Magnetically Aligned Striations in the L914 Filamentary Cloud

The CO observations toward the L914 cloud covered a region within 81° ≤ l ≤ 84° and −3° ≤ b ≤ −1°. The observations were conducted with the PMO 13.7 m millimeter telescope located in Delingha, China, from 2012 March to 2018 May. The nine-beam Superconducting Spectroscopic Array Receiver (Shan et al. 2012) was used as the front end, and the ¹²CO, ¹³CO, and C¹⁸O J = 1 − 0 emission lines were simultaneously observed in the sideband separation mode. The upper sideband (USB) contains the ¹²CO line and the lower sideband (LSB) contains the ¹³CO and C¹⁸O lines. The half-power beamwidth was ∼55'' at 110 GHz and ∼52'' at 115 GHz. The typical system temperature was ∼275 K for ¹²CO and ∼155 K for ¹³CO and C¹⁸O. A fast Fourier-transform spectrometer was used as the back end, which has a total bandwidth of 1 GHz and contains 16,384 channels. The corresponding velocity resolution is 0.16 km s⁻¹ for the ¹²CO line and 0.17 km s⁻¹ for the ¹³CO and C¹⁸O lines, respectively. The observed area is divided into individual $30^{\prime} \times 30^{\prime}$ cells. Each cell was observed in the on-the-fly mode with a scanning rate of 50'' per second and a dump time of 0.3 s. The scanning interval was 15'' (50'' s⁻¹ × 0.3 s). To reduce the scanning effects, each cell was mapped along both the Galactic longitude and latitude.

We calibrated the antenna temperature (T_A) with the standard chopper wheel method (Ulich & Haas 1976). The main-beam temperature (T_mb) was derived from the antenna temperature (T_A) using the equation of T_mb = T_A/B_eff, where the main-beam efficiencies (B_eff) were approximately 44% for the USB and 48% for the LSB during the observations. The calibration errors were estimated to be within 10%.

The raw data were reduced by the MWISP working group with the GILDAS software ⁵ and self-developed pipelines. After eliminating the abnormal data, we mosaicked the data cubes ($30^{\prime} \times 30^{\prime}$ FITS) of cloud regions and regridded the maps into 30'' × 30''. The typical rms noise level was below ∼0.5 K for ¹²CO at a channel width of 0.16 km s⁻¹ and below ∼0.3 K for ¹³CO and C¹⁸O at a channel width of 0.17 km s⁻¹. All velocities given in this work are relative to the local standard of rest (LSR).

To investigate the magnetic field of the L914 cloud, we retrieved dust polarization data from the Planck Legacy Archive. ⁶ The Planck all-sky survey (Planck Collaboration et al. 2011) observed the linear polarization in seven bands from 30 to 353 GHz, of which the 353 GHz band was the most sensitive for detecting dust polarization (Planck Collaboration et al. 2015). Additionally, the cosmic microwave background does not significantly contribute to polarized emission in this band when observing molecular clouds (Soler 2019). Therefore, Planck 353 GHz submillimeter polarization data were used in this work to trace magnetic fields. The original maps have a resolution of $4\buildrel{\,\prime}\over{.} 8$ in the HEALPIX ⁷ format, with a pixelization at N_side = 2048, which corresponds to a pixel size of $1\buildrel{\,\prime}\over{.} 7$. We smoothed the maps into $10^{\prime}$ to increase the signal-to-noise ratio of the extended regions, as suggested by Planck Collaboration et al. (2016). The polarization position angle (PA) is calculated with

$$\begin{eqnarray}&&{\theta }_{\mathrm{PA}}=-\displaystyle \frac{1}{2}\,\arctan \left(\displaystyle \frac{U}{Q}\right),\end{eqnarray} \tag{ 1 }$$

where θ_PA is given in the IAU convention, i.e., θ_PA = 0° points to the north and θ_PA increases counterclockwise. The orientation of the magnetic field is perpendicular to the PA, ${\theta }_{{\rm{B}}}={\theta }_{\mathrm{PA}}-\tfrac{\pi }{2}$.

Figure 1 presents an overview of the Cygnus X region in the MWISP ¹³CO observations. The integral velocity interval is [−100, 40] km s⁻¹. Around the center of the Cygnus X region (the Cyg OB2 cluster), there are many bright filamentary molecular clouds, and a lot of research has focused on these molecular clouds over the past few decades (e.g., Schneider et al. 2010; Cao et al. 2022; Gong et al. 2023; Li et al. 2023). However, the relatively isolated L914 molecular cloud located at the periphery of this region has received little attention. The ¹³CO J = 1 − 0 survey from the Nagoya 4 m millimeter telescope ($\sim 2\buildrel{\,\prime}\over{.} 7$ in angular resolution) showed an elongated structure of the L914 cloud at the velocity range of ∼[1, 6] km s⁻¹ (Dobashi et al. 1994). The enlarged view in Figure 1 displays the three-color image of the MWISP CO data toward the L914 cloud, with ¹²CO emission shown in blue, ¹³CO in green, and C¹⁸O in red. Based on the higher-angular-resolution MWISP CO data, we reveal a long filamentary structure in the L914 cloud.

