MUSCLE W49: A MULTI-SCALE CONTINUUM AND LINE EXPLORATION OF THE MOST LUMINOUS STAR FORMATION REGION IN THE MILKY WAY. I. DATA AND THE MASS STRUCTURE OF THE GIANT MOLECULAR CLOUD

Mapping observations were made from 2011 March to 2011 July with the 14 m telescope at the PMO¹² (hereafter, PMO 14 m), located in Delingha, Qinghai, China. CO and its isotopologues were observed in the 1–0 transition, as well as several other molecular lines. The observations were performed with a nine-pixel superconductor–insulator–superconductor receiver, which was configured with dual sideband mixers for each pixel (Shan et al. 2010). For each sideband and each pixel, fast Fourier transform spectrometers produced a bandwidth of 1 GHz and 16384 channels, resulting in a velocity resolution of ∼0.16 km s⁻¹ and a velocity coverage of ∼2700 km s⁻¹ at 110 GHz.

The mapping observations were carried out in on-the-fly (e.g., Mangum et al. 2007) scan mode. A position of 120' to the north of the center of W49A was taken as sky reference. All maps are made with uniform Nyquist sampling, except for ∼2' around the edges. The rms pointing uncertainty is estimated to be better than 5''. Typical system temperatures during the runs were ∼140 K at 110 GHz and ∼270 K at 115 GHz.

All the PMO spectral line data were reduced with the CLASS/GILDAS¹³ package developed by IRAM. We classify the spectral quality of each spectrum by the baseline flatness and system temperature levels. About 5% of the spectra were discarded due to poor baselines. Linear baselines were subtracted for each individual spectrum. All spectra were then co-added and re-grided.

We converted the antenna temperature ($T_{\rm A}^\star$) to the main beam brightness temperature (T_mb) scale using ${ T_{\rm mb} = T_{\rm A}^{\star }(\eta _{\rm f}/\eta _{\rm mb}})$, where the ratio of the main beam efficiency η_mb to the forward hemisphere efficiency η_f is 0.46.

For each molecular line, we combined all the calibrated spectra and re-gridded them to construct datacubes with weightings proportional to 1/σ², where σ is the rms noise. This routine convolves the gridded data with a Gaussian kernel of ∼1/3 the telescope beamsize, yielding a final angular resolution slightly coarser than the original beam size. The HPBW at the CO frequency is 580 (3.4 pc).

We observed the central cluster of W49A (W49N) with the SMA¹⁴ (Ho et al. 2004) in the 1.3 mm (230 GHz) band using four different array configurations: subcompact, compact, extended, and very extended (one track for each). This multi-configuration approach images both small and large scales. The dataset covers baseline lengths between 8 kλ (corresponding to scales of 31'') and 480 kλ (05). Figure 11 (Appendix A) shows the (u, v) coverage of the combined dataset.

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The upgraded SMA correlator capabilities were used, covering 2 × 2 GHz in each of the two sidebands. The lower sideband (LSB) covered the sky frequency ranges from 218.29 to 220.27 GHz in spectral windows 48 to 25 and from 220.29 to 222.27 GHz in spectral windows 24 to 1. The upper sideband (USB) covered from 230.29 to 232.27 GHz in spectral windows 1 to 24 and from 232.29 to 234.27 GHz in spectral windows 25 to 48. The spectral resolution of the raw dataset is ≈1.1 km s⁻¹.

The visibilities of each track were separately calibrated using the SMA's data calibration program, MIR.¹⁵ The phase, bandpass, and flux calibrators for each track are listed in Table 1. Imaging and basic analysis were done in CASA versions 3.3 and 3.4.

The continuum emission was subtracted in the (u, v) domain by fitting a baseline across the passband using line-free channels as input. The continuum and line data of each configuration were then combined into a single dataset and imaged. The concatenated continuum data were self-calibrated and then imaged with different weights, checking that the flux recovered at different resolutions was the same within a few percent. The continuum map presented in this paper is the result of the combination of the SMA mosaic with the Caltech Submillimeter Observatory (CSO) BOLOCAM Galactic Plane Survey (GPS) archival map (Ginsburg et al. 2013). The combination procedure is based on converting the single-dish map to Fourier space and then jointly inverting and cleaning the combined single-dish and interferometer visibilities. The ¹³CO and C¹⁸O SMA mosaics were also combined with single-dish maps to fill the short spacings. We used the IRAM 30 m maps presented in Peng et al. (2010) and Peng et al. (2013). The combining procedure is described in more detail in Liu et al. (2013).

The 11 pointing SMA mosaic is Nyquist sampled and covers all of the HC H ii regions detected in the cm by De Pree et al. (1997, 2004). All the presented SMA mosaics have been corrected for primary beam attenuation. Figure 11 (Appendix A) shows the primary beam response of the mosaic used to correct for attenuation in the final images.

Archival maps from JCMT-SCUBA¹⁶ at 678 GHz (project code M97Bu89) and the Very Large Array (VLA)¹⁷ at 8.5 GHz (project code AD324) are also used in this paper. We refer the reader to Di Francesco et al. (2008) and De Pree et al. (1997) for the respective observational details.

Further analysis of the datasets discussed above was performed in CASA,¹⁸ MIRIAD (Sault et al. 1995), GILDAS,¹⁹ DS9,²⁰ Karma (Gooch 1996), IDL, and Python.

3.1.1. CO 1–0 and Isotopologues

The largest scale maps are those obtained with the PMO 14 m telescope in CO J = 1–0 and its isotopologues ¹³CO and C¹⁸O. These maps cover the entire W49 GMC with up to 37' (119 pc) per dimension. Figure 1 shows the velocity-integrated (moment 0) CO emission maps. This emission covers the local standard of rest (LSR) velocity range from −20 km s⁻¹ to 30 km s⁻¹. Outside this range (up to V_LSR = 78 km s⁻¹), there are more CO spikes. Their line profiles are narrow and their emission covers the entire mapped area without matching the features from the W49 GMC. We infer that these features correspond to clouds in the line of sight that are not associated with W49.

The CO maps show the well known central gas clump in the inner 3', known as (W49N). It is in this region where the central embedded cluster with dozens of massive stars as traced by radio-continuum HC and UC H ii regions reside (De Pree et al. 1997, 2004). The central W49N clump appears connected to the W49 GMC via a series of filamentary extensions (see Figure 1). These filaments are hinted at in previous observations where they appear as protuberances out of W49N toward the southwest, the east–southeast, and the north (see, e.g., Figure 2 of Nagy et al. 2012 or Figure 6 of Matthews et al. 2009). The southeast filament connects W49N to W49S located 2' away; this filament hosts a cometary H ii region (Dickel & Goss 1990).

The spectrum from the W49 GMC has two prominent velocity features toward its positional centroid. Figure 2 shows the CO spectra toward the moment 0 peak. The optically thick ¹²CO is too complex to be fit with a small number of Gaussians. The isotopologues are well fit by a sum of three Gaussian components. The kinematics of the full GMC and their relation to smaller scales will be the topic of a following paper.

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3.1.2. Hydrogen and Other Molecules

Figures 12 and 13 in Appendix B show the moment 0 (integrated from −12 km s⁻¹ to 24 km s⁻¹) map of the rest of the molecules clearly detected in the PMO 14 m observations, as well as of the hydrogen RL 41α. Figures 3 and 4 show their respective spectra at the integrated-emission peak. All of the transitions peak at the same position within a few arcseconds, a fraction of the beam. Table 2 lists all the lines detected with the PMO and their velocity-integrated fluxes spatially integrated over the projected area of the GMC. The intensity conversion factor at the rest frequency of CO 1–0 is 0.027 K per Jy beam⁻¹.

