2023年2月10日星形成ゼミ：古屋玲；Star Formation News Letters Vol.359, No.1-18

7 Department of Planetary Sciences, University of Arizona, 1629 East University Boulevard, Tucson, AZ 85721, USA
8 Department of Physics & Astronomy, 118 Kinard Laboratory, Clemson University, Clemson, SC 29634, USAThe
kinematics and excitation of infrared water vapor emission from planet-forming disks:
9 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, the Netherlands
resultsfromspectrally-resolved
surveysguidelines
for JWST spectra
10 Kapteyn AstronomicalInstitute,
Universityof Groningen, PO Box 800,
9700 AV and
Groningen,The
Netherlands
11 Department of Astronomy, University of Michigan, 1085 S. University Ave, Ann Arbor, MI 48109

1
2
1
3
1
AndreaBanzatti,
Klaus
M.
Pontoppidan,
Jos
é
P
érez
Ch
ávez,
ColetteSalyk,
Lindsey
Diehl,
12 Center for Astrophysics, Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
4
5
6
7
8
8
Simonof Bruderer,
Gregory
J. Herczeg,
AndresCarmona,
IlariaPascucci,
Sean
3 Division
Geological & Planetary
Sciences,
MC 150-21, California
Instituteof Technology,
Pasadena,
CA 91125,
USABrittain, Stanley Jensen,
4
4, 9
10
11
12
14 Department
SierraGrant,Ewine
F.
van
Dishoeck,
Inga
Kamp,
ArthurD.
Bosman,Karin
I.
Öberg,of Earth Sciences, University of Hawaii at Manoa, 1680 East-West Rd, Honolulu, HI 96822, USA
13
11
14
15
15
15 Institute
GeoffforA.Astronomy,
Blake, University
MichaelR. Meyer,
EricDrive,
Gaidos,Adwin
John T. Rayner, andof Hawaii,
2680 Woodlawn
Honolulu,
HI, USABoogert,
96822
16
16 Simons Observatory - Center for Computational Astrophysics,
Caleb
Wheeler
FlatironInstitute, 162 5th Ave, NY 10010
JWSTで若い星(主にclass II)の円盤中の⽔
1 Department of Physics, Texas State University, 749 N Comanche Street, San Marcos, 蒸気分⼦輝線分光
TX 78666, USA

ABSTRACT

2 Space Telescope Science Institute 3700 San Martin Drive Baltimore, MD 21218, USA

This work 3presents ground-based spectrally-resolved water emission at R = 30000–100000 over in- 【結果1】２-9μmの回転振動遷移線は,
Department of Physics and Astronomy, Vassar College, 124 Raymond Avenue, Poughkeepsie,
NY 12604, USA
12μmの回転遷移線より線幅細い
frared wavelengths4 covered by JWST (2.9–12.8 µm). Two new surveys with iSHELL and VISIR are
Max-Planck-Institut für extraterrestrische Physik, Gießenbachstraße 1, 85748 Garching bei München
combined with previous
spectra from CRIRES and TEXES to cover parts of multiple ro-vibrational 【結果2】柱密度~10^18 1/cm^2,
5 Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871,
China
and rotational bands observable within telluric transmission bands, for a total of ⇡ 160 spectra and 4000-9500 Kからの輝線の放射領域はおそ6 Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
85 disks (30 of which are JWST targets in Cycle 1). The general expectation of a range of regions and らく円盤の鉛直⽅向に異なるところから
7 Department of Planetary Sciences, University of Arizona, 1629 East University Boulevard, Tucson, AZ 85721, USA
excitation conditions traced by infrared water spectra is for the first time supported by the combined
8 Department of Physics & Astronomy, 118 Kinard Laboratory, Clemson University, Clemson, SC 29634, USA
kinematics and excitation as spectrally resolved at multiple wavelengths. The main findings from this 【結果3】JWSTで観測できるようになった
9 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden,
5μm輝線は、複数の層(slab)からの励起モ
analysis are: 1) water lines
are progressively narrower from the ro-vibrational bands at 2–9 µm to the Netherlands
10 Kapteyn
デルでうまく説明できた.
Astronomicalof andGroningen,Box
800, 9700
AV Groningen,The
Netherlands
rotational lines
at 12 µm,
and partlyInstitute,match a University
broad (BC)narrow PO(NC)
emissioncomponents,
11 Department
respectively, as extracted
from ro-vibrational
COUniversity
spectra; 2)
diagrams
resolved waterof Astronomy,of rotation
Michigan,1085 S.ofUniversity
Ave, lines
Ann Arbor, MI 48109
12 Centerfrom upper level energies
of 4000–9500
K showHarvard
vertical &spreadand curvaturesindicativeof opticallyMA 02138, USA
for Astrophysics,
Smithsonian,
60 GardenSt., Cambridge,
18
13 Division
thick emission(⇡ of
10Geological
cm 2 ) froma range Sciences,of excitation(⇡ 800–1100
3) the new Pasadena, CA 91125, USA& Planetary
MC temperatures
150-21, California
InstituteK);of Technology,
5 µm spectra14demonstratethatslab Sciences,model fitsUniversity
to the rotationallinesatatManoa,> 10 µm
strongly
over-predict
Department ofEarthof Hawaii
1680
East-WestRd, Honolulu, HI 96822, USA
the ro-vibrational emission
bands
at < 9 µm,University
implying non-LTE
excitation.
discuss HI, USA 96822
15 Institutefor Astronomy,of Hawaii,vibrational
2680 Woodlawn
Drive,We
Honolulu,
these findings 16
in the context of emission from a disk surface and a molecular inner disk wind, andSimons Observatory - Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave, NY 10010
provide a list of guidelines to support the analysis of spectrally-unresolved JWST spectra.

iSHELL
CRIRESJH K

VISIRMulti-wavelengthwater survey
TEXES= 001-000 , Eu ~ 8000-9500 K

L

NIRSpecMN= 010-000 , Eu ~ 4500-9500 K

NIRSpec model

MIRI model

oﬀset

H2O

ro-vibrational lines(stretching mode)3

ro-vibrational
lines
OH(bending mode)iSHELLCRIRES

⼤気透過率

Q= 000-000 , Eu ~ 4000-7000 K

MIRI model

oﬀset

MIRI

oﬀset

H2O

CO
H2O

rotational lines
H2O

H2O

VISIR
TEXES

Figure 1. =Overview
of near- and mid-infrared =water
emission bands as observed fromspace and the ground (see Section 1.1).
001-000 , Eu ~ 8000-9500 K
010-000 , Eu ~ 4500-9500 K= 000-000 , Eu ~ 4000-7000 K
Top: Earth’s atmosphericNIRSpec
transmission(in green), with observingMIRI
bands
water
emission model for
model
modellabelled in orange. Middle: MIRI
model
illustration of its multi-band structure (not a fit to the data; model fits to the data are instead shown in Sections 2 and 4.4).
oﬀset
oﬀset
oﬀset
O
H
The coverage of2 di↵erent spectrographs is shown with black boxes to illustrate which
parts
of
the
spectrumcan be observed:
H2O
CO
high-resolution (R > 30000) spectrographsfrom the groundcan spectrally-resolve relatively weak high-energy lines in small
OH
Multi-wavelength water Hsurvey
21
H2O
2O
spectral windows, while JWSTfrom space can observea much wider
spectralrange
but
only at moderate
resolution (R ⇠ 1500–
H2O3700). Bottom: zoomed-in
spectral regions to illustrate the di↵erence in resolution between JWST and ground-based data (theSpitzer
CRIRES, iSHELL, and TEXES spectra are for DR Tau and adopted from this work and Banzatti et al. 2017; Salyk
et al. 2019). water survey
Multi-wavelength

