ROTATION OF THE WARM MOLECULAR GAS SURROUNDING ULTRACOMPACT H ii REGIONS

To determine the velocity shifts and angular sizes required to calculate our velocity gradients, we use the methods presented in Zhang & Ho (1997). We extracted PV diagrams in both SO₂ and OCS along the solid lines shown in the left panels of Figures 1–5. We then fit two-dimensional Gaussians to the line emission. In each PV diagram, the Gaussians were fit to the 3σ or 5σ level as stated in the figure captions. The projected major and minor axes of these ellipses gave the angular extent and velocity shift across each source. The calculated velocity gradients for each source are shown in Table 2 where the uncertainties arise from the velocity channel spacing (0.53 km s⁻¹) and spatial resolution (03) of the observations.

It is interesting to note that the velocity gradients in G28.2 are differently oriented from each other in the PV diagram, yet result in the same dynamical mass. While the change in velocity across the sources is the same for both species, the higher velocity gas is at different positions. This is possibly due to the two species being slightly offset from each other as seen in the right-hand panel of Figure 2.

If we assume that the material in these regions is in virial equilibrium, we can determine the dynamical mass of the enclosed region. Because we cannot constrain the inclination angle of these rotating structures from our observations, we will assume that the velocity gradients are primarily observed "edge on" (i.e., the observed velocities are the true velocities of the gas); and thus our derived masses are lower limits to the true masses for structures which are inclined with respect to the plane of the sky.

We find velocity gradients in the range of 92–175 km s⁻¹ pc⁻¹ and note that the values derived for a given source from SO₂ and OCS agree to within one or two times the quoted uncertainties, which is why only the SO₂ values are given in Table 2. That these values are so similar suggest that SO₂ and OCS are tracing the same bulk motions. The velocity gradients we present in Table 2 are comparable to, although generally slightly smaller than, those inferred for three other massive star forming regions (G24A1, IRAS 20126, and IRAS 18089) by applying the same analysis methods described here to the data presented by Beltrán et al. (2006), Cesaroni et al. (2005), and Beuther & Walsh (2008), respectively. These sources were observed at similar resolutions, but are, in general, closer than the sources studied here, and do not show evidence for H ii regions. We find that our results are generally higher than the velocity gradient found in the low mass star forming region L1251 (Lee et al. 2007) again using the same analysis on their presented velocity gradients. Our derived velocity gradients result in dynamical masses of between 12 and 364 M_☉. For all sources except for our unresolved source (NGC 7538), the derived dynamical masses are large enough to account for one (or more) massive star and surrounding H ii region. Because the dynamical mass accounts for all of the mass within its outer emitting region (i.e., the hot gas and the dust inside the H ii region as well as the warm molecular gas responsible for the emission), we expect these dynamical masses to be the largest values presented here.

In Figure 5, we show both an emission map (left panel) and a PV diagram (right panel) for SO₂ and OCS in W51e8. In the right panel, the gray scale shows the OCS emission, and the contours show the SO₂ emission. Here, we see that the velocity gradient in SO₂ around W51e8 extends to higher redshifted velocities than blue (from the rest velocity of the source given in Table 1). The solid ellipse shows the OCS emission. We suggest that the SO₂ emission redward of 66 km s⁻¹ is not related to dynamical rotation, and we suggest that the SO₂ velocity gradient is being contaminated by outflow emission. This excess redshifted emission is not observed in OCS (see panel (f) of Figure 6); however, the orientation of the velocity gradient in OCS is consistent with that of the SO₂. If we blindly derive a dynamical mass for this region from the full velocity gradient in SO₂, we estimate an enclosed mass of 930 M_☉. Interestingly, the redshifted lobe of the bipolar outflow (as seen in CO; P. D. Klaassen et al. 2009, in preparation) from this source is located near the redshifted part of the rotation signature. It is not clear why there is no corresponding CO blueshifted outflow lobe, which makes it hard to determine a concrete outflow direction. The correlation in both space and velocity between the SO₂ emission and the CO emission suggests we are seeing outflowing material pushing through the SO₂ shell of warm gas surrounding the region. The detection of H30α in this region is marginal at best, and while it has been detected as a continuum source at 1.3 cm (Zhang & Ho 1997), it has not been detected at 3.6 cm (down to an rms limit of ∼ 1.2 mJy beam⁻¹; Gaume et al. 1993). These results bring into question whether W51e8 is an H ii region. Given the large mass of this region however, if it is not an H ii region, we suggest that it is a very young object which is transitioning from hot core to an H ii region.

