11institutetext: Aryabhatta Research Institute of Observational Sciences
(ARIES), Nainital, 263002, India
11email<EMAIL_ADDRESS>&<EMAIL_ADDRESS>22institutetext:
Indian Institute of Astrophysics (IIA), Sarjapur Road, Koramangala, Bangalore
560034, India

# Optical polarimetry study of Lambda-Orionis star-forming region

Sharma Neha 11 Archana Soam 22 G. Maheswar 22

(accepted May 20, 2024)

We present an optical polarimetric study of a nearby star-forming region,
Lambda-Orionis, to map plane-of-the-sky magnetic field geometry to understand
the magnetized evolution of the HII region and associated small molecular
clouds. We made multi-wavelength polarization observations of 34 bright stars
distributed across the region. R-band polarization measurements focused on
small molecular clouds BRC 17 and BRC 18 located at the periphery of the HII
region are also presented. The magnetic field lines exhibit a large-scale
ordered orientation consistent with the Planck sub-mm polarization
measurements. The magnetic field lines in both the BRCs are found to be
roughly in north-south directions; however, a larger dispersion is noticed in
the orientation for BRC 17 compared to BRC 18. Using structure-function
analysis, the strength of the plane-of-the-sky component of the magnetic field
is estimated as $\sim$28 $\mu$G for BRC 17 and $\sim$40 $\mu$G for BRC 18. The
average dust grain size and the mean value of the total-to-selective
extinction ratio (RV) in the HII region are found to be $\sim$0.51 $\pm$ 0.05
$\mu$m and $\sim$2.9 $\pm$ 0.3, respectively. The distance of the whole HII
region is estimated as $\sim$392 $\pm$ 8 pc by combining astrometry
information from GAIA EDR3 for YSOs associated with BRCs and confirmed members
of central cluster Collinder 69.

###### Key Words.:

ISM: clouds, ISM: magnetic fields, galaxies: star formation, techniques:
polarimetric.

##  1 Introduction

HII regions are among the most fascinating astronomical objects at optical
wavelengths. Several analytical and numerical studies have been conducted to
comprehend their formation and expansion (see Arthur et al. 2011, Zamora-
Avilés et al. 2019 and reference therein) as well as to explain the
filamentary structures, globules, pillars, clumps, etc. found within and
around these regions (e.g., Sugitani et al. 1991, Chauhan et al. 2009). These
features could be due to the instabilities in the ionization front or the
density inhomogeneities in the molecular cloud inside which the HII region is
expanding (see Garcia-Segura & Franco 1996, Mackey & Lim 2010). Small,
isolated, and dense molecular clouds, called bright-rimmed clouds (BRCs), are
located on the periphery of the evolved HII regions. When HII regions interact
with their surrounding molecular clouds, they form the BRCs. The ultraviolet
radiation from the nearby OB stars photoionizes the outer surface layers of a
BRC, forming a layer of hot ionized gas known as the ionized boundary layer
(IBL). The recombination processes in the IBL result in the formation of
optically bright rims. The photoionization-induced shocks are driven into the
molecular clouds, forming dense cores that are then triggered to collapse to
form new stars (Elmegreen, 2011). This phenomenon of triggered star formation
by the compression of gas due to shock or ionization front is known as
radiatively driven implosion (RDI; Bertoldi 1989; Miao et al. 2006) scenario.

Magnetic field plays a very crucial role in the molecular clouds by regulating
the star formation processes (see McKee & Ostriker, 2007). The expanding HII
region and photo-dissociation region (PDR) tend to remove pre-existing small-
scale disordered magnetic field structure and produce a large-scale ordered
magnetic field in the neutral shell, with approximately parallel orientation
to the ionization front (Arthur et al., 2011). Soler et al. (2013) found
magnetic field lines are preferentially oriented parallel to most of the
density structures, and the relative orientation changes from parallel to
perpendicular if the density increases over a critical density. The strength
of the magnetic field decides whether the field lines will align themselves
along the direction of ionization radiation or remain unchanged (Henney et al.
2009, Mackey & Lim 2011).

The role of the magnetic field has been investigated in several BRCs using
polarimetry. Optical polarimetric studies have shown that the magnetic field
could shape the BRCs along with the ionizing radiation from the hot star(s)
located in the vicinity of the BRCs (Soam et al., 2017, 2018). The ALMA dust
polarization study of NGC 6334 by Cortés et al. (2021) reveals complex
morphology with a significant degree of turbulence, which could be due to the
strong interactions between the magnetic field and the turbulent gas in the
BRC. Recent sub-millimeter observations, such as POL-2 on the James Clerk
Maxwell Telescope (JCMT), have revealed complex magnetic fields in regions
where stars are yet to form (Liu et al., 2019; Pattle et al., 2021).

The Orion molecular cloud complex is a nearby giant molecular cloud complex
whose head part is known as “The Lambda Orionis Star Forming Region (LOSFR).”
It is one of the unique locations to study the young stellar population and
their environment (Mathieu, 2008). The LOSFR is an HII region (Sharpless,
1959, Sh2-264) illuminated by an O8III type star called $\lambda$-Ori or
Meissa at a distance of 450 $\pm$ 50 pc from the Sun (Dolan & Mathieu, 1999).
Another B0 type main-sequence star is in binary with Meissa at an angular
distance of 4.4′′. Zhang et al. (1989) detected a dense molecular gas and dust
ring of a diameter of 9∘ centered around $\lambda$-Ori star using Infrared
Astronomical Satellite (IRAS). This ring coincides with the shell of neutral
hydrogen previously discovered by Wade (1957). A compact open cluster,
Collinder 69, is located at the center of the LOSFR, and the $\lambda$-Ori
star is the brightest member of this cluster. At the periphery of the
$\lambda$-Ori ring, many dark clouds are located, e.g., Barnard 30 (B30),
Barnard 35 (B35), Barnard 36 (B36), and Barnard 224 (B224) cataloged by
Barnard (1919). Of these dark clouds, B30 and B35 are also termed as BRC 17 or
SFO 17 and BRC 18 or SFO 18, respectively, cataloged by Sugitani et al.
(1991). The BRC 17 is located at the northwest edge separated from
$\lambda$-Ori by $\sim$2∘, and the elongated BRC 18 cloud is projecting inward
from the eastern edge at an angular distance of $\sim$2.5∘ from the
$\lambda$-Ori.

The $\lambda$-Ori regions have been extensively studied in various aspects,
e.g., the initial discovery, the distance of the clouds, an H$\alpha$ survey,
analysis of IRAS data, and photometric and spectroscopic studies. Duerr et al.
(1982) performed an H$\alpha$ survey and identified emission line sources
predominantly distributed near the open cluster Collinder 69 and two dark
clouds, BRC 17 and BRC 18. Dolan & Mathieu (1999, 2001, 2002) studied the
whole LOSFR using Lithium survey and deep VRI photometry, concluding that
young stars are spatially distributed around $\lambda$-Ori and in front of the
BRC 17 and BRC 18. However, some young stars are found outside these high
stellar density clouds, proposing that the star formation was centered in an
elongated cloud extending from BRC 18 through $\lambda$-Ori to the BRC 17
cloud (Dolan & Mathieu, 1999). The LOSFR comprises recently formed stars from
0.2 M⊙ to 24 M⊙ and still, the star formation continues in the dark clouds,
BRC 17 and BRC 18 (Mathieu, 2008).

The magnetic field morphology in $\lambda$-Ori region will provide useful
information about the expansion and evolution of LOSFR and the globules
associated with this region. In this paper, we have mapped the global magnetic
field geometry in multi-wavelength and local magnetic field geometry in BRC 17
and BRC 18 in R-band. The structure of this paper is as follows: in Sect. 2,
we briefly describe the optical polarimetric observations and data reduction
for both. Our results and analyses are presented in Sect. 3 followed by a
discussion in Sect. 4. We present a summary and highlight our main findings in
Sect. 5.

Figure 1: Proper motion values of the known candidate YSOs associated with BRC
17 (left panel) and the known probable cluster members associated with
Collinder 69 (right panel) are plotted as a function of their distances
obtained from Gaia EDR3. (a) & (c): $\mu_{\alpha}$ versus d plot of the
sources. The candidate YSOs/cluster members lying within 5 × MAD boundary of
$\mu_{\alpha}$ versus d plot are plotted using filled blue circles, while the
outliers are plotted using open gray circles. The dashed lines indicate the
median values of $\mu_{\alpha}$ and d of the candidate YSOs/cluster members.
(b) & (d): $\mu_{\delta}$ versus d plot of the sources. The gray shaded
ellipses show the 5 x MAD boundary range in distance and proper motions within
which sources are used to estimate a distance. The candidate YSOs/cluster
members lying within 5 × MAD boundary of $\mu_{\delta}$ versus d plot are
plotted using filled blue circles, while the outliers are plotted using open
gray circles. The dashed lines indicate the median values of d and
$\mu_{\delta}$ of the candidate YSOs/cluster members.

##  2 Observation and Data Reduction

Table 1: Log of observations. Cloud ID | Date of observations (year, month, date)
---|---
BRC 17 | 2014 December 17, 18, 20
| 2015 January 17, 19
| 2015 October 11
| 2015 November 15
BRC 18 | 2014 October 19, 21, 22, 23
| 2014 November 17, 18, 19
| 2014 December 17, 20, 22
$\lambda$-Ori | 2015 November 16, 17
Region | 2015 December 14, 15
| 2016 January 8, 9, 10, 11, 12
| 2016 February 8, 9
| 2016 March 8

We performed the optical linear polarization observations of the LOSFR
containing BRC 17 and BRC 18 using the ARIES IMaging POLarimeter (AIMPOL)
mounted at the 104-cm Sampurnanand telescope, which is situated at Aryabhatta
Research Institute of Observational Sciences (ARIES), Nainital, India. We used
standard Johnson VRI filters having $\lambda_{\mathrm{Veff}}$ = 0.550 $\mu$m,
$\lambda_{\mathrm{Reff}}$ = 0.670 $\mu$m, and $\lambda_{\mathrm{Ieff}}$ =
0.805 $\mu$m for the polarimetric observations. A detailed description of
AIMPOL and the polarization measurement methods are given in Ramaprakash et
al. (1998); Rautela et al. (2004). The steps of data reduction methods are
described in previous papers (e.g., Eswaraiah et al., 2011, 2012, 2013; Neha
et al., 2016, 2018; Soam et al., 2013, 2015, 2017, 2018). The observations
were performed between 2014 and 2016. The details of the observations are
given in the Table 1. We have observed the stars that are brighter than 15
magnitudes in the V-band towards each region in LOSFR.

Unpolarized standard stars were observed during every run to check for any
possible instrumental polarization. The instrumental polarization is found to
be less than 0.1$\%$. We corrected the observed degree of polarization for the
instrumental polarization. The reference direction of the polarizer was
determined by observing polarized standard stars from Schmidt et al. (1992).
We observed these unpolarized and polarized standards using the standard
Johnson VRI filters. Schmidt et al. (1992) used standard Johnson V filter and
Kron-Cousins R and I filters for the observations of the standard stars. We
used the offset between the standard polarization position angle values
estimated from the observations and those taken from Schmidt et al. (1992) to
correct the zero point offset. The zero point offset values for polarization
position angles range from 6∘ to 9∘ for all the observations.

##  3 Results and analyses

###  3.1 Distance to the LOSFR

We have used GAIA EDR3 data to estimate the distance of LOSFR (Gaia
Collaboration et al., 2021). We separately estimated the distances towards BRC
17, BRC 18, and central cluster Collinder 69. The detailed distance estimation
for BRC 18 is presented in Saha et al. (2022). In the case of BRC 17, we have
compiled a list of YSOs from literature using the criterion given in Saha et
al. (2022). We selected candidate YSOs towards BRC 17 within a circular region
of 0.5∘ radius around the IRAS sources (Dolan & Mathieu 2001, Hayashi et al.
2012, Koenig et al. 2015, Kounkel et al. 2018, Zari et al. 2018, Hosoya et al.
2019). In the case of Collinder 69, we have selected probable cluster members
(Bayo et al. 2012). After compiling all the sources, we searched for each
source within a 1” search radius and obtained distance, proper motions in
right ascension and declination from Bailer-Jones et al. (2021) and Gaia EDR3
archive (Gaia Collaboration et al. 2021). We selected the sources having the
ratio, x/$\Delta$x $\geq$ 3, where x represents the distance (d), proper
motion in right ascension ($\mu_{\alpha}$) and declination ($\mu_{\delta}$)
values and $\Delta$x shows their respective errors. We also applied the
condition for renormalized unit weight errors (RUWE; Lindegren 2018; Lindegren
et al. 2021) for all the sources. We selected the sources having RUWE $\leq$
1.4 confirming their authentic astrometric measurements (Lindegren 2018). The
ionizing source $\lambda-$Ori for LOSFR is located in the central Collinder 69
cluster. The distance of $\lambda-$Ori is estimated at 386 $\pm$ 60 pc using
GAIA EDR3 parallax measurements, but the RUWE is found to be 4.823, which is
much higher than the cut-off value of 1.4 (Gaia Collaboration et al., 2021).
Hence, we have used all the probable cluster members to estimate the distance
of Collinder 69 and assign the same distance to $\lambda-$Ori.

Fig. 1 represents $\mu_{\alpha}$ and $\mu_{\delta}$ of the candidate YSOs
associated with BRC 17 and the known cluster members associated with Collinder
69 as a function of their distances (d). In this study, we have estimated
median absolute deviation (MAD) to measure the statistical dispersion in the
data sets since the standard deviations are generally affected by extreme
values. We identified the sources lying within 5 × MAD concerning the median
values of the distance and the proper motions for BRC 17 and Collinder 69.
Note that the distance uncertainties of individual sources have not been
considered while calculating the median distance. After applying this
condition, we excluded outliers and estimated the median and MAD values only
for the sources within the above condition. The median with their respective
MAD values for $\mu_{\alpha}$, $\mu_{\delta}$ and d are written in Table 2 for
BRC 17, BRC 18, and Collinder 69. The distances towards all three different
regions of LOSFR are found to be consistent within error limits. Hence, we
have taken the mean values of all three distance values to assign a single
distance for the LOSFR. The mean distance is 392 $\pm$ 8 pc for the LOSFR.

Table 2: The median with their respective MAD values for $\mu_{\alpha}$,
$\mu_{\delta}$ and d.

