20XX Vol. X No. XX, 000–000

11institutetext: Department of Physics, Assam University, Silchar 788011,
India<EMAIL_ADDRESS>and<EMAIL_ADDRESS>
22institutetext: Department of Physics, Gauhati University, Guwahati 781014,
India
33institutetext: Aryabhatta Research Institute of Observational Sciences
(ARIES), Nainital 263002, India
44institutetext: University of Kiel, Institute of Theoretical Physics and
Astrophysics, Leibnizstrasse 15, 24118, Kiel, Germany
Received 20XX Month Day; accepted 20XX Month Day

# The relative orientation between local magnetic field and Galactic plane in
low latitude dark clouds

Gulafsha B. Choudhury 11 Himadri S. Das 11 B. J. Medhi 22 J. C. Pandey 33 S.
Wolf 44 T. K. Dhar 11 A. M. Mazarbhuiya 11

###### Abstract

In this work, we study the magnetic field morphology of selected star-forming
clouds spread over the galactic latitude ($b$) range, $-10^{\circ}$ to
$10^{\circ}$. The polarimetric observation of clouds CB24, CB27 and CB188 are
conducted to study the magnetic field geometry of those clouds using the
104-cm Sampurnanand Telescope (ST) located at ARIES, Manora Peak, Nainital,
India. These observations are combined with those of 14 further low latitude
clouds available in the literature. Most of these clouds are located within a
distance range 140 to 500 pc except for CB3 ($\sim$2500 pc), CB34 ($\sim$1500
pc), CB39 ($\sim$1500 pc) and CB60 ($\sim$1500 pc). Analyzing the polarimetric
data of 17 clouds, we find that the alignment between the envelope magnetic
field ($\theta_{B}^{env}$) and Galactic plane ($\theta_{GP}$) of the low-
latitude clouds varies with their galactic longitudes ($l$). We observe a
strong correlation between the longitude (l) and the offset
($\theta_{off}=|\theta_{B}^{env}-\theta_{GP}|$) which shows that
$\theta_{B}^{env}$ is parallel to the Galactic plane (GP) when the clouds are
situated in the region, $115^{\circ}<l<250^{\circ}$. However,
$\theta_{B}^{env}$ has its own local deflection irrespective of the
orientation of $\theta_{GP}$ when the clouds are at $l<100^{\circ}$ and
$l>250^{\circ}$. To check the consistency of our results, the stellar
polarization data available at Heiles (2000) catalogue are overlaid on DSS
image of the clouds having mean polarization vector of field stars. The
results are almost consistent with the Heiles data. A systematic discussion is
presented in the paper. The effect of turbulence of the cloud is also studied
which may play an important role in causing the misalignment phenomenon
observed between $\theta_{B}^{env}$ and $\theta_{GP}$. We have used
Herschel111Herschel is an ESA space observatory with science instruments
provided by European-led Principal Investigator consortia and with important
participation from NASA. SPIRE 500 $\mu m$ and SCUBA 850 $\mu m$ dust
continuum emission maps in our work to understand the density structure of the
clouds.

###### keywords:

polarization – turbulence – ISM: clouds –- dust, extinction –- ISM: magnetic
fields.

##  1 Introduction

Magnetic fields are present everywhere in our galaxy, spreading the
interstellar medium and expanding beyond the Galactic disk. They are present
in a broad variety of astrophysical objects, such as, molecular clouds,
pulsars, supernova remnants (Lu et al. 2020). Various astronomers extensively
studied the large-scale galactic magnetic field (GMF), yet it remains
inadequately understood. The GMF plays an essential role in forming molecular
clouds that serve as the stellar nest in our galaxy. Galactic fields could be
sufficiently strong to inflict their direction upon individual molecular
clouds (Shetty & Ostriker 2006), that can modulate the accumulation and
fragmentation of the cloud (Li et al. 2011), thereby altering the efficiency
of star formation (Price & Bate 2008). The magnetic field in molecular clouds
plays a significant role in star formation efficiency (Hennebelle & Inutsuka
2019). Magnetic fields are also believed to have a considerable impact on the
circumstellar disc formation as well as on fragmentation in forming binary
systems (Price & Bate 2007). There are various other parameters responsible
for star formation processes that involves turbulence (Li et al. 2004; Tilley
& Pudritz 2004; Vázquez-Semadeni et al. 2005), jets and feedback from outflows
(Li & Nakamura 2006; Vázquez-Semadeni et al. 2019; Pudritz & Ray 2019),
radiation feedback from the stars themselves (Clark et al. 2005). There is
evidence of molecular clouds showing turbulent motions (Larson 1981; Mac Low &
Klessen 2004). The impact of turbulence on the magnetic field structure is
generally tough to interpret. However, some studies show that the magnetic
field may play a dominant role in shaping the dynamics of the turbulence
(Padoan & Nordlund 2002; Padoan et al. 2007, 2014). Thus, it is important to
study the magnetic field morphology to understand the ongoing activities in
molecular clouds.

When the background starlight passes through the aligned dust grains present
in the interstellar medium, it gets polarized and the polarization position
angle gives the orientation of local magnetic field. Draine & Weingartner
(1996) suggested that such alignment of the dust grains present in the
molecular clouds may be due to the effect of radiative torque. The radiative
torque mechanism is established on the interaction between radiation and grain
to spin it up. The confirmations on radiative torque alignment (RAT) was
established by Whittet et al. (2001) while studying the dense and diffuse gas
at the Taurus cloud. In recent years, diverse studies were made on grain
alignment by RAT mechanism, which reveals that RAT happens to be a successful
mechanism alignment that can explain the dust grain alignment of numerous
astrophysical environments (Hoang & Lazarian 2014; Hoang et al. 2015;
Andersson et al. 2015). Hoang & Lazarian (2014) found that the linear
polarization of nearby stars as predicted by the radiative alignment torque
agrees well with the observational data, which manifests that polarization
increases with the distance to the stars. Andersson et al. (2015) mentioned
that the theory of interstellar grain alignment by RAT allows deriving
specific, testable predictions for practical interstellar processes. Further
detailed analysis of the RAT mechanism might give a promising explanation of
grain alignment and polarimetry on the interstellar magnetic field and provide
advanced information on dust characteristics.

Several researchers studied the orientation of magnetic field through imaging
polarimetry (Chakraborty et al. 2014; Soam et al. 2015; Chakraborty & Das
2016; Das et al. 2016; Soam et al. 2017; Jorquera & Bertrang 2018; Choudhury
et al. 2019; Zielinski et al. 2021) and discussed the relative orientation of
magnetic field to the Galactic plane (GP), outflow direction and minor axis of
the cloud. The optical polarimetric analysis reveals that the envelope
magnetic field of CB130 is oriented at an angle of 53∘ with respect to the
orientation of GP (Chakraborty & Das 2016). Das et al. (2016) estimated the
magnetic field strength of two sub-mm cores of CB34 from the archival sub-
millimeter polarimetric data. They presented the relative orientation of the
envelope magnetic field with the minor axis of the cloud for both the cores,
which supports magnetically dominated star formation models. Analyzing both
optical and sub-mm polarimetric data of Bok globule CB17, Choudhury et al.
(2019) reported a parallel alignment between envelope magnetic field and the
position angle of GP in contrast to the core-scale magnetic field, which is
almost perpendicular to the GP. They also reported a relative orientation
envelope magnetic field to the outflow axis and the cloud minor axis.
Zielinski et al. (2021) discussed the magnetic field of a prototypical cloud B
335 and observed a decrease in polarization towards the center of the cloud
(dense core). They also observed a uniform pattern in the polarization
vectors.

In this article, we present the magnetic field morphology of 17 star forming
clouds (including newly observed clouds CB24, CB27 and CB188), spread over the
low galactic latitude range of $-10^{\circ}<b<10^{\circ}$. Most of these
clouds are located within a distance range 140 to 500 pc except for CB3 (2500
pc), CB34 (1500 pc), CB39 (1500 pc) and CB60 (1500 pc). We systematically
study the alignment mechanism between the envelope magnetic field of the cloud
and Galactic plane (GP) and their variation with galactic longitude. In §3, we
present the observation, data reduction procedures along with the details of
the archival data. In §4, we discuss the geometry of the envelope magnetic
field of the three observed clouds. We summarize our results in in §5.