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Figure 2 shows the velocity channel maps of the MWISP CO emission toward the L914 cloud. The grayscale background represents the ¹²CO emission, with the overlapped green and magenta contours showing the ¹³CO and C¹⁸O emission, respectively. As shown in this image, the L914 cloud is detected in the velocity range from ∼0 to 7 km s⁻¹. The two ends of the filament appear in the velocity channel ranging from roughly 1 to 4 km s⁻¹, whereas the central part is predominantly observed in about [3, 6] km s⁻¹. The integrated intensity maps of ¹²CO, ¹³CO, and C¹⁸O are shown in Figure 3, where the three molecular lines are integrated over the velocity ranges of [0, 7], [0, 6], and [0.5, 5.5] km s⁻¹, respectively. Compared with ¹²CO and ¹³CO, the C¹⁸O line traces much denser regions. Figure 3(c) shows that the L914 cloud has strong C¹⁸O emission along the filament. We adopt the Discrete Persistent Structure Extractor (DisPerSE; Sousbie 2011) algorithm on the C¹⁸O data for the dense ridge extraction. As the DisPerSE algorithm extracts persistent structures by connecting topological critical points (e.g., maximum, minimum, and saddle points), it is susceptible to local extrema. We thus smooth the C¹⁸O data to 75'' before extraction. In DisPerSE, the persistence and robustness thresholds are set to be 2 and 0.8 K km s⁻¹ (σ ∼ 0.25 K km s⁻¹; see the DisPerSE ⁸ website for more details). The results obtained from DisPerSE are further visually inspected in the integrated intensity map and minor adjustments have been applied according to the 3σ contour. The resulting ridge is depicted in Figure 3 with the solid cyan lines. Figure 4 presents the position–velocity (PV) map along the ridge from left to right. The structure extends more than 36 in length (i.e., ∼50 pc at a distance of 760 pc; see below), showing continuous and strong emission in both the ¹²CO and ¹³CO lines.

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Interestingly, as seen in Figure 2, distinct ¹²CO and ¹³CO hair-like structures are discovered in the velocity channels of [4, 5] and [1, 2] km s⁻¹, located in the central and right parts of the L914 cloud, respectively. We zoom in on these two parts and carefully choose the velocity ranges that could clearly detect the structures for integration. The ¹²CO narrow velocity-integrated intensity maps are shown in Figure 5, with the integrated velocity ranges of [4, 6] and [0, 2] km s⁻¹, respectively. As seen below, these hair-like structures display quasiperiodic characteristics and also parallel the magnetic lines derived from the Planck dust polarization (see Section 3.3.1), and therefore are identified as striations in this work (see the definition suggested by Hacar et al. 2023).

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To investigate the periodicity of the striations, we present profiles of the averaged integrated intensity along the directions (the arrow lines in Figure 5) perpendicular to the striations in Figure 6. The blue solid lines are the original averaged intensity and the dotted orange lines show the profiles after smoothing. We mark the local peaks of the smoothed intensity as the positions of the ¹²CO striations. In the central part, four ¹²CO striations are observed and it is evident that the spacing between the striations gradually decreases from left to right, ranging from about 1.4 to 0.6 pc, with a mean value of ∼1.1 pc. In the right part, six ¹²CO striations are found to show a quasiperiodic pattern with a period T of about 1.4 pc. Given that the striations are likely in a plane inclined to the POS by an angle of θ, the actual period is determined as $T/\cos (\theta$). Here, we only set a lower limit for the oscillation period. Additionally, in the right part, quasiperiodic oscillation is also observed in the velocity dispersions of both the ¹²CO and ¹³CO spectra (see Figure 7). The red dashed lines in Figure 7 show the sinusoidal function with a period of ∼1.4 pc. We assign the ¹²CO striations S1–S10 from left to right. The contrast between the striation and its surroundings can be estimated with $\tfrac{{I}_{\max }-{I}_{\min }}{{I}_{\max }}$, where ${I}_{\max }$ and ${I}_{\min }$ represent the local maximum and minimum of the integral intensity, respectively. The mean contrasts in these two parts are ∼12% and 28%, respectively. Since the ¹²CO emission is relatively diffuse, it is difficult to obtain the path of the striation skeleton. We thus choose the striations with prominent ¹³CO emission to do the ridge extraction. We present the ¹³CO narrow velocity-integrated intensity maps of these two regions in Figure 8. The integrated velocity ranges are [4.5, 5.1] and [1.5, 2.4] km s⁻¹, respectively. According to the morphology of 3σ contours, we identify the ridges for the striations S1–S6 in the ¹³CO images.

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The distance of the L914 cloud listed in previous work is about 800 pc (Dobashi et al. 1994), which is estimated through the spectrophotometry of the nearby stars. In this work, we measure the distance of the cloud based on the MWISP CO data and Gaia Data Release 3 (DR3) data (Gaia Collaboration et al. 2023), using the same method as described in Yan et al. (2019). The details of the distance measurement are presented in the Appendix and a distance of 760 pc is obtained to the L914 cloud.