Space-based spectrographs provide wide spectral covro-vibrational transitions in thebending and stretching
Spitzererage 1.
(e.g.
10–37
Spitzer-IRS,
andnow 4.9–
modes
present
compact
bands
at 4–9FigureOverview
of µm
near-withand mid-infraredwater
emissionbands as observed
space more
and theground (seeSection1.1).µm and 2.5–
H2O from
JWST
HCN
H2O
COin orange. Middle: water emission model for
H2OTop:
Earth’s
atmospherictransmission(in green),
with observing
bands labelled
28 µm
with
JWST-MIRI)
but
losekinematic
informa3.5µmrespectively.
We
includeinthefigureaskytransCHOH
illustrationofits
multi-bandstructure
(not
a
fit
to
the
data;
model
fits
to mission
the data areinstead shownin Sections
2 and
4.4).
OH together lines
OHtion on the observed emission,and blend
spectrumas obtainedfrom
the
ESO SkyCalc
The coverage of di↵erent spectrographs is shown with black boxes to illustrate which parts of the spectrum can be observed:
JWST
from multiple
andcandif-spectrally-resolve
application,
setup
forhigh-energy
the Paranal(altitude of 2640
HCN
JWSTで分光分離できるようになった.
high-resolution(Remission/absorption> 30000) spectrographscomponents
from the groundrelatively
weaklinessite
in smallH2 O
ferent windows,
chemicalwhile
species.
ground-based
m)
and
using
airmass=1
andprecipitable
vapor
spectral
JWSTConversely,from space canobserve aSpitzerのR~700
muchspecwider spectral
range
but
only
at
moderate
resolution(R⇠ 1500– Cwater(次ページの表も参照)
2H 23700).
Bottom:zoomed-in
spectralregionspower
to illustratethedi↵erence in resolution
betweenJWSTand ground-based
dataOH(thetransmissionOH
trographs
providehighresolvingthat
separates
(PWV)
=
2.5
mm.
ComparisonofEarth’s
Figure 14. Example of a portion of a Spitzer-IRS spectrum (black, upper plot), compared to an LTE slab model of water
CRIRES,iSHELL, andTEXES
spectraareTheforlower
DR plot
Taushows
and how
adopted
from
this
work
andbeBanzatti
et al. 2017; Salyk et al. 2019).
emission(in light blue)
from di↵erent
Banzatti et al.lines(2020).and
thewater tomodel
observedatthe emission
frommolecules
andre-samethewouldwater
emission
spectrum in the top two panels in
the resolution of JWST-MIRI, assuming S/N=100; representative models for other molecules previously identified in Spitzer
vealsarethegaskinematics
inhighdetail,but between
they
can
only
Figure1 demonstrates
that ground-based
Space-based
spectrographs
providewide
spectralcovro-vibrationaltransitionsin the bending
and stretching instruments
spectraincludedfor visualization ofthe
improvedde-blendingdi↵erentlines
and molecular
spectra.
22

2

erage (e.g. 10–37 µm with Spitzer-IRS, and now 4.9–

modes present more compact bands at 4–9 µm and 2.5–

H2O

H2 O

CO2
OH

outside of Earth’s atmosphere. Despite the amount ofwater spectra from disks collected to date (see previous
summary in Banzatti et al. 2017), a number of fundamental questions remain:
1) which inner disk region(s) do the infrared waterlines trace, and are there multiple water reservoirs (withdi↵erent temperature and density);
2) what is the water abundance in inner disks andwhat determines it (chemistry vs dynamics);
3) what is the relative role of di↵erent excitation processes, and is water emission in local thermodynamic
equilibrium (LTE);4) is water present in a molecular inner disk wind; and5) how can we correctly interpret the complex water
spectra observed across infrared wavelengths within aunified picture of inner disks?
In this work we o↵er a contribution to this field
at a time when the first water spectra are being observed with JWST (Yang et al. 2022). We present andanalyze spectrally-resolved water emission lines fromro-vibrational and rotational bands at multiple wavelengths between 2.9 and 12.9 µm tracing upper level
energies between 4000 and 9500 K, and compare themto the velocity and excitation of ro-vibrational CO spectra observed at 4.5–5.25 µm tracing the same range inupper level energies. One goal of this work is to present
guidelines to support the analysis of both individualand large samples of spectrally-unresolved water spectrafrom JWST.

1. ⾚外域の⽔蒸気輝線は円盤内側のどこをトレースするのか？
境下（温度密度）か、それとも複数の環境か？

⽔蒸気分⼦が存在するのは、ある環

2. 円盤内側の蒸気分⼦存在量は何で決まるのか？（化学？⼒学的作⽤？）
3. 異なる励起プロセスがあるとして、それらの役割（物理的意味）は？
LTE成⽴と⾒做してよい？

⽔蒸気分⼦が存在する相は

4. 円盤内側の⽔蒸気分⼦は、円盤⾵中に存在するのか？
5. ⾚外域⽔蒸気分⼦輝線群は、複雑なスペクトルを⽰すが、円盤⼀般を統⼀的な描像でとらえるとして、その⽂脈での「正しい」解釈とは？

4

これは地上望遠鏡のスペックであることに注意

Table 1. Summary of high-resolution water spectra observed in disks with four ground-based instruments.
Instrument

R# lines

(µm)

Eu

ncrit

SampleDetections(K)(cm 3 )(# disks)(# disks)

References

2.9–2.98

CRIRES

95,000⇡ 25

8,000–9,500

1015 –1016

46

16

1

4.52–5.24

iSHELL60,000⇡ 40

4,500–9,500⇡ 101360

10this work, 2

12.23–12.87

VISIR

30,000

2–11

3,200–7,000⇡ 101164

10

this work

12.37–12.46

TEXES

100,000

3–7

3,600–6,000⇡ 101197

3Note—Critical densities ncrit = Aul /Cul are estimated using molecular data adopted in RADEX (see Section
4.3). As collision temperature, we use the excitation temperatures from Table 3. Since upper level energies Eu
only up to 7200 K are included in Faure & Josselin (2008), as collisional rates Cul for the 2.9–2.98 µm lines wetake those of lines near 2.7 µm with same range in Aul but Eu of 6000–7200 K.

中間⾚外線12μmの⽔蒸気分⼦輝線(⿊のヒストグラム)；⾚と⻘はスタッキング解析から得たCOの⽰準(？)スペクトルのうち, 狭輝線幅成分NCと広輝線幅成分BC

狭輝線幅成分NCと広輝線幅成分BCが何に起因するかは解釈が分かれるらしい(see Sect. 5.2.2.)；著者の解釈は図15

Figure 6. Gallery of H2 O detections in VISIR spectra, using the 12.396 µm line that is the least a↵ected by telluric absorption(see Figure 22). CO components and stellar RVs are marked as in Figure 5. Due to the deep and broad absorption, CO
components are not extracted in IRAS 04303 and the full observed line profile is shown instead.

