Draft version November 15, 2021Typeset using LATEX twocolumn style in AASTeX63

Studying magnetic fields and dust in M17 using polarized thermal dust emission observed by

SOFIA/HAWC+

Thuong Duc Hoang ,1 Nguyen Bich Ngoc ,2, 3 Pham Ngoc Diep ,2 Le Ngoc Tram ,4, 5 Thiem Hoang ,6, 7

Wanggi Lim ,4 Ngan Le ,8 Kate Pattle ,9, 10 Dieu D. Nguyen ,11, 12 Nguyen Thi Phuong,6, 2

Nguyen Fuda ,11, 12 Tuan Van Bui,1 Gia Bao Truong Le ,11, 12 Hien Phan ,1 and Nguyen Chau Giang6

1University of Science and Technology of Hanoi (USTH), Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet,Hanoi, Vietnam

2Department of Astrophysics, Vietnam National Space Center, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet,Hanoi, Vietnam

3Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam4Stratospheric Observatory for Infrared Astronomy, Universities Space Research Association, NASA Ames Research Center, MS 232-11,

Moffett Field, 94035 CA, USA5Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, 53-121, Bonn, Germany

6Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea7University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea

8Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun,Poland

9National University of Ireland Galway, University Road, Galway, Ireland H91 TK3310Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

11Department of Physics, International University, Quarter 6, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam12Vietnam National University, Ho Chi Minh City, Vietnam

Submitted to ApJ

ABSTRACT

We report the highest spatial resolution measurement of magnetic fields (B-field) in M17 using

thermal dust polarization taken by SOFIA/HAWC+ centered at 154 µm wavelength. Using the

Davis-Chandrasekhar-Fermi method, we found the presence of strong B-fields of 980 ± 230 µG and

1665± 885 µG in lower-density (M17-N) and higher-density (M17-S) regions, respectively. The B-field

morphology in M17-N possibly mimics the fields in gravitational collapse molecular cores while in

M17-S the fields run perpendicular to the density structure and display a pillar and an asymmetric

large-scale hourglass shape. The mean B-field strengths are used to determine the Alfvenic Mach

numbers, revealing B-fields dominate turbulence. We calculate the mass-to-flux ratio, λ, and obtain

λ = 0.07 for M17-N and 0.28 for M17-S. The sub-critical values of λ are in agreement with the lack of

massive stars formed in M17. To study dust physics, we analyze the relationship between dust polar-

ization fraction, p, and emission intensity, I, gas column density, N(H2), polarization angle dispersion

function S, and dust temperature, Td. p decreases with intensity as I−α with α = 0.51. p also de-

creases with increasing N(H2), which can be explained by the decrease of grain alignment by radiative

torques (RATs) toward denser regions with a weaker radiation field and/or tangling of magnetic fields.

p tends to first increase with Td and then decreases at higher Td. The latter feature seen in M17-N at

high Td when N(H2) and S decrease is evidence of the RAT disruption effect.

Keywords: magnetic fields and star formation, M17, SOFIA/HAWC+, dust polarization, turbulence,

Alfvenic Mach number, mass-to-flux ratio, radiative torques

Corresponding author: Thuong Duc Hoang

hoang-duc.thuong@usth.edu.vn

1. INTRODUCTION

arX

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1

2 Thuong Hoang et al.

Star formation is a complex process that involves self-

gravity, turbulence, magnetic fields, and stellar feed-

back. Understanding the exact role of magnetic fields in

the evolution of molecular clouds (MCs) and star forma-

tion process is a challenge of modern astrophysics. In the

past decades, there are emerging evidences suggesting

the importance of magnetic fields (B-fields) in the evolu-

tion of MCs and star formation (McKee & Ostriker 2007;

Derek Ward-Thompson & McKee 2020). There are two

types of B-field models in which B-fields play contrast-

ing roles. First, the strong B-field models support a

paradigm of magnetic pressure acting against gravita-

tional collapse of MCs. This magnetic-driven support is

suppressed when the ratio of the core mass to the mag-

netic flux exceeds a critical value that turns the cloud

into a state of gravitational collapse to form a new star

(Nakano & Nakamura 1978). Second, in the weak-field

models, B-fields are sufficiently weak in MCs and dom-

inated by turbulence. Star formation takes place in fil-

aments that are likely produced by intersection of tur-

bulent supersonic flows (e.g., Padoan & Nordlund 1999;

Elmegreen 2000; Mac Low & Klessen 2004; Crutcher

2012). It is, thus, necessary to carry out observations of

B-fields in specific MCs (e.g., M17 in this work) to inves-

tigate their effects on star formation and the subsequent

evolution of the entire clouds to testify theoretical pre-

dictions (Seifried & Walch 2015; Federrath 2016; Li &

Klein 2019; Derek Ward-Thompson & McKee 2020).

Dust polarization induced by aligned grains is widely

used to map B-fields (see e.g., Crutcher 2012). This

method is based on the fact that the polarization di-

rection of thermal dust emission is perpendicular to the

B-fields. The strength of B-fields can then be estimated

using the Davis-Chandrasekhar-Fermi (DCF) method

(Davis 1951; Chandrasekhar & Fermi 1953). The DCF

method measures indirectly the strength based on the

fluctuations of B-fields that are encoded in the dis-

persion of dust polarization directions. Although we

have a full-sky map of dust polarization provided by

Planck at 353 GHz (see e.g., Planck Collaboration: et al.

2015) and many studies of B-fields at MC scales (see

e.g., filament structures and star-forming cores; Dotson

1996; Houde et al. 2002; Pellegrini et al. 2007; Chen

et al. 2012; Pattle et al. 2017, 2018; Wurster & Li 2018;

Chuss et al. 2019; Hennebelle & Inutsuka 2019; Sugi-

tani et al. 2019), dust polarization data at higher reso-

lutions are still lacking. Recently, we start to have high-

resolution polarisation observations made with the Ata-

cama Large Millimeter/sub-Millimeter Array (Liu et al.

2020; Beuther et al. 2020; San 2021).

Dust polarization also allows us to get insights into

fundamental properties of dust grains such as grain

shapes, size distribution, and alignment. Grain align-

ment is a longstanding problem of astrophysics, and

the leading theory for grain alignment is the Radiative

Torque Alignment theory (RATA; Draine & Weingart-

ner 1997; Lazarian & Hoang 2007; Hoang & Lazarian

2016) (see reviews e.g., Andersson et al. 2015; Lazar-

ian et al. 2015). Note that radiative torques (RATs)

arising from the interaction of an anisotropic radia-

tion field with an irregular grain were first suggested

by Dolginov & Mytrophanov (1976) and later numer-

ically demonstrated by Draine & Weingartner (1996),

and analytically modelled by Lazarian & Hoang (2007).

The grain alignment efficiency by RATs is found to in-

crease with increasing radiation field or dust tempera-

ture (see Hoang et al. 2021), which results in the in-

crease of the polarization fraction with the dust tem-

perature (Lee et al. 2020). Furthermore, Hoang et al.

(2019) realized that large grains will be disrupted and

depleted around a very strong radiation source via a

mechanism, the so-called Radiative Torque Disruption

(RATD; see Hoang 2020 for a review). The basic idea

of the RATD mechanism is that an intense radiation

field can spin up dust grains to extremely fast rotation,

such that the centrifugal stress can exceed the tensile

strength of the grain material and disrupts the dust

grain into smaller fragments. The RATD effect is found

to decrease the polarization fraction predicted by the

RATA theory (Lee et al. 2020). The combination of

RATA and RATD was demonstrated to successfully re-

produce the observed dust polarization data in various

regions of strong radiation fields such as Oph-A (Tram

et al. 2021a), 30 Doradus (Tram et al. 2021). Therefore,

dust polarization observations toward strong radiation

sources like M17 are crucial to test grain alignment and

disruption by RATs.

M17 is a well-known star-forming region (Povich et al.

