Gas infall in the massive star formation core G192.16–3.84

Figure 1 presents the continuum flux density maps in both color-scale and contours. From Figure 1, one can see that the continuum images at the three wavebands show compact source structure and are unresolved.

Zoom In Zoom Out Reset image size

Two dimensional (2D) Gaussian fitting was applied to the compact core. The peak position of the continuum is R.A.(J2000) = 5^h58^m13.547^s, Decl.(J2000) = 16°31'58.206'', which is consistent with that of previous continuum observations and the UC H_II region (Shepherd et al. 1998; Shepherd & Kurtz 1999; Shepherd et al. 2001; Shiozaki et al. 2011; Liu et al. 2013a). The deconvolved size, peak flux density and total flux from the Gaussian fitting are given in Table 2.

The continuum at our observed wavebands contains free-free emission (S_ν ∝ ν^−0.1). Based on measured total flux of 1.5 mJy at the 3.6 cm band (Shepherd & Kurtz 1999), we estimate that the free-free continuum emissions are 1.07 and 1.03mJy at the 230 and 345GHz bands, respectively. Comparing with the total flux of the continuum at 230 and 345GHz (0.270 to 0.769 Jy), the free-free continuum emission is negligible.

To derive physical parameters, we performed spectral energy distribution (SED) fitting based on the data from our observations and previous data at different wavelengths (Beuther et al. 2002; Shepherd et al. 1998, 2001;Williams et al. 2004). Figure 2 shows a plot of the SED. The best SED fitting gives a dust temperature T_d of 71.7±0.4 K, an H₂ gas column density N_H2 of (2.7±1.2)×10²⁴ cm⁻² and a dust emissivity index (β) of 1.7±0.4. Derived dust temperature T_d = 71.7±0.4 K is consistent with the SO₂ rotational temperature ${T}_{{\rm{rot}}}^{{{\rm{SO}}}_{{\rm{2}}}}\sim {84}_{-15}^{+18}$ K reported by Liu et al. (2013a), indicating that gas is coupled well with dust.

Zoom In Zoom Out Reset image size

Gas mass of the G192.16 continuum core can be calculated by using the following formula

$$\begin{eqnarray}&&{M}_{{{\rm{H}}}_{{\rm{2}}}}=\pi {R}^{2}\cdot {m}_{{\rm{H}}}\cdot \mu \cdot {N}_{{{\rm{H}}}_{{\rm{2}}}},\end{eqnarray} \tag{ 1 }$$

where μ = 2.8 is the mean molecular weight (Kauffmann et al. 2008) and m_H is the mass of an H atom. $R=\sqrt{ab}D$ is the source size, and the major and minor axes (a and b respectively) are obtained from 2D Gaussian fitting toward the continuum core (as listed in Table 2). Note that we take major and minor axes (a and b) as 1.3'' and 0.7'' respectively, which are averaged values of the 2D Gaussian fitting results of all continuum sources. At a distance of 1.52 kpc, the core radius is calculated as R = 0.007 pc. Core mass (M_H2) is derived to be 10.8 ± 4.8 M_⊙, which is consistent with the mass range of 4 M_⊙ ≤ M_gas + M_dust ≤ 18 M_⊙ estimated by Shiozaki et al. (2011).

Molecular transitions of CO(3–2), CO(2–1), ¹³CO(2–1), C¹⁸O(2–1), HCN(3–2), HCO⁺(3–2), SO(8₈–7₇) and SO(6₅–5₄) are detected as shown in Figure 3. In Figure 3, the CO(3–2), CO(2–1), ¹³CO(2–1), C¹⁸O(2–1), HCN(3–2) and HCO⁺(3–2) spectra display double-peaked line profiles with absorption dips at around ∼6 km s⁻¹, and the blueshifted peaks are stronger than the redshifted ones. The SO(8₈–7₇) and SO(6₅–5₄) lines show single peak profiles with local standard of rest (LSR) velocities at ∼6 km s⁻¹. These double-peaked spectral profiles are so-called "blue profiles" (Zhou et al. 1993; Wu & Evans 2003; Wu et al. 2007), indicating gas infall in this region.

Zoom In Zoom Out Reset image size

Various molecular tracers (CO, CN, HCN, H₂CO, HCO⁺, etc.) are used for identifying collapse candidates and studying infall (Fuller et al. 2002; Zapata et al. 2008; Wu et al. 2009, 2014; Liu et al. 2011b,a, 2013c,b; Pineda et al. 2012; Qin et al. 2016; Qiu et al. 2012). Simulations by Smith et al. (2012, 2013) suggested that HCN(3–2) and HCO+(3–2) are best for studying gas infall.

From Figure 3, the CO(3–2), CO(2–1), ¹³CO(2–1) and HCN(3–2) lines reveal much wider line wings, and these line wings may be produced by outflow motions (Shepherd et al. 1998; Liu et al. 2013a). Therefore, the infall "profile" of these lines will be contaminated by outflows. C¹⁸O(2–1) and HCO⁺(3–2) lines without obvious line wings will be used for further analyses. Note that observations of C¹⁸O(2–1) and HCO⁺(3–2) lines have different angular resolutions. We have smoothed higher resolution data (HCO⁺) to lower ones (C¹⁸O).