ID | $\mu_{\alpha}$ | $\mu_{\delta}$ | d
---|---|---|---
| (mas yr-1) | (mas yr-1) | (pc)
BRC 17 | 0.953 $\pm$ 0.528 | -0.799 $\pm$ 0.433 | 389 $\pm$ 9
BRC 18† | 2.189 $\pm$ 0.382 | -2.482 $\pm$ 0.114 | 394 $\pm$ 7
Collinder 69 | 0.919 $\pm$ 0.204 | -2.017 $\pm$ 0.121 | 392 $\pm$ 7

† The values for BRC 18 has been taken from Saha et al. (2022).

Murdin & Penston (1977) estimated the distance of the LOSFR using high-quality
broadband photometry of the 11 OB stars located at the center of the star-
forming region. They estimated the distance of this region to be $\sim$400 pc.
The distance of the five stars in the central area of LOSFR is $\sim$380 $\pm$
30 pc (Perryman et al., 1997). Dolan & Mathieu (2001) used Strömgren
photometry with a larger sample of OB stars and estimated the distance of the
region $\sim$450 $\pm$ 50 pc which is slightly larger than the previously
estimated distances. Recently, Kounkel et al. (2018) estimated the distances
for BRC 17 as 397 $\pm$ 4 pc, BRC 18 as 396 $\pm$ 4 pc and Collinder 69 as 404
$\pm$ 4 pc using GAIA DR2 parallax measurements. Our estimated distances for
BRC 17 and BRC 18 are consistent within error limits, but there is a small
difference in the distance of Collinder 69. That could be because we have used
the recent GAIA EDR3 distance measurements having very low uncertainties.

###  3.2 Polarimetry

Figure 2: Upper panel: Polarization angle versus distance of the foreground
stars found within $1^{\circ}$ diameter around BRC 17, BRC 18 and the Heiles
stars found within $9^{\circ}$ diameter around $\lambda$-Ori star. The
distances are calculated from the Hipparcos parallax measurements taken from
van Leeuwen (2007) and adopted from Bailer-Jones et al. (2021). The gray
circles show the bright Tycho stars lying behind the cloud. The distances for
the Tycho stars are taken from Bailer-Jones et al. (2021). Lower panel: Degree
of polarization versus distance for the same stars. The gray dashed line
corresponds to the 392 pc distance in both panels.

####  3.2.1 Foreground polarization subtraction

The distance of the LOSFR is found to be 392 $\pm$ 8 pc as described in
section 3.1. Hence, the polarization measurements for the stars towards LOSFR
could be affected by the line of sight foreground interstellar component. In
this regard, to remove the foreground contribution, we searched BRC 17 and BRC
18 within a circular region of 1∘ diameter for stars having parallax
measurements made by Hipparcos satellite in van Leeuwen (2007), since the GAIA
data-sets were not available at the time of these observations. The stars that
are found to be the emission line sources in binary or multiple systems or
peculiar sources in SIMBAD are excluded. We have chosen the stars having
parallax measurements better than 2$\sigma$. The polarization observations of
these stars were carried out using AIMPOL. We have also chosen the stars from
Heiles catalog (Heiles, 2000) within 4.5∘ radius of $\lambda$-Ori region. The
polarization results for these stars have been presented in Table 3 according
to their increasing distance from the Sun. Note that the observed R-band
polarization values are presented for BRC 17 and BRC 18, while the values from
Heiles (2000) catalog are the average values in multiple bands as taken
directly from the catalog. We have also adopted distances for all the sources
from Bailer-Jones et al. (2021) to compare with previous known distances. We
have plotted the degree of polarization and polarization angles with distance
for all the foreground stars in Fig. 2. In the same figure, we have also
included the polarization measurements for the bright Tycho stars (Høg et al.,
2000, discussed in section 3.2.2) that are lying behind the cloud. We can see
from the figure that the values of polarization angle are random for the stars
lying before 392 pc while aligned in a particular direction after 392 pc.
Similarly, the value of the degree of polarization also shows an increase of
around 392 pc, which is consistent with our measured distance. Hence, we
calculated the mean values of P and $\theta$ for the foreground stars having a
distance less than 392 pc according to a new distance estimation method
(Bailer-Jones et al., 2021) and having polarization values greater than
0.1$\%$ which is equal to the instrumental polarization of AIMPOL. We have
marked those objects with asterisks. The observed foreground R-band
polarization values are converted to V-band and I-band using Serkowski law
(Serkowski et al., 1975). The mean values of the P and $\theta$ are 0.3 $\pm$
0.1 $\%$ and 106 $\pm$ 9∘ for all the V, R and I filters. Using these mean
polarization values, we calculated the Stokes parameters, Qfg and Ufg for
selected foreground stars. We also computed the Stokes parameters for our
observed stars Q∗ and U∗. Then we calculated the foreground-corrected Stokes
parameters for our observed stars Qc and Uc using Qc = Q∗ $-$ Qfg and Uc = U∗
$-$ Ufg following the same procedure described in Neha et al. (2016). However,
the mean of the difference between observed polarization angles
$\theta\mathrm{{}_{observed}}$ and foreground corrected polarization angles
$\theta\mathrm{{}_{c}}$ is 4 degrees with a standard deviation of 4 degrees,
suggesting a smaller contribution due to foreground. We have presented the
polarization position angle values in the equatorial coordinate system.

Table 3: Polarization values of observed foreground stars and from Heiles
catalog.

Id | Star Name | V | ${P\pm\leavevmode\nobreak\ \epsilon_{P}}$ | ${\theta\pm\epsilon_{\theta}}$ | D† | D‡
---|---|---|---|---|---|---
|  | (mag) | (%) | (∘) | (pc) | (pc)
Observed foreground stars in the direction of BRC 17 in R-band
1 | HD 36860 | 8.0 |  0.02 $\pm$ 0.1 |  169 $\pm$ 22 |  63$\pm$4 |  67$\pm$1
2* | HD 35968 | 8.0 |  1.21 $\pm$ 0.1 |  80 $\pm$ 9 |  199$\pm$35 |  268$\pm$2
3* | HD 36104 | 7.0 |  0.18 $\pm$ 0.1 |  67 $\pm$ 8 |  307$\pm$55 |  291$\pm$7
4 | HD 36262 | 7.6 |  0.09 $\pm$ 0.1 |  86 $\pm$ 12 |  333$\pm$72 |  392$\pm$7
5 | HD 36838 | 8.2 |  0.71 $\pm$ 0.1 |  49 $\pm$ 3 |  458$\pm$229 |  536$\pm$7
Observed foreground stars in the direction of BRC 18 in R-band
1* | HD 38527 | 5.8 |  0.17 $\pm$ 0.1 |  57 $\pm$ 9 |  91$\pm$4 |  94$\pm$1
2* | HD 39007 | 5.8 |  0.15 $\pm$ 0.1 |  144 $\pm$9 |  110$\pm$8 |  127$\pm$1
3* | HD 37408 | 8.6 |  0.52 $\pm$ 0.1 |  130 $\pm$ 3 |  178$\pm$45 |  180$\pm$1
4* | HD 37355 | 6.7 |  0.24 $\pm$ 0.1 |  131 $\pm$ 6 |  208$\pm$29 |  184$\pm$1
5 | HD 246922 | 8.9 |  0.43 $\pm$ 0.1 |  167 $\pm$ 5 |  274$\pm$120 |  459$\pm$4
6 | HD 37926 | 8.0 |  0.04 $\pm$ 0.1 |  102 $\pm$ 13 |  291$\pm$87 |  253$\pm$2
7 | HD 38095 | 8.5 |  0.08 $\pm$ 0.1 |  31 $\pm$ 16 |  335$\pm$159 |  205$\pm$1
8* | HD 38096 | 8.0 |  0.21 $\pm$ 0.1 |  125 $\pm$ 6 |  351$\pm$92 |  316$\pm$3
9* | HD 37522 | 7.2 |  0.21 $\pm$ 0.1 |  114 $\pm$ 6 |  385$\pm$135 |  337$\pm$3
10 | HD 39229 | 8.7 |  1.31 $\pm$ 0.1 |  124 $\pm$ 1 |  387$\pm$125 |  422$\pm$4
Stars from Heiles (2000)
1 | HD 37160 | 5.8 |  0.06 $\pm$ 0.03 |  154 $\pm$ 15 |  36$\pm$1 |  35$\pm$1
2 | HD 38899 | 4.9 |  0.03 $\pm$ 0.12 |  20 $\pm$ 63 |  76$\pm$2 |  86$\pm$1
3* | HD 35468 | 1.6 |  0.30 $\pm$ 0.21 |  23 $\pm$ 20 |  77$\pm$3 | -
4* | HD 36267 | 4.1 |  0.13 $\pm$ 0.03 |  165 $\pm$ 6 |  93$\pm$6 |  99$\pm$2
5* | HD 36653 | 5.6 |  0.74 $\pm$ 0.20 |  32 $\pm$ 8 |  137$\pm$7 |  327$\pm$11
6 | HD 38710 | 5.3 |  0.09 $\pm$ 0.03 |  54 $\pm$ 10 |  165$\pm$25 |  124$\pm$2
7* | HD 38672 | 6.7 |  0.37 $\pm$ 0.20 |  169 $\pm$ 15 |  276$\pm$38 |  330$\pm$4
8 | HD 36822 | 4.4 |  0.28 $\pm$ 0.00 |  120 $\pm$ 0 |  333$\pm$28 |  392$\pm$53
9 | HD 36861 | 3.5 |  0.44 $\pm$ 0.11 |  113 $\pm$ 7 |  337$\pm$62 |  439$\pm$95
10* | HD 37232 | 6.1 |  0.27 $\pm$ 0.00 |  100 $\pm$ 0 |  345$\pm$52 |  379$\pm$9
11* | HD 36471 | 8.7 |  0.42 $\pm$ 0.07 |  127 $\pm$ 5 |  391$\pm$160 |  375$\pm$9
12 | HD 34989 | 5.8 |  0.65 $\pm$ 0.20 |  106 $\pm$ 9 |  437$\pm$69 |  392$\pm$26
13* | HD 36824 | 6.7 |  0.39 $\pm$ 0.10 |  127 $\pm$ 8 |  1176$\pm$817 |  313$\pm$5

† Distances are estimated using the Hipparcos parallax measurements taken from
van Leeuwen (2007).
‡ Distances are adopted from Bailer-Jones et al. (2021).
* Objects used to calculate foreground polarization. See details in the text.

####  3.2.2 Global magnetic field geometry of LOSFR

Figure 3: Polarization vectors of 34 bright Tycho stars plotted on the Planck
857 GHz image of LOSFR in V-band (Upper panel), R-band (Middle panel) and
I-band (Lower panel). The length of the vectors corresponds to the degree of
polarization values, while the orientation represents the polarization angle
measured from the north toward the east. A vector with 2% polarization has
been shown for reference. The white dashed line shows the position of the
galactic plane. The white star shows the position of $\lambda$-Ori star.

We have systematically made the polarization study to map the global magnetic
field in the LOSFR by observing the bright Tycho stars located behind this
region. We selected the bright Tycho stars from the Tycho-2 catalog (Høg et
al., 2000) within a 4.5∘ radius around $\lambda$-Ori star. Then we have taken
the J, H, and Ks magnitudes of these stars from 2MASS point source catalog
(Cutri et al., 2003). We plotted their J, H, and Ks magnitudes in a color-
color diagram and selected the stars with J$-$K${}_{\mathrm{s}}>$ 1, showing
the stars are reddened or behind the cloud. Among them, we made multi-band
polarimetric observations of 34 bright Tycho stars distributed in the whole
HII region. We have also obtained the distances for all these 34 bright Tycho
stars from Bailer-Jones et al. (2021) and found that all have larger distances
than the LOSFR’s distance (400 pc adopted from literature). This suggests that
our method of selecting the reddened stars is reliable. We have plotted the
polarization vectors on the Planck 857 GHz image in Fig. 3 for V, R, and I
filters from top to bottom, respectively. The direction of polarization
vectors shows the global magnetic field geometry in LOSFR, which seems to
follow the large-scale structure seen in all the images of Fig. 3. However,
the number of stars in our sample is low; therefore, observations of more
stars would be helpful. The white star shows the position of $\lambda$-Ori
star in all the images, and the white dashed line represents the position of
the galactic plane. The magnetic field lines appear almost parallel to the
Galactic plane (b = -11.99∘) in the northeast and central regions of LOSFR,
while towards the southwest region, the field lines seem random. The
polarization results for all the Tycho stars towards LOSFR in VRI filters are
given in Table 5. The mean values of the degree of polarization and
polarization angle for these bright Tycho stars are 1.3 $\pm$ 0.2$\%$ & 169
$\pm$ 6∘ for V-band, 1.1 $\pm$ 0.1$\%$ & 163 $\pm$ 6∘ for R-band and 1.0 $\pm$
0.1$\%$ and 170 $\pm$ 6∘ for I-band, respectively.

###  3.3 Dust grain size distribution

Figure 4: Serkowski Curve for 34 bright Tycho stars observed in VRI filters.
Blue, green, and red-filled circles correspond to V-band, R-band, and I-band,
respectively. Magenta solid line represents the fitting using Serkowski Law
(Serkowski et al., 1975).

The Serkowski law (Serkowski et al., 1975) with the parameter K provides an
appropriate description of the interstellar polarization with the wavelength
in the visible region, and it is defined as follows:

$\mathrm{P_{\lambda}=P_{max}\leavevmode\nobreak\ exp[-K\leavevmode\nobreak\
ln^{2}(\lambda_{max}/\lambda)]}$ (1)

where $\mathrm{P_{\lambda}}$ is the degree of polarization (%) at wavelength
$\lambda$, $\mathrm{P_{max}}$ is the maximum degree of polarization estimated
from the fitting at wavelength $\lambda_{\mathrm{max}}$ and the parameter K
determines the width of the peak in the curve and adopted as K = 1.15
(Serkowski et al., 1975). If the polarization is produced by aligned
interstellar dust grains, the observed data will follow equation 1 and the
values of $P_{\mathrm{max}}$ and $\lambda_{\mathrm{max}}$ for each star can be
calculated. We studied the dust properties of LOSFR by obtaining the
$P_{\mathrm{max}}$ and $\lambda_{\mathrm{max}}$ values using the weighted
least-squares fitting to the measured polarization in V, R, and I bands.

