Understanding the Links among the Magnetic Fields, Filament, Bipolar Bubble, and Star Formation in RCW 57A Using NIR Polarimetry

We performed aperture photometry of point-like sources on the intensity images for the HWP angles (I₀, ${I}_{22.5}$, I₄₅, and ${I}_{67.5}$) of each of the JHK_s bands using iraf¹⁴ and the idl Astronomy Library (Landsman 1993). Point sources with peak intensities above 5σ (where σ is the rms uncertainty of the particular image pixel values) of the local sky background were detected using DAOFIND. Aperture photometry was performed using the PHOT task of the DAOPHOT package in IRAF. An aperture radius was chosen to be nearly the FWHM of the point-like sources, i.e., 3.4, 3.2, and 2.9 pixels in the J, H, and K_s bands, respectively. The sky annulus inner radius was set to be 10 pixels with a 5 pixel width. A source that matched in center-to-center positions to within 1 pixel radius (i.e., 2 pixel diameter equivalent to ∼1'') in all four HWP images was judged to be the same star.

The Stokes I intensity of each point-like source was calculated using

$$\begin{eqnarray}&&I=\displaystyle \frac{1}{2}({I}_{0}+{I}_{22.5}+{I}_{45}+{I}_{67.5})\end{eqnarray} \tag{ 1 }$$

and used to estimate its photometric magnitude. There were 401 stars found with both IRSF and 2MASS JHK_s photometric magnitude uncertainties less than 0.1 mag. These stars were used to calibrate the IRSF instrumental magnitudes and colors to the 2MASS system. Details regarding this calibration can be found in Appendix A. From the HWP images, we were able to estimate JHK_s photometric magnitudes and colors ([J − H] and $[H-{K}_{s}]$) for 702 stars to uncertainties of less than 0.1 mag.

Polarimetry of point-like sources (aperture polarimetry) was performed on the combined intensity images at each HWP angle. Extracted intensities were used to estimate the Stokes parameters of each star using

$$\begin{eqnarray}&&Q=({I}_{0}-{I}_{45}),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&U=({I}_{22.5}-{I}_{67.5}).\end{eqnarray} \tag{ 3 }$$

The aperture and sky radii were the same as those used in the aperture photometry on the total intensity (I) images. To obtain the Stokes parameters (Q and U) in the equatorial coordinate system, an offset rotation of 105° (Kandori et al. 2006; Kusune et al. 2015) was applied. We calculated the degree of polarization P and the polarization angle θ as follows:

$$\begin{eqnarray}&&P=\displaystyle \frac{\sqrt{{Q}^{2}+{U}^{2}}}{I},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\theta =\displaystyle \frac{1}{2}\arctan \left(\displaystyle \frac{U}{Q}\right).\end{eqnarray} \tag{ 5 }$$

The errors in P and θ were also estimated by propagating the errors in the Stokes parameters according to Equations (4) and (5). Since the polarization degree, P, is a positive definite quantity, the derived P value tends to be overestimated, especially for low S/N cases. To correct for this bias, we calculated the de-biased P using ${P}_{\mathrm{db}}=\sqrt{{P}^{2}-\delta {P}^{2}}$ (Wardle & Kronberg 1974), where δP is the error in P. It should be noted here that, hereafter, we consider P_db to be P. The absolute accuracy of the offset polarization angle for SIRPOL was estimated to be less than 3° (Kandori et al. 2006). The polarization efficiencies of the wire grid polarizer are 95.5%, 96.3%, and 98.5% at the J, H, and K_s bands, respectively, and the instrumental polarization is less than 0.3% over the field of view at each band (Kandori et al. 2006). Due to these high polarization efficiencies and low instrumental polarization, no additional corrections were made to the data. To obtain the astrometric plate solutions, we matched the pixel coordinates of the detected sources and the celestial coordinates of their counterparts in the 2MASS Catalog (Skrutskie et al. 2006), and applied the ccmap, ccsetwcs, and cctran tasks of the iraf imcoords package to the matched lists. The rms error in the returned coordinate system was ∼003. However, since the 2MASS astrometry system is limited to about 02, the stellar positional uncertainties should take that into account. A total of 919 stars had polarization detection in at least one band with $P/{\sigma }_{P}\geqslant 1$.

The polarimetric data for the 919 stars were merged with the photometry of the 702 stars, and the resultant data are presented in Table 1. Star IDs are given in column 1. The photometric data of the stars—those do not have them from IRSF—are extracted from 2MASS (Skrutskie et al. 2006) and are denoted with an asterisk along with the star IDs in column 1. The coordinates, and aperture polarimetric and photometric results of each source are presented in columns 2–12. Column 13 reports our classifications of the stars, as described in Section 3 below. Although we presented all of the stellar data satisfying the $P/{\sigma }_{P}\geqslant 1$ criterion in Table 1, further analyses used only the 461 stars having H-band polarization data which satisfied the $P(H)/{\sigma }_{P(H)}\geqslant 2$ criterion.

Table 1.  The JHK_s Band Polarimetric and Photometric Measurements of 1074 Stars

Star ID	R.A. (°)	Decl. (°)	P(J)	P(H)	$P({K}_{s})$	$\theta (J)$	$\theta (H)$	$\theta ({K}_{s})$	J	H	Ks	Classification
	(deg)	(deg)	(%)	(%)	(%)	(deg)	(deg)	(deg)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
${1}^{\star }$	167.82417	−61.30004	⋯	⋯	1.54 ± 0.12	⋯	⋯	156.1 ± 2.2	10.926 ± 0.023	10.761 ± 0.022	10.717 ± 0.021	foreground
${2}^{\star }$	167.82453	−61.32636	⋯	⋯	2.39 ± 0.30	⋯	⋯	56.2 ± 3.6	15.745 ± 0.125	12.896 ± 0.039	11.588 ± 0.052	background
3	167.82542	−61.25781	⋯	⋯	11.74 ± 6.92	⋯	⋯	126.7 ± 16.9	⋯	⋯	⋯	⋯
${4}^{\star }$	167.82617	−61.28490	⋯	⋯	0.74 ± 0.38	⋯	⋯	125.6 ± 14.7	13.251 ± 0.023	12.364 ± 0.022	12.038 ± 0.024	⋯
${5}^{\star }$	167.82662	−61.29078	⋯	⋯	3.81 ± 3.43	⋯	⋯	135.5 ± 25.8	14.972 ± 0.033	14.590 ± 0.045	14.632 ± 0.101	⋯
6	167.82681	−61.27721	⋯	⋯	⋯	⋯	⋯	⋯	15.709 ± 0.069	14.958 ± 0.054	14.705 ± 0.062	⋯
7	167.82700	−61.27257	⋯	⋯	⋯	⋯	⋯	⋯	15.670 ± 0.051	14.537 ± 0.032	14.029 ± 0.031	⋯
8	167.82750	−61.27381	2.12 ± 0.07	1.16 ± 0.04	1.31 ± 0.05	39.0 ± 0.9	66.3 ± 0.9	81.9 ± 1.1	11.136 ± 0.006	10.148 ± 0.004	9.792 ± 0.003	background
${9}^{\star }$	167.82789	−61.24061	⋯	2.26 ± 0.90	2.13 ± 1.23	⋯	81.9 ± 11.4	84.8 ± 16.5	14.924 ± 0.043	13.789 ± 0.029	13.331 ± 0.034	background
10	167.82793	−61.28848	⋯	⋯	8.42 ± 3.82	⋯	⋯	38.7 ± 13.0	15.629 ± 0.031	14.989 ± 0.022	14.852 ± 0.035	foreground${}^{\dagger }$
11⋆	167.82798	−61.35974	⋯	9.91 ± 3.27	8.22 ± 3.22	⋯	99.8 ± 9.5	78.8 ± 11.2	17.096	15.273 ± 0.079	14.257 ± 0.078	background
${12}^{\star }$	167.82850	−61.31453	⋯	1.67 ± 1.12	⋯	⋯	66.7 ± 19.1	⋯	14.636 ± 0.036	14.248 ± 0.038	14.155 ± 0.063	⋯
13	167.82881	−61.27652	⋯	⋯	3.63 ± 1.94	⋯	⋯	97.7 ± 15.3	15.635 ± 0.044	14.374 ± 0.021	13.893 ± 0.021	⋯
14	167.82915	−61.30585	2.31 ± 1.76	⋯	⋯	53.0 ± 21.8	⋯	⋯	14.992 ± 0.020	14.057 ± 0.013	13.766 ± 0.016	⋯
${15}^{\star }$	167.82931	−61.32771	⋯	⋯	6.63 ± 2.74	⋯	⋯	55.5 ± 11.8	16.722	15.578 ± 0.164	14.359 ± 0.085	Class II
16	167.82960	−61.27960	5.00 ± 2.67	2.39 ± 1.98	⋯	30.7 ± 15.3	92.2 ± 23.6	⋯	15.393 ± 0.028	14.823 ± 0.022	14.533 ± 0.029	⋯
${17}^{\star }$	167.82972	−61.31241	⋯	2.37 ± 1.04	3.43 ± 1.48	⋯	100.6 ± 12.6	89.2 ± 12.4	15.828 ± 0.081	14.321 ± 0.055	13.752 ± 0.058	background
18	167.83039	−61.33665	⋯	1.11 ± 0.70	3.20 ± 0.75	⋯	79.4 ± 18.1	144.0 ± 6.7	14.869 ± 0.019	13.172 ± 0.009	12.342 ± 0.009	⋯
${19}^{\star }$	167.83094	−61.23723	⋯	6.24 ± 3.39	⋯	⋯	97.2 ± 15.5	⋯	14.870 ± 0.101	14.560 ± 0.114	14.444 ± 0.124	⋯
20	167.83131	−61.33597	3.37 ± 0.13	4.04 ± 0.04	1.46 ± 0.04	86.4 ± 1.1	85.6 ± 0.3	84.6 ± 0.7	12.434 ± 0.009	10.229 ± 0.003	9.275 ± 0.005	background

