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THE ASTROPHYSICAL JOURNAL, 475 :211È223, 1997 January 20
1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.(
INTERFEROMETRIC IMAGING OF IRAS 04368]2557 IN THE L1527 MOLECULAR
CLOUD CORE: A DYNAMICALLY INFALLING ENVELOPE WITH ROTATION1
NAGAYOSHI OHASHI
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; nohashi=cfa.harvard.edu
MASAHIKO HAYASHI
SUBARU Project Office, National Astronomical Observatory, Mitaka, Tokyo 181, Japan
PAUL T. P. HO
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138
AND
MUNETAKE MOMOSE
Department of Astronomical Science, Graduate University for Advanced Studies,
Nobeyama, Minamimaki, Minamisaku, Nagano 384-13, Japan
Received 1996 May 31 ; accepted 1996 August 12
ABSTRACT
We report new interferometric observations of IRAS 04368]2557 (L1527) in 13CO (J \ 1È0), C18O
(J \ 1È0), and 2.7 mm continuum emission using the Nobeyama Millimeter Array. The continuum map
shows a well-deÐned emission peak with slightly extended features. The extended features are consistent
with an 800 km continuum map. The 13CO map shows blueshifted and redshifted outÑowing shells char-
acterized by a bipolar V-shape structure with a wide opening angle toward the east and west of the
central source. Near the systemic velocity, a slightly blueshifted X-shaped condensation was detected in
13CO with its peak coincident with the central source. The symmetrical distribution of the X-shaped
condensation centered on the central source suggests that it is a circumstellar envelope surrounding the
central source. The C18O map shows a Ñattened structure elongated in the north-south direction, per-
pendicular to the outÑow axis, centered on the central source. This Ñattened structure correlates spatially
with the 13CO X-shaped condensation. Both eastern and western edges of the Ñattened structure are
concave, as the 13CO X-shaped condensation also shows, and they are spatially well anticorrelated with
the distribution of the outÑowing shells in both blueshifted and redshifted velocities. The Ñattened struc-
ture is hence naturally interpreted as a disklike Ñattened envelope with an almost edge-on conÐguration.
Its radius and gas mass are estimated to be D2000 AU and D0.038 respectively.M
_
,
The edge-on Ñattened envelope has both rotational and radial motions with the latter dominant. The
large speciÐc angular momentum carried by the envelope gas implies that the radial motion can be infall
rather than outÑow. The infall and rotation velocities are D0.3 km s~1 and D0.05 km s~1, respectively,
at the envelope radius of 2000 AU. The Ñattened envelope is clearly not supported by rotation, but it is
dynamically infalling. Its mass infall rate is D1.1 ] 10~6 yr~1 at 2000 AU in radius. This massM
_
infall rate is consistent with that estimated from the bolometric luminosity of 1.4 and the mass of 0.1L
_
of the central star. On the assumption that the mass infall rate is constant with time, the age of theM
_
central star is estimated to be D105 yr, which is comparable to the typical age of protostars in Taurus,
even though the central star in L1527 is identiÐed as a very young class 0 source. The rotating motion of
the Ñattened envelope is opposite to the large-scale rotation of the L1527 cloud, suggesting that the rota-
tion of the Ñattened envelope did not originate from the large-scale rotation.
Subject headings: accretion, accretion disks È circumstellar matter È ISM: individual (L1527) È
ISM: kinematics and dynamics È stars: formation È stars: preÈmain-sequence
1. INTRODUCTION
Increasing attention has been paid to circumstellar
envelopes around embedded young stars. Observations of
circumstellar envelopes with high angular resolution, such
as interferometric observations at millimeter wavelengths,
are necessary for us to study the role of circumstellar
envelopes in the star formation process because their size is
typically a few thousands of AU, which corresponds to
1 Based on observations made at the Nobeyama Radio Observatory
(NRO). NRO is a branch of the National Astronomical Observatory, an
interuniversity research institute operated by the Ministry of Education,
Science, and Culture, Japan.
at the distance of nearby star-forming regions, such as[20A
Taurus. Recent improvements in the sensitivity of milli-
meter wavelength interferometers have allowed us to inves-
tigate the velocity Ðeld of circumstellar envelopes in detail,
so that our understanding about the kinematics of circum-
stellar envelopes has been changed. Interferometric obser-
vations of HL Tau in 13CO (J \ 1È0) revealed infall and
rotation in the Ñattened envelope of D3000 AU in diameter
Ohashi, & Miyama see also et al.(Hayashi, 1993; Cabrit
The infall motion of 1 km s~1 appears to dominate1996).
over the rotation of 0.2 km s~1 at a radius of 700 AU.
Infalling motion in the Ñattened envelope around L1551
IRS5ofD1kms~1 at a radius of 600 AU has also been
suggested from interferometric observations et al.(Ohashi
211
212 OHASHI ET AL. Vol. 475
see also et al. These new observations1996a; Saito 1996).
demonstrate that protostars are associated with Ñattened
infalling envelopes. Although previous interferometric
observations also showed Ñattened structures around
young stars, e.g., HL Tau (Sargent & Beckwith 1987, 1991),
L1551 IRS 5 et al. IRAS 16293 et(Sargent 1988), (Mundy
al. and L1489 (Ohashi et al. their kine-1992), 1991, 1996b),
matics, such as infall or rotation, have heretofore remained
poorly deÐned because of insufficient sensitivity and veloc-
ity resolution.
To study another example of an infalling envelope, we
have made interferometric observations of L1527, which is
one of the dense cores in the Taurus molecular cloud with a
heavily obscured IRAS source (IRAS 04368]2557) located
at the center. Although recent 800 km continuum observa-
tions suggested that there is a secondary source (L1527B) in
addition to the primary (L1527A) in L1527 Ladd, &(Fuller,
Hodapp hereafter we will focus mainly on the1996, FLH),
primary source in this paper and call it the central source
throughout the paper. This central source of 1.4 in bolo-L
_
metric luminosity is considered to be in the earliest(FLH)
evolutionary stage because of its so-called class 0 spectrum
Ward-Thompson, & Barsony and its low bol-(Andre , 1993)
ometric temperature & Ladd et al.(Myers 1993; Chen
A molecular bipolar outÑow whose axis is almost in1995).
the plane of the sky is associated with L1527 et(MacLeod
al. et al. This suggests that any Ñat-1994; Tamura 1996).
tened structure around the central star, if formed as theory
predicts, will have an edge-on geometry. Asymmetric line
proÐles with stronger blueshifted emission than redshifted
emission were detected in L1527, suggestive of infall,
although the proÐles were not Ðtted by spherical infall
models et al. Interferometric observations of(Myers 1995).