Table 4: The mean values of $\lambda_{\mathrm{{max}}}$ and Pmax for UBVRI, BVRI and VRI data set for various regions. Filter set |  $\lambda_{\mathrm{{max}}}$ ($\mu$m) | Pmax(%)
---|---|---
NGC 5617
UBVRI | 0.53 $\pm$ 0.05 | 4.13 $\pm$ 0.22
BVRI | 0.57 $\pm$ 0.06 | 4.05 $\pm$ 0.21
VRI | 0.61 $\pm$ 0.05 | 3.98 $\pm$ 0.16
NGC 5749
UBVRI | 0.60 $\pm$ 0.05 | 1.77 $\pm$ 0.08
BVRI | 0.62 $\pm$ 0.09 | 1.76 $\pm$ 0.09
VRI | 0.65 $\pm$ 0.09 | 1.75 $\pm$ 0.10
LDN 1570
BVRI | 0.63 $\pm$ 0.05 | 2.86 $\pm$ 0.08
VRI | 0.63 $\pm$ 0.05 | 2.86 $\pm$ 0.08
NGC 457
BVRI | 0.57 $\pm$ 0.03 | 2.96 $\pm$ 0.09
VRI | 0.56 $\pm$ 0.04 | 2.97 $\pm$ 0.15

The $\lambda_{\mathrm{max}}$ values can also be used to infer the origin of
the polarization. The stars with $\lambda_{\mathrm{max}}$ much lower than the
average value of the interstellar medium (0.55 $\mu$m; Serkowski et al., 1975)
may have an intrinsic component of polarization due to scattering process
(Orsatti et al., 1998). Fig. 4 shows the Serkwoski fitting for 34 stars where
we obtain the $\lambda_{max}$ values between 0.37 $\mu$m to 0.66 $\mu$m. The
weighted mean values of the $P_{\mathrm{max}}$ and $\lambda_{\mathrm{max}}$
for 34 stars are found to be 1.30 $\pm$ 0.11 $\%$ and 0.51 $\pm$ 0.05 $\mu$m,
respectively. Since we have made observations only at three wavelength bands
(VRI), we have investigated the effect of using only three wavelength bands on
the measured $P_{\mathrm{max}}$ and $\lambda_{\mathrm{max}}$. Toward this, we
have compiled the polarimetric data of some randomly selected clouds, e.g.,
NGC 5617, NGC 5749 in UBVRI and LDN 1570, NGC 457 in BVRI filters from Orsatti
et al. (2010), Vergne et al. (2007), Eswaraiah et al. (2013) and Topasna et
al. (2017), respectively and estimated the values of $P_{\mathrm{max}}$ and
$\lambda_{\mathrm{max}}$ by reducing the number of wavelength bands i.e.,
using the UBVRI, BVRI, and VRI filters. The mean values of
$\lambda_{\mathrm{max}}$ and $P_{\mathrm{max}}$ for these three regions are
shown in Table 4. Using BVRI data set, the mean values of $\lambda_{max}$ and
Pmax for NGC 5749 are found to be 0.60 $\pm$ 0.05 $\mu$m and 1.61 $\pm$ 0.08%
while using only VRI filters the values are found to be 0.69 $\pm$ 0.07 $\mu$m
and 1.59 $\pm$ 0.07%. Similarly, The mean values of $\lambda_{max}$ and Pmax
for LDN 1570 are found to be 0.61 $\pm$ 0.04 $\mu$m and 2.90 $\pm$ 0.11% from
BVRI data set and 0.63 $\pm$ 0.07 $\mu$m and 2.85 $\pm$ 0.15% from VRI data
set. We found that the values of $\lambda_{max}$ for the VRI data set are
consistent with the uncertainty compared with UBVRI and BVRI data sets. The
difference in $\lambda_{\mathrm{{max}}}$ and $P_{\mathrm{max}}$ values in
different filter sets is within 10%. Hence, our results can be used to
estimate the dust grain size in LOSFR. The estimated
$\lambda_{\mathrm{{max}}}$ is 0.51 $\pm$ 0.05 $\mu$m, which is consistent with
the value corresponding to the general interstellar medium (0.55 $\mu$m;
Serkowski et al., 1975). It is also consistent with a value 0.53 $\mu$m for
LOSFR along the Galactic plane estimated from the empirical relation,
$\lambda_{\mathrm{{max}}}$ = 0.545 + 0.030 sin(l \+ 175∘) (Whittet, 1977).
This relation describes the systematic modulation of
$\lambda_{\mathrm{{max}}}$ as a function of Galactic latitude (l). We also
estimated the value of RV, the total-to-selective extinction, using the
relation RV = (5.6 $\pm$ 0.3) $\times$ $\lambda_{\mathrm{{max}}}$ (Whittet &
van Breda, 1978), for all the 34 stars. The RV values range from 1.96 to 3.70
for all 34 Tycho stars. The mean value of RV for these 34 stars comes out to
be 2.9 $\pm$ 0.3, which is in agreement with the general average value (RV =
3.1) for the Milky Way Galaxy within error limits, indicating that the size of
the dust grains within the LOSFR is normal.

###  3.4 Magnetic field geometry of BRC 17 and BRC 18

Figure 5: Polarization vectors are over-plotted on WISE 12$\mu$m image of BRC
17 (left panel) and BRC 18 (right panel). The length of the vectors
corresponds to the degree of polarization, and orientation corresponds to the
position angle measured from the north and increasing toward the east. A
vector corresponding to 2$\%$ polarization is shown for reference. The white
dashed line shows the orientation of the Galactic plane. The red star shows
the location of IRAS sources, and the yellow stars show the positions of HH
objects in both the images (Reipurth, 2000). Green arrows in both panels show
the directions of outflows. The outflow sources are HH 243 for BRC 17, while
IRAS 05417+0907 for BRC 18.

The magnetic field geometry of a molecular cloud is predominantly regulated by
the relative dynamical importance of magnetic forces to gravity, turbulence,
and thermal pressure. If the magnetic field lines strongly support the
molecular cloud against gravity, then the magnetic field lines would be
aligned smoothly. The average magnetic field orientation would be
perpendicular to the major axis of the cloud (Mouschovias, 1978). It is
believed that the cloud tends to shrink more in the parallel direction to the
magnetic field rather than the perpendicular direction. However, if the
turbulence is more important than the magnetic field, then the structural
dynamics of the molecular cloud would be controlled by the random motions, and
the turbulent eddies will drag the magnetic field lines around (Ballesteros-
Paredes et al., 1999). Thus, the magnetic field lines would become chaotic
with no preferred direction.

The results of our optical polarimetry observations of 105 stars in the
direction of BRC 17 and 171 stars towards BRC 18 are presented in Table 6. We
have tabulated the results of only those sources having a degree of
polarization measurements better than 2$\sigma$. The columns of these tables
show the star identification number in increasing order of their right
ascension, the declination, measured P ($\%$), and polarization position
angles ($\theta$ in degrees).

####  3.4.1 BRC 17

The cloud complex B30 contains Barnard clouds B31 and B32, and the Lynds
clouds LDN1580-1584 (Dolan & Mathieu, 2001). At the head part of this cloud,
an optically visible bright rim is present, and this is cataloged as BRC 17 by
Sugitani et al. 1991. The distance of BRC 17 is estimated at around 389 $\pm$
9 pc (see section 3.1). The projected angular distance of the BRC 17 from the
ionizing star $\lambda-$Ori is $\sim$2.3∘, which corresponds to $\sim$15 pc
considering the cloud distance 389 pc. Zhou et al., 1988 mapped this cloud
using CO observations and divided it into two parts: The northern part
containing RNO 43 outflow and the Southern part containing bright-rim and IRAS
source. We mapped the magnetic field geometry towards the Southern region,
which contains the bright rim of this cloud. The left panel of Fig. 5 shows
the plot of polarization vectors of 105 foreground-subtracted stars
overplotted on the WISE 12 $\mu$m image. The length and the orientation of the
vectors correspond to the measured P$\%$ and $\theta$ values, respectively.
The $\theta$ is measured from the north, increasing toward the east. A vector
with 2% polarization is shown for reference. The dashed white line represents
the orientation of the Galactic plane at the Galactic latitude of
$-11.6^{\circ}$. The mean values of the degree of polarization and
polarization angle for BRC 17 are 1.4 $\pm$ 0.4$\%$ and 175 $\pm$ 43∘,
respectively. The plot of P% vs. $\theta$ and the histogram of the $\theta$
after correcting for the foreground interstellar contribution are shown in
Fig. 6. At first, we performed a single Gaussian fit to the histogram with
bins size of 10 deg. The mean and standard deviation of the best-fit Gaussian
is found to be $172\pm 9$ deg and $52\pm 12$ deg, respectively. The
distribution of polarization position angle appears to be a mixture of
multiple Gaussians with the strongest central peak. Therefore, we also fitted
a multiple Gaussian model consisting of three Gaussians to the data. The
multi-Gaussian model shows the strongest peak at the center with a mean and
standard deviation of $167\pm 14$ deg and $24\pm 19$ deg, respectively.
Although the different peaks in the multi-Gaussian model are not well
separated and parameters are not well constrained, having large uncertainties,
we find a similar reduced $\chi^{2}$ as that of the single-Gaussian model.
However, the standard deviation value of the central Gaussian in the multi-
Gaussian model is much smaller than the single Gaussian model.

Figure 6: Degree of polarization versus the polarization position angle of
stars projected on BRC 17 (left panel) and BRC 18 (right panel). The histogram
of the position angles is also shown. These values are obtained after
subtracting the foreground interstellar component from the observed values.
The solid black curves represent a fit to the histogram of position angles
using a single Gaussian model. BRC 17 is also fitted with a multiple Gaussian
model (solid-blue) where decomposed Gaussians are shown by dashed-blue along
with the mean and standard deviation of the central Gaussian marked.

####  3.4.2 BRC 18

BRC 18 (also known as B35) lies at the periphery of the LOSFR. It is located
at $\sim$392 $\pm$ 7 pc (see section 3.1) with a dimension of 0.37 pc by 1.40
pc. The projected angular distance between the BRC 18 and the ionizing star
$\lambda-$Ori is $\sim$2.5∘, corresponding to $\sim$17 pc considering the
cloud distance 392 pc. The magnetic field geometry in BRC 18 is found to be
regular and oriented in the perpendicular direction of the cloud’s major axis
(along the east-west direction in the right panel of Fig. 5), indicating the
magnetic field dominance in the cloud (Mouschovias, 1978). The mean values of
P and $\theta$ for BRC 18 are 1.7 $\pm$ 0.3$\%$ and 171 $\pm$ 8∘,
respectively. The right panel of Fig. 5 shows the plot of polarization vectors
of 171 foreground-subtracted stars overplotted on the WISE 12 $\mu$m image. As
discussed in the previous section, the length and orientation of the
polarization vectors correspond to the measured P$\%$ and $\theta$ values,
respectively. The $\theta$ is measured from the north, increasing toward the
east. A vector with 2% polarization is shown for reference. The white-dashed
line represents the orientation of the Galactic plane at the galactic latitude
of $-10.4^{\circ}$. The plot of P% vs. $\theta$ and the histogram of the
$\theta$ with a bin size of 10 deg after correcting for the foreground
interstellar contribution are shown in Fig. 6. The yellow star corresponds to
the HH object, HH 175 (Reipurth, 2000). In BRC 18, the relatively low
dispersion ($\sigma_{\theta}$=8∘) in polarization position angles implies that
the magnetic field lines are well aligned (see right panel in Fig. 5). The
mean polarization position angle, $\sim$171∘, from the north towards the east
shows the direction of the plane-of-the-sky component of the magnetic field,
whereas the projected orientation of incoming ionizing radiation from
$\lambda-$Ori towards BRC 18 $\sim$109∘ for the north increasing towards the
east. Hence, the projected angle between the magnetic field lines and the
incoming ionizing radiation is $\sim$62∘. This suggests the magnetic field
lines in BRC 18 are $\sim$30∘ off to the perpendicular direction to the
incoming ionizing radiation.

###  3.5 Magnetic field strength using structure function analysis

After knowing the direction of the magnetic field, we estimated the magnetic
field strength using the improved Davis–Chandrasekhar–Fermi method (DCF; Davis
& Greenstein 1951; Chandrasekhar & Fermi 1953) by determining the turbulent
angular dispersion (Hildebrand et al., 2009; Houde et al., 2009). In this
method, the dispersion of the polarization angles as a function of distance or
Angular Dispersion Function (ADF) is estimated by considering that the net
magnetic field consists of a large-scale structured field, B0(x), and a
turbulent component, Bt(x). The angular dispersion function (ADF) or the
square root of the structure-function (SF) is defined as the root mean squared
differences between the polarization angles measured for two points separated
by a distance _l_ and measured as shown in eq 2. Hence, SF analysis can be
used as an important statistical tool to correlate the large-scale structured
field and the turbulent component of the magnetic field in molecular clouds
(e.g., Hildebrand et al., 2009; Franco et al., 2010; Santos et al., 2012;
Eswaraiah et al., 2013; Neha et al., 2016).

$\langle\Delta\phi^{2}(l)\rangle^{1/2}=\Bigg{\\{}\frac{1}{N(l)}\sum\limits_{i=1}^{N(l)}[\phi(x)-\phi(x+l)]^{2}\Bigg{\\}}^{1/2}$
(2)

The structure function within the range $\delta<\emph{l}\ll d$, (where
$\delta$ and $d$ are the correlation lengths which characterize Bt(x) and
B0(x), respectively), can be estimated using eq 3:

$\langle\Delta\phi^{2}(l)\rangle_{\mathrm{tot}}\simeq
b^{2}+m^{2}l^{2}+\sigma^{2}_{\mathrm{M}}(l)$ (3)

where $\langle\Delta\phi^{2}(l)\rangle_{\mathrm{tot}}$ shows the total
measured dispersion estimated from the data. $\sigma^{2}_{\mathrm{M}}(l)$ are
the measurement uncertainties and are calculated by taking the mean of the
variances on $\Delta\phi(l)$ in each bin. The quantity $b^{2}$ is the constant
turbulent contribution, estimated by the intercept of the fit to the data
after subtracting $\sigma^{2}_{\mathrm{M}}(l)$. The term $m^{2}l^{2}$ is a
smoothly increasing contribution with the length $l$ ($m$ shows the slope of
this linear behavior). All these quantities are statistically independent from
each other.

