Magnetic field structure in Serpens South

Abstract

We made near-infrared polarimetric observations toward Serpens South. This region contains three dense filaments that are roughly parallel to one another. Using the histogram of relative orientations, the three filaments are found to be roughly perpendicular to the global magnetic field. The morphology of the plane-of-sky (POS) magnetic field and molecular gas suggests that the magnetic field plays an important role in the filament formation and evolution. Applying the Davis–Chandrasekhar–Fermi method, the POS magnetic field strengths are estimated to be 10–80|$\, \mu$|G. The evaluated mass-to-flux ratios indicate that the center filament is magnetically supercritical, while the others are approximately magnetically critical. We speculate that the filaments are formed by fragmentation of a sheet-like cloud that was created through the gravitational contraction of a magnetized, turbulent cloud.

1 Introduction

Magnetic fields are believed to play an important role in the formation and evolution of molecular clouds (e.g., Shu et al. 1987; Nakamura & Li 2008; Crutcher 2012; Hull et al. 2013; Li et al. 2015). Herschel observations have revealed that filaments are the basic units of molecular clouds (e.g., André et al. 2010; Men’shchikov et al. 2010), and that most of the self-gravitating dense cores are distributed along the dense filaments (e.g., André et al. 2010; Könyves et al. 2015). Understanding the process of filament formation and evolution is important to clarify the process of dense cores where stars form. Several studies have attempted to find the relationship between the filaments and magnetic fields in molecular clouds (Soler et al. 2013; Kusune et al. 2016; Fissel et al. 2018).

For example, using the Planck polarization data, Soler et al. (2013) found that the density gradients tend to be parallel to the local magnetic field in high-density regions, implying that the filaments are preferentially perpendicular to the magnetic fields. On the basis of near-infrared (NIR) polarimetry, Kusune et al. (2016) revealed that the dense filaments in the Vela C molecular cloud complex tend to be perpendicular to the global magnetic field direction, although the relationship between the cloud structure and the magnetic field significantly varies from region to region (see also Kusune et al. 2018). Comparing the magnetic field orientation and various molecular line emission distributions, Fissel et al. (2018) found that the magnetic field orientation in Vela C is parallel to the cloud density gradients in the low-density area, whereas it tends to be perpendicular in the high-density area. Such a gradual transition in the magnetic field orientation may indicate that the magnetic fields are strong enough to influence the cloud dynamics. In the present paper, we search for further evidence to show the dynamical importance of magnetic fields in cloud structure formation in the nearby active cluster-forming region, Serpens South.

The Serpens South region contains many self-gravitating filaments, along which a number of prestellar and protostellar cores have formed (André et al. 2010; Maury et al. 2011). A bright cluster of low-mass stars is located in the southern part of the main filaments (Gutermuth et al. 2008; André et al. 2010; Maury et al. 2011). Recently, the distances of the Serpens and W 40 regions in the Aquila complex were measured to be |$436.0\, \pm \, 9.2$| pc, on the basis of multi-epoch Very Long Baseline Array (VLBA) observations (Ortiz-León et al. 2017). Assuming that Serpens South is associated with W 40, we adopt the distance of |$436.0\, \pm \, 9.2$| pc for Serpens South in the present paper. Gutermuth et al. (2008) determined the high star formation rate of |${\sim } 90\, M_{\odot }\:$|Myr⁻¹ and young age of 2 ± 1 × 10⁵ yr of the Serpens South cluster. Maury et al. (2011) identified 57 protostellar objects with |$M\gt 0.1\, M_{\odot}$| in the cluster-forming filament. On the other hand, in the associated filaments, the star formation rate outside the Serpens South cluster is significantly lower than that in the central cluster (Maury et al. 2011).

Serpens South is embedded in a much more massive molecular cloud, whose large-scale molecular distribution was recently revealed by Nakamura et al. (2017). In addition to Serpens South, there is another active star-forming site known as W 40 in the larger cloud. W 40 is an H ii region (e.g., Zeilik & Lada 1978; Vallée 1987) probably lying close to the edge of the larger cloud, and is located only ∼|${20^{\prime }}$| away from Serpens South on the sky. Shimoikura et al. (2015) identified several dense clumps around W 40 through ¹²CO (J = 3–2) and HCO⁺ (J = 4–3) observations, and more recently Shimoikura et al. (2019b) suggested that W 40 and Serpens South are located in the same system and that the expanding H ii region of W 40 is interacting with Serpens South, possibly triggering the cluster formation therein.