Notes.

Star IDs marked with a ⋆ denotes that their photometric data taken from 2MASS (Skrutskie et al. 2006).

The polarization values given in columns 4–6 are de-biased.

The uncertainties in the polarization angles given in columns 7–9 do not account for the overall angular calibration uncertainty of 3°, which is a systematic uncertainty that would affect all of the measured polarization angles.

Column 13: "Foreground" means confirmed foreground stars.

Column 13: "Background" means confirmed background stars or cluster members.

Column 13: "Foreground${}^{\dagger }$" means probable foreground stars with P(H) > 3% (see Section 3.3).

Column 13: "Background${}^{\dagger \dagger }$" means probable background stars or cluster member with excess polarization (see Section 3.3).

Column 13: "Background${}^{\ddagger}$" means probable background star or cluster member with depolarization (see Section 3.3).

The entries that do not have 2MASS photometric uncertainties are left blank

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Distributions of P(H) versus $[H-{K}_{s}]$ and $\theta (H)$ versus $[H-{K}_{s}]$ for the 461 stars are, respectively, presented in Figures 2(a) and (b). Also shown are the histograms of P(H) (Figure 2(a)), $\theta (H)$ (Figure 2(b)), and $[H-{K}_{s}]$ (Figure 2(c)). $[H-{K}_{s}]$ colors plotted in Figure 2 (also in Figures 4–6) were converted to the California Institute of Technology (CIT) system using the relations given by Carpenter (2001). The degree of polarization P(H) exhibits an increasing trend with $[H-{K}_{s}]$ color. The histogram of P(H) peaks at ∼1% of polarization. The polarization angles $\theta (H)$ of the stars span the full 0°–180° range with two groups densely concentrated around θ(H) ≃ 60° and θ(H) ≃ 150°. These two dominant θ(H) distributions seem to be different from the position angle of 101° corresponding to the orientation of the Galactic plane (GP) at b = −072, shown with a dashed line. Moreover, these two groups of stars exhibit different distributions of $[H-{K}_{s}]$ colors and are separated by a boundary at $[H-{K}_{s}]\,=0.15$ mag. Although these two groups of stars exhibit different properties of θ(H) and $[H-{K}_{s}]$ colors, they are not as clearly separated from each other in the distribution of P(H).

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Since the RCW 57A region is still enshrouded in its natal molecular cloud, as evident from the ¹³CO(1 – 0) map (magenta contour in Figure 1 and red background in Figure 7), YSOs in the region can be deeply embedded. Therefore, the Spitzer MIR observations were used to gain deeper insight into the embedded YSOs. These occupy distinct regions in the Spitzer IRAC color plane, which makes MIR TCDs a useful tool for the classification of YSOs. Since 8.0 μm data are not available for the region, we used ${[[{K}_{s}]-[3.6]]}_{0}$ and ${[[3.6]\mbox{--}[4.5]]}_{0}$ (cf. Gutermuth et al. 2009) to identify deeply embedded YSOs, as shown in Figure 3. The zones of Class I and Class II YSOs, based on the color criteria of Gutermuth et al. (2009), are also depicted. Three sources were identified as Class I and 32 sources as Class II, and so were excluded from analyses. Identified Class I and Class II sources are mentioned in column 13 of Table 1.

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NIR colors are also important tools to classify YSOs in star-forming regions. Figure 4 shows the [J − H] versus $[H-{K}_{s}]$ NIR TCD for the 461 stars. The 461 stars were classified into several types as follows. The three Class I sources and 32 Class II sources identified based on the Spitzer MIR TCD (Figure 3) are shown as the filled and unfilled stars, respectively. Fifty-seven stars exhibiting NIR excesses, falling in the "T" and "P" regions and satisfying the relation [J − H] < 1.69 $[H-{K}_{s}]$, are shown as squares. Four stars, denoted by filled triangles, are found to have nebulous backgrounds. Twenty-eight stars, shown as open diamonds, were found to have L-band excesses (Maercker et al. 2006). Two of the stars found to be Class I also have L-band excess, and similarly, three stars found to be Class II also have L-band excess. Stars identified as having an NIR excess, L-band excess, and a nebulous background are noted in column 13 of Table 1.

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The remaining 342 stars that appear to be free from intrinsic polarization and are distributed in zone "F" in Figure 4 are (i) lightly reddened foreground field stars (FG stars), (ii) moderately reddened cluster members and highly reddened background stars (hereafter, both cluster members and background stars are referred to as BG stars), and (iii) weak line T-Tauri stars (WTTSs) or Class III sources. The locations of the WTTSs in the NIR TCD overlap with those of the reddened background stars. Generally, WTTSs exhibit almost negligible NIR excess, as their disks will have been evaporated already or be very optically thin (e.g., Adams et al. 1987; Andrews & Williams 2005; Cieza et al. 2007). Therefore, it is reasonable to assume that these WTTSs are not intrinsically polarized by scattered light from the negligible amount of circumstellar material.