2009; Lim et al. 2020) which is located in the Omega

Nebula or Swan Nebula (also known as Horseshoe Neb-

ula) in the constellation of Sagittarius at a distance of

1.98 kpc (Xu et al. 2011). Figure 1 is a RGB image of

the region using Spitzer1 Galactic Legacy Infrared Mid-

plane Survey Extraordinaire (GLIMPSE) mosaic data.

Besides the study of B-fields and dust physics, since M17

is the closest giant H II region to Earth it is thus an

excellent laboratory for the investigation of stellar feed-

back from a nearby massive star cluster and a photodis-

sociation region (PDR) as well as infrared sources in

the regions such as UC 1, IRS 5, CEN 92, Anon 1, and

Anon 3 (Lim et al. 2020). In the present work, we use

1 https://www.spitzer.caltech.edu

M17 magnetic field 3

M17 N

M17 SN

E

Figure 1. An RGB image of M17 observed by Spitzer (R = 8 µm, G = 4.5 µm, and B = 3.6 µm). The white rectangle is theobserved region of SOFIA/HAWC+ used in this work.

data taken by the High-resolution Airborne Wideband

Camera Plus (HAWC+; Harper et al. 2018) accommo-

dated on Stratospheric Observatory for Infrared Astron-

omy (SOFIA; Temi et al. 2018) to serve our purposes.

The structure of the paper is organized as follows. The

SOFIA/HAWC+ observations of M17 are presented in

Section 2. In Section 3, we describe the use of the DCF

method to estimate the strengths of B-fields. We then

present the obtained results, including the B-field mor-

phologies and strengths, and discuss the implications of

dust polarization fraction for grain alignment and dis-

ruption in Section 4. A summary of our main findings

is presented in Section 5.

2. OBSERVATIONS

4 Thuong Hoang et al.

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

RA (J2000)

Dec

(J200

0)

18h20m42s 36s 30s 24s 18s 12s

-16°14'

12'

10'

08'

RA (J2000)

Dec (J2000)

0 1 2 3 4 5 6 7I [Jy/arcsec2]

0.050 0.025 0.000 0.025 0.050 0.075 0.100 0.125

Q [Jy/arcsec2]0.06 0.04 0.02 0.00 0.02 0.04 0.06

U [Jy/arcsec2]

Figure 2. From left to right: I, Q, and U maps.

The thermal dust polarization data of M17 were

obtained by SOFIA/HAWC+ instrument centered at

154 µm with a designed beam size of 13.6′′. The ob-

served region is shown in Figure 1. The inferred maps

have an original pixel-size of 6.9′′(Harper et al. 2018).

Then, Nyquist samplings were applied during the data

reduction processes to have the final Stokes parameter

maps with a re-sampled pixel-size of ∼ 3.4′′. The Stokes

I, Q, and U maps are shown in Figure 2.

The biased polarization fraction, pbias, is calculated as

follows (Gordon et al. 2018):

pbias = 100

√(Q

I

)2

+

(U

I

)2

= 100IpI

[%], (1)

where Ip =√Q2 + U2 is the polarization intensity. The

associated error on the biased polarization fraction is

σp = pbias

[(σIpIp

)2

+(σII

)2]1/2, (2)

where σIp and σI are the uncertainties on Ip and I,

respectively. The error propagation on the non-linear

function Ip(Q,U) is expanded as

σ2Ip =

∣∣∣∣∂Ip∂Q

∣∣∣∣2 σ2Q +

∣∣∣∣∂Ip∂U

∣∣∣∣2 σ2U + 2

∂Ip∂Q

∂Ip∂U

σQU . (3)

Assuming Q and U are uncorrelated, namely the covari-

ance term σQU = 0, we obtain the error for the polar-

ization intensity

σIp =

[Q2σ2

Q + U2σ2U

Q2 + U2

]1/2, (4)

where σQ and σU are the errors on Stokes Q and U ,

respectively. The debiased polarization fraction, p, is

calculated following the approach by Wardle & Kron-

berg (1974)

p =√p2bias − σ2

p. (5)

The polarization angle, θ, is defined as

θ =1

2tan−1

(U

Q

), (6)

and the error on the polarization angle is calculated as

follows

σθ =

√(QσU )2 + (UσQ)2

2(Q2 + U2). (7)

A detailed exploration of the raw data is presented in

Appendix A. In the following, we apply two quality cuts

to the data, requiring a high signal-to-noise ratio (SNR)

on the measurements of (1) the intensities SNRI > 236

and (2) the polarization fraction SNRp > 3. In what

follows, we call this ‘master cut’. This quality cut au-

tomatically satisfies the third criterion recommended by

the SOFIA collaboration for high-quality scientific data,

namely p < 50% (Gordon et al. 2018). The choice of the

cut on SNRI is to have the measurement uncertainties

on the polarization fraction, σp, better than 0.6%. The

approximate correlation between these two quantities is

SNRI =

√2

σp≈ 236 (Gordon et al. 2018). After applying

the master cut, the remaining pixels are 5139, corre-

sponding to 23% of an original map of the size 138×162

(22356 pixels). The master cut excludes the low level

emission and significantly improves the quality of the

data. Its performance is illustrated in Figure A.1 and

M17 magnetic field 5

Table A.1. Subsequent analyses are carried out using

this master cut.

Figure 3 shows the inferred B-field orientation map

of M17. The lengths of the line segments are propor-

tional to the polarization fraction, and their orientations

are obtained by rotating 90◦ from the polarization an-

gles to trace the B-fields. These segments are called

‘half-vectors’ since the directions of the vectors are not

known. The map gives the first impression of the gen-

eral B-field morphology and the polarization properties

of the 154 µm emission of the region.

3. DATA ANALYSIS

The Davis-Chandrasekhar-Fermi method is one of the

most well-known techniques for the estimation of the

B-field strength. There is some controversy around the

method (e.g., Pattle & Fissel 2019; Liu et al. 2021), how-

ever the DCF method still provides a mean for estimat-

ing the magnetic field strength from dust polarization

measurements. The method is based on the fact that

turbulent motions induce a turbulent component on top

of the mean, large-scale magnetic field and the assump-

tion that the turbulent kinetic energy is balanced by the

induced magnetic energy. The strength of B-fields in

the plane-of-sky, BPOS, is calculated using the following

equation (Crutcher 2004)

BPOS = Qc√

4πρσνσθ≈ 9.3

√n(H2)

∆V

σθ[µG], (8)

where Qc is a factor of the order of unity to correct

for the light-of-sight and beam-integration effects, ρ is

the gas density in g cm−3, ∆V = σν√

8 ln 2 = 2.355σν is

the FWHM of the one dimensional non-thermal velocity

dispersion, σν , in km s−1, n(H2) is the volume density

of the molecular hydrogen in cm−3, and σθ is the po-

larization angle dispersion in degrees. In general, the

magnetic field strength in MCs is in the range of micro-

to milligauss.

Figure 3 indicates two distinct regions encompassed by

the two ellipses in terms of physical conditions, including

density, temperature, and dynamics, as can be seen in

Figures 5, 7, and 11 in the next sections. The ellipse

in the north has a center at RA ∼ 18h20m31s.6 and

DEC ∼ −16◦08′04′′.3, major × minor axes of 137′′×69′′, and a position angle of 14◦. The ellipse in the

south has a center at RA ∼ 18h20m23s.2 and DEC ∼−16◦12′24′′, major × minor axes of 200′′× 143′′, and a

position angle of 0◦. Therefore, we divide the map into

two corresponding northern and southern regions coined

M17-N and M17-S for further analyses. Subsequently,

we are going to identify the input parameters for the

DCF method to calculate the B-field strengths of the

two regions.

3.1. Polarization angle dispersion: Structure function

Structure function method was initially proposed by

Falceta-Goncalves et al. (2008) and Hildebrand et al.

