Gas Kinematics of the Massive Protocluster G286.21+0.17 Revealed by ALMA

The observations were conducted with ALMA in Cycle 3 (Project ID 2015.1.00357.S; PI: J. C. Tan) during the period from 2015 December to 2016 September. More details of the observations can be found in Cheng et al. (2018). In summary, we divided the region into five strips, denoted as G286_1, G286_2, G286_3, G286_4, and G286_5, each about 1' wide and 53 long and containing 147 pointings of the 12 m array (see Figure 1). The position of field center is R.A. = 10:38:33, decl. = −58:19:22. We employed the compact configuration C36-1 to recover scales between 15 and 110. This is complemented by observations with the ACA, which probes scales up to 186. Total power (TP) observations were also carried out to recover the total flux (of line emission), which gives a resolution of about 30''.

Zoom In Zoom Out Reset image size

During the observations, we set the central frequency of the correlator sidebands to be the rest frequency of the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2) line at 231.32 GHz for SPW0 and the ${{\rm{C}}}^{18}{\rm{O}}$(2–1) line at 219.56 GHz for SPW2, with a velocity resolution of 0.046 and 0.048 km s⁻¹, respectively. The second baseband SPW1 was set to 231.00 GHz, i.e., 1.30 mm, to observe the continuum with a total bandwidth of 2.0 GHz, which also covers CO(2–1) with a velocity resolution of 0.64 km s⁻¹. The frequency coverage for SPW3 ranges from 215.85 to 217.54 GHz to observe DCN(3–2), DCO⁺(3–2), SiO(v = 0)(5–4), and ${\mathrm{CH}}_{3}\mathrm{OH}({5}_{\mathrm{1,4}}-{4}_{\mathrm{2,2}})$. This paper will focus mostly on dense gas tracers C¹⁸O, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$.

The raw data were calibrated with the data reduction pipeline using CASA 4.7.0. The continuum visibility data were constructed with all line-free channels. We performed imaging with the tclean task in CASA, and during cleaning, we combined data for all five strips to generate a final mosaic map. Two sets of images were produced for different aspects of the analysis, one including the TP and 7 m array data and one combining the TP and 7 and 12 m data. The 7 m array data were imaged using a Briggs weighting scheme with a robust parameter of 0.5, which yields a resolution of 732 × 442. For the combined data, we used the same Briggs parameter. In addition, since we have extra uv coverage for part of the data, we also apply a 06 uvtaper to suppress longer baselines, which results in 162 × 141 resolution. Both image sets are then feathered with the TP image to correct for the missing large-scale structures. Our sensitivity level is about 30 mJy beam^–1 per 0.1 km s⁻¹ for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${{\rm{C}}}^{18}{\rm{O}}$. A sensitivity of 45 mJy beam^–1 per 0.1 km s⁻¹ is achieved for ${\mathrm{DCO}}^{+}$(3–2), $\mathrm{DCN}$(3–2), SiO(5–4), and ${\mathrm{CH}}_{3}\mathrm{OH}$(5_1,4 − 4_2,2).

The far-IR dust continuum images of G286 were taken from the Herschel Infrared GALactic plane survey (Molinari et al. 2010, 2016). The data include Photodetector Array Camera and Spectrometer (PACS; 70 and 160 μm) and Spectral and Photometric Imaging REceiver (250, 350, and 500 μm) images. We performed pixel-by-pixel graybody fits to derive the mass surface density (Σ) of the G286 region, following the procedures in Lim et al. (2016). The background was estimated as the median intensity value between two and four times the ellipse aperture shown in Figure 1. To better probe the smaller, higher Σ structures, we generated a higher-resolution Σ map by regridding the λ ∼ 160–500 μm images to match the 250 μm data (see Lim et al. 2016, for details).

Figure 2(a) shows the spectra of CO(2–1) and C¹⁸O(2–1) averaged inside a 25 radius aperture centered on the phase center. The CO(2–1) line has a maximum around the known systemic velocity of about −20 km s⁻¹. A secondary, much weaker peak is seen around −9 km s⁻¹. This component is also seen in the Mopra CO(2–1) map, which appears to be a diffuse structure larger than our field of view. We expect that this feature is probably contributed by a foreground or background cloud along the line of sight, and there is no indication of an interaction between this cloud and G286. Emission from C¹⁸O(2–1) is only seen from the main −20 km s⁻¹ component.

Zoom In Zoom Out Reset image size

Figure 2(b) shows the spectra of the deuterated dense gas tracer ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2) and ${\mathrm{DCO}}^{+}$(3–2), averaged over the same region and compared to C¹⁸O(2–1), zooming in to the velocity range of the main −20 km s⁻¹ component. Deuterated species, such as ${\mathrm{DCO}}^{+}$ and ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, are expected to be tracers of cold, dense gas, including material that is contained in prestellar cores (e.g., Crapsi et al. 2005; Bergin & Tafalla 2007; Kong et al. 2015), and typically optically thin even at the core scale, as found in some examples in IRDCs (Tan et al. 2013). Interestingly, the C¹⁸O(2–1) line exhibits a main Gaussian-like profile with a slight skewness (or second component) to the redshifted side. The spectrum from ${\mathrm{DCO}}^{+}$(3–2) shows a more pronounced double-peaked profile, with one component at about −20.5 km s⁻¹ and the other at −18.5 km s⁻¹.