In order to estimate the level of FG contamination, a control field ($\alpha ={11}^{{\rm{h}}}{18}^{{\rm{m}}}12\buildrel{\rm{s}}\over{.} 22$, δ = −61°59'3892 [J2000]) of angular size 77 × 77 located ∼60' from the RCW 57A region was chosen. Comparing the distributions of the $[H-{K}_{s}]$ colors of the control field with colors in the RCW 57A region shows the field stars to have $[H-{K}_{s}]\lt 0.15$. Therefore, the 108 RCW 57A stars with $[H-{K}_{s}]\lt 0.15$ and lying in the "F" region of the NIR TCD are judged to be FG star candidates, and the remaining 234 stars with $[H-{K}_{s}]\geqslant 0.15$ and lying in the "F" region are judged to be BG star candidates.

Polarization efficiency is defined as the ratio of polarization degree to interstellar reddening, such as $P(\lambda )/E({\lambda }_{1}-{\lambda }_{2})$. Observed polarization efficiencies of dust grains are found to vary from one line of sight to another. Reddening ($E(B-V)$) and polarization in the V-band (P_V) are correlated and can be represented by the observational upper limit relation: ${P}_{V}/E(B-V)\leqslant 9 \%$ mag⁻¹ (Serkowski et al. 1975). Polarization measurements that exceed this upper limit relation are generally attributed to the intrinsic polarization (non-magnetic polarization) caused by scattered light from dust grains in circumstellar disks or envelopes around YSOs (e.g., Kandori et al. 2007; Eswaraiah et al. 2011, 2012; Serón Navarrete et al. 2016).

We also seek to identify and exclude the stars that suffer depolarization due to their starlight passing through multiple B-field components along the line of sight. For optically thin clouds, P(λ) is expected to be proportional to the column density if the field structure is uniform. In contrast, the presence of multiple B-fields with different orientations along a line of sight will result in depolarization (Martin 1974) and hence weaken the correlation between polarization and extinction (e.g., Eswaraiah et al. 2011, 2012). Therefore, polarization efficiency diagrams (e.g., Kwon et al. 2011; Sugitani et al. 2011; Hatano et al. 2013) will help identify stars with either intrinsic polarization or depolarization.

Figure 5 shows the P versus $[H-{K}_{s}]$ diagrams of FG and BG candidate stars (Section 3.2) with H-band data. These diagrams contain no known YSOs as we excluded them in Sections 3.1 and 3.2. The BG candidate stars show an increasing trend in polarization in accordance with an increasing $[H-{K}_{s}]$ and are well distributed below the upper limit interstellar polarization efficiency relation (gray line), $P(H)/E(H-{K}_{s})=14.5 \%$ mag⁻¹, corresponding to $P(V)/E(B-V)=9 \%$ mag⁻¹ (Serkowski et al. 1975; also see Hatano et al. 2013 for a detailed description on deriving polarization efficiency relations in NIR wavelengths.). To find the stars with non-magnetic polarizations (non-interstellar origin of polarizations) and depolarization effects, first, we fit a straight line to the polarization versus extinction for BG stars with ${\sigma }_{P(H)}\lt 0.3 \%$ (encircled filled circles). Second, we drew dashed lines with slopes of twice (upper dashed line) and half (lower dashed line) the fitted slopes. Third, we identified the stars falling above and below these lines as probable BG stars that were influenced by the non-magnetic origin of the polarization and depolarization effects, respectively. The remaining stars falling between the two dashed lines are ascertained to be confirmed BG stars. Therefore, the final number of confirmed BG stars was found to be 178 in the H-band. An additional 64 candidate BG stars falling above and below the dashed lines (plus symbols) are mentioned as probable BG stars with intrinsic polarization or depolarization in Table 1.

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FG candidate stars (open circles) exhibit two distributions and those with $P(H)\,\gt \,3 \%$ (plus symbols on open circles) may be affected by additional polarization caused by scattering or simply by larger uncertainties. We consider them to be probable FG stars. The remaining 97 stars with $P(H)\leqslant 3 \%$ are considered to be confirmed FG stars in the H-band. These confirmed and probable FG stars are mentioned in Table 1.

In further analysis, we only used the confirmed 97 FG and 178 BG stars with H-band data. The fitted slope of $P(H)/E(H-{K}_{s})=5.5{\rm{ \% }}\pm 0.8{\rm{ \% }}$ mag⁻¹ (thick line) suggests that the polarization efficiency of dust grains in the star-forming cloud RCW 57A are relatively higher than those of other Galactic lines of sight (e.g., Hatano et al. 2013; Kusune et al. 2015).

FG stars toward any distant cluster are, generally, less polarized and extincted than BG stars (Eswaraiah et al. 2011, 2012; Pandey et al. 2013). This is because the dust layer(s) between the observer and the FG star contains fewer aligned dust grains, and because the degree of polarization and extinction are linearly correlated (Aannestad & Purcell 1973; Serkowski et al. 1975; Hatano et al. 2013). If the B-field orientation of the foreground dust layer is sufficiently different from that of the cloud, then FG stars would exhibit different polarizations (P and θ) from BG stars. Therefore, FG and BG stars can also be distinguished based on their polarization characteristics (P versus θ or Q versus U), as well as with their NIR colors (Medhi et al. 2008, 2010; Eswaraiah et al. 2011, 2012; Medhi & Tamura 2013; Pandey et al. 2013; Santos et al. 2014).

Figures 6(a)–(d) depict that the 97 confirmed FG and 178 confirmed BG stars are well separated in their polarization characteristics and $[H-{K}_{s}]$ colors. FG stars have $[H-{K}_{s}]\lt 0.15$, P(H) < 3% with a peak around 1.0% and a single Gaussian distribution of $\theta (H)$ (Gaussian mean of 65° with a standard deviation of 14°). BG stars have $[H-{K}_{s}]\geqslant 0.15$, P(H) between 0.5%–12% with a peak at ∼2%, and an extended tail toward greater P values and widely distributed θ(H) (ranging from 0° to 180°) indicating the presence of a complex B-field structure in RCW 57A with a prominent peak at θ(H) ∼163°. About 55% of stars are distributed between 110° and 180°, whereas the remaining 45% of stars are distributed between 0° and 110°. This suggests that the plane-of-sky B-field structure of RCW 57A is dominated by a component with θ(H) ∼163°, which is nearly orthogonal to the foreground B-field component (65°) as well as being nearly orthogonal to the position angle of the major axis of the filament (∼60°). Figure 6(d) also reveals that the distributions of θ(H) of the confirmed FG and BG stars are different from the position angle (101°) of the Galactic plane (GP) at b = −072, shown with a thick vertical line.

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4.2.1. Contribution of Foreground Polarization

4.2.2. Magnetic Field Geometry

Figure 7 shows the vector map of the H-band polarization measurements of the 178 confirmed BG stars. The polarization vector map reveals a systematically ordered B-field that is configured into an hourglass morphology closely resembling the structure of the bipolar bubble.

The direction of the expanding I-fronts or outflowing gas is revealed based on a large north–south velocity gradient in radio recombination line observations (de Pree et al. 1999). These high-velocity outflow signatures are further traced in ¹³CO(1 – 0) position–velocity (P–V) diagrams (Figure 11; shown below). Shocked gas is visible at the SE and NW ends of the white arrows in Figure 7 (also see Figure 1), highlighting the outflow–cloud interaction. Townsley et al. (2011, see their Figures 3 and 4) have also showed that outflows from the deeply embedded protostars are responsible for the soft X-ray emission observed in the SE part of the cloud. These outflows have created the cavities depicted by the enclosed yellow contours (Figure 1). Interestingly, the directions of the expanding I-fronts and/or outflowing gas, as depicted by the white arrows (Figure 7), follow the B-field orientations.