The ratio of the turbulent component and the large-scale magnetic fields is
calculated by the eq 4:

$\frac{\langle
B^{2}_{\mathrm{t}}\rangle^{1/2}}{B_{\mathrm{0}}}=\frac{b}{\sqrt{2-b^{2}}}$ (4)

For the BRC 18 region, we estimated the ADF and plotted with the distance in
Fig. 7. We used the polarization angle of 171 stars for BRC 18 to calculate
ADF. The measured errors in each bin are very small, which are also over-
plotted in Fig. 7. Each bin denotes the
$\sqrt{\langle\Delta\phi^{2}(l)\rangle_{\mathrm{tot}}-\sigma^{2}_{\mathrm{M}}(l)}$
which is the ADF corrected for the measurement uncertainties. Bin widths are
taken on a logarithmic scale. We used only 5 points, corresponding to a
distance less than 1 pc, of the ADF in the linear fit of eq 3 shown by the
dashed line. The shortest distance we considered is $\simeq$ 0.15 pc. The net
turbulent contribution to the angular dispersion, $b$, is calculated to be
8.9∘ $\pm$ 0.3∘ (0.15 $\pm$ 0.005 rad) for BRC 18. Then, we estimated the
ratio of the turbulent component and the large-scale magnetic fields using eq
4, which is found to be 0.08 $\pm$ 0.004 for BRC 18. The result shows that the
turbulent component of the magnetic field is very small compared to the large-
scale structured magnetic field, i.e., $B_{\mathrm{t}}\ll B_{\mathrm{0}}$.

Figure 7: Angular dispersion function (ADF) of the polarization angles,
$\langle\Delta\phi^{2}(l)\rangle^{1/2}$ (∘), with distance (pc) for BRC 18
(upper panel) and BRC 17 (lower panel). The dashed line denotes the best fit
to the data up to 1pc distance.

The strength of the plane of the sky component of the magnetic field was
estimated from modified CF relation (Franco & Alves, 2015) as shown in eq 5,

$B_{\mathrm{pos}}=9.3\left[\frac{2\leavevmode\nobreak\
n(H_{2})}{cm^{-3}}\right]^{1/2}\left[\frac{\Delta
V}{kms^{-1}}\right]\left[\frac{b}{1^{\circ}}\right]^{-1}\leavevmode\nobreak\
\leavevmode\nobreak\ \mu G$ (5)

In eq 5, $n(H_{2})$ is the volume hydrogen density of the molecular hydrogen.
It is obtained by estimating the hydrogen column density of the region probed
by our optical polarimetry and from the radius of the cloud, assuming it to be
a spherical cloud. We used the relation, N(H2)/$A_{\mathrm{V}}$ = 9.4 $\times
10^{20}$ cm${}^{-2}mag^{-1}$ (Bohlin et al., 1978) for estimating the column
density. Based on the method described in the papers Maheswar et al. (2010)
and Neha et al. (2016), the average value of extinction traced by the stars
lying behind the cloud (assuming distance $\gtrsim$ 400 pc for BRC 18)
observed in this study is found to be $\sim 0.6$ mag for BRC 18. We also
determined the visual extinction, $A_{\mathrm{V}}$ using the near-infrared
color excess revised (NICER) extinction maps that are based on the 2MASS data
(Juvela & Montillaud, 2016). The value of $A_{\mathrm{V}}$ is found to be 1.6
mag for BRC 18. This is because the method is only sensitive to the extinction
of those stars lying on the cloud periphery. Hence, we have used the average
value of $A_{\mathrm{V}}$, which is found to be 1.1 mag. We estimated the
radius of BRC 18 by fitting a circle on the WISE 12 $\mu$m image. The radius
of BRC 18 is determined as $\sim$1.5 pc, and hence volume density is found to
be $\sim$230 cm-3 for BRC 18. We adopted the 12CO line width, $\Delta V$ = 1.7
km s-1 for BRC 18, from our molecular line observations (Neha et al.; in
preparation). After substituting all the values in eq 5, the value of
$B_{\mathrm{pos}}$ is found to be $\sim$40 $\mu$G for BRC 18. In this way, the
BRC 18 cloud has a magnetic field strength $\sim$40 $\mu$G, comparable to the
moderate magnetic field strength of the simulations, in an almost
perpendicular direction to the ionizing radiation. On comparing this with the
simulations, we found that the photoionization shock can be passed through the
cloud without any hindrance and can trigger the star formation (Arthur et al.,
2011).

Polarization position angles for BRC 17, as shown in Fig. 6, exhibit multiple
Gaussian features. We used 71 out of 105 sources whose polarization angles
follow the central component in the multi-Gaussian model to estimate the
magnetic field strength since it shows a relatively smaller dispersion than
the whole data and follows the ambient magnetic field direction. We performed
structure-function analysis as described above. The lower panel of Fig. 7
shows a plot of the ADF as a function of distance for BRC 17. Similar to BRC
18, we used 5 points of ADF and performed a linear fit using eq. 3. The value
of b is $26.9^{\circ}\pm 0.3^{\circ}$ for BRC 17. The ratio of turbulent to
the large-scale component of the magnetic field is found to be $0.35\pm 0.22$,
suggesting the turbulent component is smaller than the large-scale structured
magnetic field. We then estimated the strength of the plane of the sky
component of the magnetic field using eq. 5, adapting n($H_{2}$) = 2000 cm-3
and $\Delta V=1.3$ km s-1 from Zhou et al. (1988), who performed molecular
line observation of BRC 17. The magnetic field is $\sim$28 $\mu$G, which can
be considered weak magnetic field strength. Note that the calculated value of
$B_{\mathrm{pos}}$ should be considered a rough estimate due to the large
uncertainties of the individual quantities involved in its calculation,
particularly for BRC 17, which has a larger b value.

##  4 Discussion

Based on the radiation-magnetohydrodynamics (R-MHD) simulations of HII
regions, Arthur et al. (2011) presented the large-scale magnetic field maps
projected on the whole HII region, and they showed that the magnetic field
lines are mainly oriented along the large-scale ionization fronts, that forms
a ring around the HII region. The expanding HII and photo-dissociation regions
(PDR) remove the pre-existing small-scale disordered magnetic field pattern
and produce a large-scale ordered magnetic field in the neutral shell, with
approximately parallel orientation to the ionization front. They also
presented that the magnetic field lines are aligned in a perpendicular
direction to the ionization front at the head of the globules associated with
the HII region. Furthermore, Henney et al. (2009) and Mackey & Lim (2011)
included the effect of magnetic field on the globules in the presence of
ionizing radiation from the OB star. Mackey & Lim (2011) performed
3D-radiation magneto-hydrodynamics (3D-RMHD) simulations considering three
strengths of magnetic fields, 18 $\mu$G (weak), 53 $\mu$G (medium) and 160
$\mu$G (strong) for perpendicular direction to the ionizing radiation. They
found that the RDI process significantly changes the initially perpendicular
weak field orientation. The weak field is aligned along the incoming ionizing
radiation due to the RDI process and rocket effect. In the medium
perpendicular case, slight changes were noticed in the field direction,
whereas the strong perpendicular magnetic field remains unchanged. Hence, the
strong magnetic field can alter the morphology of the structure developed due
to RDI and rocket effect, partially due to shielding by the dense ionized
ridge and partially due to the effect of the magnetic field within the
globule.

Figure 8: Global magnetic field morphology in LOSFR. The layered texture in
the image represents the magnetic field geometry using sub-mm polarization,
while the black vectors, overplotted on the Planck sub-mm polarization map,
correspond to the optical magnetic field geometry using observed R-band
polarization. The red star shows the position of $\lambda$-Ori star. The
clouds, BRC 17 and BRC 18 are identified. A 2% degree of polarization
reference vector has been shown for optical polarization. The image is taken
by ESA’s Planck satellite (image credit: ESA and the Planck Collaboration).

The direction of polarization vectors represents the global plane-of-sky
magnetic field geometry in LOSFR, which seems to follow the large-scale
structure seen in all the images of Fig. 3, which is consistent with the
simulations shown by Arthur et al. (2011). Though our sample is small, the
polarization vectors follow the ring of the LOSFR clearly in Fig. 3. Fig. 8
shows the global galactic magnetic field geometry in LOSFR in optical and sub-
mm wavelengths. The Planck image,111http://sci.esa.int/planck/55910-polarised-
emission-from-orion/ taken by ESA’s Planck satellite (Planck Collaboration I
2016), shows the sub-mm polarization map indicating the global magnetic field
morphology. In contrast, the R-band polarization vectors in black color,
corresponding to the optical magnetic field geometry, are overplotted. In the
upper part of the image, the magnetic field geometry seems to be organized and
regular, which could be due to the large-scale orientation of the magnetic
field lines along the Galactic plane. Our optical polarization data is
consistent with the sub-mm, and the orientation of the magnetic field follows
the same pattern. It is also seen locally around BRC 17 and BRC 18 as shown in
Fig. 9, where the Planck sub-mm polarization vectors along with optical
polarization vectors towards BRC 17 and BRC 18 are overplotted on WISE 12
$\mu$m image. These Planck polarization vectors were extracted using Planck
public data release 3 (Planck Collaboration I 2016). Since the polarization
techniques for both optical and sub-mm wavelengths are different, as the
polarization occurs in optical due to partial extinction while in sub-mm
wavelengths, the polarization occurs due to emission, comparing the
polarization maps of both wavelengths would be interesting.

Figure 9: Polarization vectors are over-plotted on WISE 12$\mu$m image of BRC
17 (left panel) and BRC 18 (right panel) of our optical data (white color) and
of Planck data (red color). Binned Polarization vectors along galactic
longitude bins are shown in both panels for our data (thick white) and Planck
(thick red). The length of the vectors corresponds to the degree of
polarization, and orientation corresponds to the position angle measured from
the north and increasing toward the east. Vectors corresponding to 2$\%$
polarization are shown for references in their respective colors.

Polarization observations of BRC 17 show a large range of polarization angles
with a central peak at 167∘and two additional components far away. This could
be due to the combined effects of a shock wave coming from central ionizing
source $\lambda-$Ori and the presence of HH objects in the vicinity. An abrupt
change in the direction of the magnetic field around BRC 17 is noticed,
consistent with the Planck observations as shown in Fig. 9. We have binned
polarization vectors along the galactic longitude for a clear view. Although
we lack observations below the galactic longitude of 192.5∘, our polarization
vectors show a similar direction to that of Plank, being consistent above
longitude ¿192.5∘and turning towards the high-density material following
Planck vectors. This magnetic field orientation could be the reason for the
accumulation of high column densities there, as clouds generally tend to form
at “kinks” or “bends” in the magnetic field (Passot et al. 1995; Hartmann et
al. 2001; Heitsch et al. 2001; Ostriker et al. 2001).

Magakian et al. (2004) searched HH-objects and emission line stars in star-
forming regions and observed an intense molecular outflow spread over $\sim$5
pc. This is one of the high-velocity and largest giant outflows known to date.
This outflow is known as RNO 43 associated with the source (HH 243) IRAS
05295+1247 (Bence et al., 1996), having the outflow velocity around 11 km s-1
(Wu et al., 2004). Few more HH objects are present in the BRC 17 region. At
the head part of BRC 17, HH 176 is present, which is powered by a peculiar A4
type variable star HK-Ori (Lang et al., 2000). The presence of such a big
high-velocity outflow and HH objects in the BRC 17 region suggest that the
star formation activities are going on, and cloud material is dynamically more
active. Zhou et al. (1988) performed molecular line observations towards BRC
17 and showed gas temperature and column density enhancements along the edge
of the cloud, which corresponds to the optical bright rim. They also suggested
that the gas-heating mechanism in the BRC 17 is most likely due to the
photoelectric ejection of energetic electrons from dust grains induced by the
far-ultraviolet radiation from the $\lambda-$Orionis OB association. However,
these observations have very poor resolution. Further high-resolution
molecular line observations can provide a better picture of the kinematics of
BRC 17. We have calculated the magnetic field strength for BRC 17. The
strength of the turbulent component is about 30% of the large-scale magnetic
field. The strength of the plane of sky component of the magnetic field is
$\sim$28 $\mu$G, which can be considered in the weak field regime. Hence, it
could be possible that the high-energy radiation is affecting the orientation
of the magnetic field in BRC 17 (Henney et al., 2009; Mackey & Lim, 2011). A
detailed high-resolution polarimetric study is required to better understand
the magnetic field geometry in BRC 17.

BRC 18 shows that the magnetic field lines are aligned in a preferred
direction roughly perpendicular to the ionizing radiation, which is also
consistent with the simulations (Arthur et al., 2011). The directions of
optical polarization vectors are also consistent with Planck as shown in Fig.
9, where the binned polarization vectors along the galactic longitude are also
plotted, similar to BRC 17. There is also one HH object, HH 175, present in
the BRC 18 for which the driving source is IRAS 05417+0907, multiple systems
with at least 6 components (Reipurth & Friberg, 2021). Moreover, millimeter
observations suggest that the BRC 18 cloud is found to have multiple cores,
and the embedded source could be the result of compression by an ionization
front driven by the central $\lambda-$Ori OB stars (Reipurth & Friberg, 2021).
We estimated the magnetic field strength for BRC 18 (see section 3.5) and
found $\sim$40 $\mu$G, a medium-strength magnetic field roughly perpendicular
to the incoming ionization radiations. The moderate magnetic field strength
does not affect the interaction of the ionization radiations with the cloud
much but tries to align along the incoming ionizing radiations (Arthur et al.,
2011). Some of the polarization vectors in the lower region of BRC 18 (see
right panel of Fig. 5) show that they align themselves along the incoming
ionizing radiation, suggesting RDI in BRC 18.

##  5 Conclusions

We present optical polarimetric results for the stars globally projected on
the LOSFR and the associated BRC 17 and BRC 18. Using these polarimetric
observations, the importance of the magnetic field in the evolution of the HII
region has been studied. We draw the following conclusions:

  1. 1.

We estimated the distance of LOSFR as 392 $\pm$ 8 pc using astrometry
information of YSOs towards BRC 17, BRC 18, and central cluster Collinder 69
members using GAIA EDR3.

  2. 2.

We found a large-scale ordered magnetic field in the LOSFR, and our results
are consistent with the simulations and the Planck sub-mm polarization map.
The orientation of the magnetic field is almost similar in all three optical
bands, VRI, and sub-mm.

  3. 3.