The optical depth of the ¹²CO J = 1 − 0 line is estimated with the MWISP ¹²CO and ¹³CO data. Assuming that ¹²CO and ¹³CO have the same excitation temperature and beam-filling factor, we calculate the optical depth of ¹²CO as follows:

$$\begin{eqnarray}&&\displaystyle \frac{T{(}^{13}\mathrm{CO})}{T{(}^{12}\mathrm{CO})}=\displaystyle \frac{1-{e}^{-\tau }/{R}_{{\rm{i}}}}{1-{e}^{-\tau }},\end{eqnarray} \tag{ 2 }$$

where T(¹²CO), T(¹³CO), and τ are the peak intensity of the ¹²CO and ¹³CO spectra and the optical depth of ¹²CO, respectively. R_i represents the isotopic ratio of ¹²CO/¹³CO, derived from the relation [¹²C/¹³C] = 4.08D_GC + 18.8 (Sun et al. 2024). In this equation, D_GC denotes the Galactocentric distance and the isotopic ratio is estimated to be R_i ∼ 52 for the L914 cloud. The calculated optical depth (τ) varies from approximately 15 in the outskirts of the cloud to around 60 at the densest positions. The mean value of τ, approximately 32, suggests that the ¹²CO emission is optically thick in the L914 cloud.

We further convert the main-beam brightness temperature T_MB of ¹²CO to the excitation temperature T_ex under the assumption of local thermodynamic equilibrium (LTE) with the following formula:

$$\begin{eqnarray}&&{T}_{\mathrm{mb}}=[J({T}_{\mathrm{ex}})-J({T}_{\mathrm{bg}})][1-{e}^{(-\tau )}],\end{eqnarray} \tag{ 3 }$$

where T_bg = 2.7 K is the background temperature, J is the radiation temperature, and ${J}_{\nu }(T)={T}_{0}/[{e}^{(h\nu /{k}_{{\rm{B}}}T)}-1]$, where T₀ is the intrinsic temperature of ¹²CO and T₀ = h ν/k_B, k_B and h are the Boltzmann constant and Planck constant, respectively. We analyze the pixels with an integrated intensity of ¹³CO larger than 1 K km s⁻¹ ( ∼ 3σ) and find that the T_ex in L914 ranges from 6 to 15 K, with a mean value of ∼10 K. We further assume a uniform T_ex of CO and its isotopologues. The optical depth and column density of ¹³CO can be calculated as follows (Bourke et al. 1997):

$$\begin{eqnarray}&&{\tau }_{13}=-{ln}\left[1-\displaystyle \frac{{T}_{\mathrm{mb}}{(}^{13}\mathrm{CO})}{5.29}{\left({\left[{e}^{5.29/{T}_{\mathrm{ex}}}-1\right]}^{-1}-0.164\right)}^{-1}\right],\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\begin{array}{l}N{(}^{13}\mathrm{CO})=2.42\times {10}^{14}\cdot \displaystyle \frac{\tau {(}^{13}\mathrm{CO})}{1-{e}^{-\tau {(}^{13}\mathrm{CO})}}\\ \cdot \displaystyle \frac{(1+0.88/{T}_{\mathrm{ex}})\times \int {T}_{\mathrm{mb}}{(}^{13}\mathrm{CO}){dV}}{1-{e}^{-{T}_{0}{(}^{13}\mathrm{CO})/{T}_{\mathrm{ex}}}}.\end{array}\end{eqnarray} \tag{ 5 }$$

The abundance ratios of H₂/¹²CO ≈ 1.1 × 10⁴ (Frerking et al. 1982) and ¹²C/¹³C ≈ 52 (Sun et al. 2024) are used to calculate the H₂ column density. The column density map is displayed in Figure 9. The column densities of the dense ridge and diffuse striations are N(H₂) ∼ 5–7 × 10²¹cm⁻² and N(H₂) ∼ 1–3 × 10²¹cm⁻², respectively. As seen in Figure 9, the striations appear to be connected with the densest parts of the skeleton.

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We employ the Gaussian model in the Python package RadFil (Zucker & Chen 2018) to fit the column density profiles of the L914 filament and estimate the deconvolved width (${\mathrm{FWHM}}_{\mathrm{dec}}\,=\,\sqrt{{\mathrm{FWHM}}^{2}-{\mathrm{HPBW}}^{2}}$) of the filament. Assuming that the filamentary structure is a long cylinder, the line mass, volume density, and average column density can be calculated with the equations of M_line = μm_H∫N(r)dr, $n=\tfrac{{M}_{\mathrm{line}}}{\pi {r}^{2}}$, and $\overline{N}=\tfrac{{M}_{\mathrm{line}}}{2\times r}$, where μ, m_H, and r are the mean molecular mass, the hydrogen atom mass, and the radius of the filament, respectively. With the same method, we also calculate the properties of the six striations (S1–S6) identified in Section 3.1. All properties of the filamentary structures are listed in Table 1. The estimated width, line mass, and volume density of the L914 filament are ∼1 pc, 80 M_⊙ pc⁻¹, and 1300 cm⁻³, respectively. The L914 filament is thermally supercritical, with the line mass much larger than the critical equilibrium value for an isothermal cylinder (M_{line, crit} ∼ 17 M_⊙ pc⁻¹ at a gas temperature of 10 K, derived from ${M}_{\mathrm{line},\ \mathrm{crit}}=2{c}_{{\rm{s}}}^{2}/{\rm{G}}$; Ostriker 1964). The mean width of the striations is about 0.5 pc, which is half that of the L914 filament. The line masses of the striations range from 3 to 12 M_⊙ pc⁻¹, with a mean value of ∼8 M_⊙ pc⁻¹. All the striations are thermally subcritical. Unless additional pressure is supplied (such as magnetic compression), these striations are expected to disperse. Considering that striations can be so tenuous that they can easily be affected by surrounding material, large uncertainties will inevitably be introduced into the calculations.

