Near-infrared Imaging Polarimetry of the Serpens Cloud Core: Magnetic Field Structure, Outflows, and Inflows in a Cluster Forming Clump

Abstract

We made deep near-infrared (JHKs) imaging polarimetry toward the Serpens cloud core, which is a nearby, active cluster forming region. The polarization vector maps show that the near-infrared reflection light in this region mainly originates from SVS 2 and SVS 20, and enable us to detect 24 small infrared reflection nebulae associated with young stellar objects. Polarization measurements of near-infrared point sources indicate an hourglass-shaped magnetic field, of which the symmetry axis is nearly perpendicular to the elongation of the C18O (J = 1-0) or submillimeter continuum emission. The bright part of C18O (J = 1-0), submillimeter continuum cores as well as many Class 0/I objects are located just toward the constriction region of the hourglass-shaped magnetic field. Applying the Chandrasekhar and Fermi method and taking into account the recent study on the signal integration effect for the dispersion component of the magnetic field, the magnetic field strength was estimated to be ~100 μG, suggesting that the ambient region of the Serpens cloud core is moderately magnetically supercritical. This suggests that the Serpens cloud core first contracted along the magnetic field as an elongated cloud, which is perpendicular to the magnetic field, and that the central part then contracted across the magnetic field due to the high density in the central region of the cloud core, where star formation is actively continuing. Comparison of this magnetic field with previous observations of molecular gas and large-scale outflows suggests a possibility that the cloud dynamics are controlled by the magnetic field, protostellar outflows, and gravitational inflows. Furthermore, the outflow energy injection rate appears to be larger than the dissipation rate of the turbulent energy in this cloud, indicating that the outflows are the main source of turbulence and that the magnetic field plays an important role both in allowing the outflow energy to escape from the central region of the cloud core and enabling the gravitational inflows from the ambient region to the central region. These characteristics appear to be in good agreement with the outflow-driven turbulence model and imply the importance of the magnetic field to continuous star formation in the center region of the cluster forming region.

Full text

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arXiv:1004.3409v1 [astro-ph.SR] 20 Apr 2010
Near-Infrared Imaging Polarimetry of the Serpens Cloud Core:
Magnetic Field Structure, Outflows, and Inflows in A Cluster
Forming Clump
Koji Sugitani,1Fumitaka Nakamura,2Motohide Tamura,3Makoto Watanabe,4Ryo
Kandori,3Shogo Nishiyama,5Nobuhiko Kusakabe,3Jun Hashimoto,3Tetsuya Nagata,5and
Shuji Sato6
ABSTRACT
We made deep near-infrared (JHKs) imaging polarimetry toward the Ser-
pens cloud core, which is a nearby, active cluster forming region. The polar-
ization vector maps show that the near-infrared reflection light in this region
mainly originates from SVS2 and SVS20, and enable us to detect 24 small in-
frared reflection nebulae associated with YSOs. Polarization measurements of
near-infrared point sources indicate an hourglass-shaped magnetic field, of which
symmetry axis is nearly perpendicular to the elongation of the C18O (J = 1−0)
or submillimeter continuum emission. The bright part of C18O (J = 1 − 0),
submillimeter continuum cores as well as many class 0/I objects are located just
toward the constriction region of the hourglass-shaped magnetic field. Applying
the Chandrasekhar & Fermi method and taking into account the recent study on
the signal integration effect for the dispersion component of the magnetic field,
the magnetic field strength was estimated to be ∼100 µG, suggesting that the
ambient region of the Serpens cloud core is moderately magnetically supercritical.
1Graduate School of Natural Sciences, Nagoya City University, Mizuho-ku, Nagoya 467-8501, Japan;
sugitani@nsc.nagoya-cu.ac.jp
2Faculty of Education and Human Sciences,
fnakamur@ed.niigata-u.ac.jp.
Niigata University,Niigata 950- 2181,Japan;
3National Astronomical Observatory,
hide.tamura@nao.ac.jp, r.kandori@nao.ac.jp, nb.kusakabe@nao.ac.jp, Jun.Hashimoto@nao.ac.jp
2-21-1 Osawa,Mitaka,Tokyo 181-8588,Japan;moto-
4Department of Cosmosciences, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-
0810, Japan; mwata@ep.sci.hokudai.ac.jp
5Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan; shogo@kusastro.kyoto-
u.ac.jp, nagata@kusastro.kyoto-u.ac.jp
6Department
ssato@z.phys.nagoya-u.ac.jp
ofAstrophysics,NagoyaUniversity,Chikusa-ku,Nagoya464-8602,Japan;

