A Multi-Scale Picture of Magnetic Field and Gravity from Large-Scale Filamentary Envelope to Core-Accreting Dust Lanes in the High-Mass Star-Forming Region W51

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A Multi-Scale Picture of Magnetic Field and Gravity from

Large-Scale Filamentary Envelope to Core-Accreting Dust Lanes

in the High-Mass Star-Forming Region W51

Patrick M. Koch1, Ya-Wen Tang1, Paul T.P. Ho1,2, Pei-Ying Hsieh3,4, Jia-Wei Wang1,

Hsi-Wei Yen1, Ana Duarte-Cabral5, Nicolas Peretto5, and Yu-Nung Su1

1Academia Sinica, Institute of Astronomy and Astrophysics, Taipei, Taiwan

2East Asian Observatory (EAO), 660 N. Aohoku Place, University Park, Hilo, Hawaii

96720, USA

3Joint ALMA Observatory, Alonso de C´ordova, 3107, Vitacura, Santiago 763-0355, Chile

4European Southern Observatory, Alonso de C´ordova, 3107, Vitacura, Santiago 763-0355,

Chile

5School of Physics & Astronomy, Cardiﬀ University, Queen’s Building, The Parade,

Cardiﬀ, CF24 3AA, UK

pmkoch@asiaa.sinica.edu.tw

ABSTRACT

We present 230 GHz continuum polarization observations with the Atacama

Large Milimeter/Submillimeter Array (ALMA) at a resolution of 0.

001 (∼540 au)

in the high-mass star-forming regions W51 e2 and e8. These observations re-

solve a network of core-connecting dust lanes, marking a departure from earlier

coarser more spherical continuum structures. At the same time, the cores do

not appear to fragment further. Polarized dust emission is clearly detected. The

inferred magnetic ﬁeld orientations are prevailingly parallel to dust lanes. This

key structural feature is analyzed together with the local gravitational vector

ﬁeld. The direction of local gravity is found to typically align with dust lanes.

With these ﬁndings we derive a stability criterion that deﬁnes a maximum mag-

netic ﬁeld strength that can be overcome by an observed magnetic ﬁeld-gravity

conﬁguration. Equivalently, this deﬁnes a minimum ﬁeld strength that can sta-

bilize dust lanes against a radial collapse. We ﬁnd that the detected dust lanes

in W51 e2 and e8 are stable, hence possibly making them a fundamental com-

ponent in the accretion onto central sources, providing support for massive star

formation models without the need of large accretion disks. When comparing to

arXiv:2210.07593v1 [astro-ph.GA] 14 Oct 2022

– 2 –

coarser resolutions, covering the scales of envelope, global, and local collapse, we

ﬁnd recurring similarities in the magnetic ﬁeld structures and their correspond-

ing gravitational vector ﬁelds. These self-similar structures point at a multi-scale

collapse-within-collapse scenario until ﬁnally the scale of core-accreting dust lanes

is reached where gravity is entraining the magnetic ﬁeld and aligning it with the

dust lanes.

Subject headings: ISM: individual objects: (W51 e2, W51 e8) – ISM: magnetic

ﬁelds – polarization – stars: formation

1. Introduction

The formation and evolution of molecular clouds, the sites of high-mass star formation,

are a complex interaction between gravity, turbulence, and magnetic ﬁelds, covering orders

of magnitudes in physical length and density (e.g. Hennebelle & Inutsuka 2019; Li et al.

2014; Crutcher 2012). Moreover, a variety of feedback mechanisms add to the intricacy of

the formation processes. Among all these constituents, the magnetic (B-)ﬁeld still poses the

likely biggest challenge to the establishment of a ﬁrm picture of star formation across time and

scale. This has been largely due to the diﬃculty of detecting signals that originate from the

presence of B-ﬁelds (as they are typically only at the percent level of non-magnetic signals)

and the limited techniques to measure a B-ﬁeld strength to gauge its signiﬁcance against other

constituents. Recent advances in observational capabilities, oﬀering substantially improved

sensitivities, are now rapidly changing this situation. Of particular interest are observations

of dust continuum polarization. This is because a growing suite of instruments covering

complete ranges in wavelengths and resolutions is available, and because dust polarization

observations typically lead to the most connected and complete coverage in detections, unlike

e.g., Zeeman observations that remain challenging and are often limited to more localized

and small areas in a source.