Table 1. Properties of Filamentary Structures

Name	Npeak	Width	Length	Mline	n	$\overline{N}$	Mtot	Orientation
	(1021 cm−2)	(pc)	(pc)	(M⊙ pc−1)	(cm−3)	(1021 cm−2)	(M⊙)	(degrees)
Fil	3.94 ± 0.3	1.06 ± 0.2	48.5 ± 0.1	77 ± 16	1300 ± 300	3.20 ± 1.0	3700 ± 800	⋯
S1	0.76 ± 0.1	0.44 ± 0.1	4.6 ± 0.1	6 ± 2	560 ± 200	0.60 ± 0.1	28 ± 9	–120 ± 12
S2	1.34 ± 0.1	0.50 ± 0.2	3.7 ± 0.1	12 ± 5	870 ± 360	1.06 ± 0.1	44 ± 19	–138 ± 22
S3	0.47 ± 0.1	0.33 ± 0.2	4.7 ± 0.1	3 ± 2	500 ± 360	0.40 ± 0.1	14 ± 9	–129 ± 18
S4	0.80 ± 0.2	0.38 ± 0.2	4.6 ± 0.1	6 ± 4	760 ± 400	0.70 ± 0.2	28 ± 19	–129 ± 23
S5	0.99 ± 0.1	0.68 ± 0.2	6.6 ± 0.1	12 ± 4	500 ± 220	0.78 ± 0.1	79 ± 26	–138 ± 12
S6	0.83 ± 0.2	0.46 ± 0.2	5.8 ± 0.1	7 ± 4	600 ± 360	0.67 ± 0.2	40 ± 24	–141 ± 4

Note. Properties of the filamentary structures. Column (1): the names of the L914 filament and striations. Columns (2) and (3): the peak column density and width obtained from the Gaussian fitting. Column (4): the length of the structure. Columns (5)–(8): the line mass, volume density, averaged column density, and total mass. Column (9): the orientation angle of the filamentary structure, measured counterclockwise from Galactic north in degrees.

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3.3.1. Field-structure Orientation

The POS magnetic field can be derived with the Planck data based on the assumption that the short axis of the dust grains is well aligned with the local direction of the magnetic field (Andersson et al. 2015). Figure 10 shows the inferred magnetic field overlaid on the MWISP ¹³CO zeroth-moment image. In the left part of L914, the magnetic field aligns well with the dense skeleton. However, in the central and right parts, the magnetic field appears to display a sharp turn, becoming perpendicular to the dense skeleton and parallel to the diffuse striation structures. In order to quantify the relative orientation between the magnetic field and the filamentary structures, we first present the distribution of the polarization PAs in Figure 11, from which the PAs can be visually divided into three groups. We perform a multicomponent Gaussian function fitting on the PA distribution and obtain mean values of ∼296, −442, and −639, with 1σ dispersions of ∼503, 756, and 423, for the three components C1, C2, and C3, respectively. The first component C1 (the purple shadow in Figure 11) covers a range of PAs from ∼9° to 50° and corresponds to the marked region "R1" in Figure 10. The second component (C2; orange shadow) ranges from ∼ −52° to −14° and the corresponding area is "R2." The third component (C3; green shadow) spans from ∼ − 81° to −52° and is located to the right of L914, i.e., region "R3." The global B-field orientation, denoted as θ_B , can be derived from the PA, using the formula ${\theta }_{B}={\overline{\theta }}_{\mathrm{PA}}-\tfrac{\pi }{2}$.

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As for the structure orientation, we first roughly break the L914 filament into three segments (Seg1–Seg3 in Figure 9) according to the distribution of dust polarization PAs illustrated in Figures 10 and 11. We then employ cubic polynomial fitting to smooth the path of each filamentary structure (segments and striations) and compute the derivative at each point along the trajectory. The mean tangential angle along each path is adopted as the structure orientation. The structure orientations of Seg1–Seg3 also adhere to the IAU convention (see Section 2.2), with orientation angles of −88° ± 18°, −77° ± 23°, and −66° ± 12° for Seg1, Seg2, and Seg3, respectively. Figure 12 presents the relative orientations of the projected magnetic fields B_pos with respect to the dense segments and diffuse striations. As seen in this image, the magnetic fields in R2 and R3 are indeed parallel to the hair-like structures, which is consistent with the definition of striations (see Section 3.1). Moreover, a bimodal configuration is shown in subregions R2 and R3.

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3.3.2. Strength of Magnetic Field

The strength of the magnetic field projected onto the POS (B_pos) can be estimated with the Davis–Chandrasekhar–Fermi (DCF; Davis 1951; Chandrasekhar & Fermi 1953) method. Under the assumption that the observed dispersion of the polarization PAs is purely caused by incompressible and isotropic turbulence, the magnetic field strength is estimated as

$$\begin{eqnarray}&&{B}_{\mathrm{pos}}=Q\sqrt{4\pi \rho }\displaystyle \frac{{\sigma }_{\mathrm{turb}}}{{\sigma }_{\theta }}\,(\mathrm{cgs}),\end{eqnarray} \tag{ 6 }$$

where ρ is the volume density (ρ ∼ 1300 cm⁻³; see Section 3.2), σ_turb is the one-dimensional nonthermal velocity dispersion, σ_θ is the dispersion in polarization PA, and Q is the correction factor. The three-dimensional numerical MHD simulations in Ostriker et al. (2001) suggest that the correction factor of Q = 0.5 should be applied to the DCF formula when the dispersion of PAs is less than ∼25°, which is applicable for our samples (see Figure 11). The uncertainty of the Q factor is 30% (Crutcher et al. 2004).