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Table 2. Lines Detected with PMO^a

Molecule	Transition	ν0	EU	Integrated Flux
		(GHz)	(K)	(Jy km s−1)
12CO	1–0	115.2712	5.53	5.005268 × 106
13CO	1–0	110.2013	5.29	7.35425 × 105
C18O	1–0	109.7821	5.27	3.0754 × 104
HCN	1–0	88.6316	4.25	5.5959 × 104b
H13CN	1–0	86.3399	4.14	1.445 × 103
HCO+	1–0	89.1885	4.28	5.4033 × 104b
H13CO+	1–0	86.7542	4.16	1.121 × 103
CS	2–1	97.9809	7.05	5.4608 × 104b
H	41α	92.0344	...	1.262 × 103
N2H+	1–0	93.1734	4.47	6.273 × 103
SiO	2–1	86.8469	6.25	1.814 × 103
SO	2(2) − 1(1)	86.0939	19.31	7.81 × 102
SO2	8(1, 7) − 8(0, 8)	83.6880	36.71	5.25 × 102

Notes. ^aLines detected with the PMO 14 m telescope. The first four columns indicate, respectively, the molecule or atom, the transition, the rest frequency, and the upper-level energy of the transition. The fifth column lists the velocity-integrated flux of the maps in Jy beam⁻¹ km s⁻¹. The intensity conversion factor is 0.027 K per Jy beam⁻¹ at the rest frequency of the CO 1–0. The noise in the moment 0 maps ranges from 2 to 10 K km s⁻¹. ^bFrom the ¹²C to ¹³C line ratios, the average optical depths of the main isotopologues are τ_HCN = 1.4, τ_{HCO +} = 0.8, and τ_CS < 0.1.

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Table 3 gives the parameters obtained from Gaussian fitting to the cloud components for the different line tracers. The bright (peak amplitude A > 1 K) lines of HCN 1–0 and CS 2–1 follow the CO isotopologues in having at least two clear velocity features peaked at ∼3 km s⁻¹ and ∼12 km s⁻¹ (the first peak of the CO-isotopologues is at ∼4 km s⁻¹). The bright HCO+ 1–0 appears to have its two components slightly blueshifted to 2 and 11 km s⁻¹, respectively. The faint isotopologues H¹³CN 1–0 and H¹³CO+ 1–0, as well as N₂H+ 1–0, also have two components, but their parameters have larger uncertainties. The SiO 2–1, SO 2(2)–1(1), and SO₂ 8(1,7)–8(0,8) were best fit by a single Gaussian. The signal-to-noise ratio in the latter two is too low to distinguish two Gaussians. The ionized hydrogen, as traced by the H41α RL, appears single peaked at 12 km s⁻¹. As expected, this line is far broader than the molecular lines (FWHM ≈30.2 km s⁻¹).

Table 3. Line Fitting at Peak Position of PMO Data^a

Molecule	Transition	Component 1			Component 2			Component 3
or Atom		V	A	FWHM	V	A	FWHM	V	A	FWHM
		(km s−1)	(K)	(km s−1)	(km s−1)	(K)	(km s−1)	(km s−1)	(K)	(km s−1)
12CO	1–0	...	...	...	...	...	...	...	...	...
13CO	1–0	3.9 ± 0.2	9.3 ± 0.2	8.5 ± 0.5	12.0 ± 0.2	11.8 ± 0.3	5.9 ± 0.6	16.9 ± 0.5	1.7 ± 0.5	4.1 ± 0.9
C18O	1–0	4.0 ± 0.4	0.9 ± 0.1	8.7 ± 0.9	12.3 ± 0.3	1.3 ± 0.2	6.3 ± 0.7	16.4 ± 0.3	0.3 ± 0.2	1.0 ± 0.8
HCN	1–0	2.5 ± 0.3	3.4 ± 0.2	13.8 ± 2.5	11.8 ± 0.3	2.3 ± 0.4	4.0 ± 1.8	18.0 ± 0.9	0.8 ± 0.2	10.9 ± 3.7
H13CN	1–0	−2.2 ± 0.9	0.3 ± 0.2	8.3 ± 3.4	7.6 ± 0.9	0.3 ± 0.1	9.3 ± 3.5	...	...	...
HCO+	1–0	2.0 ± 0.3	5.1 ± 0.3	7.7 ± 2.0	10.8 ± 0.3	3.6 ± 0.3	4.8 ± 1.8	...	...	...
H13CO+	1–0	2.9 ± 0.5	0.3 ± 0.2	5.1 ± 2.7	10.3 ± 1.0	0.4 ± 0.1	13.2 ± 3.9b	...	...	...
CS	2–1	3.2 ± 0.2	3.6 ± 0.2	7.9 ± 1.9	11.7 ± 0.2	4.8 ± 0.2	7.8 ± 1.7	...	...	–
H	41α	12.2 ± 0.6	0.4 ± 0.1	30.2 ± 4.2	...	...	...	...	...	⋅⋅⋅
N2H+	1–0	3.0 ± 0.7	0.4 ± 0.2	8.6 ± 2.9	12.6 ± 0.7	0.6 ± 0.1	10.6 ± 3.0	...	...	–
SiO	2–1	6.9 ± 0.4	0.7 ± 0.1	12.8 ± 2.6	...	...	...	...	...	...
SO	2(2) − 1(1)	9.1 ± 0.7	0.4 ± 0.2	10.7 ± 3.4	...	...	...	...	...	...
SO2	8(1, 7) − 8(0, 8)	8.4 ± 0.8	0.3 ± 0.2	13.6 ± 3.9	...	...	...	...	...	–

Notes. ^aLine parameters from Gaussian fitting at the peak of integrated emission in the PMO maps: α(J2000) = 19^h10^m14.2^s, δ(J2000) = 9°6'23''. The first two columns indicate, respectively, the molecule or atom and the transition. The ¹²CO spectrum is too complex to be fit by three or fewer Gaussians. Most of the lines are better described by two Gaussian components, whereas a few of them are single-peaked (e.g., H41 α). ^bThe second peak of H¹³CO + 1–0 appears quite wide, possibly due to a baseline difference at both extremes of the line emission.

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Although we use several Gaussians to quantify the line features, we do not interpret them as evidence for separate clouds. From the CO spectra, it is clear that most of the double-peaked features are caused by self absorption due to the very high column densities in the line of sight to the cloud center and around ∼7 km s⁻¹. This is confirmed by our calculations of surface density maps in Section 4.1. However, there is also a velocity gradient across W49N that contributes to create the line asymmetry.

At the center of the W49 GMC lies the well known massive star formation region W49A, the most luminous in the Milky Way. W49A has two main clusters separated by ∼25 (∼8 pc): W49N (the most prominent with dozens of deeply embedded (possibly still forming) O stars as traced by UC and HC H ii regions De Pree et al. 1997) and W49S (to the southeast). These scales are mapped at subarcsecond angular resolution, but with sensitivity to scales as large as ≳ 20'' with the all-configuration SMA mosaic covering the inner ∼25. The continuum mosaic, as well as the ¹³CO and C¹⁸O 2–1 mosaics, are combined with single-dish maps to recover the missing extended emission. Archival single-dish (sub)millimeter maps, as well as VLA cm maps that cover both W49N and W49S, are also used.

3.2.1. The Continuum Emission

Figure 5 (top) shows the archival CSO BOLOCAM GPS image (Aguirre et al. 2011; Ginsburg et al. 2013) at 1.1 mm of the central ∼25 × 25 pc of the W49 GMC. It covers W49N, W49S, and filamentary extensions in between and toward them. The total flux in the BOLOCAM image is 101.0 Jy.

