古屋 玲 (徳島大学)、北村 良実（宇宙研）、新永 浩子（国立天文台）
arXiv 1407.4857
Filaments in Dark Clouds
01
Catalogued 23 “Globular Filaments”
mostly from the Lynds (1962)
catalog of dark clouds
Schneider & Elmegreen 1979
Stability and Evolution of a Cylindrical Cloud
03
Hierarchy of “sheets - filaments - cores - protostars”.
Miyama, Hayashi & Narita 84
Radial collapse of cylinder, “line-mass”, 2cs2/G.
Stodolkiewicz 63, Ostriker 64
Stability of cylinder against axial perturbations
Found (i) critical wave numbers for isothermal incompressible
cylinder composed of polytropic gas, (ii) unstable cylinder can
be stabilized by (0, 0, Bz).
Chandrasekhar & Fermi 53b
Studied dependency of B : (i) critical wavelength becomes
longer for (0, Bφ, 0), whereas shorter for (0, 0, Bz).
Stodolkiewicz 63
Growth rates are suppressed by uniform (0, 0, Bz).
Nagasawa 87
All the studies showed that a filament breaks into clumps with
Larson 85
separations of about 4H.
Merging and clustering of clumps occur within fragmentation time
Inutsuka & Miyama 97
scales.
“Cheat Sheet” —Filaments and Cylindrical Clouds04
Observations show that filaments are:
昨日の井上さん講演
Omnipresent, regardless of star formation activity.
Top of the hierarchy of “filaments - cores - protostars”.
45mデータ＋回転を考慮した安定性議論： Hanawa+93
Theory suggests to see stability of a cylinder, assess:
Critical line-mass for radial collapse
Critical wavelength for axial collapse
Keywords to study filaments:
Scale height
Velocity field and velocity dispersion
Turbulence
Magnetic fields
Previous Work
and Motivation
: GF9 “AKARI” Color Temp. + NH3
05
160, 140, 90 and 65 μmマップから導出
Kelvin
NH3 cores: Furuya, Kitamura, & Shinnaga 2008.
Kitamura, RSF in prep.
5
3
ex
deviation for the spectra existing inside the half-maximum, i.e., 50% level contour of total integrated intensity map ( Fig. 4).
in-beam brightness temperature. For N2H + and NH3 lines, those for the brightest HF components are given.
lating intrinsic velocity width (!v int ), we employed HFS analysis for the N2H + and NH3 lines, spectral moment analysis for the
C3H2 lines, and single Gaussian fitting for the CCS line (x 4.5.2). For the C 3 H2 and CCS lines, we corrected for line broadening due
depth (Phillips et al. 1979).
depth. We present ! of the brightest HF transition (F1 ; F ) ¼ (2; 3)Y (1; 2) for N 2H + (1Y 0) (x 4.1.1) and (F; F1 ) ¼ (5/2; 2)Y(5/2; 2)
) (x 4.1.5).
Previous Work
and Motivation
An Exceptionally Young Protostar
06
! !SED
Masers
No extensive outflow
Dense Core
Density structure
ated intensity maps of the (a) H13CO+ (1Y 0), (b) CCS 43Y32, (c) N2H+ (1Y 0), and (d ) NH3 (1, 1) lines observed with the 45 m telescope. The velocity
ns are between VLSR ¼ !2:95 and !2.1 km s!1 for H13CO+ and between !3.0 and !2.1 km s!1 for CCS. For the N2H + and NH3 emission, all of the
d over the velocity ranges shown by the horizontal bars in Figs. 3 and 10, respectively. Contour intervals are 3 ", starting from the 3 " levels. The 1 "
.5, 27.0, and 24.8 mK km s!1 for the H13CO+, CCS, N2H+, and NH3 maps, respectively. The central star marks the position of the 3 mm source. The
ttom left corner of each panel show beam size (see Table 1), and the small dots represent the observed grid points.
! !”Infall
Profile”
Velocity structure
Accretion rate
All the evidence strongly suggest that the core is
Gravitationally collapsing; consist w. the runaway collapse scenario
i.e., LPH solt’n (Larson 1969; Penston 1969; Hunter 1977).