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These suggest that the Serpens cloud core first contracted along the magnetic
field to be an elongated cloud, which is perpendicular to the magnetic field, and
that then the central part contracted cross the magnetic field due to the high
density in the central region of the cloud core, where star formation is actively
continuing.
Comparison of this magnetic field with the previous observations of molecular
gas and large-scale outflows suggests a possibility that the cloud dynamics is
controlled by the magnetic field, protostellar outflows and gravitational inflows.
Furthermore, the outflow energy injection rate appears to be larger than the
dissipation rate of the turbulent energy in this cloud, indicating that the outflows
are the main source of turbulence and that the magnetic field plays an important
role both in allowing the outflow energy to escape from the central region of the
cloud core and enabling the gravitational inflows from the ambient region to the
central region. These characteristics appear to be in good agreement with the
outflow-driven turbulence model and imply the importance of the magnetic field
to continuous star formation in the center region of the cluster forming region.
Subject headings: circumstellar matter infrared: stars ISM: individual (Serpens)
ISM: magnetic fields polarization stars: formation
1. Introduction
Stars are formed by gravitation in molecular clouds having both turbulence and magnetic
fields in the Galaxy, and most of stars are thought to be formed in clusters (e.g., Lada & Lada
2003; Allen et al. 2007). A mass spectrum of prestellar condensations is reported to have the
power similar to that of the stellar IMF both in dust continuum observations (Reid & Wilson
2006, and references therein) and molecular-line observations (e.g., Ikeda et al. 2007), and
theoretical studies of turbulent molecular clouds (Klessen et al. 1998, and subsequent works)
suggest that these condensations were formed through turbulent shock. One of the most
promising sources of ordinary turbulence is outflows from protostars, which are ubiquitous
in star forming regions and are believed to be formed through the mediation of magnetic
field. Magnetic fields are also considered to play an important role in dynamical evolution
of molecular clouds and control of star formation, i.e., formation of molecular cloud cores
and their collapse (e.g., McKee & Ostriker 2007).
Recently, Li & Nakamura (2006) and Nakamura & Li (2007) presented realistic 3D
MHD simulations of cluster formation, taking into account the effect of protostellar outflows
as well as initial turbulence and a magnetic field. In their simulations, they indicated that

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the initial turbulence is quickly replaced by turbulence generated by protostellar outflows,
keeping the quasi-equilibrium state with a slow rate of star formation, and that magnetic
fields are dynamically important if their initial strengths are not far below the critical value
for static cloud support because of the amplification by the outflow-driven turbulent motions.
The magnetic field is expected to influence the directions of outflow ejection and propagation
and the transmission of outflow energy and momentum to the ambient medium. However,
the magnetic field structures have not always been observationally clear in/around cluster
forming regions, particularly around nearby cluster forming regions because of the lack of
deep, wide-field near-infrared (NIR) polarimetry data.
The Serpens cloud core is one of the nearby1, active low-mass star forming regions
at the northern part of the Serpens cloud and many observational works have been done
(Eiroa et al. 2008, and references therein). Recent mid-IR studies (e.g., Kaas et al. 2004;
Harvey et al. 2007; Winston et al. 2007) revealed that a lot of embedded young stellar objects
(YSOs), including Class 0/I objects, are located toward an aggregate of (sub)millimeter
dust continuum cores (e.g., Davis et al. 1999; Kaas et al. 2004; Enoch et al. 2007), which
consists of two sub-clumps (NW and SE sub-clumps; Olmi & Testi 2002) in the central
region and is enveloped by ambient molecular gas (e.g.
2000; Olmi & Testi 2002).
13CO, and C18O; McMullin et al.
Many outflow activities that are related to star formation have been taking place in the
Serpens cloud core. CO high velocity flows are reported to be widely spread over the cloud
core (e.g., White et al. 1995; Davis et al. 1999; Narayanan et al. 2002). Compact molecular
outflows of higher density tracers and H2 jet-like knots are associated with the submil-
limeter cores (e.g., Curiel et al. 1996; Herbst et al. 1997; Wolf-Chae et al. 1998; Hodapp
1999; Williams & Myers 2000). The direction of these compact outflows was reported to be
PA∼ 155◦on an average with deviation of a few 10◦(see Table 5 of Olmi & Testi 2002),
which is nearly parallel to the alignment direction, from NW to SE, of the two sub-clumps
(e.g., Davis et al. 1999; Kaas et al. 2004; Enoch et al. 2007), or to the cloud elongation in
13CO, C18O, and other higher density tracers (e.g.
2002). In addition, Davis et al. (1999) and Ziener & Eisl¨ offel (1999) found, through opti-
cal narrow-band imaging, that many HH objects emanate from the two sub-clumps to the
ambient region, penetrating the dense part of the central region.
McMullin et al. 2000; Olmi & Testi
The Serpens Reflection Nebula (SRN) illuminated by SVS 2 (Strom et al. 1976) has been
1We assume a distance of ∼260 pc for the Serpens cloud, following the most of the recent papers on the
Serpens cloud and based on the discussion of Straiˇ zys et al. (2003) on the center distance of the Aquila Rift
system.