The double-peak profile, i.e., with a stronger blue wing, has also been seen in the ${\mathrm{HCO}}^{+}$(1–0) and ${\mathrm{HCO}}^{+}$(4–3) lines in Barnes et al. (2010), with similar central velocities for both peaks. It was interpreted by Barnes et al. (2010) as a canonical inverse P Cygni profile indicating gravitational infall (Zhou et al. 1993). However, in this picture, we would expect a single Gaussian profile for optically thin tracers at the self-absorption velocity, in contrast to our ${\mathrm{DCO}}^{+}$(3–2) spectrum. We will return in Section 5 to the question of whether the claimed inverse P Cygni profile in ${\mathrm{HCO}}^{+}$ is really tracing global clump infall or whether it is arising from distinct spatial and kinematic substructures in the protocluster.

To further explore the kinematic structure of the clump, we present the CO(2–1) channel map from −55.0 to 15.0 km s⁻¹ in Figure 3(a), where we have averaged four velocity channels in each displayed panel. The CO emission is widespread around the systemic velocity (−23 to −17 km s⁻¹). Blueward of the line center, the emission retains extension toward the SE and then, at the highest blueshifted velocities, e.g., v ≲ −45 km s⁻¹, appears more concentrated. The redshifted emission shows more complex structure, including from emission features already mentioned at around v = −9 km s⁻¹, which may be from an unrelated cloud along the line of sight. However, high-velocity (Δv ≳ 25 km s⁻¹) redshifted gas is still seen near the phase center. These high-velocity features, both blue- and redshifted, are likely to be caused by protostellar outflow activity from within the G286 star-forming clump.

Zoom In Zoom Out Reset image size

The clump-averaged spectra could be affected by multiple factors, including collapse, rotation, and outflows. To better resolve the kinematics near the systemic velocity, where ¹²CO(2–1) is expected to be mostly optically thick, in Figure 3(b), we show the C¹⁸O(2–1) channel map from −23.0 to −17.0 km s⁻¹. This C¹⁸O emission at around −20 km s⁻¹ is moderately elongated in the N–S direction. In the central 2' region, the C¹⁸O(2–1) at blueshifted velocities is mostly extended to the SE, while at the corresponding redshifted velocities, there is a more complex, widespread morphology, including some material at NE and SE locations.

Figure 4 presents summary maps of four spectral lines, C¹⁸O(2–1), ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), ${\mathrm{DCO}}^{+}$(3–2), and $\mathrm{DCN}$(3–2) (left to right), overlaid on a 1.3 mm continuum image in black contours. The top two rows show the moment 0 and moment 1 maps of the 7 m array images, respectively. As shown in the moment 0 map, C¹⁸O traces structures that are more spatially extended than other lines. Here ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$ are more closely associated with the dust continuum, but their distributions are slightly different; ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ is mainly detected toward the NW–SE filament and the southern part of the NE–SW filament. Note also that not all of the regions with strong dust continuum have detections of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$. In particular, there is a deficiency of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ emission toward the central brightest clump. On the other hand, ${\mathrm{DCO}}^{+}$ emission appears slightly more extended. There is also an E–W filamentary feature to the E of the NW–SE filament. This E–W filament is not seen clearly in continuum emission, where we only observe a few cores strung out along the E–W direction, but these do appear to be connected by weak diffuse dust emission seen at a 3σ level. Additionally, ${\mathrm{DCO}}^{+}$ is also detected toward a few positions to the S of the NW–SE filament. The spatial distribution of $\mathrm{DCN}$ emission is dramatically different from that of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$: it is strongly concentrated toward the clump in the center, where no detection or only weak detection is seen for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$. The $\mathrm{DCN}$ emission becomes weaker away from the center.

Zoom In Zoom Out Reset image size

The different morphological distributions of the deuterated species may be due to chemical differentiation. In general, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ is known as a good tracer of cold (T ≲ 20 K), dense gas, where ${{\rm{H}}}_{2}{{\rm{D}}}^{+}$ builds up in abundance but CO is mostly frozen out onto dust grains (e.g., Fontani et al. 2015). Formation of ${\mathrm{DCO}}^{+}$ requires both ${{\rm{H}}}_{2}{{\rm{D}}}^{+}$ and gas phase CO (e.g., Millar et al. 1989), which requires a temperature ≲30 K but not too cold to cause significant CO freeze-out. On the other hand, the primary DCN formation mechanisms are thought to require ${\mathrm{CH}}_{2}{{\rm{D}}}^{+}$ instead of ${{\rm{H}}}_{2}{{\rm{D}}}^{+}$, which is energetically favorable up to ∼80 K (e.g., Millar et al. 1989; Turner 2001). Additionally, sputtering from grain mantles can also lead to enhancement of the DCN abundance in shocked regions (e.g., Busquet et al. 2017). Hence, we would generally expect more DCN emission in relatively later evolutionary stages. The concentrated distribution of DCN, combined with more widespread ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$ emission, indicates a scenario that star formation, especially more massive, luminous star formation, has taken place first in the central regions of G286 compared to in the more extended filaments.