ファーストコアの用語使用を当時のレフェリーは拒絶
6
Furuya et al. 2006, 2009a
2006年前期：観測提案
07
2006年前期：観測提案
10
評価
C
評価
B
このような指摘があることも予想して別プロポーザルも同時提出
評価
B
2007年前期：2度目の観測提案
評価
B
評価
B
評価
A
乱流の散逸はカスケード的現象であることを
ご理解いただけなかった？
15
16
Observations
Nobeyama 45m + BEARS + OTF + Freq.SW + AC45s
A total of ~200 hrs over LST 17h - 2h in ’07 Dec./’08 Mar.
Observed lines =
Effective spatial resolution = 24 arcsec
12CO, 13CO,
and C18O 1-0 lines
Effective velocity resolution = 0.1 km/s
“Special support” = 澤田、樋口、高橋茂、久野
Data reduction = NOSTAR + CLASS
image courtesy: 国立天文台野辺山
Results:
12CO
J=1-0, H13CO+J=1-0
17
Results:
13CO
J=1-0, H13CO+J=1-0
20
18
Results: C18O J=1-0, H13CO+J=1-0
21
19
sAnalysis:
cloud is written
Solvingby,
CO Excitation Conditionsτ and Tex
ant.
Radiative transfer eq.
[12 CO]
α ≡ 13
= 89
[ CO] ν
Tmb (v) = f {J (Tex ) − Jν (Tbg )}[1 − exp{−τ (v)}],
13
[
CO]
observedβ ≡
= 5.5
18
[C O]
to be solved
(1)
– 39
– line as a function of radial velocit
optical
depth
of
the
where
the excitation temperature of the line, and Tbg12the
CO
assuming the solar abundance ratios of,
13CO
Optical-Depth-Corrected
Temperatu
ds for
radiation.
The function Jν (TBrightness
) is the radiation
tem
18O
[ CO]
[ CO]
C
α≡
= 89 and β ≡
= 5.5
(A1)
[C of
O] the line, T the gas temperatur
re ν is[ CO]
the frequency
(2)
he optical-depth-corrected
main beam brightness temperatur
Planck
constant.
having τ and T allows us to reproduce
12
13
13
18
ex
“opacity-free”
13CO
spectra of,
τ
=
T
(v)
(A
mb
−τ
1
−
e
Estimate
of
Optical
Depth
and
Excitation
Temp
desired
corr
Tmb
(v)
(3)
opaque of τ13 CO ∼ 1 in the
21
Analysis: Solutions — Optical depth τ
measure a mean τ13 CO of 0
Figures ?? and ??, respecti
Towards the position o
−1
= −2.3 km s , while no so
in the GF 9-2 core region is
18
leading to the C O optical
We measure a mean τ13 CO
The number in each panel represents LSR-velocity in km s-1.
⟨τ13 CO ⟩ = 1.31±0.30
CO
22
Figures ?? and ??, respec
Analysis: Solutions — Excitation temp. Tex
Towards the position
= −2.3 km s−1 , while no
in the GF 9-2 core region
18
leading to the C O optica
We measure a mean τ13 C
⟨τ13 CO ⟩ = 1.31±0.30
The number in each panel represents LSR-velocity in km s-1.
⟨Tex ⟩ = 8.4±1.0 K
ch spatial position, we produced the maps
Analysis
Map
of Molecular
Hydrogen
Column Density
D).
Since we: are
interested
in the natal
cloud
y between the Components 1 and 2 by the
23
H13CO+ core
vcent = −2.2 km s−1 in Figure 10b.
ogy of the
13
CO bright region is principally
sion (Figures 2c and 2f), and that the dense
med in the inner densest part of the filamentary
– 15 –
“LTE-Mass” assuming the X(CO)
We obtained
⟨NH2 ⟩ = (2.7 ± 0.9) × 1021 cm−2 =⇒ 24 ± 10M⊙ f or Comp. 1
⟨NH2 ⟩ = (2.4 ± 0.7) × 1021 cm−2 =⇒ 17 ± 7M⊙ f or Comp. 2
ch spatial position, we produced the maps
Analysis
Ratio
Map ofinNon-thermal
D).