Sugitani et al. (2011) first revealed that the global magnetic field is perpendicular to the main filament containing the central cluster, and that the magnetic field appears to play a crucial role in the cloud evolution. They also found that in the southern part the magnetic field is curved toward the cluster, and suggested that this is due to gravitational contraction along the main filament. However, Herschel observations revealed that the filamentary structure is more spatially extended, and the relationship between the filaments and the magnetic field remains uncertain. Thus, we conducted wide-field NIR polarimetric observations which cover the whole filamentary structure in this region in an attempt to uncover how the magnetic fields influence the Serpens South filaments.

Shimoikura et al. (2019b) carried out molecular line observations with the ¹²CO (J = 1–2), ¹³CO (J = 1–2), and C¹⁸O (J = 1–2) emission lines using the 45 m telescope at the Nobeyama Radio Observatory (NRO). The molecular line observations were made as part of the “Star Formation Legacy Project” at the NRO. An overview of the project will be given in another article (Nakamura et al. 2019a). The detailed observational results for individual regions will be described in other articles (Shimoikura et al. 2019a; Tanabe et al. 2019; Dobashi et al. 2019b; Nakamura et al. 2019b).

The present paper describes the results of NIR polarimetry toward Serpens South. In section 2, we describe the details of the CO and NIR observations and their data reduction. In section 3, we present the plane-of-sky (POS) magnetic field structure. In section 4, we show the relationship between the magnetic field and the cloud structure. In section 5, we derive the POS magnetic field strength of Serpens South and discuss the role of the magnetic field in the formation of Serpens South filamentary clouds. In section 6, we suggest a model for the filament formation and the evolution of Serpens South.

2 Observations and data reduction

2.1 C¹⁸O observations

We have carried out observations of the ¹²CO (J = 1–0), ¹³CO (J = 1–0), C¹⁸O (J = 1–0), CCS (J_N = 9₈–8₇), and N₂H⁺ (J = 1–0) lines toward one square degree Aquila Rift/Serpens South regions during the period of 2014 April to 2017 March in the on-the-fly mode (see Shimoikura et al. 2019b). In the present paper, we use only C¹⁸O data for Serpens South. In brief, we used the FOur-beam REciever System on the 45 m Telescope (FOREST) as a front end and the FX-type digital spectrometer SAM45 as a back end. During the observations, the system noise temperatures were in the range between 150 and 300 K at the observed elevation of El = 30°–50°. The telescope pointing was checked every 1.5 hr by observing SiO maser sources, VIII–Oph and IRC +00363, and was better than ∼|${5^{\prime \prime }}$| during the whole observing period. The rms noise levels of the final C¹⁸O data are ΔT_mb ≈ 0.3 K at a velocity resolution of 0.1 km s⁻¹.

2.2 Near-infrared polarimetric observations

JHK  _s polarimetric observations toward Serpens South were performed using the imaging polarimeter SIRPOL (polarimetry mode of the SIRIUS camera: Kandori et al. 2006) mounted on the IRSF 1.4 m telescope at the South African Astronomical Observatory. The SIRIUS camera is equipped with three 1024 × 1024 HgCdTe (HAWAII) arrays, JHK_s filters, and dichroic mirrors, which enable simultaneous JHK_s observations (Nagashima et al. 1999; Nagayama et al. 2003). The field of view at each band is ∼|${7{^{\prime}_{.}}7}$| × |${7{^{\prime}_{.}}7}$| with a pixel scale of |${0{^{\prime \prime}_{.}}45}$|⁠.

In figure 1, we show the observed area, the white dashed polygon, overlaid on the Herschel three-color composite image. We obtained 10 dithered exposures, each 15 s long, at four wave-plate angles (0°, |${22{^{\circ}_{.}}5}$|⁠, 45°, and |${67{^{\circ}_{.}}5}$| in the instrumental coordinate system) as one set of observations, and repeated it six times. The total on-target exposure time was 900 s per each wave-plate angle. Self-sky images were used for median sky subtraction. The average seeing size ranged from |${1{^{\prime \prime}_{.}}8}$| to |${3{^{\prime \prime}_{.}}1}$| at K_s during the observations. Twilight flat-field images were obtained at the beginning and/or end of the observations.

Fig. 1.