The second row of Figure 4 shows the moment 1 map of the 7 m array images. The C¹⁸O moment 1 map reveals redshifted emission associated with the NE–SW filament and then continuing to the S of the NW–SE filament, while the NW–SE and E–W filaments are mainly associated with blueshifted gas. Other dense gas tracers show similar velocity patterns as C¹⁸O but with the emission mainly detected toward dense continuum clumps. In particular, DCN illustrates the blue–red velocity transition across the central clump in the NW–SE direction.

A zoom-in view of G286 is presented in the third and fourth rows of Figure 4, illustrating the moment 0 and moment 1 maps of the combined 12 m+7 m array image with a resolution of ∼15. The continuum image reveals a higher level of fragmentation and many well-defined dense cores, with a typical size of a few thousand au. The E–W filament and part of the NE–SW filament are resolved out in this continuum image. The intensity and velocity distribution of C¹⁸O appears more complicated seen in high resolution. Other dense gas tracers, like ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, still have good association with the continuum at the core scale, and the velocity pattern is also consistent with that seen in the 7 m image.

In Figure 5, we present the 12 m+7 m C¹⁸O image with integrated emission in different velocity intervals shown in different colors, i.e., −23.0 to −20.5 km s⁻¹ in blue, −20.5 to −19.5 km s⁻¹ in green, and −19.5 to −17.0 km s⁻¹ in red. Besides the velocity structures seen in Figure 4, this plot also reveals highly filamentary C¹⁸O features around the systemic velocity. These filaments are more spatially extended than the continuum. While some of this morphology may be affected by artificial side lobes from imperfect cleaning of the interferometric data, at least some of the C¹⁸O(2–1) filaments have corresponding detections in the continuum and hence are most likely to be real features.

Zoom In Zoom Out Reset image size

Cheng et al. (2018) reported different numbers of identified cores, ranging from 60 to 125, depending on the detection algorithm and parameter choices of these algorithms. Here we adopt the fiducial dendrogram-identified core sample with a base threshold of 4σ and a delta threshold of 1σ, along with a minimum area of half a synthesized beam size. This parameter combination yields 76 cores.

In Appendix A, we list the properties of the dense core sample. The cores are here named as G286c1, G286c2, etc., with the numbering order from highest to lowest core mass. The masses are estimated to range from 0.19 to 80 M_⊙, assuming a constant temperature of 20 K for each core (see Cheng et al. 2018 for more details). The radius is evaluated as R_c = $\sqrt{A/\pi }$, where A is the projected area of the core. The median radius is 0.011 pc, similar to the spatial resolution (∼1'', 2500 au), indicating that many cores are not well resolved. Note that we adopt the core area returned by dendrogram, which is defined with an isophotal boundary at a certain flux level, i.e., the level where two cores merge together or the 4σ flux threshold for isolated cores. So the core area or radius could be underestimated in a crowded field.

We then evaluate the mean mass surface density of the cores as Σ_c ≡ M/A. The median mass surface density of our sample is ∼0.65 g cm⁻², and all cores have values ≳0.4 g cm⁻². We also evaluate the mean H nuclei number density in the cores, n_H,c ≡ M_c/(μ_HV), where μ_H = 1.4m_H is the mean mass per H assuming n_He = 0.1n_H and V = $4\pi {R}_{c}^{3}/3$. The mean value of log₁₀(n_H,c/cm⁻³) is 6.88, with a standard deviation of 0.24.

We extract the average C¹⁸O(2–1), ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), ${\mathrm{DCO}}^{+}$(3–2), and $\mathrm{DCN}$(3–2) spectra of each core, which are shown in Appendix B. Among the four tracers, C¹⁸O is the strongest for almost all cores, and sometimes the C¹⁸O profiles can be complex. Other lines are relatively weak and only detected for part of the core sample.

To measure the centroid velocity and velocity dispersion of each core, we only fit spectra with well-defined profiles, i.e., those with a peak greater than a certain threshold value. Here we adopt a 4σ criterion for this threshold value. Since the noise levels of the average spectra vary for different cores (depending on the pixel numbers in the core, etc.), we estimate the rms noise separately for each core and line using the signal-free channels. This signal-to-noise criterion gives 74 cores detected in C¹⁸O(2–1) (97%), 27 in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2) (36%), 45 in ${\mathrm{DCO}}^{+}$(3–2) (59%), and 29 in $\mathrm{DCN}$(3–2) (38%). We also checked the single pixel spectra at the continuum peak of each core and found that the vast majority have similar line profiles as the averaged spectra, but the signal-to-noise ratios are usually lower, so we proceed with our analysis using the core-averaged spectra.