Since we: are
interested
the natal cloudVel. Dispersion / Sound–Vel.
16 –
– 16 –
y between the Components 1 and 2 by the
– 16 –
13CO+ core
H
Turbulent Motions of the
5.1.
low-mass
(papers
andFigure
III). On the
basis of all the results
vcent =protostar
−2.2 km
s−1I in
10b.
5.1.
Turbulent
nclude that the core is physically associated with the
Component
1
Motions of the Gas in the C
We present a map of the ratio between the n
13
.3). This
is because
dense core
is located
at the local density
ogy
of the
COthebright
region
is principally
a maprange
of the
ponent 1 and the LSR-velocity of the coreWe
fallspresent
inthe
the sound
velocity
of ratio
velocity
cs inbetween
Figure
the
non-thermal
vel
?? to
examine the
sion (Figures 2c and 2f), and that the dense
Although it is impossible to separate the
components
completely,
the
thetwo
sound
velocity
c
in
Figure
?? from,
to examine the degree of turb
s
The ratio is obtained
med
in gas
theof inner
densest
the natal
the GF 9-2
core. part of the filamentary
The ratio is obtained from,
!
"2 #
σnth
∆v(τ → 0
!
"2 #
"
= $2 √!
σnth
∆v(τ
cs → 0)
thm
cs 8σln
2
Turbulent Motions of the Gas in the Component 1
cs
2
where σthm
is given by
k
map of the ratio between the non-thermal
dispersion
(σnthkT
) and
wherevelocity
σ 2 is
given by
,
s
=
thm
m13 CO
of σthmComponent
, we used
in Figure 13 to examine the degree of turbulence in the
1.
d from,
by
Calculated by
!
σnth
cs
"2
=
#
∆v(τ → 0)
√
cs 8 ln 2
√
cs 8 ln 2
kTk
,
m13 CO
−
σthm
cs
and m13 CO denotes the molecular m
the ⟨Tex ⟩ map (Figure ??).
ratio of
We obtained
(3)
means of,
cs
and m13 CO denotes th
of σthm , we used the ⟨Tex ⟩ map (Figure ??).
of"2
$2 ratio
!
−
%
σnth
cs
&
Over
Over the Compone
%
&
σnth
= 2.1 ±
= 2.1 ±cs 0.50 ≡ M
using
map
13 CO denotes
andthe
m〈T
the molecular mass of 13 CO. For calculations
ex〉
−1
corresponding to ⟨σnth ⟩ = 0.34±0.80
km
s
.
−1
corresponding to ⟨σ ⟩ = 0.34±0.80 km s . The observed
kTk
,
m13 CO
maller than the core size of ∼0.1 pc.
Color Temp.
by Chandrasekar &
Analysis: Estimating |B |
25
Fermi method (CF53a) NIR polarization
s well known that not only supersonic turbulen
lar gas from collapsing due to its self-gravity. Ap
(Chandrasekhar & Fermi 1953a), Poidevin & Ba
⃗ pos |. They derived
ength in the plane of the sky, |B
was observed by the CS (2–1) emission (Ciardi
!
⃗ pos | ≈ 9.3
ed Eq. (4) in Crutcher (2004) of |B
on in a polarization angle in degrees. Since we ha
−1
(§4.3) and the numbe
HM = 0.69 ± 0.12 km s
⃗ pos | of 55 ± 30 µG.
5.2), we recalculated |B
NIR pol.: Poidevin & Bastien 2006
NH3 cores: Furuya et al. 2008
⃗ pos | = 55 ± 30 µG
|B
19
internal pressure
of the filament. We
2
2cs ∼ 9M⊙
m
×
0.77
pc
line,crit
mline,crit
=
2⇡ !
¯ ⇢(¯
! )d¯
!