The PA dispersion has been derived in Section 3.3.1. We further evaluate the nonthermal velocity dispersion (σ_turb) with ¹³CO data by eliminating the thermal portion (σ_th) from the observed velocity dispersion (σ_obs):

$$\begin{eqnarray}&&{\sigma }_{\mathrm{turb}}^{2}={\sigma }_{\mathrm{obs}}^{2}-{\sigma }_{\mathrm{th}}^{2},\end{eqnarray} \tag{ 7 }$$

where the thermal velocity dispersion is determined by ${\sigma }_{\mathrm{th}}\,=\sqrt{\tfrac{{k}_{{\rm{B}}}{T}_{\mathrm{kin}}}{{m}_{\mathrm{obs}}}}$, where m_obs is the mass of the ¹³CO molecule (m_obs = 29 amu) and T_kin is the gas kinematic temperature, for which we adopt the excitation temperature estimated from the ¹²CO emission, under the assumption of LTE (see Section 3.2). The estimated median of σ_th is ∼0.05 ± 0.01 km s⁻¹ for all three regions, which is too small and therefore negligible compared to σ_obs. The effect of opacity (τ) broadening on the velocity dispersion can be estimated by referring to (see, e.g., Phillips et al. 1979; Hacar et al. 2016)

$$\begin{eqnarray}&&\displaystyle \frac{{\sigma }_{\mathrm{obs}}}{{\sigma }_{\mathrm{int}}}=\displaystyle \frac{1}{\sqrt{\mathrm{ln}2}}{\left[\mathrm{ln}\left(\displaystyle \frac{\tau }{{ln}\left(\tfrac{2}{{e}^{-\tau }+1}\right)}\right)\right]}^{1/2},\end{eqnarray} \tag{ 8 }$$

where σ_obs and σ_int are the observed and intrinsic velocity dispersions, respectively. As the opacity reaches 0.6, the contribution of opacity broadening can reach up to 10%. According to Equation (4), we find that more than 30% of the pixels in the L914 cloud have ¹³CO optical depth greater than 0.6. Therefore, the optical depth correction is necessary. In Equation (8), we adopt the intensity-weighted velocity dispersion σ_obs to calculate σ_int. Figure 13 presents the distributions of σ_int, with mean values of ∼0.6, 0.5, and 0.4 km s⁻¹ for subregions R1, R2, and R3, respectively.

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With Equation (6) and all the parameters obtained above, the magnetic field strengths are estimated to be ∼101 ± 71, 54 ± 27, and 75 ± 45 μG for regions R1, R2, and R3, respectively (see Table 2). Since the angular resolution of Planck data is $\sim 10^{\prime}$, any disordered structures smaller than the beam size will be smoothed and result in an overestimate of B_pos. Also, if we use the critical density of CO J = 1 − 0 (∼1000 cm⁻³; see Yang et al. 2010) at the kinematic temperature of 10 K to calculate B_pos, the estimated strength will be 88, 47, and 66 μG, respectively. Additionally, we attempt to estimate the magnetic field strength using the modified DCF method (the ST method: ${B}_{\mathrm{pos}}=\sqrt{2\pi \rho }\tfrac{{\sigma }_{{\rm{v}}}}{\sqrt{{\sigma }_{\theta }}}$; see Skalidis & Tassis 2021; Skalidis et al. 2021), which takes into account both the anisotropy and compressibility of turbulence. The estimated strengths of the magnetic field are 42, 28, and 29 μG in the three subregions, nearly half of the DCF results. However, as mentioned in Skalidis & Tassis (2021), the ST method will underestimate the magnetic field strength for regions where self-gravitation is non-negligible. We thus consider the results from the ST method as a lower limit of B_pos.

Table 2. Properties of Subregions

Region	δ V	δ θ	Bpos (DCF)	Bpos (ST)	λobs (DCF)	λobs (ST)	${V}_{{\rm{A}},3{\rm{D}}}^{\mathrm{DCF}}$	${V}_{{\rm{A}},3{\rm{D}}}^{\mathrm{ST}}$	${M}_{{\rm{A}}}^{\mathrm{DCF}}$	${M}_{{\rm{A}}}^{\mathrm{ST}}$
	(km s−1)	(degree)	(μG)	(μG)			(km s−1)	(km s−1)
R1	0.64 ± 0.4	5.03	101 ± 71	42 ± 27	0.24 ± 0.19	0.58 ± 0.42	4.62 ± 3.3	1.92 ± 1.3	0.24 ± 0.23	0.58 ± 0.54
R2	0.51 ± 0.2	7.57	54 ± 27	28 ± 12	0.45 ± 0.27	0.87 ± 0.46	2.47 ± 1.3	1.28 ± 0.6	0.36 ± 0.24	0.69 ± 0.42
R3	0.40 ± 0.2	4.23	75 ± 45	29 ± 15	0.32 ± 0.22	0.84 ± 0.51	3.43 ± 2.1	1.33 ± 0.7	0.20 ± 0.16	0.52 ± 0.38

Note. Properties of the three subregions R1, R2, and R3. Columns (2) and (3): the velocity dispersion and the dispersion of the polarization PAs. Columns (4) and (5): the magnetic field strengths derived from the DCF and ST methods, respectively. Columns (6), (8), and (10): the mass-to-flux ratio, the three-dimensional $\mathrm{Alfv}\acute{{\rm{e}}}{\rm{n}}$ velocity, and the Mach number calculated with the B_pos obtained from the DCF method. Columns (7), (9), and (11): the corresponding values computed based on the B_pos derived from the ST method.