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B-fields are compressed along the rim of the BRC (located inside the white box in Figure 7); more details on these are addressed in Appendix B.

To test whether B-fields play an active role in the formation of bipolar bubbles, it is essential to estimate the B-field strength by using the Chandrasekhar & Fermi (1953) relation (the CF method). For this purpose, below we determine the dispersion in θ(H) for the BG stars, the gas velocity dispersion using CO data, and the dust and gas volume density using Herschel data.

4.3.1. Dispersion in Polarization Angles: ${\sigma }_{\theta (H)}$

The presence of multiple components of B-fields in RCW 57A can be seen from the H-band polarization vector map overlaid on the ¹³CO(1 – 0) (Purcell et al. 2009) total integrated intensity image (Figure 8) and the histogram of θ(H) (continuous histogram in Figure 6(d)). Each component follows its own spatial distribution and exhibits its own θ(H) distribution and dispersion. For this reason, we divided the observed area into five regions, named A, B, C, D, and E, as shown in Figure 8 and Table 2. The spatial extent of each region is visually chosen in such a way that it should not include multiple components of θ(H). This criterion constrains the dispersion of θ(H) to be less than 25° (Ostriker et al. 2001) in order to apply the CF method to estimate the B-field strength. Some portions are not included because they either have polarization data but not CO data (the area to the right of the C region), or have CO data but multiple θ(H) distributions (area slightly above the E region), or they contain few randomly oriented vectors (area distributed between the D and E regions). We believe that the bias involved in the selection of the five regions may not have significant impact on the final scientific results.

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Table 2.  Central Coordinates, Widths, Number of Stars, Mean (${\mu }_{\theta (H)}$) and Dispersion (${\sigma }_{\theta (H)}$) in Polarization Angles (Using Gaussian Fitting), Velocity Dispersion (${\sigma }_{{V}_{\mathrm{LSR}}}$) Using ¹³CO(1 – 0) Data, Volume Density ($n({{\rm{H}}}_{2})$) Using Herschel Data and Plummer-like Profile Fitting on Column Density Maps, and Magnetic Field Strength Estimated using the Chandrasekhar–Fermi Method for Regions A, B, C, D and E

Region	R.A. (J2000)	Decl. (J2000)	Width in R.A.	Width in Decl.	No. of Stars	${\mu }_{\theta (H)}$	${\sigma }_{\theta (H)}$	${\sigma }_{{V}_{\mathrm{LSR}}}$	$n({{\rm{H}}}_{2})$	B (CF)a	B (CF)b
	(deg)	(deg)	(arcmin)	(arcmin)		(deg)	(deg)	(km s−1)	(×103 cm−3)	(μG)	(μG)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
A	168.0640	−61.2732	1.35	1.87	7	26 ± 6	10 ± 7	0.8 ± 0.1	5.15 ± 0.68	123 ± 89	123 ± 21
B	168.0088	−61.2763	1.76	2.24	24	164 ± 3	16 ± 3	1.1 ± 0.1	3.51 ± 0.41	89 ± 21	89 ± 13
C	167.9485	−61.2594	1.65	2.54	20	153 ± 2	11 ± 3	1.0 ± 0.2	1.01 ± 0.09	63 ± 23	63 ± 15
D	168.0562	−61.3415	2.99	3.48	27	132 ± 2	14 ± 3	1.4 ± 0.3	2.52 ± 0.21	108 ± 36	108 ± 27
E	167.8658	−61.3180	1.53	1.53	6	74 ± 6	15 ± 10	0.9 ± 0.1	3.33 ± 0.52	74 ± 50	74 ± 8

Notes.

^aErrors in B-field strengths were estimated by propagating uncertainties in $n({{\rm{H}}}_{2})$, ${\sigma }_{\theta (H)}$, and ${\sigma }_{{V}_{\mathrm{LSR}}}$. ^bErrors in B-field strengths were estimated by propagating uncertainties only in $n({{\rm{H}}}_{2})$ and ${\sigma }_{{V}_{\mathrm{LSR}}}$.

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A Gaussian function was fit to the θ(H) distribution for each region, as shown in Figure 9. The fitted means and dispersions in polarization angles, along with their errors, are listed in columns 7 and 8 of Table 2, respectively. The mean $\theta (H)(={\mu }_{\theta (H)}$) values of regions A, B, C, D, and E are found to be 26°, 164°, 153°, 132°, and 74°, respectively. Dispersions in the θ(H) ($={\sigma }_{\theta (H)}$) of the five regions lie between 10° and 16°.

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4.3.2. Velocity Dispersion: ${\sigma }_{{V}_{\mathrm{LSR}}}$

To derive the velocity dispersion in regions A, B, C, D, and E, we used ¹³CO(1 – 0) emission line mapping (Figure 8) performed using the Mopra telescope by Purcell et al. (2009). The observed ¹³CO(1 – 0) data have a velocity resolution of 0.4 km s⁻¹ and a spatial resolution of 40''. CASA software was used to extract the mean velocity (V_LSR) versus brightness temperature (T) spectrum of each region, which is plotted in Figure 10 using small filled circles. All of the regions exhibit at least two velocity components, with clear asymmetric spectra toward higher velocities. These asymmetric, spatially extended spectra correspond to outflowing gas from the embedded YSOs, expanding I-fronts, or both. Each of these spectra (T versus V_LSR) were then fitted by a multi-Gaussian function using the custom IDL routine "gatorplot.pro."¹⁵ Details regarding this multi-Gaussian fitting are described in Appendix C.

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The resulting multi-Gaussian fitting parameters of each spectrum are presented in Table 3 and plotted with black lines in Figure 10. The resulting combined spectrum of each region, the sum of all fitted multi-Gaussians (orange line), closely match the observed spectrum. The difference between the observed and fitted spectra, the residuals, are shown with open squares and are closely distributed around zero T. Among the multiple velocity components of each region, we attribute the one related to the peak of the spectrum to the turbulent cloud component of that region (red Gaussian curve). These are used to estimate the B-field strength. The remaining Gaussian velocity components (black lines) are ascribed to the expanding I-fronts and outflowing gas. These values are also given in column 9 of Table 2.

Table 3.  Multiple Gaussian Fitted Components of the ¹³CO Brightness Temperature (T) versus V_LSR Spectra of Regions A, B, C, D, and E

No	${T}_{\mathrm{peak}}$	VLSR	σ
	(K)	(km s−1)	(km s−1)
Region A
1a	3.38 ± 0.42	−26.81 ± 0.13	0.78 ± 0.12
2	4.48 ± 0.28	−24.42 ± 0.16	1.60 ± 0.13
3	0.71 ± 0.29	−28.75 ± 0.88	1.45 ± 0.74
4	0.76 ± 0.25	−20.94 ± 0.90	1.81 ± 0.69
Region B
1a	3.34 ± 0.33	−26.46 ± 0.16	1.10 ± 0.14
2	1.43 ± 0.39	−19.93 ± 0.31	0.70 ± 0.29
3	1.27 ± 0.28	−23.13 ± 0.48	1.28 ± 0.45
4	0.39 ± 0.27	−28.95 ± 1.55	1.51 ± 1.24
5	0.74 ± 0.44	−18.53 ± 0.56	0.53 ± 0.46
6	0.44 ± 0.45	−17.09 ± 0.81	0.49 ± 0.66
Region C
1a	1.80 ± 0.46	−26.35 ± 0.29	0.99 ± 0.24
2	0.38 ± 0.28	−27.22 ± 2.21	3.27 ± 2.05
3	0.58 ± 0.31	−23.18 ± 1.03	1.35 ± 1.10
4	0.69 ± 0.33	−19.79 ± 0.66	0.91 ± 0.66
5	0.39 ± 0.45	−16.99 ± 0.78	0.48 ± 0.68
Region D
1a	3.16 ± 1.31	−25.96 ± 0.49	1.37 ± 0.34
2	1.15 ± 1.19	−26.27 ± 1.45	1.72 ± 1.07
3	1.54 ± 0.30	−21.24 ± 0.44	1.57 ± 0.39
4	1.15 ± 0.42	−23.21 ± 0.38	0.77 ± 0.35
5	0.72 ± 0.29	−18.20 ± 0.80	1.34 ± 0.64
Region E
1a	6.05 ± 0.38	−23.04 ± 0.08	0.87 ± 0.07
2	3.98 ± 0.30	−25.23 ± 0.14	1.19 ± 0.12
3	0.68 ± 0.24	−20.34 ± 1.08	2.05 ± 0.96

Note.