Appendixにある、こちらが⽣データ
Figure 16. Multi-wavelength infrared spectra included in this work. The stellar RV is showed with a dashed line on top of COlines, where available. High-resolution spectral lines are shown in velocity space and continuum-normalized (the L-band lines
are shown in reference to 2.9283 µm), those from Spitzer spectra are shown in wavelength and in calibrated flux units of Jy.
H2 O emission is marked with dashed lines while H2 and OH emission is marked with dotted lines in the Spitzer spectra.

emission (in lightblue) from Banzatti et al. (2020). The lower plot shows how the same water model would狭輝線幅成分NCと広輝線幅成分BC
be observed at
Spitzer
中間⾚外線12μmの⽔蒸気分⼦輝線(⿊のヒストグラム)；⾚と⻘はスタッキング解析から得たCOの⽰準(？)スペクトルのうち,
the resolution of JWST-MIRI, assuming S/N=100; representative models for other molecules previously identified in Spitzer
spectra are included for visualization of the improved de-blending between di↵erent lines and molecular spectra.

JWST

HCN

H2O
C 2H 2
OH

NC
OH

H2O

H2O

Abs.

Abs.

CO2

OH

BC

Exampleof Gallery
a portionof a Spitzer-IRS
spectrum(black,upperspectraplot), ofcompared
toobserved
an LTEwith
slabiSHELL
model ofwater
Figure 15.
of representative
CO lineshapes fromM -bandinner disks(data
in grey,
from blue)
Banzatti
et al.
2022, andthis(2020).
work), illustratingof kinematic
blendingof di↵erent
components
light
from
Banzatti
et al.
The lower the
plotlossshows
how theinformation
same waterand
model
would
be observed
atobserved at theresolutionof MIRI representative(in black, note models
how absorption
emissionpreviously
may cancelidentified
each otherin MIRI
onwhenof JWST-MIRI,
assuming
S/N=100;
for otherandmolecules
in outSpitzer
spectra).for visualization of the improved de-blending between di↵erent lines and molecular spectra.
included
狭輝線幅成分NCと広輝線幅成分BCが何に起因するかは解釈が分かれるらしい(seeSect.
5.2.2.)；著者の解釈(この論⽂のひとつの結論)は,
図15
disks.
For a limited number of disks observed
spread of observed rotation diagrams and betterfromthe12.396
ground,thiscanthatbe donebyleastdirectly
us- by telluric absorption
measurethe observable
columndensityinbyVISIR
detect-spectra, using
Figure6. Galleryof H2 O
detections
the
µm
line
is thea↵ecteding spectrally-resolved
water
emission
atdeepmultiple11). stellar RVs are marked
weak lines
Aul (Figureand(seeing
Figure22). with
COlow
components
asin
Figure
5.
Due
to
the
and broad absorption, CONC
Abs.
wavelengths(Table3). is shown instead.
Abs.
components
arenotextracted
in
IRAS
04303
and
the
full
observed
line
profile• Single-temperature slab models in LTE can be expected to provide good fits to JWST spectra overnarrow ranges of Eu and within theBCsame band(e.g. the ro-vibrational bending mode around
6.5 µm), but the rotational spectrum at > 10 µm,
which overall spans a large range in Eu from alarger emitting area, will require accounting for• The ro-vibrational bands at 2.7 and 6.5 µm showdi↵erent temperature and non-LTE vibrational excitation as compared to the rotational lines at> 10 µm, and trace di↵erent disk regions as shownby their di↵erent FWHM (Section 4); modeling of
JWST spectra will need to account for these dif-12S￼ は, 輝線形状の太り具合：
S>2.5は三⾓形的で「円盤と円盤⾵」起源
S<2.5は円盤起源を⽰唆

⽔蒸気分⼦輝線を特徴づける、
諸元同⼠の相関：トレンドとして控えめにSect.4.2で議論

Figure 9. Overview of line luminosity for CO and water lines between 2.9 and 30 µm, as a function of stellar and disk
parameters (Section 4.2). Datapoints are classified according to the kinematic shape of the CO line using a line shape parameter
S (Banzatti et al. 2022): “triangular” lines with S > 2.5 associated to disk+wind emission (marked with blue triangles), anddouble-peak lines with S < 2.5 associated to purely Keplerian motion (marked with orange squares). Upper limits are marked
with thin symbols. Line flux measurements included in this figure are reported in Appendix C.

古屋メモ：
・すべての量が独⽴？
・選択バイアスは⼊り込んでいない？
・non-detectionの天体はない？

produce distinct features in water rotation diagrams.

14

4.3.1. LTE case
Rotation diagrams are defined such that, in conditionsof optically thin emission at a single excitation temperature and in local thermal equilibrium (LTE), the fluxes
from lines at frequency ⌫ observed from an unresolved
point source form a straight line as (see Larsson et al.
2002):
◆
✓
◆
✓
Eu
N⌦
4⇡F
,
(1)
ln
= ln
h⌫gu Aul
Q(T )T

Log(o)

ln(4pF/(hvAulgu))

Log(o)

ln(4pF/(hvAulgu))