L1527 in 13CO and C18O(J\1È0) using the BIMA array
at resolution Evans, & Wang here-11.A9 ] 7.A8 (Zhou, 1996,
after suggested that the line proÐles with the interfer-ZEW)
ometer are also qualitatively consistent with the infall
model based on the collapse solution by Shu, &Terebey,
Cassen However, their maps did not directly demon-(1984).
strate infalling signatures because of insufficient sensitivity,
angular resolution, and the velocity resolution of their
observations.
In the present study, we have carried out new 13CO,
C18O(J\1È0), and 2.7 mm continuum observations of
L1527 using the Nobeyama Millimeter Array. In contrast
with we did not combine our interferometric dataZEW,
with single-dish data, thereby focusing only on the compact
structures (see This strategy, together with a factor of° 2).
2È4 better sensitivity, a factor of 2 better angular resolution,
and a factor of 2 better spectral resolution, produced a very
di†erent picture. Our 13CO maps show bipolar outÑowing
shells with a V-like shape as well as a circumstellar envelope
centered on the central source. Our C18O map shows a
Ñattened envelope of D2000 AU radius overlaying the
central source and perpendicular to the outÑow axis. The
velocity structure of the Ñattened envelope can be modeled
with great success in terms of the infalling motion of a disk
with rotation. We will discuss the nature of the Ñattened
envelope in detail as well as the evolutionary status of the
central protostar.
2. OBSERVATIONS
13CO and C18O(J\1È0) observations were made using
the Nobeyama Millimeter Array (NMA), which consists of
six 10 m antennas. SIS receivers with of D200KinT
sys
double sideband at the zenith were employed (Sunada,
Kawabe, & Inatani and spectral information was1993),
obtained with FX correlators with 1024 channels each
et al. We applied a 80 MHz Ðlter to the FX(Chikada 1987).
correlator, which resulted in D0.21 km s~1 velocity
resolution at the frequencies of 13CO and C18O. The 13CO
observations were carried out in 1995 January with the D
conÐguration (two tracks) and in 1995 February with the C
conÐguration (one track), while the C18O observations were
made in 1995 December with the D conÐguration (three
tracks) and in 1996 February with the C conÐguration
(three tracks). The projected baseline length in these observ-
ations ranged from 10 to 160 m, so that our observations
were insensitive to structures extended more than D56A,
which corresponds to D7800 AU at the distance to L1527
(140 pc; The phase and amplitude of the arrayElias 1978).
were calibrated by observing 0528]134, and the complex
passband of each baseline was determined from observ-
ations of 3C 454.3 or 0528]134. The Ñux density of
0528]134 (D5.9 Jy in the 13CO observations and D7.2 Jy
in the C18O observations) was estimated from observations
of Uranus on the assumption of its brightness temperature
of 130 K. After we subtracted continuum emission from the
calibrated u-v data, 13CO and C18O channel maps were
made with natural weight and CLEANed using the Astron-
omical Image Processing System (AIPS). The resultant
beam size was (P.A. \ 157¡) for 13CO and5.A9 ] 4.A76.A0
(P.A. \ 163¡) for C18O.] 4.A9
Two sets of 2.7 mm continuum data were obtained from
13CO and C18O data separately by averaging the line-free
channels. The two continuum maps with natural weight
were CLEANed using AIPS. The resultant 1 p rms noise
levels of the maps were 7.7 mJy beam~1 (from 13CO data)
and 4.7 mJy beam~1 (from C18O data), respectively. While
we detected the 2.7 mm continuum emission in both maps,
which were consistent with each other within the errors, the
data obtained from the C18O observations showed more
signiÐcant emission than that from the 13CO observations
because of the lower sensitivity of the 13CO observations
due to bad weather conditions. Therefore, we present only
the continuum map obtained from the C18O observations
in this paper.
3. RESULTS
3.1. 2.7 mm Continuum Emission
shows the 2.7 mm continuum map atFigure 1 6.A0 ] 4.A9
(P.A. \ 163¡) resolution, obtained from the C18O obser-
vations. Its peak position [R.A. decl.(1950) \ 4h36m49s.6,
(1950) \ 25¡57@21A] agrees with the position derived from
Owens Valley Radio Observatory (OVRO) observations at
2.7 mm Chandler, & Andre and NMA(Terebey, 1993)
observations at 2 mm et al. We will adopt(Ohashi 1996b).
this position as the position of the central source in this
paper. The peak Ñux density and total Ñux of the continuum
emission are measured to be 37 ^ 4.7 mJy beam~1 and
47 ^ 5.6 mJy, respectively, which are also consistent with
the results obtained by et al. The spectralTerebey (1993).
energy distribution (SED) of L1527 shows clearly that the
continuum emission at 2.7 mm originates from thermal dust
emission (e.g., et al.Ladd 1991).
Recent continuum observations at 800 km with JCMT
detected a fainter continuum source (called L1527B) located
No. 1, 1997 IRAS 04368]2557 213
FIG. 1.È2.7 mm continuum map. Contours are drawn every 1.5 p level
from 1.5 p (solid line) and from [1.5 p (dashed line). The 1 p level corre-
sponds to 4.4 mJy beam~1. The gray square indicates the position of the
800 km secondary source by and the gray ellipse represents the beamFLH,
size in FWHM.
20A northwest of the central source though very(FLH),
recent observations in 1.3 mm continuum emission with the
IRAM 30 m telescope do not conÐrm it In the(Andre 1996).
present continuum observations, the secondary source was
not detected, which is consistent with the IRAM result. This
might suggest that the secondary source does not exist. If
the secondary source were not detected because of insuffi-
cient sensitivity of our observations, then an upper limit to
its Ñux density at 2.7 mm is estimated to be D13 mJy (3 p
level).
The continuum emission appears to be marginally resolv-
ed: the emission extends to the northwest, and slightly
northeast and southwest at the 3 p level. The size of the
continuum emission estimated from Gaussian Ðtting is 7.A4
which is slightly larger than the synthesized beam] 5.A4,
size of Such extended features can also be seen in6.A0 ] 4.A9.
the 800 km continuum map by and the 1.3 mm contin-FLH
uum map with an D2 times larger beam than(Andre 1996)
ours, suggesting that these features may be real and more
extended. The deconvolved size of the continuum emission
corresponds to 600 ] 290 AU at the distance of L1527. This
size scale is larger than that of the compact dust disk
associated with the central star, D100 AU, predicted from
theoretical Ðttings to the SED of L1527 (e.g., Kenyon,
Calvet, & Hartmann This suggests that the extended1993).
emission arises from the envelope rather than the compact
disk.
3.2. 13CO (J \ 1È0)
13CO (J \ 1È0) emission was detected signiÐcantly at the
LSR velocities ranging from 3.41 to 7.65 km s~1, except for
5.54È6.18 km s~1, with a typical rms noise level of 190 mJy
beam~1 or 0.7 K in brightness (1 p), as shown in Figure 2.
