The protoplanetary disk of FT Tauri: multi-wavelength data analysis
and modeling
Garufi et al.: The protoplanetary disk of FT Tauri

Garufi et al., arXiv:1405.7692
・FT Tauという星+円盤のSEDを文献から作成

ル:MCFOST and ProDiMo)
・観測結果の解釈

1x10-10λ·F (λ) (erg·s⁻¹·cm⁻²)

・合うモデルを輻射輸送込みで計算(モデPhotometry
TNG
WHT
NOT
Keck
Spitzer/IRS
Herschel/PACS
Reddened photospheric model

1x10-91x10-11

1x10-12

1x10-13

1x10-14

1x10-15Garufi et al.: The protoplanetary disk of FT Tauri

中心星: 0.3Msun, 0.35Lsun, 年齢 1.6Myr
Table 9. Parameters of the FT Tau model. The di↵erence between an ‘explored’ and ‘free’ parameter is that the for1

an exploratory parameter study while the latter is derived using

2 10

100

fittingof the SED.
Wavelength
(μm)

1000

M型星にしては高い降着率(3.1 · 10−8 Msun/yr) Parameter
Fig. 2. SED of FT Tau. All the available photometric and spectroscopic non-simultaneous observations are plotted. Th
Comments
Value
Phoenix model is reproducing the Symbol
stellar photospheric emission(grey line). The SED clearly shows
UV/optical excess
それなりに重い円盤(0.02Msun)←中心星の0.06倍
円盤内縁が非常に小さい(0.05AU)←COのline幅から導出。inclinationは輻射輸送モデルから持ってくる

小さいsilicate (0.1μm)は円盤表面にまだ存在←silicate feature at 10 μmが見えるから

excess beyond
2 µm. IRAS photometry is excluded
Stellarwavelengths
luminosityshorter than ⇠ 0.8 µm andL⇤infrared Derived
from⇠observations
0.35 Land the higher IR
8µm
photometryisomittedgivingmoreweighttothe
IRS
spectrum.
Error
bars
are
not
visibleat
thisMscale.
Stellar massM⇤”
0.3
Stellar radius
R⇤
”
1.7 R
E↵ectivetemperatureT”
3400
K indicative of a
Table 5. Estimated stellar properties. e↵⇠ 10 µm, as in the case of FT Tau, aresmall
Distanced” lation dominated by grains as140
pcas 0.1 µm. The flthese features (see Furlan et al. 2006
Slope of UV excess distributionpUVFixed in MCFOST
2.0 for a large samp
canbea
traceroftheevolutionof the dust population
Visualextinction
A
1.8
±
0.6
V
Slope of grain size distribution
apow
”
3.5
Spectral type
M3 ± 1surface. Some processes such as stellar3winds and rad
Dust mass density” sure can deplete sub-µm size
3.5grainsg cm(Olofsson et al.
E↵ective temperature T e↵ ⇢d 3400 ± 200 K
Slope of surface
mass density” narrow and prominent nature of 1the silicate feature
LuminosityL⇤ ✏ 0.35 ± 0.09 L
RadiusR⇤ R0 1.7 ± 0.2 ExploredR
Flaring reference
radiuswith MCFOST
100 AU are not yet effi
FT Tau suggests that these processes
MassM⇤
0.3 ± 0.1 M
disk. The 10 µm featurecanalso
provide insight
Flaring reference
height
H
”
12,
14
AU
(high/lowfUV ) in
0Age
1.6 ± 0.3 Myr
Flaring exponent” tallinity of the silicate (e.g. Sargent
1.15 et al. 2006). The
MIR
spectrumof FT Tauf indica
Disk inner radiusRin” substructure in the
0.09,
0.05
AU (high/low
UV )silicates are mostly amorphous.
Minimum dust grain size
amin”
0.05, 0.1 µm (high/low fUV )Finally, the MIR spectrum does not show
3.2. Disk properties
Maximum dust grain size
amax
” Aromatic Hydrocarbon (PAH)1emissioncm
features. PA
3.2.1. Diskflaring and dust composition
Stratification
exponent
sset” is indeed hardly detected
0.2, 0.3(high/low) 2006
UVal.
in TTSs(Furlan fet
Stratification
grain
dimension
a
”
0.05,
0.1
µm
(high/lowf) e.
commoninmoremassive
Herbig
Ae/Be
stars
(see
set
UV
FT Tau shows a very prominent IR excess (see Fig. 2). By inteal.
2001).
Thiscanbeexplained
either
in
terms
of
di↵
Inclinationi”
60
grating the excess emission over the photosphere, we obtained
compositionortheweakerUV
radiation
field
of
low
Disk outerradiusluminosity LIR = 0.12 ±R0.01
”
50,
100,
200
AU
an IR excess
L.
out
We also measured the IR excess atAdi↵erent
wavelengths(see in MCFOST
Optical extinction
Freeparameter
1.6
V
Table
6)
by
subtracting
thephotospheric
model
from
the
obDisk dust massMd
” 3.2.2. Disk inner radius 9 · 10 4 M
served photometry. This provides qualitative information on the
Cosmic Ray Ionization rate⇣
Fixed in ProDiMo
1.7 · 10 17 s 1
geometry of the disk. As the dust grows and settles toward the Most of the CO ro-vibrational lines dete
UV excessfUV
Exploredcauswith ProDiMo
0.025 from the
Keck/NIRSPEC are from0.07,
transitions
mid-plane, the vertical scale height ofthe disk decreases,
2
3
PAH abundance
fPAH and, thus, a smaller” tional level (⌫ = 1 0) and10 their, 10fluxes, 10are4 typicallying less reprocessing of the stellar radiation
2 Table 4).
from
2 ·10
1 (seeMIRmass
excess. According to the evolutionary
scheme by Fang et
Disk gasMg” few higher than those(9,4.5,⌫ =
1.8)
M
al. (2009), the excess shown by FT Tau is typical of objects withdisks that are evolving from a mildly flaring to a flat geometry.
The MIR spectrum of FT Tau (see Fig. 1e) shows prominent,All ⌫ = 1 0 low-J (up to J=12) lines are strong
inated by atmospheric absorption/emission lines whi
allow to recover the full line profile. The uncertainty

