The Magnetic Field in the Colliding Filaments G202.3+2.5

We observe the magnetic field morphology toward a nearby star-forming filamentary cloud, G202.3+2.5, using James Clerk Maxwell Telescope/POL-2 850 μm thermal dust polarization observations with an angular resolution of 14.″4 (∼0.053 pc). The average magnetic field orientation is found to be perpendicular to the filaments, while showing different behaviors in the four subregions, suggesting various effects from the filaments’ collision in these subregions. With the kinematics obtained by the N2H+ observation by IRAM, we estimate the plane-of-sky magnetic field strength by two methods, the classical Davis–Chandrasekhar–Fermi (DCF) method and the angular dispersion function (ADF) method, giving B pos,dcf and B pos,adf of ∼90 and ∼53 μG. We study the relative importance between the gravity (G), magnetic field (B), and turbulence (T) in the four subregions, and find G > T > B, G ≥ T > B, G ∼ T > B, and T > G > B in the north tail, west trunk, south root, and east wing, respectively. In addition, we investigate the projection effects on the DCF and ADF methods, based on a similar simulation case, and find the 3D magnetic field strength may be underestimated by a factor of ∼3 if applying the widely used statistical B pos-to-B 3D factor when using the DCF or ADF methods, which may further underestimate/overestimate the related parameters.


Introduction
The magnetic field (B-field) is one of the major players in the star formation process, along with gravity and turbulence (Crutcher 2012;Brandenburg & Lazarian 2013;Seifried & Walch 2015;Offner & Liu 2018;Pattle et al. 2023).With the increasing polarization observations toward molecular clouds in the last decades, the B-field has been found to be dynamically important in different stages of the star formation process over a large range of spatial scales: (1) on the scale of a few to ten parsecs, the molecular clouds tend to be either parallel with or perpendicular to the global average B-field orientation (e.g., Li et al. 2013;Soler et al. 2013;Gu & Li 2019), suggesting that the B-field is strong enough to guide gas flow; and (2) on the scale of a few tenths to a parsec, the B-field is found to interact with the gas motion from filaments to cores and provide support against gravitational collapse (e.g., Seifried & Walch 2015;Tang et al. 2019).
Filaments are ubiquitous in molecular clouds and have been found to be a significant stage of the star formation process (Myers 2009;Arzoumanian et al. 2011;Liu et al. 2012b;André et al. 2014;Lin et al. 2017;Lu et al. 2018), among which velocity-coherent fiber-like structures have been identified (e.g., Li & Goldsmith 2012;Liu et al. 2012a;Hacar et al. 2013;Henshaw et al. 2016), with chains of dense cores embedded (e.g., Zhang et al. 2009Zhang et al. , 2015;;Tafalla & Hacar 2015), suggesting fragmentation from the fibers to chains of cores.Recent large-scale MHD simulations of the formation of filamentary clouds (e.g., Klassen et al. 2017;Li et al. 2018;Li & Klein 2019) have found that the B-field is generally piercing through the elongated direction of filaments or fibers.Liu et al. (2018) reported a pinched B-field in IRDC G035.39-0.33 at a distance of 2.9 kpc, hinting at an accretion flow along the filaments.Busquet et al. (2013) reported a network of filaments in the infrared dark cloud G14.225-0.506at a distance of 2.3 kpc.The B-fields probed by polarized dust emissions in the near-infrared (Santos et al. 2016) and submillimeter wavelengths (Añez-López et al. 2020) are nearly perpendicular to the main axis of the filaments.Velocity gradients are identified along the filaments, suggestive of mass accretion (Chen et al. 2019).Here, we report on a much more nearby source, G202.3+2.5, which provides more evidence that accretion flows can be traced via the pinched B-field surrounding chains of cores.G202.3+2.5 is a nearby star-forming filamentary structure that is located at the edge of the massive (3.7 × 10 4 M e ) molecular complex Monoceros OB 1 at a distance of 723 pc (Cantat-Gaudin et al. 2018).With observations of the Taeduk Radio Astronomy Observatory 14 m and the Institut de Radio Astronomie Millimétrique (IRAM) 30 m telescopes, Montillaud et al. (2019a) found that G202.3+2.5 is a complex and ramified structure (Figure 1(a)), among which two filaments (hereafter, the northwestern and northeastern filaments) join into another larger and denser one (hereafter, the main filament).Red and blue CS (J = 2−1) contours show two well-separated velocity components, standing for the northernmost part of the main filament and the southernmost part of the northeastern filament, respectively.Based on the typical chemical age of Montillaud et al. (2019a) proposed that the junction region (marked as a black rectangle) is the result of a collision that started ∼10 5 yr ago between the two components and that might trigger the formation of the cores in the main filament (listed in Table 1).
However, details of the present state and history of G202.3 +2.5, especially the role the B-field plays in the process, are poorly known, Carrière et al. (2022) and Alina et al. (2022) found that G202.3+2.5 and its host complex Monoceros OB 1 both tend to be parallel with the B-field by ¢ 4. 8 resolution (∼1 pc at a distance of 723 pc) Planck 353 GHz polarization data, suggesting that the B-field remains dragged and is providing support against fragmentation at the scale larger than 1 pc, but how the B-field behaves in the denser region is still unknown.Here, we present James Clerk Maxwell Telescope (JCMT)/POL-2 850 μm dust polarization observations to investigate the interaction between the B-field and star formation process in G202.3+2.5 from a deeper view at a scale of 0.05 pc.
This paper is organized as follows: in Section 2, we describe the observations and data reduction; we show the results in Section 3; in Section 4, we discuss our result and further analyses with an MHD simulation; and finally, we summarize our findings in Section 5.