Although the emission is weak in some channels, the detec-
tion may be real because the emission is detected in some
serial channel maps at the same positions. Within the veloc-
ity range from km s~1 to 4.69 km s~1, which areV
LSR
\ 3.41
blueshifted more than 1 km s~1 with respect to the systemic
velocity of D5.7 km s~1 (see et al. emissionOhashi 1996b),2
is not detected at the central source position, but weak
emission is detected on the east and west sides of the source.
Similarly, the emission redshifted by D0.5È2kms~1 from
the systemic velocity km s~1) is not coin-(V
LSR
\ 6.18È7.65
cident with the central source, but weak emission is located
on both the east and west sides of the source. In contrast,
the emission detected at km s~1, which areV
LSR
\ 4.69È5.54
D0.2È1kms~1 blueshifted with respect to the systemic
velocity, is coincident with the central source. It must be
noted that no redshifted emission coincident with the
central source was detected, even though blueshifted emis-
sion was detected toward the central source. The absence of
emission between 5.54 and 6.18 km s~1 is due to resolving
out extended components because of the lack of short
spacing data in the present observations. In fact, the
channel maps by obtained from combination ofZEW,
interferometer and single-dish observations, show 13CO
emission to be extended by D120A in this velocity range.
Such an extended feature cannot be detected in our data.
Note that the absence of the emission at the systemic veloc-
ity is not only due to the absence of short spacings, but also
due to the self-absorption of 13CO emission as seen in 13CO
spectra by Our observations show that the 13COZEW.
emission toward the central source is optically thick (see
° 3.4.2).
In order to examine the overall distributions of the 13CO
emission with better signal-to-noise ratio, we integrated the
channel maps over the above three di†erent velocity ranges,
i.e., 3.41È4.69 km s~1, 4.69È5.54 km s~1, and 6.18È7.65 km
s~1. In each of these velocity ranges, the channel maps
presented in basically show similar distributions ofFigure 2
the emission. Note that the weak emission to the east and
west of the central star in the channel maps becomes more
clear in the integrated intensity maps. In the map integrated
over 3.41È4.69 km s~1 a strong peak appears(Figure 3a),
D10A west of the source, and weak features are elongated to
the northwest and southwest from the peak, with several
peaks. The overall distribution at fainter levels seems to be a
V shape opened widely toward the west. There is also
fainter emission, detected to the east of the central source,
also with a marginal V shape distribution opened widely
toward the east. The western and eastern V-shaped com-
ponents are distributed symmetrically with respect to the
central source and resemble the edges of a biconical struc-
ture. The same biconical/bipolar structure is also seen in the
map integrated from 6.18 to 7.65 km s~1 Note that(Fig. 3c).
in both these maps there is no emission coincident with the
central source. In contrast, in the map integrated over 4.69È
5.54 km s~1 a strong peak appears almost at the(Fig. 3b)
position of the central source with a secondary peak
occurring D15A to the southeast of the central source. At
fainter levels, the emission is elongated to the northeast,
southeast, northwest, and southwest, forming an X-shaped
2 This systemic velocity of 5.7 km s~1 was estimated from C18O(1È0)
observations with the Nobeyama 45 m telescope at Nobeyama Radio
Observatory (NRO) and is consistent with the present C18O data taken
with the NMA. Note that the LSR velocity measured with the NMA and
the 45 m telescope at NRO has been shifted by D0.27 km s~1 for the
Taurus region from those measured at other radio observatories since 1990
December. This is because in calculating the LSR velocity NRO assumes a
basic solar motion, which is slightly di†erent from the conventional basic
solar motion.
214 OHASHI ET AL. Vol. 475
FIG. 2.È13CO (J \ 1È0) channel maps with 0.21 km s~1 velocity resolution. The corresponding central LSR velocities of individual velocity bins are
denoted at the top in each panel. The systemic velocity is D5.7 km s~1. Solid contours are drawn every 2 p level from 2 p, and dashed contours represent [2
p level. The 1 p level corresponds to 190 mJy beam~1 or 0.7 K in brightness temperature. The cross in each panel shows the position of the central source
derived from the central position of the 2.7 mm continuum emission. The gray ellipse at the bottom left corner in the Ðrst panel indicates the FWHM beam
size.
structure of D4000 AU maximum extension with its center
coincident with the central source. This X-shaped conden-
sation is spatially located just between the blueshifted and
redshifted bipolar V compontents.
We note that the V-shaped structures may be part of the
outÑowing shells or cones ejected from the central regions
in the east-west direction. Both the 13CO outÑow imaged
with the BIMA array and the 12CO outÑow imaged(ZEW)
with the NMA et al. appear to Ðt inside our(Tamura 1996)
V-shaped structures. In addition, the V-shaped structures
delineate a 2.2 km infrared reÑection nebula, which orig-
inates from scattering of radiation from the central star by
the dust in the outÑow et al. Our 13CO map(Tamura 1996).
emphasizes the shell structure more than that by ZEW
because the extended smoother component is resolved out
by the interferometer. The outÑowing shell associated with
L1527 has also been mapped in CS (J \ 2È1) with the NMA
et al. although only the southern part of the(Ohashi 1996b),
shell was detected in CS. The opening angle of the V-shaped
shells is almost 90¡, which is wider than the estimates by
The nearly identical spatial distribution of the blue-ZEW.
shifted and redshifted V-shaped components suggests
strongly that the axis of the outÑow is almost in the plane of
the sky, such as the outÑow associated with B335 et(Hirano
al. estimated the angle between the outÑow axis1992). ZEW
and the plane of the sky to be 6¡È8¡.
No. 1, 1997 IRAS 04368]2557 215
FIG. 3.È13CO integrated channel maps. Contours are drawn in the same manner as in The labels are the same as in While V-shapedFig. 1. Fig. 2.
components are demonstrated in (a) and (c), the X-shaped condensation is shown in (b). (a) Integrated from to 4.69 km s~1, which are blueshiftedV
LSR
\ 3.41
by more than 1 km s~1 with respect to the systemic velocity. (b) Integrated from 4.69 to 5.54 km s~1, which are blueshifted by D0.2È1kms~1.(c) Integrated
from 6.18 to 7.65 km s~1, which are redshifted by D0.5È2kms~1.
