CS emission near MIR-bubbles

Eighteen sources displayed emission greater than 3$\sigma$. A typical spectrum is shown in Figure 1. Emission lines were fit using fitgauss, the standard Gaussian fitting routine in GBTIDL. Fitting parameters (amplitude in T_mb units, central velocity and FWHM) are listed in Table 3. For sources that displayed a double peak, two simultaneous Gaussian functions were fit to the emission and are listed in consecutive rows. CS column densities, $N_{CS}$, were calculated assuming LTE, optically thin emission and an excitation temperature T_ex=15 K, a typical ISM value (see review in Zinnecker & Yorke (2007)). Increasing or decreasing the assumed excitation temperature by 5 K changes the column density by about 30%. If CS(1-0) is optically thick, as we assume for three sources in section 4.2 below, then our calculation would be a lower limit. Given these assumptions we used the following relation (see Miettinen (2012) for a detailed discussion of the relations below):

where

Here $\epsilon_{0}$ is the vacuum permittivity, $\mu_{el}$ is the permanent electric dipole moment, S is the line strength, Z_rot is the rotational partition function, $\nu$ is the frequency, g_K is the K-level degeneracy, g_I is the reduced nuclear spin degeneracy, E_u is the energy of the upper-transition state, T_ex is the excitation temperature and T_bg is the background temperature. The dipole moment line strength ($\mu^{2}_{el}$ S) is taken from the JPL spectral line catalog (Pickett et al., 1998). The partition function (Z_rot) is a linear fit to JPL data between T=37 to 75 K. T_bg was taken to be the cosmic microwave background temperature, 2.725 K. The uncertainty in the fit amplitudes and derived column densities is dominated by our flux-calibration uncertainty. Since the relationships are linear, we estimate the uncertainty in both as 20%.

The three mapped regions are shown as boxes overlaid on the GLIMPSE 8 $\mu$m images in Figures 2-4. The maps were cropped to just those regions showing emission above 3$\sigma$. The regions containing emission were then exported to a FITS file using custom-built IDL tools and the FITS-format datacubes were analyzed using CASA. The standard moment maps (total intensity, average velocity and velocity width) are shown next to the corresponding 8 $\mu$m emission images in Figures 2-4.

The three maps of CS in N56, N65, and N77 (Figs. 2-4) show evidence of supersonic gas motion in areas near each YSO. N56 has a weak peak in CS that corresponds to a velocity shift of $\sim$2 km/s in the gas immediately to the north. The CS emission in N65 has a clear, strong comma-like shape. The peak in emission is clearly near the top of the shape, but there is a slight, secondary peak below and to the right in Fig 3b. There is also a shift in gas velocity of $\sim$1 km/s at the same location. Two spectra from the map, centered at the primary and secondary peaks, are shown in Figs. 3e and f. The spectrum at the primary peak shows two components, with the red-shifted component stronger. At the secondary peak, this component appears to shift further redward. We interpret the secondary peak, shift in first-moment map and the double-Gaussian peak from single pointing spectra as all caused by at least two overlapping clouds at different velocities. Using this interpretation, the emission peak (Fig. 3b) is highest where emission from both clouds is present. This peak is coincident with the blue-shifted gas (Fig. 3c) because emission from the bluer cloud is present at the location of the pointing shown in Fig. 3b but not at the location of the pointing shown in Fig. 3c. There may be further motion within each cloud, which could be responsible for the redward shift of the stronger component. The least distinct of the regions, N77 shows weak emission with some evidence of shifts in velocity of $\sim$1 km/s. These shifts could be caused by several mechanics: outflow from or infall toward the YSO or shock-induced velocity shifts caused by the expanding HII region. The limited nature of the data prevents an exclusive interpretation.

To calculate the abundance of CS, we first must estimate the total gas column density along each line of sight. We used FIR (60$\mu$m-600$\mu$m) imaging taken as part of the HiGal survey. Within CASA, we measured the integrated emission in all five survey bands in regions exactly coincident with the GBT beamsize, centered at each source of CS emission. The emission was then modeled as a modified blackbody:

where T is temperature, $\nu$ is frequency, B₀ is a scaling constant and $\beta$, the emissivity index, is assumed to be 2 (Désert et al., 2008). B₀ and T were taken as free parameters and a Levenberg–Marquardt algorithm was used to find the best-fit. The fitting was done to the flux density in Jy, so B₀ carries these units. The total column density, N_tot, was calculated following Miettinen & Harju (2010). Briefly, we used the following relations:

where m_H is the mass of hydrogen and 3.73 x 10^-16 converts the surface brightness from Jy/(1″beam) to SI units. We make the following assumptions: the opacity at 1.3 mm is $\kappa_{1.3mm}$ = 0.11 $\frac{m^{2}}{kg}$, appropriate for ice-covered dust grains from Ossenkopf & Henning (1994), $\theta$=15.0″, the beamsize of the GBT at 49 GHz, the mean molecular weight $\mu$ = 2.3 and dust to mass ratio $R_{d}$ = 1/100. Note that B_ν, B_mod and $\kappa$ all require a choice of frequency or wavelength. However, these dependencies cancel in the final calculation of N_tot. These results are summarized in Table 4, where we report the flux density at five wavelength bands for each CS detection, the best-fit temperature, the total column density and the CS abundance. We estimate the error in determining the extended flux to be dominated by defining the edge of the object. These sources all appear extended in the Herschel bands and some lie in confused regions. Thus, the gas sampled by FIR and CS are likely different. This difference should lead to a cautious association between the dust temperatures and the CS emission. To estimate the influence of this uncertainty on the calculated properties, we examined the effect of a 20% change up or down in FIR flux. The results were a change of 4 K in temperature and 20% in column density.