Observations
The plane-of-sky (POS) B-field orientation is derived from polarized 850 μm continuum observations through SCUBA-2/ POL-2 on JCMT.G202.3+2.5 was observed 37 times from 2019 February to 2019 March and 2019 December to 2020 January (project codes: M19AP032 and M19BP019; PI: Tie Liu) using the SCUBA-2/POL-2 DAISY mapping mode (Holland et al. 2013;Friberg et al. 2016Friberg et al. , 2018) ) under Band 1 weather conditions (τ 225 GHz < 0.05, where τ 225GHz is the atmospheric opacity at 225 GHz), providing a total integration time of ∼21.2 hr.The effective beam size is 14 4 at 850 μm (Mairs et al. 2021), equivalent to ∼0.050 pc at a distance of 723 pc.A single POL-2 observation consists of around 40 minutes of observing time and produces a ¢ 12 diameter output map, of which the central ¢ 3 has approximately uniform noise and the central ¢ 6 has a useful level of coverage (Friberg et al. 2016).The data were reduced using a STARLINK package named SMURF (Chapin et al. 2013;Currie et al. 2014), which has been specifically developed for submillimeter data reduction from JCMT.The main processes are as follows:14 1.The calcqu command converted raw bolometer time streams into separate Stokes I, Q, and U time streams, and the makemap routine in the script pol2map generated individual I maps from I time streams and coadded them to produce an initial reference I map. 2. The pol2map command was rerun with the initial I map to create two masks: ASTMASK (which defines background regions in the reference I map) and PCAMASK (which defines the source regions to exclude when creating the background model within the makemap routine).3. The pol2map command was rerun again with ASTMASK and PCAMASK to create improved final I maps, which were coadded to the final I map.With the same parameters and masks, Q and U maps, along with the corresponding variance maps and polarization catalog, were created as well.The final I, Q, U maps, and polarization catalog were gridded to 7″ pixel −1 for a Nyquist sampling. 15he final I, Q, and U maps are in units of picowatts.We converted them to units of Jy beam −1 by applying the flux conversion factor (FCF) of 668 Jy beam −1 pW −1 .This value is 1.35 times larger than the standard SCUBA-2 850 μm FCF 495 Jy beam −1 pW −1 because of the flux loss from POL-2 (Mairs et al. 2021).Figures 1(b)-(d) shows the Stokes I,16 Q, and U maps of these JCMT/POL-2 observations.The rms levels of the background regions are ∼10 mJy beam −1 in I and ∼1.5 mJy beam −1 in Q and U .

and ( )
Therefore, the debiased p and its uncertainty (δp) are derived by where δI is the uncertainty of I. Finally, the polarization angle (θ) and its uncertainty (δθ) (Naghizadeh-Khouei & Clarke 1993) are estimated by We note that there are many debiasing methods for polarization data (e.g., Montier et al. 2015aMontier et al. , 2015b)), but in this work, we use P for pseudo-vectors selection only, thus the effect of our debiasing method is minimal on our results.The derived B-field angles are not determined from the absolute calibration, but the relative values of Q and U (Pattle et al. 2017).