Three-color composite Herschel image of the Aquila region (250|$\, \mu$|m in red, 160|$\, \mu$|m in green, and 70|$\, \mu$|m in blue). The areas of our NIR polarimetric observations and the C¹⁸O image we used in the present paper are indicated by the white solid and dashed polygons, respectively. (Color online)

2.3 Herschel archival data

In order to reveal the cloud structure, Herschel column density maps were taken from the Herschel Gould Bert Survey Archive,¹ and are part of the Herschel Gould Belt survey (André et al. 2010; Könyves et al. 2015). The spatial resolution of the column density map is ∼|${36{^{\prime \prime}_{.}}3}$|⁠. The original column density map shows the whole Aquila region. In the present paper, we show a close-up view around Serpens South.

2.4 Data reduction of the polarimetric observations

Reduction was done in a standard way using the IRAF package. Aperture polarimetry was performed at J, H, and K_s with an aperture radius of full-width at half maximum (FWHM) size of point sources by using APHOT from the DAOPHOT package. The Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006) was used for the absolute photometric calibration. We calculated the Stokes parameters as follows:

$$\begin{eqnarray} Q&=&I_{0}-I_{45}, \end{eqnarray}$$

(1)

$$\begin{eqnarray} U&=&I_{22.5}-I_{67.5}, \end{eqnarray}$$

(2)

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

(3)

where I₀, I_22.5, I₄₅, and I_67.5 are intensities at four wave-plate angles. To obtain the Stokes parameters in the equatorial coordinate system (Q′ and U′), Q and U were rotated by 105° (Kandori et al. 2006; Kusune et al. 2015). We calculated the degree of polarization P and the polarization angle θ as follows:

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

(4)

$$\begin{eqnarray} \theta &=&\frac{1}{2}{\rm arctan}\frac{U^{\prime }}{Q^{\,{\prime }}}. \end{eqnarray}$$

(5)

The absolute accuracy of θ was estimated to be better than 3° (Kandori et al. 2006; Kusune et al. 2015). The polarization efficiencies were estimated to be 95.5%, 96.3%, and 98.5% in the J, H, and K_s bands, respectively, and the measurable polarization is ∼0.3% over the entire field of view at each band (Kandori et al. 2006). With these high polarization efficiencies and low instrument polarization, no particular corrections were made. The errors of the polarization degrees ΔP and of the polarization angles Δθ were calculated from the photometric errors, and the degrees of polarization were debiased as |$P_{\rm debias}=\sqrt{P^2-\Delta P^2}$| (Wardle & Sramek 1974). Hereafter, we use P as a substitute for this debiased value. In consideration of the above measurable polarization of ∼0.3%, for the sources with ΔP < 0.3% we adopt 0.3% as the errors of the polarization degrees when we calculate Δθ. We confirmed an agreement of polarization angles within their errors between two independent observations for almost all the stars that were located commonly in the two neighboring fields.

We measured H-band polarizations for point sources to examine the magnetic field structure. We selected sources for our polarization measurements using the following three procedures. First, we used only the sources with photometric errors of <0.1 mag. Second, for the sources detected at all bands, we excluded NIR sources with IR excess as candidates of young stellar objects (YSOs). They are defined as the sources plotted red-ward of the reddening line from the A0 star on the J − H versus H − K_s diagram, which is shown in figure 2. Here we adopt the reddening line of E(J − H)/E(H − K_s) ≈ 1.95 (Chini & Wargau 1998). The sources meeting the above condition are shown in black in figure 2. Most of them appear to be giants or reddened giants. The excluded YSO candidates are indicated by red points in figure 2. Third, we excluded the sources whose polarization degrees significantly deviate from the interstellar polarization relation, because the polarizations of such sources may not be caused by the dichroic process and therefore they are not likely to trace the magnetic field structure. Figure 3 shows the polarization degree P_H versus H − K_s color diagrams for the point sources with ΔP < 0.3%. We obtained the best-fit linear line (interstellar polarization relation), which is expressed as P_H = 2.73[(H − K_s) − 0.2], where we assumed an intrinsic color (H − K_s)₀ = 0.2 for background sources based on the model calculations by Wainscoat et al. (1992). Then we adopted as upper and lower limits of the interstellar polarization thrice and one-third of the best-fit line, respectively. We show this best-fit linear line and the upper and lower limits in figure 3, indicated by the dashed lines. With these criteria, the foreground sources, which show small polarization, are located blue-ward of the upper limit of the interstellar polarization, and thus are excluded from the sources used for our analysis. In the third procedure, we excluded nearly 15% of sources. Finally, we used the sources with P/ΔP > 3.0, which corresponds to Δθ ≈ 10°.