Is the X-shaped condensation the inner part of the
outÑow such as entrained gas, or is it a circumstellar
envelope associated with the central source? Its coincidence
with the central star as well as its clear spatial separation
from both the outÑowing shells, as was shown in Figure 3,
may suggest that the X-shaped condensation is a circum-
stellar envelope associated with the central source, while the
X morphology may suggest that some part of the X conden-
sation may be interacting with the outÑow. A striking point
is that the X-shaped condensation shows only blueshifted
emission without corresponding redshifted emission. It
seems that this can be attributed mainly to confusion with
an extended redshifted component which is suppressed by
the interferometer. The origin of the X condensation and its
asymmetric velocity structure becomes clearer with the
examination of the C18O emission in °° and3.3 4.1.
3.3. C18O(J\1È0)
We detected C18O(J\1È0) emission only in the velocity
range from km s~1 to 6.39 km s~1 with aV
LSR
\ 4.90
typical sensitivity of 88 mJy beam~1 or 0.3 K in brightness
(1 p). Note that because C18O is optically thin, the outÑow
that is seen in 12CO and 13CO is not detected in this line.
(Plate 18) shows the C18O total intensity mapFigure 4
integrated over the above velocity range. We can see a clear
Ñattened structure, which is well resolved at the present
angular resolution, with a peak coincident with the position
of the central source. The Ñattened structure is elongated
symmetrically across the central source in the north-south
direction and is almost perpendicular to the axis of the
12CO outÑow, with an apparent size of in15.A5 ] 8.A5
FWHM, corresponding to 2200 ] 1200 AU. There are faint
extensions to the northeast and southeast and weakly to the
northwest and southwest. The east and west sides of the
Ñattened structure can be described as concave. Compari-
son with the C18O map of L1527 obtained from com-
bination of both single-dish and interferometric data (ZEW)
shows that our map detects only the compact structures
around the central source.
The Ñattened structure perpendicular to the outÑow can
be interpreted naturally as a disk or a disklike envelope
around the central source in L1527. Because the axis of the
outÑow is almost in the plane of the sky, as was suggested in
the previous section, the disk associated with L1527 must
be nearly edge-on. Hence, the resolved size of the Ñattened
structure (2200 ] 1200 AU) suggests that it is not spatially
thin. Otherwise the structure should not be resolved along
its minor axis (east-west direction) with the present angular
resolution. Moreover, the concave morphology of the Ñat-
tened condensation suggests that the edges are Ñared.
Therefore, we propose that the C18O emission traces a disk-
like envelope rather than a thin disk, as was implied from
theoretical calculations (Galli & Shu 1993a, 1993b;
et al. Calvet, & BossHartmann 1994; Hartmann, 1996;
Hanawa, & NakanoNakamura, 1995).
(Plate 19) compares the Ñattened C18O envelopeFigure 5
with the 13CO structures presented in The 13COFigure 3.
X-shaped condensation correlates well with the Ñattened
C18O envelope (Fig. 5b). This coincidence suggests that the
X-shaped condensation traces basically the same circum-
stellar material as the C18O emission traces, even though
some part of the X condensation may be interacting with
the outÑow. At the same time, Figures 5a and 5c show that
the Ñattened envelope is located just between the bipolar
V-shaped outÑowing shells, and that the east and west
concave boundaries of the Ñattened envelope are well traced
with the V-shaped shells. This anticorrelation between the
outÑowing shells and the Ñattened envelope supports a
picture in which a bipolar molecular cavity is evacuated
with a wide opening angle when a molecular outÑow is
ejected from the vicinity of a central star that is embedded
in a circumstellar envelope elongated and perpendicular to
the outÑow.
illustrating the channel maps of C18O, showsFigure 6,
the detailed velocity structures of the Ñattened envelope. At
the most blueshifted velocity of 5 km s~1, weak emission is
detected at the position of the central source with an exten-
sion to the south. At 5.21 km s~1, a peak appears at D3A
south of the central source with a component elongated to
the south. In addition to this prominent emission, much
weaker emission extends to the northeast of the source. The
emission becomes most prominent at 5.43 km s~1, where an
elongated structure in the north-south direction can be seen
with a peak almost coincident with the central source posi-
tion and another weaker peak located at D10A north to the
central source. At 5.64 km s~1, close to the systemic velocity
216 OHASHI ET AL. Vol. 475
FIG. 6.ÈC18O channel maps with 0.21 km s~1 velocity resolution. The corresponding central LSR velocities of individual velocity bins are denoted at the
top left corner in each panel. The systemic velocity is D5.7 km s~1. Contours are drawn in the same manner as in The 1 p level corresponds to 88 mJyFig. 4.
beam~1 or 0.3 K. The labels are the same as in Fig. 2.
(D5.7 km s~1 ; see the emission becomes much° 3.2),
weaker and is located at the position of the central source.
This might be due to resolving out of extended features. At
5.85 km s~1, the emission extends to the north side of the
source with a slight extension to the south. At 6.07 km s~1,
a faint hourglass-like emission centered on the central
source can be seen in the north-south direction with a weak
peak at D3A north of the central source. At the most red-
shifted velocity, 6.28 km s~1, weak emission is detected
again toward the central source. The radius of the Ñattened
envelope is estimated to be D2000 AU from the maximum
extent of the emission at 5.43 km s~1.
The above inspection of the channel maps shows that the
emission peak appears to the south of the central source at
blueshifted velocities, and to the north at redshifted veloci-
ties. Such a velocity gradient along the major axis of the
Ñattened envelope can be explained in terms of rotation of
the envelope. We note, however, that there is a north-south
elongation across the central star at both blueshifted and
redshifted velocities, even though the emission peak shifts
from south to north as the velocity increases. Such a veloc-
ity structure cannot be explained by pure rotation. Hence,
an additional radial motion along the plane of the Ñattened
envelope, such as infall, must be present together with rota-
tion. We will discuss the kinematics of the Ñattened
envelope in detail in In the newly detected° 4.1. Figure 7,
components in the present observations, i.e., the 13CO
V-shaped outÑowing shells, the 13CO X-shaped condensa-
tion, and the C18O Ñattened envelope with both radial and
rotational motions, are visualized as a schematic picture
together with components detected previously in other
observations.