Dust Polarization Properties
Based on the grain alignment theory that the shortest axis of dust grains tends to align with the B-field (Lazarian 2003), we can derive the projected POS B-field orientation by rotating the observed polarization pseudo-vectors by 90°.The polarization pseudo-vectors used here are selected with criteria of I/δI 10, P/δP 2, and δp 5%.The inferred B-field segments are shown in the left panel of Figure 2, overlaid on the N(H 2 ) column density map with an average orientation of 113°± 33°, roughly showing a perpendicular alignment with the main structure of G202.3+2.5.
As shown in the middle right panel of Figure 2, there is a trend of decreasing polarization fraction with increasing dust emission intensity (i.e., the depolarization effect).A power law with index −0.89 is fitted to all data (the dashed black line; the power-law indices are −0.90 and −1.00 for data with P/δP 3 and 3 P/δP 2, respectively).The upper right panel shows a histogram of the inferred B-field angles with different P/δP levels, with an average value of 113°± 33°1 7 marked as a dashed gray line and average values of P/δP 3 and 3 P/ δP 2 of 112°± 31°and 117°± 37°.The lower right panel shows the distribution of the polarization fraction.The distribution peaks at ∼3%, with a tail extending to ∼10%-20%.The average, standard deviation, and median of the polarization fraction are 4.2%, 3.0%, and 3.3% for the whole data.For the data with P/δP 3, the corresponding values are 4.8%, 3.5%, and 3.8%, and for data with 3 P/δP 2, the values are 3.6%, 2.4%, 2.9%.As shown in the right panels, segments with P/δP 3 and 3 P/δP 2 have similar B-field angle and polarization fraction distributions, thus we include them together for the following analysis and discussion to increase the statistics.

B-field Strength of G202.3+2.5
Because of the lack of direct ways to measure the B-field strength in molecular clouds, the Davis-Chandrasekhar-Fermi (DCF) method (Davis 1951;Chandrasekhar & Fermi 1953) is widely used to give a rough estimate.The DCF method relies on the assumption that there is a prominent mean (uniform/ordered) B-field component (B 0 ) with a perturbation (B t , a turbulent B-field) caused by turbulence, which assumes there is equipartition between the turbulent magnetic energy ( ) and the turbulent kinetic energy ( , where V is the volume, σ v,⊥ is the transverse turbulent velocity dispersion, and ρ is the gas density).In addition, assuming the turbulence is isotropic, σ v,⊥ equals the line-of-sight (LOS) velocity dispersion σ v .Thus, the strength of the POS turbulent B-field, B pos,t , could be derived from , and the strength of the POS uniform B-field could be estimated from where f DCF is a correction factor, and the B pos,t /B pos could be roughly estimated from the angular dispersion between the local B-field orientation and the mean one (σ θ ).
Recently, studies of DCF methods have shown different ways to quantify B pos,t /B pos more accurately (e.g., Heitsch et al. 2001;Falceta-Goncalves et al. 2008;Cho & Yoo 2016;Liu et al. 2021;Chen et al. 2022).Here we propose two of them to estimate the B-field strength: the modified classical DCF method and the calibrated angular dispersion function method (hereafter, the angular dispersion function or ADF method-a modified DCF method raised by Hildebrand et al. 2009;Houde et al. 2009Houde et al. , 2016)).

Estimation of Gas Density and LOS Velocity Dispersion
Before estimating the gas density (ρ), we apply the J-comb algorithm (Jiao et al. 2022) to get a column density map with higher resolution (the left panel of Figure 2) than the one adopted from Montillaud et where Ω m is the solid angle, B ν (T dust ) is the Planck function at temperature T dust , and the column density N(H 2 ) then can be approximated by where κ ν = 0.1 cm 2 g −1 (ν/1000 GHz) β is the adopted dust opacity, assuming a gas-to-dust ratio of 100 and an opacity index β of 2 (Hildebrand 1983;Beckwith et al. 1990),19 μ = 2.8 is the mean molecular weight, and m H is the atomic mass of hydrogen.
The new column density map (the left panel of Figure 2) has a resolution of 18″, and the mass above N(H 2 ), a contour of 1.5 × 10 22 cm −2 (the inner dashed contour in the left panel of Figure 2), is 274 M e and the mass above N(H 2 ), a contour of 8.0 × 10 21 cm −2 (the outer dashed contour in the left panel of Figure 2), is 330 M e .20 Considering G202.3+2.5 is found to be the junction region of two colliding filaments with lengths of ∼1.3 pc and radius of ∼0.1 pc (Montillaud et al. 2019a), we assume G202.3+2.5 as two cylinders with a length of ∼1.3 pc and a radius of ∼0.1 pc to estimate the volume.According to the two values of mass estimated above, ρ is then derived as 2.27 × 10 −19 g cm −3 and 2.73 × 10 −19 g cm −3 , respectively, and we take the average value (2.50 ± 0.23) × 10 −19 g cm −3 (the corresponding volume density is (5.34 ± 0.49) × 10 4 cm −3 ) for the following analysis.
As for the LOS velocity dispersion, σ v , we extracted kinematic information from IRAM 30 m observations with a resolution of 27 8, adopted from Montillaud et al. (2019a).As shown in Figure 3(a), the detected is the isothermal sound speed and T is the dust temperature (the average is 13.0 K, with a standard deviation of 1.0 K), adopted from Montillaud et al. (2019a), and the average σ v of G202.3+2.5 is 0.66 ± 0.21 km s −1 .