Shadows and cavities in protoplanetary disks: HD163296,
HD141569A, and HD150193A in polarized light
Garufi et al., arXiv:1406.7387
・近赤外の高分解能偏光観測により円盤を観測（VLTのNACOという装置）
・観測天体：HD163296, HD141549A, HD150193A
・結果：HD163296ではHとKsの両方で円盤を検出、他２つは受からない
AOの引き残りがたくさん

Garufi et al.: Shadows and cavities in protoplanetary disks

2. Observations and data reduction

tween 2012 July 23 and 25 with VLT/NACO in PDI mode, conof AO assisted high resolution imaging polarimetry with→transitional sisting
diskっぽい？？→self-shadowingの議論
a Wollaston prism and a rotatable half-wave plate for beam exchange. These sources were observed in the context of a mini【コメント】（外側2’’以遠の明るさの変動を円盤内側の変動＋self-shadowing
survey of six young stars, where the other objects (HD169142,
HD142527, and SAO206462) were discussed by Quanz et al.
Garufiet al.: Shadowsand cavities
in protoplanetarydisks et al. (2013).
(2013),
Avenhaus
et al. (2014),
and Garufi
で議論しているが、本観測からは有益な結論はあまりなさそう…）
We used the NACO SL27 camera (pixel scale = 27 mas
Radius (AU)pixel 501 ) in HighDynamicmode
and readout
in Double
RdRstRd
125
100
75
25
0
25
50
75
100
125
mode.
The
targets
wereobservedinH
andK
bands,
aswellS
H bandKs bandas in the respective narrow band filters (NB 1.64 and NB 2.17).
H band 3σ sensitivity
Since no photometric standard star was observed, narrow bandKs band 3σ sensitivity
1filters were necessary to obtain unsaturated exposures for photometric calibration. Observing conditions were photometric withaverage seeing varying from 0.5800 to 1.6600 (see Table 1 for ob0.1
serving settings and conditions).
The data were reduced with the procedure described in Aven0.01
haus et al. (2014). Besides
dark current, flat field, and bad pixRegion
maskedout
els corrections, thismethodconsists of (i) performing a row1 0.9 0.8 0.7 0.6 by-row
0.5 0.4 subtraction
0.3 0.2 0.1 to
0.0compensate
0.1 0.2 0.3 for
0.4a non-static
0.5 0.6 0.7 readout
0.8 0.9 noise,
1.0
Radius(arcsec)(ii) determining the center of the stellar profile by fitting a two動径分布, 赤:Ks,
青:Hバンド右: total I (どちらもr^2でスケール)
dimensional
gaussian to the point spread function (PSF),左:偏光,
(iii)

ec²)

