MOLECULAR OUTFLOWS WITHIN THE FILAMENTARY INFRARED DARK CLOUD G34.43+0.24

With the APEX telescope, we observed the CO(3 → 2), ¹³CO(3 → 2), C¹⁸O(3 → 2), and CS(7 → 6) lines. The observations were carried out during three epochs: 2005 July, 2005 October, and 2006 May–July. The telescope beam size at the frequency of the observed lines ranged from 17'' to 19'' (FWHM). We used the heterodyne receiver (APEX-2a), which provided a channel separation of 122 kHz and a total bandwidth of 1 GHz with 8192 spectral channels.

In CO(3 → 2) and ¹³CO(3 → 2), we mapped the emission within a 100''×680'' region which covers a spatial extent similar to that exhibited by the 1.2 mm dust continuum emission map (see Garay et al. 2004). The spacing between adjacent points on a regular grid was 20'' and the position-switching mode was used. The on-source integration time per map position was typically ∼40 s in both molecules. System temperatures were in the range 110–340 K in CO(3 → 2) and 200–300 K in ¹³CO(3 → 2), resulting in an rms noise per channel, in antenna temperature, of typically 0.27 K and 0.37 K, respectively. In C¹⁸O(3 → 2), we mapped the emission within a 80''×100'' zone, covering the central region of the filament also known as the IRAS 18507+0121 region. System temperatures were typically ∼190 K. The on-source integration time per map position was ∼50 s resulting an rms noise per channel of typically 0.29 K in antenna temperature. In CS(7 → 6), we mapped the emission within a 40''×120'' region. System temperatures were typically ∼200 K. On-source integration time was ∼80 s resulting an rms noise per channel of typically 0.18 K in antenna temperature.

The molecular line data were reduced according to the standard procedure using CLASS, a GILDAS working group software.

With the NRO 45 m telescope we observed the CS(2 → 1), SiO(2 → 1), C³⁴S(2 → 1), HCO⁺(1 → 0), H¹³CO⁺(1 → 0), and CH₃OH(2 → 1) lines toward the central region of the filament. The observations were undertaken during 1996 February–April. The telescope beam size at the frequencies of the observed lines is 15''–18''. We used an acousto-optical spectrometer with 37 kHz resolution covering a total bandwidth of 40 MHz.

The emission was mapped in all lines within a 80''×140'' region. The spacing between adjacent points on a regular grid was 20'', using the position-switching mode. System temperatures were in the range between 160 and 390 K. On-source integration times per map position ranged from 300 to 600 s resulting in an rms noise of typically 0.08 K per channel in antenna temperature in all lines. First-order polynomials were fitted in order to estimate and remove the baselines. Part of these data were used by Ramesh et al. (1997) to model the kinematics at the peak position of IRAS 18507+0121.

With the SEST telescope we observed the CS(2 → 1) and C¹⁸O(2 → 1) lines toward the northern part of the filament (MM3 core). The telescope beam size is 24'' at the frequency of the C¹⁸O(2 → 1) line and 51'' at the frequency of the CS(2 → 1) line. The observations were carried out in 2003 March. We used the high-resolution acousto-optical spectrometers, which provided a channel separation of 43 kHz and a total bandwidth of 43 MHz. We observed, with 30'' spacing between adjacent points on a regular grid, 25 positions within a 150''×150'' region. The on-source integration times per map position were typically ∼130 s for CS and ∼70 s for C¹⁸O. System temperatures were in the range 230–270 K for CS and 400–540 K for C¹⁸O, resulting in an rms noise, in antenna temperature, of typically 0.07 K and 0.18 K per channel, respectively.

Figure 1 shows the ¹³CO(3 → 2) spectra observed with APEX along the whole filamentary structure detected in the 1.2 mm dust continuum observations of Garay et al. (2004; see their Figure 4). Emission in the ¹³CO(3 → 2) line was detected across the whole mapped region.

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Figure 2 shows contour maps of the velocity-integrated ambient gas emission (velocity range from 52.9 to 61.1 km s⁻¹, determined by inspection of the line profiles) in the ¹³CO(3 → 2), CS(7 → 6), CS(2 → 1), SiO(2 → 1), H¹³CO⁺(1 → 0), and C¹⁸O(3 → 2) lines observed toward the central ∼15 × 3' region of the filament. The maps are overlaid on a grayscale image of the 1.2 mm dust continuum emission observed with SIMBA/SEST by Garay et al. (2004). We find that the morphology of the molecular line emission resembles that of the dust continuum emission, showing two components: a northern component associated with the MM1 core and a southern component associated with the MM2 dust core. There are, however, some differences in the morphology of the emission in the different molecular lines. These are likely due to chemistry and/or optical depth effects and/or differences in the regimes of density and temperature traced by the different lines. In particular, the emission in the CS(7 → 6) line is less extended than in the other transitions and runs nearly parallel to the north–south direction.

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Figure 3 presents contour maps of the velocity-integrated ambient gas emission (velocity range from 55.8 to 60.6 km s⁻¹) in three methanol lines [CH₃OH(2₀ → 1₀) A+, CH₃OH(2₋₁ → 1₋₁) E, CH₃OH(2₀ → 1₀) E] observed toward the central region of G34.43+0.24. The maps are overlaid on a gray scale image of the 1.2 mm dust continuum emission observed with SIMBA/SEST. The morphology of the emission in the three methanol lines is all similar. They are, however, different from the morphology exhibited by the dust continuum emission and the rest of the molecular lines. The methanol peaks do not coincide with the dust peaks; on the contrary they seem to be slightly anticorrelated. A similar situation is reported by Beuther et al. (2009) who attributed it to a high optical depth of the methanol emission. Other possible explanations are enhancements of methanol in the envelopes of the cores due to shocks or depletion of methanol within the central regions of the dust cores.