The Classical DCF Method
A f DCF of 0.5 is widely used, based on the simulation result from Ostriker et al. (2001), and Equation (7) could be modified as However, this formula is only applicable on a scale larger than 1 pc with σ θ < 25° (Heitsch et al. 2001;Liu et al. 2022;Pattle et al. 2023).In order to remove the small-σ θ restriction, Li et al. (2022) replaced σ θ with ( ) s q tan (cf., Heitsch et al. 2001;Falceta-Goncalves et al. 2008).Thus, the modified classical DCF method could be written as and the B pos,dcf of G202.3+2.5 is derived as 90 ± 37 μG.

The Calibrated ADF Method
Alternatively, B pos,t /B pos can be represented as ( ) , the ratio of the turbulent-to-total B-field strength on the POS, which is determined by the structure function of the polarization angles (Falceta-Goncalves et al.   1. method to account for larger-scale field structures and LOS effects, respectively.Further, with a numerical simulation, Liu et al. (2021) calibrated the ADF method and found it correctly accounts for the ordered B-field structure and beam smoothing.Here, we use the calibrated ADF method (Liu et al. 2021(Liu et al. , 2022) ) and the routine is outlined as follows: (1) Derive the ADF that accounts for the ordered field and the POS turbulent correlation effect from where ΔΦ(l) is the angular difference of two B-field line segments separated by a distance of l, l δ is the turbulent correlation length for the local turbulent B-field, W is the standard deviation of the Gaussian beam, and ¢ a l 2 2 is the first term of the Taylor expansion of the ordered component of the ADF.For the case that l ?l δ and l ?W, Equation (13) can be simplified to (2) Fit the large-scale portion of the ADF (Equation ( 14)) to estimate , which is the intercept of the fitted ordered ADF as shown in Figure 4-the reduced function in Equation ( 14) constructed with the best-fit results is shown as dashed cyan curves.The best-fit ( ) of G202.3+2.5 and its subregions are listed in Table 2.
(3) Estimate the total POS B-field strength, B pos,adf , by where f DCF is taken as 0.21 (with 45% uncertainty at scales between 0.1 and 1 pc; Liu et al. 2021), which gives B pos,adf ; 52.7 ± 24.5 μG.Also, the strength of the total 3D B-field, B 3D,adf , could be estimated as 67.1 ± 31.2 μG by the same process described in Section 3.2.2.

Discussion
As shown in the left panel of Figure 2, the B-field morphology is different in different regions of G202.3+2.5, thus we divide G202.3+2.5 into four regions to conduct further analysis: the north tail, east wing, west trunk, and south root. 21n north tail, the B-field is roughly perpendicular to the dense core 1453, whose long axis is parallel with the filament, but with larger dispersion.In the west trunk, the B-field is perpendicular to the filament and shows a typical "hourglass" shape around the dense core 1446.The situation is different in the other two regions.In the south root, where the southernmost tip of the northeastern filament has already merged into the main filament, the B-field is parallel with the filament, but perpendicular to the core 1450.As for the east wing, the front line of the collision, the B-field is significantly disturbed, which is reflected in the orientation of the B-field changing from parallel with the northeastern filament to perpendicular to it.

Gravity versus B-field versus Turbulence
To quantitatively compare the relative importance of the B-field (B), turbulence (T), and gravity (G) toward the subregions, we have calculated some key parameters as follows, based on the B-field strength calculated above.The results are listed in Table 2.As the B-field strength has been estimated by two methods, these parameters also have two versions.