Polarized surface brightness (mJy/asec²)

動径分布はぱっと見0.6’‘くらいにピークを持つようにみえる
HD163296, HD141569A, and HD150193A were observed be-

l.
y

e
n
s
l
L
ut

8
0
r
ll
”
p
d
a,
s
d

Relevant parameters from the fit results are presented inTable 4. To illustrate the fit quality, we present in Appendix
Themasses of young stars: CN as a probe of dynamical masses(Fig.B.1) channel maps for the strongest group of hyperfine comGuilloteaual.,observations,
arXiv:1406.3805
ponents in GOet
Tau:
best model and residuals. On
average, there is no systematic dependency of the residuals withvelocities, and channels with strong emission have similar resid・中心星の質量を知りたい。COは分子雲などのコンタミが大きいので、ここ
uals than channels without. Although a few channels have somesystematic residuals, this can be ascribed by the limitations ofでは円盤のCN(1-0)のフィッティングによる中心星質量の導出を提案する。
ourdisk model, such as the assumption of power law for the
CN surface density, and should not affect the derived velocity
field.
For all other sources, we obtained
signal・サンプルは12天体(うちTsignificantly
Tauri星がless
9個)
to noise than for GO Tau, and noise is the limiting factor in thevelocity field derivation.
・Kepler回転からのズレはごくわずか
v ∝r^(0.5+ 0.005)くらい→星の質量がA comparison between geometric parameters derivedfromCN and dust emission is given in Table 2. The stellar mass isderivedfrom the Keplerian rotation of the disks. Because the
正確に決まる
maps provide only an angular scale the derived masses are proportional to the distance to the star. The masses listed in Table
4 are given at the star-forming region’s (SFR) average distance,
140 pc (Kenyon et al. 1994).

Fig. 3. Velocity gradient for GO Tau. Contour spacing is 0.2 km s−1 .

1.5

1.5

1.0

1.0

0.5

0.5

Log (L/M2)

Log (L/M2)