3.4. Mass
3.4.1. 13CO OutÑowing Shell
Assuming local thermodynamic equilibrium, we esti-
mated the gas masses contained in the 13CO outÑowing
shells as follows:
M
gas
\ 5.37 ] 10~5T
ex
exp
A
5.29
T
ex
B
q
13
CO
1 [ exp ([q
13
CO
)
]
A
d
140 pc
B
2
C
10~6
X(13CO)
DP
S
l
dv M
_
, (1)
No. 1, 1997 IRAS 04368]2557 217
FIG. 7.ÈA schematic illustration of the newly detected components in
the present observations, i.e., the 13CO V-shaped outÑowing shells, the
13CO X-shaped condensation, and the C18O Ñattened envelope with both
infall and rotation. The L1527 dense core was observed originally in NH
3
by & Myers and the 12CO outÑow was mapped byBenson (1989),
et al. and et al.MacLeod (1994) Tamura (1996).
where is the excitation temperature, d is the distance toT
ex
the source, X(13CO) is the fractional abundance of 13CO
with respect to and is the optical depth of 13CO.H
2
, q
13
CO
Because outÑowing gas is generally thought to be opti-
cally thin in 13CO (e.g., & Lada we assumeMargulis 1985),
Upper limits in our C18O observations of theq
13
CO
> 1.
outÑowing shells (1 p) imply Because theq
13
CO
\ 0.5.
outÑow in L1527 was detected in CO (J \ 6È5) emission
et al. we assume also that is high (see(MacLeod 1994), T
ex
also For K and X(13CO) \ 10~6, the gasZEW). T
ex
\ 50
masses of the outÑowing shells are on the order of 10~2 M
_
(see Comparing with the total Ñux of the 13COTable 1).
outÑow derived from combination of single dish and inter-
ferometric observations we Ðnd that only D15%(ZEW),
of the total mass of the 13CO outÑow is within the shell
structures.
3.4.2. C18O Flattened Envelope
Similar to the 13CO case mentioned above, gas mass
contained in the C18O Ñattened envelope can be estimated
from the C18O integrated intensity using the following
TABLE 1
GAS MASSES OF 13CO OUTFLOWING SHELLS
BLUESHIFTED SHELL REDSHIFTED SHELL
/ S
v
dv Mass / S
v
dv Mass
DIRECTION (Jy km s~1) (10~3 M
_
) (Jy km s~1) (10~3 M
_
)
East ....... 0.57 1.7 1.5 4.4
West ...... 2.0 6.0 1.5 4.4
Total ...... 2.6 7.7 3.0 8.8
formula:
M
gas
\ 5.49 ] 10~4T
ex
exp
A
5.27
T
ex
B
q
C
18
O
1 [ exp ([q
C
18
O
)
]
A
d
140 pc
B
2
C
10~7
X(C18O)
DP
S
l
dv M
_
, (2)
where is the optical depth of C18O and X(C18O) is theq
C
18
O
fractional abundance of C18O with respect to AssumingH
2
.
X(C18O) \ 1.8 ] 10~7 Langer, &q
C
18
O
> 1, (Frerking,
Wilson and K et al. the1982), T
ex
\ T
dust
\ 26 (Ladd 1991),
C18O total integrated intensity of 3.0 Jy km s~1 for the
Ñattened envelope gives us a gas mass of 3 ] 10~2 TheM
_
.
observed ratio of brightness temperatures of 13CO to C18O
is D2, suggesting that (see Linke, &q
C
18
O
D 0.5 Myers,
Benson The mass estimates would then be higher by1983).
D30%, or 3.8 ] 10~2 (see Note that theM
_
eq. [2]).
derived mass is more than 1 order of magnitude smaller
than the core mass of L1527 derived by This isZEW.
because our observations are not sensitive to the extended
components. Even so, most of the emission from the Ñat-
tened envelope may be detected in the present observations,
because large-scale C18O in L1527 is extended mainly in the
east-west direction which is perpendicular to the(ZEW),
direction of the Ñattened envelope.
4. DISCUSSION
4.1. Kinematics of the Flattened Envelope
As was discussed in the kinematics of the Ñattened° 3.3,
envelope can be explained in terms of the combination of
rotation and radial motion of the Ñattened envelope. One
possible radial motion is infall toward the central star.
Although expansion is also possible, the infalling motion is
more likely for the Ñattened envelope, as discussed later. We
discuss here the kinematics of the Ñattened envelope using a
simple model in which a disk has both rotation and infall.
Note that we consider that the Ñattened envelope surrounds
a single star, even though the extended L1527 cloud prob-
ably has an additional source, as suggested by WeFLH.
assume further that the stellar mass dominates over the disk
mass.
In our simple model, we assume a spatially thin disk of
2000 AU radius with an edge-on conÐguration with respect
to the observers, even though the Ñattened envelope is not
spatially thin. In addition, we suppose that the disk is con-
tracting dynamically with rotation. In that case, the angular
momentum of the disk is conserved. Therefore, we assume
that the rotational velocity is inversely proportional to the
radius of the disk, while the infall velocity is inversely pro-
portional to the square root of the radius. For such rota-
tion, the rotational velocity is independent of the central
stellar mass but depends on the initial angular momentum,
or on the rotational velocity at the outer radius. Details of
the model are described in the Appendix.
presents the observed position-velocity diagramFigure 8
of the Ñattened envelope along the north-south direction
across the central source (Fig. 8a) and the corresponding
diagram obtained from the model, in which the central
stellar mass is 0.1 and the rotational velocity is 0.05 kmM
_
s~1 at 2000 AU in radius The observed data in(Fig. 8b).
show the following characteristics:Figure 8a
1. At higher blueshifted and redshifted velocities, the
emission is conÐned to the vicinity of the central star, while
218 OHASHI ET AL. Vol. 475
FIG. 8.ÈPosition-velocity diagram of C18O, cutting along the north-
south direction across the central source, is compared with position veloc-
ity diagrams obtained from model calculations. The vertical and
horizontal lines in each panel show the systemic velocity and the position
of the central source, respectively. (a)C18O position-velocity diagram
obtained from observations. Contours are drawn in the same manner as in
(b) Position-velocity diagram obtained from a model, where a diskFig. 6.
of 2000 AU in radius has both dynamical infall and rotation with a 0.1 M
_
central star. The infall velocity yielded by the 0.1 central star is D0.3M
_
km s~1 at 2000 AU in radius, while the rotation velocity at the same radius
is assumed to be 0.05 km s~1.(c) Same as (b), but obtained from a model in
which a disk of 2000 AU in radius has only Kepler rotation with a 0.1 M
_
central star. The resultant Kepler motion at 2000 AU in radius is D0.2
km s~1.
the emission extends to the north and south as the velocity
approaches the systemic velocity.
2. Two emission peaks appear in the vicinity of the
source in addition to a peak at D1400 AU north of the
source: one is D0.3 km s~1 blueshifted and the other is
D0.2 km s~1 redshifted. The blueshifted peak is shifted to
the south from the position of the central source with an
extension to the higher blueshifted velocity, while the red-
shifted peak is shifted to the north from the center with any
extension to the higher redshifted velocity.
3. Near the systemic velocity, the emission is relatively
weak.