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Figure 4 shows contour maps of velocity-integrated ambient gas emission (velocity range from 56.1 to 61.5 km s⁻¹) in the ¹³CO(3 → 2), CS(2 → 1), and C¹⁸O(2 → 1) lines observed toward the MM3 core, overlaid on a grayscale image of the 1.2 mm dust continuum emission. Whereas the morphology of the emission in the ¹³CO(3 → 2) line is similar to that of the dust continuum emission, that in the C¹⁸O(2 → 1) line is somewhat different, showing a peak that is displaced from the peak of the dust emission.

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Table 3 gives the observed parameters of the molecular cores. The angular sizes, determined from the contour maps, correspond to the observed semi-major and semi-minor axes. The line center velocity, line width, and velocity-integrated brightness temperature were determined from Gaussian fits to the composite spectra of the ambient cloud emission within each core. The cores are assumed to be at a distance of 3.7 kpc, which corresponds to the kinematical distance of IRAS 18507+0121 reported by Faúndez et al. (2004) and the kinematical distance of the IRDC given by Simon et al. (2006b).

There are notable differences between the line profiles observed in different molecular species, for different positions. In what follows, we describe the spectra observed toward three selected positions (0'', 20''), (20'', −20''), and (40'', 200'') associated with, respectively, the MM1, MM2, and MM3 dust peaks.

Figure 5 shows the spectra observed toward the (0'', 20'') position, which corresponds to the MM1 core. The CO(3 → 2) profile shows, in addition to considerable self-absorption, the presence of both blueshifted and redshifted high-velocity emissions. The strong CO(3 → 2) wing emission at redshifted velocities is also clearly seen in the SiO(2 → 1), CS(2 → 1), and HCO⁺(1 → 0) spectra.

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Figure 6 shows the spectra observed toward the (20'', −20'') position (MM2 core). The CO(3 → 2) profile shows considerable self-absorption, and the presence of high-velocity emission at both blueshifted and redshifted velocities. The ¹³CO(3 → 2) line profile exhibits a strong blueshifted feature, with a peak at the velocity of 55.8 km s⁻¹, and a flat redshifted shoulder. The C¹⁸O(3 → 2) line shows strong emission toward blueshifted velocities, with a peak at the velocity of 56.1 km s⁻¹, and a skewed profile toward redshifted velocities. A similar profile is seen in the H¹³CO⁺(1 → 0) line. The CS(2 → 1) and HCO⁺(1 → 0) lines show double-peaked profiles; the former exhibits a strong blue peak and a weaker red peak whereas the later shows an opposite asymmetry, namely a strong redshifted peak and a weaker blueshifted peak. The CS(7 → 6) and C³⁴S(2 → 1) lines exhibit symmetrical profiles, with peak line center velocities, determined from Gaussian fits, of 58.1 ± 0.1 km s⁻¹ and 57.4 ± 0.2 km s⁻¹, respectively.

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Ramesh et al. (1997) modeled the observed CS(2 → 1), C³⁴S(2 → 1), HCO⁺(1 → 0), and H¹³CO⁺(1 → 0) profiles toward MM2 as being produced by a collapsing hot core hidden behind a cold intervening screen or envelope. We have modeled here the line profiles of ¹³CO(3 → 2), C¹⁸O(3 → 2), and CS(7 → 6) using the simple model of spectral-line profiles from contracting clouds of Myers et al. (1996). We concluded that the MM2 core is undergoing large-scale inward motions with an infall velocity of ∼1.3 km s⁻¹ (see Section 4.1.2).

Figure 7 shows the spectra observed toward the (40'', 200'') position, which corresponds to the MM3 core. The CO(3 → 2) spectrum shows, in addition to considerable self-absorption, strong blueshifted wing emission up to a velocity of 42.2 km s⁻¹. The ¹³CO(3 → 2) spectrum exhibits a strong Gaussian line, with a center velocity of 58.5 ± 0.1 km s⁻¹, and blueshifted wing emission up to a velocity of 53.6 km s⁻¹. These observations strongly indicate the presence of an energy source within the MM3 core. The C¹⁸O(2 → 1) and CS(2 → 1) spectra exhibit nearly Gaussian line profiles with peak line center velocities of 58.9 ± 0.1 and 58.8 ± 0.1 km s⁻¹, respectively.

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3.3.1. Central Region

Figure 8 shows position–velocity diagrams of the CO(3 → 2), CS(2 → 1), SiO(2 → 1), and ¹³CO(3 → 2) emission, toward the central region of G34.43+0.24, along two cuts in the north–south direction passing through the peak position of the MM1 (left panel) and MM2 (right panel) cores. Strikingly seen in this figure is the presence of high-velocity gas associated with the MM1 and MM2 cores, most likely due to molecular outflows emanating from both cores. Particularly notable is the detection of emission in the silicon monoxide line, which is a powerful tracer of the presence of strong shocks. The abundance of SiO molecules is highly enhanced, with respect to ambient abundances, in molecular outflows as a result of destruction of dust grains by shocks, giving rise to the injection into the gas phase of Si atoms and/or Si-bearing species. Once silicon is injected into the gas phase, chemical models based on ion–molecule reactions predict a large abundance of SiO molecules (Turner & Dalgarno 1977; Hartquist et al. 1980).