The magnetic field lines traced by the polarization position angles in BRC 17
are roughly oriented in north-south directions but show a large dispersion. In
the case of BRC 18, the magnetic field morphology is regular, having an
approximately perpendicular orientation with the incoming ionizing radiations.
The magnetic field geometry in these two regions is also consistent with the
Planck magnetic field map.

  4. 4.

The average dust size in the LOSFR is also determined using Serkowski’s curve
fitting, which comes out to be $\sim$0.51 $\pm$ 0.05 $\mu$m and the average
value of total-to-selective extinction ratio, RV is equal to $\sim$2.9 $\pm$
0.3 which is consistent with the general value of ISM for the Milky Way.

  5. 5.

The turbulent to large scale magnetic field strength ratio is estimated to be
higher $\sim$30 % in BRC 17 compared to 10% in BRC 18. The plane of the sky
magnetic field strength, calculated using the structure-function analysis, is
$\sim$28 $\mu$G for BRC 17 and $\sim$40 $\mu$G for BRC 18.

###### Acknowledgements.

We thank the referee for her/his constructive suggestions/comments, which
helped us to improve the quality of our manuscript. This research has made use
of the SIMBAD database, operated at CDS, Strasbourg, France. We also
acknowledge the use of NASA’s SkyView facility (http://skyview.gsfc.nasa.gov)
located at NASA Goddard Space Flight Center. NS acknowledges the financial
support provided under the National Post-doctoral Fellowship (NPDF; File
Number: PDF/2022/001040) by the Science & Engineering Research Board (SERB), a
statutory body of the Department of Science & Technology (DST), Government of
India. NS thanks Suvendu Rakshit for the useful discussions.

## References

  * Arthur et al. (2011) Arthur, S. J., Henney, W. J., Mellema, G., de Colle, F., & Vázquez-Semadeni, E. 2011, MNRAS, 414, 1747
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, The Astronomical Journal, 161, 147
  * Ballesteros-Paredes et al. (1999) Ballesteros-Paredes, J., Hartmann, L., & Vázquez-Semadeni, E. 1999, ApJ, 527, 285
  * Barnard (1919) Barnard, E. E. 1919, ApJ, 49, 1
  * Bayo et al. (2012) Bayo, A., Barrado, D., Huélamo, N., et al. 2012, A&A, 547, A80
  * Bence et al. (1996) Bence, S. J., Richer, J. S., & Padman, R. 1996, MNRAS, 279, 866
  * Bertoldi (1989) Bertoldi, F. 1989, ApJ, 346, 735
  * Bohlin et al. (1978) Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, ApJ, 224, 132
  * Chandrasekhar & Fermi (1953) Chandrasekhar, S. & Fermi, E. 1953, ApJ, 118, 113
  * Chauhan et al. (2009) Chauhan, N., Pandey, A. K., Ogura, K., et al. 2009, MNRAS, 396, 964
  * Cortés et al. (2021) Cortés, P. C., Sanhueza, P., Houde, M., et al. 2021, The Astrophysical Journal, 923, 204
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, 2246, 0
  * Davis & Greenstein (1951) Davis, Jr., L. & Greenstein, J. L. 1951, ApJ, 114, 206
  * Dolan & Mathieu (1999) Dolan, C. J. & Mathieu, R. D. 1999, AJ, 118, 2409
  * Dolan & Mathieu (2001) Dolan, C. J. & Mathieu, R. D. 2001, AJ, 121, 2124
  * Dolan & Mathieu (2002) Dolan, C. J. & Mathieu, R. D. 2002, AJ, 123, 387
  * Duerr et al. (1982) Duerr, R., Imhoff, C. L., & Lada, C. J. 1982, ApJ, 261, 135
  * Elmegreen (2011) Elmegreen, B. G. 2011, in EAS Publications Series, Vol. 51, EAS Publications Series, ed. C. Charbonnel & T. Montmerle, 45–58
  * Eswaraiah et al. (2013) Eswaraiah, C., Maheswar, G., Pandey, A. K., et al. 2013, A&A, 556, A65
  * Eswaraiah et al. (2012) Eswaraiah, C., Pandey, A. K., Maheswar, G., et al. 2012, MNRAS, 419, 2587
  * Eswaraiah et al. (2011) Eswaraiah, C., Pandey, A. K., Maheswar, G., et al. 2011, MNRAS, 411, 1418
  * Franco & Alves (2015) Franco, G. A. P. & Alves, F. O. 2015, ApJ, 807, 5
  * Franco et al. (2010) Franco, G. A. P., Alves, F. O., & Girart, J. M. 2010, ApJ, 723, 146
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1
  * Garcia-Segura & Franco (1996) Garcia-Segura, G. & Franco, J. 1996, ApJ, 469, 171
  * Hartmann et al. (2001) Hartmann, L., Ballesteros-Paredes, J., & Bergin, E. A. 2001, ApJ, 562, 852
  * Hayashi et al. (2012) Hayashi, M., Itoh, Y., & Oasa, Y. 2012, PASJ, 64, 96
  * Heiles (2000) Heiles, C. 2000, AJ, 119, 923
  * Heitsch et al. (2001) Heitsch, F., Mac Low, M.-M., & Klessen, R. S. 2001, ApJ, 547, 280
  * Henney et al. (2009) Henney, W. J., Arthur, S. J., de Colle, F., & Mellema, G. 2009, MNRAS, 398, 157
  * Hildebrand et al. (2009) Hildebrand, R. H., Kirby, L., Dotson, J. L., Houde, M., & Vaillancourt, J. E. 2009, ApJ, 696, 567
  * Høg et al. (2000) Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27
  * Hosoya et al. (2019) Hosoya, K., Itoh, Y., Oasa, Y., Gupta, R., & Sen, A. K. 2019, International Journal of Astronomy and Astrophysics, 9, 154
  * Houde et al. (2009) Houde, M., Vaillancourt, J. E., Hildebrand, R. H., Chitsazzadeh, S., & Kirby, L. 2009, ApJ, 706, 1504
  * Juvela & Montillaud (2016) Juvela, M. & Montillaud, J. 2016, A&A, 585, A38
  * Koenig et al. (2015) Koenig, X., Hillenbrand, L. A., Padgett, D. L., & DeFelippis, D. 2015, AJ, 150, 100
  * Kounkel et al. (2018) Kounkel, M., Covey, K., Suárez, G., et al. 2018, AJ, 156, 84
  * Lang et al. (2000) Lang, W. J., Masheder, M. R. W., Dame, T. M., & Thaddeus, P. 2000, A&A, 357, 1001
  * Lindegren (2018) Lindegren, L. 2018, gAIA-C3-TN-LU-LL-124
  * Lindegren et al. (2021) Lindegren, L., Klioner, S. A., Hernández, J., et al. 2021, A&A, 649, A2
  * Liu et al. (2019) Liu, J., Qiu, K., Berry, D., et al. 2019, The Astrophysical Journal, 877, 43
  * Mackey & Lim (2010) Mackey, J. & Lim, A. J. 2010, MNRAS, 403, 714
  * Mackey & Lim (2011) Mackey, J. & Lim, A. J. 2011, MNRAS, 412, 2079
  * Magakian et al. (2004) Magakian, T. Y., Movsessian, T. A., & Nikogossian, E. H. 2004, Astrophysics, 47, 162
  * Maheswar et al. (2010) Maheswar, G., Lee, C. W., Bhatt, H. C., Mallik, S. V., & Dib, S. 2010, A&A, 509, A44
  * Mathieu (2008) Mathieu, R. D. 2008, The $\lambda$ Orionis Star Forming Region, ed. B. Reipurth, 757
  * McKee & Ostriker (2007) McKee, C. F. & Ostriker, E. C. 2007, ARA&A, 45, 565
  * Miao et al. (2006) Miao, J., White, G. J., Nelson, R., Thompson, M., & Morgan, L. 2006, MNRAS, 369, 143
  * Mouschovias (1978) Mouschovias, T. C. 1978, in IAU Colloq. 52: Protostars and Planets, ed. T. Gehrels, 209–242
  * Murdin & Penston (1977) Murdin, P. & Penston, M. V. 1977, MNRAS, 181, 657
  * Neha et al. (2018) Neha, S., Maheswar, G., Soam, A., & Lee, C. W. 2018, MNRAS, 476, 4442
  * Neha et al. (2016) Neha, S., Maheswar, G., Soam, A., Lee, C. W., & Tej, A. 2016, A&A, 588, A45
  * Orsatti et al. (2010) Orsatti, A. M., Feinstein, C., Vergne, M. M., Martínez, R. E., & Vega, E. I. 2010, A&A, 513, A75
  * Orsatti et al. (1998) Orsatti, A. M., Vega, E., & Marraco, H. G. 1998, AJ, 116, 266
  * Ostriker et al. (2001) Ostriker, E. C., Stone, J. M., & Gammie, C. F. 2001, ApJ, 546, 980
  * Passot et al. (1995) Passot, T., Vazquez-Semadeni, E., & Pouquet, A. 1995, ApJ, 455, 536
  * Pattle et al. (2021) Pattle, K., Lai, S.-P., Francesco, J. D., et al. 2021, The Astrophysical Journal, 907, 88
  * Perryman et al. (1997) Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 323, L49
  * Planck Collaboration I (2016) Planck Collaboration I. 2016, A&A, 594, A1
  * Ramaprakash et al. (1998) Ramaprakash, A. N., Gupta, R., Sen, A. K., & Tandon, S. N. 1998, A&AS, 128, 369
  * Rautela et al. (2004) Rautela, B. S., Joshi, G. C., & Pandey, J. C. 2004, Bulletin of the Astronomical Society of India, 32, 159
  * Reipurth (2000) Reipurth, B. 2000, VizieR Online Data Catalog, 5104
  * Reipurth & Friberg (2021) Reipurth, B. & Friberg, P. 2021, MNRAS, 501, 5938
  * Saha et al. (2022) Saha, P., Gopinathan, M., Ojha, D. K., & Neha, S. 2022, MNRAS, 510, 2644
  * Santos et al. (2012) Santos, F. P., Roman-Lopes, A., & Franco, G. A. P. 2012, ApJ, 751, 138
  * Schmidt et al. (1992) Schmidt, G. D., Elston, R., & Lupie, O. L. 1992, AJ, 104, 1563
  * Serkowski et al. (1975) Serkowski, K., Mathewson, D. S., & Ford, V. L. 1975, ApJ, 196, 261
  * Sharpless (1959) Sharpless, S. 1959, ApJS, 4, 257
  * Soam et al. (2013) Soam, A., Maheswar, G., Bhatt, H. C., Lee, C. W., & Ramaprakash, A. N. 2013, MNRAS, 432, 1502
  * Soam et al. (2015) Soam, A., Maheswar, G., Lee, C. W., et al. 2015, A&A, 573, A34
  * Soam et al. (2017) Soam, A., Maheswar, G., Lee, C. W., Neha, S., & Andersson, B. G. 2017, MNRAS, 465, 559
  * Soam et al. (2018) Soam, A., Maheswar, G., Lee, C. W., Neha, S., & Kim, K.-T. 2018, MNRAS, 476, 4782
  * Soler et al. (2013) Soler, J. D., Hennebelle, P., Martin, P. G., et al. 2013, ApJ, 774, 128
  * Sugitani et al. (1991) Sugitani, K., Fukui, Y., & Ogura, K. 1991, ApJS, 77, 59
  * Topasna et al. (2017) Topasna, G. A., Daman, E. A., & Kaltcheva, N. T. 2017, PASP, 129, 104201
  * van Leeuwen (2007) van Leeuwen, F. 2007, A&A, 474, 653
  * Vergne et al. (2007) Vergne, M. M., Feinstein, C., & Martínez, R. 2007, A&A, 462, 621
  * Wade (1957) Wade, C. M. 1957, AJ, 62, 148
  * Whittet (1977) Whittet, D. C. B. 1977, MNRAS, 180, 29
  * Whittet & van Breda (1978) Whittet, D. C. B. & van Breda, I. G. 1978, A&A, 66, 57
  * Wu et al. (2004) Wu, Y., Wei, Y., Zhao, M., et al. 2004, A&A, 426, 503
  * Zamora-Avilés et al. (2019) Zamora-Avilés, M., Vázquez-Semadeni, E., González, R. F., et al. 2019, MNRAS, 487, 2200
  * Zari et al. (2018) Zari, E., Hashemi, H., Brown, A. G. A., Jardine, K., & de Zeeuw, P. T. 2018, A&A, 620, A172
  * Zhang et al. (1989) Zhang, C. Y., Laureijs, R. J., Chlewicki, G., Wesselius, P. R., & Clark, F. O. 1989, A&A, 218, 231
  * Zhou et al. (1988) Zhou, S., Butner, H. M., & Evans, Neal J., I. 1988, ApJ, 333, 809

##  Appendix A Additional table

Table 5: Polarization results of observed Tycho stars in VRI filters towards
$\lambda$-Ori region.