If this high velocity redshifted excess is due to the outflow pushing through the warm SO₂ emitting region, as suggested by our data, then the molecular outflow observed toward this source is continuing to be powered from within the H ii region itself. If outflows are driven by accretion, this result suggests that accretion is continuing onto the star(s) present in this H ii region. It is unlikely that this red extension in the emission could come from a remnant type outflow (see, for instance, Klaassen et al. 2006) since, by the time the H ii region would have grown onto observable scales, the outflow mechanism from within would have stopped; there would be nothing pushing the SO₂ outward. We suggest that the rotation signatures of the other sources are not contaminated by outflow since the outflows from those sources are perpendicular to the velocity gradients present in SO₂ and can be fitted well with a Keplerian orbit centered on the local standard of rest velocity of the sources with no red or blue excesses as seen toward W51e8.

CH₃CN is a symmetric top molecule, and as such can be used to trace the temperature in its emitting region. The individual K levels within a specific J transition (in this case, J = 12–11) are radiatively decoupled, meaning that the different K levels are populated through collisions alone (Solomon et al. 1971), and the relative populations of the K components give an estimate of the ambient (kinetic) temperature through the rotational temperature diagram method described in Goldsmith & Langer (1999). We defined the emitting region for CH₃CN as twice the area of the FWHM of the integrated intensity of the combined emission from the K = 0–8 components. The CH₃CN spectra shown in Figure 7 are averaged over this masked region. In order to determine the integrated intensity of each component in a systematic way, we followed the procedures outlined in Remijan et al. (2004), Araya et al. (2005), and Purcell et al. (2006) which assume local thermodynamic equilibrium and that the gas is optically thin. Gaussian profiles were fitted to each component, keeping the widths and the relative rest velocities fixed for a given source. This procedure allows the fitting routines to find the best fit to the rest velocity of CH₃CN in each source. As highlighted in the middle and bottom panels of Figure 7, HNCO and CH¹³₃CN were within our spectral window but not fit by Gaussians.

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From the fitted Gaussians to each K component, we determined the column density of the upper level which is related to the integrated intensity of the line through

$$\begin{equation} N_u=\frac{8\pi k \nu ^2}{A_{u\ell }hc^3}\int Tdv, \end{equation} \tag{ 1 }$$

where N_u is the column density in the upper level of the K component, ν is the frequency of the transition, A_uℓ is the Einstein A-coefficient for that transition, and ∫Tdv is the integrated intensity in units of K km s⁻¹. N_u is related to the total column density for the emitting region through

$$\begin{equation} \frac{N_u}{g_u}=\frac{N_{\rm TOT}}{Q(T)}e^{-E_u/kT}, \end{equation} \tag{ 2 }$$

where g_u is the degeneracy of the upper state, Q(T) is the partition function, N_TOT is the total column density of the species, and E_u is the energy above the ground state of the transition (see the appendix of Araya et al. 2005). Taking the log of both sides of the equation gives ln(N_u/g_u) ∝ −E_u/kT. The ambient temperature can then be determined from the slope of the line of best fit.

In Figure 8, we show this plot for each of our regions; and the derived temperatures are shown in Table 3. Since these lines were observed simultaneously, the relative intensities of the lines are not affected by calibration uncertainties. The error bars for each data point come from the uncertainties in the Gaussian fits, and the uncertainties in the temperatures come from the uncertainty in the linear fit to the points in Figure 8. The signal-to-noise ratios of the Gaussian fits to the K = 8 components for each source (as well as the K = 7 components for G10.6 and G28.2) were not high enough to be included in the fits, or the plots presented in Figure 8. Also, due to the blending of the K = 0, 1 components they were also excluded from the linear fits presented in Figure 8. CH¹³₃CN is detected in three of our sources. The isotopic ratio of ¹²C and ¹³C is approximately 55 (Wilson & Rood 1994), so the detection of CH¹³₃CN suggests our CH₃CN emission is optically thick. Using Equation (1) of Choi et al. (1993), we find optical depths of <5.8, 50.4, 35.8, <8.9, and 16.3 for G10.6, G28.2, NGC 7538, W51e2, and W51e8, respectively. The lower limits on the optical depths are for sources in which CH¹³₃CN was not detected and the rms noise was used as an upper limit on the CH¹³₃CN emission peak. If the gas is optically thick, then we are overestimating the temperatures in our regions and underestimating the column density.