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In the cut passing through the peak of MM1, the most prominent outflow emission is seen redshifted with respect to the ambient gas velocity, extending up to velocities of 80.7 km s⁻¹ in CO(3 → 2) and 70.2 km s⁻¹ in CS(2 → 1) and SiO(2 → 1). Weak or no outflow emission is detected in the ¹³CO(3 → 2) line, indicating low optical depths. In the cut passing through the peak of MM2, both blueshifted and redshifted high-velocity emissions are clearly seen emanating from the MM2 core. In CO(3 → 2), the blueshifted and redshifted emissions extend up to velocities of 42.0 and 74.2 km s⁻¹, respectively. Also seen in this cut is wing emission emanating from the MM1 core as well as from the MM4 core, suggesting that MM4 also contains an outflow.

Maps of the velocity-integrated line wing emission, in the CO(3 → 2), SiO(2 → 1), and CS(2 → 1) lines toward the central 15 × 3' region of G34.43+0.24, including the MM1, MM2, and MM4 dust cores, are shown in Figure 9. In SiO(2 → 1) and CS(2 → 1), the range of velocity integration of the blueshifted emission (blue contours or solid lines) is 49.0 < v_lsr < 52.9 km s⁻¹, whereas that of the redshifted emission (red contours or dashed lines) is 61.1 < v_lsr < 65.2 km s⁻¹. In CO(3 → 2), the ranges of velocity integration of the blueshifted and redshifted emissions are, respectively, 42.0 < v_lsr < 53.0 km s⁻¹ and 62.0 < v_lsr < 74.0 km s⁻¹. In Figure 9, we identify two, possibly three, outflows associated with the dust cores within the region considered. The northernmost outflow (labeled O-MM1) is associated with the MM1 core. It is roughly oriented in the NE–SW direction, with the peaks of the redshifted and blueshifted emissions being located, respectively, SW and NE of the 3 mm continuum source detected by Shepherd et al. (2004; marked with a star). There is, however, a large spatial overlap between the blueshifted and redshifted emissions.

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The outflow associated with the MM2 core, (labeled O-MM2), shows a complex morphology with the blueshifted and redshifted emissions exhibiting a considerable spatial overlap. The peak positions of the redshifted and blueshifted emissions are located ∼7'' south of the UC H ii region (marked with a triangle) and are coincident within the errors. This suggest that the symmetry axis of the outflow is close to the line of sight.

Outflow MM4 is associated with the MM4 dust core (marked with a square). The blueshifted and redshifted emissions exhibit a large overlap in their spatial distribution, suggesting that the flow is unresolved or that its axis of symmetry is close to the line of sight.

3.3.2. Northern Region

Figure 10 shows position–velocity diagrams of the CO(3 → 2) and ¹³CO(3 → 2) emissions toward the northern region of G34.43+0.24, along a line in the north–south direction passing through the peak position of the MM3 core. Clearly seen in the CO(3 → 2) cut is the presence of wing emission emanating from MM3, with velocities extending up to 42.2 km s⁻¹ in the blueshifted side and 69.2 km s⁻¹ in the redshifted side. In the ¹³CO(3 → 2) line, the wing emission is barely seen.

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Figure 11 shows maps of the integrated line wing emission, in the CO(3 → 2) and ¹³CO(3 → 2) lines, toward the MM3 core. The range of velocity integration of the blueshifted emission (blue contours) is 41.2 < v_lsr < 56.1 km s⁻¹ for CO(3 → 2) and 52.6 < v_lsr < 56.1 km s⁻¹ for ¹³CO(3 → 2), whereas that of the redshifted emission (red contours) is 61.5 < v_lsr < 69.4 km s⁻¹ for CO(3 → 2) and 61.5 < v_lsr < 63.8 km s⁻¹ for ¹³CO(3 → 2). In the CO(3 → 2) map, the peak positions of the redshifted and blueshifted wing emissions are located, respectively, NE and SW of the peak position of the millimeter dust core. The red and blue wing emissions exhibit, however, a considerable overlap in their spatial distribution.

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4.1.1. Physical Parameters

From the observations of the ¹³CO(3 → 2) and C¹⁸O(3 → 2) lines, it is possible to estimate the column density and the mass of molecular gas within the central region (MM1 and MM2 cores) as follows. Assuming that the C¹⁸O(3 → 2) line is emitted under local thermodynamic equilibrium (LTE) conditions and its emission is optically thin, then the column density is given by (e.g., Bourke et al. 1997)

$$\begin{eqnarray} N({\rm C}^{18}{\rm O}) &=& 8.084\times 10^{13} \frac{(T_{\rm ex}+0.88)\exp (15.81/T_{\rm ex})}{1-\exp (-15.81/T_{\rm ex})}\nonumber \\ && \times \int \!\!\int \tau _{18} dv, \end{eqnarray} \tag{ 1 }$$

where τ₁₈ is the optical depth of the C¹⁸O(3 → 2) line, T_ex is the excitation temperature, and v is in km s⁻¹. The LTE mass can be obtained from