^aThese Gaussian spectra correspond to the cloud velocity and are shown by the thick red lines in Figure 10. The gas velocity dispersion (σ) and error corresponding to the cloud component for each region are also quoted in column 9 of Table 2.

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The dashed line drawn at V_LSR = −26.5 km s⁻¹ (Figure 10) corresponds to the line center velocity over the areas covered by regions A, B, C, and D of RCW 57A. This V_LSR = −26.5 km s⁻¹ component closely matches the center of the red Gaussian components of all regions, except for region E. However, based on the dense gas tracers (NH₃, N₂H⁺, and CS), Purcell et al. (2009) witnessed that the peak V_LSR of the filament remained constant around −24 km s⁻¹ (see their Figure 13), which is slightly different from V_LSR = −26.5 km s⁻¹. This is mainly because of the following reasons: (a) CO is optically thick and hence traces the less dense outer parts of the cloud and (b) the regions A, B, C, and D, located slightly away from the cloud center, contain less dense gas that is influenced by the H ii region.

Below, we try to resolve and quantify the contributions from the turbulent cloud component, outflowing gas, and expanding I-front using P–V diagrams. P–V diagrams are useful diagnostics of gas kinematics in star-forming molecular clouds (e.g., Purcell et al. 2009; Zhang et al. 2016). Figures 11(a) and (b) show the P–V diagrams corresponding to the two cuts shown and labeled "1" and "2," respectively, in Figure 8. Cut "1" is along the orientation of the expanding I-front or outflowing gas (parallel to the minor axis of the filament), and cut "2" is along the major axis of the filament.

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The velocity range over the whole region, based on the extent of the contours shown in Figures 11(a) and (b), spans ≃−28.5 to ≃−16.5 km s⁻¹ with width ΔV ≃ 12 km s⁻¹. This implies that the entire region is dynamically active under the influence of the H ii region. However, among all parts of the cloud that we observed, one of the most quiescent clumps, S4 (André et al. 2008; Purcell et al. 2009), is situated to the SE of the filament. This clump is situated at ∼250'' and at ∼−26.5 km s⁻¹ in Figure 11(b). The dust temperature T_d (∼19–24 K; André et al. 2008) and kinetic temperature T_k (∼15–25 K; Purcell et al. 2009) of the cores in S4 suggest that this clump is dynamically quiescent as it is far from the H ii region. The gas velocity around this clump spans over ∼−25 to ∼−28 km s⁻¹ (centered at ∼−26.5 km s⁻¹) and a width of 2–3 km s⁻¹ (Figure 11(b)). Therefore, this velocity component at ∼−26.5 km s⁻¹  is considered the cloud V_LSR component. Turbulent velocity dispersions of the A, B, C, D, and E regions also lie in the similar range of 2–3 km s⁻¹ as noted in Table 3. According to the collect and collapse model of triggered star formation (see Torii et al. 2015 and references therein), the velocity separation due to the expanding I-front based on the P−V diagrams is ∼4 km s⁻¹. Therefore, the outflowing gas may have a remaining contribution of ∼5–6 km s⁻¹ in addition to the cloud turbulent component of ∼2–3 km s⁻¹.

Below, we decompose the relative contributions of the various velocity components in each region. In Figure 11(a), there exist two prominent redshifted, high-velocity components with peak intensities at ≃−20 km s⁻¹ and ≃−23 km s⁻¹. These components are concentrated close to the cloud center. While the former component is attributed to the outflowing gas, the latter is attributed to the expanding I-front. The signatures of both components prevail in the A, B, C, and D regions. However, as shown in the bottom panel of Figure 10, the E region seems to be less influenced by the above two components, but it has two other prominent components: (a) ∼−25 km s⁻¹, related to the expanding I-front, and (b) ∼−23 km s⁻¹, attributed to the turbulent cloud region. Moreover, spatially, the E region, in comparison to the others, is located far from the area influenced by the outflowing gas as depicted by the white arrows (cf. Figure 7). This implies that the E region, containing a BRC, has a contribution from the expanding I-fronts alone, while the rest of the regions had influences from both expanding I-fronts and outflowing gas. Therefore, the gas velocity dispersion due to the cloud turbulent component (red lines in Figure 10) is well-decomposed from the other components using multi-Gaussian spectrum fitting.

4.3.3. Number Density: $n({{\rm{H}}}_{2})$

Herschel PACS (Poglitsch et al. 2010) 160 μm and SPIRE (Griffin et al. 2010) 250, 350, and 500 μm images of RCW 57A were used to construct a dust column density map using a modified blackbody function (details are given in Appendix D). The resolution of the final column density map is 364. To obtain the number densities, we further used Plummer-like profile fitting on the column density profiles to obtain the volume density map as described below.

To construct the column density ($N({{\rm{H}}}_{2})$) profiles, first we manually identify the cloud spine using the pixels that have maximum column densities and are distributed along the filament. Thus, the identified spine, depicted by the green squares in Figure 12(c), divides the entire cloud region into two parts, the NW and SE. Second, for each spine element, we identify the $N({{\rm{H}}}_{2})$ profile elements distributed on a line that bisects the filament long axis and passes through that spine element. The dimensions of the spine elements as well as the $N({{\rm{H}}}_{2})$ profile elements are chosen to be 364 × 364. To achieve Nyquist sampling, the separation between adjacent elements was chosen as 182. Third, we constructed $N({{\rm{H}}}_{2})$ profiles as a function of projected distances from the filament spine elements toward both the NW and SE regions; they are plotted using gray circles in Figures 12(a) and (b), respectively. Every point and its uncertainty, in these plots correspond to the mean and standard deviation of the column density values in a particular $N({{\rm{H}}}_{2})$ profile element. The mean column density profiles, using distance-wise averaged column densities of the $N({{\rm{H}}}_{2})$ profile elements distributed parallel to the spine, are shown by the red filled circles. Similarly, the error bars correspond to the standard deviations in the corresponding mean column densities of the $N({{\rm{H}}}_{2})$ profile elements.