where F is the integrated line flux, ⌦ is the solid angle
A/d2 (A the emitting area of the source and d the distance to the source), gu is the statistical weight of theupper level, Q(T ) is the partition function. Throughout this paper, we use Eu in units of K and cgs units
for the rotation diagram. The excitation temperature
T and the column density N can be easily derived fromthe slope and intercept of a linear fit using Equation
1. This technique is useful, however, even when theemission becomes optically thick and/or the excitation
deviates from LTE. In fact, in these cases the observed
molecular line fluxes would produce specific curvatures
and/or a large vertical spread in line fluxes in the diFigure
Rotation
infrared given
waterbyrotationallines (Section 4.3). Three di↵erent models are used to illustrate theagram 10.
departingfromdiagrams
the linearofbehavior
thee↵ectsof di↵erent
temperatures,line opacity, and LTE/non-LTE excitation: a slab model in LTE (Banzatti et al.
LTE opticallythinexcitationcase, as describedin the following.
2012),
slab modelin non-LTE
using
RADEX
(van der Tak et al. 2007), and a two-dimensional disk structure in LTE using
Thea basic
propertiesof rotation
diagramsof infrared
RADLite(Pontoppidan
et al.in2009).
and model, larger symbols mark transitions that are stronger than 1% of thewater emission
are displayed
FigureIn10each
usingplot
a singlestrongest
line,
simulatea detection
threshold;weaker lines are marked with small dots.
slab model
intoLTE(describedin Banzatti
et al. 2012),
with the temperature T and the column density N as
free parameters. For this demonstration,18we adopt
a refT = 600 K , N = 10 cmï2
T = 300 K , N = 1024 cmï2
erence15 distance of 140 pc and a thermal line broadening15of 1 km/s, and we fix the slab surface area A to a disk 8
8
Q1,
2,
and
3(下に再掲)を念頭に,
15
10 radius 1 au. In the optically thin case (N = 10
with
10
2
cm , top left in the figure), water lines form a straight 66まずモデルを３通りつくって↑、個々の天体に適⽤してみると→
5
line5in the diagram, with slope set by the temperature.
It is worth noting that higher T increasingly populate 4400transitions
from higher energy levels, as indicated by thelarger symbols in the figure. When the column density 2
2
ï5
is ï5
increased, instead, line opacities increase and lines
1.
⾚外域の⽔蒸気輝線は円盤内側のどこをトレースするのか？
⽔蒸気分⼦が存在するのは、ある環境
spreadover the diagram following a specific pattern. 00ï10下（温度密度）か、それとも複数の環境か？
ï10Whena line gets optically thick (⌧1) it “freezes”
on the diagram, i.e. its intensity is only weakly depen- ï2
ï2
ï15 on the column density. This happens first to those
ï15
dent
2.
円盤内側の蒸気分⼦存在量は何で決まるのか？（化学？⼒学的作⽤？）
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
lines with large Aul (the low-energy,
bottomleft
cornerEu (K)Eu (K)
3.
異なる励起プロセスがあるとして、それらの役割（物理的意味）は？
⽔蒸気分⼦が存在する相はof thediagram, see also Figure 11), as the line opacity
Figure11. Similar to Figure 10, but including two more properties: the line intensity proportional to dot sizes, and the line
LTE成⽴と⾒做してよい？
opacity ⌧ (proportional to Aul ) in blue-color scale. Moderate to high column densities produce optically thick emission andincreasethe vertical spread of lines in the diagram. The model to the right assumes a very high column density to better
4. 円盤内側の⽔蒸気分⼦は、円盤⾵中に存在するのか？
illustrate the e↵ect of the spread in line opacities.

5.

⾚外域⽔蒸気分⼦輝線群は、複雑なスペクトルを⽰すが、円盤⼀般を統⼀的な描像でとらえるとしis proportional to Aul . The optically thin lines, instead,edge of the spread, while the most optically thick onesて、その⽂脈での「正しい」解釈とは？

still follow Equation 1 and can rise in the diagram to-progressively set the middle and lower edge (Figure 11).

CRIRES: Ro-vibrational lines at 2.9 µm
iSHELL: Ro-vibrational lines at 5 µm
VISIR/TEXES: Rotational lines at 12.4 µm
IRS: Rotational lines at 16-33 µm

Figure 12. Rotation diagram of water emission as observed at multiple wavelengths in a selection of disks with water detections.
Line flux measurements are reported in Appendix C. The last two plots at the bottom are examples of rotationally-cold water
detected in Spitzer-IRS spectra (see also the multi-wavelength plots in Appendix A).

under-excited as compared to the M -band lines in all
disks. While real variability and the non-simultaneous
flux calibration may o↵set the emission as observed withdi↵erent instruments at di↵erent times, the apparent
systematic o↵set between ro-vibrational bands suggests
a di↵erence in their excitation (see Section 5).
Considering line fluxes from di↵erent instruments, theobserved rotation diagrams show an overall curvaturethat is reminiscent of what is found from the 2D disk
model in Figure 10 as due to emission from a range oftemperatures at di↵erent disk radii. These curvatures
could not be seen before in previous work that only cov-of large water column densities (Figure 10). The vertical spread is more visible than in the case of spectra from ground-based instruments, because these havemore stringent sensitivity limits and only detect stronger
lines close to the upper edge of the rotational spread(Figure 11). By better de-blending line fluxes at midinfrared wavelengths and detecting weaker lines withlower Aul , the analysis of JWST spectra will reveal the
shape and spread in rotation diagrams in higher detail(see Section 5).
4.4.1. LTE slab fits

右上パネルの縦軸：COの広輝線幅領域の線幅に対する、それぞれの輝線幅の⽐
結局, ３つのモデルの組み合わせが必要そうだ

Figure 13. Overview of excitation and kinematics of water emission as spectrally-resolved at multiple wavelengths in this work.
Top left and bottom: representative LTE slab models from results in Table 3; the overall curvature in the observed rotation
diagrams (Figure 12) can be approximated by a series of slab model fits to the di↵erent wavelengths covered by di↵erent
instruments (Section 5.1.1). Non-LTE excitation may cause the suppression of ro-vibrational bands as compared to slab model
fits to the rotational lines (see Section 5.1.2). Top right: observed gradient in line widths as a function of upper level energy
for water and CO (Section 5.1.3); grey datapoints at 100–2400 K are model predictions for three water lines in RNO 90 using
RADLite, from Blevins et al. (2016). Critical densities ncrit are reported for reference (see Table 1).

この相関は、円盤内側ほど⾼温で線幅がひろがるというBlevins et al. (2016)のモデルと合う. (Sect. 5.1.3)

tion.
The main findings of this work are:• ro-vibrational water lines at 2.9 µm and 5 µm (Eu • 2.9 and 5 μmの⽔蒸気回転振動遷移は広い線幅であるのに対し, より低温のガスをトレースする回転遷移の線幅は狭い.
of 4500–10000 K) have larger FWHM and higher
excitation temperature (1000–1100 K), while ro- • slabモデルとの⽐較から(そうは⾔うものの、結局)、すべての輝線は同程度の柱密度をトレース.
tational lines near 12.4 µm (Eu of 4000–6000 K)
have narrower FWHM and lower excitation temperature (800 K); LTE slab model fits suggest thata similar column density is observed in all waterbands (a few ⇥1018 cm 2 , Section 4.4);• the new 5 µm spectra from iSHELL for the first• 新たな5 μmの⽔蒸気回転振動遷移データから、 >10 μmの輝線に対するslabモデルフィットは<9 μmの輝time directly demonstrate that slab model fits to線の強度を過⼤評価していた（今⽇のゼミでこの部分はスキップしている）. この結果は、振動遷移はLTE仮
the rotational lines at > 10 µm strongly over定が成⽴していない領域起源という説明(Bosman+22)を⽀持.
predict the ro-vibrational emission bands at <9 µm; this is interpreted as evidence for non-LTE
vibrational excitation, as discussed in Bosman
et al. (2022);• the picture emerging from combining line kinematics and excitation is in good agreement with therange in critical density for the di↵erent bands:
1) an inner, hotter, and denser disk region exciting the ro-vibrational water bands and the broad
CO component, and 2) a progressively cooler disk
surface (and low-velocity region in an inner diskwind) exciting the rotational lines and the narrow
CO component (with density < 1012 cm 3 so as
to sub-thermally excite the ro-vibrational lines);
the relative contribution of disk vs wind emission
across the di↵erent radial regions remains to beclarified.

• ⼀連の結果は他の観測とも⽭盾なく,(1) 内側の暖かく⾼密度領域で⽔蒸気分⼦回転振動遷移が励起され、(2) より低温の円盤表⾯と円盤内側の冷たい部分で⽔蒸気分⼦回転遷移が励起されている。また、このような領域は, <1e12 1/cm^3でサーマライズしていないCOの狭輝線成分が励起される領域でもある。
(3)しかし, ⽔蒸気分⼦回転振動遷移と回転遷移が円盤起源なのか、円盤⾵起源なのか、両⽅なのか、の問題は決着しなかった.