A&A proofs: manuscript no. printer

0.0

0.0

-0.5

-0.5

-1.0
3.8

-1.0
3.8

3.7

3.6
Log (Teff)

3.5

3.4

3.7

3.6
Log (Teff)

3.5

3.4

s
theFormation
fastest-growing,
gravitationallyunstable
elow n ∼ 300 cm−3 (see also
2.1
by Sweep-up
of Diffuse
Gas mode λH =Troland. & Heiles 1986,The solution(9) Cloud
to
eq.
10
is
a magnetized sheet (Larson 1985, see panel(c), longut Marchwinski, Pavel, & Clemens πGΣ
2012 for newer results#cloud$We assumelines).
that theiswhileforming
due toλ the ,collision
the accretion
ratedensities,
onto thethe
sheet
is given
by
Note
that
we
show
the
growthrate
omThen,polarimetry).
At higher
maximum
field
max
1
1/2
2
2
of two identicalflows aof diffuseatomic gas,
constant
Σ(t)
t +
2aΣ
4b
+
Σ . For, instan
rengthincreases
as BHartmann,∝ n2/3 , whicharXiv:1406.2191
Crutcher et al. suggest
Heitschand
only=slowly
forwavelengths
λ with
> λ
0 t+
max0
Σ̇ = 2ρ0 vz contraction under gravity. In addition,
4 , vthedensity n0 and velocity
0 . The flows are parallel to thedue to isotropic
λ=5λtimescale is only ∼ 60% longer t
max
""1/2
!
!
backgroundmagnetic
field
B.
Then,
the cloud can be treatedcent studies of star formation occurringin filamentarywith the initialH
columndensityΣ0 =gasmN(trate= 0) tλmax. Thus,density
we slightly
underestimate
therelevance
星形成において、subcriticalからどうやってsupercriticalになるか、遷移過程を知りたい。
=
4ρ
πGz
Σ
1
−
as
a
”sheet”
ofcolumnN,accreting
at
a
0
ref
H
as structures, which appears to be zcommon(André et al.
refmentation
FigureSincesolving
this length
is unchosen.
this inwitheq. 1.2 andforscale
the accre
2n0 vEquating
0 , or010), also provide support
for
the
idea
of
building
dense
for µ ≤ 1, we also show the corresponding hydrod=initiallya (Σ −viab)1/2. along the magnetic field. Intime (10)τ
yieldssubcritical状態でも磁力線に沿ってものが降着した場合、そのうちsupercriticalになる
ructuresflows
acc
NH = 2n(1)
0 t . Yetcal0τvscale(Larson1985,
long-dashed
lines
in
panel
(c)
>
that
drop
is
irrelevant
for
our
purp
Model
acc
%
&
#
$
meInwell-studied
cases,
suchas
B216/17,
B18,
L1506
!
"
!
"
!nline"the last step we defined
1/2 tv0thecritical
0
20
short-dashedshows
scaleheightH−2accretion
(eq.
9) fo
ment
already
has
grown
due
to
Heyer etal.
1987;
Goodman
et
al.
1990;
Moneti
et
al.
=
6.31
×
10
cm
.
B
1
1/2
−1
→accretionとdiffusion/gravitational
fragmentationのどちらが早いかで決まる−3
llow theevolutionof)1/2a filament
under
free-fall,steadycmlatter
Myr
10km−sbe
parison.
The
would
anlikely
inappropriate
2
τ
=
bare
− Σto0 reach. choiceacc984)a andin Taurus(Palmeirimetal.
2013),
and≡ B211/13
4ρ0 (πGz(11)
the sheetcase,filaments
critic
ref
1/2
a
2πG
accretion,
using
a
model
seriesofexternallypressurambipolar
diffusion scalein this context,
we arehe Pipe Nebula(Alves et cal.
2 2008) the magnetic field apA thin sheetthat is permeatedby a magnetic
field B sincecanaccretion,
beforeambipolar
diffusion
can
have
H
s
1/2
→なのでタイムスケールを調べる
terestedintheverticaldiffusionofthemagnetic
field
b relatively≡
Σ = andwith. Bperpendicular
(12)
ears
orderednearlyto the fil- 2013b).
accretingcylinders,∝ ρ(Heitschfragment if
zref
πGz
effect.
Note
that
the
timescalesin duepanel(b)r
To develop physicalinsight,
wefurther
simplify
equatiorefmentary
gas,
as
would
be
expectedinthis
scenario.
Furmarizing,
the
sheet
turns
supercriticaltoaccretmptions, derivations and expressions can be found inBpressurized
cylinders(FischechooseΣ
initialcolumndensity,hermore,Palmeirim
Nsubstantially>,(2)
The solution
to eteq.al.10(2013)is show that the CO emis-First, we cannally
0 , the(truncated)timescales
shorterthanthelaminaramt
H
1/2√
paper.
Since
we
envisagethefilaments
tobeembedded
2πmG#$ negligibly small,on around B211 exhibits1 differingradial velocities on either
2012b).
The
correspondingtimescales
for cylidiffusion
timescale.
i.e.
Σ
#
Σ
≡
B/(2π
G).
Second,1/20c22
flattened,evolvedcloud,
weforsetor, if the mass-to-flux
ratio at1964;
a givenmass column
densitydiffer
Σ(t)interpreting= moleculara t this+ 2aΣ+inflowΣthe(13)
de of the filament,
asevidence
0 ,ofambient
0 t + 4bCan
turbulence
accelerate
ambipolar
diffusionuum(Ostriker
Nagasawa
1987)
os
4
−3
the
ratiothanof theH/zwhich for an evolved
ref , value,Σ = mNHis larger
critical
・
シートがものを重力で集めるタイムスケール。圧力無視してfree-fallで落ちてくるとす
ty to 100cm gas.
, corresponding
diffusemoleculargas.
mbientmolecular
For a systematictostudyof thealign-essentiallyciently to win
overbeingaccretion?
While
therethanis a fevolution
times,
alwayslargerwith
theinitialcolumndensity
Σ
=
mN
(t
=
0)
to
be
−1
#
$
0
ent
of ambient
magnetic
fieldsawith
also be small,
if weΣset zref
= 3 pc.ambipolar
With thesesimvelocities
range
aroundkmlocals molecular(see Fig.clouds,
1 of will
HeitschΣ
1ofimplementationsofturbulent
diffusion
cylinders>(only shown
in, Fig. 2 for the
chosen.
Equating this with eq. 2 and solving for the accretione Li
et るとaccretional. (2013).
(3)length s≡
rateが出る。これでmass-to-flux
ratioがを超えるためには
1/2
fications,
equation
14
turns
into
b).
We
calculatetwocriticality
parameters:TheradialB
B through
2πG stagnation point flows (Zas accelerationctime τobservational
These
results motivate us to address the
(c)
shows
the
lengthscales of the fastest growi
acc yields! through"1/22002), stochastic acceleration
field and densit
ality parameter% turbulent!
"1/2vs. mass &uestionof ambipolar anddiffusionac(Nakano &rived
Nakamura
1978). The
time τaccΣneeded
forsolid
the lines)forinfinite(Nagasawa
1987,
c turbulent
B1−1/2
ations(Fatuzzo&
Adams
2002),
mixing g
1/2
umulation using
setup.
We.
m geometriccloud to reachcriticality
resultsfromequations
1
and
2,
τ
≈
(2πGρ
)
,
2 simpleτacca =relatively
−
b
−
Σ
(14)
acc
0
0
ized
(Fischera& Martin2012a,µraddiffusion≡(19)
ing smallscales (Heitschet Σal.
2004)dashedand – tolines)
a la
2πG1/2timescales for magneompare the accretion aand
acc
mrad
B
discuss,
converge
tent authors
combiningmuch ofthe
the expressions
above – turbulent
comp
zed sheets (Sec. 2) and filaments (Sec. 3), based on anτacc = ter(4)
1/2
To thedevelop physicalline
insight,wem
further
simplify
equation14.
4πn0&v0Nakamura
mGi.e. larger
masses,overpressures.
ares
mass
the nebula
criticalmagarlierstudyfilament’s
discussing the evolution
ofwiththe Pipe(Li2004),
they all sugest
that turbule
#
$!
"
!
"
−1
−1
First,
wecanchooseΣ,theinitialcolumndensity,tobe
Bdiffusionn0 can break thev0 flux-freezing assumpt
Heitschet al. 2009). We find 0for both sheet- and√filamentbipolar2013式を超えるまで。
line mass,= 5.65Myr.
・filamentの場合のaccretionも計算。質量がTomisaka−1−3
negligibly
small,
i.e.
Σ
#
Σ
≡
B/(2π
G).
Second,
b
is
0
c
5µG
cm
10km
s
ke geometries that accretion will dominate a cloud’s evodynamical rather than on diffusive timescales. While2
essentially
the
ratio
of
H/z
,
which
for
an
evolvedsheet
tion from subcritical to supercritical.
BRrefcs
focus our diffusion
discussion
on turbulent
ambipolar
The ambipolartimescale
at a given
lengthdiffusion