Alfvén Mach Numbers
The relative importance between the turbulence and B-field can be parameterized by the Alfvén Mach number , based on the isotropic turbulence assumption, and is the velocity of the Alfvén wave.It is worth noting that considering Equations ( 12) and (15), and assuming = p B B 3D 4 pos (Crutcher et al. 2004),  A could be written as a function of ( ) (Equation ( 17)) or σ θ (Equation ( 18)): In all subregions,  A is larger than 1, indicating a T > B status.However, it is worth noting that as v A depends on B 3D , which relates to the the B pos -to-B 3D factor a lot.The B pos -to-B 3D factor applied here is derived statistically as 4/π, which may cause a large bias for a specific case, as further discussed in Section 4.3.

Virial Parameters
The virial parameter, α vir , is used to estimate the relative importance of the kinetic support against gravity and is defined via where a is the index of the radial density profile (ρ ∝ r − a ) and σ v , R, G, M, and M K are the velocity dispersion, radius, gravitational constant, mass, and kinetic virial mass, respectively (Bertoldi & McKee 1992).If taking the effects of the B-field into account, the magnetic virial parameter, α vir,B , can Notes.The rows give the parameters of the subregions Row (1): velocity dispersion.Row (2): mean column density.Row (3): average mass of masses calculated above the N(H 2 ) levels of 8.0 × 10 21 cm −2 and 1.5 × 10 22 cm −2 .Row (4): effective radius.Row The shape of G202.3+2.5 is filamentary, and the effective radius value and related parameters are for reference only.
be calculated following Liu et al. (2020) via where The effective radius could be estimated from p = R A , where A is the effective area above the column density of 1.5 × 10 21 cm −2 , then α vir,B,adf and α vir,B,dcf could be derived, respectively.
Due to the limited resolution, the value of a is hard to estimate, as a = 0 and a = 2 indicate a uniform density profile and a gravitationally bounded one, respectively, whereas the real a toward subregions should be in between, thus we calculate α vir with a ä [0, 2], as shown in Figure 5, to give an estimated region of α vir .Considering the west trunk and south root have higher N(H 2 ) and embed dense cores already, we speculate a being between 1 and 2 in these two regions, which gives α vir,B ∼ 1 and α vir < 1 in the west trunk and α vir,B 1 and α vir < 1 in the south root, indicating the statuses of G T and G ∼ T, respectively.For the other two subregions, α vir and α vir,B are smaller than 1 in the north tail and larger than 1 in the east wing, suggesting statuses of G > T and T > G, respectively.

Mass-to-flux Ratios
We determine the ratio of mass to magnetic flux, M/Φ, in units of the local magnetic stability critical parameter λ (Crutcher et al. 2004), to estimate the relative importance of the B-field and gravity: where (M/Φ) observed is the observed ratio given by and (M/Φ) critical is the critical ratio given by Thus, we estimate λ by the relation in Crutcher et al. (2004): ´-B 7.6 10 N H , 2 6 21 2 pos where N(H 2 ) is the column density in units of cm −2 and B pos is the POS total B-field strength in units of μG.A value λ < 1 indicates that the B-field is strong enough to support the gravitational collapse (magnetically subcritical), while λ > 1 means that the B-field cannot prevent gravitational collapse (magnetically supercritical).λ in the host region of G202.3 +2.5 (north main) is 0.95 ± 0.41 (Alina et al. 2022), indicating a transcritical status at the scale larger than 1 pc or (e.g.) the large-scale B-field is still relatively comparable to the gravity.As for G202.3+2.5, B pos,adf and B pos,dcf are 52.7 ± 24.5μG and 89.6 ± 36.7μG, respectively, and the average column density is (3.18 ± 0.47) × 10 22 cm −2 , thus we find λ adf ∼ 3.5 ± 1.8 and λ dcf ∼ 2.1 ± 1.1.Crutcher et al. (2004) proposed that the (M/Φ) observed will be overestimated by up to a factor of 3 due to geometrical effects, so this implies that λ adf ∼ 1.2 ± 0.6 and λ dcf ∼ 0.7 ± 0.4, respectively.However, since G202.3+2.5 appears to lie in or near the POS (Montillaud et al. 2019a), the factor of 3 is too large, thus a λ that is slightly larger than 1 is more convincing, suggesting that on the scale of the filament, G202.3+2.5 is slightly magnetically supercritical or transcritical.Toward the four subregions, λ is also larger than 1, even if excessively accounting for the geometrical effect, suggesting a magnetically supercritical status (G > B) on the scale of 0.05 pc.Therefore, we are able to conclude the relative importance of G, B, and T: in the north tail, G > T > B, where there is the starless core 1453 with a mass of 22.3 M e ; in the west trunk, G T > B, where the dense cores 1446 and 1448 with mass of 15-22 M e have already formed and embedded a Class I YSO; in the south root, G ∼ T > B, where the massive core 1450, with a mass of 51.7 M e , has formed and is still accumulating mass from gas flows from the filaments' collision, which makes T as large as G; and in the east wing, T > G > B, where the turbulence dominates, and no dense cores have formed.