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The combined MWISP CO and Planck dust observations show a filamentary structure in the L914 cloud, with a string of magnetically aligned striations perpendicular to the dense ridge (see, e.g., Figure 10). Similar striation structures are also observed in the Taurus B211 (e.g., Palmeirim et al. 2013) and Musca filaments (e.g., Cox et al. 2016; Bonne et al. 2020). In comparison to the L914 cloud, these two objects are located at relatively higher Galactic latitudes and are much closer (140 pc for Taurus; 200 pc for Musca), so there is very low line-of-sight (LOS) contamination. The main filament of L914 spans ∼50 pc in length, which is roughly five times longer than that of B211 and Musca (∼10 pc). Besides, the line mass of the L914 filament (∼80 M_⊙ pc⁻¹) is also much larger than that of the Musca and Taurus B211 filaments (∼20 M_⊙ pc⁻¹ and 50 M_⊙ pc⁻¹, respectively). It must be noted that the properties of filaments can vary significantly due to different tracers, sensitivities, and spatial resolutions. ⁹ Furthermore, we reveal the quasiperiodic arrangements in both the CO intensity (see Figure 6) and velocity dispersion (see Figure 7), which are not observed in the cases of B211 and Musca. These newly discovered characteristics may help us to better understand the nature of the striations associated with filaments and provide new observational constraints on the theoretical models. The morphology of the B-field, revealed by polarization measurements from either starlight or dust emission, demonstrates a large-scale ordered field parallel to the striations in all three clouds. The estimated B-field strengths in the Musca, Taurus, and L914 clouds are ∼12 μG (Planck Collaboration et al. 2016), 25 μG (Chapman et al. 2011), and 80 μG (this work), respectively.

André et al. (2014) proposed that filaments gain mass through magnetized accretion. In this scenario, the B-field is dynamically dominant in the formation of filaments, by channeling the material along the substructures onto the dense ridge. So far, there have been several cases of accretion activity identified by velocity gradients, such as the OMC-1 (Hacar et al. 2017), OMC-3 (Ren et al. 2021), DR21 (Cao et al. 2022), M120.1 + 3.0 (Sun et al. 2023), California (Guo et al. 2021), and Serpens (Gong et al. 2018, 2021) regions. In these cases, accretion flows converge toward the gravity center, either along the main filament or the substructures in the hub–filament system. In the Musca and B211 clouds, large-scale velocity gradients perpendicular to the main filaments are observed and are considered as evidence that the main filament is accreting material from its surroundings via striations (see Palmeirim et al. 2013; Shimajiri et al. 2019; Bonne et al. 2020). For L914, we check the PV profiles along the striations and find increasing velocity gradients and dispersions along the striations S5 and S6 toward the dense ridge. The PV maps are exhibited in Figure 14. If gravity is responsible for the velocity gradients, we can quantitatively delineate the motion of material in the potential well. We assume that the main filament is an infinite cylinder and then use the observed line mass to estimate the freefall velocity v_ff at a radius r (Palmeirim et al. 2013):

$$\begin{eqnarray}&&{v}_{\mathrm{ff}}=2\times \sqrt{{{GM}}_{\mathrm{line}}\cdot {ln}\left(\displaystyle \frac{D}{r}\right)},\end{eqnarray} \tag{ 9 }$$

where D is the distance from the tail end of the striation to the dense ridge. Since we can only derive the LOS velocity V_LSR and the projected position p, Equation (9) can be rewritten as ${v}_{\mathrm{LSR}}={v}_{\mathrm{sys}}+2\sqrt{{{GM}}_{\mathrm{line}}\cdot {ln}(\tfrac{D}{p/\sin \theta })}\cdot \cos \theta$, where v_sys is the system velocity and θ is the inclination angle of the striation against the LOS. In Figure 14, we display the fitted velocity profiles under the line masses of 60, 80, and 100 M_⊙ pc⁻¹, respectively. The derived systematic velocities are ∼1.37 and 1.52 km s⁻¹, respectively. The velocity reaching the surface of the dense ridge is estimated to be 2.7–3.1 km s⁻¹, resulting in an estimated freefall velocity of ∼1.3–1.7 km s⁻¹. With the estimated freefall velocity, we further calculate the current mass accretion rate with the equation of ${\dot{M}}_{\mathrm{line}}=\rho (R)\,\times {v}_{\mathrm{ff}}\times 2\pi R$, where ρ(R) ∼ 600cm⁻³ is the density at the radius of the dense ridge R ∼ 0.5 pc. This results in an accretion rate of ∼170–230 M_⊙ pc⁻¹ Myr⁻¹. It means that the main filament of L914 would be formed in roughly 0.3–0.5 Myr. Using a similar method, the timescales in the B211 and Musca systems are estimated to be 1–2 Myr (Palmeirim et al. 2013) and 1 Myr (Bonne et al. 2020), respectively. Our results suggest that the L914 cloud is in an earlier stage of evolution compared to the B211 and Musca filaments.