$$\begin{eqnarray} \left(\frac{M_{\rm {LTE}}}{M_{\odot }}\right) &=& 0.565 \left(\frac{\mu _m}{2.72 m_{\rm H}}\right) \left(\frac{[{\rm H}_2/{\rm C}^{18}{\rm O}]}{3.8\times 10^{6}}\right) \left(\frac{D}{\rm kpc}\right)^2 \nonumber \\ && \frac{(T_{\rm ex}+0.88)\exp (15.81/T_{\rm ex})}{1-\exp (-15.81/T_{\rm ex})} \int \!\!\int \tau _{18} dv d\Omega, \nonumber \\ \end{eqnarray} \tag{ 2 }$$

where μ_m is the mean molecular mass per H₂ molecule, m_H is the mass of a hydrogen atom, D is the source distance, [H₂/C¹⁸O] is the H₂ to C¹⁸O abundance ratio, and Ω is in arcmin². The opacities in the C¹⁸O(3 → 2) line are obtained from the ratio of the observed brightness temperatures in the C¹⁸O(3 → 2) and ¹³CO(3 → 2) lines as follows (see Bourke et al. 1997, for derivation):

$$\begin{equation} \frac{1-\exp {(-\tau _{18}/r)}}{1-\exp {(-\tau _{18})}} = \frac{[J_{18}(T_{\rm ex})-J_{18}(T_{\rm bg})]}{[J_{13}(T_{\rm ex})-J_{13}(T_{\rm bg})]}\,\frac{T_{\rm mb}(^{13}{\rm CO})}{T_{\rm mb}({\rm C}^{18}{\rm O})}, \end{equation} \tag{ 3 }$$

where T_bg is the background temperature, T_mb is the main beam brightness temperature of the line, J is given by (the subscripts "18" and "13" refer to the C¹⁸O and ¹³CO isotopes, respectively)

$$\begin{equation} J(T) = \frac{h\nu }{k}\frac{1}{\exp (h\nu /kT)-1}, \end{equation} \tag{ 4 }$$

and r = τ₁₈/τ₁₃ is the optical depth ratio:

$$\begin{eqnarray} \frac{\tau _{_{18}}}{\tau _{_{13}}} &=& \left[\frac{\rm {C}^{18}\rm {O}}{^{13}\rm {CO}}\right]\frac{(kT_{\rm ex}/hB_{13} + 1/3)}{(kT_{\rm ex}/hB_{18} + 1/3)}\,\frac{\exp (E_{_{J_{13}}}/kT_{\rm ex})}{\exp (E_{_{J_{18}}}/kT_{\rm ex})}\nonumber \\ && \times \frac{[1 - \exp (-h\nu _{_{18}}/kT_{\rm ex})]}{[1 - \exp (-h\nu _{_{13}}/kT_{\rm ex})]}, \end{eqnarray} \tag{ 5 }$$

where B is the rotational constant of the molecule, $E_{_J}=hBJ(J+1)$ is the rotational energy at the lower state, and J is the rotational quantum number. Assuming a [¹³CO/C¹⁸O] abundance ratio of 7.6, we derive average optical depths in C¹⁸O(3 → 2) of 0.10 and 0.18 toward the MM1 and MM2 cores, respectively. Using an excitation temperature of 30 K and an [H₂/C¹⁸O] abundance ratio of 3.8 × 10⁶ (Wilson & Rood 1994), we derive total masses of 330 and 1460 M_☉ for the MM1 and MM2 cores, respectively. The derived core parameters are listed in Table 4.

Table 4. Derived LTE Core Parameters

			Na	N(H2)	MLTE
Core	Transition	τν	(cm−2)	(cm−2)	(M☉)
MM1	C18O(3 → 2)	0.10	5.2 × 1015	2.0 × 1022	330
	13CO(3 → 2)	0.75	3.9 × 1016
MM2	C18O(3 → 2)	0.18	1.1 × 1016	4.3 × 1022	1460
	13CO(3 → 2)	1.39	8.7 × 1016

Notes. Velocity range for the MM1 core: 54.6–59.3 km s⁻¹. Velocity range for the MM2 core: 53.4–59.3 km s⁻¹. ^aColumn density for each molecule.

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Masses can also be estimated assuming that the clouds are in virial equilibrium. Neglecting magnetic fields and external forces, the virial mass, M_vir, for a spherical cloud of radius R is given by (MacLaren et al. 1988)

$$\begin{equation} M_{\rm vir} = B \left({{R}\over {\rm pc}}\right) \left({{\Delta v}\over {\rm km\, s^{-1}}}\right)^2 M_{\odot }, \end{equation} \tag{ 6 }$$

where Δv is the average line width in km s⁻¹, R in pc, and B is a constant which depends on the density profile of the cloud. Assuming that the cores have uniform densities (B = 210), we derive virial masses of 1.1 × 10³, 1.5 × 10³, and 1.4 × 10³ M_☉ for, respectively, the MM1, MM2, and MM3 cores. These values correspond to the geometric mean of the masses determined from the transitions given in Table 5. The molecular hydrogen densities were computed from the mass assuming that the cloud has a spherical morphology and a uniform density.

Table 5. Derived Virial Core Parameters

		Radiusa	ΔV	Mvir	n(H2)
Core	Transition	(pc)	(km s−1)	(M☉)	(cm−3)
MM1	CS(7 → 6)	0.25	5.69	1700	3.9 × 105
	CS(2 → 1)	0.35	5.29	2060	1.7 × 105
	H13CO+(1 → 0)	0.26	2.75	410	8.3 × 104
MM2	CS(7 → 6)	0.27	5.27	1580	2.8 × 105
	CS(2 → 1)	0.35	5.19	1980	1.6 × 105
	H13CO+(1 → 0)	0.33	3.96	1090	1.1 × 105
MM3	13CO(3 → 2)	0.57	3.01	1090	2.1 × 104
	CS(2 → 1)	0.69	3.43	1710	1.8 × 104

Note. ^aGeometric mean of the observed semi-major and semi-minor axes.