Table 1: Observation log. Object ID | Name of | Date | Fields | RA(2000) | DEC(2000)
---|---|---|---|---|---
| Observatory |  |  | (h m s) | (∘ ′ ′′)
CB24 | ARIES, Nainital | Dec 23, 2017 | F1 | 04:58:30 | 52:12:17
|  |  | F2 | 04:58:23 | 52:16:31
|  |  | F3 | 04:59:03 | 52:17:02
|  |  | F4 | 04:59:00 | 52:10:49
CB27 | ARIES, Nainital | Dec 22, 2017 | F1 | 05:04:07 | 32:38:19
|  |  | F2 | 05:03:31 | 32:42:16
|  |  | F3 | 05:03:33 | 32:48:51
|  |  | F4 | 05:04:09 | 32:51:33
CB188 | ARIES, Nainital | May 8, 2019 | F1 | 19:20:25 | 11:33:10
|  |  | F2 | 19:20:29 | 11:40:33
|  |  | F3 | 19:19:59 | 11:32:06
|  |  | F4 | 19:20:06 | 11:39:56

##  2 Description of sources

###  2.1 CB24

CB24 is a starless, small spherical cloud at a distance of $293\pm 54$ pc (Das
et al. 2015). There was no association with an IRAS point source is
identified. Kane et al. (1994) found that CB24 is a considerably less dense
cloud, and the low column density may indicate that Bok globules as CB24 did
not undergo significant core contraction and represent an ideal sample of
starless small dark clouds.

###  2.2 CB27

CB27, also known as L1512, is an isolated Taurus core cloud near the GP. The
distance of CB27 is found to be 140 pc (Kenyon et al. 1994). A compact
submillimeter source (FWHM $\sim$ 104 AU) is found to be present at the center
of CB27 (Di Francesco et al. 2008; Kirk et al. 2005). The central density of
the cloud is near to the maximum stable density, which is required for a
pressure-supported, self gravitating cloud, and this makes the cloud
indistinguishable whether the core is a starless stable or a prestellar one
(Launhardt et al. 2013).

###  2.3 CB188

CB188 is an isolated small cloud at a distance $262\pm 49$ pc (Das et al.
2015). The bolometric luminosity of this cloud is 2.6 $L_{\odot}$ and the
envelope mass is of about 0.7 $M_{\odot}$ obtained from an interferometric
study of the $N_{2}H^{+}$ (1–0) emission (Chen et al. 2007). The mean density
of the core is $\sim 2\times 10^{6}$ $cm^{-3}$. CB188 is found to be
physically associated with L 673 (Tsitali et al. 2010), as shown by the dotted
rectangle in the lower region of Figure 3. In our study, we only covered the
northern region of the cloud CB188.

##  3 OBSERVATION, DATA REDUCTION and ARCHIVAL DATA

###  3.1 Observations

We conducted the optical polarimetric observations of four fields towards the
Bok Globules CB27, CB24 and CB188 each on December 22, 2017, December 23, 2017
and May 8, 2019, respectively. We have selected these three globules because
of their close proximity with the GP ($-10^{\circ}<b<10^{\circ}$) as we aim to
study the magnetic field morphology of low latitude clouds. Also, no
polarimetric study of these clouds was performed in the past. Moreover, the
availability of dust continuum emission maps of CB27 (Herschel SPIRE 500 $\mu
m$) and CB188 (and SCUBA 850 $\mu m$) also motivated us to select these
globules. Polarimetric observations were conducted in the R-band (filter:
$\lambda$ = 630 nm, $\Delta\lambda$ = 120 nm). The observed region around each
globule is divided into four fields of 8${}^{\prime}\times$8′ dimension
because the CCD has a diameter field of view of $\sim$ 8′. The observations
were carried out with the 104 cm Sampurnanand Telescope (ST) at Aryabhatta
Research Institute of observational sciencES, Nainital, India (for exemplary
previous polarimetric observations using this telescope see Chakraborty et al.
2014; Das et al. 2016; Chakraborty & Das 2016). The observation log is
presented in Table 1. The 104 cm ST is an f/13 Cassegrain telescope. An
Imaging Polarimeter (AIMPOL) is connected to the back-end of the telescope
that has a Wollaston prism and a rotating half-wave plate (HWP). The Wollaston
prism splits the incoming unpolarized light into two orthogonal components
(ordinary and extraordinary), and the HWP rotates the polarization state of
light into four angles $0^{\circ}$, $22.5^{\circ}$, $45^{\circ}$ and
$67.5^{\circ}$ which gives the four polarized components (see Das et al. 2013,
for detailed observational procedures). The detailed theory and design of
AIMPOL are presented in Rautela et al. (2004) and Medhi et al. (2008).

Table 2: Standard star polarimetry: Object ID, date of observation, observed values of $p$ and $\theta$, literature values of $p$ and $\theta$, reference. |  | Observed values |  | Literature values |
---|---|---|---|---|---
Object ID | Date of observation |  $p$ $\pm$ $e_{p}$ |  $\theta$ $\pm$ $e_{\theta}$ |  |  $p$ $\pm$ $e_{p}$ | $\theta\pm e_{\theta}$ | Literature reference
|  |  ($\%$) |  (∘) |  |  ($\%$) |  (∘) |
|  | High polarized standard stars |  |
HD 251204 | December 23, 2017 |  4.84$\pm$0.17 |  154.3$\pm$1.0 |  |  4.79$\pm$0.30 | 155.7 | Serkowski (1974)
HD 19820 | December 23, 2017 |  4.83$\pm$0.18 |  115.4$\pm$1.0 |  |  4.53$\pm$0.03 |  114.5$\pm$0.2 | Schmidt et al. (1992)
HD 154445 | May 8, 2019 |  3.48$\pm$0.09 |  89.7$\pm$0.7 |  |  3.78$\pm$0.06 |  88.8$\pm$0.5 | Schmidt et al. (1992)
HD 161056 | May 8, 2019 |  3.85$\pm$0.10 |  69.5$\pm$0.7 |  |  4.03$\pm$0.03 |  66.9$\pm$0.2 | Schmidt et al. (1992)
|  | Unpolarized standard stars |  |
HD 21447 | December 23, 2017 |  0.11$\pm$0.18 | 111.7 |  |  0.06$\pm$0.03 | 110 | Breeveld & Puchnarewicz (1998)
$\gamma$Boo | May 8, 2019 |  0.19$\pm$0.12 | 23.1 |  |  0.065$\pm$0.02 | 21.3 | Schmidt et al. (1992)
$\beta$UMa | May 8, 2019 |  0.10$\pm$0.14 | 109.2 |  |  0.009$\pm$0.02 | 107.8 | Schmidt et al. (1992)
Table 3: Details of target globules (our observation along with archival
references of polarimetric studies). Cloud ID, Right ascension (RA),
Declination (DEC), Galactic longitude ($l$), Galactic latitude ($b$), Name of
observatory, Date of observation, Reference and distance to the cloud (d).

ID | RA(2000) | DEC(2000) | $l$ | $b$ | Name of | Date of | Reference | Distance (ref)
---|---|---|---|---|---|---|---|---
| (h m s) |  (∘ ′ ′′) |  (∘) |  (∘) | observatory | observation |  | (pc)
CB24 | 04 58 30 |  $+$52 15 41 | 155.76 | 5.90 |  ∗ST | Dec 23, 2017 |  |  293$\pm$54 (1)
CB27 | 05 04 09 |  $+$32 43 12 | 171.82 |  $-$5.18 | ST | Dec 22, 2017 | Our observations | 140 (2)
CB188 | 19 20 17 |  $+$11 36 12 | 46.53 |  $-$1.01 | ST | May 8, 2019 |  |  262$\pm$49 (1)
|  |  |  |  |  | Archival Data |  |
CB3 | 00 28 45 |  $+$56 42 08 | 119.80 |  $-$6.03 |  ∗∗MA | Dec 23, 1997 | Sen et al. (2000) | 2500 (3)
CB4 | 00 39 03 |  $+$52 51 29 | 121.03 |  $-$9.96 |  †MB | Dec 1986 | Kane et al. (1995) |  350$\pm$150 (4)
CB17 | 04 04 37 |  $+$56 56 41 | 147.02 | 3.39 | ST | March 9, 2016 | Choudhury et al. (2019) |  253$\pm$43 (5)
CB25 | 04 59 04 |  $+$52 03 24 | 155.97 | 5.84 | MA | Dec 23, 1997 | Sen et al. (2000) | –
CB26 | 05 00 09 |  $+$52 05 00 | 156.05 | 5.99 | ST | Dec 29 & 30, | Halder et al. (2022) |  140$\pm$20 (6)
|  |  |  |  |  | 2016 |  |
CB34 | 05 47 02 |  $+$21 00 10 | 186.94 |  $-$3.83 | ST | March 12–13, | Das et al. (2016) | 1500 (3)
|  |  |  |  |  | 2013 |  |
|  |  |  |  |  | Feb 20, 2015 |  |
CB39 | 06 01 58 |  $+$16 30 26 | 192.63 |  $-$3.04 | MA | Dec 25, 1997 | Sen et al. (2000) | 1500 (3)
CB56 | 07 14 36 |  $-$25 08 54 | 237.90 |  $-$6.45 | IGO | March 4, 2011 | Chakraborty et al. (2014) | –
CB60 | 08 04 36 |  $-$31 30 47 | 248.89 |  $-$0.01 |  ‡IGO | March 5, 2011 | Chakraborty et al. (2014) | 1500 (3)
CB69 | 17 02 42 |  $-33$ 17 00 | 351.23 | 5.14 | IGO | March 5, 2011 | Chakraborty et al. (2014) | 500 (3)
CB130 | 18 16 16 |  $-$02 33 01 | 26.61 | 6.65 | IGO | April 26, 28 | Chakraborty & Das (2016) |  250$\pm$50 (3)
|  |  |  |  |  | & 30, 2014 |  |
|  |  |  |  |  | May 2-4, 2014 |  |
CB246 | 23 56 44 |  $+$58 34 29 | 115.84 |  $-$3.54 | MA | Dec 24, 1997 | Sen et al. (2000) | 140 (3)
L1014 | 21 24 07 |  $+$49 59 05 | 92.45 |  $-$0.12 | ST | Nov 14, 2010 | Soam et al. (2015) |  258$\pm$50 (7)
|  |  |  |  |  | Nov 22, 2011 |  |
L1415 | 04 42 00 |  $+$54 26 00 | 152.41 | 5.27 | ST | Nov 23, 2011 | Soam et al. (2017) | 250 (8)
|  |  |  |  |  | Dec 19, 20 |  |
|  |  |  |  |  | & 24, 2011 |  |
|  |  |  |  |  | Oct 29, 2013 |  |