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extensively studied by polarimetric measurements both in optical and near-infrared (NIR)
wavelengths (King et al. 1983; Warren-Smith et al. 1987; Gomez de Castro et al. 1988; Sogawa et al.
1997; Huard et al. 1997). NIR polarimetric measurements (Sogawa et al. 1997; Huard et al.
1997) probed also some other obscured reflection nebulae around SVS 2 in detail. Gomez de Castro et al.
(1988) suggested the magnetic field of a NW-SE direction based on the elongation of the
reflection nebulae around several YSOs in the central region of Serpens cloud core. In con-
trast, the NIR polarization measurement of a background star candidate suggested rather
different direction of magnetic field because its polarization angle was nearly perpendicular
to the NW-SE direction (Sogawa et al. 1997). However, this measurement was only for one
background candidate, which in fact has a possibility of being a YSO in the Serpens cloud
core and its polarization originating from the YSO itself. Therefore, it is vitally important
to measure more background stars to resolve this discrepancy and to know the magnetic
field structure toward the Serpens cloud core.
We conducted deep, JHKs imaging polarimetry of the Serpens cloud core to reveal the
magnetic field structure in this region. We also searched for more NIR reflection nebulae
associated with YSOs. Here, we present the results of our imaging polarimetry in the Serpens
cloud core by comparing the data from the previous observations and discuss the role of the
magnetic field in this region.
2. Observations and Data Reductions
Toward the Serpens cloud core (Figure 1), simultaneous JHKs polarimetric observations
were carried out on 2006 June 23 UT with the imaging polarimeter SIRPOL (Kandori et al.
2006), which is an attachment of the near-infrared camera SIRIUS mounted on the IRSF 1.4-
m telescope at the South Africa Astronomical Observatory. The SIRIUS camera is equipped
with three 1024 × 1024 HgCdTe (HAWAII) arrays, JHKs filters, and dichroic mirrors,
which enables simultaneous JHKs observations (Nagashima et al. 1999; Nagayama et al.
2003). The field of view at each band is ∼7.′7 x 7.′7 with a pixel scale of 0.′′45 pixel−1.
We obtained 10 dithered exposures, each 10 s long, at four wave-plate angles (0◦, 22.5◦,
45◦, and 67.5◦in the instrumental coordinate system) as one set of observations and repeated
this 9 times. Sky images were also obtained in between target observations. Thus, the total
on-target exposure time was 900 s per wave-plate angle. The seeing was ∼ 1.2′′at Ks during
the observations. Twilight flat-field images were obtained at the beginning and end of the
observations.
Standard procedures, dark subtraction, flat-fielding with twilight-flats, bad-pixel sub-

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stitution, sky subtraction, and averaging of dithered images, were applied with IRAF.
We first calculated the Stokes parameters as follows; Q = I0− I45, U = I22.5− I67.5,
I = (I0+I22.5+I45+I67.5)/2, where I0, I22.5, I45, and I67.5are intensities at four wave-plate
angles. To obtain the Stokes parameters in the equatorial coordinate system, a rotation of
105◦(Kandori et al. 2006) was applied to them. We calculated the degree of polarization
P, and the polarization angle θ as follows; P =
polarization intensity (PI) is obtained by multiplying the total intensity (I) by the degree
of polarization (P). The absolute accuracy of the position angle of polarization was esti-
mated to be better than 3◦at the first light observation of SIRPOL (Kandori et al. 2006).
The polarization efficiencies are 95.5%, 96.3%, and 98.5% at J, H, and Ks, respectively,
and the instrumental polarization is less than 0.3% all over the field of view at each band
(Kandori et al. 2006). Due to these high polarization efficiencies and low instrument polar-
ization, no particular corrections were made here.
?Q2+ U2/I, θ = (1/2)tan−1(U/Q). The
Aperture polarimetry was performed for H and Ks band point sources detected by
DAOFIND in the field of view. No polarimetry for J band sources was done due to their
much smaller number, compared with those of H and Ks band sources (see Figure 2 a, c, and
e). APHOT of the DAOPHOT package was used to evaluate the point source magnitudes
for four wave-plate angles at H and Ks. An aperture radius of 3 pixels was adopted for
each band. The errors of the degree of polarization (∆P) and the position angle were
calculated from the photometric errors, and the degrees of polarization were debiased as
Pdebias=√P2− ∆P2(Wardle & Kronberg 1974). Hereafter, we use P as substitute for this
debiased value for the aperture photometry data. Only the sources with photometric errors
of <0.1 mag and P/∆P > 2 were used for analysis. The 2MASS catalog (Skrutskie et al.
2006) was used for absolute photometric calibration. The limiting magnitudes at 0.1 mag
error level were estimated to be 18.6 at H and 17.5 at Ks.
3.Results
3.1.Polarizations of extended emission
The JHKs polarization vector maps of the Serpens cloud core are shown, superposed
on the total and polarization intensity images in Figure 2. These polarization maps clearly
indicate that the central part of the reflection nebula is illuminated mainly by two sources;
the north part (SRN) by SVS 2 and the south part by SVS 20, at H and Ks with two
centrosymmetric patterns (see also Sogawa et al. 1997; Huard et al. 1997), while at J only
SRN is dominant (see also Sogawa et al. 1997) as is seen in the optical (Warren-Smith et al.
1987; Gomez de Castro et al. 1988). This invisibleness at shorter wavelengths suggests that