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Table 6 summarizes the core masses determined from different methods and authors. Columns 2 and 3 give the LTE and the virial masses, respectively, determined in this work; Column 4 gives the LTE mass from Shepherd et al. (2007); and Columns 5 and 6 give the masses derived from dust continuum observations by Garay et al. (2004) and Rathborne et al. (2006), respectively. In our estimate, if the excitation temperature is 25 or 35 K, the LTE mass is decreased or increased by ∼20%, respectively. Given the uncertainties associated with each method—such as in the abundance, excitation, dust temperature, and dust opacity—the agreement is good between the masses determined in this work and the masses determined from dust emission. Differences in the mass obtained by different authors using dust emission are mostly due to different dust temperatures and core sizes used in their calculations. There are, however, discrepancies with the masses determined by Shepherd et al. (2004) from H¹³CO⁺(1 → 0) observations, of 4000 and 5000 M_☉ for MM1 and MM2, respectively, and a total cloud mass of 50,000 M_☉. We note that Rathborne et al. (2005) estimated from dust emission observations a total cloud mass of 7500 M_☉ assuming a dust temperature of 30 K. A possible explanation of the larger mass estimate of Shepherd et al. (2004) is that the actual abundance of HCO⁺ is probably larger than the adopted one, due to an enhancement produced by the molecular outflows. Moreover, Shepherd et al. (2007) determined, from observations of the C¹⁸O(1 → 0) line using the OVRO array, masses of 75 and 690 M_☉ for MM1 and MM2, respectively. These values probably correspond to the inner mass of the cores. We note that masses derived from molecular lines might not be tracing all of the emission, and their emission may be optically thick, specially C¹⁸O(1 → 0). However, the assumption that the C¹⁸O(3 → 2) is optically thin seems to be adequate and it is supported for the inspection of the line profiles and values obtained for the optical depths.

Table 6. Core Masses from Different Authors

	LTE Mass	Virial Mass	LTE Mass	Dust Mass (1.2 mm)
Core	(This Work)	(This Work)	Shepherd et al. (2007)	Garay et al. (2004)	Rathborne et al. (2006)
(1)	(2)	(3)	(4)	(5)	(6)
MM1	330	1130	75	550	1187
MM2	1460	1510	690	2700	1284
MM3	⋅⋅⋅	1370	⋅⋅⋅	780	301

Note. Masses are in M_☉.

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Optical depths and column densities toward the peak position of the MM1 and MM2 cores are given in Table 7. The C³⁴S(2 → 1) and CS(2 → 1) values were obtained in an analogous way to that described above for the C¹⁸O(3 → 2) and ¹³CO(3 → 2) lines, adopting a [CS/C³⁴S] abundance ratio of 22.5 and an [H₂/CS] ratio of 1 × 10⁸ (e.g., van der Tak et al. 2000).

Table 7. Core Parameters at Peak Positions

			Na	N(H2)
Core	Transition	τν	(cm−2)	(cm−2)
MM1	C18O(3 → 2)	0.04	2.3 × 1015	8.5 × 1021
	13CO(3 → 2)	0.30	1.7 × 1016
	C34S(2 → 1)	0.02	1.9 × 1013	4.3 × 1022
	CS(2 → 1)	0.41	4.3 × 1014
MM2	C18O(3 → 2)	0.37	2.3 × 1016	8.5 × 1022
	13CO(3 → 2)	2.80	1.7 × 1017
	C34S(2 → 1)	0.03	3.5 × 1013	8.0 × 1022
	CS(2 → 1)	0.69	8.0 × 1014

Notes. Velocity range for the MM1 core: 54.0–59.3 km s⁻¹. Velocity range for the MM2 core: 53.5–59.2 km s⁻¹. ^aColumn density for each molecule.

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4.1.2. MM2: a Collapsing Core

The ¹³CO(3 → 2) line emission at the peak position of the MM2 core shows a bright blueshifted peak and a flat redshifted shoulder. Such line shape can be modeled as due to inward motions (Mardones et al. 1997). The blue peak is produced by high-excitation gas on the far side of the envelope, while the redshifted peak results from low-excitation gas in the near side of the envelope. The self-absorption due to low-excitation, low-velocity gas in the near side of the envelope gives rise to the central dip (Evans 1999). An estimate of the infall velocity, V_in, can be obtained using the two-layer infall model of Myers et al. (1996).