Accretion and Diffusion Timescales in Sheets and Filaments

Timescales in Sheets and Filammsmall,0.24(20)+ 1.66
rad = ifwill also be
we √set zref= 3 pc., With these simpliscale L can4be writtenas (see App.
G
sakeof consistency
withA)
previous literature (Li & Nak
DISCUSSION
G
fications, equation 14 turns into
2004; #Kudoh$2 #& Basu 2011),$3/2the# exact$−2mechanism!
"
termined
numerically by Tomisaka (2013).
n
B
L
1/2 For the lon3comparedWe
ambipolar
diffusionandaccretioflux-freezingis broken
atthesmallestscalesmay
not b
ACCRETION AND
ΣcτAD = 1.38×10
Myr.
−1/2
2
−3
pc
3
×
10
cm
5µG
τ
≈
(2πGρ
)
,
(15)
inal
criticality acc
parameter,0 we DIFFUSION
adapt
the expressionsforsheets2)theandfilaments(Sec. 3),finding
AMBIPOLAR/TURBULENT
relevant,as(Sec.
long asturbulent
diffusivity
λtrb
( λl
Σ
acc
(5)
これらのタイムスケールを、ambipolar diffusionなどのタイムスケールと比べる
TIMESCALES
FOR
SHEET
by
Bastien (1983)
forAthenumber of Jeans masses inaccretion
dominate
Note that geometries,
we use a different
scalingwill
for thedensity thecor- evoluti

Timescales in Sheets and Filaments

7フィラメント
gravitational fragmentation, accretion(磁場に沿った方向), accretion(radial),
laminar ambipolar diffusion