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the southern part of SRN around SVS 20 is more obscured than the northern part around
SVS 2, consistent with the AV map deduced from H − K color (Huard et al. 1997). The
centrosymmetric patterns are more clearly shown in Figure 3, which is a Ks polarization
vector map shown with a resolution higher than Figure 2e.
The PI images and vector patterns of SVS 2 clearly show that SVS 2 is associated with
a bipolar structure with a dark lane. In the JHKs intensity images of Figures 2 a, c, and
e, at shorter wavelengths, the NW lobe of the bipolar nebula is brighter than the SE lobe,
while at longer wavelengths the SE lobe is brighter. This suggests that the NW lobe is near
side and that the SE lobe is far side. The nebula structure and dark lane of SRN have been
already reported in the two polarimetric studies (Sogawa et al. 1997; Huard et al. 1997). In
addition, Pontoppidan & Dullemond (2005) modeled SRN as a disk shadow system with
their imaging data, and suggested that SVS 2 is associated with a small disk, which is not
unresolved, and a spherically symmetric envelope.
The nebula illuminated by SVS 20 is clearly recognized at H and Ks with a centrosym-
metric pattern around SVS 20. This object has a peculiar morphology with a ring and two
arms protruded from that ring. Because we plan to report its details in a separate paper,
including other YSOs with reflection nebulae, we will not mention the details here.
3.2.Polarizations of nebulosities associated with YSOs
3.2.1. The central region
Figure 3 presents an higher resolution Ks polarization vector map with 3×3 pixel binning
toward the central region of the overall image, superposed on the Ks intensity map. With
this map and/or the highest resolution vector maps without binning, we identified stellar
sources having reflection nebulae locally illuminated by themselves with centrosymmetric
or centrosymmetric-like patterns. It is not easy to identify such sources only from Figure
3 due to the strong contamination from SVS 2 and SVS 20. It is also not easy toward
the SVS 4 cluster, which is a compact cluster located to the south of SVS 20, due to the
source congestion. We therefore used the highest resolution vector maps without binning for
the sources having the strong contamination (see Appendix). The identified sources with
reflection nebulae illuminated by themselves are marked in Figure 3, including SVS 2 and
SVS 20, and are listed in Table 1.
Most of the identified sources are relatively bright in the central region. This is probably
due to the strong light from SVS 2 and SVS 20 and only brighter sources with reflection
nebulae may be detected. Except EC117 (SSTc2dJ 18300065+0113402), all the identified

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sources are classified as sources that have outer disks with an excess at least 8 and/or 24
µm, i.e., class 0/I, flat spectrum, class II and transition disk sources (Winston et al. 2007).
Although EC117 is classified as a class III source without an outer disk due to no detection
of 24µm continuum (Table 4 of Winston et al. 2007), it was reported that EC117 has a flux
of 3.20±1.43 mJy at 24µm (Table 3 of Harvey et al. 2007). This could suggest the outer
disk of EC117, but the signal to noise ratio of ∼2 is not high enough for the robust detection
at 24µm. Almost all members of the SVS 4 cluster seem to be associated with reflection
nebulae.
3.2.2. The NW region
Figure 4 presents a high resolution Ks polarization vector map without binning toward
the NW region of SRN. Here we identified stellar sources associated with self-luminous neb-
ulae as well as those with reflection nebulae by using this map and listed them in Table
2. Three sources, DEOS, EC53, and EC67, are associated with reflection nebulae having
centrosymmetric or partially centrosymmetric vector patterns. The other sources are asso-
ciated with elongated nebulae or jet-like knots emanating from the sources in a straight line
and their polarization vectors are almost perpendicular to their elongation directions. The
elongated structures or knots are likely to be created/excited by outflows from these sources.
The jet-like knots are clearly seen near the north-west of EC41, which was considered
to be an embedded star but not a driving source of this jet (Eiroa & Casali 1989; Hodapp
1999). These jet-like knots are reported to be mostly H2 emission with weak continuum
(Hodapp 1999), and their polarization of these knots is nearly perpendicular to the jet
elongation, though the polarization directions are more scattered in the northern knots than
in the southern knots of this jet-like structure. At H-band, the polarization vectors of
weak continuum emission of the southern knots are also nearly perpendicular to the jet
elongation, which is parallel to the radial direction from SMM1-FIRS1, not from EC41.
Thus, SMM1-FIRS1 is the illuminating source of these jet-like knots, and the jet-like knots
could correspond to the cavity walls that were created by the outflow from SMM1-FIRS1.
The jet-like structure from SMM1-FIRS1 seems to continue farther away to a bow-shock-
like nebulosity located at ∼80-90′′north-west of SMM1-FIRS1 (or at ∼ 20′′north-west of
EC28). The polarization vectors at this bow nebulosity indicate either SMM1-FIRS1 or EC28
is illuminating or exciting it. No information is available on whether the bow nebulosity is
really shock-excited H2 emission or not, due to its position outside Figure 3 of Hodapp
(1999), although week H-band continuum emission is detectable with polarization angles
similar to those of Ks-band. The alignment with the jet structure, the bow nebulosity and