ID | RA | Dec | PV $\pm$ $\epsilon_{P_{V}}$ |  $\theta_{V}$ $\pm$ $\epsilon_{\theta_{V}}$ | PR $\pm$ $\epsilon_{P_{R}}$ |  $\theta_{R}$ $\pm$ $\epsilon_{\theta_{R}}$ | PI $\pm$ $\epsilon_{P_{I}}$ |  $\theta_{I}$ $\pm$ $\epsilon_{\theta_{I}}$ |  $\lambda_{max}$ $\pm$ $\epsilon_{\lambda_{max}}$ | Pmax $\pm$ $\epsilon_{P_{max}}$ | RV $\pm$ $\epsilon_{R_{V}}$ | D $\pm$ $\epsilon_{D}$
---|---|---|---|---|---|---|---|---|---|---|---|---
| (∘) | (∘) | (%) | (∘) | (%) | (∘) | (%) | (∘) | ($\mu$m) | (%) |  | (pc)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
1 | 79.683675 | 11.227991 | 0.5 $\pm$ 0.2 | 101 $\pm$ 6 | 0.4 $\pm$ 0.1 | 134 $\pm$ 7 | 0.4 $\pm$ 0.2 | 133 $\pm$ 7 | 0.56 $\pm$ 0.06 | 0.46 $\pm$ 0.02 | 3.14 $\pm$ 0.38 | 1059 $\pm$ 19
2 | 80.334997 | 6.959988 | 1.4 $\pm$ 0.2 | 123 $\pm$ 5 | 1.3 $\pm$ 0.1 | 126 $\pm$ 6 | 1.2 $\pm$ 0.1 | 127 $\pm$ 6 | 0.60 $\pm$ 0.04 | 1.35 $\pm$ 0.04 | 3.36 $\pm$ 0.27 | 1601 $\pm$ 67
3 | 80.450959 | 13.120884 | 0.8 $\pm$ 0.2 | 111 $\pm$ 5 | 0.8 $\pm$ 0.2 | 119 $\pm$ 6 | 0.6 $\pm$ 0.2 | 115 $\pm$ 6 | 0.48 $\pm$ 0.03 | 0.85 $\pm$ 0.05 | 2.69 $\pm$ 0.24 | 939 $\pm$ 25
4 | 81.025895 | 11.663095 | 0.5 $\pm$ 0.2 | 82 $\pm$ 7 | 0.3 $\pm$ 0.2 | 95 $\pm$ 7 | 0.3 $\pm$ 0.2 | 100 $\pm$ 7 | 0.41 $\pm$ 0.07 | 0.48 $\pm$ 0.08 | 2.30 $\pm$ 0.40 | 584 $\pm$ 7
5 | 81.100961 | 7.859315 | 0.5 $\pm$ 0.2 | 74 $\pm$ 5 | 0.5 $\pm$ 0.2 | 96 $\pm$ 7 | 0.3 $\pm$ 0.2 | 92 $\pm$ 8 | 0.39 $\pm$ 0.07 | 0.59 $\pm$ 0.12 | 2.18 $\pm$ 0.38 | 551 $\pm$ 8
6 | 81.380420 | 9.098704 | 0.7 $\pm$ 0.2 | 170 $\pm$ 7 | 0.5 $\pm$ 0.2 | 159 $\pm$ 7 | 0.5 $\pm$ 0.2 | 157 $\pm$ 7 | 0.41 $\pm$ 0.06 | 0.77 $\pm$ 0.12 | 2.30 $\pm$ 0.35 | 696 $\pm$ 8
7 | 82.017076 | 11.218365 | 1.1 $\pm$ 0.2 | 147 $\pm$ 5 | 1.1 $\pm$ 0.2 | 149 $\pm$ 5 | 1.0 $\pm$ 0.2 | 46 $\pm$ 6 | 0.58 $\pm$ 0.04 | 1.14 $\pm$ 0.04 | 3.25 $\pm$ 0.29 | 1214 $\pm$ 26
8 | 82.475707 | 5.422993 | 1.2 $\pm$ 0.2 | 158 $\pm$ 5 | 1.1 $\pm$ 0.1 | 157 $\pm$ 7 | 0.9 $\pm$ 0.1 | 149 $\pm$ 6 | 0.51 $\pm$ 0.03 | 1.17 $\pm$ 0.05 | 2.86 $\pm$ 0.21 | 1921 $\pm$ 73
9 | 82.609959 | 9.636632 | 0.5 $\pm$ 0.2 | 154 $\pm$ 7 | 0.4 $\pm$ 0.1 | 147 $\pm$ 7 | 0.4 $\pm$ 0.1 | 160 $\pm$ 7 | 0.60 $\pm$ 0.05 | 0.46 $\pm$ 0.02 | 3.36 $\pm$ 0.32 | 946 $\pm$ 16
10 | 82.619749 | 8.075273 | 0.8 $\pm$ 0.2 | 149 $\pm$ 5 | 0.7 $\pm$ 0.2 | 135 $\pm$ 6 | 0.6 $\pm$ 0.2 | 130 $\pm$ 6 | 0.47 $\pm$ 0.04 | 0.82 $\pm$ 0.06 | 2.63 $\pm$ 0.27 | 988 $\pm$ 18
11 | 82.713199 | 14.039175 | 1.5 $\pm$ 0.2 | 43 $\pm$ 5 | 1.4 $\pm$ 0.2 | 41 $\pm$ 6 | 1.1 $\pm$ 0.2 | 33 $\pm$ 7 | 0.46 $\pm$ 0.02 | 1.56 $\pm$ 0.05 | 2.58 $\pm$ 0.17 | 919 $\pm$ 17
12 | 83.158619 | 9.086116 | 1.4 $\pm$ 0.2 | 153 $\pm$ 4 | 1.4 $\pm$ 0.1 | 149 $\pm$ 7 | 1.3 $\pm$ 0.1 | 144 $\pm$ 7 | 0.60 $\pm$ 0.00 | 1.41 $\pm$ 0.00 | 3.36 $\pm$ 0.18 | 1161 $\pm$ 65
13 | 83.325927 | 6.805111 | 0.9 $\pm$ 0.2 | 142 $\pm$ 6 | 0.8 $\pm$ 0.2 | 149 $\pm$ 6 | 0.7 $\pm$ 0.2 | 148 $\pm$ 7 | 0.53 $\pm$ 0.01 | 0.88 $\pm$ 0.01 | 2.97 $\pm$ 0.17 | 932 $\pm$ 17
14 | 83.361726 | 7.842497 | 0.7 $\pm$ 0.2 | 167 $\pm$ 7 | 0.5 $\pm$ 0.2 | 156 $\pm$ 7 | 0.5 $\pm$ 0.2 | 152 $\pm$ 9 | 0.40 $\pm$ 0.09 | 0.79 $\pm$ 0.18 | 2.24 $\pm$ 0.49 | 1399 $\pm$ 56
15 | 83.483675 | 10.600003 | 0.9 $\pm$ 0.2 | 162 $\pm$ 5 | 0.7 $\pm$ 0.1 | 142 $\pm$ 7 | 0.7 $\pm$ 0.2 | 158 $\pm$ 7 | 0.44 $\pm$ 0.14 | 0.92 $\pm$ 0.27 | 2.46 $\pm$ 0.79 | 1267 $\pm$ 30
16 | 83.580072 | 11.654027 | 0.7 $\pm$ 0.2 | 176 $\pm$ 7 | 0.6 $\pm$ 0.2 | 165 $\pm$ 7 | 0.5 $\pm$ 0.2 | 175 $\pm$ 9 | 0.45 $\pm$ 0.01 | 0.70 $\pm$ 0.02 | 2.52 $\pm$ 0.16 | 1096 $\pm$ 23
17 | 83.713086 | 5.758289 | 0.7 $\pm$ 0.2 | 13 $\pm$ 11 | 0.5 $\pm$ 0.2 | 11 $\pm$ 13 | 0.6 $\pm$ 0.2 | 12 $\pm$ 7 | 0.46 $\pm$ 0.13 | 0.72 $\pm$ 0.17 | 2.58 $\pm$ 0.76 | 1090 $\pm$ 38
18 | 84.201449 | 10.201707 | 2.6 $\pm$ 0.1 | 143 $\pm$ 4 | 2.3 $\pm$ 0.1 | 142 $\pm$ 8 | 2.2 $\pm$ 0.1 | 145 $\pm$ 8 | 0.54 $\pm$ 0.04 | 2.53 $\pm$ 0.11 | 3.02 $\pm$ 0.29 | 905 $\pm$ 20
19 | 84.329903 | 11.133247 | 1.1 $\pm$ 0.2 | 173 $\pm$ 5 | 0.9 $\pm$ 0.1 | 172 $\pm$ 6 | 0.9 $\pm$ 0.1 | 177 $\pm$ 6 | 0.55 $\pm$ 0.16 | 1.00 $\pm$ 0.19 | 3.08 $\pm$ 0.93 | 1274 $\pm$ 30
20 | 84.458219 | 9.303417 | 1.1 $\pm$ 0.2 | 169 $\pm$ 5 | 1.0 $\pm$ 0.1 | 169 $\pm$ 7 | 1.0 $\pm$ 0.1 | 168 $\pm$ 6 | 0.66 $\pm$ 0.06 | 1.05 $\pm$ 0.03 | 3.70 $\pm$ 0.41 | 2220 $\pm$ 91
21 | 84.851907 | 14.632194 | 1.8 $\pm$ 0.2 | 171 $\pm$ 5 | 1.6 $\pm$ 0.1 | 167 $\pm$ 7 | 1.6 $\pm$ 0.2 | 168 $\pm$ 6 | 0.55 $\pm$ 0.08 | 1.75 $\pm$ 0.13 | 3.08 $\pm$ 0.50 | 1092 $\pm$ 32
22 | 84.882692 | 9.287090 | 0.9 $\pm$ 0.3 | 160 $\pm$ 7 | 0.9 $\pm$ 0.1 | 168 $\pm$ 6 | 0.9 $\pm$ 0.2 | 167 $\pm$ 7 | 0.66 $\pm$ 0.03 | 0.90 $\pm$ 0.01 | 3.70 $\pm$ 0.26 | 1272 $\pm$ 39
23 | 84.989390 | 9.698935 | 1.0 $\pm$ 0.1 | 174 $\pm$ 6 | 1.0 $\pm$ 0.1 | 171 $\pm$ 6 | 0.9 $\pm$ 0.1 | 170 $\pm$ 6 | 0.60 $\pm$ 0.01 | 0.97 $\pm$ 0.00 | 3.36 $\pm$ 0.18 | 940 $\pm$ 16
24 | 85.054662 | 8.675390 | 1.4 $\pm$ 0.2 | 146 $\pm$ 4 | 1.4 $\pm$ 0.2 | 150 $\pm$ 6 | 1.2 $\pm$ 0.2 | 48 $\pm$ 6 | 0.57 $\pm$ 0.02 | 1.36 $\pm$ 0.03 | 3.19 $\pm$ 0.22 | 1421 $\pm$ 37
25 | 85.102108 | 10.114206 | 1.6 $\pm$ 0.2 | 172 $\pm$ 5 | 1.2 $\pm$ 0.1 | 163 $\pm$ 6 | 1.1 $\pm$ 0.1 | 164 $\pm$ 6 | 0.48 $\pm$ 0.13 | 1.45 $\pm$ 0.35 | 2.69 $\pm$ 0.75 | 1957 $\pm$ 89
26 | 85.354677 | 14.360165 | 2.1 $\pm$ 0.2 | 170 $\pm$ 5 | 1.8 $\pm$ 0.1 | 170 $\pm$ 7 | 1.9 $\pm$ 0.1 | 169 $\pm$ 6 | 0.63 $\pm$ 0.13 | 1.93 $\pm$ 0.16 | 3.53 $\pm$ 0.75 | 646 $\pm$ 9
27 | 85.846172 | 10.807565 | 2.2 $\pm$ 0.2 | 4 $\pm$ 5 | 2.0 $\pm$ 0.2 | 5 $\pm$ 5 | 1.4 $\pm$ 0.2 | 79 $\pm$ 6 | 0.40 $\pm$ 0.04 | 2.59 $\pm$ 0.32 | 2.24 $\pm$ 0.27 | 1194 $\pm$ 24
28 | 86.410384 | 13.849815 | 2.9 $\pm$ 0.2 | 156 $\pm$ 4 | 2.6 $\pm$ 0.2 | 154 $\pm$ 6 | 2.4 $\pm$ 0.1 | 154 $\pm$ 6 | 0.55 $\pm$ 0.03 | 2.84 $\pm$ 0.10 | 3.08 $\pm$ 0.23 | 910 $\pm$ 21
29 | 86.495363 | 8.237844 | 1.6 $\pm$ 0.2 | 174 $\pm$ 4 | 1.4 $\pm$ 0.2 | 174 $\pm$ 7 | 1.2 $\pm$ 0.2 | 174 $\pm$ 7 | 0.51 $\pm$ 0.00 | 1.56 $\pm$ 0.00 | 2.86 $\pm$ 0.15 | 985 $\pm$ 27
30 | 87.914164 | 7.541778 | 0.9 $\pm$ 0.1 | 14 $\pm$ 6 | 0.8 $\pm$ 0.1 | 10 $\pm$ 9 | 0.8 $\pm$ 0.1 | 8 $\pm$ 6 | 0.54 $\pm$ 0.07 | 0.89 $\pm$ 0.06 | 3.02 $\pm$ 0.41 | 807 $\pm$ 14
31 | 88.040171 | 7.731424 | 0.8 $\pm$ 0.2 | 168 $\pm$ 11 | 0.7 $\pm$ 0.2 | 172 $\pm$ 7 | 0.4 $\pm$ 0.2 | 3 $\pm$ 7 | 0.35 $\pm$ 0.12 | 1.00 $\pm$ 0.48 | 1.96 $\pm$ 0.69 | 944 $\pm$ 18
32 | 88.091171 | 12.577652 | 1.9 $\pm$ 0.1 | 4 $\pm$ 7 | 1.6 $\pm$ 0.1 | 171 $\pm$ 6 | 1.5 $\pm$ 0.1 | 174 $\pm$ 7 | 0.48 $\pm$ 0.08 | 1.92 $\pm$ 0.23 | 2.69 $\pm$ 0.45 | 1035 $\pm$ 27
33 | 88.442286 | 7.989944 | 1.0 $\pm$ 0.2 | 35 $\pm$ 8 | 0.8 $\pm$ 0.2 | 27 $\pm$ 9 | 0.6 $\pm$ 0.2 | 23 $\pm$ 10 | 0.38 $\pm$ 0.01 | 1.20 $\pm$ 0.03 | 2.13 $\pm$ 0.12 | 1893 $\pm$ 106
34 | 88.475476 | 10.499152 | 3.5 $\pm$ 0.2 | 167 $\pm$ 5 | 3.1 $\pm$ 0.2 | 164 $\pm$ 6 | 3.0 $\pm$ 0.2 | 164 $\pm$ 6 | 0.55 $\pm$ 0.04 | 3.41 $\pm$ 0.12 | 3.08 $\pm$ 0.27 | 1152 $\pm$ 24

222Columns are listed as follows: (1) serial number; (2) RA; (3) Dec; (4), (6)
& (8) degree of polarization with their respective errors in V, R & I bands,
respectively; (5), (7) & (9) polarization position angles with their
respective errors in V, R & I bands, respectively; (10)$-$(11) maximum
wavelength and degree of polarization estimated from Serkowski fitting; (12)
total-to-selective extinction; (13) distances with their respective errors
from Bailer-Jones et al. 2021.