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Table 3. Temperatures and Molecular Emission Derived Gas Masses

Source		SO2				OCS	CH3CN
	Tkina (K)	Vel. Rangec (km s−1)	∫Tdv (K km s−1)	$N_{\rm SO_2}$ (1015 cm−2)	$M_{\rm H_2}$b (M☉)	$M_{\rm H_2}$b (M☉)	ln(N/Q(T))	$N_{\rm CH_3CN}$ (1015 cm−2)	$M_{\rm H_2}$b (M☉)	$M_{\rm H_2}^{\tau >1}$ (M☉)
G10.6 − 0.4	323 ± 105	−6, 4	113 ± 15	37 ± 4	85 ± 11	57 ± 3	24.2 ± 0.2	1 ± 0.3	1 ± 0.3	5.6 ± 1.6
G28.2 − 0.04	300 ± 89	90, 100	175 ± 27	52 ± 7	131 ± 20	65 ± 6	24.4 ± 0.1	1 ± 0.7	1 ± 0.6	47 ± 28
NGC 7538	310 ± 94	−65, -45	297 ± 12	92 ± 3	7.6 ± 0.6	3.1 ± 0.4	24.2 ± 0.2	1 ± 0.6	0.2 ± 0.1	5.9 ± 3.6
W51e2	460 ± 130	45, 75	799 ± 58	429 ± 27	525 ± 45	294 ± 32	26.3 ± 0.1	21 ± 14	16 ± 11	265 ± 188
W51e8	350 ± 83	45, 75	634 ± 58	232 ± 18	385 ± 37	220 ± 27	25.9 ± 0.1	8 ± 4	7 ± 4	66 ± 34

Notes. Listed uncertainties are due to measurement error, not calibration uncertainty, which we estimate at 20%. ^aUpper limit on gas temperature due to optical depth effects in the CH₃CN emission. ^bSO₂, OCS, and CH₃CN abundances used to calculate the total gas mass were 1 × 10⁻⁷, 2.5 × 10⁻⁸, and 2 × 10⁻⁷, respectively. ^cListed velocity ranges were used to create the zeroth and first moment maps.

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From these data, we find that the temperatures in the warm molecular gas are between 300 and 460 K. These values are slightly higher than the temperature range in which SO₂ is expected to be most abundant, which is consistent with our derivations giving upper limits to the temperatures. Doty et al. (2002) show that the abundance of SO₂ dramatically increases at 100 K, and then begins to decline again at temperatures greater than 300 K. This lower temperature limit comes from the activation energy required for H₂ to combine with OH (Doty et al. 2002). At temperatures greater than ∼ 300 K, this reaction becomes much less efficient (Charnley 1997). The temperature range over which OCS has a high abundance is unclear; however, from the observations of Hatchell et al. (1998), it appears to have fairly similar abundances toward a number of hot cores. Charnley (1997) shows that after 10⁵ yr, the abundance of OCS should fall as HOCS⁺ is removed from the system (the primary source of OCS).

The peak velocities of the CH₃CN lines are consistent with the V_LSR for each source (given in Table 1), and have similar emitting regions to the SO₂ and OCS gas. Thus, we suggest the CH₃CN is tracing the same gas as the SO₂ and OCS, and will use the temperatures derived here to estimate the column densities of OCS and SO₂.

We can find from Equation (2) not only an upper limit to the rotational temperature of the CH₃CN emitting region, but also the column density of CH₃CN gas responsible for the emission. The slope of the line of best fit gives the temperature of the region while the y-intercept gives ln(N/Q(T)). Using Equation (A33) from Araya et al. (2005) we can solve for the column density of CH₃CN, assuming the temperatures derived above for the partition function. Using the optical depth correction technique described in Goldsmith & Langer (1999), we calculated the function C_τ for the optical depths (see their Equations (16) and (22)) and correct our total column density values accordingly. We use a CH₃CN abundance of 2 × 10⁻⁷ (an average of the values presented in Remijan et al. 2004), and we note that other authors find lower abundances in Orion (i.e., 10⁻⁸ to 10⁻⁹; Wilner et al. 1994), and that these abundances would increase our CH₃CN derived gas masses closer to those presented below from our analysis of SO₂ and OCS; however, the abundances presented in Remijan et al. were derived partially based on observations of one of the sources observed here (W51e2). We present the masses derived from the CH₃CN emission both assuming optically thin and optically thick emission in Table 3 (the second last and last columns, respectively).

From the integrated intensity of a single transition of a molecule (such as SO₂ or OCS), we can also determine the average column densities of the gas responsible for that emission. The column density of either SO₂ or OCS can be derived by solving Equation (2) for N_TOT. The column density in the observed species can be converted into a molecular gas column density by scaling by the abundance of the species (here SO₂ or OCS) with respect to H₂.