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HH 460, which is located at ∼ 4′north-west to SMM1-FIRS1 (Davis et al. 1999), gives a
hint that the bow nebulosity is related to the outflow from SMM1-FIRS1. The associations
of the blueshifted CO lobe with HH 460 (Davis et al. 1999) and of the bow nebulosity with
the CS emission (CS1; Testi et al. 2000), which is considered to be related to the outflow,
support the shock excitation of the bow nebulosity. However, it is impossible to completely
exclude the possibility that EC28, which is the closest NIR source to the bow nebulosity,
or SMM1-FIRS1 itself contributes to the illumination of the bow nebulosity, due to the
scattering of the polarization vector directions. In the midway from SMM1-FIRS1 to this
bow nebulosity, there exist some faint knots that are almost H2emission (see Figure 3 of
Hodapp 1999), but no polarization is detectable for these knots.
The chain of nebulosity knots, located just south-east to the 3 mm continuum core
S68Nc (Testi & Sargent 1998; Williams & Myers 2000), was reported to be H2emission jets
that originate from the 3mm subknot a3/S68Nc (Hodapp 1999). Although only several
polarization vectors are shown toward these knots, they could imply that their polarization
direction is nearly perpendicular to the jet elongation.
A nebulosity protruding from EC38/S68Nb is seen, and its polarization vectors appear
to be nearly perpendicular to the protruding direction. A faint, small, elongated nebulosity is
recognized just south-east to SMM10-IR. Although some nebulosities illuminated from SVS
2 are also seen near SMM10-IR, this nebulosity is most likely a nebulosity related to SMM10-
IR based on its morphology. No information is available on whether these two nebulosities
are shock-excited H2emission or not, because they are out of Figure 3 of Hodapp (1999).
We note that no H-band emission is detectable toward SMM10-IR, while very week H-band
continuum is seen toward the nebulosity protruding from EC38/S68Nb.
3.3.Polarizations of point sources
We have measured H and Ks polarization for point sources, in order to examine the mag-
netic field structures. Only the sources with photometric errors of <0.1 mag and P/∆P > 3
were used for analysis.
The top panel of Figure 5 presents the polarization degrees at H versus H − Ks color
diagram for sources having polarization errors of < 0.3%. YSOs identified by Winston et al.
(2007) are not included in this diagram. In this diagram, the maximum of polarization degree
at an H − K color is roughly proportional to the H − K color, i.e., the extinction, having
consistency that the origin of the polarization is dichroic absorption. Therefore, we consider
the polarization of these point sources as the polarization of the dichroic origin, and that

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their polarization vectors represent the directions of the local magnetic field averaged over
their line of sight of the sources. In the nearby star forming regions such as the Taurus and
Ophiuchus clouds, the highest value of the maximum polarization efficiency was reported to
be P(H)/E(H −K) = 4.6 or P(H)/A(H) = 1.6 (Kusakabe et al. 2008), which were derived
from the data of Whittet et al. (2008). In Figure 5, a dashed line represents P(H)/(H −
Ks) = 4.6 where the offset of the intrinsic H − Ks color is ignored. Our sources have the
maximum polarization efficiency of P(H)/(H −Ks) = 6.2 (thick line) similar to that of the
nearby star forming regions, and this is also consistent with the dichroic origin.
The bottom panel of Figure 5 shows the H-band polarization angles of the point sources
with P < 6.2(H − Ks), of which the polarization vectors are shown in Figure 6. YSOs are
not included in the bottom panel, but included in Figure 6.
The polarization angles are mostly in a range of ∼0–140◦and their median and average
angles are 63.5◦and 64.6±35.6◦, respectively.
scattered, there is a tendency that the degree of scatter becomes smaller in the redder
H −Ks color region. This tendency suggests that the polarization angles are more confined
in the inner region (redder color region) than in the outer region.
While the polarization angles are largely
The magnetic field is neither simply straight nor random over the whole field (Figure
6). The vectors appear to be systematically ordered and gradually curved, suggesting a
clear hourglass shape that is left-handedly tilted by ∼ 60–80◦and the direction of the global
magnetic field that is nearly perpendicular to the elongation of the Serpens cloud core from
NW to SE, ∼ 150◦(e.g., the C18O maps of McMullin et al. 2000; Olmi & Testi 2002).
Signs of hourglass shapes in the magnetic field have been already reported in high-
mass star forming cores such as NGC 2024 (Lai et al. 2002), OMC-1 (Schleuning 1998;
Houde et al. 2004; Kusakabe et al. 2008), and DR21 Main (Kirby 2009). In low mass cores
such as NGC 1333 IRAS 4A (Girart et al. 2006) and Barnard 68 (Kandori et al. 2009) hour-
glass shapes have been more clearly shown. These examples, except OMC-1, of the hourglass-
shaped magnetic field have been found only in isolated cores or cores with simple structures
in the star forming regions. However the Serpens cloud core is a molecular cloud complex
consisting of many molecular cloud cores or sub-millimeter cores (e.g., Davis et al. 1999),
which form a cluster of low-mass YSOs, and the hourglass-shaped magnetic field spreads
widely over the Serpens cloud core. Thus, this is a clear example that the hourglass-shaped
magnetic field is associated with a low-mass star forming complex, while OMC-1 is an ex-
ample of a hight-mass star forming complex.