When utilizing dust polarization observations in the (sub-)millimeter regime, dust grains

are thought to be aligned with their shorter axis parallel to the B-ﬁeld. Rotating detected

polarization orientations by 90◦then yields magnetic ﬁeld orientations (Cudlip et al. 1982;

Hildebrand et al. 1984; Hildebrand 1988; Lazarian 2000; Andersson et al. 2015). At the den-

sities and scales probed with the here presented observations, radiative torques can provide

an explanation for this B-ﬁeld-dust alignment (Draine & Weingartner 1996, 1997; Lazarian

2000; Cho & Lazarian 2005; Lazarian & Hoang 2007; Hoang & Lazarian 2016). A growing

literature is mapping magnetic ﬁeld structures based on this property and investigating both

statistical ﬁndings and detailed higher-resolution features. The survey conducted by Zhang

– 3 –

et al. (2014) with the SubMillimeter Array (SMA) towards a sample of 14 high-mass star-

forming regions resolving scales around 0.1 pc (resolutions θof 100 to several arcseconds) at

345 GHz provides statistical evidence for magnetic ﬁelds playing an important role during

the collapse and fragmentation of massive molecular clumps. Further enlarging this sample

to 18 massive dense cores, the recent work in Palau et al. (2021) ﬁnds a tentative positive

correlation between the number of fragments and the mass-to-ﬂux ratio, hinting that mag-

netic ﬁelds can possibly suppress fragmentation. Investigating the role of the B-ﬁeld in the

infrared dark cloud G14.225−0.506 using the Caltech Submillimeter Observatory (CSO) ob-

servations with SHARP with θ∼1000 at 350µm, A˜nez-L´opez et al. (2021) ﬁnd that diﬀerent

B-ﬁeld morphologies and strengths can explain the diﬀerent observed fragmentation proper-

ties. Also observed with the CSO/SHARP, the diﬀerent fragmentation types in G34.43+0.24

are explained by a diﬀerent relative signiﬁcance of gravity, turbulence, and magnetic ﬁeld

(Tang et al. 2019). Observed with POL-2 on the James Clerk Maxwell Telescope (JCMT)

with θ∼1400 at 850 µm, the NGC 6634 ﬁlamentary network is resolved down to about

0.1 pc, revealing detailed B-ﬁeld structures and variations across the main ﬁlament and sub-

ﬁlaments (Arzoumanian et al. 2021). Higher-resolution (sub-)arcsecond observations with

ALMA (mostly around 850 µm and 1.2 mm) have started to reveal detailed morphological

features in the magnetic ﬁeld, such as an expanding UCHII region in G5.89−0.39 leaving a

clear imprint in the B-ﬁeld morphology (Fern´andez-L´opez et al. 2021), sharpening the earlier

coarser SMA observations (Tang et al. 2009a); a highly fragmented ﬁlament in W43-MM1

(Cortes et al. 2016); a resolved hour-glass magnetic ﬁeld structure in G31.41+0.31 (Beltr´an

et al. 2019); and ring-like and arm-like structures likely resulting from toroidal wrapping of

the magnetic ﬁeld in OMC-3 (Takahashi et al. 2019).

W51 is a high-mass star-forming complex at parallax distances around 5.41 kpc for

W51 e2 and e8 (Sato et al. 2010) and 5.10 kpc for W51 North (Xu et al. 2009), located in

a region with little foreground and background contamination. The entire complex shows

star-formation activities at various evolutionary stages (Ginsburg et al. 2017; Saral et al.

2017; Ginsburg et al. 2015). Collimated small-scale SiO outﬂows are detected in W51e2-

E, e8, and North (Goddi et al. 2020), and they appear to connect to larger-scale outﬂows

seen in 12CO(2–1) in all three sources (Ginsburg et al. 2017) and also in 12CO(3–2) in e2-

E (Shi et al. 2010). The plane-of-sky B-ﬁeld morphology has been mapped with a series

of polarization observations with increasingly higher angular resolutions θ, starting from

the earliest interferometric observations with BIMA (θ∼300 ; Lai et al. 2001) to the SMA

(θ∼0.

007; Tang et al. 2009b, 2013) and to the ﬁrst observations with ALMA (θ∼0.

0026; Koch

et al. 2018). The BIMA observations at 1.3 mm showed W51 e2 and e8 as an elongated

connected north-south structure with a magnetic ﬁeld mostly perpendicular to it (Lai et al.

2001). The e2 region manifested itself as a clear polarization hole. The higher-resolution

– 4 –

SMA observations at 0.87 mm revealed more complex magnetic ﬁeld structures which are

likely the reason for the depolarization in the larger BIMA beam. The ﬁner B-ﬁeld structures

in e2 and e8 showing hourglass-like topologies with clearly bent ﬁeld lines were interpreted

as gravitational collapse imprinted onto the B-ﬁeld morphology (Tang et al. 2009b). The

ﬁrst ALMA observations at 1.3 mm (Koch et al. 2018), again improving the resolution by a

factor of 10 in area, revealed striking new features. In particular, they clearly resolved the

satellite core e2-NW with bow-shock shaped B-ﬁeld structures that are hinting infall of this

smaller core towards the dominating mass center e2-E. Additionally, areas with centrally

converging symmetrical B-ﬁeld structures (convergence zones) and possibly streamlined B-

ﬁeld morphologies were detected. A generic feature seen in many of the resolved cores inside

e2, e8, North, and also on larger scale between e2 and e8, is B-ﬁeld structures resembling

gravitational pull towards the core’s center on one side with the other side showing B-

ﬁeld lines appearing to be dragged away towards the next more massive neighboring core.