We characterize the C¹⁸O(2–1) spectra with 1D Gaussian fitting using the curve_fit function in the Scipy.optimize Python module. Most cores can be well described with a single Gaussian component. In general, we expect that C¹⁸O(2–1) traces lower-density envelope gas surrounding the dense core and thus could be more affected by multiple components along the line of sight. In 31 cores where a spectrum has more complex profiles and hence cannot be well approximated by a single Gaussian, we allow for a second Gaussian component.

For the ${\mathrm{DCO}}^{+}$(3–2) and $\mathrm{DCN}$(3–2) lines, we also perform the Gaussian fitting with the curve_fit function. For the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2) line, to account for the full blended hyperfine components, we use the hyperfine line-fitting routine in pyspeckit (Ginsburg & Mirocha 2011), with the relative frequencies and optical depths for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ taken from Dore et al. (2004) and Pagani et al. (2009). These dense gas tracers are usually well described with one Gaussian component. Figure 9 shows a example of the line fitting. In particular, in one case (i.e., G286c3), two separate components were clearly required for a good fit for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$. These two components are mostly likely to belong to two separate entities that are not resolved in their continuum emission.

Zoom In Zoom Out Reset image size

G286c1. This is the most massive core in G286, with a mass of 80 M_⊙ and an equivalent radius of 0.036 pc. It is associated with strong infrared emission and a wide angle bipolar CO outflow (Y. Cheng et al. 2020, in preparation), and hence it is already in a relatively evolved protostellar stage. If we adopt a higher temperature, such as 70 K, typical of massive protostellar sources (e.g., Zhang & Tan 2018), then its mass would be ∼20 M_⊙. It is not detected in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), but we see broad line profiles from ${\mathrm{DCO}}^{+}$(3–2), $\mathrm{DCN}$(3–2), and C¹⁸O(2–1). In particular, there is very strong $\mathrm{DCN}$(3–2) emission from −22 to −15 km s⁻¹, which is even broader than C¹⁸O. Our high-resolution ALMA observation in Cycle 5 has revealed further fragmentation and substructures in G286c1 (Y. Cheng et al. 2020, in preparation). Here we still use a one Gaussian component to model the spectral lines of G286c1, and the resulting fitting parameters should be treated more cautiously as reflecting the average properties of the core.

G286c3. This is also a massive core, with ∼12 M_⊙. We have detected C¹⁸O(2–1), ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), ${\mathrm{DCO}}^{+}$(3–2), and $\mathrm{DCN}$(3–2) toward G286c3. Interestingly, these spectra of C¹⁸O, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, and ${\mathrm{DCO}}^{+}$ all exhibit a double-peak profile, with one peak centered around −19.5 km s⁻¹ and another at ∼−18 km s⁻¹, though $\mathrm{DCN}$ is only detected in one velocity component. Since we expect the deuteratated species, such as ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$, to be optically thin, these line profiles are more likely to be contributed by two separate entities inside G286c3 instead of a central dip caused by self-absorption. A detailed inspection from the continuum also reveals that G286c3 is very elongated in the NE–SW direction. Thus, it is possible that there are further subfragmentations in G286c3 that are not identified by our fiducial dendrogram algorithm; e.g., there could be two cores overlapping along the line of sight. Here we use two-component Gaussian fitting to model the spectrum of C¹⁸O, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, and ${\mathrm{DCO}}^{+}$ and treat them as two individual cores (i.e., two data points per line in Figure 10). We split the mass of G286c3 assuming that the mass of each component is proportional to the C¹⁸O flux for relevant analysis.

Zoom In Zoom Out Reset image size

G286c4. This core has an estimated mass of ∼9 M_⊙. There is no ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ detection, but we see very strong C¹⁸O, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$ emission. Here $\mathrm{DCN}$(3–2) has a very strong peak centered at −19.5 km s⁻¹, similar to C¹⁸O and ${\mathrm{DCO}}^{+}$. Additionally, there are two secondary peaks at around velocities of −16 and −23 km s⁻¹. These may be real features resulting from unresolved condensations or more dynamical activities like outflows, but we are unsure about their origin with the current information. Here for $\mathrm{DCN}$, we only fit the central major velocity component that is consistent with other tracers.

G286c8, G286c20, and G286c41. These are special in terms of their ${\mathrm{DCO}}^{+}$(3–2) spectra. All three cores have a ${\mathrm{DCO}}^{+}$ peak around −18 km s⁻¹. For G286c20 and G286c41, ${\mathrm{DCO}}^{+}$ has a large velocity offset (∼1 km s⁻¹) compared with other tracers, like C¹⁸O. For G286c8, this offset is even larger (∼3 km s⁻¹), and there is another obvious ${\mathrm{DCO}}^{+}$ peak around −21 km s⁻¹, similar to the peaks of the C¹⁸O and $\mathrm{DCN}$ lines. A possible explanation is that G286c8 has a core velocity around −21 km s⁻¹, as traced by multiple tracers, while the ${\mathrm{DCO}}^{+}$ feature around −18 km s⁻¹ is not associated with the dense core. From the continuum map, we find that all three cores are close together and lie on a filamentary feature that is only seen in ${\mathrm{DCO}}^{+}$. This filamentary feature is clear in the ${\mathrm{DCO}}^{+}$ channel map and does not appear to be associated with a dense dust continuum. Hence, we exclude this ${\mathrm{DCO}}^{+}$ velocity component near −18 km s⁻¹ for G286c8, G286c20, and G286c41 in our analysis.