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Assuming that the filament follows an idealized cylindrical model, we extracted the volume density (n(r)) profile corresponding to each $N({{\rm{H}}}_{2})$ profile by using the Plummer-like profile (Nutter et al. 2008; Arzoumanian et al. 2011; Juvela et al. 2012; Palmeirim et al. 2013) fit to the $N({{\rm{H}}}_{2})$ profile,

$$\begin{eqnarray}&&n(r)=\displaystyle \frac{{n}_{c}}{{[1+{(r/{R}_{\mathrm{flat}})}^{2}]}^{(p/2)}},\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&N(r)=\displaystyle \frac{{A}_{p}{n}_{c}{R}_{\mathrm{flat}}}{{[1+{(r/{R}_{\mathrm{flat}})}^{2}]}^{(p-1)/2}}.\end{eqnarray} \tag{ 7 }$$

The factor A_p = π is estimated using the equation ${A}_{p}={\int }_{-\infty }^{+\infty }{[{(1+{u}^{2})}^{p/2}\cos i]}^{-1}{du}$ (Arzoumanian et al. 2011) and by assuming that the filament is on the plane of the sky, implying an inclination angle of i = 0, and p = 2. In Equation (7), N(r) is the column density profile as a function of offset distance (r) from the cloud spine. The fitting was performed using the IDL mpfit nonlinear least-squares fitting program (Markwardt 2009), and it extracted three parameters: (i) n_c, the central mean volume density of the spine point, (ii) R_flat, the radius within which the $N({{\rm{H}}}_{2})$ profile is flat, and (iii) p, the power-law index that determines the slope of the power law falling beyond R_flat. The Plummer-like profile fit was performed only to the data spanning to ∼5 pc (7.3 arcmin) from the spine, beyond which the background column density dominates (horizontal dashed lines in Figures 12(a) and (b)). The fitted values of n_c, R_flat, and p are (7.6 ± 1.3) × 10⁴ cm⁻³, 0.24 ± 0.11 pc, and 2.1 ± 0.1 for the NW part (Figure 12(a)), and (5.1 ± 0.9) × 10⁴ cm⁻³, 0.37 ± 0.18 pc, and 2.0 ± 0.1 for the SE part (Figure 12(b)). These fit results, as indicated in the plots, are similar.

The volume density map, created using the n(r) profiles of all filament spine elements, is shown in Figure 12(c). Since we considered the spine point on the filament as the zeroth element while performing Plummer-like profile fitting for both the NW and SE regions, each spine point will have two volume density values and are averaged in the final map. The minimum and maximum $n({{\rm{H}}}_{2})$ values on the filament spine lie between 2.48 × 10³ cm⁻³ and 1.52 × 10⁵ cm⁻³. The mean $n({{\rm{H}}}_{2})$ values for pixels at the extreme end of the NW and SE regions are 111 ± 26 cm⁻³ and 228 ± 74 cm⁻³, respectively. This implies that RCW 57A is still embedded in a diffuse background cloud.

We found that more than 95% of the polarization vectors are centered outside of the blue isodensity contour corresponding to the volume density $n({{\rm{H}}}_{2})\,=$ 13,000 cm⁻³. It implies that our NIR polarimetry fails to trace adequately the highly extincted parts as shown in Figure 12(c). Therefore, we exclude the pixels with n ≥ 13,000 cm⁻³ while estimating the mean volume densities in regions A, B, C, D, and E. The means and Poisson errors (standard deviation divided by the square root of the number of measurements) of the volume densities for the five regions (A, B, C, D, and E) are estimated and are listed in column 10 of Table 2. More details on producing the volume density map from the column density can also be found in Smith et al. (2014) and Hoq et al. (2017).

It should be noted here that there exist 12 stars within the high column density regions (within the contour of the volume density $n({{\rm{H}}}_{2})\,=$ 13,000 cm⁻³ or column density $N({{\rm{H}}}_{2})\simeq 1\times {10}^{23}$ cm⁻²). Only one star (star ID = 290; Table 1) is found to lie on the intrinsic locus of the late-type stars in the NIR TCD (with [J − H] = 0.56 ± 0.01 and $[H-{K}_{s}]=0.19\pm 0.01$). The polarization characteristics (P(H) = 0.55 ± 0.13 and θ(H) = 68.5 ± 6.5) of this star are consistent with those of the FG stars. Although this star is classified as a BG star based on its $[H-{K}_{s}]\gt 0.15$, this star could be located close, but foreground, to the cloud. The remaining 11 stars are consistent with either reddened cluster members embedded in the cloud or reddened field stars lying in the outskirts of the cloud but projected on the high-density parts of the cloud region.

Using the dispersion in the polarization angles (${\sigma }_{\theta (H)};$ column 8 of Table 2), velocity dispersion values (${\sigma }_{{V}_{\mathrm{LSR}}};$ column 9 of Table 2), and mean volume densities ($n({{\rm{H}}}_{2}$); column 10 of Table 2) for the five regions of RCW 57A, we estimated the B-field strength using the Chandrasekhar & Fermi (1953) relation,

$$\begin{eqnarray}&&B=Q\,\sqrt{4\pi \rho }\,\left(\displaystyle \frac{{\sigma }_{{V}_{\mathrm{LSR}}}}{{\sigma }_{{\theta }_{{\rm{H}}}}}\right).\end{eqnarray} \tag{ 8 }$$

The mass density $\rho =n({{\rm{H}}}_{2}){m}_{H}{\mu }_{{{\rm{H}}}_{2}}$, where $n({{\rm{H}}}_{2})$ is the hydrogen volume density, m_H is the mass of the hydrogen atom, and ${\mu }_{{{\rm{H}}}_{2}}\,\approx 2.8$ is the mean molecular weight per hydrogen molecule and includes the contribution from helium. The correction factor Q = 0.5 is included based on the studies using synthetic polarization maps generated from numerically simulated clouds (Heitsch et al. 2001; Ostriker et al. 2001), which suggest that for ${\sigma }_{\theta }\leqslant 25^\circ$, the B-field strength is uncertain by a factor of two. Uncertainties in the B-field strength were estimated by propagating the errors in ${\sigma }_{\theta (H)}$, ${\sigma }_{{V}_{\mathrm{LSR}}}$, and $n({{\rm{H}}}_{2})$ values. The estimated B-field strengths and corresponding uncertainties are given in column 11 of Table 2. The uncertainties in the B-fields, derived by propagating errors in $n({{\rm{H}}}_{2})$, ${\sigma }_{{V}_{\mathrm{LSR}}}$, and ${\sigma }_{{\theta }_{{\rm{H}}}}$, are considerably large (see column 11 of Table 2). We also estimate the B-field strengths and corresponding uncertainties without considering errors in the ${\sigma }_{{\theta }_{{\rm{H}}}}$ values. The resultant B-field strengths, given in column 12 of Table 2, for regions A, B, C, D, and E are 123 ± 21 μG, 89 ± 13 μG, 63 ± 15 μG, 108 ± 27 μG, and 74 ± 8 μG, respectively. The mean B-field strength over the five regions is estimated to be 91 ± 8 μG.