Table 6: Polarization results of 105 stars observed in the direction of BRC 17 and 171 stars observed towards BRC 18 with P/$\sigma_{P}$ $\geq$ 2 in R filter. | Star |  $\alpha$ (J2000) |  $\delta$ (J2000) | P $\pm$ $\epsilon_{P}$ |  $\theta$ $\pm$ $\epsilon_{\theta}$
---|---|---|---|---
Id | (∘) | (∘) | (%) | (∘)
BRC 17
1 | 82.568436 | 12.238192 | 0.9 $\pm$ 0.2 | 23 $\pm$ 8
2 | 82.599312 | 12.227496 | 2.3 $\pm$ 0.9 | 14 $\pm$ 13
3 | 82.601128 | 12.094558 | 1.3 $\pm$ 0.4 | 26 $\pm$ 11
4 | 82.601219 | 12.198106 | 0.8 $\pm$ 0.2 | 50 $\pm$ 8
5 | 82.602654 | 12.087220 | 0.8 $\pm$ 0.1 | 155 $\pm$ 5
6 | 82.603317 | 12.230099 | 3.3 $\pm$ 0.6 | 44 $\pm$ 6
7 | 82.604851 | 12.068765 | 1.9 $\pm$ 0.6 | 165 $\pm$ 9
8 | 82.616081 | 12.116481 | 1.8 $\pm$ 0.6 | 22 $\pm$ 10
9 | 82.627769 | 12.216683 | 0.7 $\pm$ 0.2 | 19 $\pm$ 8
10 | 82.634521 | 12.121438 | 1.1 $\pm$ 0.3 | 152 $\pm$ 7
11 | 82.638466 | 12.123507 | 0.4 $\pm$ 0.2 | 164 $\pm$ 8
12 | 82.646278 | 12.116957 | 0.6 $\pm$ 0.2 | 133 $\pm$ 6
13 | 82.647423 | 12.222106 | 1.1 $\pm$ 0.3 | 21 $\pm$ 11
14 | 82.648911 | 12.214931 | 1.8 $\pm$ 0.6 | 60 $\pm$ 10
15 | 82.660690 | 12.138010 | 1.7 $\pm$ 0.8 | 111 $\pm$ 11
16 | 82.661232 | 12.234212 | 0.6 $\pm$ 0.1 | 14 $\pm$ 8
17 | 82.667831 | 12.075129 | 1.6 $\pm$ 0.6 | 127 $\pm$ 9
18 | 82.676125 | 12.123517 | 1.7 $\pm$ 0.6 | 148 $\pm$ 10
19 | 82.677361 | 12.146648 | 1.3 $\pm$ 0.3 | 1 $\pm$ 7
20 | 82.692673 | 12.224899 | 1.4 $\pm$ 0.5 | 29 $\pm$ 12
21 | 82.695663 | 12.190128 | 1.4 $\pm$ 0.2 | 26 $\pm$ 5
22 | 82.698982 | 12.070744 | 2.4 $\pm$ 0.5 | 102 $\pm$ 5
23 | 82.700195 | 12.076781 | 0.5 $\pm$ 0.1 | 7 $\pm$ 10
24 | 82.700844 | 12.086476 | 0.8 $\pm$ 0.2 | 170 $\pm$ 8
25 | 82.702469 | 12.060691 | 0.9 $\pm$ 0.2 | 5 $\pm$ 7
26 | 82.702957 | 12.115624 | 1.0 $\pm$ 0.2 | 99 $\pm$ 6
27 | 82.708870 | 12.030152 | 1.1 $\pm$ 0.4 | 66 $\pm$ 8
28 | 82.714439 | 12.097614 | 0.7 $\pm$ 0.2 | 10 $\pm$ 8
29 | 82.715256 | 12.156046 | 0.5 $\pm$ 0.2 | 113 $\pm$ 7
30 | 82.724586 | 12.007061 | 0.5 $\pm$ 0.1 | 150 $\pm$ 5
31 | 82.733559 | 12.025238 | 1.1 $\pm$ 0.3 | 113 $\pm$ 5
32 | 82.739586 | 12.017054 | 1.5 $\pm$ 0.7 | 94 $\pm$ 11
33 | 82.743492 | 12.009210 | 0.4 $\pm$ 0.2 | 111 $\pm$ 6
34 | 82.747086 | 12.030783 | 0.7 $\pm$ 0.3 | 86 $\pm$ 7
35 | 82.747955 | 12.210904 | 2.3 $\pm$ 0.9 | 28 $\pm$ 13
36 | 82.750214 | 12.070655 | 1.6 $\pm$ 0.4 | 75 $\pm$ 6
37 | 82.751984 | 12.215071 | 1.1 $\pm$ 0.1 | 70 $\pm$ 5
38 | 82.754005 | 12.083478 | 1.0 $\pm$ 0.3 | 72 $\pm$ 5
39 | 82.754349 | 11.992623 | 0.7 $\pm$ 0.2 | 149 $\pm$ 7
40 | 82.756210 | 11.996511 | 1.0 $\pm$ 0.2 | 146 $\pm$ 5
41 | 82.764862 | 12.166323 | 1.6 $\pm$ 0.2 | 19 $\pm$ 6
42 | 82.766769 | 12.180549 | 2.2 $\pm$ 0.2 | 17 $\pm$ 4
43 | 82.772522 | 11.981793 | 0.9 $\pm$ 0.3 | 136 $\pm$ 6
44 | 82.774445 | 12.002536 | 1.0 $\pm$ 0.5 | 118 $\pm$ 10
45 | 82.776337 | 12.075002 | 1.0 $\pm$ 0.4 | 43 $\pm$ 11
46 | 82.784729 | 12.160297 | 1.0 $\pm$ 0.2 | 158 $\pm$ 7
47 | 82.788124 | 12.295055 | 1.9 $\pm$ 0.6 | 47 $\pm$ 8
48 | 82.793694 | 12.319737 | 2.1 $\pm$ 0.3 | 85 $\pm$ 4
49 | 82.796494 | 12.039086 | 0.3 $\pm$ 0.1 | 177 $\pm$ 8
50 | 82.799156 | 12.253103 | 0.8 $\pm$ 0.2 | 178 $\pm$ 7
Star |  $\alpha$ (J2000) |  $\delta$ (J2000) | P $\pm$ $\epsilon_{P}$ |  $\theta$ $\pm$ $\epsilon_{\theta}$
---|---|---|---|---
Id | (∘) | (∘) | (%) | (∘)
51 | 82.803902 | 12.133664 | 2.6 $\pm$ 0.1 | 19 $\pm$ 4
52 | 82.808525 | 12.271837 | 2.0 $\pm$ 1.0 | 110 $\pm$ 12
53 | 82.812210 | 12.318285 | 2.8 $\pm$ 0.4 | 57 $\pm$ 4
54 | 82.814453 | 12.202498 | 2.3 $\pm$ 0.4 | 118 $\pm$ 4
55 | 82.827515 | 12.333557 | 1.1 $\pm$ 0.4 | 55 $\pm$ 8
56 | 82.828484 | 12.260856 | 1.6 $\pm$ 0.5 | 180 $\pm$ 11
57 | 82.830978 | 12.166741 | 2.5 $\pm$ 0.3 | 144 $\pm$ 4
58 | 82.835464 | 12.167185 | 0.7 $\pm$ 0.3 | 130 $\pm$ 9
59 | 82.837013 | 12.071788 | 2.2 $\pm$ 0.8 | 77 $\pm$ 9
60 | 82.838844 | 12.283099 | 0.8 $\pm$ 0.3 | 127 $\pm$ 7
61 | 82.840187 | 12.096471 | 0.3 $\pm$ 0.1 | 102 $\pm$ 4
62 | 82.856598 | 12.245782 | 2.2 $\pm$ 0.1 | 179 $\pm$ 5
63 | 82.859009 | 12.292132 | 2.1 $\pm$ 0.2 | 148 $\pm$ 3
64 | 82.869324 | 12.046968 | 1.4 $\pm$ 0.4 | 140 $\pm$ 6
65 | 82.881615 | 12.048403 | 1.5 $\pm$ 0.6 | 44 $\pm$ 12
66 | 82.906693 | 12.028670 | 0.4 $\pm$ 0.2 | 158 $\pm$ 9
67 | 82.914528 | 12.183977 | 2.7 $\pm$ 0.8 | 138 $\pm$ 8
68 | 82.922920 | 12.217783 | 1.6 $\pm$ 0.5 | 150 $\pm$ 8
69 | 82.924316 | 12.098646 | 2.1 $\pm$ 0.5 | 110 $\pm$ 6
70 | 82.928040 | 12.241245 | 3.5 $\pm$ 1.5 | 164 $\pm$ 12
71 | 82.932304 | 12.028439 | 2.8 $\pm$ 0.8 | 89 $\pm$ 7
72 | 82.943199 | 12.228580 | 0.7 $\pm$ 0.2 | 175 $\pm$ 7
73 | 82.948074 | 12.319831 | 0.7 $\pm$ 0.3 | 154 $\pm$ 11
74 | 82.949745 | 12.182503 | 1.2 $\pm$ 0.4 | 70 $\pm$ 6
75 | 82.952950 | 12.171328 | 1.2 $\pm$ 0.5 | 157 $\pm$ 10
76 | 82.975975 | 12.368179 | 1.1 $\pm$ 0.2 | 18 $\pm$ 7
77 | 82.984650 | 12.411470 | 2.6 $\pm$ 0.2 | 7 $\pm$ 3
78 | 82.984703 | 12.239669 | 1.8 $\pm$ 0.4 | 171 $\pm$ 6
79 | 82.989380 | 12.106259 | 0.4 $\pm$ 0.1 | 0 $\pm$ 9
80 | 82.989792 | 12.209799 | 0.5 $\pm$ 0.1 | 53 $\pm$ 6
81 | 82.991608 | 12.101281 | 1.8 $\pm$ 0.6 | 167 $\pm$ 9
82 | 82.994530 | 12.370210 | 2.3 $\pm$ 0.5 | 159 $\pm$ 5
83 | 82.995323 | 12.180933 | 0.4 $\pm$ 0.1 | 169 $\pm$ 9
84 | 82.996674 | 12.244583 | 0.8 $\pm$ 0.3 | 171 $\pm$ 11
85 | 83.002495 | 12.126358 | 1.4 $\pm$ 0.4 | 158 $\pm$ 8
86 | 83.007202 | 12.057828 | 0.5 $\pm$ 0.1 | 2 $\pm$ 8
87 | 83.008606 | 12.207569 | 1.2 $\pm$ 0.6 | 105 $\pm$ 11
88 | 83.014168 | 12.470267 | 2.4 $\pm$ 0.4 | 27 $\pm$ 5
89 | 83.018013 | 12.199817 | 2.3 $\pm$ 0.8 | 132 $\pm$ 10
90 | 83.019943 | 12.425723 | 1.4 $\pm$ 0.2 | 159 $\pm$ 5
91 | 83.022797 | 12.404117 | 3.1 $\pm$ 1.3 | 157 $\pm$ 11
92 | 83.023544 | 12.399603 | 2.0 $\pm$ 0.6 | 152 $\pm$ 7
93 | 83.030342 | 12.153024 | 1.4 $\pm$ 0.5 | 108 $\pm$ 8
94 | 83.034149 | 12.339017 | 3.4 $\pm$ 0.3 | 15 $\pm$ 3
95 | 83.034348 | 12.091753 | 0.8 $\pm$ 0.2 | 166 $\pm$ 7
96 | 83.036903 | 12.111020 | 1.6 $\pm$ 0.4 | 166 $\pm$ 7
97 | 83.037979 | 12.323105 | 0.6 $\pm$ 0.1 | 174 $\pm$ 8
98 | 83.040497 | 12.442880 | 1.7 $\pm$ 0.2 | 16 $\pm$ 5
99 | 83.040894 | 12.451411 | 0.6 $\pm$ 0.1 | 12 $\pm$ 7
100 | 83.044777 | 12.450017 | 2.6 $\pm$ 0.4 | 40 $\pm$ 4