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4. Analysis and Discussion
4.1.Shape of the magnetic field
We have modeled the shape of the magnetic field with the polarization vectors measured
at H for point sources, following Girart et al. (2006) and Kandori et al. (2009). The magnetic
field was fitted with a parabolic function of x = g+gCy2, with a counterclockwise tilted y-axis
(the parabolic magnetic field axis of symmetry) by θPAand a symmetric center (x,y)center,
where the y is the distance from the horizontal axis (x = 0) and the x is the distance from
the parabolic magnetic field axis of symmetry. The value of tan−1(dy/dx)+90◦corresponds
to the position angle of the polarization (θ). Only the point sources, except YSOs, having
P/∆P > 3 and P < 6.2(H − Ks), were used for the fitting. The error of the polarization
angle (∆θ) was used to compute a weight for the datum, 1/(∆θ)2.
In Figure 7, the best-fit magnetic field is shown as well as the measured polarization
vectors for 149 sources. The position angle of the parabolic magnetic field axis of symmetry
is ∼ 70◦, and the coefficient C of y2is ∼ 7.1 × 10−6pixel−2. The root mean square (r.m.s.)
of the residuals is ∼ 22◦.
We executed one-parameter fitting of the magnetic field in local areas, in order to more
accurately calculate the r.m.s. of the residuals, with the same θPAand (x,y)centerobtained
in the global fitting above. We selected three corners and one more area of the image
where the source density is relatively high and/or the magnetic field seems to be rather
ordered (areas outlined by dashed boxes in Figure 7). Toward the SE corner of the image
( x < 400 and y < 400 in Figure 7; 30 sources), the coefficient C of y2was determined to
be (7.99 ± 0.76) × 10−6pixel−2, similar to that of the global fitting, and the r.m.s. of the
residual was calculated to be 12.9±0.9◦, and toward the SW corner (x > 500 and y < 230; 20
sources), C = (7.52±1.00)×10−6pixel−2and r.m.s. = 27.0±2.0◦were obtained. Removing
the dispersion due to the measurement uncertainties of the polarization angles 4.2±3.0◦and
3.2 ± 2.2◦, we obtained the dispersions from the best-fit model, 12.2 ± 1.4◦and 26.8 ± 2.0◦
for the SE and SW corners, respectively. Toward the NE corner (x < 300 and y > 800; 18
sources), C = (3.36 ± 0.92) × 10−6pixel−2and r.m.s. = 14.8 ± 1.6◦were evaluated, and
the intrinsic dispersion from our model of 13.7 ± 2.0◦was obtained with the measurement
uncertainty of 5.6 ± 2.4◦. This smaller C indicates that the curvature of the magnetic field
here is rather looser than that expected from the global fitting, i.e., slightly bended to the
direction parallel to the symmetry axis of the magnetic field. Toward the area next to the
NE corner (400 < x < 700 and y > 800; 17 sources), C = (6.85 ± 0.55) × 10−6pixel−2and
r.m.s. = 13.3±1.4◦were evaluated, and the intrinsic dispersion of 12.6±1.8◦was obtained
with the measurement uncertainty of 4.2 ± 2.9◦.

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4.2. Comparison of the magnetic field with the submillimeter and millimeter
data
4.2.1.850 µm continuum
We compare our H-band measured polarization vectors and the modeled magnetic field
with the 850 µm dust continuum map of Davis et al. (1999) in Figure 8. Note that the green
lines of this figure do not present lines of magnetic force, just the direction of the magnetic
field.
The high intensity ridge of the 850 µm continuum is elongated along the NW-SE di-
rection, having two sub-clumps (NW and SE sub-clumps), both of which consist of several
dense cores (e.g., SMM 1–11, S68Nb–d, and PS2 in Figure 8). This distribution of the
850 µm continuum is very similar to that of the bright parts of the13CO(J = 1 − 0) and
C18O(J = 1 − 0) emission (McMullin et al. 2000; Olmi & Testi 2002), although the global
distribution of the13CO(J = 1 − 0) emission is not always elongated, but rather roundly
extended (Olmi & Testi 2002). It is evident that the symmetric axis (y′-axis) of the best-fit
magnetic field with a parabolic function is nearly perpendicular to the elongation direction of
these continuum and molecular line emissions. The horizontal axis (x′-axis) of the parabolic
magnetic field is situated nearly along the 850 µm continuum ridge, although there are some
deviations of the continuum emission from the horizontal axis. The symmetric axis of the
parabolic magnetic field runs through the northern part of the SE sub-clump, not through
the middle point of the two sub-clumps, which looks like the center of gravity of the Serpens
cloud core when we glance at the 850 µm continuum map.
Davis et al. (1999) suggested the presence of three extended cavity-like structures to the
east of SMM 3 (hereafter CLS 1), south-west of SMM 2 (hereafter CLS 2), and north-west
of SMM 4 (hereafter CLS 3), which consist of three pairs of filaments that protrude the 850
µm continuum ridge. They mentioned that these cavity structures (CLS 1–3) are probably
shaped by outflows rather than by global cloud collapse along, say, magnetic field lines.
As is in Figure 8, the filaments to the north-east of SMM 3 and east of SMM 2 form
CLS 1, those to the south-east of SMM2/PS2 and south of SMM11 form CLS 2, and those
to west of SMM3 and east of SMM4 form CLS 3. It appears that the two filaments of CLS
1 jut almost along the magnetic field from the SE sub-clump and that the symmetry axis
(y′-axis) of the magnetic field go through the inside of CLS 1 as well as CLS 3.