(2009) for evaluating the polarization angle dispersion,

σθ, in the plane-of-sky. Fundamentally, this method cal-

culates a two-point correlation function for pairs of the

polarization angles as follows,

〈∆θ (`)〉1/2 =

{1

N (`)

N(`)∑i=1

[θ (x)− θ (x + `)]2

}1/2

, (9)

where 〈...〉 denotes an average; N(`) is the number of

pairs of pixels having a displacement between the two

pixels |`| = `; x and x+` are the location vectors of the

two considered pixels with corresponding polarization

angles θ(x) and θ(x+`), respectively. We note that only

the pairs with ∆θ(`) = |θ(x)− θ(x + `)| < 90◦ are re-

tained for further analyses because the directions of the

half-vectors are unknown. Assuming that the B-fields

have two independent components (a large-scale struc-

ture field, B0, and a turbulent one, δB), the structure

function can be written as below for a small displace-

ment ` (Hildebrand et al. 2009; Crutcher 2012)

〈∆θ (`)〉 = b2 +m2`2 + σ2M (`), (10)

where b is the contribution of turbulence, m` of the

large-scale structure component; and σM (`) is the mea-

surement uncertainties calculated for each pair of polar-

ization angles. In practice, σM (`) is taken into account

while calculating 〈∆θ (`)〉1/2 in Equation 9. The ratio

of the turbulent to large-scale structure components is

expressed as (Hildebrand et al. 2009)

δB

B0=

b√2− b2

. (11)

From the definition of polarization angle dispersion,

σθ, in Equation 9 combining with Equation 10 neglecting

the contribution of the large-scale structure component,

m`, we have σθ = b/√

2.

We calculate the structure functions for M17-N and

M17-S separately. In general, they display similar rising

tendencies at small displacements ` and reach the value

of random field of 52◦ at large displacements (see Figure

4). The extent of M17-N is smaller than that of M17-S,

hence the maximum displacement of M17-N is smaller.

We then fit the calculated structure functions with the

`-dependence of the polarization angle dispersion using

Equation 10. The fits were carried out for ` > 13.6′′ to

avoid the beam effects. The upper `-limits were chosen

to achieve the best fits (black curves in Figure 4). Table

1 lists the obtained values b = 4.9 ± 0.2 and 8.8 ± 0.7

6 Thuong Hoang et al.

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

RA (J2000)

Dec

(J200

0)

Beam FWHM

M17 N

M17 S

p = 10%

0

1

2

3

4

5

6

7

Inte

nsity

[Jy/

arcs

ec2 ]

Figure 3. The inferred B-field orientation map of the M17 region observed by SOFIA/HAWC+. The half-vectors are propor-tional to the polarization fraction and rotated by 90◦ from the polarization angles to trace the B-fields. The color scale showsthe total intensity in units of Jy arcsec−2. The intensity map is smoothed with a kernel beam of 3×3 pixels across. A linesegment of 10% polarization is shown as a reference in the upper right corner. The beam size is shown in the lower left corner.The blue ellipses are the M17-N and M17-S regions mentioned in the text.

which means σθ = 3.5◦ ± 0.2◦ and 6.2◦ ± 0.5◦ for M17-

N and M17-S, respectively. The uncertainties on b are

from the fits. We note these values are smaller than

that found by Hildebrand et al. (2009), σθ ∼ 10◦, using

data from Caltech Submillimeter Observatory at 350 µm

with a spatial resolution of ∼ 20′′ for M17. Table 1 also

lists the ratios of the turbulent to large-scale structure

B-field components calculated using Equation 11 which

shows that the turbulent fields are much smaller than

the large-scale one in M17.

3.2. Velocity dispersion

We estimate the velocity dispersion of M17 using the

publicly available archival data 13CO (J = 1 → 0)

taken by Nobeyama 45-m telescope (Nakamura et al.

2019). The measurements were made at the cen-

M17 magnetic field 7

0 20 40 60 80 100 120Distance [arcsec]

0

10

20

30

40

50Di

sper

sion

21/

2[d

egre

es]

M17-NFitted

0 60 120 180 2400204060

0 20 40 60 80 100Distance [arcsec]

05

10152025303540

Disp

ersio

n 2

1/2

[deg

rees

]

M17-SFitted

0 60 120 180 2400

20

40

60

Figure 4. Structure functions 〈∆θ2(`)〉1/2 for M17-N (left), and M17-S (right): black dot lines are the data and black curves arethe fitted models. In the inserts, 〈∆θ2(`)〉1/2 of M17-N and M17-S are shown in black curves for the full range of `, respectively.The horizontal dashed lines are the random field value of π/

√12 ∼ 52◦ (Serkowski 1962; Planck Collaboration: et al. 2015).

The vertical dashed lines are the SOFIA/HAWC+ beam size of 13.6′′at 154 µm.

tral frequency νcentral ∼ 110.201 GHz with a spec-

tral resolution of 0.1 km s−1. The resulting map has

a pixel size of 7.5′′and a beam size of 14.9′′which was

then cropped to match with the M17 observed region

by SOFIA/HAWC+. Figure 5 presents the velocity-

integrated intensity (left) and the mean velocity (right)

maps. The integration was done over the entire veloc-

ity range from −20 to 60 km s−1 in the local stan-

dard of rest (LSR) frame. Figure 6 displays the inte-

grated spectra averaged over the number of pixels for

M17-N (left) and M17-S (right). They can be well-

described by two-Gaussian fits giving the mean positions

and corresponding standard deviations, σν;13CO, of the

peaks. The spectra of M17-N and M17-S show the main

peaks at 22.7± 1.6 and 19.9± 2.3 km s−1, respectively.

These main peaks are much higher than the second ones.

Therefore, we only use the velocity dispersion of these

two peaks for the calculation of B-field strengths in M17-

N and M17-S. Table 1 summarizes the results of the

fits which are in agreement with the results obtained

by Nakamura et al. (2019); Nguyen-Luong et al. (2020),

although their results are for wider areas of M17. The

statistical uncertainties of the velocity dispersion from

the two-Gaussian fits are smaller than the spectral reso-

lution of Nobeyama, therefore, we take the uncertainties

equal to the spectral resolution of 0.1 km s−1. We note

that M17-N is affected by the outflows and shocks from

G015.1282 (Lim et al. 2020) which is expected to be

more turbulent than M17-S.

The obtained standard deviations are then converted

to the non-thermal velocity dispersion using σ2ν =

σ2ν;13CO −

kBT

m13CO, where m13CO is the 13CO molecule

mass equal to 29 amu, kB is the Boltzmann constant,

and T is the gas temperature. It turns out that the

thermal contribution to the velocity dispersion is negli-

gible if we adopt the average gas temperature of 20 K

according to Nguyen-Luong et al. (2020). Therefore, we

take the non-thermal velocity dispersion for the M17-N

and M17-S regions equal to the standard deviations of

their corresponding main peaks listed in Table 1.

3.3. Column and volume densities

The column density, N(H2), has been derived based

on a graybody (i.e., modified blackbody) fit with the

filter weighted opacity, κν , and blackbody radiation,

Bν(Td). As following the techniques described in Lim

et al. (2016), Herschel 160, 250, and 350 µm data of M17

have been convolved to the beam size of Herschel 500 µm

images (∼ 36′′) before executing the pixel-by-pixel gray-

body fitting via all four band data. The template Td of

angular resolution ∼ 36′′ is re-gridded to match to the

pixel geometry of SCUBA2 850 µm map (angular reso-

lution ∼ 14′′ and pixel size=4′′). We then repeated the

graybody fit by utilizing SCUBA2 850 µm map (Reid &

2 G015.128 is a massive young stellar object (MYSO) and likelyan A-type super-giant star (Pomohaci et al. 2017). The currentSOFIA/HAWC+ data does not fully cover this source.