Table A.2. continued.  Star $\alpha$ (J2000) $\delta$ (J2000) P $\pm$
$\epsilon_{P}$ $\theta$ $\pm$ $\epsilon_{\theta}$ Id (∘) (∘) (%) (∘) 101
83.057884 12.316232 0.6 $\pm$ 0.2 128 $\pm$ 7 102 83.057983 12.409883 2.3
$\pm$ 0.3 47 $\pm$ 4 103 83.068832 12.094130 0.8 $\pm$ 0.3 171 $\pm$ 10 104
83.073029 12.106179 0.8 $\pm$ 0.3 161 $\pm$ 10 105 83.075089 12.124679 0.4
$\pm$ 0.2 157 $\pm$ 11 BRC 18 1 85.996071 9.090541 2.8 $\pm$ 0.2 172 $\pm$ 4 2
86.008682 9.260374 2.2 $\pm$ 0.3 95 $\pm$ 4 3 86.010780 9.102589 1.1 $\pm$ 0.4
174 $\pm$ 9 4 86.017776 9.253828 1.8 $\pm$ 0.3 179 $\pm$ 5 5 86.018143
9.157030 1.4 $\pm$ 0.3 1 $\pm$ 6 6 86.032570 9.136529 1.8 $\pm$ 0.3 179 $\pm$
5 7 86.036148 9.275244 1.7 $\pm$ 0.2 3 $\pm$ 5 8 86.037628 9.082024 1.3 $\pm$
0.4 8 $\pm$ 9 9 86.040085 9.070679 1.8 $\pm$ 0.5 2 $\pm$ 9 10 86.045395
9.290759 2.3 $\pm$ 0.4 4 $\pm$ 4 11 86.045616 9.269732 2.3 $\pm$ 0.6 172 $\pm$
7 12 86.045921 9.138239 1.3 $\pm$ 0.2 166 $\pm$ 5 13 86.046082 9.238827 2.2
$\pm$ 0.4 178 $\pm$ 5 14 86.054008 9.077346 1.8 $\pm$ 0.3 168 $\pm$ 5 15
86.056496 9.113747 1.9 $\pm$ 0.3 170 $\pm$ 5 16 86.058495 9.155698 1.2 $\pm$
0.2 175 $\pm$ 5 17 86.058922 9.060800 1.1 $\pm$ 0.3 170 $\pm$ 9 18 86.060120
9.321529 2.6 $\pm$ 0.4 174 $\pm$ 5 19 86.063675 9.083546 2.2 $\pm$ 0.6 1 $\pm$
8 20 86.065529 9.365006 0.3 $\pm$ 0.1 176 $\pm$ 8 21 86.069878 9.358155 1.9
$\pm$ 0.4 175 $\pm$ 5 22 86.072441 9.318766 1.8 $\pm$ 0.4 175 $\pm$ 7 23
86.074135 9.343622 2.0 $\pm$ 0.2 166 $\pm$ 4 24 86.075256 9.294579 1.1 $\pm$
0.5 173 $\pm$ 11 25 86.078064 9.356351 1.6 $\pm$ 0.3 166 $\pm$ 5 26 86.080666
9.089832 0.9 $\pm$ 0.4 150 $\pm$ 11 27 86.082092 9.220636 1.7 $\pm$ 0.1 179
$\pm$ 4 28 86.082748 9.072447 1.8 $\pm$ 0.5 1 $\pm$ 7 29 86.086159 9.306302
2.1 $\pm$ 0.3 162 $\pm$ 4 30 86.087486 9.308671 1.7 $\pm$ 0.5 162 $\pm$ 7 31
86.087769 9.349596 0.6 $\pm$ 0.2 169 $\pm$ 9 32 86.089050 9.308807 4.8 $\pm$
0.6 119 $\pm$ 3 33 86.094055 9.265513 1.9 $\pm$ 0.3 172 $\pm$ 4 34 86.094940
9.237477 1.8 $\pm$ 0.3 170 $\pm$ 5 35 86.103493 9.391103 1.3 $\pm$ 0.2 167
$\pm$ 6 36 86.103500 9.231409 2.2 $\pm$ 0.3 176 $\pm$ 5 37 86.105469 9.091146
2.3 $\pm$ 0.4 178 $\pm$ 4 38 86.112007 9.250659 1.7 $\pm$ 0.2 170 $\pm$ 5 39
86.118973 9.206998 1.7 $\pm$ 0.3 171 $\pm$ 6 40 86.120583 9.294956 1.7 $\pm$
0.2 175 $\pm$ 5 41 86.123268 9.218368 2.4 $\pm$ 0.3 169 $\pm$ 4 42 86.124565
9.041305 1.2 $\pm$ 0.4 3 $\pm$ 12 43 86.124680 9.213189 1.9 $\pm$ 0.5 163
$\pm$ 7 44 86.127502 9.218301 3.5 $\pm$ 0.2 1 $\pm$ 3 45 86.128441 9.314024
2.0 $\pm$ 0.3 170 $\pm$ 4 46 86.128914 8.990820 2.4 $\pm$ 0.4 1 $\pm$ 5 47
86.129539 9.006216 2.7 $\pm$ 0.3 175 $\pm$ 5 48 86.130562 9.378459 1.8 $\pm$
0.3 179 $\pm$ 5 49 86.130806 9.386317 1.9 $\pm$ 0.5 168 $\pm$ 8 50 86.132439
8.970585 1.8 $\pm$ 0.2 174 $\pm$ 4 Star $\alpha$ (J2000) $\delta$ (J2000) P
$\pm$ $\epsilon_{P}$ $\theta$ $\pm$ $\epsilon_{\theta}$ Id (∘) (∘) (%) (∘) 51
86.132782 9.398228 2.0 $\pm$ 0.2 176 $\pm$ 3 52 86.134117 9.344035 1.9 $\pm$
0.2 171 $\pm$ 5 53 86.134506 9.382899 0.7 $\pm$ 0.1 180 $\pm$ 6 54 86.136421
9.320812 2.0 $\pm$ 0.3 161 $\pm$ 4 55 86.136726 9.380013 1.2 $\pm$ 0.1 169
$\pm$ 4 56 86.137741 9.393141 1.8 $\pm$ 0.2 171 $\pm$ 4 57 86.141449 9.300094
2.0 $\pm$ 0.3 172 $\pm$ 5 58 86.147583 9.043317 1.9 $\pm$ 0.4 173 $\pm$ 6 59
86.156700 8.953581 2.7 $\pm$ 0.4 168 $\pm$ 4 60 86.157463 9.273091 2.7 $\pm$
0.1 176 $\pm$ 4 61 86.157883 9.270731 4.9 $\pm$ 2.2 156 $\pm$ 13 62 86.163757
9.006329 1.2 $\pm$ 0.4 165 $\pm$ 9 63 86.163773 9.327895 2.1 $\pm$ 0.5 159
$\pm$ 7 64 86.166702 8.995458 1.8 $\pm$ 0.2 1 $\pm$ 5 65 86.171822 9.409552
2.6 $\pm$ 0.6 173 $\pm$ 7 66 86.173531 9.021292 2.0 $\pm$ 0.5 171 $\pm$ 8 67
86.176399 9.426946 1.1 $\pm$ 0.2 13 $\pm$ 7 68 86.179832 8.990156 2.0 $\pm$
0.4 174 $\pm$ 6 69 86.181885 9.288206 3.4 $\pm$ 0.2 15 $\pm$ 2 70 86.183594
9.433202 2.3 $\pm$ 0.4 176 $\pm$ 5 71 86.184059 9.054083 2.8 $\pm$ 0.5 176
$\pm$ 5 72 86.184166 9.290176 2.1 $\pm$ 0.4 3 $\pm$ 5 73 86.184479 9.020583
1.7 $\pm$ 0.7 169 $\pm$ 12 74 86.184624 9.024846 1.8 $\pm$ 0.6 167 $\pm$ 10 75
86.186218 9.217989 1.0 $\pm$ 0.3 74 $\pm$ 7 76 86.189857 9.426837 2.0 $\pm$
0.2 175 $\pm$ 3 77 86.197639 8.984843 1.3 $\pm$ 0.4 153 $\pm$ 8 78 86.198196
9.247959 2.8 $\pm$ 0.3 3 $\pm$ 3 79 86.198570 9.345872 1.8 $\pm$ 0.2 165 $\pm$
5 80 86.198761 9.389240 2.3 $\pm$ 0.2 168 $\pm$ 4 81 86.201401 9.402506 2.1
$\pm$ 0.4 3 $\pm$ 5 82 86.201805 8.962544 1.5 $\pm$ 0.2 168 $\pm$ 5 83
86.201859 8.962573 1.8 $\pm$ 0.3 175 $\pm$ 5 84 86.204926 9.022941 0.9 $\pm$
0.2 147 $\pm$ 6 85 86.206192 9.020267 1.5 $\pm$ 0.2 164 $\pm$ 4 86 86.206825
9.378925 1.6 $\pm$ 0.3 174 $\pm$ 5 87 86.220009 9.338388 1.3 $\pm$ 0.2 12
$\pm$ 6 88 86.223259 8.902828 1.7 $\pm$ 0.3 179 $\pm$ 6 89 86.231506 9.266651
3.4 $\pm$ 0.7 171 $\pm$ 6 90 86.233208 8.912957 1.8 $\pm$ 0.2 170 $\pm$ 4 91
86.236847 9.377953 2.0 $\pm$ 0.3 165 $\pm$ 5 92 86.237694 8.960582 0.6 $\pm$
0.1 153 $\pm$ 6 93 86.239525 9.395449 2.2 $\pm$ 0.2 168 $\pm$ 3 94 86.241272
9.356718 0.7 $\pm$ 0.3 3 $\pm$ 12 95 86.242500 9.450074 2.8 $\pm$ 0.3 173
$\pm$ 3 96 86.242744 9.059106 4.5 $\pm$ 0.5 141 $\pm$ 3 97 86.242882 9.232504
2.3 $\pm$ 0.5 176 $\pm$ 6 98 86.243347 9.365779 1.8 $\pm$ 0.6 172 $\pm$ 10 99
86.245682 8.935081 1.4 $\pm$ 0.3 174 $\pm$ 6 100 86.246887 9.059897 3.1 $\pm$
0.2 140 $\pm$ 4 101 86.248924 8.915370 3.1 $\pm$ 0.5 173 $\pm$ 5 102 86.249535
9.167620 1.1 $\pm$ 0.4 171 $\pm$ 12 103 86.258911 9.155283 1.2 $\pm$ 0.2 172
$\pm$ 6 104 86.260796 9.063945 2.5 $\pm$ 0.1 136 $\pm$ 6 105 86.261047
9.430109 1.5 $\pm$ 0.3 170 $\pm$ 6 106 86.265808 9.169325 1.3 $\pm$ 0.4 137
$\pm$ 7

Table A.2. continued.  Star $\alpha$ (J2000) $\delta$ (J2000) P $\pm$
$\epsilon_{P}$ $\theta$ $\pm$ $\epsilon_{\theta}$ Id (∘) (∘) (%) (∘) 107
86.270256 9.068852 2.0 $\pm$ 0.4 135 $\pm$ 5 108 86.270340 9.258509 1.5 $\pm$
0.3 2 $\pm$ 6 109 86.273323 9.187541 1.5 $\pm$ 0.6 179 $\pm$ 12 110 86.275368
9.218266 1.1 $\pm$ 0.3 173 $\pm$ 8 111 86.277069 9.167779 1.1 $\pm$ 0.4 170
$\pm$ 11 112 86.278572 9.396746 1.7 $\pm$ 0.2 171 $\pm$ 5 113 86.286713
9.218583 1.6 $\pm$ 0.2 7 $\pm$ 5 114 86.287544 8.930645 1.3 $\pm$ 0.2 166
$\pm$ 4 115 86.293060 9.198799 1.7 $\pm$ 0.2 179 $\pm$ 5 116 86.295547
8.942298 1.0 $\pm$ 0.3 173 $\pm$ 9 117 86.296295 8.915566 1.3 $\pm$ 0.2 175
$\pm$ 5 118 86.301781 8.936301 1.3 $\pm$ 0.3 173 $\pm$ 7 119 86.302681
8.998691 1.9 $\pm$ 0.3 143 $\pm$ 4 120 86.307884 9.078981 1.5 $\pm$ 0.1 124
$\pm$ 5 121 86.310135 8.929467 1.2 $\pm$ 0.3 166 $\pm$ 6 122 86.312378
9.302844 1.9 $\pm$ 0.4 166 $\pm$ 5 123 86.312469 9.454061 2.1 $\pm$ 0.3 176
$\pm$ 4 124 86.313522 9.272567 1.4 $\pm$ 0.1 4 $\pm$ 6 125 86.323395 9.453463
1.3 $\pm$ 0.4 6 $\pm$ 9 126 86.328117 9.445957 1.1 $\pm$ 0.2 177 $\pm$ 7 127
86.329376 9.415783 1.4 $\pm$ 0.2 174 $\pm$ 5 128 86.332329 9.228611 0.9 $\pm$
0.1 177 $\pm$ 6 129 86.334602 9.283645 1.0 $\pm$ 0.2 172 $\pm$ 6 130 86.334671
9.083313 1.6 $\pm$ 0.4 173 $\pm$ 7 131 86.335464 9.038640 2.3 $\pm$ 0.4 133
$\pm$ 5 132 86.336929 9.465528 1.9 $\pm$ 0.3 176 $\pm$ 4 133 86.338112
9.311886 1.2 $\pm$ 0.1 173 $\pm$ 5 134 86.343285 9.242063 0.5 $\pm$ 0.1 38
$\pm$ 8 135 86.346771 9.030640 1.3 $\pm$ 0.4 165 $\pm$ 9 136 86.351921
9.396746 1.4 $\pm$ 0.3 169 $\pm$ 7 137 86.353699 9.426005 1.3 $\pm$ 0.2 165
$\pm$ 6 138 86.363251 9.257471 2.8 $\pm$ 0.9 16 $\pm$ 10 139 86.363678
9.417241 1.4 $\pm$ 0.6 170 $\pm$ 11 140 86.371529 9.181946 1.1 $\pm$ 0.4 158
$\pm$ 9 141 86.373787 8.945542 1.1 $\pm$ 0.5 150 $\pm$ 10 142 86.374512
9.408002 1.0 $\pm$ 0.3 159 $\pm$ 7 143 86.375862 8.947497 1.2 $\pm$ 0.5 166
$\pm$ 11 144 86.378395 9.299932 0.9 $\pm$ 0.1 169 $\pm$ 6 145 86.378502
9.133583 2.8 $\pm$ 0.5 168 $\pm$ 5 146 86.386871 9.399343 1.5 $\pm$ 0.3 176
$\pm$ 5 147 86.388138 9.417358 2.3 $\pm$ 0.4 160 $\pm$ 4 148 86.390251
8.931575 0.8 $\pm$ 0.3 176 $\pm$ 10 149 86.392273 9.261717 0.9 $\pm$ 0.1 17
$\pm$ 6 150 86.393578 9.217236 1.3 $\pm$ 0.2 0 $\pm$ 5 151 86.394753 9.177710
1.2 $\pm$ 0.3 14 $\pm$ 8 152 86.398598 9.418167 1.9 $\pm$ 0.4 164 $\pm$ 5 153
86.409279 8.944745 0.7 $\pm$ 0.2 158 $\pm$ 7 154 86.411713 9.411193 2.1 $\pm$
0.4 166 $\pm$ 6 155 86.414032 9.420681 2.0 $\pm$ 0.2 158 $\pm$ 4 Star $\alpha$
(J2000) $\delta$ (J2000) P $\pm$ $\epsilon_{P}$ $\theta$ $\pm$
$\epsilon_{\theta}$ Id (∘) (∘) (%) (∘) 156 86.415398 8.945398 1.4 $\pm$ 0.3
177 $\pm$ 5 157 86.422096 9.155535 1.1 $\pm$ 0.3 123 $\pm$ 5 158 86.425629
9.407340 1.1 $\pm$ 0.1 177 $\pm$ 5 159 86.425873 9.157034 1.9 $\pm$ 0.3 169
$\pm$ 5 160 86.426407 9.129604 0.8 $\pm$ 0.1 169 $\pm$ 5 161 86.427895
9.289151 3.2 $\pm$ 0.9 118 $\pm$ 8 162 86.429314 9.167664 1.0 $\pm$ 0.3 166
$\pm$ 9 163 86.435654 9.163746 0.7 $\pm$ 0.2 175 $\pm$ 9 164 86.444221
9.210876 1.4 $\pm$ 0.1 173 $\pm$ 6 165 86.445435 9.206098 1.1 $\pm$ 0.1 178
$\pm$ 5 166 86.447556 9.193343 0.7 $\pm$ 0.3 166 $\pm$ 9 167 86.448502
9.191902 1.2 $\pm$ 0.2 175 $\pm$ 7 168 86.450058 8.928351 1.1 $\pm$ 0.2 175
$\pm$ 5 169 86.450966 8.983732 1.7 $\pm$ 0.3 10 $\pm$ 6 170 86.451347 9.174396
1.2 $\pm$ 0.2 3 $\pm$ 7 171 86.458473 9.167095 1.4 $\pm$ 0.3 179 $\pm$ 6