Fig. 2.

J − H vs. H − K_s color–color diagram toward Serpens South. The green and red curves indicate the loci of dwarfs and giants, respectively. The data for A0–M6 dwarfs and G0–M7 giants are from Bessell and Brett (1988). The blue dashed line denotes the classical T Tauri star locus of Meyer, Calvet, and Hillenbrand (1997). These loci are transformed to the 2MASS system by using the equations in the explanatory supplement (Cutri et al. 2003). YSO candidates are indicated by the red points. The black arrow shows the reddening vector of A_V = 5 mag. The three orange dashed lines are parallel to the reddening vector. (Color online)

Fig. 3.

Polarization degree in the H band vs. H − K_s color diagram for the sources having ΔP < 0.3%. The best-fit linear line obtained for the sources with H − K_s > 0.2 is shown by the solid line. The dashed lines are thrice and one-third of the best-fit line, which we adopted as the maximum and minimum polarization efficiencies, respectively.

3 Results

3.1 Cloud structure

Figure 4 shows the Herschel H₂ column density map of the Serpens South region. We identified three filaments by eye, which are indicated with the dashed lines in figure 4. Here we designate these as Filaments I, II, and III from east to west in the equatorial coordinate system. These filaments run side by side in the NW–SE direction. Filament II is a dominating filament in the Serpens South cloud. The Serpens South cluster is located at the center of Filament II.

Fig. 4.

Herschel H₂ column density map toward Serpens South. The rainbow-colored bar gives the scale of the H₂ column density (cm⁻²). We designate the three prominent filamentary structures, which are indicated by the white dashed lines, as Filaments I, II, and III. (Color online)

In the upper-left panel of figure 5, we show the C¹⁸O integrated intensity map around Serpens South. We also present the C¹⁸O channel maps in figure 5. Although a filamentary structure is not immediately evident from the integrated intensity map, it can be clearly seen in the channel maps. First, at 5.9 km s⁻¹ the southern part of Filament III appears. Then, at 6.4 km s⁻¹ the whole of Filament III is visible, and the southern part of Filament II comes into view. At 6.9 km s⁻¹ we can see all three filaments. Over 7.4 km s⁻¹ Filament III becomes invisible, while Filaments I and II are still visible. Finally, at 7.9 km s⁻¹ another component associated with Filaments I and II appears. This component is elongated in the NE–SW direction, which is almost perpendicular to the NW–SE filamentary structure. In summary, (i) Filaments I and II have nearly the same velocity (from 6.9 km s⁻¹ to 7.4 km s⁻¹), (ii) Filament III has a slightly different velocity (from 6.4 km s⁻¹ to 6.9 km s⁻¹), and (iii) another velocity component, which is elongated in the NE–SW direction, can be seen (at 7.9 km s⁻¹).

Fig. 5.

Integrated intensity map and the channel maps of C¹⁸O. The color scale units are K km s⁻¹. The integrated intensity map is shown in the upper-right panel, and the velocity range is 5.8 to 8.5 km s⁻¹ in v_LSR. The center LSR velocity of each channel map is shown on the top of each panel. The contours overlaid on all panels represent the Herschel H₂ column density map, the levels of which are 1.5 × 10²² cm⁻², 3.5 × 10²² cm⁻², and 5.5 × 10²² cm⁻². (Color online)

3.2 Magnetic field structure

Figure 6 shows the H-band polarization vector map for Serpens South, overlaid on the column density map. Since the vector maps of the J and K_s bands are largely similar to that of the H band, we use only the H-band map in the following. The length of each vector is proportional to the polarization degree, P. Figure 7 shows the histogram of polarization angle θ for the H band. The histogram has a main peak at ∼60°, indicating that the direction of the global POS magnetic field toward Serpens South is ∼60°. Since the global cloud structure is elongated from northwest to southeast, the large-scale magnetic field is roughly perpendicular to the elongation of the Serpens South cloud. Figure 7 also shows a secondary peak at ∼0°, which is mainly due to polarization vectors on the southwest region (indicated by the white arrow in figure 6).

