Fig. 3

Intensity-weighted mean velocity maps of representative molecular line emission toward all dense-gas-traced sources, overlaid with the SMA 1.3 mm continuum emission contours, the same as in Fig. 1. The background color map shows the relative velocity to the systemic velocity of the source. The blue and red arrows represent the blueshifted and redshifted CO outflow axis, respectively. The dashed black lines indicate the velocity gradient orientation inferred from molecular line kinematics. Each panel is labeled with the species name and the excitation energy (in Kelvin) of the upper level of the transition. The label “disk candidate” on the bottom right marks the disk candidates in our sample.
In the text
thumbnail Fig. 4

PV diagram of spectral lines toward the disk candidates, cut along the dashed black lines shown in Fig. 3. The dashed red lines show the Keplerian rotation curves for central masses labeled in the upper left. The black contours correspond to 3, 5, 7, 9,11, and 13 σ levels. The vertical line marks the reference point. The horizontal line indicates the systemic velocity.
In the text
thumbnail Fig. 5

Schematic diagram of our envelope-disk model. The outflow axis is aligned with the ζ axis. The inner part of the Keplerian disk starts from the inner boundary, rin = 10 au, and extends to the centrifugal barrier, rCB = 100 au. The outer envelope ranges from the centrifugal barrier, rCB, to the outer boundary, rout = 2000 au.
In the text
thumbnail Fig. 6

Synthetic SMA observations made with the CASA task “simobserve” from the outputs of radiative transfer calculations of the envelope-disk model shown in Fig. 5. From left to right, the inclination angle of the rotation axis with respect to the line of sight changes from 10° to 80 °. The color scale shows the CH3CN (123−113) first-moment map. The red and blue arrows represent redshifted and blueshifted outflows, respectively. The bottom left of each panel shows the synthesized beam.
In the text
thumbnail Fig. 7

Dust temperature distribution of all dense-gas-traced condensations in relation of gas mass. Red and blue dots represent disk candidates and non-disk dense-gas-traced condensations, respectively. The dashed red line shows the median temperature of the disk candidates, 34 K. The dashed black line shows the median temperature of the non-disk dense-gas-traced condensations, 22.5 K. In the lower right corner, the vertical and horizontal black error bar indicates the uncertainties of the dust temperature (σT = 4 K) and the gas mass (~0.26 dex) from Cao et al. (2021), respectively.
In the text
thumbnail Fig. A.1

SMA 1.3 mm continuum map of DR15. Similar to Fig. 1
In the text
thumbnail Fig. A.2

SMA CO outflow maps of DR15. Similar to Fig. 2
In the text
thumbnail Fig. A.3

SMA 1.3 mm continuum map of DR21OH. Similar to Fig. 1
In the text
thumbnail Fig. A.4

SMA CO outflow maps of DR21OH. Similar to Fig. 2
In the text
thumbnail Fig. B.1

XCLASS fitting results of CH3CN and H2CO toward Field5 MM1. The black lines represent line emission averaged in the FWHM of the condensation. The red lines are the fitting results from XCLASS. The derived gas temperature from XCLASS is labeled in the map.
In the text

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