Compressed B-field in the Collision Filaments
In order to study the interaction between the B-field and collision, we compare the relative orientation between the B-field and filament structure in Figure 6 by applying the autocorrelation function to estimate the elongation direction of the column density contour (Figure 7).The north tail and west trunk have no overlap with the northeastern filament, the velocity dispersion (Figure 3(b)) and gradient (Figure 6(a))22 are relatively small, and the B-field morphology is simple, suggesting that the B-field is not affected by the collision badly in these two regions.To be specific, in the north tail, which is the most diffuse subregion, with an average ( ) N H 2 of 2.49 × 10 22 cm −2 , a bimodal distribution of the B-field angle is found (Figure 6(b)), which results in a large σ θ of 42°± 14°.The peak at 60°comes from the outskirt B-field, while the other at 110°is contributed to the perpendicular B-field inside the protostellar core 1453.In the west trunk, the densest part of the main filament where two Class I sources (core 1446 and core 1448) are embedded, the B-field shows a perpendicular alignment with the structure, and a λ adf = 4.8 (λ dcf = 3.0) indicates the magnetically supercritical status of the west trunk, thus we suggest the gravity is dominating the B-field and drags the field lines.
In Figure 6, the red arrows mark the possible direction of the gas flow traced by the velocity gradient, showing the possible gas flow accumulation toward core 1450.Along the longest arrow, the B-field orientation changes rapidly, with a large velocity dispersion (Figure 3(b)), indicating that the B-field has been disturbed significantly in the east wing.In contrast, in the south root, where the two filaments are overlapped in the LOS, the B-field strength is the strongest of the four subregions, and its average orientation is close to the one in the east wing, suggesting the B-field is compressed from the east wing to the south root by the collision.The orientation of the B-field is turned around to be parallel with the filament, and the transition is clear in the interface of the west trunk and south root, where the B-field orientation turns nearly 90°.The compression signature shown in the south root may hint that the gas flows toward the dense cores in return; similar behavior is also seen in a distant IRDC (Liu et al. 2018) and simulation results (Li et al. 2018).
On the scale larger than 1 pc, Carrière et al. (2022) and Alina et al. (2022) have found a roughly parallel cloud-field alignment toward the host region of G202.3+2.5 (north main), based on Planck data.In this work, we find a perpendicular cloud-field alignment toward G202.3+2.5 on the scale of 0.05 pc, but in the south root, the denser region of G202.3+2.5, the alignment turns back to parallelism, due to the compression from the gas flow caused by the filaments' collision.Pillai et al. (2020) found a similar parallel-to-perpendicular-to-parallel transition with increasing density in a hub-filament system, the Serpens South Cloud, where the perpendicular-to-parallel transition that happens at 2 ) is thought to be caused by merging gas flow reorienting the B-field.Though the south root has a simpler structure than the Serpens South Cloud, the similar perpendicular-to-parallel transition at a similar density indicates the B-field can be reoriented by the gas flow to be parallel with the filament at a high-density region.
Based on the discussion above, we suggest the following scenario: in the east wing, the northeastern filament dashes toward the main filament.The collision causes a large velocity gradient and dispersion and disturbs the B-field orientation, which results in a large B-field angle dispersion, but the B-field is still resisting the alignment with the gas flow and is compressed in the front line of the collision.While in the south root, gravity effects dominate, gas flow compresses the B-field  (2) LOS depth of the structures.We calculate the volume of the subregions by multiplying the area that is above the N(H 2 ) contour of 1.5 × 10 22 cm −2 and the estimated depth with a value of 0.2 pc, based on the cylindrical shape.Here, an uncertainty of 0.05 pc is expected, which would cause a ∼25% uncertainty in the density, causing a ∼ 15% uncertainty in the calculation of the B-field strength due to the error propagation.
(3) The correction factor, f DCF , in Equation (7).The ADF and classical DCF take different f DCF , which are 0.21 and 0.5, respectively.The classical f DCF is taken as 0.5 based on the simulation result from Ostriker et al. (2001), which is applicable to low-density regions with scales larger than 1 pc and σ θ < 25°, thus ( ) s q tan is applied to replace σ θ to remove the small-σ θ restriction.Later, Liu et al. (2021) adopted the value of 0.21, as they found the contribution from the ordered field structure could cause an overestimation of the angular dispersion by an average factor of ∼2.5 when calibrating the ADF method.The value of f DCF affects the final result of the B-field strength directly, and as shown in the result in Section 4.3, both methods may underestimate the B-field strength by a factor of ∼2-3, but still within an acceptable range.Thus, we suggest it is necessary to compare with similar simulation cases to constrain the result.