Fig. 6.

H-band polarization vector map of the Serpens South cloud superposed on the column density map. The color bar gives the Herschel H₂ column density (cm⁻¹). The lengths of the vectors are proportional to the polarization degree. For reference, the length for the 10% polarization is shown by the white line at the bottom right. The white arrow indicates the region considered to be responsible for the small peak ∼0° of the histogram in figure 7 (see subsection 3.2), and presumably they are background components not associated with the Serpens South cloud. (Color online)

Fig. 7.

Histogram of polarization vector angles for the H band in position angle.

4 Magnetic field structure relative to filaments

We investigated the magnetic field configuration for each filament. In order to examine the relation between the magnetic field direction and the cloud column density structures, we constructed the histogram of relative orientations (HROs; Soler et al. 2013) using our H-band polarimetric data and the gradient of the gas column density estimated from the Herschel data. We calculated the column density gradient using the Gaussian derivative method following Soler et al. (2013), and then derived the angle φ between the polarization vector and the gradient vector. In the HROs, the filamentary structures of the molecular cloud can be characterized by their column density gradients. For example, a histogram peaked around 0° means that the POS magnetic field is predominantly perpendicular to the filamentary structure of the cloud, while a histogram peaked around 90° means that the POS magnetic field is predominantly parallel to the filamentary structure.

Figure 8 shows the HROs for each filament. For both Filaments I and II the HRO has a peak at ∼0°, indicating that the POS magnetic field runs perpendicularly to the column density gradients. On the other hand, for Filament III the HRO takes its maximum at ∼20°, meaning that the POS magnetic field is roughly perpendicular to the column density gradients. In summary, the POS magnetic fields around the three dominating filaments of Serpens South are perpendicular to the filamentary structures.

Fig. 8.

Histogram of the relative orientations (HROs) for Filaments I, II, and III. In order to calculate the angle φ between the polarization vector and the gradient vector, we used the vectors and column density within the white solid boxes shown in figure 9.

5 Magnetic field strength

In this section, we estimate the strengths of the magnetic fields associated with the filaments, applying the Hildebrand method (Hildebrand et al. 2009) and the Davis–Chandrasekhar–Fermi (hereafter DCF) method (Davis 1951; Chandrasekhar & Fermi 1953). We first calculate the dispersion of the H-band polarization angles in the sub-region for each filament, following the Hildebrand method. Using this method, the dispersion due to the small-scale turbulence on the large-scale magnetic field can be obtained. Hildebrand et al. (2009) used the difference in angle, ΔΦ(l) ≡ Φ(x) − Φ(x + l), between the N(l) pairs of vectors separated by a displacement l, to compute the angular dispersion function (ADF), defined as

$$\begin{equation} \langle \Delta \Phi ^2(l)\rangle ^\frac{1}{2}\equiv \left\lbrace \frac{1}{N(l)}\sum _{i=1}^{N(l)}[\Phi (x)-\Phi (x+l)]^2\right\rbrace ^\frac{1}{2} . \end{equation}$$

(6)

Then, the ADF can be approximated by

$$\begin{equation} \langle \Delta \Phi ^2(l)\rangle _{\rm tot}\simeq b^2+m^2l^2+\sigma ^2_{\rm M}(l), \end{equation}$$

(7)

where b, ml (m is a proportionality constant), and σ_M(l) represent the contributions of the turbulent dispersion, large-scale structure, and measurement uncertainties, respectively. This equation can be used to fit our polarimetric data, and the intercept at l = 0 provides us with the turbulent dispersion, b.

Using the DCF method, we estimate the POS magnetic field strength as in the following equation:

$$\begin{equation} B_\Vert =f\sqrt{4\pi \rho }\frac{\sigma _v}{\sigma _\theta }, \end{equation}$$

(8)

where ρ is the mean volume density of the cloud, σ_v is the velocity dispersion of the line of sight, σ_θ is the dispersion of the polarization vector angles, and f is a correction factor. The correction factor was approximated by Houde et al. (2009) as

$$\begin{eqnarray} f &\approx & N^{1/2}, \end{eqnarray}$$

(9)

$$\begin{eqnarray} N &=& \frac{(\delta ^2 + 2W^2) \Delta }{\sqrt{2\pi }\delta ^3}, \end{eqnarray}$$