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It is known that HC and UC H ii regions can have rising spectral indices (α_ff, where the flux $S_\nu \propto \nu ^\alpha _{\rm ff}$) in their free–free emission from cm all the way up to mm wavelengths, with values α_ff ∼ 0.5. This is due to their high densities and non-zero optical depths (Keto et al. 2008; Galván-Madrid et al. 2009; Peters et al. 2010b). Therefore, to obtain dust masses when young H ii regions are present, it is necessary to subtract the free–free contribution to the millimeter flux. We use the 3.5 cm (8.5 GHz) and 7 mm (45.5 GHz) VLA data presented by De Pree et al. (1997, 2004) to separate the total ionized-gas emission from the total dust emission. The 3.5 cm map covers both W49N and W49S and matches the BOLOCAM map. The 7 mm map covers only W49N where most of the HC sources reside. The total free–free flux at 8.5 GHz is 29.7 Jy. The compact sources have an effective α_ff = 0.2 and contribute 4.4 Jy at 7 mm and 3.2 Jy at 3.5 cm, only 11% of the total flux at the longer wavelength. We take an effective α_ff = 0 for the free–free flux from 3.5 cm to 1 mm. Therefore, the contributions at 1 mm are ∼29% free–free and ∼71% dust (71.3 Jy in the BOLOCAM map). Feasible values of the effective α_ff of the compact+extended emission are limited to being between −0.1 (optically thin emission) and 0.1 (a few compact sources may be outside W49N); the limits on the dust contribution at 1 mm are 58%–79%.

We now proceed to estimate the total gas mass in the central clusters (W49N+W49S) from the dust emission. For this, we use Equation (D6) of Appendix D and a gas-to-dust mass ratio of 100. Studies of the spectral energy distributions (SEDs) of W49N from the MIR to the millimeter have found dust temperatures T_d ranging from 20–50 K (Ward-Thompson & Robson 1990; Sievers et al. 1991). We assume an effective T_d = 30 K. For T_d in the extremes of the range discussed above, the derived masses change by about +70% and −45%. However, the main uncertainty in deriving masses from dust emission comes from the assumed dust absorption coefficient κ_ν. For high-mass star formation regions, values in the range of 0.1–0.5 cm² g⁻¹ (per unit mass of dust) at 1.1 mm are appropriate (Ossenkopf & Henning 1994; Galván-Madrid et al. 2010; Beuther et al. 2011). The total gas mass that we obtain from 1 mm dust emission is M_{gas, d} ∼ 1.5 × 10⁵ to 7.6 × 10⁵ M_☉ for T_d = 30 K. The lower end of this estimation (higher dust opacity) agrees with the CO measurements presented in Section 4. The estimations are also within the range of values obtained by Nagy et al. (2012) and Peng et al. (2013).

Figure 6 shows an archival JCMT-SCUBA map at 678 GHz (0.4 mm) of the central clusters W49N+W49S. The angular resolution of this map is 81, intermediate between the combined SMA+BOLOCAM and the BOLOCAM images. Because dust is so much brighter at higher frequencies, this map is sensitive enough to image the filamentary structures joining W49N to W49S and extending to the southwest (sometimes called W49SW), southeast, and north. The magnetic field in W49 has been detected by Curran & Chrysostomou (2007) using polarized submillimeter dust continuum emission. The plane-of-the sky magnetic field is relatively weak (less than 0.1 mG) and well aligned along the filament joining W49N to W49S. In the rest of the paper, we show that the filamentary structures are also seen in CO-integrated intensity and column density maps and that they continue all the way up to the scale of the full GMC (>100 pc).

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The dust mass can be independently derived from the 0.4 mm emission. Note that at 678 GHz and for T_d = 30 K, we are completely out of the Rayleigh-Jeans regime (hν/kT ∼ 1), so we have to use the full Planck function as in Equation (D6). At this wavelength, there is no significant contribution from free–free emission and the values of the dust absorption coefficient κ_ν at shorter wavelenghts are less sensitive to the properties of dust (e.g., see Figure 5 in Ossenkopf & Henning 1994). From Ossenkopf & Henning (1994), we consider the range of κ_0.4 mm values for coagulated dust grains without thick ice mantles, 6.5 to 9.8 cm² g⁻¹. Then, the flux in the 0.4 mm map S_0.4 mm = 1.96 × 10⁴ Jy corresponds to a gas mass M = 4.2 × 10⁵ to 6.3 × 10⁵ M_☉.

We now describe the features of the high angular resolution SMA+BOLOCAM mosaic of W49N (Figure 5 (bottom), covering the region marked by contours in Figure 5 (top)). The combining procedure is based on creating a visibility dataset from the single-dish map that then is combined with the interferometer visibilities, Fourier transformed back to the image plane, and jointly cleaned, as described in Liu et al. (2012b, 2013). The combined SMA+BOLOCAM map has an angular resolution of ∼23. The subarcsecond resolution dust maps from the SMA mosaic only, which do not recover the extended emission but are sharper, will be discussed along with the subarcsecond-resolution SMA line mosaics in a future paper. In this paper, we focus on the mass structure of the W49N cluster as a whole.

To quantify the structure in the SMA+BOLOCAM continuum map, we prefer to measure the total mass in the maps above a series of intensity (mass surface density) thresholds, rather than trying to extract sources using source-finding algorithms. The reason is that these algorithms tend to artificially fragment the emission (Pineda et al. 2009). If one acknowledges the fact that the interstellar medium (ISM) is hierarchical at all scales (except possibly at <0.1 pc where structures will end up forming a single star/binary system), it follows that trying to count sources is not very meaningful. We created masked maps with intensities >5 mJy beam⁻¹ × 5, 10, 20, 40, 80, 160, and 320 (the peak in the map is 3.302 Jy beam⁻¹) and measured their total flux. The positive contour in Figure 5 (bottom) is at 25 mJy beam⁻¹. Table 4 lists the results. The quoted values for surface densities and dust-derived masses correspond to κ_1mm = 0.25 cm² g⁻¹ and the errors on the results from varying κ_1mm from 0.1 to 0.5 cm² g⁻¹. As discussed above, variations in T_d introduce an extra uncertainty (see Appendix D for details). We have subtracted a free–free contribution of 58%.²¹

Table 4. Mass Structure of W49N from SMA+BOLOCAM^a

Intensity Threshold	Surface Density Threshold	Flux from Dust	H2 Mass
I > (Jy beam−1)	Σ > (g cm−2)	(Jy)	(M☉)
0.025	2.1 ± 1.4	17.017	1.484 × 105 ± 9.89 × 104
0.050	4.0 ± 2.7	12.745	1.111 × 105 ± 7.41 × 104
0.100	8.1 ± 5.4	9.216	8.03 × 104 ± 5.36 × 104
0.200	16.3 ± 10.8	7.462	6.51 × 104 ± 4.33 × 104
0.400	32.6 ± 21.6	6.267	5.47 × 104 ± 3.64 × 104
0.800	65.0 ± 43.3	4.253	3.71 × 104 ± 2.47 × 104
1.600	130.0 ± 86.7	2.239	1.95 × 104 ± 1.30 × 104

Notes. ^aThe masses and threshold mass surface densities correspond to κ_1mm = 0.25 cm² g⁻¹ (per unit mass of dust). The quoted range of values correspond to variations in κ_1mm = 0.25 from 0.5 to 0.1 cm² g⁻¹.