The best-fit parameters of centroid velocity and velocity dispersion are displayed along with the spectral lines in Appendix B. Figure 10 illustrates the distribution of these parameters, along with their individual uncertainties. As can be seen, the centroid velocities range from −22.5 to −17.0 km s⁻¹, and there is a modest clustering near −21.5 km s⁻¹. The velocity dispersions range from 0.1 to 1.0 km s⁻¹ for deuterated species, while those of C¹⁸O are systematically larger. Here ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$ usually give smaller velocity dispersions, with median values of 0.35 and 0.36 km s⁻¹, respectively. The $\mathrm{DCN}$-measured dispersions are larger, with a median value of 0.43 km s⁻¹. Centroid velocity uncertainties range from 0.01 to 0.08 km s⁻¹, while velocity dispersion uncertainties vary from 1% to 20%, with a few cases ≳30%, depending on the signal-to-noise ratio and shape of the line profiles.

Figure 11 illustrates the line detection situation of the core sample, with different colored circles denoting detections in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), ${\mathrm{DCO}}^{+}$(3–2), and $\mathrm{DCN}$(3–2). As C¹⁸O(2–1) is detected for almost all of the cores (except c68 and c75), it is not shown here. As already apparent in Figure 8, $\mathrm{DCN}$(3–2) is mostly detected in the central region, while ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2)– and ${\mathrm{DCO}}^{+}$(3–2)–detected cores are more widespread. Overall, we have 54 cores that are detected in at least one of these three dense gas tracers. In particular, all of the cores with ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ detection also have strong ${\mathrm{DCO}}^{+}$ emission.

Zoom In Zoom Out Reset image size

The cores that are detected in more than one line are of particular interest, since differences in fitted parameters could be a reflection of chemical differentiation. There are 14 cores that are detected in all three lines, 26 in both ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$, 14 in both ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and $\mathrm{DCN}$, and 21 in both ${\mathrm{DCO}}^{+}$ and $\mathrm{DCN}$. Figure 12 illustrates the differences in the fitted parameters of these species when commonly detected. From this figure we see that there is no significant offset in centroid velocity or velocity dispersion as derived from the different species. This similarity in velocity distributions is expected if these species are tracing the same molecular gas material.

Zoom In Zoom Out Reset image size

For the centroid velocities, the median offsets between ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and $\mathrm{DCN}$, and ${\mathrm{DCO}}^{+}$ and $\mathrm{DCN}$ are 0.07, 0.09, and 0.03 km s⁻¹, respectively. The sampling error of the velocity offset distribution due to the finite number of cores is estimated to be about 0.04 km s⁻¹, so these offsets are not very significant.

The 1D velocity dispersion σ are generally consistent among different tracers within a factor of 2. The median values of ${\sigma }_{\mathrm{DCN}}/{\sigma }_{{\mathrm{DCO}}^{+}}$, ${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{\mathrm{DCN}}$, and ${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\mathrm{DCO}}^{+}}$ are 1.16, 0.99, and 0.95, respectively. The observed scatter is consistent with the fitting uncertainties.

We next compare dense core centroid velocities with the larger-scale gas reservoir (or envelope) traced by C¹⁸O. Previous studies in relatively low-mass environments have shown that cores mostly have subsonic core-to-envelope motions (e.g., Walsh et al. 2004, 2007; Kirk et al. 2007; Walker-Smith et al. 2013). Our work here provides a measure of core-to-envelope motions within a more massive protocluster. Additionally, most previous works measured the centroid velocity offset between C¹⁸O and ${{\rm{N}}}_{2}{{\rm{H}}}^{+}$. Here we have observations of lines from deuterated species like ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$, which should be better tracers of localized dense cores rather than more extended filaments and usually not affected by multiple velocity components that may complicate the interpretation (e.g., Henshaw et al. 2014; Ragan et al. 2015).

As mentioned above, we have 54 cores that are detected in at least one of the three deuterated species. For those detected in more than one line, we define the core velocity, v_c, as an average of the detected centroid velocities, weighted by their measurement uncertainties.

The core velocities v_c are illustrated in Figure 11. For cores with only one C¹⁸O(2–1) component, we compare the difference in centroid velocity between C¹⁸O and v_c directly. If multiple CO velocities are found along the line of sight, we assume the component closest to v_c is the one associated with the core, following the discussion in Kirk et al. (2007). This comparison is shown in Figure 13.

Zoom In Zoom Out Reset image size

The median value of the velocity offset is 0.01 km s⁻¹, with a standard deviation of about 0.3 km s⁻¹. The majority of cores (71%) have core and envelope velocity offsets less than the sound speed of the ambient medium (0.27 km s⁻¹ for 20 K temperature). This percentage is higher than that in NGC 1333, for which Walsh et al. (2007) found that half of their cores have differences greater than the sound speed, but similar to that seen in the Perseus cloud (Kirk et al. 2007). As discussed in Walsh et al. (2004), small relative motions between cores and envelopes could be interpreted as an indication of quiescence on small scales, and this would appear to argue against a competitive accretion scenario for star formation (Bonnell & Bate 2006), in which dense cores gain most of their mass by sweeping up material as they move through the cloud.