∗ST: Sampurnanand Telescope, ARIES, Nainital

∗∗MA: Mount Abu, India

†MB: Mount Bigelow, North of Tucson, Arizona

‡IGO: IUCAA Girawali Observatory, Pune

Distance References: (1) Das et al. (2015). (2) Kenyon et al. (1994). (3)
Launhardt & Henning (1997). (4) Perrot & Grenier (2003). (5) Choudhury et al.
(2019). (6) Launhardt et al. (2010). (7) Soam et al. (2015). (8) Soam et al.
(2017)

###  3.2 Data reduction: Imaging polarimetry

We conducted the observation using the four rotations of HWP as mentioned in
§3.1. For a particular rotation of HWP ($\alpha$), the intensities
(extraordinary, $I_{e}$ and ordinary, $I_{o}$) of the two orthogonal polarized
components are determined. If the HWP is rotated by $\alpha$, the electric
vector rotates by 2$\alpha$. For calculation of the linear polarization it is
useful to define the ratio $R_{\alpha}$

$R_{\alpha}=\frac{(I_{e}/I_{o})-1}{(I_{e}/I_{o})+1}=p~{}cos(2\theta-4\alpha)$
(1)

where, $\theta$ and $p$ are the position angle and degree of linear
polarization, respectively (Rautela et al. 2004). This ratio becomes $Q/I$ and
$U/I$ when $\alpha=0^{\circ}$ and $22.5^{\circ}$ respectively, i.e. the values
of normalised Stokes parameters $q$ and $u$ ($I$: total intensity). The linear
polarisation ($p$) and the polarization position angle ($\theta$) are given by

$p=\sqrt{q^{2}+u^{2}}\hskip 28.45274pt\text{and}\hskip
28.45274pt\theta=\frac{1}{2}tan^{-1}\bigg{(}\frac{u}{q}\bigg{)}$ (2)

In principle, the linear polarization and the position angle of polarization
can be measured from the first two rotations of HWP. However, the additional
two rotations $45^{\circ}$ and $67.5^{\circ}$ are observed due to non-
responsivity of the system.

The observed polarimetric data have been reduced using the IRAF (Image
Reduction and Analysis facility) package, (see Rautela et al. 2004, for
detailed data reduction procedures). The uncertainties associated with $p$ and
$\theta$ are calculated using the relations (Ramaprakash et al. 1998)

$e_{p}=\frac{\sqrt{N+N_{b}}}{N}~{}~{}~{}~{}~{}and~{}~{}~{}~{}~{}e_{\theta}=28.65^{\circ}\times\frac{e_{p}}{p}$
(3)

where $N$ and $N_{b}$ represent the flux counts corresponding to the source
and background, respectively.

Figure 1: Polarization map of CB24: White solid lines represent the
polarization vectors of the background field stars plotted on a DSS image of
the globule CB24 (25${}^{\prime}\times 25^{\prime}$). At the bottom right
corner, a vector of 1$\%$ polarization is shown for reference. The vector at
the top left corner shows the orientation of the GP
($\theta_{GP}=142^{\circ}$). The center of the globule is shown by the cross
mark. The dashed rectangular boxes of dimension 8${}^{\prime}\times
8^{\prime}$ show the fields of observation (details are given in Table 1) of
the cloud.

####  3.2.1 Instrumental Calibration

The instrumental calibration is determined by analyzing three low polarized
standard stars HD 21447, $\gamma$Boo, and $\beta$UMa taken from Breeveld &
Puchnarewicz (1998) and Schmidt et al. (1992) which are in sound agreement
with the literature. The instrumental calibration for zero position angle of
polarization is determined by analyzing four high polarized standard stars HD
251204, HD 19820, HD 154445, and HD 161056 taken from Serkowski (1974) and
Schmidt et al. (1992). The results obtained from our observations are
presented in Table 2.

###  3.3 Archival Data

Our observed clouds are situated at low galactic latitude close to GP, which
allows us to map the magnetic field morphology of the star forming clouds near
the GP. We collected additional 14 low galactic latitude star forming clouds
for which polarimetric observations at optical wavelength are available in
literature allowing us to perform a systematic statistical significant
analysis. These include 12 Bok globules (viz. CB3, CB4, CB17, CB25, CB26,
CB34, CB39, CB56, CB60, CB69, CB130 and CB246) and two Lynd’s clouds (viz.
L1014 and L1415). All these clouds are located in the galactic latitude ($b$)
ranging from $-10^{\circ}<b<10^{\circ}$. Optical polarimetric observation of
CB26 was performed by our group (Halder et al. 2022, in prep.). The details of
the 17 clouds are compiled in Table 3.

##  4 Geometry of envelope magnetic field

We reduce the optical polarimetric data of CB24, CB27 and CB188 using IRAF (as
discussed in §3.2). The values of $\theta$ and $p$ of the background stars
detected towards the field of the three clouds are calculated using equation
2. We consider only those sources with $p/e_{p}\geq$ 3 (here $e_{p}$ denotes
the polarization error). To avoid the foreground polarization, we make use of
Gaia EDR3 parallaxes (Gaia Collaboration et al. 2016, 2021) to determine the
distance of the individual field stars towards each cloud. The critical
distance is set to be the distance of the respective cloud ($293\pm 54$ pc for
CB24, 140 pc for CB27 and $262\pm 49$ pc for CB188, respectively). For further
analysis, we consider only sources with distances beyond the critical
distance. In the case of CB24, polarization measurements of 20 fields stars
are found, out of which three sources (#7, #12 and #14) have been identified
to be foreground to the cloud. Moreover, Gaia parallaxes for two sources (#11
and #13) are not available, so we discarded these five sources from further
analysis. In the case of CB27, polarization measurements of 27 field stars are
found, 26 of which have been identified to be background to the cloud while
one source (#16) does not have Gaia parallax available and hence we discard
this star from the analysis as well. However, in the case of CB188,
polarization measurements of 24 field stars are found and all these 24 sources
have been identified to be background to the cloud.

Fifteen field stars are detected towards CB24, twenty six field stars towards
CB27 and twenty four field stars are detected in the field of CB188,
respectively. The values of $p$ and $\theta$ with the uncertainties of the
field stars towards these three clouds are presented in Table 4, Table 5, and
Table 6, respectively. The mean value of degree of polarization ($<p>$) along
with the standard error222$S.E=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the
sample standard deviation and $n$ is the number of samples. are estimated to
be $(2.67\pm 0.27)\%$ for CB24; $(2.10\pm 0.19)\%$ for CB27 and $(3.11\pm
0.28)\%$ for CB188, respectively. The mean orientation of polarization
position angle ($<\theta>$) with the standard error are estimated to be
$(142.8\pm 5.7)^{\circ}$ for CB24; $(145.5\pm 3.7)^{\circ}$ for CB27; and
$(98.5\pm 2.3)^{\circ}$ for CB188, respectively.