These three characteristics are well reproduced in the
diagram obtained from the model except for the peak at
D1400 AU north, indicating that dynamical infall and rota-
tion of a disk can explain the kinematics of the Ñattened
TABLE 2
PHYSICAL PARAMETERS OF THE INFALLING ENVELOPE WITH
ROTATION AROUND IRAS 04368]2557
Radius (AU) ..................................... D2000
Mass (M
_
) ....................................... D0.04
Infalling velocity (km s~1, at 2000 AU) ...... D0.3
Rotation velocity (km s~1, at 2000 AU) ...... D0.05
Mass infall rate (M
_
yr~1, at 2000 AU) ...... D10~6
envelope. In contrast, where Kepler motion withFigure 8c,
a 0.1 central star is represented, shows clearly that aM
_
disk with only rotation cannot explain the observed data.
Similarly, a disk with only infall cannot explain the
observed data: in the case of only infall, the obtained
diagram shows two peaks located just at the position of the
central source (i.e., on the horizontal axis through the
center; see the not shifted from the central posi-Appendix),
tion as observed. Simultaneous existence of infall and rota-
tion is, therefore, essential to explain the kinematics of the
Ñattened envelope.
The shape of the position-velocity diagram calculated
from the model including both infall and rotation depends
on the central stellar mass and the rotational velocity at the
outer radius. In the present calculation, we adopted a
central stellar mass of 0.1 which yields a dynamicalM
_
,
infall velocity of D0.3 km s~1 at 2000 AU radius, and a
rotational velocity of 0.05 km s~1 at the same radius. The
0.1 central stellar mass is consistent with that estimatedM
_
from the bolometric luminosity (1.4 of the centralL
_
; FLH)
source. If we use a higher stellar mass, such as 0.3 theM
_
,
two peaks in the vicinity of the central source in Figure 8b
will appear at higher blueshifted and redshifted velocities,
which is inconsistent with the observations. On the other
hand, if we use a higher rotational velocity, such as 0.2 km
s~1 at 2000 AU, the resultant position-velocity diagram
resembles those calculated with only rotation (see the
This suggests that the envelope must rotateAppendix).
slower as compared with infall. This second restriction leads
us to another important point: that the rotating motion of
the Ñattened envelope is not Keplerian. In the case in which
a disk is accreting with Kepler rotation, such as a viscous
accreting disk, the radial motion is very small as compared
with the rotational velocity, which is inconsistent with the
second restriction above. This suggests that the envelope is
not supported rotationally but is contracting dynamically.
Physical parameters of the infalling envelope with rotation
are summarized in Table 2.
One might argue that the observed result could be
explained in terms of a radially expanding disk with rota-
tion rather than an infalling disk with rotation. Indeed, we
cannot distinguish a radially expanding motion from a radi-
ally infalling motion because the Ñattened envelope is
almost However, if the Ñattened envelope orig-edge-on.3
inates from expanding material ejected from the central
star, or from the vicinity of it, the ejected matter may not
have enough angular momentum imparted from the star. If
a central protostar rotates at breakup speeds, D140 km s~1
Adams, & Lizano et al. then the(Shu, 1987; Shu 1988),
3 If a disk is not edge-on, we can Ðnd from morphology of an associated
outÑow which side of the disk is the far side, so that we can distinguish
radial expansion from radial infall in the disk plane. In this case, however,
we cannot distinguish expanding motions in the outÑow from infall in the
disk.
No. 1, 1997 IRAS 04368]2557 219
ejected matter rotates at 0.001 km s~1 at 2000 AU in radius,
which is really 2 orders of magnitude smaller than the
detected rotation of 0.05 km s~1 for the Ñattened envelope.
If the additional angular momentum is provided by a stellar
wind, then a very high wind velocity, such as º500 km s~1,
is required & Shu This fact supports our infall(Najita 1994).
scenario.
Another point that may support our infall scenario is the
asymmetry of intensity between the stronger blueshifted and
the weaker redshifted emission seen in AccordingFigure 8a.
to a spherical molecular envelope with infallZhou (1992),
shows asymmetric line proÐles with stronger blueshifted
emission when it is observed in relatively optically thick line
emission: blueshifted emission arising from the back side of
the envelope traces gas close to the central source, where the
temperature of the envelope is relatively high, while red-
shifted emission arising from the front side of the envelope
traces gas far away from the center, where the temperature
of the envelope is relatively low. Such asymmetric line pro-
Ðles were detected from L1527 in other observations (Myers
et al. Because the Ñattened envelope is not1995; ZEW).
spatially thin and almost edge-on (see ZhouÏs argu-° 3.3),
ment can be applied to the present data even if we do not
have spherical symmetry, as long as C18O in the Ñattened
envelope is relatively optically thick.
The 13CO X condensation, which traces the same circum-
stellar gas as the Ñattened envelope, also shows a similar
asymmetric velocity structure, in which only blueshifted
emission was detected while redshifted emission was sup-
pressed because of missing short spacings (see ° 3.2).
Because the 13CO emission from the circumstellar envelope
is more optically thick than the C18O (see the 13CO° 3.4.2),
redshifted emission from the envelope must trace gas
located further away from the central star as compared with
the redshifted C18O emission. This suggests that the
envelope observed in the 13CO redshifted emission must be
more extended than the gas traced by the redshifted C18O.
This may be the reason why the redshifted 13CO emission
from the X condensation is resolved out. In contrast, the
13CO blueshifted emission from the circumstellar envelope
must trace gas located closer to the central star (i.e., more
compact) than the redshifted C18O. Thus, the blueshifted
13CO is not suppressed by the interferometer.
We must note that part of the Keplerian disk of 100 AU
scale around the central star may be entrained by a high-
velocity wind. Thus, the Ñattened envelope might be
a†ected by such an entrained outÑow/expanding motion
et al. Even so, it is likely that the entrained(Cabrit 1996).
matter moves in the vicinity of the concave surfaces of the
envelope on the east and west sides, where the molecular
outÑow may interact with the envelope. Hence, the fraction
of the entrained matter in the Ñattened envelope must be
small. Moreover, if the whole Ñattened envelope might be
expanding, then its mass outÑow rate would be D10~6 M
_
yr~1, which is comparable to the mass accretion rate onto
the central star estimated from the bolometric luminosity of
the central source (see This means that matter is° 4.2).
ejected through the Kepler disk at the same rate as the
accretion onto the central star. Such a situation may be
physically unnatural. Taking the above discussion into con-
sideration, we conclude that infall motions with rotation
seem to be more appropriate than expanding motions with
rotation for explaining the kinematics of the Ñattened
envelope.
If our infall scenario is correct, the dynamically infalling
envelope with rotation should form a centrifugally sup-
ported disk at the radius at which the infall velocity is com-
parable to the rotation velocity et al. et(Hayashi 1993; Lin
al. Using the 0.1 stellar mass and the 0.05 km s~11994). M
_
rotation at 2000 AU in radius, the radius of the centrifugally
supported disk is estimated to be D100 AU, which is com-
parable to the value predicted from Ðttings to the SED of
the central star (e.g., et al.Kenyon 1993).