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3.2.2. The Line Emission

To identify the spectral features, we first imaged the full bandwidth covered by the SMA using the subcompact array data only. Figure 7 shows these spectra spatially averaged in a contour matching the 5σ 1.3 mm continuum shown in Figure 5 (bottom). The molecules/atoms producing the line emission are labeled. The details on the species, transition, rest frequency, and upper-level energy are listed in Table 5. All 57 lines that were clearly identified (including some blended features) above an intensity threshold of 50 mJy beam⁻¹ are listed. Many of the detected lines are typical "hot-core" tracers characteristic of luminous star formation regions (e.g., Kurtz et al. 2000; Cesaroni et al. 2010; Beltrán et al. 2011), although W49A appears to be less line-rich than its cousin Sgr B2 near the Galactic center (e.g., Nummelin et al. 1998; Belloche et al. 2013). We have unambiguously identified 40 individual lines, plus 14 lines that are clearly identified but their profiles are blended (e.g., the CH₃CN J = 12–11, K = 0, and K = 1 lines whose centers are only separated by 5.7 km s⁻¹). Three more identified lines possibly have significant contamination (see Table 5).

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Table 5. Molecular Lines Detected with SMA^a

Species	Transition	ν0	Eu	Integrated Flux	Note
		(GHz)	(K)	(Jy km s−1)
LSB low
HC3N	24–23	218.3247	130.9	322
CH3OH	4(2,2)–3(1,2)	218.4400	45.4	372
H2CO	3(2,2)–2(2,1)	218.4756	68.0	282
...	3(2,1)–2(2,0)	218.7600	68.1	294
HC3N v6 = 1	24–23 l = 1f	218.8543	848.9	63	(1)
HC3N v7 = 1	24–23 l = 1e	218.8608	452.1	63	(1)
33SO2	22(2,20)–22(1,21)	218.8754	251.7	38
OCS	18–17	218.9033	99.8	197
HNCO	10(1,10)–9(1,9)	218.9810	101.0	89
HC3N v7 = 1	24–23 l = 1f	219.1737	452.3	60
SO2	22(7,15)–23(6,18)	219.2759	352.7	203
34SO2	11(1,11)–10(0,10)	219.3550	60.1	305
CH3CH2CN	22(2,21)–21(1,20)	219.4636	112.4	33
C18O	2–1	219.5603	15.8	1.6943 × 104
HNCO	10(2,9)–9(2,8)	219.7338	228.4	80	(1)
...	10(2,8)–9(2,7)	219.7371	228.2	80	(1)
...	10(0,10)–9(0,9)	219.7982	58.0	198
H213CO	3(1,2)–2(1,1)	219.9084	32.9	63
SO	6(5)–5(4)	219.9494	34.9	3.042 × 103
CH3OH	8(0,8)–7(1,6)	220.0784	96.6	118
CH3OCHO	17(4,13)–16(4,12) E	220.1668	103.1	93
CH3CHO vt = 1	10(3,8)–11(0,11) E	220.1800	275.4	63
LSB high
13CO	2–1	220.3986	15.86	1.23553 × 105
HNCO	10(1,9)–9(1,8)	220.5847	101.5	90
CH3CN	12(6)–11(6)	220.5944	325.8	53
33SO2	11(1,11)–10(0,10)	220.6174	61.0	92
CH3CN	12(5)–11(5)	220.6410	247.3	40
...	12(4)–11(4)	220.6792	183.1	54
...	12(3)–11(3)	220.7090	133.1	150
...	12(2)–11(2)	220.7302	97.4	96
...	12(1)–11(1)	220.7430	76.0	295	(1)
...	12(0)–11(0)	220.7472	68.8	295	(1)
33SO2	14(3,11)–14(2,12)	220.9857	120.2	47
34SO2	22(2,20)–22(1,21)	221.1149	248.1	116
...	13(2,12)–13(1,13)	221.7357	92.5	153
SO2	11(1,11)–10(0,10)	221.9652	60.3	1397
H	38β	222.0117	...	159	(2)
CH3CCH	13(4)–12(4)	222.0991	190.2	33	(3)
...	13(3)–12(3)	222.1288	139.6	118
CH3OCHO v = 1	18(6,12)–17(6,11) A	222.1488	312.3	106
CH3CCH	13(1)–12(1)	222.1627	81.7	427
H2CCO	11(0,11)–10(0,10)	222.1976	63.9	13	(1)
...	11(3,8)–10(3, 7)	222.2002	181.3	13	(1)
USB low
CO	2–1	230.5380	16.5	...
OCS	19–18	231.0609	110.8	255
13CS	5–4	231.2207	33.3	202
H	30α	231.9009	...	747
CH3OCH3	13(0,13)–12(1,12) AA	231.9877	80.9	122	(1)
CH3OCH3	13(0,13)–12(1,12) EA+AE	231.9879	80.9	122	(1)
USB high
CH3OH	10(2,8)–9(3,7) ++	232.4185	165.4	90
...	10(−3,8)–11(−2,10)	232.9458	190.3	60	(4)
CH3CH2CN	26(6,21)–25(6,20)	233.2050	190.9	47	(1)
...	26(6,20)–25(6,19)	233.2073	190.9	47	(1)
...	42(4,38)–41(5,37)	233.2910	410.1	33	(1)
34SO2	10(5,5)–11(4,8)	233.2964	109.8	33	(1)
CH3OCHO	26(21,5)–27(20,7) E	233.7284	499.2	75
SO2	28(3,25)–28(2,26)	234.1870	403.0	591

Notes. (1) Blended lines. (2) From the measured line intensity of the H30α line and assuming local thermodynamic equilibrium (LTE) conditions, this feature is dominated by H38β. It could have a contribution of <25% from CH₃CCH 13(6)–12(6), ν₀ = 222.0144 GHz. (3) From the measured line intensity of the H30α line and assuming LTE conditions and a 10% Helium abundance, this feature is dominated by CH₃CCH 13(4)–12(4). It could have a contribution of <20% from He38β, ν₀ = 222.1022 GHz. (4) Could be contaminated by CH₃CHO 4(4,1)–5(3,2) A–, ν₀ = 232.9518 GHz. ^aMolecular lines detected above an intensity I_ν > 50 mJy beam⁻¹ at line peak in the subcompact array maps, averaged over an area equal to the 5σ contour of the continuum map shown in Figure 5 (bottom). The first column refers to the molecule tag, the second column refers to the transition, the third refers to its rest frequency as found in Splatalogue (http://www.splatalogue.net/), the fourth column refers to the upper level energy, the fifth column refers to the velocity-integrated flux in the all-configuration maps, and the sixth column refers to additional notes. Data used from Splatalogue are compiled from the CDMS catalog (Müller et al. 2005) and the NIST catalog (Lovas 2004). A single flux is listed for blended lines. The ¹³CO and C¹⁸O 2–1 maps have been combined with IRAM 30 m single-dish data.

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W49A appears to be rich in SO₂ and its isotopologues. Younger massive star formation regions devoid of ionization or with only faint H ii regions tend to lack emission in these lines (e.g., Galván-Madrid et al. 2010; Liu et al. 2012a), whereas regions in which O stars have already formed and with HC and UC H ii regions tend to be brighter in the SO₂ lines in this band (e.g., Galván-Madrid et al. 2009; Baobab Liu et al. 2010).