Myers et al. (1996) made a simple analytic model of radiative transfer in order to inspect if the observed spectra show any evidence of infall motions and to provide an estimate of the characteristic V_in. They assumed two uniform regions of equal temperature and velocity dispersion σ, whose density and velocity are attenuation-weighted means over the front and rear halves of a centrally condensed, contracting cloud with n/n_max = (r/r_min)^−3/2 and V/V_max = (r/r_min)^−1/2. We modeled the profile of the ¹³CO(3 → 2), C¹⁸O(3 → 2), and CS(7 → 6) lines toward the MM2 core using their prescription and obtained the following model parameters: the peak optical depth, τ₀; the kinetic temperature, T_k; the infall velocity, V_in; and the nonthermal velocity dispersion, $\sigma _{_{\rm {NT}}}$. Figure 12 shows the observed and the best model line profiles, indicating motions consistent with a "fast" infall, V_in ∼ σ. The values derived by the model are shown in the top right corner of the same figure. We note that some of the parameters for each fit are different; for example, the infall velocities are 1.5, 1.3, and 1.0 km s⁻¹ for ¹³CO, C¹⁸O, and CS, respectively. This decreasing order is in accord with the level of asymmetry in the lines. The most asymmetric line, a single peak in the blue and a red shoulder, has the largest values of V_in (Myers et al. 1996; Fuller et al. 2005). Although the velocity dispersion in the CS line is σ ∼ 2V_in, the other two lines have σ ∼ V_in indicating a fast infall. The derived systemic velocities show some scatter, most likely due to the influence of the molecular outflow, which is more intense toward redshifted velocities. If the contribution of the outflow is removed, the blue peak becomes stronger than the red shoulder, and this will have the effect of increasing the derived infall velocity.

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Ramesh et al. (1997) modeled the profile of the CS(2 → 1), C³⁴S(2 → 1), HCO⁺(1 → 0), and H¹³CO⁺(1 → 0) lines toward the MM2 core using both the large velocity gradient (LVG) method and the simple model of Myers et al. (1996). For the LVG method they adopted a constant temperature of 22 K (we determined a kinetic temperature of ∼36 K) and found a collapse velocity that varies radially as 8(r/r₀)^−0.6 km s⁻¹ with r₀ = 4.5 × 10¹⁶ cm. At a radius of r = 5.5 × 10¹⁷ cm (equivalent to an angular size of 10'') we get V_in = 1.8 km s⁻¹. Given the uncertainties associated with each method, the agreement is good with the values determined by us. The infall speed estimated by Ramesh et al. (1997) using the Myers et al. (1996) analytic model is about 1 order of magnitude smaller than the velocities they determine from the LVG analysis; however, since the fit of the Myers model is admittedly not too good, they argue in favor of the larger value, which agrees well with ours here.

The mass infall rate can be estimated assuming $\dot{M} = M_R V_{\rm in}/R$, where M_R is the mass within the radius R and V_in is the infall speed at radius R. Using the LTE mass derived at the central position of MM2, of 240 M_☉, an average infall velocity of 1.3 km s⁻¹ and a radius of 5.5 × 10¹⁷ cm (corresponding to a 10'' angular radius); we obtain a mass infall rate of 1.8 × 10⁻³ M_☉ yr⁻¹. Such accretion rate is high enough to overcome the radiation pressure of the central star and to form a massive star. Shepherd et al. (2007) identified two likely massive stars (M > 8 M_☉) with the MM2 core, with one of them, located near the projected center of the UC H ii region, having a spectral type of B0.5 (Shepherd et al. 2004). Models of massive envelopes accreting onto this kind of young stars require accretion rates of $\dot{M} > 5\times 10^{-4}$ M_☉ yr⁻¹ (Osorio et al. 1999), in agreement with our results.

To compute physical parameters of the outflowing gas, we followed the standard LTE formalism described in Bourke et al. (1997) using the emission in the CO(3 → 2) line. The main source of error in determining the mass in the outflow arises from the difficulty in separating the contribution to the outflows of the emission in the velocity range of the ambient cloud. We adopt as velocity boundary between the blue and red wing emissions and the ambient emission the values of, respectively, 53.0 and 60.8 km s⁻¹ for the MM1 outflow, 51.8 and 60.9 km s⁻¹ for the MM2 outflow, and 56.1 and 61.5 km s⁻¹ for the MM3 outflow. Another source of error is the possibility that the CO(3 → 2) line might not be optically thin, particularly at low flow velocities. Fortunately, with the available data, we can asses this effect and make corrections.

The mass in the high-velocity wings is estimated from the CO(3→2) observations as follows. Assuming that the energy levels of CO are populated according to LTE and that the outflow emission is optically thin, then the total CO column density, N(CO), at each observed position is given by (e.g., Garden et al. 1991)

$$\begin{eqnarray} N({\rm CO}) &=& 7.7 \mbox{$\times $}10^{13}\,\, \frac{(T_{\rm ex}+0.92)\,\exp (16.60/T_{\rm ex})}{[1-\exp (-16.60/T_{\rm ex})]} \nonumber \\ &&\times \frac{1}{[J(T_{\rm ex}) - J(T_{\rm bg})]} \int T_{B}(v)dv, \end{eqnarray} \tag{ 7 }$$

where T_ex is the excitation temperature of the population in the rotational levels, T_bg is the background temperature, T_B is the brightness temperature of the CO(3→2) emission at velocity v, v is measured in km s⁻¹, and J is defined by Equation (4). The mass is then computed from the derived column densities as

$$\begin{equation} M = [{\rm H}_2/{\rm CO}] \mu _m A \sum N({\rm CO}), \end{equation} \tag{ 8 }$$

where μ_m is the mean molecular mass per H₂ molecule, [H₂/CO] is the molecular hydrogen to carbon monoxide abundance ratio, A is the size of the emitting area in an individual position, and the sum is over all the observed positions inside each lobe.