4.2. Mass Infall Rate of the Flattened Envelope and
Evolutionary Status of the Central Star
We estimate the mass infall rate of the Ñattened envelope
using the formula where R is the radius ofM0
R
\ MV
R
/R,
the envelope, is the mass infall rate at R, M is the massM0
R
of the envelope within R, and is the infall velocity at R.V
R
From M \ 0.038 (see and km s~1 atM
_
° 3.4.2), V
R
\ 0.3
R \ 2000 AU (see the mass infall rate is estimated to° 4.1),
be D1.1 ] 10~6 yr~1. The derived mass infall rate isM
_
consistent with the mass accretion rate onto the central star
of 1.8] 10~6 yr~1, derived from the bolometric lumi-M
_
nosity of 1.4 and the central stellar mass of 0.1L
_
(FLH)
In contrast to L1527, HL Tau et al.M
_
. (Hayashi 1993)
and L1551 IRS 5 et al. show a higher mass(Ohashi 1996a)
infall rate by 1 order of magnitude. This is not surprising
because the bolometric luminosity of L1527 is 1 order of
magnitude smaller than those of HL Tau and L1551 IRS 5.
Such di†erences in mass infall rate in the envelope may
result in di†erences in Ðnal mass of the central sources.
The 0.1 central stellar mass is small as comparedM
_
with the typical mass of 0.4È0.8 for preÈmain-sequenceM
_
stars in Taurus & Kuhi suggesting that the(Cohen 1979),
mass infall in the envelope may continue for at least a
few ] 105 yr after the present epoch. The mass of the Ñat-
tened envelope is, however, only D0.04 which will beM
_
,
consumed in 4000 yr at the mass infall rate of 10~6 M
_
yr~1. This suggests that the more extended envelope in
L1527 should accrete onto the Ñattened envelope and even-
tually onto the central star. et al. detectedMyers (1995)
asymmetric line proÐles over a 40A region in L1527, indicat-
ing that the infalling region may be more extended than the
size scale of the Ñattened envelope.
The small central stellar mass of 0.1 might suggestM
_
that the central star is extremely young, as expected from
the result that the central source is identiÐed as a class 0
source et al. However, we must note that the(Andre 1993).
mass infall rate in the envelope is also small: the small
central stellar mass may be attributed to the small mass
infall rate. If the mass infall rate in the envelope is almost
constant in the star formation process on average, it takes
D105 yr to form the 0.1 star at the mass infall rate ofM
_
10~6 yr~1. This means that the age of the central starM
_
may be D105 yr, which is a typical age for protostars in
Taurus et al. et al. If this(Beichman 1986; Kenyon 1990).
argument is correct, the central source is not extremely
young, even though the SED of the central source is charac-
terized by the class 0 spectrum et al. The SED(Andre 1993).
of the central source may be a†ected by high extinction
resulting from the edge-on geometry of the Ñattened
envelope et al.(Tamura 1996).
4.3. Comparison with the Rotation of the L 1527 Cloud Core
We found from the present observations that the Ñat-
tened envelope of 2000 AU in radius in L1527 rotates
220 OHASHI ET AL. Vol. 475
counter-clockwise as viewed from the east side of the Ñat-
tened envelope. On a larger scale than the Ñattened
envelope, the L1527 molecular cloud core shows a velocity
gradient, which may also be identiÐed as rotation.
et al. who analyzed data of L1527Goodman (1993), NH
3
obtained by & Myers found that theBenson (1989), NH
3
core of 0.1 pc in radius has a velocity gradient from north to
south; i.e., the blueshifted emission is located to theNH
3
north of the source, and the redshifted emission is located to
the south. If this is rotation, the core rotates clockwise as
viewed from the east side of the core: the rotational direc-
tion of the cloud core on a large scale is opposite to that of
the Ñattened envelope on a small scale. Moreover, the veloc-
ity gradient of the core gives a relatively large speciÐcNH
3
angular momentum, 8.14 ] 10~3 km s~1 pc, corresponding
to a rotation of D0.8 km s~1 at 2000 AU in radius on the
assumption that the rotation velocity is inversely pro-
portional to the radius of the cloud core (the case of the
angular momentum conservation). This rotation velocity is
more than 1 order of magnitude larger than the observed
rotational velocity of the Ñattened envelope at 2000 AU in
radius.
The inconsistency in rotation between the large and small
scales in L1527 suggests that the rotation on the small scale
might not originate from the rotation on the large scale, but
rather via some other mechanisms such as magnetic Ðeld.
Alternatively, the velocity gradient on the large scale may
not be rotation but rather due to the outÑow or motions of
some small clumps. Indeed some cores presented by
et al. show velocity gradients that are dueGoodman (1993)
to motions other than rotation.
5. CONCLUSIONS
We carried out interferometric observations of L1527 in
13CO, C18O(J\1È0), and 2.7 mm continuum emission
using the NMA. The main results are summarized as
follows:
1. The 2.7 mm continuum emission had a well-deÐned
peak with a slightly extended structure. The peak position
and Ñux density of the emission are consistent with previous
measurements with interferometers.
2. The 13CO maps showed bipolar V-shaped com-
ponents with wide opening angles toward the east and west
of the star at the velocities more than 1 km s~1 blueshifted
and redshifted with respect to the systemic velocity. The
bipolar V-shaped components delineate well the 12CO
outÑow, suggesting that the V-shaped emission originates
from outÑowing cones or shells.
3. At the velocities blueshifted by less than 1 km s~1,an
X-shaped 13CO condensation was seen with its peak coin-
cident with the position of the central source. No 13CO
emission was detected toward the central star at the corre-
sponding redshifted velocities. The X condensation is dis-
tributed symmetrically with respect to the central star and is
spatially separated from the outÑowing shells. The X con-
densation is hence considered to be a circumstellar envelope
associated directly with the central star.
4. The C18O map showed a well-resolved Ñattened com-
ponent elongated in the north-south direction, almost per-
pendicular to the outÑow axis, with concave boundaries on
the east and west sides of the central star. This Ñattened
structure, spatially coincident with the 13CO X-shaped con-
densation, is interpreted naturally as a Ñattened disklike
envelope associated with the central star. The gas mass and
radius of the Ñattened envelope are estimated to be D0.038
and D2000 AU, respectively.M
_
5. The Ñattened envelope seen in C18O has a velocity
structure that can be explained in terms of the combination
of both infall and rotation in an edge-on disk. According to
a simple model calculation, it is found that the kinematics of
the envelope can be characterized by the infalling and rota-
tional velocities of D0.3 km s~1 and D0.05 km s~1, respec-
tively, at the radius of 2000 AU from a central star of D0.1
Such a slow rotational velocity compared with infallM
_
.
suggests that the envelope is not supported rotationally, but
dynamically infalling.