For those sources where the modified blackbody model was a poor fit, as judged by eye, we have excluded the temperature, column density and abundance. The cause for the poor fit in these cases appeared to be caused by emission extending well outside the the GBT beam. For these poorly-fit sources, the fluxes reported here probably do not represent the emission from the same object. For those sources with a double-Gaussian CS line profile, we add the CS column densities calculated using both Gaussians. If this shape is caused by optical depth effects, as we discuss below, than the reported column density would be a lower limit.

Four sources, N62-1, N65-2, N90-2 and N117-3, have a non-Gaussian line profile. In three cases the line profile is stronger on the blue-side (see Fig. 6). Of these three sources, N117-3 has the strongest red-shifted emission, with two clear peaks present. The line-profiles of N62-1 and N90-2 are single-peaked but with a plateau on the red-shifted side. We interpret these three profiles as evidence of infall. N62-1 and N90-2 both are located in infrared dark clouds that intersect their nearby bubble (N62 and N90). Thus, infall, if present, could be triggered by an expanding HII region via radiatively driven implosion or collect-and-collapse. N117-3 is located within in the bubble, in projection. There is no obvious interpretation for this infall candidate’s interaction with the associated bubble N117.

Myers et al. (1996) and Williams & Myers (1999) present a model of infall that predicts line profiles similar to these observations. They assume two clouds (near and far) falling toward a common center and estimate the resulting line profiles accounting for optical depth effects as well as standard radial-dependencies of velocity and excitation temperature. Myers et al. (1996) show that an optically thick line and a higher excitation temperature in the cloud on the far side can produce a blue-shifted weighted line-shape. With further simplifications they show that by measuring five parameters, the Myers et al. (1996) model allows an estimate of the infall velocity. The measured parameters are: $\sigma$ (velocity dispersion of an optically thin tracer), T_BD (the blue-shifted excess emission), T_RD (the red-shifted emission), T_D (the plateau emission), v_red (the red-shifted peak emission velocity) and v_blue (the blue-shifted peak emission velocity). See Figure 2 in Myers et al. (1996) for a diagram of these different quantities. When all quantities can be measured, the infall velocity is estimated to be:

When the optical depth and V_in/$\sigma$ are sufficient large, the red peak can disappear (see Myers et al. 1996 for discussion of this effect). Thus, we are limited in our numerical analysis to N117-3. We estimated the relevant line parameters by eye. Our line profile measurements and infall velocity calculation are given in Table 5. Since we do not have an optically thin measurement of this source, we have assumed the value of the velocity dispersion based on the optically thin ³⁴CS observations by Williams & Myers (1999). They found a typical value to be 1.5 km/s. A smaller value would decrease the infall velocity (see equation above).

Further analysis requires determining a distance. We assume a rotation curve following Brand & Blitz (1993) and adopt the near kinematic distance of 4.4 kpc. We then can use the mid-IR integrated fluxes for toward N117-3 as measured by Herschel/Hi-Gal to estimate N117-3’s mass and mass accretion rate. The mid-IR fluxes can be fit using the same modified blackbody model described above, yielding a mass of 96 M_⊙. We can further roughly estimate the mass infall rate $\dot{M}_{in}$ using:

where R is the radius where infall has been detected, $v_{in}$ is the detected infall velocity and $\rho$ is the density of the infall gas. If we use the GBT beamsize projected to the near kinematic distance for R (0.32 pc), then we calculate a mass infall rate of 7 $\times$ 10^-5 M_⊙/yr. The dominant source of error in this calculation is likely due to the infall velocity. We estimate the uncertainty to be about a factor of 2. However, if we used a smaller value for R, as suggested by the small source size visible in the 8 $\mu$m GLIMPSE image, the mass infall rate would be proportionally smaller (by a factor of about 3). This result is consistent with massive or intermediate-mass star formation.

For the infall analysis, we have assumed an optically thick line. An alternative interpretation of these three line-profiles is that they are caused by alignment of two clouds along the line-of-sight. Observing an optically-thin tracer, such as ³⁴CS would distinguish between these interpretations since the infall-model would predict a single-peak whereas the two cloud model predicts a double-peak.

N65-2, the other source which shows a non-Gaussian line shape, is stronger on the red-shifted side. This shape is not consistent with the infall model of Myers et al. (1996). This shape could be caused by two unrelated clouds along the line of the sight. There is further evidence of this interpretation in the map of N65 (see section 3.2).