After line identification, individual line cubes with the all-configuration SMA data were created. The synthesized beam of these maps varies smoothly from 102 × 069, position angle (P.A.)=768 at the lowest frequency (36.4 K per Jy beam⁻¹) to 098 × 064, P.A. =741 at the highest (31.5 K per Jy beam⁻¹). The resolution of the final maps was chosen such that nearly all of the flux of the subcompact array maps is recovered but at the highest possible angular resolution. The CO, however, is affected severely by missing flux in interferometric observations. We have therefore combined the multiconfiguration SMA maps with IRAM 30 m maps for the ¹³CO 2–1 and C¹⁸O 2–1. Figure 8 shows the velocity-integrated (moment 0) map of these two CO isotopologues. As with the larger-scale PMO data, the emission has been integrated in the LSR velocity range from −20 km s⁻¹ to 30 km s⁻¹. The angular resolution of the single-dish+interferometer maps is ≈2''.

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A striking feature of the SMA+IRAM 30 m maps is that the radially converging, triple filamentary structure seen at the full GMC scales (from ∼10 to 100 pc) as traced by the PMO maps (Section 3.1) is preserved all the way down to the inner few pc. In Section 4, we discuss in more detail the morphological matching between these structures and its physical interpretation. Their dynamics will be discussed on a following paper.

Appendix C (on-line only) shows the velocity-integrated (moment 0) line emission of all the SMA-detected lines listed in Table 5. A single map is shown for neighboring lines whose profiles are blended. The last column of Table 5 lists the velocity-integrated line fluxes. For the science discussion of this paper (Sections 4 and 5), we use the combined SMA+IRAM 30 m CO maps together with the dust maps and the larger-scale PMO CO maps to study the mass of the W49 GMC as a function of scale.

We calculate maps of the mass of the GMC from scales of ∼1 pc to >100 pc using the PMO CO maps on the larger scales and the SMA+IRAM 30 m CO maps on the smaller scales. The methodology is described in Appendix D and it is based on solving for the optical depth in every 3D pixel, or voxel, of data from the CO isotopologue ratios. Uncertainty in this mass determination comes from uncertainties in the isotopologue abundances (typically ±50%), in the CO to H₂ conversion factor and in the assumed excitation temperature T_ex (typically ±25%). All added up, masses are uncertain within a factor of two each way (see Appendix D). Figure 9 shows the resulting maps of molecular gas surface density Σ in units of M_☉ pc⁻². We derive a total mass for the GMC M_tot = 1.14 × 10⁶ M_☉. In the area covered by the 0.4 mm dust map (Section 3.2.1), the CO mass map gives a mass M_{W49N + S + SW} = 4.1 × 10⁵ M_☉, in agreement with the lower values in the range of masses as derived from 0.4 mm dust emission (M = 4.2 × 10⁵ to 6.3 × 10⁵ M_☉).

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On the full-GMC map (top panel), the central cluster W49N is the most prominent feature in the center. The known triple filamentary structure of scale ∼30 pc is seen connecting radially from W49N to W49S (to the southeast), to W49SW (to the southwest), and extending north of W49N. W49S appears to be connected to a clump ∼4' (∼13 pc) to the northeast.²² W49SW appears to end in a high-density peak. Another high column density clump is seen ∼55 (∼18 pc) southwest of the main W49N peak and is joined by a north–south extension to the brighter filament joining W49N to W49SW. A chain of filaments extend north of W49N and all of them appear curved with a similar orientation. The full GMC mass distribution is clumpy, which indicates fragmentation also along the filaments in the periphery. All the bright UC and HC H ii regions reside in the central main clusters and W49N is by far the richest in ionized gas structures (De Pree et al. 1997, 2004). A possible future line of research would be to study star formation in detail in the rest of the high column density peaks as it has been done with W49N, looking for fainter H ii regions and molecular gas cores.

The bottom panel of Figure 9 shows the high angular resolution column density map obtained from the combination of the CO SMA mosaics with the IRAM 30 m observations presented in Peng et al. (2013). These maps cover the area marked by a black square on the full GMC map. The global column density peak is right in the middle of the ring of HC H ii's (see Figure 8 for an overplot), at the position of the HC H ii region labeled B by De Pree et al. (1997). The highest column density features (Σ > 10⁴ M_☉ pc⁻²) are indeed the highest volume density regions: in Figure 14 of Appendix C, we see that many of the molecular lines that trace the densest gas (n > 10⁵ cm⁻³) peak at the same position as the high-resolution CO column density maps.

It is striking to note that the larger scale (10 to 100 pc) structure of the cloud is preserved all the way to the inner <10 pc. This triple structure consists of one structure of filaments oriented toward the east–southeast (which join W49N to W49S), one structure of filaments toward the southwest, and filaments extending to the north. Each of the filamentary structures is seen to be composed of a tree of filaments.

The maps reveal that the mass structure of the W49 GMC is organized in a hierarchical network of filaments that appear to converge in the central, densest region harboring the W49N and W49S clusters. This network extends all the way from the inner pc where the embedded O-type stars in W49N reside (as traced by the dozens of UC and HC H ii regions; see Figure 8 or Figure 1 in De Pree et al. 1997) to the >100 pc scales of the full GMC (see Figure 1). The network is also preserved at intermediate scales (∼10 pc), where the filaments connect W49N to W49S and both of them to the surrounding GMC (Figures 5 and 6).

This type of hierarchical, centrally condensed network of filaments appears to be common in clouds harboring the most luminous (L > 10⁵ L_☉) star formation regions in the Galaxy. For example, the global structure of the W49 GMC appears to be a scaled-up version of the GMC in the G10.6–0.4 massive star formation region (L ∼ 9.2 × 10⁵ L_☉; see Figure 3 of Liu et al. 2012b). In this scenario, the densest, central regions of the GMC collapse first because they have shorter free–fall times (t_ff∝ρ^−1/2). Furthermore, departures from spherical to sheet or filamentary geometries increase the free–fall time with the aspect ratio of the configuration (Toalá et al. 2012; Pon et al. 2012). Although never completely spherical, the central W49N clump is closer to sphericity than the larger-scale filaments.²³ Therefore, it is natural to expect that the central clump (scales <10 pc) with an average number density n ∼ 10⁴ to 10⁵ cm⁻³ can collapse and form massive stars on a timescale of the order of a few times the spherical-collapse free–fall time t ∼ 10⁵ yr, whereas the more filamentary, larger-scale GMC, even with an initial density close to that of the central clump, will collapse in a timescale >1 Myr. Figure 1 of Liu et al. (2012b) shows a schematic diagram that accounts for the aspects discussed above.

Filament networks are often also present in low- and intermediate-mass star formation regions (Gutermuth et al. 2008; Myers 2009; Molinari et al. 2010; Pineda et al. 2011; Kirk et al. 2013; Takahashi et al. 2013). However, it is unclear why some of them look only like a filamentary network and some others also have prominent hub-like condensations. This could be due to evolution/mass differences or due to different observational techniques.²⁴ We hypothesize that centrally condensed networks are the main morphology in the most massive clusters born out of the most massive clouds like W49 or Carina (Preibisch et al. 2012; Roccatagliata et al. 2013), but more systematic studies are needed. In W49, for example, many previous high-resolution studies focused only on the central few parsecs of the main clusters (e.g., Wilner et al. 2001; Peng et al. 2010), whereas studies that captured the entire GMC lacked the sensitivity to recover the external filaments (e.g., Simon et al. 2001; Matthews et al. 2009).

Hierarchical filamentary networks surrounding a central cluster (or small system of clusters) are also naturally expected from simulations of massive clouds that form massive star clusters (e.g., Bonnell et al. 2001; Smith et al. 2009b; Vázquez-Semadeni et al. 2009; Dale et al. 2012). In these simulations, the primordial GMC has density inhomogeneities (presumably caused by the process of GMC formation itself) that give rise to filamentary structure while the full cloud contracts. These filaments can then converge²⁵ into the hubs where cluster formation occurs (e.g., Galván-Madrid et al. 2010; Duarte-Cabral et al. 2011; Inoue & Fukui 2013), preferably at locations deep within the global gravitational potential. When feedback from the formed stars is included, it is usually found that it has an important effect in regulating the star formation efficiency (SFE; e.g., Peters et al. 2010a, 2011; Krumholz et al. 2011; Dale et al. 2012; Colín et al. 2013).