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4.2.2.CO emission
Here we compare our best-fit magnetic field with the12CO J = 2 − 1,12CO J = 1 − 0,
13CO J = 1 − 0, and C18O J = 1 − 0 observations (White et al. 1995; Davis et al. 1999;
McMullin et al. 2000; Narayanan et al. 2002; Olmi & Testi 2002).
12CO J = 2 − 1
As was mentioned above, the bright parts of the13CO J = 1−0 and C18O J = 1−0 emission
maps are elongated and confined in the ridge, while the global distributions of12CO J = 2−1
and13CO J = 1−0, i.e., the low density molecular gas, are extended (e.g., White et al. 1995;
Davis et al. 1999; Olmi & Testi 2002).
Figure 9 presents our best-fit magnetic field superposed on the CO J = 2−1 contour map
and 850 µm image of Davis et al. (1999), where the CO J = 2−1 map is considered to show
the ambient molecular gas of the Serpens cloud core, but not the dense cores. Davis et al.
(1999) mentioned that toward the two filaments of CLS 1 and one CLS 2 filament to the
south-east of SMM2/PS2 the CO J = 2 − 1 emission and 850 µm continuum distributions
coincide well. As mentioned above, the two filaments seem to run almost along the magnetic
field, indicating that the CO J = 2 − 1 filaments are also related with the magnetic field.
For the CLS 2 filament to the south-east of SMM2/PS2, the same situation as the CLS 1
filaments may be also seen. Two other CO J = 2−1 filaments/extensions to the north-west
of SMM 9 and west of SMM 1 are also noticeable in Figure 9. Although considerable parts
of these two filaments are out of our polarimetry image, the extrapolation of our best-fit
magnetic field cloud predict that these two filaments run along the magnetic lines.
C18O J = 1 − 0 and13CO J = 1 − 0
McMullin et al. (2000) showed that a velocity gradient running from a LSR velocity centroid
of 9 km s−1at the north-west end of the C18O J = 1−0 emission to 7.5 km s−1at the south-
east end (Figure 2 of McMullin et al. 2000), i.e., along the elongation direction of C18O. On
the other hand, Olmi & Testi (2002) suggested that the Serpens cloud exhibits a velocity
gradient roughly from east to west, based on their model fitting of velocity gradients in C18O
J = 1 − 0,13CO J = 1 − 0, C34S J = 1 − 0, adopting their map center, which is the middle
point of the two sub-clumps, as the reference position for analysis. However, according to
their channel and centroid velocity maps (Figures 7 and 8 of Olmi & Testi 2002), the bright
parts of C18O J = 1 − 0 and13CO J = 1 − 0 are similar to that of McMullin et al. (2000),
and a steep velocity gradient from NW to SE almost along the normal line of the symmetry

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axis (y′-axis) of the magnetic field can be seen at just south of their reference position in
13CO, although at the reference position a velocity gradient from West to East is seen. It
is surprising that the normal line of the steep velocity gradient almost coincides with the
symmetry axis (y′-axis) of the magnetic field.
In summary, the direction of velocity gradient is nearly along the elongation of the
Serpens cloud core and is nearly perpendicular to the symmetry axis of the magnetic field
with a coincidence of the normal line of the steep velocity gradient and the axis of the
magnetic field. It could be possible that this normal line of the velocity gradient is an axis
of the global rotation of the Serpens cloud core if the real center of gravity of the Serpens
cloud core is located on the symmetry axis of the magnetic field.
It is interesting to examine the presence of C18O J = 1−0 and13CO J = 1−0 features
that coincide with the filaments of the CO J = 2 − 1 emission and 850 µm emission. In
the C18O 1−0 integrated emission maps of White et al. (1995), McMullin et al. (2000) and
Olmi & Testi (2002), a feature to the north-east of SMM 3 could coincide with one of the
CSL 1 filament, but one to the east of SMM 2 is not clear. In the channel map of13CO
J = 1−0 (Figure 7 of Olmi & Testi 2002), a filament feature to the east of SMM 2 is clearly
visible in the blue-shifted emission at the panel of VLSR=5–7.3 km s−1. This filament looks
likely to coincide with the CSL 1 filament to the east of SMM 2, but we can clearly recognize
that it is located just outside this CSL 1 filament, i.e., between this CSL 1 filament and
the CSL 2 filament to the south-east of SMM 2/PS2. At the same panel, a feature to the
north and north-east of SMM 3 or near SMM 8 is also visible. This feature appears to be
just outside the CLS 1 filament to the north-east of SMM 3. At the panel of VLSR=8.4–
12.4 km s−1, a red-shifted feature that protrudes from the SE sub-clump is visible, but it is
located toward the inside region of CLS 1. The presence of this red-shifted feature and the
blue-shifted features are probably consistent with red-shifted velocity region that jut from
the SE sub-clump and with blue-shifted regions toward both sides of this red-shifted region,
respectively, in the13CO J = 1 − 0 centroid velocity map of Olmi & Testi (2002).
CO outflows
Davis et al. (1999) presented the integrated intensity contours of CO J = 2 − 1 blue- and
red-shifted outflows (Figures 4 and 8 of Davis et al. 1999). These figures imply that the 850
µm filaments that coincide the CO J = 2−1 filaments are shaped by outflows. On the basis
of a fact that these filaments run along the magnetic field, the outflows that protruded from
the ridge to its ambient are most likely to be guided by the magnetic field or to drag the
magnetic field. The outflows may be guided by the magnetic field since the magnetic field
seems to be strong enough to be ordered at least over our polarimetric imaging area.