To understand the importance of B-fields with respect to turbulence, we estimated the magnetic pressure and turbulent pressure using the relations ${P}_{B}={B}^{2}/8\pi$ and ${P}_{\mathrm{turb}}=\rho {{\sigma }_{\mathrm{turb}}}^{2}$ (where ${\sigma }_{\mathrm{turb}}={\sigma }_{{V}_{\mathrm{LSR}}}$ is given in Table 2), respectively, and the results are given in Table 4. The mean P_B/${P}_{\mathrm{turb}}$ is estimated to be 2.4 ± 0.6. These estimated parameters suggest that the magnetic pressure is more than the turbulent pressure at least by a factor of ∼2 in all five regions, signifying the dominant role of B-fields over turbulence. For the five regions together, the mean magnetic and turbulent pressures are estimated to be (35 ± 7) × 10⁻¹¹ (dyn cm⁻²) and (15 ± 3) × 10⁻¹¹ (dyn cm⁻²), respectively. Danziger (1974) estimated the mean electron density, n_e, to be ∼20 cm⁻³, and mean electron temperature, T_e, to be ∼10,000 K for the RCW 57A region. For the entire region, the thermal pressure P_th using the relation ${P}_{\mathrm{th}}\simeq 2{n}_{e}{{kT}}_{e}$ (where k is the Boltzmann constant) is estimated to be 6 × 10⁻¹¹ dyn cm⁻², which is smaller than the mean magnetic pressure. The ratio of the mean magnetic to thermal pressure, ${P}_{B}/{P}_{\mathrm{th}}$, is found to be ∼6. A lower value of P_th again suggests dominant magnetic pressure over thermal pressure. Therefore, in comparison to thermal and turbulent pressures, magnetic pressure plays a crucial role in guiding the expanding I-fronts or outflowing gas in RCW 57A. The implications on the relative importance of B-field pressure in comparison to turbulent and thermal pressures on the formation and evolution of bipolar bubble is discussed in the Section 5.3.

Table 4.  Magnetic and Turbulent Pressures along with Their Uncertainties in Regions A, B, C, D, and E

Region	PB	${P}_{\mathrm{turb}}$	PB/${P}_{\mathrm{turb}}$
	10−11 (dyn cm−2)	10−11 (dyn cm−2)
(1)	(2)	(3)	(4)
A	60 ± 20	15 ± 5	4 ± 2
B	32 ± 9	20 ± 6	2 ± 1
C	16 ± 8	5 ± 2	3 ± 2
D	46 ± 23	22 ± 11	2 ± 1
E	22 ± 5	11 ± 3	2 ± 1

Note. In this table, the B-field pressure values and their uncertainties are derived using the B-field strength and corresponding uncertainties given in column 12 of Table 2.

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Based on the CO and Spitzer images, number of stars with polarization detection, and the column density profiles we infer for the distribution of gas and dust in RCW 57A. The quiescent molecular cloud gas traced by CO (red background in Figure 7) is absent at the footpoints of, as well as along, the bipolar bubbles. Moreover, the spatial distributions of the CO gas and the bubbles (green background in the Spitzer images) appear to be anti-coincident with each other. This implies that cloud material has either been eroded or blown out by the expanding I-fronts, outflowing gas, or strong stellar winds from the embedded early-type protostars. Therefore, the CO and Spitzer maps suggest that the bipolar bubble likely blown by the massive stars emanated stellar winds, outflowing gas, and expanding I-fronts (see Townsley 2009).

Although the SE bubble appears to be closed toward the SE, the NW bubble is widely extended toward the NW (Figures 1 and 7) and exhibits large-scale loops, likely due to the anisotropic distribution of material toward the SE and NW regions. This is further corroborated by the following facts. Although the area covered together by regions A, B, and C (located in the NW) is similar to that covered by D (located in SE), the total number of background stars with polarization detection (51) in A, B, and C exceeds that in D (21; see Table 2 and Figures 7 and 8). Furthermore, the mean $N({{\rm{H}}}_{2})$ profiles suggest that the anisotropic distribution of gas and dust in RCW 57A i.e., the SE part ($N({{\rm{H}}}_{2})\sim 1.3\times {10}^{22}$ cm⁻²), has relatively more background material than in the NW ($N({{\rm{H}}}_{2})\sim 0.70\times {10}^{22}$ cm⁻²) as depicted by the dashed lines in Figures 12(a) and (b). A similar asymmetric distribution of column density profiles was seen toward other regions (e.g., the Taurus B211/3 filament; Palmeirim et al. 2013).

An X-ray study (Townsley et al. 2011, see their Figures 3 and 4) revealed the presence of an OB stellar association (NGC 3576OB) toward the NW of the main embedded star-forming region RCW 57A (or NGC 3576 GHIIR). Furthermore, the presence of hard X-ray emission and a pulsar (+PSR J1112–6103 and PWN) in the NGC 3576OB region suggests the fast occurrence of supernova events. This supernova, together with the OB stars of the NGC 3576OB stellar association, most probably evacuated the material in the NW part of RCW 57A. This could be the plausible reason behind the low-density material observed in the NW region. The observed large-scale loops in the NE possibly formed due to the newly formed material as a result of the expanding I-fronts driven by the embedded massive protostars of RCW 57A.

A high-velocity outflow signature is discernible close to eastward from the center, while the same feature is absent westward as shown in Figure 11(b). This could be attributed to the confined ionized gas flow toward the west from the center, possibly due to the presence of a dense clump (thin black contours in Figure 7). The high-velocity component is only seen toward the east, which implies a dearth of dense material there, and hence, the ionized gas expanded with relatively more velocity. de Pree et al. (1999) and Purcell et al. (2009) have also shown that the H ii region expands more freely toward the east and is bounded on the west.

We fitted a Gaussian to the mean column density profiles spread over ∼5 pc radii, and the resultant FWHM, corresponding to the filament characteristic width, is found to be 1.55 ± 0.09 pc. However, a constant filament width of ∼0.1 pc was determined for the central dense sections of the filaments of nearby star-forming regions in the Herschel Gould Belt survey by fitting a Gaussian to the inner sections (radii up to 0.3–0.4 pc) of the filaments (Arzoumanian et al. 2011). Therefore, we fit a Gaussian to the inner 1 pc width of the clubbed mean column density profiles of the NW and SE regions, and the resultant σ and FWHM are found to be 0.21 ± 0.08 pc and 0.50 ± 0.18 pc, respectively. Within the error, the filament width (0.50 pc; green lines in Figures 12(a) and (b)) of RCW 57A is higher than the constant filament width of ∼0.1 pc (Arzoumanian et al. 2011). Filament widths larger than 0.1 pc (spanning over 0.1 –1 pc with typical widths of ∼0.2–0.3 pc) have also been witnessed in a number of studies (e.g., Hennemann et al. 2012; Juvela et al. 2012). However, the filament width of RCW 57A has not been resolved because of the limited resolution (364 corresponds to 0.42 pc as shown by the cyan lines) of the column density map.

The mean power-law index p = 2.02 ± 0.05, derived from the Plummer-like profile fitting for RCW 57A, is consistent with other studies (Arzoumanian et al. 2011; Juvela et al. 2012; Palmeirim et al. 2013; Hoq et al. 2017). A similar value of this index (p = 2) is expected if the filament is supported by B-fields (Hennebelle 2003; Tilley & Pudritz 2003), in accordance with our observational results supporting the active role of B-fields in the formation and evolution of filaments, as described in Section 5.3 below.

Based on the morphological correlations among the (i) dense filamentary cloud structure seen in the submillimeter (in the 0.87 mm ATLASGAL and 1.1 mm SIMBA dust continuum emission maps), (ii) bipolar bubble seen in mid-infrared images, and (iii) B-field morphology of RCW 57A traced by NIR polarimetry, we postulate a scenario illustrated by the four schemas in Figure 13. Each schema describes our observational evidence along with our prediction at a particular evolutionary state of RCW 57A.

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Schemas A and B: Per the background star polarimetry, the filament (position angle ∼60°; Figure 7) is oriented perpendicular to the B-fields (the dominant component of θ(H) = ∼163°; Figure 6(d)). From this observational evidence, we speculate the formation history of the filament and the role of the B-fields in them. Initially, a subcritical molecular cloud is supported by the B-fields, as shown in schema A; it is later compressed into a filamentary molecular cloud due to B-field-guided gravitational contraction as per schema B.