(10)

where N is the number of independent turbulent cells for the magnetic field, δ is the turbulent correlation length, W is the telescope beam radius, and Δ is the thickness of the cloud along the line of sight. In our case, where the telescope beam radius is much smaller than the size of a turbulent cell (i.e., δ ≫ W) due to the point sources, equation (10) can be rewritten as

$$\begin{equation} N = \frac{\Delta }{\sqrt{2\pi }\delta }. \end{equation}$$

(11)

Here we assume that the thickness Δ of the filament along the line of sight is as long as the width of the filament. Because the turbulent correlation length δ has not been reported for the Serpens South cloud, here we adopt δ = 16 mpc based on previous works (OMC-1; Houde et al. 2009). Using these values, we obtain N ≈ 20 and then f ≈ 0.22. The mean volume densities are calculated to be the mean column densities divided by the mean width as a depth for the corresponding sub-region, assuming that a filament has a cylindrical shape. If the line-of-sight depth of the cloud does not coincide with the width of the cloud in the plane of the sky, the mean volume density of such a cloud is given as ρ = ρ_cyl/a, where a is the ratio between the depth and the width, and ρ_cyl is the density of the cylinder. Although it is difficult to estimate the actual value of a, here we assume that a is of order unity. The velocity dispersions are obtained from the C¹⁸O data. Here, the C¹⁸O profile of Filament III has a double peak, and we evaluate the velocity dispersion of the main component at ∼6.5 km s⁻¹. We calculate σ_θ from our H-band polarimetric data within the two or three sub-regions set at the northern (labeled “North” in figure 9), central (“Center”), and southern (“South”) parts of each filament, using the above Hildebrand method.

Fig. 9.

Sub-regions used for the analysis shown on the column density map. For the HROs in section 4, and for estimating the POS magnetic field strength in section 5, we used the vectors within the white rectangles. (Color online).

The derived POS magnetic field strength and other physical quantities are listed in table 1. As shown there, the POS magnetic field strengths for each sub-region lie in the range 10–80|$\, \mu$|G, where the clouds are assumed to be cylindrical (a = 1). The estimated magnetic field strengths have uncertainties of a factor of a few for 0.1 < a < 10. This may be the first systematic study evaluating the POS magnetic field strength for each filament in Serpens South. Our estimated magnetic field strengths are somewhat different from those estimated by Sugitani et al. (2011), in which the magnetic field strengths were estimated to be |${\sim } 150\, \mu$|G and |${\sim } 200\, \mu$|G toward the north and south zones of Filament II, respectively (see figure 8 of Sugitani et al. 2011). The following points can be given as reasons for this difference. In the present paper we have taken the distance to Serpens South as 436 pc and the velocity width as ∼0.7–1.5 km s⁻¹ from the C¹⁸O data, while Sugitani et al. (2011) used a distance of 260 pc and a velocity width of ∼1.5–2 km s⁻¹ from the HCO⁺ observations. In addition, they calculated polarization angle dispersions σ_θ of |${8{^{\circ}_{.}}4}$| and |${6{^{\circ}_{.}}9}$| toward the local north and south zones, respectively, where the polarization vectors are well ordered. If we correct for the adopted physical quantities mentioned above, our estimated magnetic field strengths agree with the previous value estimated by Sugitani et al. (2011).

Table 1.

Physical quantities at each sub-region of three filaments.

Filament	Sub-region	Number*	|$N_{\rm H_2}$|†	|$n_{\rm H_2}$|  ‡	σv§	σθ♯	|$B_\Vert$|**	놆
			(1022 cm−2)	(104 cm−3)	(km s−1)	(°)	(μG)
I	North	97	1.26	0.49	0.52	8.7	39	2.2
	South	73	1.89	0.69	0.65	6.0	82	1.5
II	North	71	2.35	1.05	0.51	15.6	29	5.0
	Center	87	3.60	1.32	0.64	11.6	54	3.9
	South	124	1.97	0.62	0.63	12.5	36	3.6
III	North	154	1.55	0.65	0.39	7.6	37	2.7
	Center	129	1.07	0.41	0.42	8.1	31	2.5
	South	120	1.01	0.44	0.42	19.0	14	5.4

* The number of sources used for calculating the angular dispersion.

^† The mean column density evaluated from the Herschel data.

^‡ The mean number density.

^§ The velocity dispersion calculated from C¹⁸O data.

^♯ The angular dispersion calculated by using the Hildebrand method.