Horrobin1 , Z. Hubert2 , L. Jocou2 , P. Kervella13 , S. Lacour13 , V. Lapeyrère13 , J.-B. Le Bouquin2 , P. Léna13 , D. Lutz4 , F.
The
GRAVITY
young
stellarobjectsurvey
4
4
13
13
3
4
Mang , T. Ott , T. Paumard , G. Perrin , S. Scheithauer , J. Shangguan , T. Shimizu4 , S. Spezzano4 , O. Straub4 , C.
1 , E. Sturm4 , E. van Dishoeck4, 14 , F. Vincent13 , and F. Widmann4
Straubmeier
IX. Spatially resolved kinematics of hot hydrogen gas in the star-disk interaction(Affiliations
can be found
the references)
regionof Tafter
Tauri
stars

95v3 [astro-ph.SR] 23 Nov 2022

accepted
GRAVITY Collaboration: J. A. Wojtczak1 , L. Received
Labadie1 ,-;K.
Perraut-2 , B. Tessore2 , A. Soulain2 , V. Ganci1, 5 , J. Bouvier2 ,C. Dougados2 , E. Alécian2 , H. Nowacki2 , G. Cozzo2, 15 , W. Brandner3 , A. Caratti o Garatti3, 6, 7 , P. Garcia9, 10 , R.
9, 12 , M. Benisty2 , J.-P. Berger2 , G. Bourdarot4 , P. Caselli4 , Y.
ABSTRACT
Garcia Lopez3, 6, 11 , J. Sanchez-Bermudez3, 8 , A. Amorim
Clénet13 , P. T. de Zeeuw4, 14 , R. Davies4 , A. Drescher4 , G. Duvert2 , A. Eckart1, 5 , F. Eisenhauer4 , F. Eupen1 , N. M.
Context. HotFörster-Schreiber
atomic hydrogen4emission
lines13in
stars
serve
as tracers
forHeißel
physicalprocesses
in 3theof
4 , S. Grant
4 , R.
1 , G.
13 , Th.
, E. Gendron, S.pre-main
Gillessensequence
GrellmannHenning, S.innermost
Hippler3 , regions
M.
circumstellar accretion1 disks, whereinteraction
between13a star and disk
the dominanton the formationof13infalls and4 outflows.
2 , the2 , P. Kervella
13 , is
13 ,influence
2 , P. Léna
Horrobin,Z.
Hubert
L.
Jocou
,
S.
LacourV.
Lapeyrère
J.-B.
Le
Bouquin
,
D.
Lutz
,
F.
星と円盤の相互作⽤領域をIn the highly magnetically
activeT
Tauristars,
thisinteraction
regionisparticularly
shapedbythestellarmagnetic
field
and
the
associated
4 , T. Ott4 , T. Paumard13 , G. Perrin13 , S. Scheithauer3 , J. Shangguan4 , T. Shimizu4 , S. Spezzano4 , O. Straub4 , C.
Mang
直接⾒る必要がある.
magnetosphere, covering the inner five stellar radiiaroundthecentral
star.
Even
for
the
closestT
Tauristars,
aregionascompact
as
this
is
only
1 , E. Sturm4 , E. van Dishoeck4, 14 , F. Vincent13 , and F. Widmann4
Straubmeierobserved on the sky plane at sub-mas scales. To resolve it spatially, the capabilities of optical long baseline interferometry are required.
Aims. We aim to spatially and spectrally resolve the Br
hydrogenlinethewiththe methods of interferometry in order to examine the(Affiliations
can emission
be found afterreferences)kinematics of the hydrogen gas emission region in the inner accretion disk of a sample of solar-like young stellar objects. The goal is to identify
Received-; accepted
trends and categories among the sources of our sample and to discuss
whetheror not- they can be tied to di↵erent origin mechanisms associatedwith Br emission in T Tauri stars, chiefly and most prominently magnetospheric accretion.
Methods. We observed a sample of seven T Tauri stars for the first timewith VLTI GRAVITY, recording spectra and spectrally dispersed inter- VLT⼲渉計GRAVITYでABSTRACT
ferometric quantities across the Br line at 2.16 µm in the near-infrared K-band. We used the visibilities and di↵erential phases to extract the ２μm帯の￼Brγ輝線分光撮像
Hot region
atomic hydrogen
emission lines
in pre-main
sequence stars servebasis,
as tracers
for physicalprocesses
in the innermostof radialsize of the BrContext.
emissionand the photocentre
shiftson a channel-by-channel
probing
the variationof spatial
extent at regionsdi↵erent⇨ “チャネルマップ”
circumstellar
accretion
disks,
wheretheinteraction
between
a
star
and
disk
is
the
dominant
influenceontheformationofinfallsandoutflows.
velocities. To assist in the interpretation, we also made use of radiative transfer models of magnetospheric accretion to establish a baseline of
In the highly magnetically active T Tauri stars, this interaction region is particularly shaped by the stellar magnetic field and the associatedexpected interferometricsignatures
if accretionis the radii
primary
driverof Br star.
emission.
magnetosphere,
covering theinner five stellar
aroundthe central
Even for the closest T Tauri stars, a region as compact as this is only
Results. Fromamongonour
find thatfive Toof theseven
T Taurithe
stars
show anofemission
regionwitha half-flux are
radiusin the four to seven • 7天体のうち, 5天体で, 強observed
the sample,
sky planewe
at sub-mas
scales.
resolveit spatially,
capabilities
optical long
baselineinterferometry
required.
stellar radii range
thataimis broadly
expectedfor magnetospheric
Two ofline
thewith
fivetheobjectsalsoofshow
Br emission
originating
Aims. Weto spatiallyand spectrally
resolve the Br truncation.
hydrogen emission
methods
interferometry
in orderprimarily
to examinethe
度が1/2になる領域の半径
kinematicsof theradius,hydrogengas emission
region in criterion
the inner accretion
disk of a sample
of solar-likestellarobjects.
The goal
is to identify
from within the
co-rotation
which
is an importantfor magnetosphericaccretion.
Twoyoung
objects
exhibitextendedemissionon a scale は, 4-5 times of ￼R , 2天体*
andcategories
among
the
sourcesof
oursampleandtodiscuss
whether
or
not
they
can
be
tied
to
di↵erent
originmechanisms
associatedbeyond 10 Rtrends
,
one
of
them
is
even
beyondthe
K-bandcontinuum
half-flux
radius
of
11.3
R
.
The
observedphotocentre
shiftsacross
the
line
can
⇤
⇤
で, >10 times of ￼R*with toBr whatemissionin T Tauristars,
chiefly
and mostorprominently
magnetosphericaccretion.
be either similar
is expected
for
disks
in rotation
show patternsof higher complexity.
We observed a sample of seven T Tauri stars for the first time with VLTI GRAVITY, recording spectra and spectrally dispersed interConclusions.Methods.
Based onthe observational findings and the comparison with the radiative transfer models, we find strong evidence to suggest that • 速度構造も検出
ferometric quantities across the Br line at 2.16 µm in the near-infrared K-band. We used the visibilities and di↵erential phases to extract thefor the two weakest
accretors
in theregion
sample,magnetosphericaccretionis the primary driverof Br theradiation.
resultsextent
for theremainingsources • 輝線形状 ⇨ weakest
size of theBr emission
and thephotocentre shifts
on a channel-by-channel
basis, probing
variationTheof spatial
at di↵erent
radial
imply either velocities.
partial orTostrong
contributions
comingfrommade
additional,
spatially
extendedcomponents
in theto formof outflows,
such as accretionが有りそう.
assist in
the interpretation,
we alsouse of radiativetransfermodelsemissionof magnetosphericaccretion
establish
a baseline ofstellar or diskexpected
winds. interferometric
We expect thatin actively
accreting
T Tauristars,
these
signatures
if accretionis theprimary
driverof Brphenomena
emission. typically occur simultaneously on di↵erent spatial scales.
Results.
From modelling,
among our sample,
we find thatfivebeof athekeyseven
T Tauristars show an emission
region witha half-flux radius
the foursevenarisingThrough moreadvancedinterferometry
willfactorin disentangling
their distinct
contributions
to theintotal
Br to flux
stellar radiithat is broadly expected for magnetospheric truncation. Two of the five objects also show Br emission primarily originatingfrom the innermost
diskrange
regions.