Timescales in Sheets and Filaments

9

Figure 5. Map of the shortest timescales in the lengthscale-density plane, for a filament. For a given combination of (L, n), all relevanttimescales are compared, and the regime is color-coded as longitudinal criticality (blue, lon), radial criticality (pink, rad), gravitational
fragmentation (frg, red), and laminar ambipolar diffusion (light green, lam). The solid line shows the wavelength of the most unstablemode, λmax (Nagasawa 1987) against the filament density, and the dashed line shows the filament’s core-radius R0 (eq. 23). Longitudinal
criticality is indicated by the long-dashed line (eq. 21), and radial criticality by the dotted line. Symbols denote the evolution of the two
filament accretion models shown in Fig. 2.

ambipolar diffusionはシートやフィラメントの成長に効かない。
それより先にものがaccretionしてsupercriticalになる。

＊ただし、乱流拡散がシートでは強磁場の場合(20μG以上)重要。フィラメントでは乱流拡
散は小スケールしか効かない

結論：アクリーションが重要。

Two Extreme Young Objects in Barnard 1-b
Hirano and Liu, arXiv:1406.0068
B1-bというコアは4.7Msun、0.12×0.07pc (野辺山45mのH13CO(1-0)より,左下図)– 30 –
B1-bは２つの点源からなる(B1-bNとB1-bS,
3.3mm連続波より, 右下図)

COでoutflow確認。3-5km/s for B1-bN, 7-8km/s for B1-bS

Fig. 1.— Integrated H13 CO+ (J=1-0) emission from B1 (contours) on top of the Spitzer
IRAC band 2 (4.5 µm) image (grey scale). The velocity range of the H13 CO+ map is from
VLSR = 5.0 to 8.0 km s−1 . The contours start from 0.67 K km s−1 (3 σ) with an interval of
0.44 K km s−1 (2 σ).

– 34 –

Fig. 4.— 850 µm (dot contours) and 3.3 mm (solid contours) continuum maps of the B1-b
region on top of the Spitzer MIPS 24 µm image (grey scale). The 3.3 mm continuum has
been applied for the primary beam correction. The gray-filled and black-filled circles in thelower-left courner are the beams of 850 µm and 3.3 mm, respectively. The contours are
drawn every 0.08 Jy/beam (3 σ) for 850 µm and 3.4 mJy/beam (2.5 σ) for 3.3 mm.

このうちB1-bNはファーストコアだと思われる
B1-bN
Lint<0.01-0.03Lsun
Fig. 5.— Maps of the continuum emission at millimeter wavebands. All the maps arecorrected for the primary beam response. (a) 7 mm continuum map observed with the VLA.
The contours are drawn every 3 σ. The cross denotes the position of B1-bW. (b) 3.3 mm
continuum map observed with the NMA. The contours are drawn every 3 σ. The crosses
indicate the positions of B1-bN, B1-bS, and B1-bW. (c) 1.3 mm continuum map observedwith the SMA. The contours start at 3σ and are drawn at 6, 12, 18, 27, 39, 54, 72, 93, 117,
and 144σ. (d) 1.1 mm continuum map observed with the SMA. The contours start at 3σ
and are drawn at 6, 12, 18, 27, 39, 54, 72, 93, and 117σ.

B1-bS
Lint=0.1-0.2Lsun

・それぞれmm波でcompactな天体→diskの起源か？

Lbol~0.14-0.31Lsun
Fig. 7.— Spectral energy distributions of B1-bN (upper panel) and B1-bS (lower panel).
The data are from Spitzer MIPS (24 and 70 µm), CSO SHARC (350 µm), JCMT SCUBA(850 µm), SMA (1.1 mm and 1.3 mm), NMA (3.3 mm), and VLA (7 mm). Arrows markthe upper limits. The solid red curves are the single-component greybody fits with Tdust ≈16 K and β = 2.0 for B1-bN and with Tdust ≈ 18 K and β = 1.3 for B1-bS. The dashed blue
curves are the results of the two component model with a compact blackbody component
and an extended greybody component. The parameters of the two component models are
Tdust (ext) ≈ 11 K, β(ext) = 2.0, and Tdust (cmp) = 23 K for B1-bN, and Tdust (ext) ≈ 16 K,
β(ext) = 1.5, and Tdust (cmp) ≈ 24 K for B1-bS.