8 Thuong Hoang et al.

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

RA (J2000)

Dec

(J200

)

20

20

20

35

35

3535

353535

70

7010

0100

100

200

50 100 150 200Intensity [K km s 1]

18h20m42s 36s 30s 24s 18s 12s

RA (J2000)20

20

20

35

35

3535

353535

70

7010

0100

100

20020 25 30 35 40

Velocity [km s 1]

Figure 5. Left: velocity-integrated intensity map. Right: mean velocity map. The contour levels are at 20, 35, 70, 100, and200 K km s−1 for both maps.

20 0 20 40 60LSR [km s 1]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

T [K

]

20 0 20 40 60LSR [km s 1]

0

5

10

15

20

25

T [K

]

Figure 6. Average integrated spectra (black) with two-Gaussian fits (red) for M17-N (left) and M17-S (right).

M17 magnetic field 9

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

Right Ascension (degrees)

Decli

natio

n (d

egre

es)

30

3336

36

3639

39

4343

43

5353

5353

53

63

63

6376

76

0.0 × 100

5.0 × 1022

1.0 × 1023

1.5 × 1023

2.0 × 1023

2.5 × 1023

3.0 × 1023

3.5 × 1023

Colu

mn

Dens

ityN(

H 2)[

cm2 ]

Figure 7. Map of the column density, N(H2), of M17. The contours display the dust temperature, Td, values as shown inFigure 11. The blue ellipses are the same as in Figure 3. In M17-S, the relation of Td and N(H2) is complex. Td is positivelycorrelated to N(H2) up to ∼ 43 K, but turns to negatively otherwise.

Table 1. Summary of the obtained results. b is the rms contribution of the turbulent component and m of the large-scaleB-fields to the polarization angle dispersion, σθ. δB/B0 is the ratio of the turbulent to the large-scale fields. Detailed descriptionof the parameters can be found in the text.

Parameters M17-N M17-S

b 4.9± 0.2 8.8± 0.7

m 0.55± 0.002 0.55± 0.01

Polarization angle dispersion, σθ [deg] 3.5± 0.2 6.2± 0.5

δB/B0 0.06 0.11

Peak position, νLSR [km s−1] 22.7 ± 0.1 19.9 ± 0.1

Velocity dispersion, σν,13CO [km s−1] 1.6 ± 0.1 2.3 ± 0.1

Column density, 〈N(H2)〉 [cm−2] (9.1± 4.0)× 1021 (6.2± 6.5)× 1022

Volume density, n(H2) [cm−3] (9.3± 4.1)× 103 (4.2± 4.4)× 104

10 Thuong Hoang et al.

Wilson 2006) of M17 with the re-gridded Td map. Fig-

ure 7 shows the resulting N(H2) map superimposed by

the dust temperature (Figure 11). Using this map, we

calculate the total column densities, Ntotal,H2 , the av-

erage column densities, 〈N(H2)〉, as well as their asso-

ciated uncertainties, σN(H2), for the M17-N and M17-S

regions. The results are presented in Table 1.

We then follow the approach described in Lee et al.

(2012); Li et al. (2014); Ngoc et al. (2020) to estimate

the volume density, n(H2). The mass of a region is cal-

culated by M = βmH2Ntotal,H2

(D∆)2, where β = 1.39

accounts for He of 10% abundance in addition to H2 in

the total mass, mH2 is the mass of hydrogen molecules,

D = 1.98 kpc is the distance to M17 (Xu et al. 2011),

and ∆ = 4′′ is the pixel size of the N(H2) map. Then

the volume density n(H2) is expressed as

n(H2) =3M

4πR3mH2

=3βNtotal,H2

(D∆)2

4πR3[cm−3],

(12)

where R is the radius of a considered clump equal to

R =√

(ab)/2 (a and b are the major and minor axes of

an ellipse covering the clump (Li et al. 2014)). Equa-

tion 12 is deduced assuming spherical geometry of the

molecular clump. As shown in Figure 3 and 7, we define

two ellipses that encompass the observed M17-N and

M17-S regions with corresponding angular radii of 69′′

and 120′′, respectively. The physical radii of the two

clumps are obtained by multiplying R with the distance

D to M17. Employing Equation 12, the volume densi-

ties, n(H2), are calculated, and the results are shown in

Table 1 for both M17-N and M17-S regions. The un-

certainty on n(H2) is calculated assuming that its rela-

tive uncertainty is the same as that of Ntotal,H2 , namelyσn(H2)

n(H2)=

σN(H2)

〈N(H2)〉 .

4. RESULTS AND DISCUSSION

In this section, we first describe the magnetic field

morphology of the observed region and report the mag-

netic strengths in the plane of the sky, BPOS, using the

DCF method for the M17-N and M17-S regions. We

then explore the relative contribution of B-fields, grav-

ity, and turbulence by calculating the mass-to-flux ra-

tios and Alfvenic Mach numbers. Finally, we investigate

dust grain alignment and disruption based on the polar-

ization fraction in the observed regions.

4.1. Magnetic field morphology

The magnetic field morphology is imprinted on star

formation processes. We thus can use the observational

data to test theoretical predictions of star formation.

Overall, over the whole region, B-fields in the outer,

low-density regions are perpendicular to the density

structure. Figure 3 and its close-up version (Figure A.3)

illustrate well this point with many half-vectors in the

low-density regions orthogonal to the intensity contours.

Another prominent feature is that when the field lines

pass through the H II region, east of the observed region

(see Figure 1 of Povich et al. (2009) for a more precise

location of the H II region), they tend to run parallel

threading M17-N and M17-S. However, in M17-S, the

fields run perpendicular to these fields behind the high-

density areas at the center (see Figure 8).

In the M17-N region, the main B-fields line up along

the north-south direction through the highest density

area and curve in the eastern and western sides of the

region (see Figures 8 and A.3). The morphology of

the B-fields in M17-N mimics the fields of a gravita-

tionally collapsed molecular core with the presence of

strong magnetic fields where we see the classical hour-

glass geometry with straight fields in the middle and

curved ones at the two wings. This is a common struc-

ture which we often find in observations and simulations

(see e.g., Kandori et al. 2018; Wurster & Li 2018; Pattle

et al. 2019). On the other hand, M17-N is only a small

part of a much larger M17-N region (see Figure 9) which

is not fully covered by the current SOFIA/HAWC+ ob-

servations. Therefore, the observed structure may be

just a coincidence with the fields following the emis-

sion by Polycyclic Aromatic Hydrocarbons (PAHs) at

8 µm wavelength observed by Spitzer (the bright pink

color structure in the northern region in Figure 9). Dis-

tinguishing these two scenarios requires observations of

higher angular resolution and larger areas of M17-N.

In the M17-S region, generally, the fields run perpen-

dicular to the elongation of the high-density structure.

In the region, the fields also form an asymmetric large-

scale hourglass shape (see Figures 8, 9, and 10). In the

southern side of the hourglass, just below Anon 1 and

Anon 3, the fields run from east toward west while grad-

ually bending the to south. The fields are highly curved

in the most southern part of the region and perturbed in

the high density regions at the center. On the northern

side of the hourglass, just above UC 1 and CEN 92, we

see the curved fields (see Figures 8 and 10). This hour-

glass structure seems to be clearly caused by the gravi-

tational contraction of the massive cores at the center of

M17-S. Moreover, the asymmetry is due to the complex

distribution of matter in the center and north-western

part of the region. Another prominent feature of M17-S,

which is commonly found in PDR regions (see e.g., Pat-

tle et al. (2018)), is the pillar structure. Here, we find a

‘triangular’ pillar with the top-end coincident with the

positions of UC 1 and IRS 5 and a ‘base’ in the western

direction (see Figures 8 and 10). It is interesting to note

M17 magnetic field 11

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

RA (J2000)

Dec

(J200

0)

Beam FWHM

Star cluster

KW

IRS 5UC 1

CEN 92

Anon 1Anon 3

1

23

4

5

67

9

M17 N

M17 SNE

0

1

2

3

4

5

6

7

Inte

nsity

[Jy/a

rcse

c2 ]

Figure 8. The B-field morphology of M17 superimposed on the intensity map. Half-vectors are rotated by 90◦ from thepolarization angles to represent the magnetic field orientations. Here, the half-vectors are plotted with uniform length. Thestar symbols represent the most massive (>O7) stars in the open cluster NGC 6618 (Hanson et al. 1997). There are severalinfrared sources present in M17-S such as UC 1, IRS 5, CEN 92, Anon 1, and Anon 3. The KW (Kleinmann-Wright) object isa binary-star system Kleinmann & Wright (1973). The locations of the sources are adopted from Lim et al. (2020).