We now examine the dynamical state of the dense cores, i.e., the comparison of their internal kinetic energy (E_K) and gravitational energy (E_G). This ratio is captured by the virial parameter (Bertoldi & McKee 1992), defined as

$$\begin{eqnarray}&&\alpha \equiv 5{\sigma }_{c}^{2}{R}_{c}/({{GM}}_{c})=2{{aE}}_{K}/| {E}_{G}| ,\end{eqnarray} \tag{ 4 }$$

where σ_c is the intrinsic 1D velocity dispersion of the core and R_c is the core radius. The dimensionless parameter a accounts for modifications that apply in the case of nonhomogeneous and nonspherical density distributions. For a spherical core with a radial density profile that is a power law $\rho \propto {r}^{-{k}_{\rho }}$, then, for k_ρ = 0, 1, 1.5, 2, a = 1, 10/9, 5/4, 5/3. We adopt a fiducial value of k_ρ = 1.5 and a = 5/4, following McKee & Tan (2003). For a self-gravitating, unmagnetized core without rotation, a virial parameter above a critical value α_cr = 2a indicates that the core is unbound and may expand, while one below α_cr suggests that the core is bound and may collapse.

We measure core 1D velocity dispersions, σ_c, from each of the three dense gas tracers, i.e., ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$. As shown above, their line widths can vary for the same core, so we calculate the virial parameters separately using each tracer. We derive the intrinsic velocity dispersion from the observed dispersion following Equation (3) (replacing C¹⁸O with other species). For the core masses, we use the values estimated assuming a temperature of 20 K, as listed in Appendix A.

For core radius, we attempt two methods. The first is to use the effective radius calculated from the dendrogram-returned area (see Section 5.1). For the second method, we adopt a deconvolved size defined as R_c = $\sqrt{(A-{A}_{\mathrm{beam}})/\pi }$, where A and A_beam are the core area and synthesized beam size, respectively. Note that in our core identification process, we have allowed for cores with an area smaller than the synthesized beam size. Here, for the virial analysis, we ignore the cores with areas smaller than 1.5 × A_beam, for which the deconvolved sizes could have very large uncertainties. This criterion excludes 34 out of 76 cores.

Figures 14(a) and (b) display the virial parameters measured with different tracers versus core mass for the two methods described above. In Figures 14(c) and (d), we combine the measurements from different tracers by taking the linear average of their nonthermal velocity dispersion in the virial parameter derivation.

Zoom In Zoom Out Reset image size

We see virial parameters range from 0.5 to 10 as measured by individual dense gas tracers. There is a trend for more massive cores to have smaller virial parameters, but this is generally expected, since $\alpha \propto {M}_{c}^{-1}$. The scatter is significantly reduced for the deconvolved size method, with most measurements ranging from 0.5 to 3. This suggests that most data points with virial parameters >5 in panel (a) could arise from overestimation in the core radius. We do not find significant systematic differences between different tracers. The median values are 1.35, 1.19, and 1.23 for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$, respectively.

The virial parameters estimated by averaging all of the available dense gas data for each core show a further reduction in the scatter. For the second method with deconvolved sizes that focus on the larger cores, we obtain a median value of 1.22 and a standard deviation of 0.88. Most cores have a virial parameter that is consistent with a value expected in virial equilibrium, given the uncertainties.

The uncertainties in the derived virial parameters come from uncertainties in measured 1D line dispersion σ_obs, mass, and temperature. The fitting error of σ_obs is typically ≲20%, resulting in ∼40% uncertainty in σ_obs². The assumed temperature will systematically affect the estimation of the dense core mass and also the thermal line width component in Equation (3). For example, with a typical ${\sigma }_{{\mathrm{DCO}}^{+}}$ = 0.36 km s⁻¹, if temperatures of 15 or 30 K were to be adopted, then the virial parameters would differ by factors of 0.6 and 1.9, respectively. Also considering other uncertainties in the mass estimate, like dust opacity, gas-to-dust mass ratio, dust emission fluxes, and distances, overall, we estimate the absolute virial parameter uncertainties to be about a factor of 2.5. However, this uncertainty factor is itself quite uncertain and includes systematic effects, some of which are not expected to vary that much from core to core.

Given the best case derived average value of α_vir = 1.22, we conclude that the dense cores in G286, which span a wide range of masses from ≲1 to ∼100 M_⊙, have properties that are consistent with them being close to virial equilibrium. In this case, self-gravity would have been important in forming the cores, and a basic assumption of the turbulent core accretion model of star formation (McKee & Tan 2003) would be confirmed. However, given the potentially large systematic uncertainties, it is difficult to be more certain about whether the dense cores are actually closer to a supervirial or subvirial state or whether magnetic fields are playing a role in supporting the cores. The situation could be improved in the future with accurate core-scale temperature and magnetic field measurements.