Several interpretations have been put forth to explain the observations of W49N. Welch et al. (1987) proposed a global collapse scenario based on interferometric observations of RLs of the ring of HC H ii's and molecular-line absorption toward their line of sight. Keto et al. (1991), based on modeling the line profiles resulting from a hydrodynamical simulation, showed that the observations of Welch et al. (1987) could be explained by a global-local collapse scenario where fragmentation from the larger-scale contracting cloud produces denser molecular cores that themselves collapse into individual H ii regions. Serabyn et al. (1993) proposed that the multiply peaked single-dish line profiles are due to different molecular clumps whose collision triggered the vigorous star formation activity. The morphological evidence presented in this paper shows that the most likely situation is similar to a scaled-up version of the Keto et al. (1991) model. The filamentary ∼100 pc scale GMC has fragmented and the denser W49N clump (extending further toward the southeast, southwest, and north) is the converging region of a hierarchical (triple) network of filaments that converge toward the ring of HC H ii's. If the different filaments are viewed as separate entities, then they could be interpreted as colliding clouds. However, the observations presented in this paper show that they are part of a larger, common structure. Kinematical evidence supporting this interpretation will be shown in the second paper of this project. Further evidence comes from looking at the available single-dish line profiles: the larger the optical depth, the more prominent the ∼7 km s⁻¹ dip is, indicating that it is produced by self absorption due to the large column of gas toward the center of W49N. Indeed, we obtain our larger optical depths from the line ratios at these positions and velocities.

However, the ring of HC H iis is not the entire story. There is already a NIR massive star cluster concentrated within 1 pc and located ∼3 pc east of the Welch ring (cluster 1 of Alves & Homeier 2003). This cluster likely is the ionizing source of the extended halo of free–free emission next to the HC H ii's (see Figure 8), whose edge matches the shell reported by Peng et al. (2010) from 4.5 and 8.0 μm observations. These two YMCs (which may be parts at different evolutionary stages of the same YMC), together with the rest of the young massive stars in W49N, W49S, and W49SE, formed from the same GMC.

We now proceed to use the column density maps described in Section 4.1 to compute the mass of the GMC as a function of distance from the central cluster W49N and to compare with other massive GMCs in the Galaxy that are believed to be progenitors of YMCs. Figure 10 shows the result. The match between the calculation using the CO 1–0 ratios on larger scales overlaps remarkably well with the result on smaller scales using CO 2–1 ratios. The mass in a region around W49N with a diameter D = 8.0 pc is M ∼ 1.2 × 10⁵ M_☉, equivalent to a mean density under the assumption of spherical symmetry of ∼9 × 10³ cm⁻³. The mean density is likely higher because of the filamentary geometry and substructure. Indeed, summing the CO mass in an aperture matching the dust filaments seen at 0.4 mm gives M ∼ 4 × 10⁵ M_☉. The full GMC on scales of D ∼ 110 pc (diameter) reaches a mass of M ∼ 1.1 × 10⁶ M_☉. In Figure 10, we compare the W49 GMC with the Galactic center cloud G0.253+0.016 (Longmore et al. 2012; Kauffmann et al. 2013), which has a mass M ∼ 1.3 × 10⁵ M_☉ in a diameter D = 5.6 pc. Also plotted are the most massive clumps of the G305 GMC (Hindson et al. 2010) and the results of the recent study of the Carina complex by Preibisch et al. (2012). Unlike W49 and G0.253+0.016, the clusters in the latter two clouds are already optically visible. G0.253 and the W49 GMC also differ in other properties. G0.253 is almost starless (Kauffmann et al. 2013; Rodríguez & Zapata 2013), appears to be externally confined to a total size of a few parsecs (Longmore et al. 2013), and is in a more extreme environment in the Central Molecular Zone of the Milky Way that may hinder further star formation. On the other hand, W49 has already formed a copious amount of stars, as seen in the infrared and radio continuum.

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It is seen that GMCs like Carina or W49 have a gas mass reservoir large enough (∼10⁶ M_☉) and the right size (radius ∼10¹–10² pc) to form stellar clusters with a typical stellar mass (M_⋆ ∼ 10⁵ M_☉) and radius (∼10 pc) of GCs (Portegies Zwart et al. 2010). The gas-mass reservoir of the central few parsecs is still enough to form a YMC with a stellar mass M_⋆ > 10⁴ M_☉, even if it decouples completely from the rest of the cloud.

We note that the gas mass is dominated by molecular gas at all the scales relevant to this discussion. From the 3.5 cm free–free map and for a range of turn-off frequencies²⁶ from 8 to 230 GHz, the total H ii mass is between M_H ii ∼ 1700 and 5400 M_☉.

The GMC can be disrupted by a series of feedback processes, of which the most important are protostellar jets and outflows, H ii pressure, and radiation pressure. In W49A, the luminosity output is heavily dominated by the most massive stars. Massive, collimated outflows do not appear to be important.

In principle, the over-pressurized ionized gas at temperature T ∼ 10⁴ K can clear out the surrounding molecular gas, which is at a temperature of tens to hundreds of Kelvin (Keto 2007). However, W49A is at a stage at which, in spite of its enormous luminosity, several of its H ii regions are still confined within ∼1000 AU (De Pree et al. 2000, 2004). Various mechanisms may be responsible for delaying H ii region growth, including confinement by denser molecular gas (De Pree et al. 1995), molecular infall from the surrounding clump (Walmsley 1995), and continued accretion through filamentary, partially ionized accretion flows (Peters et al. 2010a; Galván-Madrid et al. 2011; Dale et al. 2012). W49A has already had a lifetime of several × 10⁵ yr since the onset of massive star formation,²⁷ given the presence of HC H ii regions and hot molecular cores (Wilner et al. 2001). After this time, only ∼1% of the gas mass in the inner ∼6 pc around W49N is ionized; the rest is molecular. The difference is even more dramatic (∼0.1% of gas is ionized) if the full GMC is considered. Therefore, it is evident that in this timescale ionization is not efficient at disrupting the cloud. Even if the few central parsecs of gas were fully ionized, the main disruptive force would be radiation pressure rather than ionized gas pressure. From Figure 2 of Krumholz & Matzner (2009), for an ionizing photon rate Q ∼ few × 10⁵¹ s⁻¹ and an average particle density n ∼ few × 10³ cm⁻³, the radiation pressure would be dominant by a factor ∼100.