From the observations of the CO(3 → 2) and ¹³CO(3 → 2) lines, it is possible to estimate the opacities of the flowing gas and therefore to assess whether or not the assumption that the CO(3 → 2) wing emission is optically thin is correct. Using expressions (3) and (5) for ¹²CO and ¹³CO, assuming T_ex = 30 K, and [¹²CO/¹³CO] = 50, we find that the average CO(3 → 2) opacities of the blueshifted gas (in the velocity range from 49.5 to 53.0 km s⁻¹) and redshifted gas (in the velocity range from 60.8 to 68.9 km s⁻¹) of the MM1 flow are 3.4 and 2.5, respectively. The given ranges are those in which emission is detected in both lines. For the MM2 outflow, we find that the average optical depths of the blueshifted gas (in the velocity range from 47.2 to 51.8 km s⁻¹) and redshifted gas (in the velocity range from 60.9 to 68.7 km s⁻¹) are 5.4 and 4.4, respectively. For the MM3 outflow, we find that the average optical depths of the blueshifted gas (velocity range from 52.8 to 56.1 km s⁻¹) and redshifted gas (velocity range from 61.5 to 65.2 km s⁻¹) are 7.1 and 4.2, respectively. These calculations indicate that the CO(3 → 2) emission from the flowing gas, in the given velocity ranges, is moderately optically thick for the three flows. On the other hand, as the position–velocity diagrams suggested, the ¹³CO flow emission is optically thin, with optical depths between 0.05 and 0.13.

To correct the mass determined under the optically thin assumption by the opacity effect, we divided the CO(3 → 2) wing emission into two regimes, an optically thin regime, in which no ¹³CO(3 → 2) emission is detected, and an optically thick regime. We assumed an [H₂/CO] abundance ratio of 10⁴ (Frerking et al. 1982) and an excitation temperature of the outflowing gas of 30 K. We derived masses in the optically thin regime of the 0.5, 1.1, and 1.6 M_☉ for the blueshifted lobes of MM1 (38.6 < v_lsr < 49.5 km s⁻¹), MM2 (35.9 < v_lsr < 47.2 km s⁻¹), and MM3 (40.1 < v_lsr < 52.8 km s⁻¹), respectively, and masses of 0.7, 0.8, and 0.7 M_☉ for the redshifted lobes of MM1 (68.9 < v_lsr < 74.5 km s⁻¹), MM2 (68.7 < v_lsr < 74.5 km s⁻¹), and MM3 (65.2 < v_lsr < 74.3 km s⁻¹), respectively. In the optically thick regime, the mass determined under the optically thin assumption is multiplied by the factor $\tau _{\rm{w}}/(1-e^{-\tau _{\rm{w}}})$, where $\tau _{\rm{w}}$ is the average CO(3 → 2) optical depth of wing emission in the optically thick velocity range. We derive masses in the optically thick regime, corrected by opacity, of 2.6, 13.6, and 8.5 M_☉ for the blueshifted lobes of MM1 (49.5 < v_lsr < 53.0 km s⁻¹), MM2 (47.2 < v_lsr < 51.8 km s⁻¹), and MM3 (52.8 < v_lsr < 56.1 km s⁻¹), respectively. Similarly, for the redshifted lobes we derived masses of 11.9, 30.8, and 7.3 M_☉ toward MM1 (60.8 < v_lsr < 68.9 km s⁻¹), MM2 (60.9 < v_lsr < 68.7 km s⁻¹), and MM3 (61.5 < v_lsr < 65.2 km s⁻¹), respectively.

To estimate the contribution to the flow mass from the low-velocity material emitting in the same velocity range as the ambient cloud gas, we followed the prescription of Margulis & Lada (1985). Using expression (A16) of Bourke et al. (1997),

$$\begin{equation} \int _{{\rm lobe}} \int _{v_b}^{v_r} T_{{\rm mb}}\, dv\, d\Omega = \int _{{\rm lobe}}\left(\frac{T^b + T^r}{2}\right)(v_r - v_b)\,d\Omega, \end{equation} \tag{ 9 }$$

where T^b, v_b and T^r, v_r are the brightness temperatures and velocities at the blue and red velocity boundaries, respectively. We estimated that the hidden flow masses corrected by opacity in the low-velocity range within the blueshifted lobes toward MM1, MM2, and MM3 are 3.0, 20.6, and 13.9 M_☉, and within the redshifted lobes are 6.2, 11.9, and 8.9 M_☉, respectively (see Table 8). Finally, the total mass of the outflows are 24.9 M_☉ for MM1, 78.8 M_☉ for MM2, and 40.9 M_☉ for MM3.

Table 8. Derived Parameters of Molecular Outflows

		Mlobe	Mhidden	Mtotal	P$^{\mathrm{\rm min}}\qquad$ P$^{\mathrm{\rm max}}$	E$_{\rm{k}}^{\mathrm{\rm min}}\qquad$ E$_{\rm{k}}^{\mathrm{\rm max}}$
Core	Lobe	(M☉)	(M☉)	(M☉)	(M☉ km s−1)	(M☉ km2 s−2)
MM1	Blueshifted	3	3	6	2.8 × 101 1.1 × 102	9.2 × 101 9.2 × 102
	Redshifted	13	6	19	9.5 × 101 3.3 × 102	3.5 × 102 2.9 × 103
	Total	16	9	25	1.2 × 102 4.4 × 102	4.4 × 102 3.8 × 103
MM2	Blueshifted	15	21	36	1.8 × 102 5.5 × 102	6.4 × 102 4.2 × 103
	Redshifted	32	12	44	2.2 × 102 6.7 × 102	7.8 × 102 5.2 × 103
	Total	47	33	80	4.0 × 102 1.2 × 103	1.4 × 103 9.4 × 103
MM3	Blueshifted	10	14	24	6.8 × 101 3.5 × 102	1.8 × 102 2.5 × 103
	Redshifted	8	9	17	4.9 × 101 2.4 × 102	1.1 × 102 1.8 × 103
	Total	18	23	41	1.2 × 102 5.9 × 102	2.9 × 102 4.3 × 103