Figure 2: Polarization map of CB27: White solid lines represent the polarization vectors of the background field stars plotted on a DSS image of the globule CB27 (25${}^{\prime}\times 25^{\prime}$). At the bottom right corner, a vector of 1$\%$ polarization is shown for reference. The vector at the top left corner shows the orientation of the GP ($\theta_{GP}=142.5^{\circ}$). The cross mark shows the center of the globule. The dashed rectangular boxes of dimension 8${}^{\prime}\times 8^{\prime}$ show the fields of observation (details are given in Table 1) of the cloud. Also, the contours extracted from Herschel SPIRE $500\mu m$ dust continuum emission map in the range of 18 to 74 mJy beam-1 with an increasing step size of 8 mJy beam-1 are plotted (magenta) over the polarization map. Table 4: Polarimetric results of 20 field stars towards CB24. The Right Ascension (RA) and Declination (DEC) of the field stars are given in Column–2 and Column–3, column-4 and 5 represent the degree of linear polarization ($p$) and position angle of polarization ($\theta$), column-6 gives the distance (d in pc) to the individual field stars collected from Gaia EDR3 database. The star having distance more than the distance of the cloud CB24 ($\sim$ 360 pc) is considered to be background to the cloud and is shown in column-7. Star ID | RA(2000) | Dec(2000) |  $p$ $\pm$ $e_{p}$ |  $\theta$ $\pm$ $e_{\theta}$ |  $d$ $\pm$ $e_{d}$ | Background star
---|---|---|---|---|---|---
| (h m s) | (∘ ′ ′′) | ($\%$) | (∘) | (pc) | (yes/no)
1 | 4 59 17.76 | 52 08 31 | 3.85 $\pm$ 0.46 | 146.8 $\pm$ 3.4 | 1739 $\pm$ 70 | yes
2 | 4 59 12.72 | 52 07 33 | 1.99 $\pm$ 0.29 | 86.0 $\pm$ 4.2 | 726 $\pm$ 8 | yes
3 | 4 59 11.28 | 52 08 09 | 1.66 $\pm$ 0.49 | 98.3 $\pm$ 8.4 | 700 $\pm$ 10 | yes
4 | 4 59 11.04 | 52 17 34 | 1.52 $\pm$ 0.39 | 158.5 $\pm$ 7.3 | 643 $\pm$ 7 | yes
5 | 4 59 06.24 | 52 18 21 | 2.31 $\pm$ 0.40 | 161.5 $\pm$ 4.9 | 361 $\pm$ 2 | yes
6 | 4 59 03.36 | 52 08 09 | 2.38 $\pm$ 0.54 | 143.4 $\pm$ 6.5 | 3702 $\pm$ 307 | yes
7 | 4 58 59.76 | 52 19 15 | 1.91 $\pm$ 0.20 | 159.9 $\pm$ 3.0 | 297 $\pm$ 2 | no
8 | 4 58 48.72 | 52 20 20 | 1.39 $\pm$ 0.39 | 145.8 $\pm$ 8.0 | 817 $\pm$ 38 | yes
9 | 4 58 47.28 | 52 12 43 | 2.24 $\pm$ 0.74 | 137.5 $\pm$ 9.5 | 2330 $\pm$ 164 | yes
10 | 4 58 34.80 | 52 19 33 | 2.00 $\pm$ 0.35 | 159.5 $\pm$ 5.0 | 501 $\pm$ 14 | yes
11 | 4 58 32.16 | 52 18 18 | 3.54 $\pm$ 0.62 | 150.0 $\pm$ 5.0 |  NA | $-$
12 | 4 58 27.60 | 52 17 13 | 2.03 $\pm$ 0.25 | 169.1 $\pm$ 3.6 | 324 $\pm$ 1 | no
13 | 4 58 23.28 | 52 09 39 | 1.22 $\pm$ 0.21 | 125.4 $\pm$ 4.8 |  NA | $-$
14 | 4 58 22.80 | 52 16 37 | 1.76 $\pm$ 0.47 | 162.1 $\pm$ 7.6 | 334 $\pm$ 2 | no
15 | 4 58 21.12 | 52 17 34 | 3.85 $\pm$ 0.66 | 147.1 $\pm$ 4.9 | 3891 $\pm$ 269 | yes
16 | 4 58 18.24 | 52 17 45 | 1.58 $\pm$ 0.29 | 153.6 $\pm$ 5.3 | 617 $\pm$ 6 | yes
17 | 4 58 12.00 | 52 11 24 | 3.24 $\pm$ 0.35 | 165.0 $\pm$ 3.1 | 510 $\pm$ 4 | yes
18 | 4 58 10.32 | 52 16 15 | 4.01 $\pm$ 0.35 | 143.5 $\pm$ 2.5 | 3165 $\pm$ 226 | yes
19 | 4 58 09.36 | 52 18 43 | 3.89 $\pm$ 1.14 | 145.8 $\pm$ 8.4 | 3942 $\pm$ 486 | yes
20 | 4 58 06.48 | 52 18 36 | 4.13 $\pm$ 0.84 | 149.7 $\pm$ 5.8 | 4498 $\pm$ 1354 | yes
Figure 3: (a) Polarization map of CB188: White solid lines represent the polarization vectors of the background field stars plotted on a DSS image of the globule CB188 (25${}^{\prime}\times 25^{\prime}$). At the bottom right corner, a vector of 1$\%$ polarization is shown for reference. The vector at the top right corner shows the orientation of the GP ($\theta_{GP}=28^{\circ}$). The cross mark shows the center of the globule. The dashed rectangular boxes of dimension 8${}^{\prime}\times 8^{\prime}$ show the fields of observation (details are given in Table 1) of the cloud. Also, the contours extracted from SCUBA $850\mu m$ dust continuum emission map in the range of 112 to 336 mJy beam-1 with an increasing step size of 54 mJy beam-1 are plotted (magenta) over the polarization map. The dotted rectangle on the lower region represents the Lynd’s cloud L673, which is physically associated with the field of CB188 (see §2 for details). (b) The zoomed-in view of the central region for better visual of the contours extracted from SCUBA $850\mu m$ dust continuum emission map are plotted over a 5${}^{\prime}\times 5^{\prime}$ DSS image of the Globule CB188. Table 5: Polarimetric results of 27 field stars in CB27. The Right Ascension (RA) and Declination (DEC) of the field stars are given in Column–2 and Column–3, column-4 and 5 represent $p$ and $\theta$ and column-6 gives the distance (d in pc) to the individual field stars collected from Gaia EDR3 database. The star having distance more than the distance of the cloud CB24 ($\sim$ 140 pc) is considered to be background to the cloud and is shown in column-7. Star ID | RA(2000) | Dec(2000) |  $p$ $\pm$ $e_{p}$ |  $\theta$ $\pm$ $e_{\theta}$ |  $d$ $\pm$ $e_{d}$ | Background star
---|---|---|---|---|---|---
| (h m s) | (∘ ′ ′′) | ($\%$) | (∘) | (pc) | (yes/no)
1 | 05 04 24.72 | 32 54 10 | 0.64 $\pm$ 0.19 | 139.8 $\pm$ 8.6 | 1255 $\pm$ 38 | yes
2 | 05 04 24.48 | 32 51 46 | 1.58 $\pm$ 0.22 | 103.0 $\pm$ 4.0 | 316 $\pm$ 5 | yes
3 | 05 04 18.48 | 32 52 44 | 1.20 $\pm$ 0.34 | 159.5 $\pm$ 8.1 | 937 $\pm$ 15 | yes
4 | 05 04 16.32 | 32 40 04 | 0.93 $\pm$ 0.21 | 147.0 $\pm$ 6.4 | 2829 $\pm$ 168 | yes
5 | 05 04 16.08 | 32 38 31 | 1.20 $\pm$ 0.31 | 83.1 $\pm$ 7.3 | 2266 $\pm$ 406 | yes
6 | 05 04 14.40 | 32 38 16 | 1.14 $\pm$ 0.25 | 159.5 $\pm$ 6.4 | 1337 $\pm$ 30 | yes
7 | 05 04 11.28 | 32 35 34 | 0.89 $\pm$ 0.21 | 150.0 $\pm$ 6.9 | 1409 $\pm$ 35 | yes
8 | 05 04 07.92 | 32 49 37 | 2.96 $\pm$ 0.57 | 165.1 $\pm$ 5.5 | 2286 $\pm$ 184 | yes
9 | 05 03 58.32 | 32 41 16 | 1.51 $\pm$ 0.28 | 123.9 $\pm$ 5.4 | 1293 $\pm$ 28 | yes
10 | 05 03 53.76 | 32 54 14 | 2.18 $\pm$ 0.22 | 146.7 $\pm$ 2.9 | 1364 $\pm$ 32 | yes
11 | 05 03 50.64 | 32 50 42 | 1.76 $\pm$ 0.47 | 158.4 $\pm$ 7.6 | 363 $\pm$ 2 | yes
12 | 05 03 48.24 | 32 51 14 | 5.20 $\pm$ 1.10 | 149.9 $\pm$ 6.0 | 1829 $\pm$ 117 | yes
13 | 05 03 47.04 | 32 40 22 | 3.18 $\pm$ 0.35 | 135.4 $\pm$ 3.1 | 766 $\pm$ 18 | yes
14 | 05 03 42.24 | 32 47 02 | 2.43 $\pm$ 0.30 | 158.5 $\pm$ 3.5 | 1526 $\pm$ 63 | yes
15 | 05 03 42.00 | 32 46 01 | 1.56 $\pm$ 0.28 | 159.3 $\pm$ 5.1 | 424 $\pm$ 3 | yes
16 | 05 03 39.84 | 32 48 10 | 2.76 $\pm$ 0.68 | 142.0 $\pm$ 7.0 |  NA | –
17 | 05 03 39.60 | 32 45 46 | 1.59 $\pm$ 0.29 | 157.2 $\pm$ 5.2 | 1077 $\pm$ 19 | yes
18 | 05 03 38.88 | 32 50 06 | 2.83 $\pm$ 0.49 | 148.8 $\pm$ 4.9 | 2826 $\pm$ 166 | yes
19 | 05 03 34.32 | 32 38 27 | 2.61 $\pm$ 0.37 | 129.8 $\pm$ 4.1 | 5155 $\pm$ 492 | yes
20 | 05 03 30.48 | 32 51 46 | 2.45 $\pm$ 0.58 | 157.4 $\pm$ 6.8 | 655 $\pm$ 9 | yes
21 | 05 03 28.56 | 32 49 33 | 2.84 $\pm$ 0.72 | 147.5 $\pm$ 7.2 | 5176 $\pm$ 721 | yes
22 | 05 03 24.00 | 32 50 45 | 2.97 $\pm$ 0.75 | 150.8 $\pm$ 7.3 | 5288 $\pm$ 590 | yes
23 | 05 03 23.52 | 32 48 54 | 2.82 $\pm$ 0.34 | 150.7 $\pm$ 3.4 | 1860 $\pm$ 93 | yes
24 | 05 03 22.32 | 32 52 04 | 2.72 $\pm$ 0.35 | 148.3 $\pm$ 3.7 | 644 $\pm$ 10 | yes
25 | 05 03 21.12 | 32 48 39 | 2.10 $\pm$ 0.27 | 153.1 $\pm$ 3.7 | 710 $\pm$ 13 | yes
26 | 05 03 17.04 | 32 43 08 | 1.33 $\pm$ 0.24 | 135.6 $\pm$ 5.1 | 1586 $\pm$ 69 | yes
27 | 05 03 16.32 | 32 45 43 | 1.92 $\pm$ 0.21 | 165.4 $\pm$ 3.1 | 711 $\pm$ 9 | yes
Table 6: Plarimetric results of 24 field stars in CB188. The Right Ascension (RA) and Declination (DEC) of the field stars are given in Column–2 and Column–3, column-4 and 5 represent $p$ and $\theta$ and column-6 gives the distance (d in pc) to the individual field stars collected from Gaia EDR3 database. The star having distance more than the distance of the cloud CB24 ($\sim$ 300 pc) is considered to be background to the cloud and is shown in column-7. Star ID | RA(2000) | Dec(2000) |  $p$ $\pm$ $e_{p}$ |  $\theta$ $\pm$ $e_{\theta}$ |  $d$ $\pm$ $e_{d}$ | Background star
---|---|---|---|---|---|---
| (h m s) | (∘ ′ ′′) | ($\%$) | (∘) | (pc) | (yes/no)
1 | 19 20 43.57 | 11 39 34 | 3.30 $\pm$ 1.02 | 100.0 $\pm$ 8.9 | 2919 $\pm$ 167 | yes
2 | 19 20 40.52 | 11 41 50 | 4.53 $\pm$ 1.16 | 96.3 $\pm$ 7.4 | 2520 $\pm$ 164 | yes
3 | 19 20 40.15 | 11 41 47 | 4.30 $\pm$ 1.18 | 96.9 $\pm$ 7.9 | 2229 $\pm$ 136 | yes
4 | 19 20 38.12 | 11 42 59 | 3.04 $\pm$ 1.01 | 126.6 $\pm$ 9.5 | 666 $\pm$ 8 | yes
5 | 19 20 34.64 | 11 41 31 | 2.40 $\pm$ 0.39 | 86.1 $\pm$ 4.6 | 1166 $\pm$ 17 | yes
6 | 19 20 31.70 | 11 41 07 | 3.81 $\pm$ 1.22 | 105.5 $\pm$ 9.2 | 2704 $\pm$ 184 | yes
7 | 19 20 30.77 | 11 38 37 | 3.42 $\pm$ 0.68 | 90.4 $\pm$ 5.7 | 2498 $\pm$ 166 | yes
8 | 19 20 30.43 | 11 40 10 | 4.13 $\pm$ 1.29 | 89.6 $\pm$ 8.9 | 1448 $\pm$ 46 | yes
9 | 19 20 28.00 | 11 43 59 | 2.82 $\pm$ 0.40 | 93.3 $\pm$ 4.1 | 1016 $\pm$ 18 | yes
10 | 19 20 24.52 | 11 43 45 | 5.14 $\pm$ 1.45 | 97.8 $\pm$ 8.1 | 1462 $\pm$ 50 | yes
11 | 19 20 23.11 | 11 38 35 | 1.54 $\pm$ 0.51 | 93.9 $\pm$ 9.5 | 394 $\pm$ 3 | yes
12 | 19 20 22.20 | 11 42 48 | 4.29 $\pm$ 1.21 | 88.8 $\pm$ 8.1 | 1453 $\pm$ 56 | yes
13 | 19 20 21.95 | 11 34 15 | 1.69 $\pm$ 0.47 | 119.5 $\pm$ 7.9 | 2661 $\pm$ 214 | yes
14 | 19 20 16.00 | 11 41 30 | 5.82 $\pm$ 0.37 | 96.8 $\pm$ 1.8 | 2938 $\pm$ 298 | yes
15 | 19 20 15.34 | 11 40 53 | 1.68 $\pm$ 0.53 | 92.5 $\pm$ 9.0 | 857 $\pm$ 11 | yes
16 | 19 20 12.79 | 11 39 01 | 2.94 $\pm$ 0.98 | 99.4 $\pm$ 9.5 | 929 $\pm$ 33 | yes
17 | 19 20 10.97 | 11 42 05 | 1.83 $\pm$ 0.61 | 90.4 $\pm$ 9.6 | 903 $\pm$ 15 | yes
18 | 19 20 07.00 | 11 36 13 | 2.81 $\pm$ 0.93 | 116.4 $\pm$ 9.5 | 717 $\pm$ 18 | yes
19 | 19 20 05.72 | 11 31 45 | 1.24 $\pm$ 0.41 | 95.3 $\pm$ 9.5 | 869 $\pm$ 13 | yes
20 | 19 20 02.06 | 11 36 11 | 1.89 $\pm$ 0.32 | 82.0 $\pm$ 4.9 | 1072 $\pm$ 22 | yes
21 | 19 20 01.69 | 11 42 57 | 1.58 $\pm$ 0.52 | 88.3 $\pm$ 9.4 | 838 $\pm$ 12 | yes
22 | 19 19 59.76 | 11 31 36 | 1.65 $\pm$ 0.55 | 97.1 $\pm$ 9.5 | 838 $\pm$ 11 | yes
23 | 19 19 59.64 | 11 39 52 | 4.80 $\pm$ 1.51 | 112.7 $\pm$ 9.0 | 2479 $\pm$ 189 | yes
24 | 19 19 56.55 | 11 41 02 | 4.01 $\pm$ 1.01 | 108.5 $\pm$ 7.1 | 1063 $\pm$ 25 | yes