This imprint in the B-ﬁeld morphology was interpreted as a scenario where local collapse

is ongoing while a locally collapsing core, as an entity, is pulled to the next more massive

gravitational center which itself is also collapsing (Koch et al. 2018). Recent numerical work

by V´azquez-Semadeni et al. (2019) is exactly presenting such a scenario as a result of a global

hierarchical collapse where a ﬂow regime leads to collapses within collapses.

While the successively higher-resolution observations in W51 keep revealing new mag-

netic ﬁeld features from imprints of dynamical processes, the W51 region has, at the same

time, served as a mine of information for our developments of new analysis techniques. The

SMA observations (Tang et al. 2009b) served as a testbed for the polarization–intensity gra-

dient technique (Koch et al. 2012a,b). This technique uses the measurable angle δbetween

a magnetic ﬁeld orientation and an intensity gradient as a key observable which, in combi-

nation with a second angle between intensity gradient and local gravity, makes it possible

to derive a magnetic ﬁeld strength. The technique gives a local magnetic ﬁeld strength – at

every position where a magnetic ﬁeld orientation is detected – and therefore, leads to maps

of ﬁeld strengths. At the same time, the technique puts forward a magnetic ﬁeld-to-gravity

force ratio, ΣB, based solely on measurable angles which allows for a completely indepen-

dent estimate of a mass-to-ﬂux ratio (Koch et al. 2012b). The establishment of δas a prime

observable as well as an approximation for ΣBis presented in Koch et al. (2013) with an

application to a 50-source sample of low- and high-mass star-forming sources in Koch et al.

(2014). A main result from this series of papers is the recognition of a spatially varying role

of the magnetic ﬁeld, e.g., mass-to-ﬂux ratios can transition from outer sub-critical to inner

super-critical areas in a star-forming region, and force ratios ΣBare clearly varying from

zones where collapse and infall are slowed down or prohibited by the magnetic ﬁeld to other

zones, within the same source, where collapse is possible. With the ﬁrst ALMA data in Koch

– 5 –

et al. (2018) an additional measure was introduced, the sin ωmeasure. The angle ω, in the

range between 0 and 90◦, measures the projection of the local magnetic ﬁeld tension force

along the local direction of gravity, and hence quantiﬁes the fraction (in a range of 0 to 1) of

the magnetic ﬁeld tension force that can work against the gravitational pull. Maps of sin ω

of all the cores in W51 e2, e8, and North systematically display zones where the magnetic

ﬁeld is maximally opposing gravity and other zones where the magnetic ﬁeld is nearly or

completely ineﬀective in slowing down gravity (Koch et al. 2018). It should be noted that

all of these techniques are utilizing a combination of the geometry and shape of both the

magnetic ﬁeld and the underlying emission (density) structures to infer the local role of the

magnetic ﬁeld.

As presented in the following sections, this current work is resolving once more ﬁner

structures with a resolution of θ∼0.

001, an improvement in area by a factor of 7 over the

earlier 0.

0026 observations, reaching a physical length scale of about 2.6 mpc or 540 au at

the distance of W51 e2/e8. With this, the earlier near-spherical structures are resolved,

revealing connecting dust lanes. Together with earlier observations covering larger scales we

propose a synergetic multi-scale scenario of the evolving role of the magnetic ﬁeld in the W51

high-mass star-forming region starting from the large ﬁlamentary envelope scale (∼0.5 pc),

global-collapsing-core scale (∼0.05 pc), inside-core fragmenting scale (∼10 mpc) down to

the scale of dust lanes (∼2.6 mpc) accreting onto central cores. The paper is organized

as follows. Section 2 describes our ALMA observations. Polarization properties are given

in the appendix. The detected key structural features are introduced in Section 3. Section

4 analyzes the gravitational vector ﬁeld together with the magnetic ﬁeld morphology and

derives a stability criterion for ﬁlaments and ﬁbers. The discussion in Section 5 presents a

road towards a synergetic multi-scale picture.

2. Observations

The project was observed with the ALMA Band 6 receiver (around a wavelength of

1.3 mm) in Cycle 4 and Cycle 5, project codes #2016.1.01484.S and #2017.1.01242.S. Ob-

servations were done in two execution blocks (EBs) on August 17, 2017. The two EBs

were calibrated separately in ﬂux, bandpass, and gain. The polarization calibrations were

performed after merging the two calibrated EBs. The array included 44 antennas with (pro-

jected) baselines ranging from 21 m to 3638 m. The four basebands were set in TDM mode

(64 channels for a 2 GHz bandwidth per baseband). The calibration (bandpass, phase, ampli-

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AMulti-ScalePictureofMagneticFieldandGravityfromLarge-ScaleFilamentaryEnvelopetoCore-AccretingDustLanesintheHigh-MassStar-FormingRegionW51PatrickM.Koch1,Ya-WenTang1,PaulT.P.Ho1;2,Pei-YingHsieh3;4,Jia-WeiWang1,Hsi-WeiYen1,AnaDuarte-Cabral5,NicolasPeretto5,andYu-NungSu11AcademiaSinica,InstituteofAstro...

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A Multi-Scale Picture of Magnetic Field and Gravity from Large-Scale Filamentary Envelope to Core-Accreting Dust Lanes in the High-Mass Star-Forming Region W51

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