GRAVITY Collaboration: First light for GRAVITY
Phase reference
ObjectWavefront reference2” FoV

Metrology fringes

Telescope #1

Metrology
sensor

Telescope #2

MetrologyStarseparator

Starlight

DeformablemirrorIR wavefront
sensorDelay line

2” FoV

Laser

Laser
Guiding

Acquisition
cameraBeam combiner instrument

Tiptilt
Pupil

dOPD
control

IO beam combiner

Spectrometer
A
D

Fiber
couplerB

Phase
shifter
Polarization control

C

Metrology
laser

OPD control

Fig. 1. Overview and working principle of GRAVITY: the instrument coherently combines the light of the four 8 m UTs of the VLTI or thefour 1.8 m ATs. It provides infrared wavefront sensing to control the telescope adaptive optics, two interferometric beam combiners one forfringe-tracking and one for the science object , an acquisition camera and various laser guiding systems for beam stabilization, and a dedicatedlaser metrology to trace the optical path length di↵erences for narrow angle astrometry. The overview illustrates the light path and location of thevarious subsystems. For clarity, we show only two telescopes, one beam combiner, and one wavefront sensor. The wavefront sensor star (green)
can be outside the VLTI field of view. Depending on the brightness of the science object (red), the fringe tracker is either fed by a beam splitter,or as illustrated in this figure by a bright o↵-axis phase reference star (blue). The GRAVITY subsystems (light blue boxes) are embedded andtake advantage of the already existing VLTI infrastructure (light red boxes).

the ATs was carried out in June and September 2016, with first GRAVITY concept. For clarity, only two of four telescopes, that
results published in, for example, Le Bouquin et al. (2017) and is, one out of six baselines, are shown.
Kraus et al. (2017). Science operation with the ATs started in
The working principle of GRAVITY is as follows: a brightA&A 2016,
602, A94(2017)by the UTs in April 2017.
Octoberfollowed
wavefront reference star (e.g., in the Galactic center this isDOI:
10.1051/0004-6361/201730838
00This paper provides a comprehensive description of the in- GC IRS 7, a mK = 6.5 mag star at 5.5&
separation from the suc ESO 201700
strument (Sect. 2) and presents a set of early observations that permassive black hole) outside the 2 field-of-view of the VLTI
illustrate its power (Sect. 3). The detailed description of the in- is picked with the PRIMA star separator (Delplancke et al. 2004)
strument subsystems and software, and of the analysis and inter- and imaged onto the GRAVITY Coudé infrared adaptive oppretation of the observations, will be given in several forthcom- tics (CIAO) wavefront sensors. The wavefront correction is apFirst light for GRAVITY: Phase referencing
opticalinterferometry
ing papers.
plied using the MACAO
deformablemirrors of the UTs. The
00
2 field-of-view of the VLTI contains both the science target
for the Very Large Telescope(Sgr A*) and Interferometerthe phase reference star (GC IRS 16C, 1.2300 separation, mK = 9.7 mag).
Both objects are re-imaged via the main
? : R. Abuter8 , M. Accardo8 , A. Amorim6 , N.
7 , G. Ávila8 , N. Azouaoui2 , M. Benisty5 ,2. TheGRAVITY
instrument
GRAVITY
Collaboration
Anugu
delay lines (Derie 2000) to the GRAVITY beam combiner in-

Astronomy
Astrophysics

Table 1. Properties of the stars of the T Tauri sample.
A&A proofs: manuscript no. SpatiallyResolvedKinematicsWojtczak2022

Name

Sp. Type Te↵
[K]

d
[pc]

M⇤
[M ]

L⇤
[L ]

R⇤
[R ]

Age
Ṁacc
[10 8 M yr 1 ] [Ma]AS 353K54450 399.6 ± 4.2

3.9 ± 0.67 3.32 ± 0.29

7.9 - 45

1

RU LupK74050 157.5 ± 1.3 0.6 ± 0.2 1.64 ± 0.22 2.60 ± 0.17

1.8 - 30

1-2 Hercz

VV CrA SW

K74050 156.6 ±1.2 0.6 ± 0.2 1.73 ± 0.24 2.67 ± 0.19

3.33 - 22

1-2

TW HyaK64200 60.14 ± 0.07 0.9 ± 0.1 0.41 ± 0.05 1.21 ± 0.07

0.13 - 0.23

4-12

K5-K6 4300 160.5 ± 2.2 0.9 ± 0.2 3.82 ± 0.54 3.52 ± 0.25

7.8 - 50

1S4200 125.2 ± 2.3 0.8 ± 0.2 1.58 ± 0.37 2.37 ± 0.28

4.6 - 74

1-2

K2-K3 4840 146.3 ± 0.6 1.5 ± 0.2 1.61 ± 0.21 1.80 ± 0.12

0.63 - 0.9

3-6

W
Whi

S CrA NDG TauDoAr 44K6

1 ± 0.2

星の半径

S

E

Notes. References are referring to the lower and upper limit Ṁacc literature values. We note that R⇤ was computed
stellar luminosity. Other properties were adopted from Gravity Collaboration et al. (2021b).