Using the values of $p$ and $\theta$, polarization maps are generated for the
three clouds. The polarization vectors are plotted on a 25${}^{\prime}\times
25^{\prime}$ DSS (Digital Sky Survey) image of CB24, CB27 and CB188 and are
presented in Figure 1, Figure 2, and Figure 3, respectively. The solid lines
represent the polarization vectors whose length represents $p$, and the
inclination represents $\theta$. The cross mark represents the center of the
cloud. At the bottom right corner of each map, a vector of 1$\%$ polarization
is shown for reference. The vector at the top corner represents the
orientation of the GP ($\theta_{GP}$), which is $142^{\circ}$ for CB24;
$142.5^{\circ}$ for CB27 and $28^{\circ}$ for CB188, respectively. The mean
value of the position angle of polarization $<\theta>$ represents the
orientation of envelope magnetic field $\theta_{B}^{env}$ of the cloud i.e.
$<\theta>$ = $\theta_{B}^{env}$. Also, on the polarization map of CB27 (Figure
2), the contours extracted from Herschel SPIRE $500\mu m$ dust continuum
emission map are plotted (magenta). The thermal dust continuum map is used to
understand the density structure of the globule. In Figure 3, the
$SCUBA$333SCUBA is Submillimetre Common User Bolometer Array to obtain various
astronomical objects. The 850$\mu$ and 450$\mu$ square-degree maps from the
Fundamental Dataset and the 850$\mu$ maps from the Extended Dataset are
available for download from the SCUBA Legacy catalogues repository at the
Canadian Astronomical Data Centre (CADC) at:
http://www.cadc.hia.nrc.gc.ca/community/scubalegacy $850\mu m$ dust continuum
emissions is overlaid (magenta) on the polarization map of CB188. The region
of cloud L673 which is physically associated with the field of CB188 as
mentioned in §2.3 is also marked by the yellow dotted rectangle in Figure 3.