=
Stability of the
Filament
—
Radial
Collapse
G
0
pressures
due
(
✓
◆2 ) to predominantly the su
Z
meff
line,crit
"
me↵
line,crit
2 kTkin
=
G µmH
26
1
2 kTkin
nth
%
=#
1
+
$2
G σµm
Hfield as cwell
s
nth
1+
cs
(described
inper§??),
Max. mass
length altho
(4) supported by thermal and
non-thermal
⟨Tkin ⟩ = 7.5 ± 1.0
K (§4.3)pressures
and ⟨σnth /
eff
observed
yields,
mline,crit ×
eff
critical mass ( Mcrit
= 51+32
−22 M⊙ for
eff
+32
eff
mline,crit × 0.77 pc = 51−22 M⊙ ≡ Mcrit
observed
length
of
the
filament
(0.77
p
⇥ 0.77 pc ⇠ 9M
(5)
mline,crit
Recall that we obtained,
+32
me↵
⇥
0.77
pc
=
51
line,crit
22 M
e↵
⌘ Mcrit
MLTE = 24 ± 10 M⊙ (§4.4), we su
(6)
mline,crit × 0.77 pc ∼ 9M⊙
e↵
<Highly
Mcrit
likely the filament is supported by the turbulence because of
(7)
MLTE <
5.2.2.
Hereeffwe call the ratio of
mline,crit × 0.77 pc =
eff
Mcrit
Application
to
The
Column
Density
Map
MLTE
e↵
51+32
M
M
⊙
−22 crit
= 0.5eff± 0.2 as a “stability parameter”.
≡ Mcrit
dual NH2 map (Figure ??c). The position and extent of the
ma
(1992).].
The
line
mass
of
the
filament
+ can be calculate
The
line
mass
of
the
filament
can
be
calculated
from t
with
those ofofthe
core observed
in the
N2 H (1–0),
Stability
thedense
Filament
— Axial
Collapse
bserved
length
as
d
NH
(1,1)
lines
(paper
I). We therefore speculate that it
3
thThe
as“line-mass” estimated from
observations is
nding the dynamically infalling
dense core (paper III). The
24M
LTE
⊙⊙ where TEC denotes the
s calculatedM
to
be
M
∼
0.8
M
−1
TEC
24M
LTE
⊙ =
= −1
31M⊙ pc
rthermore,
can estimate=
a “core
formation
= we
31M
length
0.77
pc
⊙ pc efficiency” for
gth
0.77
pc
=
M
/(M
F
LTE
LTE + MTEC ) = 1.3 M⊙ /(1.3 M⊙ + ∼ 0.8M⊙ )
Thethe
critical
clump
mass
produced
by the
of
dense
core
traced
by the
N2axial
H+ perturbation
and H13 COis+ lines
27
“clump”
Mcrit
“clump”
Mcrit
=
−1
=
31M
pc
⊙
−1
=
37 ∼ 87 M⊙
31M⊙ pc
× 4H
× 4H
ility of the Component 1 against
Perturbations
= 37Axial
∼ 87
M⊙
(4LTE-masses
∼&8)H
=(1997)
0.4showed
∼ 0.8that
pc
which is (1987)
clearly larger
of the
NH3 cores
(Furuya+08).
agasawa
and than
Inutsuka
Miyama
(4
∼
8)H
=
0.4
∼
0.8
pc
hich →
makes
an
infinite
filament
unstable
against
perturbations
The filament would be gravitationally stable against axial perturbations.
min ∼ 4H, meff
× (4 ∼ 8)H = 16 ∼ 40 M
line,crit
An infinite cylinder
becomes unstable against perturbations along ⊙
the axis of
λ > λmin ∼ 4H regardless of |B|.
(Nagasawa
⊙ 87, Inutsuka & Miyama 97)
e,crit ∼×
(4 ∼ 8)H
=
16 ∼ 40 M
Discussion: Core Formation
GF9-2: An Unstable Core
in the Stable Filament
The central issues to be addressed:
How has the turbulence decayed locally at the
spatial scale of the core?
Can such dissipation determine the initial
conditions of the core collapse?
Core formation Scenario：金曜日に
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あるいは秋の学会で
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