The integrated intensity maps of C¹⁸O(2–1) and HCO⁺(3–2) are presented in Figure 4. The red cross in each panel represents the continuum emission peak. From the C¹⁸O(2–1) map, one can see that the gas emission peak is associated with the continuum peak position. However, the HCO⁺(3–2) gas is separated into two components, and one of them is also associated with the continuum peak position.

Zoom In Zoom Out Reset image size

For a collapsing cloud, in case the brightness temperature of the background continuum is brighter than the excitation temperature of a "blue profile" line transition tracing infall motion, the "blue profile" line will become an "inverse P Cygni" profile. The modified two-layer model (Myers et al. 1996; Di Francesco et al. 2001) can not only fit both the "blue profile" and the "inverse P Cygni" profile, but also the "red profile" and "P Cygni" profile characterizing outflows or expansion. Then the modified twolayer model (Myers et al. 1996; Di Francesco et al. 2001) is adopted to fit the spectral profiles of C¹⁸O(2–1) and HCO⁺(3–2).

Panels (a) and (b) of Figure 5 show observed spectra in black and two-layer modeling in red for C¹⁸O(2–1) and HCO⁺(3–2), respectively. The two-layer model can be simply described as follows:

$$\begin{eqnarray}\begin{array}{lll}\Delta {T}_{{\rm{B}}} & = & ({J}_{{\rm{f}}}-{J}_{{\rm{cr}}})\left[1-{e}^{(-{\tau }_{{\rm{f}}})}\right]\\ & & +(1-\Phi )({J}_{{\rm{r}}}-{J}_{{\rm{b}}})\left[1-{e}^{(-{\tau }_{{\rm{r}}}-{\tau }_{{\rm{f}}})}\right],\end{array}\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&{J}_{{\rm{cr}}}=\Phi {J}_{{\rm{c}}}+(1-\Phi ){J}_{{\rm{r}}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\tau }_{{\rm{f}}}={\tau }_{0}{e}^{\left[\frac{-{(V-{V}_{{\rm{in}}}-{V}_{{\rm{LSR}}})}^{2}}{2{\sigma }^{2}}\right]},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\tau }_{{\rm{r}}}={\tau }_{0}{e}^{\left[\frac{-{(V+{V}_{{\rm{in}}}-{V}_{{\rm{LSR}}})}^{2}}{2{\sigma }^{2}}\right]}.\end{eqnarray} \tag{ 5 }$$

The model takes optical depth (τ₀), front layer radiation temperature (J_f), rear layer radiation temperature (J_r), LSR velocity (V_LSR), velocity dispersion (σ), infall velocity (V_in), radiation temperature of the continuum source (J_c) and fill factor (Φ) into account. We adopted dust temperature T_d = 71.7 K from our SED fitting as radiation temperature (J_c) of the continuum source, and the fill factor (Φ) is fixed at 0.3 during the fitting process. A similar procedure was also used by Pineda et al. (2012). The V_LSR is set at 6 km s⁻¹, which is derived from the SO(6₅–5₄) line. During the fitting process, only τ₀, J_f, J_r, σ and V_in are free parameters; the parameter spaces are 0.1∼10 for τ₀, 3∼100 K for J_f and J_r, and 0.1∼10 km s⁻¹ for V_in. The Levenberg-Marquardt algorithm was adopted to search for the best solution.

Zoom In Zoom Out Reset image size

The best fitting gives infall velocities for the C¹⁸O(2–1) and HCO⁺(3–2) spectra of 2.0±0.2 and 2.8±0.1 km s⁻¹, respectively. The detailed fitting results are presented in Table 3. We find that τ₀, J_f and J_r are interdependent and very sensitive to initial values. Thus, they cannot be determined accurately. In contrast, σ and V_in mainly determine the line profile. Thus, they are much less sensitive to initial values and are more reliable.

Assuming that the cloud has a power-law density profile (ρ ∝ r^1.5), the mass enclosed in r₀ can be calculated by (Liu et al. 2018)

$$\begin{eqnarray}&&M=\displaystyle {\int }_{0}^{{r}_{0}}4\pi {r}^{2}{\rho }_{0}{\left(\frac{r}{{r}_{0}}\right)}^{-1.5}dr,\end{eqnarray} \tag{ 6 }$$

where r₀ is the outer radius and ρ₀ is the density at r₀. Thus, the mass infall rate can be estimated as

$$\begin{eqnarray}&&{M}_{{\rm{in}}}\,=4\pi {r}_{0}^{2}{\rho }_{0}{V}_{{\rm{in}}}=1.5M{V}_{{\rm{in}}}/{r}_{0}.\end{eqnarray} \tag{ 7 }$$

We adopt the mass of 10.8 M_⊙ from the SED fitting for M and the averaged source size (R) of 0.007 pc for r₀. Thus the mass infall rates of C¹⁸O(2–1) and HCO⁺(3–2) are estimated to be (4.7±1.7) × 10⁻³ and (6.6 ± 2.1) × 10⁻³ M_⊙ yr⁻¹, respectively. The infall rates are also summarized in Table 3.