To estimate the effect of radiation pressure, since most of the gas is molecular and not ionized, we should consider that the dominant form will be onto dust grains.²⁸ The GMC is disrupted if the outward radiation pressure from the central clusters overcomes the cloud's self gravity, i.e., if the luminosity from the clusters L_⋆ is greater than the Eddington luminosity L_Edd. Under spherical symmetry (an assumption only valid to some extent in the inner ∼10 pc of the central clusters),

$$\begin{equation} L_{\rm Edd}(r)=4\pi c{\it G M}(r) / \kappa _{\rm R}, \end{equation} \tag{ 1 }$$

where M(r) is the dust mass at radius r and κ_R is the Rosseland mean dust opacity. We take M(r = 6.5pc) ∼ 2.1 × 10³ M_☉ from our CO and dust measurements²⁹ and κ_R in the range from 0.1 to 1 cm² g⁻¹ (Semenov et al. 2003). Therefore, L_Edd(r = 6.5pc) is in the range from 2.7 × 10⁷ to 2.7 × 10⁸L_☉. Sievers et al. (1991) obtained the luminosity of the central clusters by fitting their SED from the MIR to the millimeter. We rescale their result to a distance of 11.1 kpc (those authors used 14 kpc) to obtain a total luminosity L_bol ≈ 1.7 × 10⁷L_☉. The Eddington ratio L_bol/L_Edd is then in the range 0.06 to 0.6. Note that the radius selection corresponds to the distance of W49N to W49S and therefore is roughly the minimum gas mass that encloses most of the luminosity. If larger radii are adopted or if larger mass estimates are used from taking an aperture following the central filaments in the CO maps or from the 0.4 mm observations, then the Eddington ratio L_bol/L_Edd would be even lower. Also, if the totality of the GMC is considered, it is possible that the filaments that are seen to radially converge in the central clusters will continue to feed them during the star-formation timescale. A dynamical study of the filamentary network will follow this paper, however, even in the static case, we can conclude that the current cluster is not able to entirely clear its own cloud.

Murray et al. (2010) investigated the disruption of GMCs across a wide range of conditions, from Galactic starburst regions like W49 to ultra-luminous infrared galaxies. They indeed conclude that radiation pressure is the dominant force in cloud dispersal. For their W49A case, however, they pick a cluster luminosity L = 6.4 × 10⁷L_☉ from correcting the free–free luminosity for dust absorption. This higher cluster luminosity in their model allows it to marginally disperse the GMC. Although the luminosity derived from the far-infrared by Sievers et al. (1991) is more accurate, it is also true that the cluster may still gain more mass and become more luminous. An appealing idea is that the cluster will continue to gain mass until L_bol/L_Edd ≈ 1. Indeed, there is evidence that star formation in the central clusters is continuous: part of the stellar population is already visible in the NIR³⁰ (Conti & Blum 2002; Alves & Homeier 2003); part of it is barely visible in the NIR and MIR (Smith et al. 2009a) but their massive stars are seen as HC and UC H ii regions in the radio (e.g., De Pree et al. 1997, 2000). Finally, there are also hot molecular cores without associated H ii regions (Wilner et al. 2001).

Regarding the future of the star clusters, W49N and W49S may form more than one YMC or coalesce into a single system. They could also dissolve. Observations and models of YMC dynamics suggest that if the SFE is low enough (<50%), "rapid"³¹ gas dispersal leaves unstable star clusters that end up dissolving (Lada et al. 1984; Bastian & Goodwin 2006). However, if the gas dispersal timescale is comparable to or larger than the crossing time of the GMC, the resulting star cluster has more time to adjust to the new gravitational potential and it is easier for it to remain bound even with SFEs as low as 10% (Lada et al. 1984; Pelupessy & Portegies Zwart 2012).

We argue that because the star formation efficiency SFE = M_⋆/(M_⋆ + M_gas) and the gas dispersal timescale are large enough, the most likely outcome is that the star clusters W49N+W49S (or at least part of their stellar content) will remain bound.

From NIR observations, Homeier & Alves (2005) estimate a stellar mass in frames of length ∼5' (∼16 pc) of M_⋆ ∼ 4 × 10⁴ to 7 × 10⁴ M_☉. The total stellar mass should be somewhat larger when the embedded population not visible in the infrared (e.g., the HC H ii regions) is taken into account. The total gas mass in the same area from the CO and submillimeter continuum data is M_gas ∼ 4 × 10⁵ to 6 × 10⁵ M_☉. Therefore, within the W49N+W49S region, the current SFE is >10% and will likely increase with time until star formation is terminated.

Observations of the most luminous star formation regions in the Galaxy show that their star clusters are still deeply embedded on large scales even after the formation of subsequent generations of UC H ii's, HC H ii's, and hot molecular cores, which requires timescales of at least several × 10⁵ yr from the onset of significant feedback (Galván-Madrid et al. 2009; Liu et al. 2011, 2012a, 2012b). Older, optically visible clusters like the one in Carina (Preibisch et al. 2012) are still surrounded by hundreds of thousands of solar masses of molecular gas. Therefore, observations show that gas dispersal is slow compared with the star formation timescale. It is harder to estimate the star formation rate of the entire GMC because although in this paper we have presented a good account of its gas content, most of the stellar content is deeply embedded.

The central part of the W49 GMC satisfies other proposed criteria for bound massive cluster formation. Bressert et al. (2012) proposed that massive clusters need to have an escape velocity v_esc greater than the sound speed of ionized hydrogen c_H ii ≈ 10 km s⁻¹. The central clusters in W49A satisfy this criterion. For a current star cluster mass M_cl ∼ 7 × 10⁴ M_☉, the maximum bound-cluster radius is $r_{\rm cl}=2GM_{\rm cl}/c_{{\rm H}\,\scriptstyle {II}}^2\approx 6$ pc. If the embedded population is taken into account, assuming M_cl = 10⁵ M_☉, r_cl = 8.6 pc. The NIR clusters³² identified by Alves & Homeier (2003) have individual radii r < 1 pc. If further contiguous star formation ends up making a single cluster covering all the central part of the cloud, from W49S to W49SE, the radius of the resultant cluster will be r < 6 pc, compact enough to satisfy the criterion of Bressert et al. (2012) for boundness. This, however, may be a very restrictive condition, since it assumes that even a fully ionized cloud is contained by gravity and will eventually be used to form stars. Our observations show that in the W49 GMC the ionized gas mass fraction is very small.

Kruijssen (2012) presented a model in which bound star clusters are formed out of the high-density end of the ISM. This model accounts for possible dissolution effects like gas expulsion and external tidal forces and for conditions from the typical Milky Way to extragalactic starbursts. Kruijssen (2012) finds that for gas mass surface densities above Σ_gas ∼ 1000 M_☉ pc⁻², about 70% of the formed clusters will remain bound. Our surface density map (Figure 9, bottom right) shows that almost all of the W49N gas is above this threshold. This further suggests that the central cluster W49N³³ will remain as a bound one.

If we assume that the ¹³CO emission is optically thin, the ¹²CO opacity ($\tau _\mathrm{^{12}CO}$) in a given voxel of data (a position–position–velocity cell) can be calculated from the intensity (brightness) ratio of the lines (Snell et al. 1984):

$$\begin{equation} \frac{T_\mathrm{B,^{12}CO}}{T_\mathrm{B,^{13}CO}}=\frac{1-\exp (-\tau _\mathrm{^{12}CO})}{1-\exp (-\tau _\mathrm{^{12}CO}/\chi _{^{13}C})}, \end{equation} \tag{ D1 }$$

where $\chi _{^{13}C}$ is the relative abundance of ¹²C to ¹³C. We use $\chi _{^{13}C}=65$ using the fit of Wilson & Rood (1994) for a galactocentric distance of 7.6 kpc for W49, derived using its parallax distance to the Sun of 11.1 kpc (Zhang et al. 2013).

In the voxels where there is a ¹²CO detection but no ¹³CO, we use the optically thin approximation to the column density of ¹²CO [cm⁻²]:

$$\begin{equation} N_\mathrm{thin,^{12}CO}=4.31\times 10^{13} \frac{T_\mathrm{ex}+0.9}{\exp (-5.5/T_\mathrm{ex})} T_\mathrm{B,^{12}CO} \Delta v, \end{equation} \tag{ D2 }$$

where temperatures are in K and velocity widths in km s⁻¹.