The relative motion between dense cores can be quantified using the core-to-core velocity dispersion σ_c−c, i.e., the standard deviation of the core centroid velocities. It can be compared with the velocity dispersion of the large-scale diffuse gas out of which these dense cores presumably formed or the initial velocity dispersion of newborn stars and, as such, provides important constraints on theoretical models and simulations of star cluster formation (e.g., Kirk et al. 2010; Foster et al. 2015).

Here our target G286 offers an interesting case of a massive protocluster that is still in the gas-dominated phase and actively forming stars. To measure the core velocity dispersion, we show the core velocity distributions measured with C¹⁸O(2–1), ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3–2), ${\mathrm{DCO}}^{+}$(3–2), and $\mathrm{DCN}$(3–2) in Figure 15. For comparison, the large-scale TP spectra of each line are also overlaid. The results combining velocities measured with deuterated tracers (54 cores; see Section 5.4) are also displayed in Figure 15(a). We then calculate the standard deviation of these distributions, obtaining 1.27 ± 0.11 km s⁻¹ for the C¹⁸O-detected sample, 1.52 ± 0.21 km s⁻¹ for the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ sample, 1.40 ± 0.15 km s⁻¹ for the ${\mathrm{DCO}}^{+}$ cores, 1.50 ± 0.20 km s⁻¹ for the $\mathrm{DCN}$ cores, and 1.39 ± 0.13 km s⁻¹ for the combined results. The uncertainties here only account for sampling errors due to limited sample size, assuming the data points are drawn from a normal distribution.

Zoom In Zoom Out Reset image size

In contrast to previous results in nearby cluster-forming clouds like Ophiuchus and Perseus (André et al. 2007; Kirk et al. 2007, 2010), our core velocities cover a wide range from −22.5 to −17 km s⁻¹, and the distribution is not well approximated with a single Gaussian component. This is particularly clear for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$; for these two tracers, the core velocities exhibit a bimodal distribution with two velocity groups, which agrees well with the averaged TP spectra. The $\mathrm{DCN}$ picks up core velocities in a relatively uniform pattern, filling in the gap around −19 km s⁻¹; hence, the distribution combining all of the deuterated species is flatter, though more cores still cluster in the "blue" group at ∼−21 km s⁻¹. On the other hand, though the C¹⁸O profile can be characterized with a Gaussian (with some skewness) peaking aroud −20 km s⁻¹, and we do have more C¹⁸O-detected cores close to the systemic velocity (−20 to −19 km s⁻¹), the C¹⁸O-measured core velocity distribution is still relatively flat. This indicates that the core-to-core velocity dispersion we measured here is largely contributed by the global velocity patterns.

The core velocity dispersion σ_c−c can be compared with the dispersion required for virial equilibrium on the protocluster clump scale, σ_cl,vir, and its actual gas velocity dispersion, σ_cl. For σ_cl,vir, we again follow Bertoldi & McKee (1992):

$$\begin{eqnarray}&&{\sigma }_{\mathrm{cl},\mathrm{vir}}=\sqrt{\displaystyle \frac{{{aGM}}_{\mathrm{cl}}}{5{R}_{\mathrm{cl}}}}.\end{eqnarray} \tag{ 5 }$$

As with cores, we again adopt k_ρ = 1.5, so that a = 5/4. We choose a size of R_cl = 1.54 pc, which is the geometric mean of the major and minor axes of the large ellipse boundary shown in Figure 1. From the Herschel SED-derived mass surface density map, we obtain a mass for this region of ∼2900 M_⊙. Thus, σ_cl,vir = 1.42 ± 0.36 km s⁻¹, where the error comes assuming a 50% uncertainty in the mass estimate. We also tried a smaller aperture (by using major and minor axes that are a factor of 1/$\sqrt{2}$ smaller than the current ones) to more closely encompass the region containing dense cores, which gives σ_cl,vir = 1.54 ± 0.39 km s⁻¹. The mass here only accounts for the gas component, since we do not expect a significant contribution from stellar mass: Andersen et al. (2017) estimated a total current stellar mass of ∼240 M_⊙ in a similarly sized region. Thus, the observed values of σ_c−c are comparable or slightly smaller than σ_cl,vir, depending on which tracer is used.

For σ_cl, we measure the line width of the average TP spectra of C¹⁸O(2–1) in this region. The purpose here is to compare core-to-core motions with the spread of motions seen over the region as a whole to reveal how connected the dense cores are to the larger-scale gas in the region. A Gaussian fit of the C¹⁸O(2–1) line gives ${\sigma }_{\mathrm{cl},{{\rm{C}}}^{18}{\rm{O}}}$ = 1.09 ± 0.01 km s⁻¹. To account for the thermal component, we correct this value following Equation (3) assuming a temperature of 20 K and obtain σ_cl = 1.12 km s⁻¹.