Figure 1 .
Figure 1.(a) Column density of molecular hydrogen in G202.3+2.5 with a resolution of 38 5 (adopted form Montillaud et al. 2015).The blue and red contours show the CS (J = 2−1) moment 0 data from the IRAM data (adapted from Montillaud et al. 2019a), which are integrated from the velocity channels 4.2 to 6.6 km s −1 and 7.8 to 9.6 km s −1 , respectively.The curved dashed white lines sketch the structures of the main filament, the northeastern filament, and the northwestern filament.The white segments represent the B-field orientations inferred from Planck 353 GHz polarization data, and the black rectangle denotes the region shown in (b)-(d).A 1 pc scale bar is shown in the lower right corner.(b)-(d) JCMT/POL-2 850 μm Stokes I, Q, and U maps of G202.3+2.5, respectively, where the contours show the intensity of Stokes I at the levels of [35, 100, 300 and 1000] mJy beam −1 , with an average measured rms level of 10 mJy beam −1 .The beams are shown in the left corners.

Figure 2 .
Figure 2. Left: observed B-field of the G202.3+2.5 region.The color map is the N(H 2 ) of molecular hydrogen with a resolution of 18″.The beam is shown in the lower left corner.The dashed purple lines divide G202.3+2.5 into four subregions: the east wing, north tail, west trunk, and south root, respectively.The black dashed contour marks the N(H 2 ) level of 1.5 × 10 22 cm −2 , and the solid contours show the intensity of Stokes I at the levels of [35, 100, 300 and 1000] mJy beam −1 .The red and blue segments represent JCMT/POL-2 B-field orientations with S/N levels of P/δP 3 and 3 P/δP 2, respectively.The black ellipses mark the locations of the cores listed in Table 1.A 0.2 pc scale bar is shown in the lower right corner and the 18″ beam is shown in the lower left corner.Upper right: histogram of B-field orientations inferred from JCMT/POL-2 with different P/δP levels.The dashed line represents the average B-field orientation of all the segments and the gray region marks the standard deviation range.Middle right: polarization fraction vs. Stokes I.The blue and red colors represent data with different P/δP levels, and the dashed red and blue lines show the power-law fits, respectively.The dashed black line is the power-law fit for all data.Lower right: histogram of polarization fraction with different P/δP levels.
region matches well with the [0.8, 1.5] × 10 22 cm −2 N(H 2 ) contours and Stokes I contours, suggesting region of G202.3+2.5.The FWHM line width, Δv, is derived from hyperfine structure line fitting, and the nonthermal component σ v (Figure 3(b)) is then derived from of f between the LOS and B, the strength of the total 3D B-field, B 3D,dcf , can be estimated statistically as 114 ± 47 μG by = p 2008).Hildebrand et al. (2009) and Houde et al. (2009) further expanded the

Figure 4 .
Figure4.ADFs of G202.3+2.5 and its subregions.An effective depth is calculated based on the data set before ADF fitting, and only dots that are at a distance smaller than the effective depth are fitted.
(5): mean density.Row (6): the elongation direction of the structure derived by the autocorrelation function above a column density of 8.0 × 10 21 cm −2 .Row (7): the elongation direction of the structure derived by the autocorrelation function above a column density of 1.5 × 10 22 cm −2 .Row (8): the mean B-field orientation direction.Row (9): the angular dispersion.Row (10): turbulent-to-uniform B-field strength on the POS.Row (11): turbulent-to-total B-field strength on the POS.Row (12): total POS B-field strength derived by ADF.Row (13): total POS B-field strength derived by classical DCF.Row (14): magnetic stability critical parameter based on B pos,adf (not considering the factor of geometrical effect).Row (15): magnetic stability critical parameter based on B pos,dcf (not considering the factor of geometrical effect).Row (16): Alfvén wave velocity based on B pos,adf .Row (17): Alfvén wave velocity based on B pos,dcf .Row (18): Alfvén Mach number based on B pos,adf .Row (19): Alfvén Mach number based on B pos,dcf .Row (20): range of virial parameter by applying the value of a from 0 to 2. Row (21): range of magnetic virial parameter based on B pos,adf by applying the value of a from 0 to 2. Row (22): range of magnetic virial parameter based on B pos,dcf by applying the value of a from 0 to 2. Row (23): relative importance between gravity (G), B-field (B), and turbulence (T). a The uncertainties in (1) and (2) are the standard deviations of the means.b