In the voxels with ¹³CO emission, we calculate the optically thick column density with

$$\begin{equation} N_\mathrm{thick,^{12}CO}=\frac{\tau _\mathrm{^{12}CO}}{1-\exp (-\tau _\mathrm{^{12}CO})} N_\mathrm{thin,^{12}CO}. \end{equation} \tag{ D3 }$$

Once the column density is known for each position–position–velocity voxel, we integrate them to obtain the mass surface density maps shown in Section 4. We note that in principle the same procedure can be used with the C¹⁸O to ¹²CO ratio. However, the PMO C¹⁸O maps are not sensitive enough to detect emission except for the very center of the cloud (see Section 3.1).

Two small corrections have been applied to the straightforward procedure outlined above. First, there is a dip in the spectra between 14 and 18 km s⁻¹ that appears to be caused by an extended, foreground cloud (Peng et al. 2013). We have interpolated the measurements within this range. The corrected mass is <1% larger. Second, a few voxels close to the map center and around ∼7 km s⁻¹ have very large optical depths (i.e., the ¹²CO and ¹³CO maps have the same intensity within the uncertainty).

For a cloud that is fully molecular, a hydrogen to helium number ratio of 10, and an abundance of H₂ to ¹²CO χ_CO = 10⁴, the gas mass surface density Σ is then obtained from

$$\begin{equation} \Sigma =\mu m_\mathrm{H} \chi _\mathrm{CO} N_\mathrm{^{12}CO}, \end{equation} \tag{ D4 }$$

where [Σ] = g cm⁻² for [$N_\mathrm{^{12}CO}$] = cm⁻², μ = 2.8, and m_H = 1.6733 × 10⁻²⁴ g.

On the scales of W49N (∼10 pc), we follow a similar procedure to the one outlined above, but with the ¹³CO and C¹⁸O 2–1 maps at ∼2'' angular resolution combined from the SMA mosaics and IRAM 30 m data. In this case, we have

$$\begin{eqnarray} N_\mathrm{thin,^{13}CO}&=&1.17\times 10^{13} \exp (5.3/T_\mathrm{ex})\nonumber\\ &&\times \frac{T_\mathrm{ex}+0.9}{\exp (-10.6/T_\mathrm{ex})} T_\mathrm{B,^{13}CO} \Delta v. \end{eqnarray} \tag{ D5 }$$

The rest of the procedure is as in the larger-scale maps. The relative abundance of ¹³CO to C¹⁸O (7.5) is the ratio of the abundance of ¹⁶O to ¹⁸O ($\chi _{^{18}O}=484.3$) to the abundance of ¹²C to ¹³C ($\chi _{^{13}C}=65$) (Wilson & Rood 1994). The maximum optical depth $\tau _\mathrm{C^{18}O}$ solved in our calculations is 20. As with the larger-scale GMC, we have interpolated the spectra within the velocity range from 14 and 18 km s⁻¹.

Dust grains can be assumed to emit as a graybody at temperature T_d. At millimeter and submillimeter wavelengths, their emission is optically thin, so the total mass in dust grains is given by

$$\begin{equation} M_\mathrm{d}=3.25\times 10^6 d^2 \left (\frac{\exp (0.048\nu / T_\mathrm{d}) -1}{\nu ^3} \right) \frac{S_\nu }{\kappa _\nu }, \end{equation} \tag{ D6 }$$

where the units of mass (M_d), distance (d), frequency (ν), dust temperature (T_d), flux (S_ν), and dust absorption coefficient (κ_ν) are, respectively, M_☉, kpc, GHz, K, Jy, and cm² g⁻¹.

The total molecular-gass mass is then M_gas = 100 M_d. Often the Rayleigh–Jeans regime (hν ≪ kT_d) is assumed, but this is not the case for T_d ∼ 30 K and the frequencies we deal with, especially at 678 GHz (0.4 mm), where hν/kT_d ≈ 1. Therefore, we prefer to use the full Planck function.

Many sources of uncertainty make the estimation of masses derived from CO ratios and dust continuum emission accurate to a factor of two, at most. For the CO ratio measurements, we handle uncertainties in the isotopologue abundances and the excitation temperature and do not consider uncertainties in the CO-to-H₂ abundance factor, which is usually set in the literature to χ_CO = 10⁴. For the dust measurements, we handle uncertainties in the dust absorption coefficient and the dust temperature, but again leave the gas-to-dust mass conversion factor at 100.

The uncertainty in the mass determinations from CO isotopologue abundances is estimated from the fits of Wilson & Rood (1994). The abundance of ¹²C with respect to ¹³C is $\chi _{^{13}\mathrm{C}}=65\pm 27$ and the abundance of ¹⁶O to ¹⁸O is $\chi _{^{18}\mathrm{O}}=484\pm 172$. For the optically thin and the non-saturated optically thick voxels, uncertainty in the mass propagates as the uncertainty in abundance. However, this is not the case for the saturated voxels in which we set τ to a maximum value τ_max. τ_max is defined as the value at which the line brightness ratio equals 1 + σ, where σ is the rms noise in the maps, i.e., larger optical depths are not distinguishable, within the noise. We have found empirically how this affects our calculations by re-running them within the allowed range of abundance values. In the large scale PMO maps, very few pixels are affected by saturation in all cases. Therefore, the masses scale almost linearly with the used abundance. In the smaller-scale SMA maps, several voxels are saturated mainly in the central parts of the map, therefore larger abundances permit increasingly large τ_max and larger mass estimates. The mass uncertainty due to the effect discussed above grows at smaller radii, up to +130% and −57% within r = 0.5 pc.

If the excitation temperature T_ex is not position dependent, then its effect on the uncertainty of the mass estimate is almost linear and affects equally all the radial measurements. We pick T_ex = 30 K. Reasonable T_ex values are in the range from 20 to 40 K. Therefore, we estimate a respective mass uncertainty of ±26%. We also explore the effect of a possible radial dependence T_ex∝r^−1.5, with T_ex(r = 0) = 50 K, and T_ex(r = 5 pc) = 20 K (i.e., a warm W49N). The results show that the mass in the inner 5 pc would be systematically underestimated by ∼54% close to the center and ∼27% at r = 5 pc and then at larger radii the mass difference would converge to ∼3% at r = 50 pc. However, we do not include the effects of this hypothetical temperature profile in our error budget.

Propagating the uncertainties from abundances and excitation temperatures gives a total uncertainty of ∼ ± 50% for the PMO masses. For the SMA+IRAM 30 m masses, typical values are +80% and −50%, but uncertainties are larger at smaller radii. The error bars in Figure 10 include the individual contributions from abundance uncertainty and from shifts in T_ex.

Uncertainties in mass determinations from dust are as large or larger than from CO. The dust absorption coefficient κ_ν, dependent on the properties of dust grains, is the main source of uncertainty. We take as possible values for κ_ν those corresponding to coagulated dust grains without significant ice mantles from the calculations of Ossenkopf & Henning (1994). The dispersion of these values is smaller at 0.4 mm than at 1 mm. We estimate the mass uncertainty from κ_ν to be ± ∼ 20% at the former wavelength and ± ∼ 65% at the latter wavelength. Possible variations from the adopted dust temperature T_d = 30 K also contribute to the total uncertainty in mass. From the graybody fits of Sievers et al. (1991) and Ward-Thompson & Robson (1990), T_d is restricted to the range between 20 and 50 K. Therefore, the uncertainty from temperature in the mass determination is ∼ ± 50%. Again, we do not consider further uncertainties from the dust-to-gas mass conversion factor, which we fix at 100. Therefore, we estimate a total mass uncertainty of ±55% at 0.4 mm and ±90% at 1 mm, including uncertainties from the free–free subtraction at the latter wavelength.