It is evident from Figure 1 and Figure 2 that the polarization vectors of all
the field stars are more or less unidirectional and almost aligned along the
GP. As can be further noticed from the contours over-plotted on the
polarization map of CB27 (Figure 2) that the polarization vectors are oriented
along the direction of the core (extracted from the SPIRE data). Also, there
are two polarization vectors (#8 & #3) in the range of contours that show
parallel orientation with the alignment of the core. The offset between the
envelope magnetic field (given by the mean orientation of the polarization
vectors) and the orientation of the GP,
$\theta_{off}=|\theta_{B}^{env}-\theta_{GP}|$, which is $0.8^{\circ}$ in CB24
and $2.9^{\circ}$ in CB27 respectively. So, the envelope magnetic field
orientation is clearly aligned along the GP in both the clouds. A similar
trend was observed for cloud CB17 by Choudhury et al. (2019). In contrast, in
the case of CB188, $\theta_{off}=70.5^{\circ}$ (Figure 3) though all the
polarization vectors are unidirectional. Also, the envelope magnetic field
orientation is different from the alignment of the $850\mu m$ dust emission
contours. Thus, it can be inferred that the orientation of the envelope
magnetic field in CB188 is not parallel with the GP, unlike CB24 and CB27. To
build a basis for statistically relevant conclusions about the relative
orientations of magnetic field traced in the envelope region of the globules
with respect to the GP, we include polarimetric data of 14 further low
galactic latitude ($-10^{\circ}<b<10^{\circ}$) clouds from the literature. The
corresponding results are summarised in Table 7.

Figure 4: The variation of the alignment of envelope magnetic field of star
forming clouds along the GP, $\theta_{off}=|\theta_{B}^{env}-\theta_{GP}|$
(along Y-axis) with their galactic longitude $l$ (along X-axis) in case of low
latitude clouds ($-10^{\circ}<b<10^{\circ}$). “C” stands for CB cloud and “L”
stands for Lynd’s cloud. Also, note that the errors associated with the
$\theta_{B}^{env}$ are the standard error of the mean.  Figure 5: The stellar
polarization vectors obtained from Heiles catalogue (shown by red line) over
the ranges $-10^{\circ}<b<10^{\circ}$ and $88^{\circ}<l<195^{\circ}$ are
plotted along with the mean degree of polarization and position angle of
polarization of the stars background to the clouds (taken from Table 7 and
shown by yellow lines) viz. CB3, CB4, CB17, CB24, CB25, CB26, CB27, CB34,
CB39, CB246, L1415 and L1014. These clouds are situated towards the region of
GAC except for L1014 which is situated in the region towards GC. A reference
polarization vector of 1$\%$ polarization is shown on the bottom right corner.
Figure 6: The stellar polarization vectors obtained from Heiles catalogue
(shown by red line) over the ranges $-10^{\circ}<b<10^{\circ}$ and
$235^{\circ}<l<250^{\circ}$ are plotted along with the mean degree of
polarization and position angle of polarization of the stars background to the
two clouds (taken from Table 7 and shown by yellow lines) viz. CB56 and CB60
situated towards the region of GAC. A reference polarization vector of 1$\%$
polarization is shown on the bottom left corner. Figure 7: The stellar
polarization vectors obtained from Heiles catalogue (shown by red line) over
the ranges $-10^{\circ}<b<10^{\circ}$ and $l>345^{\circ}$ and $l<50^{\circ}$
are plotted along with the mean degree of polarization and position angle of
polarization of the stars background to the three clouds (taken from Table 7
and shown by yellow lines) viz. CB69, CB130 and CB188 situated towards the
region of GC. A reference polarization vector of 1$\%$ polarization is shown
on the bottom left corner.

##  5 Results and Discussion

Table 7: Parameters related to the target globules obtained from our study as
well from literature: Cloud ID, galactic longitude ($l$), galactic latitude
($b$), mean value of degree of polarization ($<p>$), position angle of GP
($\theta_{GP}$), position angle of envelope magnetic field
($\theta_{B}^{env}$), offset ($\theta_{off}=|\theta_{B}^{env}-\theta_{GP}|$),
FWHM line width ($\Delta V$), uncertainty associated with $\Delta V$ and
position angle of core magnetic field ($\theta_{B}^{core}$).

ID | $l$ | $b$ | $<p>$ |  $\theta_{GP}$ $\pm$ $e_{\theta_{GP}}$ |  $\theta_{B}^{env}$ $\pm$ $e_{\theta_{B}^{env}}$ |  $\theta_{off}$ $\pm$ $e_{\theta_{off}}$ |  $\Delta$ V $\pm$ $e_{\Delta V}$ |  $e_{\Delta V}$ associated | $\theta_{B}^{core}$
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  | (FWHM) |  with $\Delta V$ are: |  |
|  (∘) |  (∘) |  ($\%$) |  (∘) |  (∘) |  (∘) |  (kms-1) |  |  (∘)
CB3 | 119.8 |  $-$6.03 | 1.41 |  85.0$\pm$0.03 |  65.4$\pm$2.8 |  19.6$\pm$2.8 |  1.60$\pm$0.03a |  S.E.∗ |  69.0f
CB4 | 121.03 |  $-$9.96 | 2.84 |  87.2$\pm$0.03 |  70.6$\pm$2.9 |  16.7$\pm$2.9 |  0.51$\pm$0.01c | S.E. | $-$
CB17 | 147.02 | 3.39 | 3.52 |  132.0$\pm$0.04 |  136.0$\pm$0.7 |  4.0$\pm$0.7 |  0.97$\pm$0.03c | S.E. |  44.0g
CB24 | 155.76 | 5.9 | 2.67 |  142.0$\pm$0.04 |  142.8$\pm$5.7 |  0.8$\pm$5.7 |  0.80$\pm$0.50b |  S.D.† | $-$
CB25 | 155.97 | 5.84 | 2.35 |  142.0$\pm$0.04 |  150.9$\pm$1.3 |  8.9$\pm$1.3 |  0.70$\pm$0.50b | S.D. | $-$
CB26 | 156.05 | 5.99 | 3.00 |  142.0$\pm$0.04 |  148.2$\pm$1.0 |  6.2$\pm$0.0 |  1.17$\pm$0.02c | S.E. |  25.3h
CB27 | 171.82 |  $-$5.18 | 2.10 |  142.6$\pm$0.04 |  145.5$\pm$3.7 |  2.9$\pm$3.7 |  0.89$\pm$0.01c | S.E. | $-$
CB34 | 186.94 |  $-$3.83 | 2.14 |  148.8$\pm$0.04 |  143.3$\pm$1.3 |  5.5$\pm$1.3 |  1.50$\pm$0.08a | S.E. |  46.7 for Core1i
|  |  |  |  |  |  |  |  |  90.4 for Core2i
CB39 | 192.63 |  $-$3.04 | 1.95 |  150.4$\pm$0.03 |  150.3$\pm$7.7 |  0.1$\pm$7.7 |  2.05$\pm$0.50b | S.D. | $-$
CB56 | 237.9 |  $-$6.45 | 1.08 |  152.3$\pm$0.02 |  150.9$\pm$2.4 |  1.4$\pm$2.4 |  1.44$\pm$0.50b | S.D. | $-$
CB60 | 248.89 |  $-$0.01 | 1.30 |  147.7$\pm$0.01 |  155.2$\pm$3.0 |  7.5$\pm$3.0 |  1.82$\pm$0.40b | S.D. | $-$
CB69 | 351.23 | 5.14 | 2.00 |  37.7$\pm$0.04 |  155.8$\pm$3.3 |  118.1$\pm$3.3 |  2.35$\pm$0.50b | S.D. | $-$
CB130 | 26.61 | 6.65 | 2.53 |  28.4$\pm$0.03 |  80.0$\pm$3.2 |  51.6$\pm$3.2 |  4.20c $\pm$ $-$ | $-$ | $-$
CB188 | 46.53 |  $-$1.02 | 3.11 |  28.0$\pm$0.01 |  98.5$\pm$2.3 |  70.5$\pm$2.3 |  4.40$\pm$1.1b | S.D. | $-$
CB246 | 115.84 |  $-$3.54 | 1.92 |  77.9$\pm$0.03 |  67.4$\pm$5.2 |  10.5$\pm$5.2 |  1.62$\pm$0.50b | S.D. | $-$
L1014 | 92.45 |  $-$0.12 | 1.90 |  45.2$\pm$0.02 |  15.0$\pm$2.2 |  30.2$\pm$2.2 |  2.26$\pm$0.05d | S.E. | $-$
L1415 | 152.41 | 5.27 | 3.10 |  138.0$\pm$0.04 |  155.0$\pm$0.7 |  17.0$\pm$0.7 |  1.65$\pm$0.02e | S.E. | $-$

(a)Wang et al. (1995) (b)Clemens et al. (1991) (c)Lippok et al. (2013)
(d)Crapsi et al. (2005) (e)Soam et al. (2017) (f)Ward-Thompson et al. (2009)
(g)Choudhury et al. (2019) (h)Henning et al. (2001) (i)Das et al. (2016)

∗S.E.: Standard error of the mean & †S.D: Standard deviation

In this section, we discuss the results of the presented polarization
measurements. In Table 7, we present the angular offset in the orientation of
envelope magnetic field ($\theta_{B}^{env}$, traced through optical
polarimetry) with the orientation of GP ($\theta_{GP}$). The uncertainties in
$\theta_{B}^{env}$ considered here are the standard error of the mean. Note
that, due to the unavailability of the orientation of core-scale magnetic
field ($\theta_{B}^{core}$) for the majority of the clouds, it is not possible
to estimate the morphology of the core-magnetic field of the clouds. The
interpretations based on the results obtained are discussed in the following
subsections.