For both SO₂ and OCS, there are large variations in the abundances given in the literature. By averaging the abundances of these two species from a number of sources (Watt & Charnley 1985; Leen & Graff 1988; Blake et al. 1994; Charnley 1997; Hatchell et al. 1998; van der Tak et al. 2003; Viti et al. 2004), we find SO₂ and OCS abundances of 1 × 10⁻⁷ and 2.5 × 10⁻⁸, respectively. The ranges in abundances for these two species were 5 × 10⁻⁸ to 1 × 10⁻⁶ for SO₂ and 1 × 10⁻⁹ to 5 × 10⁻⁷ for OCS. The mass of each emitting region was determined by multiplying the average molecular column density by the area and by the mass of molecular hydrogen. We find that, within our uncertainty estimates, the masses derived from the SO₂ are approximately twice of those derived from the OCS emission. For both species, overestimating the temperature acts to overestimate the mass. We find that, in general, SO₂ is observed at a higher signal-to-noise ratio than OCS, however, given that SO₂ begins to deplete out of the gas phase at temperatures greater than 300 K (Doty et al. 2002); we may be overestimating the mass from the SO₂ emission by overestimating the abundance with respect to H₂. This could be artificially inflating our SO₂ derived emission masses. These derived masses represent only the warm gas surrounding each H ii region, and do not reflect the hot material within the H ii region, or the cold gas exterior to the hot core. Thus, we expect these masses to be lower than the dynamical masses which include the stellar and ionized gas masses within the H ii region.

The two main components of the continuum emission in our sources are free–free emission from the H ii region and the warm dust from its surroundings. The predicted emission from the free–free component of the continuum flux can be calculated by Equation (2.124) of Gordon & Sorochenko (2002). This free–free emission can then be removed from our observed 1.4 mm continuum, and we assume that the remaining continuum emission is due to thermal dust.

Using the equations and relations presented in Hildebrand (1983), we determined the dust masses in the regions producing the dust continuum emission. We have extrapolated the dust emissivity from Hildebrand (1983) as Q_λ = 7 × 10⁻⁴(0.125/λ_mm)^β, where 0.125 and λ_mm are both wavelengths in units of millimeter (here, λ_mm = 1.4). This expression was derived without assuming that β = 1 at 250 μm. For our calculations, we assume a gas-to-dust ratio of 100 which allows for the conversion from dust mass to gas mass. We further assume that the gas and dust temperatures are not well coupled within the H ii region, since the gas temperature within the H ii region is well above the dust sublimation temperature. Instead, we assume that the central star is heating the dust, and the temperature falls off as T_dust = (R_*/R)^0.4 × T_* (Lamers & Cassinelli 1999). For the region in which the temperature is below the dust sublimation threshold, the temperature gradient was then averaged over our 1'' beam (or, a linear size of 6400 AU at the average distance to our sources) to give an average temperature of 400 K. The masses listed in Table 2 were calculated using this single temperature and assuming β = 1.5. Increasing β to 2 (while keeping the temperature at 400 K) increases the derived masses by more than a factor of 3. If we use the gas temperatures derived from our CH₃CN, the changes in the masses derived from the dust emission are within 1σ of the values listed in Table 2.

We find, in general, that the dust masses derived in this manner (and presented in Table 2) are lower than the derived dynamical masses presented in Section 3.1. In fact, we find that the average dust-derived mass is approximately half of the average derived dynamical mass. This result is expected since our calculated dust masses are for regions which are not quite as extended as the SO₂ emitting region and do not reflect the masses of the central star(s) as is the case for the dynamical masses.

Using the spectral energy distribution fits to the continuum data presented in Keto et al. (2008; both with and without density gradients within the H ii region), we estimate the masses of the central stars powering the observed H ii regions. From their continuum measurements, the ionizing flux required to maintain the H ii region was determined and a minimum stellar mass was inferred. If the H ii region were expanding, then the stellar mass required to produce the necessary ionizing flux would be higher. The required minimum stellar masses to maintain these H ii regions (assuming density gradients within the H ii region) are presented in Table 2 for all sources except W51e8 which were not included in the analysis of Keto et al.

As stated above, we find that the average source mass derived from the continuum emission is approximately half of the dynamically derived mass. When the stellar mass is added to the dust mass, we find that the combined mass is within approximately 1σ of the dynamical mass for G10.6 and G28.2. For NGC 7538, the combination of dust and stellar mass is much greater than the dynamical mass; hence, the estimate of 12 M_☉ for the dynamical mass must be an underestimate. For W51e2, we find that the dynamically derived mass is much greater than the combined dust and stellar mass estimates, which suggests that perhaps the dust-derived mass may be underestimated.