Figure 5 .
Figure 5. Virial parameter α vir,B as a function of the index a of the radial density profile.The solid and dashed lines with dot markers show α vir,B,adf and α vir,B,dcf , respectively.The solid lines with cross markers show α vir .An α vir = 1 line is shown with the dotted black line.

Figure 6 .
Figure 6.Relative N 2 H + velocity gradient overlaid by the B-field.The red and blue show the outermost contours of CS (J = 2−1), shown in panel (a) of Figure 1, and the black ellipses mark the locations of the cores.(b)-(e) Distributions of the B-field orientations in the four subregions.The solid red and pink lines mark the density elongation direction derived by the autocorrelation function based on N(H 2 ) contours of 1.5 × 10 22 and 8.0 × 10 21 cm −2 , respectively.The dashed black lines show the average orientation of the B-field, and the gray regions mark the standard deviation range.(f) Centroid map of the isolated hyperfine component of N 2 H + in G202.3+2.5 overlaid by the velocity gradient direction segments.In (a) and (f), the dashed yellow lines divide G202.3+2.5 into the north tail, west trunk, east wing, and south root, respectively.The red arrows indicate the possible gas flow directions.

Figure 7 .
Figure7.The autocorrelation maps of G202.3+2.5 and four subregions.The upper and lower panels show the result based on the column density above the contour levels of 8.0 × 10 21 and 1.5 × 10 22 cm −2 , respectively.The background maps show the column density maps after applying the autocorrelation function, and white ellipses are fitted to estimate the elongation directions.

( 4 )
The estimation of B 3D .Crutcher et al. (2004) suggested = p which is applicable for the big sample where B 3D shows a random alignment with the POS.For a specific case like G202.3+2.5, the factor of p 4 would be a very rough estimation, by comparing the simulation result shown in Section 4.3, which gives a factor of ∼3-4.And this further affects the calculation of the Alfvén wave velocity (v A ), the Alfvén Mach number ( A ), and the magnetic virial parameter (α vir,B ).

Figure 8 .
Figure 8. Analysis of an MHD simulation of colliding filaments.The contours in all panels show the column density with levels of [1.5, 5, 10]×10 22 cm −2 , and the overlaid segments show the B-field orientations (plotted every 2 × 2 pixels, for clarity).(a) Column density of the simulated filamentary structures with a pixel size of 10,000 au.(b-c) LOS velocity and velocity dispersion maps of the colliding region of the MHD simulation case, which matches the structure of G202.3+2.5, to make a fair comparison.(d) Histogram of the B-field orientations for pixels with N(H 2 ) larger than 1.5 × 10 22 cm −2 .The dashed black line shows the average orientation, 118°.8, and the gray region shows the standard deviation range ±40°.3.

Figure 9 .
Figure 9. Left: correlation between the uncertainty of the B-field angles from the JCMT/POL-2 observations and the corresponding S/N of the polarization intensity, P/δP.Right: distribution of the P/δP level of the JCMT/POL-2 B-field data.

Table 1
Parameters of Cores inside G202.3+2.5 The obtained deconvolved Planck map has an angular resolution close to the SPIRE 500 μm map and preserves the flux level of the initial Planck map.The deconvolved map was then combined with the JCMT/SCUBA-2 850 μm Stokes I (Lucy 1974)ombined Stokes I map.We extrapolated an 850 μm flux map from the spectral energy distribution (SED) of the Herschel SPIRE data and used this map as a model image to deconvolve the 353 GHz Planck map (Planck Collaboration et al. 2011) with the Lucy-Richardson algorithm(Lucy 1974).beam, and all maps were regridded to have the same pixel size.We weighted the data points by the measured noise level in the least-squares fits.As a modified blackbody assumption, the flux density S ν at the frequency ν is given by

Table 2
Parameters of the Four Subregions