12 Thuong Hoang et al.

18h21m00s 20m40s 20s 00s

-16°00'

05'

10'

15'

20'

Right Ascension (J2000)

Decli

natio

n (J2

000)

M17 N

M17 S

N

E

Figure 9. A RGB image of M17 using Spitzer data as described in Figure 1. The white box is the observed area ofSOFIA/HAWC+ toward M17. The half-vectors are plotted with uniform lengths using SOFIA/HAWC+ data and rotatedby 90◦ to trace the magnetic fields. In this figure, we can see the larger scale structure mentioned in the text connected to theM17-N region.

M17 magnetic field 13

Figure 10. Same as Figure 8 with the ‘drapery’ patterns produced by the line integral convolution (LIC) tool (Cabral &Leedom 1993).

14 Thuong Hoang et al.

that the magnetic field morphology found here is similar

to the ones reported by Pattle et al. (2018) where the

fields run parallel to the pillar in the H II region side

and perpendicular to the pillar on and behind the base.

Dotson (1996) reported that magnetic field lines are

elongated into the cloud core and bulged away from the

H II region, heated by OB stars. This could be an ev-

idence that the H II region is expanding into its sur-

rounding medium (Zeng et al. 2013). As a conclusion,

our magnetic field morphology is consistent with the sce-

nario that the magnetic field is distorted by H II region

(see more in Section 4.5), several IR sources, and stellar

clusters.

4.2. Magnetic field strengths

Given the estimated values of the polarization angle

dispersion, σθ, the one dimensional non-thermal velocity

dispersion, σν , and the volume densities, n(H2), in Table

1, we calculate the strengths of B-fields in the plane of

the sky using Equation 8, yielding BPOS = 980±230 µG

and 1665 ± 885 µG for M17-N and M17-S, respec-

tively (see more details in Table 2). The magnetic field

strength of M17-S is greater than that of M17-N because

of its higher density.

We note that the DCF method is applicable here since

all the polarization angle dispersion is smaller than 25◦

(Crutcher 2004). The uncertainties are propagated from

the uncertainties on σθ, σν , and n(H2) using the follow-

ing equation

δBPOS

BPOS=

√(1

2

δn(H2)

n(H2)

)2

+

(δ∆V

∆V

)2

+

(δσθσθ

)2

,

(13)

where δn(H2), δ∆V, and δσθ are the uncertainties on

σν , ∆V = 2.355σν , and σθ, respectively.

Table 2. Results of the magnetic field strengths, AlfvenicMach numbers, mass-to-flux ratios for M17-N and M17-S. γis the inclination angle of the B-fields with respect to the lineof sight.

Region BPOS Mach number Mass-to-flux ratio

[µG] MA λ

M17-N 980± 230 0.12 sin γ 0.07 ± 0.04

M17-S 1665± 885 0.22 sin γ 0.28 ± 0.33

Previous study by Pellegrini et al. (2007) found the

magnetic field strength around the southwestern part of

the M17 photodissociation region with the peak value of

∼ 600 µG. Brogan et al. (1999) measured directly the

magnitude of the B-fields along the line-of-sight (LOS)

using the Zeeman observations of H I absorption lines

toward the H II region and obtained BLOS ∼ −450-550

µG. Chen et al. (2012) carried out a rough estimation of

the magnetic field strength based on the polarization of

point sources in NIR and FIR using a sampling rectangle

in the M17-S region, and they found the total magnetic

field strength of B =√B2

LOS +B2POS ∼ 230 µG and

the inclination angle of the magnetic field vector with

respect to the plane-of-sky of ∼ 40◦. Therefore, our

estimated values of BPOS = 980±230 µG and 1665±885

µG with rather large uncertainties are still comparable

with previous results.

Several factors affect the estimation of the magnetic

field strengths. One is that we assumed spherical geome-

tries of the molecular clumps to estimate the radii of the

observed regions when estimating the volume densities.

Depending on the real 3D geometry of the clouds, this

assumption could lead to a large uncertainty in BPOS

values. In addition, polarization observations integrate

over all of the structure along the line of sight, which

leads to the reduction of σθ, therefore, an overestimate of

B-field strengths. Also it is important to note that, sta-

tistically, margin of overestimation by the DCF method

on the magnetic field strengths can be up to a factor

of 2 for an individual cloud (Crutcher 2004). There are

efforts to improve the DCF method such as of Cho &

Yoo (2016) who modified the method to reduce the over-

estimate of BPOS strength by a factor equal to the ra-

tio of the average line-of-sight velocity dispersion and

the standard deviation of centroid velocities. We calcu-

lated the standard deviation of centroid velocities for the

M17-N and M17-S which are equal to 0.59 km s−1 and

1.46 km s−1, respectively. This means that the conven-

tional DCF method overestimates the strength of the

mean magnetic field in the plane-of-the-sky by a fac-

tor of (1.6/1.46)=1.1 and (2.3/0.59)=3.9 in M17-N and

M17-S, respectively (the line of sight velocity dispersion

is taken from Table 1). Therefore, the strengths of B-

fields now are 891±209 µG and 427±227 µG for M17-N

and M17-S, respectively.

The calculated B-field strengths have quite large un-

certainties which are mostly propagated from the un-

certainties on column densities averaged over large re-

gions (see the results in Table 1). We, therefore, ex-

amine the B-field strength limiting to the highest den-

sity regions with N(H2) > 1022 cm−2. With this new

cut, only the densest regions of M17-S are retained (see

Figure A.4) and the new results are N(H2) = (7.6 ±6.5)× 1022 cm−2, n(H2) = (6.9± 5.9)× 104 cm−3, while

∆V = (2.3± 0.1) km s−1 and σθ = 6.5◦ ± 0.5◦ are the

same as before the cut is applied. Therefore, the mag-

netic field strength obtained is BPOS = 2134 ± 738 µG

and λ = 0.27 ± 0.25 with smaller uncertainties as ex-

M17 magnetic field 15

pected. This calculation serves as a reference providing

a more precise measurement of the average magnetic

strength in the dense region of M17 and a sense of pos-

sible changes of its value depending on the choices of the

regions of interest. In reality, the magnetic field strength

is expected to change with the local gas density.

4.3. Alfvenic Mach number MAThe Alfvenic Mach number,MA, represents the rela-

tive contribution of turbulence to magnetic fields. MAis an important parameter for describing the evolution of

molecular clouds (Kritsuk et al. 2017). A sub-Alfvenic

Mach (MA < 1) means the cloud has a strong magnetic

field while a super-Alfvenic (MA > 1) implies a weak

magnetic field compared to turbulence. In the super-

Alfvenic case, the magnetic field morphology is signif-

icantly affected by turbulence due to it subdominance.

In this scenario, the morphology of the magnetic field is

therefore expected to be random.

MA can be calculated from the velocity dispersion

following Padoan et al. (2001); Nakamura & Li (2008);

Wang et al. (2019) as

MA =σνvA

=σν√

4πρ

B, (14)

where vA is the Alfvenic velocity. Combining with Equa-

tion 8, we obtain

MA =σθ sin γ

Qc, (15)

where γ is the inclination angle of B-fields with respect

to the line-of-sight in the range of [0◦, 90◦] with BPOS =

B sin γ, and Qc = 0.5 (Ostriker et al. 2001).