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To date, numerous filamentary molecular clouds have been observed in various environments (see, e.g., the review by Hacar et al. 2023). However, the striation-associated samples have only been discovered in a few of them, such as B211 (Palmeirim et al. 2013), Musca (Cox et al. 2016), and L914 in this work. Based on a comparison of the striations in B211, Musca, and L914, we consider the following reasons for the limited number of observed striations: (1) striations may be transient, short-lived structures and only appear at the early formation stage of filamentary molecular clouds; and (2) striations are more diffuse and slender than the main filament. Consequently, in observations, the striations will drown in backgrounds due to a lack of strong contrast with the surrounding emission or because of their small beam-filling factors (Heyer et al. 2016). Therefore, large-scale surveys with both high sensitivity and spatial resolution are needed to search for more striation samples.

Similar to the field structure orientations in R2 and R3 (see Figure 12), the bimodal configurations have been revealed in multiple studies. For example, Planck Collaboration et al. (2016) statistically measured the relative orientations between gas structures and magnetic fields within 10 nearby Gould belt molecular clouds, using the Histogram of Relative Orientations (HRO; Soler et al. 2013) technique, and found that the relative orientation changes systematically with column density N_H, transitioning from being parallel in the lowest-density regions to perpendicular in the highest-density regions. With the same method, other molecular clouds, such as Vela C (Soler et al. 2017) and Serpens Main (Kwon et al. 2022), have also been studied and yielded the same conclusion. The HRO method calculated the relative orientation pixel by pixel and the Planck results focused on the high- and low-density medium, while Li et al. (2013) defined the global cloud orientation and demonstrated that the bimodal configuration exists in the 2 < A_v < 5 medium as well (see also Gu & Li 2019). Such strong coupling of B-fields and filamentary structures indicates the important role that magnetic fields play in shaping the morphology of molecular clouds. In addition, we note that subregion R1 has a column density comparable to the dense ridges of R2 and R3, while the magnetic field in R1 is parallel to the gas structure. We consider that the sharp turn in the relative orientation may be caused by the stellar feedback, which compresses and reshapes both the arc-like gas and magnetic field in subregion R1 (see, e.g., Chapman et al. 2011; Chen et al. 2022). Alternatively, the parallel configuration observed in R1 may result from projection effects. For instance, if the magnetic field is primarily oriented along the LOS but slightly tilted toward the longitudinal direction, we would observe a projected magnetic field (B_pos) parallel to the filamentary structure on the POS. However, the verification of these hypotheses is beyond the scope of this work. In this work, we focus on the subregions exhibiting striations (i.e., subregions R2 and R3).

The bimodality in the orientation between the B-field and filamentary structures is also seen in synthetic polarization maps of numerical simulations (e.g., Hennebelle 2013; Soler et al. 2013; Chen et al. 2016; Li & Klein 2019). Soler et al. (2013) conducted a series of three-dimensional MHD simulations with varying initial magnetic field strengths threading molecular clouds and demonstrated that the bimodal configurations are observed exclusively in the strongly magnetized clouds (β = 0.1, where β is the squared ratio of the sound speed to the $\mathrm{Alfv}\acute{{\rm{e}}}{\rm{n}}$ speed).

In order to evaluate whether the subregions in L914 are gravity-bound or magnetically supported, we calculate the mass-to-flux ratio in units of the critical value via

$$\begin{eqnarray}&&{\lambda }_{\mathrm{obs}}=\displaystyle \frac{{(M/{\rm{\Phi }})}_{\mathrm{obs}}}{{(M/{\rm{\Phi }})}_{\mathrm{cri}}},\end{eqnarray} \tag{ 10 }$$

where the observed mass-to-flux ratio is ${(M/{\rm{\Phi }})}_{\mathrm{obs}}=\tfrac{\mu {m}_{{\rm{H}}}N({{\rm{H}}}_{2})}{B}$, and the critical value is ${(M/{\rm{\Phi }})}_{\mathrm{cri}}=\tfrac{1}{2\pi \sqrt{G}}$ (Nakano & Nakamura 1978). Then, Equation (10) can be simplified as described in Crutcher et al. (2004):

$$\begin{eqnarray}&&{\lambda }_{\mathrm{obs}}=7.6\times {10}^{-21}\displaystyle \frac{N({{\rm{H}}}_{2})}{{B}_{\mathrm{pos}}},\end{eqnarray} \tag{ 11 }$$

where N(H₂) is the mean column density in units of cm⁻², and B_obs is the projected B-field strength in μG. The cloud region with the ratio λ > 1 is in a supercritical state and will collapse under gravity. On the contrary, the region with λ < 1 is magnetically supported. We adopt the magnetic field strengths derived from both the DCF and ST methods to calculate the ratios (see Table 2) and find that all the subregions are subcritical. According to the velocity profile fitting in Section 4.1, the inclination angles of the striations (S5 and S6) against the LOS are estimated to be θ ∼ 45°. Thus, the corrected mass-to-flux ratio should be ${\lambda }_{\mathrm{obs}}\cdot \cos \theta$. This correction reinforces our conclusion that the L914 cloud is in a magnetically subcritical state.