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Using the standard LTE formalism, it is also possible to estimate the momentum, P, and the kinetic energy, $E_{\rm {k}}$, in the flow as follows (Margulis & Lada 1985; Bourke et al. 1997):

$$\begin{eqnarray} P & = & \int \!\! \int \!\! \int M(v,\alpha,\delta)\,v\,dv\,d \alpha \,d\delta, \nonumber \\ E_{\rm k} & = & \frac{1}{2}\int \!\! \int \!\! \int M(v,\alpha,\delta)\,v^2\,dv\,d \alpha \,d\delta. \end{eqnarray} \tag{ 10 }$$

These equations assume no correction for flow inclination, and so are strict lower limits. Another method to compute the physical parameters of the outflowing gas is to assume that all the mass is flowing at a velocity characteristic of the entire flow, $V_{\rm {char}}$. The flow parameters are, in this approach, given by

$$\begin{equation} P = M V_{\rm{char}}, E_{\rm{k}} = \frac{1}{2} M V_{\rm {char}}^2, \end{equation} \tag{ 11 }$$

where M is the total mass of the outflow lobe. The blueshifted and redshifted emissions from the outflows show considerable overlap in their spatial distribution, indicating that the symmetry axis of the flows is likely to be near the line of sight. Hence, we adopt as a characteristic flow velocity the average of the maximum observed outflow velocities. The parameters determined under this assumption are likely to correspond to upper limits. The maximum velocities observed toward the blue and red lobes are, respectively, 12.0 and 23.1 km s⁻¹ for the MM1 outflow, 15.0 and 15.9 km s⁻¹ for the MM2 outflow, and 17.3 and 11.6 km s⁻¹ for the MM3 outflow. Table 8 gives the derived parameters of the blueshifted gas and redshifted gas of the flows calculated using both methods. The geometric mean values for the outflow parameters are $\bar{P_1} \sim 230$, $\bar{P}_2 \sim 690$, and $\bar{P}_3 \sim 270$ M_☉ km s⁻¹; and $\bar{E}_{{\rm k}_1} \sim 1290$, $\bar{E}_{{\rm k}_2} \sim 3630$, and $\bar{E}_{{\rm k}_3} \sim 1120$ M_☉ km² s⁻² (subscripts 1, 2, and 3 refer to the MM cores). If the excitation temperature is increased to 50 K, the flow parameters increase by 7%. The derived values of the outflow parameters are similar to those of massive and energetic molecular outflows driven by high-mass YSOs (Shepherd & Churchwell 1996; Beuther et al. 2002; Wu et al. 2004). We do not provide estimates of the dynamical timescale, mechanical luminosity, and mass outflow rate of the outflows toward G34.43+0.24 because they are likely to be aligned close to the line of sight, and therefore the lengths of the lobes are difficult to estimate.

Rathborne et al. (2005) reported an excess 4.5 μm emission toward the MM cores. The Spitzer IRAC 4.5 μm band contains the H i Brα line (at 4.052 μm), the CO(1 → 0) P(8) band head (4.6–4.8 μm), and many H₂ vibrational transitions (the most important being H₂(0 → 0) S(9) line at 4.694 μm), but unlike the other three bands it does not contain any strong polycyclic aromatic hydrocarbon features (e.g., Smith et al. 2006). It has been postulated that the main contributors of the excess 4.5 μm emission could be emission from the CO(1 → 0) P(8) band head (e.g., Marston et al. 2004) and/or emission from the H₂(0 → 0) S(9) line (e.g., Noriega-Crespo et al. 2004). Thus, the enhancement of the 4.5 μm emission could be a probe of jets and molecular outflows (e.g., Teixeira et al. 2008; Smith et al. 2006; Noriega-Crespo et al. 2004); therefore of current star formation. Rathborne et al. (2005) first found evidence for the presence of high-velocity gas toward the MM1 and MM3 cores from the broad line widths (ΔV∼ 10 km s⁻¹) observed in the CS(3 → 2) and HCN(3 → 2) lines. A detailed study of the central region of G34.43+0.24 was carried out by Shepherd et al. (2007), who reported two molecular outflows emanating from MM1 (G34.4 MM, in their paper), and three outflows originating from the MM2 core. They estimate a total mass, momentum, and kinetic energy of 34.8 M_☉, 350 M_☉ km s⁻¹, and 4.9 × 10⁴⁶ erg (2460 M_☉ km² s⁻²) for the outflows in MM1; and 111.2 M_☉,  830 M_☉ km s⁻¹, and 7.8 × 10⁴⁶ erg (3920 M_☉ km² s⁻²) for the outflows in MM2. The masses are ∼20% greater than our estimate, and the momenta and kinetic energies are within our estimated range. In spite of the different molecular transitions, angular resolutions, and assumptions used, Shepherd et al. and our results are in agreement, within the observational errors.

4.2.1. The Discovery of a New Molecular Outflow Toward the Core G34.43+0.24 MM3