Using the inferred polarization angular dispersion in

Table 1, we obtained MA = 0.12 sin γ and 0.22 sin γ

for M17-N and M17-S, respectively. Thus, M17 is sub-

Alfvenic, implying that the magnetic fields in the region

dominate turbulence. The sub-Alfvenic Mach numbers

are also in agreement with the generally well-ordered

magnetic field morphology in the region (see Figure 8).

4.4. Mass-to-flux ratio

The mass-to-flux ratio, M/Φ, refers the ratio of the

mass to the magnetic flux. This is a crucial parameter

describing the role of B-fields relative to gravity in star

formation (Crutcher 2012). Usually, it is determined by

the critical value, defined as follows (Crutcher 2004)

λ =(M/Φ)observed(M/Φ)critical

= 7.6× 10−21〈N(H2)〉BPOS

, (16)

where the critical mass-to-flux ratio (M/Φ)critical =1

2π√G

(Nakano & Nakamura 1978), 〈N(H2)〉 is the av-

erage column density of the considered region in units of

cm−2, and BPOS is given in units of µG.3 The errors on

the mass-to-flux ratio are calculated using the following

equation

σλλ

=

√(σN(H2)

〈N(H2)〉

)2

+

(δBPOS

BPOS

)2

. (17)

A super-critical value of λ > 1 means that the gravity

dominates the magnetic field pressure, and the cloud can

undergo gravitational collapse to form a protostar. Con-

versely, a sub-critical value of λ < 1 indicates that the

magnetic field is strong enough to counteract the gravi-

tational collapse (Crutcher 2004; Pattle et al. 2017).

We obtained λ = 0.07 and 0.28 for the M17-N and

M17-S regions, respectively (see Table 2). Overall, the

M17 cloud is sub-critical. It means that M17 is magneti-

cally supported and belongs to the strong magnetic field

model of star formation theory (Nakano & Nakamura

1978). However, the λ values here are calculated by av-

eraging over the whole considered regions. Therefore,

the highest density cores can still become super-critical

and then gravitationally collapse to form new stars. The

inferred values of the mass-to-flux ratio are compatible

with theoretical predictions of the am-bipolar diffusion

model where the B-field morphology is dragged inward

from the outer layers of the cloud to the massive cores

in both M17-N and M17-S. In addition, these results

are compatible with the deficiency of forming massive

stars and the lack of gravitationally bound clumps in

the regions (Nguyen-Luong et al. 2020).

4.5. Stellar feedback from the massive star cluster

As shown in Figures 8 and 10, the magnetic fields in

the vicinity of the star cluster (yellow symbols in Fig-

ure 10) appear to be bent and aligned with the density

structure (see more in Section 4.1). This suggests the

effects of stellar feedback of the massive star cluster.

To understand the importance of feedback, we esti-

mate the ratio of the ram pressure, Pram, by stellar winds

(or expansion of HII region) to the magnetic pressure,

Pmag, which is given by

Pram

Pmag=

ρv2wd

B2/8π

' 4.7( vwd

20 km s−1

)2(1000 µG

B

)2(n(H2)

104 cm−3

), (18)

where the wind speed vwd ∼ 20 km s−1 is adopted

from Pellegrini et al. (2007). The mass density ρ =

3 We note that an analysis by Crutcher (2004) indicated that sta-tistically the true mass-to-flux ratio can be over-estimated by afactor of three.

16 Thuong Hoang et al.

18h20m42s 36s 30s 24s 18s 12s

-16°08'

10'

12'

14'

Right Ascension (J2000)

Decli

natio

n (J2

000)

30

33

3636

36

39

39

4343

43

5353

5353

53

63

63

6376

76

40

60

80

100

120

140

Tem

pera

ture

[K]

Figure 11. Dust temperature map of M17 with the contours indicating the corresponding temperatures. In M17-S, the dusttemperature tends to decrease from the east to the west, in the direction away from the star cluster.

2.8mHn(H2). The volume densities, n(H2), and mag-

netic field strengths, B, close to those from Table 1 and

2 have been used. The dominance of the ram pressure

over the magnetic pressure as shown in Equation 18 im-

plies that the winds can bend the magnetic fields frozen

in the gas. Stellar feedback due to the star cluster may

also trigger star formation in the M17-S region, as re-

vealed by the presence of numerous IR sources.

4.6. Dust temperature map

As described in Section 3.3, the dust temperature, Td,

map has been derived via the graybody fit with Herschel

160-500 µm data. Then, the template T d-map has been

re-gridded to match to SCUBA2 850 µm map where the

final map has the pixel size of 4′′.

Figure 11 shows the temperature map of the ob-

served region by Herschel. The average temperatures

are 74 ± 11 and 43 ± 10 K for the M17-N, and M17-S,

respectively. Globally, the M17 dust temperature gradu-

ally decreases from east to west and from north to south.

This general trend is consistent with the scenario that

dust is heated by the massive star cluster (see e.g., Fig-

ure 10). The higher temperatures in M17-N and the

eastern and northeastern parts of M17-S arise from the

fact that these regions are located next to the star clus-

ter and thus strongly heated by this intense radiation

M17 magnetic field 17

source as well as the H II region in the east. M17-N

is additionally affected by shocks from G015.128 result-

ing in an obvious temperature excess. In the M17-S,

the dust temperatures decrease along the direction away

from the star cluster, which stems from dust absorption

within dense structures of an order of magnitude higher

than that of M17-N.

4.7. Polarization fraction vs. emission intensity,

column density, and dust temperature

We now study the dependence of the polarization frac-

tion, p, on the total intensity, I, the column density,

N(H2), and the dust temperature, Td, which reveal ba-

sic properties of grain alignment and disruption in M17.

Firstly, we investigate the relationship between the

polarization fraction, p, and the total intensity, I. It

is clearly seen from Figure 3 that polarization fraction

decreases when intensity increases. Generally, the de-

pendence of p ∝ I−α describes the variation of the

grain alignment efficiency and the magnetic field geom-

etry across the cloud. For a uniform magnetic field, the

slope α = 1 implies that the grain alignment is present

only in the outer layer of the cloud and becomes com-

pletely lost in the inner region. Figure 12 shows a fit-

ted power-law model p ∝ I−α with the power index

α = 0.51±0.01 for the whole M17 region. The values of

α do not change much when we fit only with pixels from

M17-N (α = 0.54 ± 0.02) or M17-S (α = 0.55 ± 0.01)

separately. A best-fitted value of α = 0.51 reveals that

grain alignment is significant toward the high emission

intensity. As a conclusion, we observe that the polariza-

tion fraction, p, decreases with increasing the emission

intensity, I.

To better understand the variation of p, we now study

the relationship between the polarization fraction, p,

and the column density, N(H2), as well as the dust tem-

perature, Td. Figure 13 (top-left) shows the p−N(H2)

relation. Here we derive the slopes by fitting piece-wise

linear functions to the data. In the M17-S region, the

polarization fraction gradually decreases with increas-

ing the gas column density, before it experiences a steep

drop with a slope of −0.71 for NH2> 3 × 1022 cm−2

or the visual extinction4 AV > 37 mag for the typical

total-to-selective extinction RV ≈ 3.1. In the M17-N

region, a steep decrease with slope of −0.67 occurs at

N(H2) > 5× 1021 cm−2 or AV > 6 mag. The strong de-

polarization occurs in the region where the gas density

is relatively low and the dust temperature is relatively

4 AV(mag) = RV × 2N(H2)/(5 × 1021 cm−2)

high compared to that of M17-S (see Figure 11), which

is unexpected from the RATA theory.

The top-right panel of Figure 13 shows the p − Tdrelation. It appears that the polarization fraction first

decreases, then increases before decreasing again as the

dust temperature increases. The decrease-increase fea-

ture originates from the M17-S region, while the depo-

larization is from M17-N.