As a key parameter to describe the relative importance of turbulence and the magnetic field, the $\mathrm{Alfv}\acute{{\rm{e}}}\mathrm{nic}$ Mach number is also calculated with the following formula:

$$\begin{eqnarray}&&{M}_{{\rm{A}},3{\rm{D}}}=\displaystyle \frac{\sqrt{3}{\sigma }_{\mathrm{NT}}}{{V}_{{\rm{A}},3{\rm{D}}}},\end{eqnarray} \tag{ 12 }$$

where ${V}_{{\rm{A}},3{\rm{D}}}=\tfrac{B}{\sqrt{{\mu }_{0}\rho }}$ is the three-dimensional $\mathrm{Alfv}\acute{{\rm{e}}}{\rm{n}}$ velocity, μ₀ is the permeability of the vacuum, and $B=\tfrac{4}{\pi }{B}_{\mathrm{pos}}$ (Crutcher et al. 2004) is the total magnetic field strength. The $\mathrm{Alfv}\acute{{\rm{e}}}\mathrm{nic}$ Mach numbers of the three subregions are all less than 1 (see Table 2), indicating that the L914 cloud is sub-$\mathrm{Alfv}\acute{{\rm{e}}}\mathrm{nic}$.

These results demonstrate the significant dominance of the magnetic field over gravity or turbulence in the L914 cloud. In this case, the magnetic field introduces anisotropies into the cloud, assisting in the formation of filamentary structures, since motions perpendicular to the field lines are restricted by the Lorentz force (Soler et al. 2017). Conversely, in the case of super-$\mathrm{Alfv}\acute{{\rm{e}}}\mathrm{nic}$ turbulence (M_A > 1), motions are expected to be more random. The MHD and hydrodynamical simulations presented in Hennebelle (2013) also suggest that the magnetic field could increase the ellipticity of the clumps, making them more filamentary.

Tritsis & Tassis (2016) conducted Kelvin–Helmholtz instability and MHD simulations to reproduce the Taurus striations ¹⁰ (Goldsmith et al. 2008). The contrast of the intensity on and off the Taurus striations is ∼25% and Tritsis & Tassis (2016) suggested that only the nonlinear coupling of MHD waves can reproduce the density contrast. The contrasts in the subregions R2 and R3 of the L914 cloud are roughly 12% and 28%, respectively (see Section 3.1). We further estimate the magnetic Jeans length (λ_J,mag) of the L914 filament using the following equation (Krumholz & Federrath 2019):

$$\begin{eqnarray}&&{\lambda }_{{\rm{J}},\mathrm{mag}}={\lambda }_{{\rm{J}}}\,{\left(1+{\beta }^{-1}\right)}^{\tfrac{1}{2}}={\left[\displaystyle \frac{\pi {c}_{{\rm{s}}}^{2}(1+{\beta }^{-1})}{G\rho }\right]}^{\tfrac{1}{2}},\end{eqnarray} \tag{ 13 }$$

where ρ and λ_J represent the mass density and the standard Jeans length including only thermal pressure, respectively. The plasma beta (β) is calculated as $\beta =\tfrac{{c}_{{\rm{s}}}^{2}}{{V}_{{\rm{A}},\ 3{\rm{D}}}^{2}}$. Using the parameters obtained above, we estimate the magnetic Jeans length to be in the range of ∼2–10 pc. However, the H₂ number densities of the striations tend to be much lower than those in the filaments (i.e., R1, R2, and R3). According to the relation that magnetic field strengths are proportional to the H₂ number densities (Crutcher & Kemball 2019), the magnetic field strengths of the striations are estimated to be much weaker. For instance, if we take B = 11 μG, the plasma parameter β becomes 0.1, a value commonly adopted in the high-magnetization model (Soler et al. 2013). Consequently, the estimated magnetic Jeans length is approximately 1.4–1.8 pc, which is consistent with the period of the striations observed in this work (see Section 3.1). Our results suggest that the striations are likely produced by MHD processes. If the striations are created by fast magnetosonic waves, Tritsis et al. (2018) predict that the power spectra of column density cuts perpendicular to striations have peaks at roughly the same wavenumbers as the velocity centroid power spectra, proposing a new method to calculate the magnetic field strength,

$$\begin{eqnarray}&&{B}_{\mathrm{pos}}={{\rm{\Gamma }}}_{n}{N}_{{{\rm{H}}}_{2}}\sqrt{4\pi \rho },\end{eqnarray} \tag{ 14 }$$

where Γ_n is the square root of the ratio of the power in the velocity power spectrum and the power in the column density power spectrum, ${{\rm{\Gamma }}}_{n}=\sqrt{\tfrac{| {P}_{v1}{| }^{2}}{| {P}_{{N}_{{{\rm{H}}}_{2}}^{1}}{| }^{2}}}$. The mean column densities ${N}_{{{\rm{H}}}_{2}}$ and the mean density ρ can be computed from the $\overline{N}$ and n of the striations listed in Table 1. We present the power spectra in subregions R2 and R3 in Figure 15 and the left panel of Figure 16, respectively. The correlation of the periodicity of the velocity and the density exists only in subregion R3 (not in subregion R2). Based on this correlation, we calculate a magnetic field strength of 47 ± 12 μG, which falls within the range of the results obtained by the DCF and ST methods.

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Combining the identified accretion activities in Section 4.1, we suggest a simple scenario where, at the early stage, a sheet-like cloud with the magnetic field parallel to it fragments into filaments under the Jeans instability. The self-gravitating filaments, perpendicular to the magnetic field, continuously accrete material from their surroundings along the magnetic field lines (through striations observed in the sensitive observations). When the filaments gain sufficient material, axial fragmentation then occurs in the MHD process, with a characteristic scale corresponding to the magnetically Jeans length (i.e., the period observed in this work).