** The POS magnetic field strength.

^†† The mass-to-flux ratio normalized against a critical value.

The dynamical state of a magnetized cloud can be measured by the ratio of the cloud mass to the magnetic flux, i.e., the mass-to-flux ratio. Here we define the dimensionless mass-to-flux ratio normalized against a critical mass-to-flux ratio λ_crit as follows:

$$\begin{eqnarray} \tilde{\lambda }\equiv \frac{\lambda _{\rm obs}}{\lambda _{\rm crit}}=\frac{\mu m_{\rm H}N_{\rm H_2}}{B_\Vert }\lambda _{\rm crit}^{-1}, \end{eqnarray}$$

(12)

where μ is the mean molecular weight of 2.8, |$N_{\rm H_2}$| is the column density, and λ_crit is the critical value for the magnetic stability of the cloud, and we adopt the critical value of (4π²G)^−1/2 obtained by Nakano and Nakamura (1978) for the sake of simplicity. The mass-to-flux ratio for each sub-region is evaluated using the POS magnetic field strength derived from the DCF method. The evaluated mass-to-flux ratios are given in table 1. Here we only take into account the POS components to estimate the mass-to-flux ratios. In this sense, the values listed in table 1 provide upper limits. We find that in Filament II and the south section of Filament III the mass-to-flux ratios are ∼3.6–5.4 for the cylindrical geometry (a = 1), indicating that filaments are magnetically supercritical. On the other hand, in Filaments I and III (except for the south part), the mass-to-flux ratios are ∼1.5–2.7, indicating that these filaments are close to magnetically critical. If we consider a global gravitational contraction model for filament formation (Case A: see section 6 for details), the clouds are expected to have depths larger than the plane-of-sky width (i.e., a > 1) resulting in mass-to-flux ratios somewhat larger than those in table 1. In that case, the clouds become magnetically supercritical.

6 Model for the formation and evolution of Serpens South

As we showed in section 3, the global magnetic field of Serpens South is almost perpendicular to the filaments, indicating that the magnetic field plays an important role in the formation process of the filaments. In this section, we attempt to discuss possible formation scenarios of the Serpens South filaments.

We suggest two possible scenarios to create the observed cloud and magnetic structures, which are illustrated in figure 10. One is a global gravitational contraction of a single molecular cloud (Case A in figure 10). Recently, B. Wu (in preparation) performed three-dimensional MHD simulations of the gravitational collapse of a molecular clump of |$\sim 10^{3}\, M_{\odot }$| and a radius of ∼2 pc. They found that such a cloud evolves as follows. The cloud contracts preferentially along the magnetic field, forming a sheet-like cloud. At the same time, the cloud turbulence creates filamentary structures due to local turbulent compression. Some of the filaments tend to merge, forming self-gravitating filaments, which then fragment into dense cores where stars are created. In the presence of moderately strong magnetic fields, the sheet-like cloud, and thus dense filaments, formed tend to be perpendicular to the global magnetic fields (Nakamura & Li 2008). However, along the filaments, the star formation rate may not become so high in the presence of a near-critical magnetic field. Some triggering mechanisms such as cloud collision (Nakamura et al. 2014) and external compression (Shimoikura et al. 2019b) are likely to be needed to make the star formation rate higher in the Serpens South cluster-forming clump. To form the Serpens South filaments, the parent molecular cloud may have had a mass of a few |$\times 10^{3}\, M_{\odot}$| and a size of a few parsecs.

Fig. 10.

Schematic drawings of two possible scenarios for filamentary structure formation. Case A: Spontaneous formation scenario, i.e., global gravitational contraction of a molecular cloud. The parent cloud may have a mass of a few 10|$^{3}\, M_{\odot }$| and a radius of ∼5 pc. See, e.g., B. Wu (in preparation) for the numerical simulation of this scenario. Case B: Externally triggered formation scenario. The global magnetic field should have some hints of the external triggered events.