The bottom panel of Figure 13 shows the gas col-

umn density as a function of the dust temperature. The

column density decreases rapidly with increasing Td in

M17-S, but it varies slowly in M17-N. The first decrease

of p for Td < 40 K corresponds to the highest gas density

(AV ∼ 100 mag). This depolarization is caused by de-

crease of grain alignment due to the attenuation of the

radiation field and the enhancement of collisional damp-

ing. Towards higher dust temperatures, the gas density

drops, and the grain alignment efficiency enhances to-

ward the central luminous source, which results in the

following increment of p. These features are expected

from the context of the RATA theory. In M17-N, the

dust temperature could be up to 150 K and the gas den-

sity becomes more diffuse at AV < 10 mag, the polar-

ization fraction, however, appears to monotonically de-

crease to higher Td, which is completely contradictory

to what expected from RATA theory.

4.8. Implications for grain alignment and rotational

disruption by RATs

We now discuss the implications of the observed po-

larization fraction toward M17 for physics of grain align-

ment and disruption based on radiative torques.

According to the RATA theory (see Lazarian & Hoang

2007), the polarization fraction of thermal emission in-

creases with decreasing alignment size, aalign, which is

the minimum size of aligned grains. The alignment size

is determined by the balance between spin-up by RATs

and spin-down by gas collisional damping, which is a

function of the local dust temperature (or radiation in-

tensity) and gas density as aalign ∼ n2/7H T

−12/7d (Tram

et al. 2021). As a result, a denser gas and lower dust

temperature increase aalign (see details in Hoang et al.

2021), which results in the decrease of the polarization

fraction. Such a prediction by the RATA theory can ex-

plain the decrease of the polarization fraction with in-

creasing the gas column density observed in the M17-S

region (see Figure 13; left panel). However, it can not ex-

plain the decrease of p with increasing Td in the M17-N

region where the gas density changes slowly (see Figure

13; right panel), which reveals evidence of the RATD.

The polarization fraction at far-IR/submm is very sen-

sitive to the maximum size of the grain size distribution

18 Thuong Hoang et al.

10 1 100 101

Intensity [Jy/arcsec2]

10 1

100

101

p [%

]

= 0.54 ± 0.02= 0.55 ± 0.01= 0.51 ± 0.01= 1

M17-SM17-N

Figure 12. The variation of the polarization fraction with the total intensity. The orange, yellow and red lines are the bestfit to a power law model for M17-N, M17-S and the whole map, respectively. The black solid line is the same power law modelwith α = 1.

because large grains dominate long-wavelength emission.

Following the RATD mechanism (Hoang et al. 2019), the

maximum grain size above which large grains are dis-

rupted by RATs is determined by the local dust temper-

ature (radiation field), gas density, and the grain tensile

strength, Smax, which follows by adisr ∼ n1/2H T−3d S

1/4max

(Tram et al. 2021). For the average estimated vol-

ume density nH2 ' 3 × 104 cm−3 (see Table 1), and

the temperature at the breaking point in Figure 13 of

Td ' 53 K, one obtains adisr = 0.16, 0.28, and 0.49µm

for Smax = 107, 108, and 109 erg cm−3, assuming the

mean wavelength of radiation field of 1µm. The de-

crease of the disruption size by RATD leads to the de-

crease of the dust polarization as the dust temperature

increases (Lee et al. 2020; Tram et al. 2021b), which

successfully reproduces the observed trend toward the

M17-N (see Figure 13).

To quantify the magnetic field tangling at small scales

on the depolarization, we calculate the polarization an-

gle dispersion function, S, (see Section 3.3 in Planck

Collaboration: et al. 2015). For each pixel at location

x, S is calculated as the standard deviation of the polar-

ization angle difference, Sxi, of pixel x and pixel i which

lies on a circle having x as the center and a radius of δ

S2(x, δ) =1

N

N∑i=1

S2xi, (19)

where Sxi = θ(x) − θ(x + δ) is the polarization angle

difference and N is the number of pixels lying on the

circle.

For the current SOFIA/HAWC+ data set, we calcu-

late S for δ = 27.2′′ (∼ 2 beam sizes). The left panel

of Figure 14 shows the S - Td relation where it can be

seen that the angular dispersion function S strongly cor-

relates with the dust temperatures but not the high-

est ones, Td > 90 K, in M17-N. Thus, the decline of p

at Td > 90 K (see the upper-right panel of Figure 13)

cannot be explained by the magnetic field tangling and

presents an evidence for the RATD effect. The right

panel of Figure 14 shows a general anti-correlation of

the angular dispersion function S and polarization frac-

tion p, except, again, for the highest temperatures pix-

els (red dots) whose temperatures are greater than 90 K.

For Td < 35 K located in M17-S (blue dots in Figure 13

and 14), we can see that the rapid decrease of p is due to

B-field tangling in the high density region (see bottom

M17 magnetic field 19

10−1 100 101 102AV (mag)

1020 1021 1022 1023

NH2(cm−2)

10−1

100

101

p(%

)

M17− S

M17− N

all data

α = −0.04± 0.01

α = −0.71± 0.02

α = −0.09± 0.05

α = −0.67± 0.07

1023× 101 4× 101 6× 101

Td (K)

10−1

100

101

102

p(%

)

M17− S

M17− N

all data

α = −7.24± 0.26

α = 2.55± 0.27

α = −0.64± 0.07

101

102

AV

(mag

)

40 60 80 100 120 140Td (K)

1021

1022

1023

N(H

2)(

cm−

2)

M17− S

M17− N

Figure 13. Upper-left: the relationship of the polarization fraction and column density. Upper-right: the relationship of thepolarization fraction and temperature. α is the power index of a power-law model. The SOFIA/HAWC+ polarization map issmoothed to 14′′angular resolution of SCUBA2 850 µm which were used together with Herschel data to get the N(H2) and Td

maps. Bottom: the variation of the gas column density, N(H2), with the dust temperature, Td.

panel of Figure 13). For the temperature range from

35 K to 65 K, in both M17-N and M17-S, N(H2) and S

decrease, therefore, p increases. This clearly shows the

important contribution of field tangling to the depolar-

ization at low dust temperatures.

A detailed modeling of dust polarization using the

grain alignment and disruption by RATs for M17 is be-

yond the scope of this paper, and will be addressed in a

follow-up study.

5. SUMMARY

In this study, we use the dust polarization data taken

by SOFIA/HAWC+ at 154 µm to study magnetic fields

and dust physics in the M17 nebula. Our main results

are summarized as follows:

1. Using the DCF method, we estimated the mag-

netic field strengths to be 980 ± 230 µG in the

lower-density region (M17-N) and 1665 ± 885 µG

in the higher-density region (M17-S). The strong

magnetic field could be a result of the pressure

exerted by the H II region in the eastern part of

20 Thuong Hoang et al.

1023 × 101 4 × 101 6 × 101

Td (K)

101

S (d

eg)

M17 - SM17 - N

10 1 100 101

P (%)

101

S (d

eg)

S: -0.65 + 0.01N: -0.52 + 0.02M17 - SM17 - NM17 - N (Td > 90 K)

Figure 14. Left: Variation of the polarization angle dispersion function, S, with the dust temperature, Td. The black curveshows the mean and the standard deviation per bin. Right: Variation of S with the polarization fraction, p. Red dots are pixelswith Td > 90 K. The orange and red lines are the fit to a power law model for M17-N and M17-S, respectively.

the observed region by SOFIA/HAWC+ toward

M17. In the M17-N, the B-field morphology can

be that of a gravitational collapse molecular core.

The morphology of B-fields in M17-S displays a

well-organized elongated structure along with the

gravitational collapse directions from the outer re-

gions to the denser central regions. The fields are

dragged inward to the gravitational center. The

whole B-field morphology represents an asymmet-

ric large-scale hourglass structure. We also found

a pillar structure which is one of the common fea-

tures of PDR regions. A rough estimation of the

contribution of ram over the magnetic pressure

suggests that the wind from the PDR region is

strong enough to impact on the B-field morphol-

ogy of M17.