【通説と疑問】
atmosphere (Lacour et al. 2019). We made use of the FT capa- whereas FT data is only used in￼take輝線は,magnetosphere領域のうち,bility to Brγ
the SC observations
in GRAVITY’s high resolution described further below. For an overmode (R=4000) with a width of ⇠ 5 Å, or 75 km/s, per chan- K-band continuum, based on the sa
共動半径内の安定領域,
円盤や星⾵が駆動するアウトフローなど,
nel, enabling
us to spectrally resolve
the Br feature and trace GRAVITY, we refer to the work of
the gas kinematics over a range of up to ± six channels from the (2021b).
であるが, 共動半径の外側や星の極⽅向からも￼Brγ輝線は放射されていないのか？
centre of the line, depending on the strength of the feature in the Each of the individual files obtai
contains four sets of flux data co
individual
sources.
【この観測】The observations of the di↵erent targets are subdivided into a set Telescopes, six sets of normalised
coming1.6-1.7
from thewas
six UT baselines
shortterm runsof about
5 minutes
in length, each of which
8.2-m
telescopes,
Max.基線⻑130m⇨ resolution
Fig. 1. Schematic depiction of the innermost parts of the circumstellar disk of a T Tauri star. Br emission in T Tauri stars is associatedofwiththe Fourconcept of magnetospheric accretion, but outflows caused by certain types of disk or stellar winds (dashed lines) can heat the hydrogengassavedtowasas a separate file, stretching over a total observation visibility phase data, and four sets
the necessary temperatures to produce Br emission as well. Di↵erent origin mechanisms can be tied to di↵erent spatial scales. Magnetospheric R
￼with= 4000⇨ hours
速度分解能75
km/s；ただし,fringetracker(FT)の￼
R closed= 23 baseline trian
the fouruniquetimeofaround
1
1/2
for
most
of
the
objects,althoughthematic
depictionoftheinnermost
parts
of
the
circumstellar
disk
of
a
T
Tauri
star.
Br
emission
in
T
Tauri
stars
is
associatedtheaccretion flows (depicted in red) can only stably form in a compact region within the co-rotation radius Rco , where the gaseous disk rotates at theagnetosphericaccretion,
butstar.
outflows
types
diskRorstellar winds (dashed lines) can heat theandhydrogengas
oftoDoAr 44 went on for notably longer with a total the UTs.
same angular velocity⌦ as theSpatiallycaused
extendedby
Br certain
emissionfrom ofoutsidemust
co cannot be attributed to magnetospheric accretion observation(観測中の)遅延線の計算の詳細はAppendix
be caused by someother emission
temperaturesto produce
Br component.
emission as well. Di↵erent origin mechanisms can be tied to di↵erent spatial scales.
Magnetospheric
timeof slightly
over 4 hours. Measurements of suitable calibra- The individual files were merged b
figure specificallyshowscommoncaseinofaa compact
non-axisymmetricfeaturing a radiustilt between
stellarthe
rotational
axisdisk⌦⇤ andwsThis(depicted
in red) can
onlythestably
form
region magnetosphere,
within the co-rotation
Rco ,thewhere
gaseousrotates
the
tor
stars
in aatsufficiently
close part of the sky were predominantly the post-processing routine of thethemagnetic
dipoleµ.
Theobliquityofthemagnetosphere
leads
to
the
formationoftwoaccretioncolumns,which
funnel
gas
from
a
wide
arc
at
velocity ⌦ as the star. Spatially extended Br emission from outside Rco cannot be attributed to magnetospheric accretion and must
tively time-averaging our observab
the truncation radius onto one primary hot spot per hemisphere, as first suggested in Bertout et al. (1988) and Calvet & Hartmann (1992).
Theeither up to 45 minutes before the beginning or after the
taken
some
other
emissioncomponent.
equations and physical quantities relevant for the determination of the co-rotation radius Rco and the magnetic truncation radius Rtr are discussed
endhotoftoaxis
the⌦telescope
run and thus potentially probing the sky un- over the 1 1/2 hours of observatio
ecificallytheequations
commonof a non-axisymmetricfeaturinga whichtilt between
the stellar
rotationalin Section shows
5. For theusedcaseto estimate
the sublimation radiusmagnetosphere,
Rsub , which indicatesthe area atthe disk becomes
sufficiently⇤ anddestroyµ.dust
grains,we refer
Gravity
Collaboration leads
et al. (2021b).
dipoleTheobliquity
oftothemagnetosphereto the formation of two accretion columns, which funnel gas der
fromclosea widebut
arc not
at entirely identical atmospheric conditions. For shifted to the local standard of rest5.
Resultsf the AS 353 observation, taken with the four unit

Fig. 3. Total and pure line visibilities for an exemplary baseline fromTI.
the AS 353 observation.
5.1. General results
fore the application of the spectral calibration. The Top: Visibilities before the spectral correction was applied. Blue ands In
the thismeansection
position ofthefirst
line peak.
Beforecor- greyof
shadedwe
presenta thebreakdown
the regions
generalindicate
re- the uncertainties on the total and pure line
al spectra for most of our objects were misaligned visibilities, respectively. Bottom: Same baseline after the correction.
sults
obtainedfrom
the GRAVITY
TauriEspeciallydata, introduce
somethetelluriclines andalso between
each other.TBotwith respect
to the computation of the pure line visibilities,
additional
the interpretation,and give
an in the red wing of the signal.
fter
they were concepts
brought intorelevantalignmenttothroughthe the change appears
significant
The
correctedover
spectrarecomputed
overview
theandglobaltrendsobservables
we were able to identify acrosshiftedto bringsample.
them to thestandard of rest
the entire
In localthe following
sections, we then proceed
A&A proofs: manuscript no. SpatiallyResolvedKinematicsWojtczak2022