###  5.1 Relative orientation between the magnetic field and the Galactic
plane

Various studies were carried out to find a correlation between the orientation
of envelope magnetic field in molecular clouds with the orientation of the GP
(e.g. Sen et al. 2000; Soam et al. 2015; Das et al. 2016; Chakraborty & Das
2016; Choudhury et al. 2019). The magnetic lines of force in the spiral arm of
our galaxy are parallel to the arm everywhere (Ireland & Hoyle 1961). In our
previous work, the polarimetric study of CB17 reveals that the projected
envelope magnetic field of the globule is oriented along the GP (Choudhury et
al. 2019).

Based on the results of 17 clouds presented here, the mean value of position
angle of polarization ($\theta_{B}^{env}$) determined for 13 clouds shows that
the envelope magnetic field is almost aligned along the position angle of GP
($\theta_{GP}$) (see Figure 4). The offset between the orientation of magnetic
filed and the GP ($\theta_{off}$) for these 13 clouds are within 20∘ with an
average offset of $7.8^{\circ}$. However, for other 4 clouds, a decoupling in
the relative orientation between the magnetic field and the GP is observed
with an average offset of $67.6^{\circ}$. The details are listed in Table 7.

###  5.2 Variation in the relative orientation between the magnetic field and
the GP with the galactic longitude

In this section, we discuss the possible correlation in the relative
orientation between the magnetic field and the GP with the galactic longitude.
In Figure 4, we show the variation in the offset between the orientation of
envelope magnetic field and the GP, $\theta_{off}$
($=|\theta_{B}^{env}-\theta_{GP}|$) with the galactic longitude ($l$). In this
plot, we have considered only the magnitude of the offset and not the sign.

In our sample size, we have adequate data points in longitude range
$0^{\circ}$ to $250^{\circ}$. A second order polynomial fitting is done with
these data points (solid curve) and a strong correlation is observed between
$l$ and $\theta_{off}$, with an equation,
$\theta_{off}=a_{1}.l^{2}-b_{1}.l+c_{1}$, where $a_{1}=0.0020\pm 0.0006$,
$b_{1}=0.8380\pm 0.1841$, and $c_{1}=90.5358\pm 14.09$. The fitting is done by
including the error (standard error of the mean) in $\theta_{off}$. To test
the goodness of the fit, we have estimated the co-efficient of determination
($R^{2}$) of the best fitted equation. $R^{2}$ is a key output of regression
analysis that may be interpreted as the proportion of the variance in the
dependent variable predicted from the independent variable, which lies between
0 and 1. The higher the coefficient, the better is the goodness of fit. In
this case, $R^{2}$ is estimated to be $\approx 0.87$. It is evident from this
figure that the offset between the orientation of GP and the envelope magnetic
field is considerably low in the regions of $115^{\circ}<l<250^{\circ}$ (which
corresponds to the region towards galactic anti-center (GAC)). This indicates
that the local magnetic of the clouds situated towards the GAC region is
oriented along the GP. The significant offset between the $\theta_{B}^{env}$
and $\theta_{GP}$ observed in the region $l<100^{\circ}$ (correspond to the
region towards the galactic center, (GC)) show that the orientation of the
magnetic field in the clouds lying in those regions (CB130, CB188 and L1014)
tend to become perpendicular to the GP. Hence, for the clouds located at those
longitudes, the envelope magnetic field has a local deflection of its own
irrespective of the orientation of GP.

Note that, no CB cloud is located in the region $250^{\circ}<l<350^{\circ}$ in
the molecular clouds catalogue of Clemens & Barvainis (1988). However, since
there is one single cloud (CB69) available between $350^{\circ}$ and
$360^{\circ}$ which has a huge offset between the orientation of envelope
magnetic field and GP, we have included this cloud in our sample size to
observe the best fitting parameters. A second order polynomial fitting is done
which is represented by the dashed curve. The curve appears to follow the same
trend as in the region $l<100^{\circ}$, which indicates that, towards the GC
region the clouds possess their own local deflection irrespective of the
orientation of GP. In this case, $R^{2}$ is estimated to be $\approx 0.81$ and
the fitting equation is $\theta_{off}=a_{2}.l^{2}-b_{2}.l+c_{2}$, where
$a_{2}=0.0032\pm 0.0004$, $b_{2}=1.1177\pm 0.1484$, and $c_{2}=105.559\pm
13.82$. Although we have made an attempt to fit the equation including CB69,
the fitting parameters obtained may not be significant enough due to
insufficient data points beyond $l>250^{\circ}$.

We compare the polarization of the clouds with the polarization of the stars
by Heiles (2000) to interpret the relative orientation of the local magnetic
field and the GP. The stellar polarization catalogues agglomerated by Heiles
(2000) contains polarization data of 9268 stars in the whole sky
($-90^{\circ}<b<90^{\circ}$) with $p$ and $\theta$ ranging from $0-12.47\%$
and $0^{\circ}-180^{\circ}$. As the region of interest in our study is
$-10^{\circ}<b<10^{\circ}$, we have extracted 2386 polarization data of stars
from the Heiles catalogue within this range. In Figure 5, Figure 6, and Figure
7, the mean degree of polarization ($<p>$) and position angle of polarization
vectors ($<\theta>$) of the field stars located in the clouds are overlaid
along with the stellar polarization vectors obtained from Heiles catalogue on
DSS image. The red lines represent stellar polarization vectors obtained from
the Heiles catalogue and yellow lines represent the mean polarization vectors
of the stars background to the clouds (shown by the cloud IDs). In Table 8, we
have presented the mean position angle of stellar polarization vectors
($<\theta_{Heiles}>$) and the standard deviation ($\sigma_{\theta_{Heiles}}$)
in the selected longitude range where the studied clouds are located. The
polarization vectors of 1523 stars obtained from Heiles catalogue are plotted
in Figure 5 along with $<p>$ and $<\theta>$ of twelve clouds viz., CB3, CB4,
CB17, CB24, CB25, CB26, CB27, CB34, CB39, CB246, L1014 and L1415 in the
longitude range $88^{\circ}<l<195^{\circ}$. In Figure 6, 156 stellar
polarization vectors are plotted along with $<p>$ and $<\theta>$ of CB56 and
CB60, situated in the longitude range $235^{\circ}<l<250^{\circ}$ that
corresponds to the region of GAC. We have also presented polarization vectors
of 724 stars along with $<p>$ and $<\theta>$ of CB69, CB130, and CB188
situated in the longitude range $l>350^{\circ}$ and $l<60^{\circ}$ corresponds
to the region of GC in Figure 7. Misalignment among stellar polarization
vectors at particular longitude ranges is noted to be strong when
$\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $<2$ (see Table 8). As
revealed from Figure 5 and Table 8, the observed nine star-forming clouds in
the longitude range $110^{\circ}<l<180^{\circ}$
($\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $>2$) are found to be
almost aligned with the stellar polarization vectors at their local regions
which corresponds towards the region of GAC. A slight randomness is observed
in the region $185^{\circ}<l<195^{\circ}$
($\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $=1.67$) where CB34 and
CB39 are located. However, in the region around $l\sim 90^{\circ}$ towards GC
($\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $=1.08$), a significant
randomness in the alignment of stellar polarization vectors is seen where the
cloud L1014 is located. In Figure 6, almost unidirectional orientation of the
stellar polarization vectors is observed in the region
$235^{\circ}<l<250^{\circ}$
($\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $\approx 2$). However,
in Figure 7, misalignment in the orientation of stellar polarization vectors
as well as the star-forming clouds is observed in the regions
$345^{\circ}<l<355^{\circ}$ and $20^{\circ}<l<50^{\circ}$
($\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}$ $<2$). Thus, a local
irregularity is observed towards GC revealed from the stellar polarization
data of Heiles, which is found to be consistent with our results.

Table 8: Heiles polarization data averaged over particular galactic longitude
ranges: longitude range over which the mean polarization is estimated
($l-$range), mean position angle of Heiles polarization vectors
($<\theta_{Heiles}>$), standard deviation in the position angle of Heiles
polarization ($\sigma_{\theta_{Heiles}}$), number of polarization vectors
found (n), position angle of envelope magnetic field averaged over star
forming clouds located in the longitude range given in column-1 along with the
standard deviation ($<\theta_{B}^{env}>$ $\pm$ $\sigma_{\theta_{B}^{env}}$)
and cloud IDs.