2. The Mach numbers are determined to be sub-Alfvenic (MA < 1) which indicate that the mag-

netic field dominates turbulence. In addition, the

inferred sub-critical values of mass-to-flux ratios,

λ < 1, imply that the magnetic fields in the regions

are strong enough to resist gravitational collapse.

These results are consistent with the deficiency of

the formation of massive stars in the region from

previous studies.

3. To study dust physics, we analyzed the relation

of the polarization fraction, p, with the emission

intensity, I, gas column density, N(H2), and dust

temperature, Td. The power index of the p vs I

relation, α = 0.51, implies that dust grains could

still be aligned by radiation in the region. The

decrease of the dust polarization with the col-

umn density in the M17-S can be explained by

the RATA theory as well as the tangling of the

magnetic field.

4. To study the effect of magnetic field tangling on

the dust polarization, we also analyzed the varia-

tion of the polarization angle dispersion function,

S, with dust temperature and gas column density.

In the M17-N, the decrease of p with Td at high

temperatures when both N(H2) and S decrease is

most consistent with the theoretical predictions of

dust polarization by both RATA and RATD ef-

fects.

5. There are large statistical biases on the estimation

of the polarization angle dispersion, σθ, as well as

the volume density, n(H2), due to the fact that

the magnetic field strengths are estimated over

a large areas. These biases lead to large uncer-

tainties on the measurement of the magnetic field

strengths. It is also known that for a random sam-

ple of magnetic field orientations, using the DCF

method the mass-to-flux ratio will on average be

overestimated by a factor ∼ 3. In fact, using a

method proposed by Cho & Yoo (2016) we found

the overestimate factors equal to 1.1 and 3.9 for

the M17-N and M17-S, respectively. Therefore,

new methods of estimating magnetic field strength

which are able to identify the fields and accom-

panied useful parameters such as Alfvenic Mach

numbers and mass-to-flux ratios in the basis of

pixel by pixel would provide detailed and more

precise conditions of star formation in the M17

molecular cloud.

M17 magnetic field 21

ACKNOWLEDGMENTS

This research is based on observations made with the

NASA/DLR Stratospheric Observatory for Infrared As-

tronomy (SOFIA). SOFIA is jointly operated by the

Universities Space Research Association, Inc. (USRA),

under NASA contract NNA17BF53C, and the Deutsches

SOFIA Institut (DSI) under DLR contract 50 OK

0901 to the University of Stuttgart. Nobeyama Ra-

dio Observatory is a branch of the National Astro-

nomical Observatory of Japan, National Institutes of

Natural Sciences, part of the data were retrieved from

the JVO portal (http://jvo.nao.ac.jp/portal/) operated

by ADC/NAOJ. We thank Joseph M. Michail for his

line integral convolution (LIC) Python tool. T.H. ac-

knowledges the support by the National Research Foun-

dation of Korea (NRF) grants funded by the Korea

government (MSIT) through the Mid-career Research

Program (2019R1A2C1087045). P.N.D., N.B.N., and

N.T.P. are grateful to the funding from the Vietnam

National Foundation for Science and Technology De-

velopment (NAFOSTED) under grant number 103.99-

2019.368. N.L. acknowledges the support from the First

TEAM grant of the Foundation for Polish Science No.

POIR.04.04.00-00-5D21/18-00. K.P. is a Royal Society

University Research Fellow.

Facilities: SOFIA HAWC+, Nobeyama 45m Tele-

scope, GLIMPSE Spitzer Data, Herchel

Software: spectral cube (Ginsburg et al. 2019), aplpy

(Robitaille 2019), astropy (Astropy Collaboration et al.

2013, 2018), reproject (Robitaille et al. 2020)

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24 Thuong Hoang et al.

APPENDIX

A. APPENDIX

This appendix shows the characteristics of the observational data and the behavior of the master cut applied to the

data.

Figure A.1 shows the distributions of the SNRs of I, p, and Ip before and after applying the master cut defined in

the text. Their corresponding mean and RMS values are listed in Table A.1. The mean values of the SNRs increase

significantly after the cut by 45%, 18%, and 17% for I, p, and Ip, respectively.

Table A.1. Means and RMS of the distribution of SNRI, SNRp, SNRIp .

SNRI SNRp SNRIp

Before cutMean 1477.4 22.2 22.3

RMS 2186.3 19.6 19.6

After cutMean 2138.5 26.1 26.1

RMS 2366.7 20.8 20.9

0 5000 10000 15000SNRI

100

101

102

103

Occu

rrenc

e

0 50 100 150SNRp

100

101

102

0 50 100 150SNRIp

100

101

102

Figure A.1. Left to right: Distributions of signal-to-noise ratios of the total intensity (SNRI), polarization fraction (SNRp),and polarization intensity (SNRIp). The histograms are before cut and blue parts after cut.

Figure A.2 presents one dimensional histograms of the raw data of I, σI , p, σp, Ip, σIp , θ, σθ. The associated

mean and RMS values of these quantities presented in Table A.2.

Table A.2. Mean and RMS values of I, σI , Ip, σIp , p, σp, θ, and σθ.

I σI Ip σIp p σp θ σθ

[Jy/pixel] [Jy/pixel] [Jy/pixel] [Jy/pixel] [%] [%] [◦] [◦]

Mean 9.4 0.0078 0.247 0.0119 5.0 0.367 -11.1 2.5

RMS 12.7 0.0046 0.215 0.0054 5.9 0.507 48.9 2.8

Figure A.3 defines the upper and lower regions used for the data analysis. We present in the figure different total

intensity scales for better vision of the emission structure of the two regions.

Figure A.4 presents the highest density region of M17-S when applying a cut on N(H2) > 1022 cm−2.

M17 magnetic field 25

0 25 50 75I [Jy/pixel]

100

101

102

103

Occu

rrenc

e

0.01 0.02 0.03I [Jy/pixel]

100

101

102

103

0 20 40p [%]

100

101

102

103

Occu

rrenc

e

0 1 2 3 4p [%]

101

102

103

0.0 0.5 1.0 1.5Ip [Jy/pixel] )

100

101

102

Occu

rrenc

e

0.02 0.04Ip [Jy/pixel]

100

101

102

50 0 50 [degrees]

102

Occu

rrenc

e

0 10 20[degrees]

100

101

102

103

Figure A.2. From left to right, top to bottom: Distributions of I, σI , p, σp, Ip, σIp , θ, and σθ of the raw SOFIA/HAWC+data.

26 Thuong Hoang et al.

18h20m40s 35s 30s 25s

-16°07'

08'

09'

10'

Right Ascension (J2000)

Decli

natio

n (J2

000)

Beam FWHM

0.0 0.2 0.4 0.6 0.8 1.0Intensity [Jy/arcsec2]

18h20m36s 30s 24s 18s 12s

-16°10'

12'

14'

Right Ascension (J2000)

Decli

natio

n (J2

000)

Beam FWHM

0 1 2 3 4 5 6 7Intensity [Jy/arcsec2]

Figure A.3. A close-up view of B-fields of the SOFIA/HAWC+ M17 regions: M17-N (top) and M17-S (bottom). Descriptionof the maps is the same for Figure 3.

M17 magnetic field 27

18h20m30s 24s 18s 12s

-16°10'

12'

14'

Right Ascension (degrees)

Decli

natio

n (d

egre

es)

30

3033

3636

36

39

39

43

43

43

53

53

5353

63

5.0 × 1022

1.0 × 1023

1.5 × 1023

2.0 × 1023

2.5 × 1023

3.0 × 1023

3.5 × 1023

Colu

mn

Dens

ityN(

H 2)[

cm2 ]

Figure A.4. The highest density region of the M17-S with N(H2) > 1022 cm−2. The ellipse has a center at RA ∼ 18h20m22s.17and DEC ∼ −16◦12′48′′.3, major × minor axes of 171′′× 118′′, and a position angle of 350◦. The contours are the dusttemperature.