Although the role of B-fields in the formation and evolution of filamentary molecular clouds is still a matter of debate, their morphology with respect to the geometry of filaments is well established. The geometry of B-fields in a molecular cloud is mainly governed by the relative dynamical importance of magnetic forces to gravity and turbulence.

If the B-fields are dynamically unimportant compared to the turbulence, then random motions dominate the structural dynamics of the clouds, and the field lines would be dragged along the turbulent eddies (Ballesteros-Paredes et al. 1999). In that case, B-fields would exhibit chaotic or disturbed B-field structures. Based on the fact that the B-field structure is more regular with an hourglass morphology and that B-field pressure dominates over turbulent pressure (see Section 4.4), we do not favor a weak B-field scenario in RCW 57A.

If B-fields are dynamically important, then the support against gravity in the molecular cloud is rendered predominantly by the B-fields. In this case, B-fields would be aligned, preferentially, perpendicular to the major axis of the cloud (Mouschovias 1978). This is expected as the cloud tends to contract more in the direction parallel to the B-fields than in the direction perpendicular to it. Recent polarization studies have also demonstrated that B-fields are well-ordered near dense filaments and are perpendicular to their long axis (Moneti et al. 1984; Pereyra & Magalhães 2004; Alves et al. 2008; Chapman et al. 2011; Sugitani et al. 2011; Li et al. 2013; Palmeirim et al. 2013; Franco & Alves 2015; Cox et al. 2016; Planck Collaboration et al. 2016a). Numerical simulations have also shown that filamentary molecular clouds form by gravitational compression guided by B-fields (e.g., Nakamura & Li 2008; Li et al. 2013). Therefore, we believe that the filament in RCW 57A could have formed due to the gravitational compression of cloud along the B-fields.

Schema C: Due to the accumulation of more mass at the center, the filament reaches a supercritical state from its initial B-field-supported subcritical state. B-fields are dragged along the gravity-driven material contraction toward the strong gravitational potential at the cloud center, and subsequently they are configured into an hourglass morphology (schema C). Similar hourglass morphologies of B-fields were observed toward the Orion molecular cloud 1 (Schleuning 1998; Vaillancourt et al. 2008; Ward-Thompson et al. 2017) and Serpens cloud core (Sugitani et al. 2010), signifying ongoing gravitational collapse.

In RCW 57A, B-fields in some portions exhibit clear evidence for hourglass morphology. In the NE part of the filament (covered by two regions, A and D; see Figure 8), B-fields are bent by ∼90° as the mean θ(H) for region A is ∼26° and ∼132° for region D (see column 7 of Table 2). Therefore, B-fields are distorted in the NE part of the filament, signifying a collapsing filamentary molecular cloud. However, this similar distortion is not clearly apparent in the SW part of the filament, partly because the light from the background stars is obscured by the dense cloud material. Therefore, the NIR polarimetric observations were unable to detect sufficient numbers of background stars in the SW part to delineate the detailed structure of the B-field there.

Schema D: Gravitational instability caused the filament fragmentation into seven cores (blue diamonds in Figure 7), evident from the dust continuum emission maps (André et al. 2008) as well as dense gas tracers (Purcell et al. 2009). Star formation began at the central region due to the onset of gravitational collapse, during which B-fields were not strong enough to stop the cloud collapse. Ionization and shock fronts, driven by the H ii region, are propagated in to the ambient medium. Interaction between the H ii region and dense cloud material is evident from Figure 7, and as a consequence of this, several IRSs are formed at the boundary of the interaction, signifying triggered star formation at the edges of the H ii region of RCW 57A.

Our observational results suggest that B-field pressure dominates over thermal pressure (see Section 4.4), implying an active role of B-fields in governing the feedback processes. Since B-fields are observed to be responsible for the formation of the filament in RCW 57A (Schema B), it is expected that B-fields anchored through the filament may also have a significant influence on the expanding I-fronts. In addition to the anisotropic pressure that the I-fronts experience while they expand anisotropically in the filament, they undergo an additional anisotropic pressure in the presence of strong B-fields (Bisnovatyi-Kogan & Silich 1995). As a result, I-fronts experience accelerated flows along the B-fields (i.e., low pressure) and hindered flows (i.e., high pressure) in the direction perpendicular to the B-fields (Tomisaka 1992; Gaensler 1998; Pavel & Clemens 2012; van Marle et al. 2015). Therefore, I-fronts expand a greater extent along the hourglass shaped B-fields, and eventually form the bipolar bubble as shown in schema D of Figure 13.

Similar applications for the influence of B-fields on I-fronts have been found in other environments. Bubbles around young H ii regions and supernova remnants have been found to be elongated along the Galactic B-field orientation (Tomisaka 1992; Gaensler 1998; Pavel & Clemens 2012). Falceta-Gonçalves & Monteiro (2014) showed that strong B-fields can lead to the formation of a bipolar planetary nebula. van Marle et al. (2015) investigated the influence of B-fields on the expanding circumstellar bubble around a massive star using magnetohydrodynamical simulations. They found that that the weak B-fields cause circumstellar bubbles to become an ovoid, rather than a spherical, shape. On the other hand, strong B-fields lead to the formation of a tube-like bubble.

Therefore, according to the proposed evolutionary scenario (Figure 13), initially, B-fields in molecular clouds may be important in guiding the gravitational compression of cloud material to form a filament. In the later stage, hourglass B-fields might have guided the expansion and propagation of I-fronts to form the bipolar bubble.

Based on the presence of 29 NIR-excess sources (Persi et al. 1994) and the finding of 51 stars earlier than A0 (Maercker et al. 2006), it was found that RCW 57A hosts a massive infrared cluster at the center (within the cyan contour enclosing the H ii region in Figure 7) of the filament. Furthermore, the Chandra X-ray survey by Townsley et al. (2014; see also Townsley et al. 2011) provided the first detailed census of the members in the embedded massive young stellar cluster (MYSC; see their Figures 9(c) and (d)). Their study unraveled many highly obscured but luminous X-ray sources (one source exhibits photon pile-up) that are likely the cluster's massive stars ionizing its H ii region. This highly obscured X-ray cluster is situated at the SW edge of the infrared cluster. The formation history of this cluster is poorly understood. Below, we propose that the large-scale B-fields traced by NIR polarimetry may also govern their crucial role in the formation of this massive cluster.

Initial turbulence in the molecular clouds may decay rapidly. To maintain turbulence in the cloud and hence to maintain cloud stability against rapid gravitational collapse, supersonic turbulence should be replenished by means of protostellar outflows. In the model of outflow-driven turbulence cluster formation (Li & Nakamura 2006; Nakamura & Li 2007, 2011, and references therein), B-fields are dynamically important in governing two processes. First, the outflow energy and momentum are allowed by the B-fields to escape from the central star-forming region into the ambient cloud medium. Second, B-fields guide the gravitational infalling material (just outside of the outflow zone) toward the central region. Therefore, the competition between protostellar outflow-driven turbulence and gravitational infall regulates the formation of stellar clusters in the presence of dynamically important B-fields. Observational signatures toward the Serpens cloud core (Sugitani et al. 2010) are in accordance with the scenario of a B-field regulated cluster formation: (a) B-fields should align with the short axis of the filament, outflows, and gravitational infall motions, and (b) outflow-injected energy should be more than the dissipated turbulence energy in order to maintain the supersonic turbulence in the cloud. In the case of RCW 57A, the presence of a deeply embedded cluster and the alignment of the I-fronts, outflowing gas, and bipolar bubbles with the NIR-traced B-fields trace the preexisting conditions favoring protostellar outflow-driven turbulence cluster formation in the presence of dynamically strong B-fields.