$l$ | $<\theta_{Heiles}>$ | $\sigma_{\theta_{Heiles}}$ |  $<\theta_{Heiles}>$/$\sigma_{\theta_{Heiles}}$ |  n† |  $<\theta_{B}^{env}>$ $\pm$ $\sigma_{\theta_{B}^{env}}$ | Cloud IDs
---|---|---|---|---|---|---
(∘) |  (∘) |  (∘) |  |  |  (∘) |
20–30 | 89.47 | 52.39 | 1.71 | 43 |  80 $\pm$ 3.20 | CB130
40–50 | 72.77 | 48.01 | 1.52 | 65 |  98.5 $\pm$ 2.30 | CB188
88–100 | 53.90 | 49.81 | 1.08 | 89 |  15.0 $\pm$ 2.2 | L1014
110–122 | 77.01 | 27.69 | 2.78 | 129 |  67.8 $\pm$ 2.58 | CB3, CB4, CB246
147–157 | 130.49 | 29.70 | 4.39 | 81 |  147.10 $\pm$ 7.14 | CB17, CB24, CB25, CB26, L1415
167–177 | 122.13 | 54.91 | 2.22 | 92 |  145.5 $\pm$ 3.7 | CB27
185–195 | 113.72 | 68.26 | 1.67 | 58 |  146.79 $\pm$ 4.93 | CB34, CB39
235–250 | 103.83 | 53.13 | 1.95 | 156 |  153.05 $\pm$ 2.98 | CB56, CB60
345–355 | 79.06 | 67.66 | 1.17 | 177 |  155.8 $\pm$ 3.3 | CB69

† Number of Heiles polarization vectors present in the longitude range given
in column-1

Based on the theory given by Davis & Greenstein (1951), Ireland & Hoyle (1961)
found that polarization effect tends to attain maximum intensity in galactic
longitudes close to $102^{\circ}$. At such longitude, the direction of
polarization is close to being parallel to the plane of the galaxy. Ireland &
Hoyle (1961) also found that, for $70^{\circ}<l<130^{\circ}$, polarization is
high and the magnetic field lines are oriented along to the GP in Orion arm.
However, for $170^{\circ}<l<220^{\circ}$, the polarization is much weaker, and
there is a marked tendency for a few polarization to be normal to the GP.
Berkhuijsen et al. (1964) while studying the linear polarization of the
galactic background observed that there is a homogeneous magnetic field
parallel to the GP around $l=140^{\circ}$, $b=6^{\circ}$. Generally, the
magnetic field lines of the Milky Way galaxy are found to follow the
orientation of the spiral arms (Han et al. 2006). Fosalba et al. (2002)
observed a net alignment of the magnetic field with Galactic structures on
large scales. Beck & Wielebinski (2013) found evidence of turbulence in
polarized intensity towards the inner Galaxy ($270^{\circ}<l<90^{\circ}$,
$|b|<30^{\circ}$). The region towards the GC holds most uniform fields of up
to milligauss strength that are oriented normal to the plane (Beck 2004).
Thus, the results obtained from this study is in good agreement with the
previous studies of the homogeneous magnetic field parallel to the GP for a
certain longitude range as discussed above.

###  5.3 The effect of turbulence on the cloud

The GC is considered to have higher turbulence, indicating high activities in
star forming regions (Boldyrev & Yusef-Zadeh 2006). So, the observed
misalignment in the orientation between the envelope magnetic field and the GP
towards the GC led us to study the effect of turbulence. The 12CO line-width
or velocity dispersion values are considered to be a good measure of
turbulence in molecular clouds. We have listed the 12CO line-width ($\Delta V$
km s-1 in column-7 of Table 7) taken from Wang et al. (1995), Clemens et al.
(1991), Lippok et al. (2013), Crapsi et al. (2005) and Soam et al. (2017). The
uncertainties associated with $\Delta V$ taken from Clemens et al. (1991) are
the dispersion of the distribution and not the standard error of the mean,
they provided the dispersion based on three cloud categories viz. Group-A
(uncertainty=0.5), Group-B (uncertainty=0.4) and Group-C (uncertainty=1.1). In
our sample, the clouds CB24, CB25, CB39, CB56, CB69, and CB246 fall into
Group-A category; CB60 falls into Group-B and CB188 into Group-C (See Table 3
of Clemens et al. (1991) for details).

It can be seen from Table 7 (column-7) that the clouds which show noticeable
misalignment between the envelope magnetic field and the orientation of GP
($\theta_{off}>30^{\circ}$) are seen to have comparatively higher $\Delta V$
($>2$ km s-1). Thus, it can be commented that the clouds having higher $\Delta
V$, which is an indication of more dynamical activities within the cloud, are
seen to have weaker alignment amongst the polarization vectors. However, most
of the clouds with $\Delta V$ $<$ 2 kms-1 appears to have low $\theta_{off}$
($<$ 20∘), which shows that the polarization vectors of the molecular clouds
with less dynamical activities show comparatively better alignment amongst
themselves as well as with the orientation of the GP. The clouds having more
dynamical activities exhibit randomness in the alignment of polarization
vectors. This is because the regions with high turbulent activities are
supposed to be warmer and have better grain alignment. However, precise
measurements of the turbulence velocity is not available for these clouds
preventing us from reaching firm conclusions.

##  6 Conclusions

  1. 1.

We present optical polarimetric analysis of three Bok Globules CB24, CB27 and
CB188. The observations were conducted with the 104cm ST in R-band at ARIES,
Nainital, India. The mean value of polarization, $<p>$ along with the standard
error are found to be $(2.67\pm 0.27)\%$, $(2.10\pm 0.19)\%$, and $(3.11\pm
0.28)\%$ for CB24, CB27, and CB188, respectively. The mean value of
polarization position angle, $<\theta>$ with the standard error are estimated
to be $(142.8\pm 5.7)^{\circ}$, $(145.5\pm 3.7)^{\circ}$, and $(98.5\pm
2.3)^{\circ}$ for CB24, CB27, and CB188, respectively.

  2. 2.

As revealed by the imaging polarimetry, we have found that the envelope
magnetic field in CB24 and CB27 are aligned along the GP. However, in CB188,
the envelope magnetic field is almost normal to the GP. Since all these three
clouds are situated close to GP, the dissimilarities in the results motivated
us to extend our study for 14 more low galactic latitude clouds, which are
available in the literature.

  3. 3.

Based on the observational evidences discussed in §5, we may reasonably
conclude that the magnetic field has its own local deflection irrespective of
the orientation of GP in the clouds which are situated in the region
$l<100^{\circ}$ towards the GC. However, in the region
$100^{\circ}<l<250^{\circ}$ towards the of GAC, the conventional view of the
orientation of magnetic field of the clouds along the GP is observed. This is
apparent from the fit obtained between $l$ and $\theta_{off}$ by a second
order polynomial equation, $\theta_{off}=a_{1}.l^{2}-b_{1}.l+c_{1}$, where
$a_{1}=0.0020\pm 0.0006$, $b_{1}=0.8380\pm 0.1841$, and $c_{1}=90.5358\pm
14.09$ with $R^{2}=0.87$ (solid black curve, Figure 4). However, on inclusion
of the single cloud CB69 situated at a galactic longitude of $351.23^{\circ}$
towards GC, the fitting equation becomes
$\theta_{off}=a_{2}.l^{2}-b_{2}.l+c_{2}$, where $a_{2}=0.0032\pm 0.0004$,
$b_{2}=1.1177\pm 0.1484$, and $c_{2}=105.559\pm 13.82$ with $R^{2}=0.81$
(dashed black curve, Figure 4).

  4. 4.

We have compared our results with the stellar polariation data obtained from
Heiless catalogue. We have found a misalignment among stellar polarization
vectors towards the region of GC where
$\frac{<\theta_{Heiles}>}{\sigma_{\theta_{Heiles}}}<2$. In the longitude range
$110^{\circ}<l<180^{\circ}$ (region towards GAC), almost unidirectional
orientation in the stellar polarization vectors is seen, which is also
observed in our study. We have also noted a little misalignment in
$185^{\circ}<l<195^{\circ}$. However, in the longitude range
$20^{\circ}<l<50^{\circ}$, $l\sim 90^{\circ}$, and $345^{\circ}<l<355^{\circ}$
(region towards GC), a strong misalignment in the orientation of the stellar
polarization vectors is observed, which are in good agreement with our
results.

  5. 5.

The presence of high turbulent activities towards the GC makes the star
forming clouds dynamically more active. Hence, the high turbulence may
possibly play a pivotal role on the misalignment between the magnetic field
and the GP.

###### Acknowledgements.

We would like to acknowledge the Aryabhatta Research Institute of
observational sciencES (ARIES), Nainital for making telescope time available.
We would also like to acknowledge the Herschel Science Archive from which we
have downloaded _Herschel_ SPIRE 500$\mu m$ map of CB27. We collected _SCUBA_
850$\mu m$ map from the CADC repository of the SCUBA Polarimeter Legacy
catalogue and is greatly acknowledged. This work has made use of data from the
European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia),
processed by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. The anonymous reviewer of
this paper is highly acknowledged for his/her comments and suggestions which
definitely helped to improve the quality of the paper. The author G. B.
Choudhury acknowledges the funding agency Department of Science and Technology
(DST), Government of India for providing DST INSPIRE fellowship (IF 170830).

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