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The CLS 1 filaments are associated with red-shifted outflows, but no red-shifted CO
J = 2 − 1 emission is visible at the root of CLS 1. However, CO J = 1 − 0 obervations
(Narayanan et al. 2002) showed U-shaped, red-shifted high velocity flow at the root of CLS
1. This CO J = 1−0 feature and our best-fit magnetic field support the idea of Davis et al.
(1999) that the CLS 1 filaments of the CO J = 2 − 1 and 850 µm emission illustrate the
action of a wide-angled wind powered by a source within the SMM 2/3/4 cluster, which has
swept up gas and dust into a warm, compressed shell, although there is a possibility that
the wind is powered by multiple sources within the cluster.
4.3.Magnetic field strength
We try to make an evaluation of the magnetic field strength toward four areas where we
calculated the angular dispersions (residuals) for our best-fit magnetic field, using the Chan-
drasekhar & Fermi (CF) method (Chandrasekhar & Fermi 1953). On the basis of the con-
clusions of recent MHD studies that the introduction of a correction factor is needed for eval-
uating the plane-of-sky component of the magnetic field (Ostriker et al. 2001; Padoan et al.
2001; Heitsch et al. 2001; Kudoh & Basu 2003), Houde (2004) mentioned that a correction
factor of ∼0.5 is appropriate in most cases when the magnetic field is not too weak. Since
the magnetic field seems to be ordered over the Serpens cloud core, the magnetic field is
expected to be strong. Therefore we first adopt a correction factor of 0.5 to evaluate the
magnetic field strength. We need the mass density and velocity dispersion of the matter
coupled to the magnetic field to evaluate the magnetic field strength. Here, we use those
estimated from the C18O observation (Olmi & Testi 2002).
Toward the four areas, the H2column densities from C18O could be estimated to be
∼ 6 × 1022cm−2from Figure 11 of Olmi & Testi (2002). Adopting the approximate C18O
extent of ∼12′(∼0.9 pc at d∼260 pc; Figure 2 of Olmi & Testi 2002) as the depth of these
area, we obtain the H2densities of ∼ 2.1×104cm−3. From Figure 10 of Olmi & Testi (2002),
the C18O velocity widths could be estimated to be ∼1.6–1.8 km s−1toward the SE and NE
corners, and ∼1.8–2.0 km s−1toward the area next to the NE corner. Toward the SW corner
with a complex distribution of velocity width, the velocity width may be ∼1–2 km s−1.
Using a mean molecular mass, µ, of 2.3 and these values to derive the velocity dispersions,
we roughly evaluated the magnetic field strength of the plane-of-the-sky of B? ∼160–180
µG toward the SE corner, ∼150–160 µG toward the NE corner, and ∼180–200 µG toward
the area next to the NE corner. Although ∼50–90 µG can be evaluated toward the SW
corner, this value might be more uncertain than those toward the other areas due to the
larger uncertainty of the velocity width.The magnetic field strength evaluated here is

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higher than those measured around dark cloud complexes and prestellar cores, a few 10 µG
(e.g., Alves et al. 2008; Kandori et al. 2009, respectively), but smaller than those around HII
regions, a few mG (e.g., Houde 2004) and of a protostellar envelope, a few mG (Girart et al.
2006).
Recently, Houde et al. (2009) showed how the signal integration through the thickness of
the cloud and the area of the telescope beam affects on the measured angular dispersion and
apply their results to OMC-1. Based on their estimated number (N=21) of the independent
turbulent cells contained within the column probed by the telescope beam, they found that
a correction factor of 1/√N ∼ 0.2 is applicable to OMC-1. In our case, although the area
of the telescope beam is negligibly small due to the point sources, the thickness of the cloud
should be taken into account and the correction factor should be somewhat smaller than
∼ 0.5. If we assume that the effect of the cloud thickness is similar to that of OMC-1,
we obtain N ∼ 11, suggesting a factor of ∼ 0.3. Adopting this factor of ∼ 0.3, the above
estimated values are reduced by a factor of ∼ 0.6 and B?∼ 100 may be appropriate for the
ambient region of the Serpens cloud core, except the SW corner.
Here, we roughly derive the mass to magnetic flux ratio Mcloud/Ψ using our estimated
value of B ∼100 µG, and compare it with the critical value for a magnetic stability of
the cloud, (Mcloud/Ψ)critical = (4π2G)−1/2(Nakano & Nakamura 1978). With a formula
Mcloud/Ψ = (πR2µmHN)/(πR2B) = µmHN/B and the H2column density N ∼ 6 × 1022
cm−2where we estimated B, we derive Mcloud/Ψ ∼ 3.8 × (Mcloud/Ψ)critical, where R is a
radius of the cloud and mHis the mass of a hydrogen atom. Although this derived value is
slightly larger than the critical value, Mcloud/Ψ could be much larger in the inner region of the
cloud core because the column density of the inner region is much higher than those where
we estimated B, but the magnetic field may be slightly larger than that we estimated in the
ambient region, judged from the slowly curved shape of the magnetic field. We note that the
adopted strength of the magnetic field is that estimated for the projection of the magnetic
field in the plane of the sky, suggesting a slightly smaller Mcloud/Ψ than the estimated one.
These imply that the ambient region is marginally supercritical, while the inner region is
supercritical. This situation is considered to be quite consistent with the hourglass shape of
the magnetic field and with the cluster formation within the sub-clumps.
It is interesting to examine whether the magnetic field can maintain the outflow colli-
mation along the magnetic field in the ambient region of the sub-clumps, i.e., whether the
magnetic field can guide the outflows. The magnetic pressure, PB= B2/8π, is calculated to
be ∼ 4 ×10−10dyn, adopting B ∼ 100µG. Assuming the average density and velocity width
due to turbulence for the outflow to be 3 × 103cm−3, which would be consistent with the
optically thin condition of the high velocity gas (White et al. 1995), and 3 km s−1, which is