The other scenario is the fragmentation of a sheet-like cloud that was created by an expanding shell or flows formed by external events such as an expanding H ii region (e.g., Shimoikura et al. 2015, 2019b), supernovae (e.g., Tatematsu et al. 1990; Dobashi et al. 2014, 2019a; Matsumoto et al. 2015), or superbubbles (e.g., Inutsuka et al. 2015), as illustrated as Case B in figure 10. In a sheet-like cloud the magnetic fields tend to be roughly parallel to the equatorial plane, because the magnetic field component parallel to the sheet is preferentially amplified by the dynamical compression (e.g., Nagai et al. 1998; Kusune et al. 2015). When the sheet becomes self-gravitating, such a sheet fragments into self-gravitating filaments which are perpendicular to the magnetic fields. Frisch (1998) found that several superbubble shells converged into the Aquila Rift region which contains the Serpens South cloud. In fact, Nakamura et al. (2017) found many arc-like molecular structures, which might originate from superbubbles, in the Aquila Rift. The relationship between the arc-like structure and the Serpens South cloud remains uncertain. However, in addition to the possible influence of the expanding shell of W 40 (Shimoikura et al. 2019b), external flow on a large scale driven by superbubbles might have played a role in the formation of the Serpens South cloud.

In the second scenario, we expect that the global magnetic field should be distorted by the expanding shells or flows. To find such distorted magnetic field structures, we show the wide-field Planck map² of the Aquila Rift in figure 11. Our NIR observed area is shown by the dashed lines. The global magnetic field of the Serpens South region appears to smoothly connect with a much larger-scale magnetic field. In other words, there is no evidence to show large-scale shock contributing to the formation of the filaments.

Fig. 11.

(a) The red vectors show the orientation of the magnetic field as projected on the plane of the sky, derived from the Planck data. The vectors are shown approximately every |${15{^{\prime}_{.}}8}$|⁠, and the lengths are the same as each other. The background image is the extinction map of A_V derived from the color excess map of E(J − H) formed by Dobashi et al. (2013). The black dashed polygon indicates the area of our NIR polarimetric observations. The black contour indicates the column density level of 1.3 × 10²² cm⁻². (b) An enlarged view of the area around Serpens South from panel (a) with NIR polarimetric vectors, which are indicated in green. (Color online)

Recently, Shimoikura et al. (2019b) suggested that the expanding shell created by the W 40 H ii region is interacting with the Serpens South region. However, we do not find significant distortion of the magnetic field due to the shell from our NIR polarimetric data. The cluster formation is likely to have been triggered after the filament formation in this region.

Thus, we propose that the Serpens South filaments are formed by the global gravitational contraction of a magnetized molecular cloud, i.e., the first scenario, although there is a possibility that some external events also affected the structure formation and star formation.

7 Conclusions

We have presented NIR polarimetric observations toward Serpens South. The main results are summarized as follows:

1. In the H-band polarization map, the global POS magnetic field of Serpens South is well ordered, and perpendicular to the cloud elongation. This suggests that the magnetic field is likely to restrict the cloud/filament formation.

2. Using the method of HROs, we investigated the relation between the POS magnetic field direction and column density structure for each filament. The HROs indicate that the POS magnetic field orientation is roughly perpendicular to the cloud density gradients for each filament.

3. Applying the DCF method, the POS magnetic field strengths toward each sub-region of filament are estimated to be 10–80 μG, assuming that a cloud has a cylindrical shape. The evaluated mass-to-flux ratio for each filament indicates that Filament II is magnetically supercritical, while Filaments I and III (except for the south sub-region) are close to magnetically critical.

4. Considering two possible formation scenarios for the filaments, we speculate that the filaments of Serpens South are formed by the fragmentation of a sheet-like cloud, which evolved through the global gravitational contraction of a magnetized molecular cloud along the magnetic field.

Acknowledgments

This CO work was carried out as one of the large projects of the Nobeyama Radio Observatory (NRO), which is a branch of the National Astronomical Observatory of Japan, National Institute of Natural Sciences. We thank the NRO staff for both operating the 45 m telescope and helping us with the data reduction. This work was partly supported by Grants-in-Aid for Scientific Research (JP16H05730, JP17H01118, JP17H02863, JP26287030, and JP17K00963) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The IRSF project is a collaboration between Nagoya University and the South African Astronomical Observatory (SAAO) supported by Grants-in-Aid for Scientific Research on Priority Areas (A) (Nos. 10147207 and 10147214) and the Optical & Near-Infrared Astronomy Inter-University Cooperation Program from MEXT of Japan and the National Research Foundation (NRF) of South Africa.

Footnotes

1

〈http://www.herschel.fr/cea/gouldbelt/en/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=66〉.

2

〈http://irsa.ipac.caltech.edu/data/Planck/release_2/all-sky-maps/〉.