6. The mass infall rate of the Ñattened envelope is esti-
mated to be D1.1 ] 10~6 yr~1 at 2000 AU in radius.M
_
This rate is consistent with that onto the central star esti-
mated from the bolometric luminosity of the central star
and the central stellar mass of 0.1 The age of theM
_
.
central star is estimated to be D105 yr using the derived
mass infall rate and the stellar mass on the assumption that
the mass infall rate is constant with time. The derived age is
comparable to a typical age of protostars in Taurus, which
may suggest that the central star is not extremely young,
even though the central star is identiÐed as a class 0 source.
7. If the previously reported velocity gradient of the
L1527 cloud originates from the rotation, then thisNH
3
rotation on a large scale is in the opposite direction to the
rotation of the Ñattened envelope, with a larger speciÐc
angular momentum than the Ñattened envelope. This sug-
gests that the rotation of the Ñattened envelope may not be
directly related to the rotation of the L1527 molecular cloud
core on a large scale.
We acknowledge the sta† members of NRO. We would
like to thank P. Andre for showing us a new 1.3 mm contin-
uum map of L1527 prior to publication. We also thank T.
Hanawa, L. Hartmann, J. Najita, T. Nakamoto, T. Nakano,
and K. Tomisaka for fruitful discussions. An anonymous
referee provided invaluable suggestions that improved the
paper. N. O. is supported by a Smithsonian Postdoctoral
Fellowship. P. T. P. H. is supported in part by NASA Grant
NAGW-3121.
APPENDIX
In this we describe calculations of position-velocity diagrams using a simple model discussed in We assumeAppendix, ° 4.1.
a spatially thin disk of 2000 AU radius with an edge-on conÐguration with respect to observers. As illustrated in Figure 9,
Cartesian coordinates within the disk plane are adopted with the x-axis along the line of sight and the y-axis as the projected
distance in the plane of the sky across the disk plane.
In the present model, the disk has both dynamical infall and rotation. The infall velocity is inversely proportional to the
square root of the disk radius, while the rotational velocity is inversely proportional to the radius because of angular
No. 1, 1997 IRAS 04368]2557 221
FIG. 9.ÈSchematic illustration of our model. A disk with both infall and rotation is edge-on with respect to the observers.
momentum conservation. Using the coordinates in the infall and rotational velocities at the position (X, Y ) areFigure 9,
written as
V
infall
\
(2GM
*
)1@2
(X2]Y2)1@4
, (A1)
V
rotation
\ V
rotation
0
R
d
(X2]Y2)1@2
, (A2)
where G is the gravitational constant, is the central stellar mass, is the disk radius, and is the rotational velocityM
*
R
d
V
rotation
0
at We adopted AU in this calculation. Note that the rotational velocity is independent of but depends onR
d
. R
d
\ 2000 M
*
Detectable components of the infall and rotation are the velocities projected onto the line of sight. Hence, theirV
rotation
0 .
observable components are written, respectively, as
V
infall
obs \ V
infall
X
(X2]Y2)1@2
\
(2GM
*
)1@2X
(X2]Y2)3@4
, (A3)
V
rotation
obs \ V
rotation
Y
(X2]Y2)1@2
\ V
rotation
0
R
d
Y
X2]Y2
. (A4)
By adding to we obtain the observed velocity including both the infall and rotation as below,equation (A3) equation (A4),
V
total
obs (X, Y ) \
(2GM
*
)1@2X
(X2]Y2)3@4
] V
rotation
0
R
d
Y
X2]Y2
. (A5)
The observed brightness temperature was simply assumed to be proportional to the disk column density integrated along
the line of sight. We suppose that the disk surface density has a power-law dependence on the disk radius with an index p, i.e.,
&(X, Y ) P [(X2]Y2)1@2]p, where & is the disk surface density. We adopted p \[1.5 in the present calculation. We
calculated both and & at (X, Y ) every 5 AU along the x-axis and every 10 AU along the y-axis with limitation ofV
total
obs
(X2]Y2)1@2 ¹ R
d
.
To illustrate position-velocity diagrams, we calculated integrated surface densities by summing up the disk surface density
along the line of sight (i.e., along the x-axis) for each Y as follows:
&(V3 , Y ) \ ;
X/X
1
[&(X, Y )] if V
1
¹ V (X
1
, Y ) \ V
2
, (A6)
by stepping every 5 AU from [2000 to 2000 AU and [0.8, ...,0.7km s~1 with km s~1.InX
1
V
1
\[0.9, V
2
\ V
1
] 0.21
is the horizontal axis of the position-velocity diagram with a grid of 0.1 km s~1. The values of are given byequation (A6), V3 V3
The velocity width between and km s~1, is equivalent to the actual velocity resolution of(V
1
] V
2
)/2. V
1
V
2
, V
2
[ V
1
\ 0.21
the observations. After this summation, the brightness temperature of position-velocity diagrams is calculated byT
b
(V3 , Y3 )
smoothing Y ) along the y-axis with *Y \ 700 AU, corresponding to the angular resolution of the observations, as&(V3 ,
follows:
T
b
(V3 , Y3 ) \ ;
Y/Y
1
Y2
[&(V3 , Y )] , (A7)
where [2100, ...,1750 AU with AU, and is the vertical axis of the calculated position-velocityY
1
\[2450, Y
2
\ Y
1
] 700 Y3
diagram with a grid of 350 AU. The values of are given byY3 (Y
1
] Y
2
)/2.
222 OHASHI ET AL. Vol. 475
FIG. 10.ÈResultant position-velocity diagrams obtained from model calculations with a 0.1 central star. All the diagrams show a cut along the y-axis.M
_
(a) A disk with only an infall motion. The 0.1 star yields infall of D0.3 km s~1 at 2000 AU in radius. (b) A disk with an infall and rotation of 0.05 km s~1M
_
at 2000 AU in radius. (c) Same as (b), but with rotation of 0.15 km s~1 at 2000 AU in radius. (d) A disk with only Kepler rotation.
shows the resultant position-velocity diagrams. We adopt for all the cases. The case of KeplerFigure 10 M
*
\ 0.1 M
_
rotation was calculated using instead of It is found easily that the caseV
total
obs \ (GM
*
)1@2Y /(X2]Y2)3@4 equation (A5).
without rotation (Fig. 10a) shows a position-velocity diagram that is axisymmetric with respect to the velocity axis, though
the cases including both infall and rotation (Figs. 10b and 10c) do not show such an axisymmetric diagram. As V
rotation
0
becomes larger, blueshifted and redshifted peaks move away from the central position toward the opposite directions and the
whole shape resembles the case without infall (Fig. 10d).
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