In summary, the 1D dispersion measured in gas tracers, σ_cl (1.12 ± 0.01 km s⁻¹), is slightly smaller than but still consistent with σ_cl,vir (1.48 ± 0.37 km s⁻¹), indicating that the G286 clump could be in approximate virial equilibrium (assuming it is a single, coherent dynamical system) or modestly subvirial, but it is hard to be more precise given the uncertainties. We also see a range of σ_c−c values using different tracers, and the value using C¹⁸O(2–1), which includes most cores in this sample, i.e., ${\sigma }_{{\rm{c}}-{\rm{c}},{{\rm{C}}}^{18}{\rm{O}}}$ = 1.27 ± 0.11 km s⁻¹, is similar to σ_cl,vir but slight larger than σ_cl. Here the dense core velocity distribution is more flat, while both the C¹⁸O core velocities and the TP C¹⁸O spectrum cover a similar velocity range. This means there is a deficiency of dense cores near the systemic velocity (∼20 km s⁻¹), where the bulk of the C¹⁸O-traced gas is located. This deficiency is clearer in the distributions traced by ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$; hence, an even larger σ_c−c is measured with these two tracers. The two velocity groups seen in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$ (at ∼−21 and −18 km s⁻¹) are actually spatially distinct (see Figures 4, 8, and 11), with the more redshifted cores mostly located in the NE–SW filament and the more blueshifted cores in the NW–SE and E–W filaments. A similar velocity pattern is also seen for C¹⁸O in Figure 4, indicating that the dense cores are still well coupled with the large-scale motions within the cloud.

To better characterize the core-to-core velocity dispersions of the two velocity groups, we adopt a simple boundary to spatially differentiate them, shown as the dashed green line in the right panel of Figure 11. The blueshifted subsample (NW of the boundary) has a core-to-core velocity disperion σ_c−c,blue of 0.83 ± 0.10 km s⁻¹ for C¹⁸O-detected cores (or 0.78 ± 0.10 km s⁻¹ for measurements combining ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$). Similarly, we have σ_c−c,red = 0.75 ± 0.10 km s⁻¹ for C¹⁸O and 0.79 ± 0.12 km s⁻¹ for the combined dense gas results. For the dispersion required for virial equilibrium, σ_cl,vir, we estimate the mass and radius using two approximate ellipse boundaries for each velocity group (shown in Figure 1), which yields σ_cl,vir,red = 0.96 ± 0.24 and σ_cl,vir,blue = 1.48 ± 0.37 km s⁻¹. These numbers are also summarized in Table 2. Therefore, at least for the "blue" group, the core velocity dispersion σ_c−c is appears to be smaller than σ_cl,vir, potentially indicating that it is kinematically cold and subvirial, perhaps due to coherent motions within a filament. We also see that the dispersion in core velocities for the whole cloud mainly arises from the global velocity pattern of the red and blue groups.

Table 2.  Comparison of Core-to-core Velocity Dispersion and Velocity Dispersion Required for Virial Equilibrium (in km s⁻¹)

	${\sigma }_{{\rm{c}}-{\rm{c}},{{\rm{C}}}^{18}{\rm{O}}}$	σc−c,deua	σvir
Blue group	0.83 ± 0.10	0.78 ± 0.10	1.48 ± 0.37
Red group	0.75 ± 0.10	0.79 ± 0.12	0.96 ± 0.24
Total	1.27 ± 0.11	1.39 ± 0.13	1.42 ± 0.36

Note.

^aFor core velocity measurements combining deuterated species of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$, ${\mathrm{DCO}}^{+}$, and $\mathrm{DCN}$.

Download table as:  ASCIITypeset image

The origin of this velocity pattern is uncertain. In the filament-collapse scenario, as observed in some hub–filament systems, accretion flows are channeling gas to the junctions where star formation is often most active (e.g., Kirk et al. 2013; Peretto et al. 2014; Liu et al. 2016). It is possible that these converging flows are reflected in different line-of-sight velocities depending on the 3D configurations. We will presumably have more massive cores in the hub region (near the systemic velocity) but not necessarily a larger number of cores, as suggested by our observations. Smoothly varying velocities along filaments are expected in this picture. We do see indications of a velocity gradient of dense cores along the filaments, but it is not clear in C¹⁸O, for which the spectra are often complex. Further higher-sensitivity observations of ${{\rm{N}}}_{2}{{\rm{H}}}^{+}$ and ${\mathrm{NH}}_{3}$ will help investigate the gas velocity gradient along filaments.

Alternatively, the two main velocity components seen in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$ and ${\mathrm{DCO}}^{+}$ could be tracing two interacting clouds/filaments, with the central region as the collision interface (e.g., Nakamura et al. 2014). Such a mechanism could be consistent with a larger-scale cloud–cloud collision scenario that has been reported in other star-forming regions (e.g., Furukawa et al. 2009; Fukui et al. 2014; Gong et al. 2017).

Andersen et al. (2017) analyzed the stellar population in G286 and found evidence for at least three different subclusters associated with the molecular clump based on differences in extinction and disk fractions. It is unclear how the dense gas distribution and ongoing cluster formation might be related to these past star formation events. Future studies of the radial velocity of optically revealed stars, e.g., the velocity dispersion and its distribution, will be of great interest to understanding the cluster formation in G286.