to go over each source individually in detailcontextualiseline andto continuumdi↵erence in visibility of only about 0.01 at
even the longest
our findings by drawing upon relevant references,
if and baselines.
wherelevels canwith low continuum
Fig.greatly,
4. Relationships
between Brdis-emission region sizes and selectedavailable. Table 3 summarises key results Noise
concerning
the equallychar- vary
in wavelength
adjacent
to the Br line again fories
on the flux
derivedfrom theinstru-andpersion
stellarproperties.
acteristics
ofratios,
the Bremission
regionaccretion
properties,regions
RU Lup,where wea continuum
standard
deviationof line emission region of the cengivenby the pipeline,
are4ofand
the 5
order
of 0.01
Fitted HWHM
of theBr purerespectively.
Figuresserve
as a visual
overviewof measure
the Top:noisy
dataversus
obtainedfor
VV CrAf the T Tauri sample, although in the case of 0.0023, compared to the verytral
channelthemass-accretion
rate. The latter is depicted insampleresultswithregards
tothemost
importantcriteria
weuse
standard
deviation
can goup
to denotes the range of Ṁ values
a severe increase to around 0.03, even though (Fig. D.6) where the continuum
twoforms:
Once
as
a
grey
bar
which
ヴィジビリティ・スペクトル(⾃⼰相関)の例
interpret our
0.035.
hetocontinuum
flux results.
values remains comparable
found in the literature on the respective source, then as the instantaneous
Theforsampleconsists
Br Weemitters,with norfound non-zerodi↵erential
phases at theof Br
at from the equivalent width of theound
the othersources.of mostly strong• 上下のパネルは(何らかのオフライン)補正前後
mass-accretionrate,position
which wasderivedmalisedpeak
linevicinity
to continuum
ratios between
1.91 andfor1.53
several baselines
each target
in the sample,
with typicalabso-coding represents the classification
sibilitydata
in theof the Brflux
featureGRAVITY
Br
spectra.
The
colour
多くの天体は,for six
outsampleof ourranges
eightfromdatavisibilities
sets and• ofranging
down幅広で低輝度の成分と幅狭く⾼輝度の成分からなる.
to 1.19
for of0.5thetosample
lute phasevaluesof around
1 , although
jects
in theobjectsthe
aslargesteither meaweak (green) or intermediate to strongdi↵erential
up to 6.3(red).
tudes
close to 1,
indicating
that44.
theMany
total line
. S-shaped
as exthe weakest
emitterDoArthesuredobjects
exhibitphaselinegoesaccretors•of
幅狭く⾼輝度の成分は,ブルーシフトしている.
Most offeatures,
the T Tauristars cluster in a 4-7 R⇤ range, whichndthe surrounding
continuum werepartiallyan excess
pected forin rotation,observed
for some
sourcesshapesthat are asymmetric,
featuringof systems
blueshifted
is ofcanthebeorderof typicalmagnetosphericsizes.
•(pole-onで⾒ているものを除外しても)inverse
P-Cygniプロファイ
entireK-bandat approximatebaseline lengths
between
40 atbysomebaselines(e.g. RUBottom:
Lup 2021,
see Fig.
D.3), luminosities. The colour coding
BrUT4-UT1,
HWHM versus
accretion
emission.
We
thisasymmetry
fittinga superpoルは⾒られない.
lsitionof the targets.
TheBr
visibilities
signalsarebut basicallyare rather exceptional
notably absent
from plot.
many othercorresponds
to the upperof two Gaussian functions to the data,
dividing andinFig.
mostcases
well aligned
withtheposition oftargets.
The
featuresappearsinglepeakedin visibilities
many cases,
but
the
2.
Br
spectra
of
the
AS
353
observation,
taken
with
the
four
unit
Fig.
3.
Total
and
pure
line
for
an
exemplary baseline fromthefeatureintoanarrow
centredlowvelocity
component
andig. 2. Br spectra of the
AS 353 observation,
takenwith the four
unit Fig.
3. Totaland pureline visibilities
foran lineexemplarybaselinefromorresponding
spectrum,see, forinstance,Fig.
peak
is notalignedwith
thecentre,suggestingthat in suchtelescopes
of
the
VLTI.
the
AS
353
observation.
lescopesof the VLTI.
AS 353 observation.
a broadero↵set high velocity component.thecases
Whetherthese GausD.
apotential
S-shapemightmaskedone correctionof the twowas applied. Blue andTop:
The spectra
theof applicationof the The
spectralThe
Top:correction
Visibilities
beforespectralop:
The spectra
before thebefore
application
the spectral calibration.
Top: calibration.
Visibilities before
the spectral
was beapplied.
Bluethe
andby
is
also
reflected
intheequivalent
widths.
We
computed
the
line
sian
components
cannecessarilybedirectly
attributed
tospecific
erticalline
indicatesthemeanposition
of
the
line
peak.
Beforethecorgrey
shadedregions
indicatetheuncertainties
on
the
total
and
pure
line
tinctions
in
terms
of
visibility
signalstrengthconstituent
peaks
being
somehow
attenuated.
vertical line indicates the mean position of the line peak. Before the cor- grey shaded regions indicate the uncertainties on the total and pure line
ction, the individual spectra for most of our objects were misaligned visibilities, respectively. Bottom: Same baseline
after the correction.
luminositiesforeach Sameobjectfrom after
the equivalent
widths and Kphysicalphenomena,suchasadditional
outflows
on
top
of
an
acweenthedi↵erent
sources.
Particularly
clear
The
di↵erential
phase
data
is
significantly
more
noisybaseline
whenthetoindividual
spectramostofother.
ourBotobjects
were withmisaligned
visibilities,
respectively.
Bottom:the correction.
othrection,with respect
the telluric lines
and also for
betweeneach
Especiallyrespect to the computationof thepure line visibilities,
Fig.
2.PBr
spectraofvisibilities.
theASobservation,
taken
with
the
Fig.
3. Total
and2003).
pure line
visibilities
for an exemplary baseline from
Samewith
spectraafter theybrought
intolinesalignment
throughthethechangeappears
inEspeciallythered353wingof
the magnitudes
signal.
ヴィジビリティ・スペクトル(相互相関)の例
band
from
2MASS
(Cutriet al.
Wethen usedbothrespecttothetelluric
also
betweeneachother.
Botwithrespect
to thecomputationof thepureline
visibilities,sm:
were
observed
inwerebothepochs
ofand
RU
Lup,
compared
tosignificant
theStandard
deviations
in four
the unit
contincreting
magnetosphere,isnotcertain.
InverseCygni
features,pectral calibration. The corrected spectra and recomputed observables
telescopesof the the
VLTI.
the
ASsignal.
353
observation.
tom:
Same
spectra
after
they
were
brought
intoalignment
throughthechangeappears
significant
in
the
red
wing
of
the
ce
betweenBrpeak
andsurrounding
continuum
adjacent
to
Br
,
even
for
sourceswithclear
di↵erential
theempirical
relationshipfrom
Alcalá
etal. (2014),
as
expected
to
be
seen
when
observingmagnetosphericaccreere then further shifted to bring them to the local standard of rest
seismicな⾊付けをしている□印が,この論⽂でもっとも重要なデータ
Top:
The
spectrabeforetheapplicationofthespectralcalibration.
The
Top:
Visibilities
beforethe spectral correction was applied. Blue anspectralcalibration.
The
corrected
spectraandrecomputed
observables
LSR).
h tionas 0.12(Fig. D.3),
comparedto the relatively
phaseBr
peaks,
aretheon
averagethetheorder
ofat 0.4
. For
the
very
columnsatlow
inclination,aregenerally
absentfromline
to continuumdi↵erenceinvisibilityof onlyabout
0.01
verticalline
indicatesthemeanposition
of
line
peak.
Beforethecorgrey shaded regions indicate the uncertainties on the total and pure lin
were
then
further
shifted
to
bring
them
to
the
local
standardofrest
何かの補正(よく理解できなかった)のオフライン補正をしている.
ted
at profiles
the position
of Br
for DoAr
44for
witha even
noisy
data
of
VV CrAthecontinuumevengoes!dispersion! up tothe longest
baselines.
rection,theindividual
spectra
for
most
of
our
objectsweremisaligned
visibilities, respectively. Bottom: Same baseline after the correction
line
of
the
sample,even
those
objects
observedata(LSR).
Noise levels can equally vary greatly, with low
L continuum disL
acc

Line

mixed profile with a decreasing size at low velocities and then an is more complex for objects with higher accretion rates, as there
own to 1.19 for extremeof the sample
objects
as either(green)2,orwhilst
intermediatetoshowstronga N, and VV CrA SW), and those with highly spatially extended
cases
this
can
go
upweaktovelocities.
almostothersprofiles
increase
as
we
move
to
higherThese
mixed
is no clear correlation between the relative region sizes and theectsline relatively
accretors (red).
Most
of
the
T
Tauri
stars
clusterina
4-7
Rrange,
which
5.exhibit
Results⇤flat profileofrelative
to their error Br
bars.emission
Under aregion,
magne- mass-accretion
Br regions outsidethetypicalrange
of magnetospheric
sizes
could
be
indicativeamulti-component
rates
for
those
targets.
A&A
proofs:manuscript
no. SpatiallyResolvedKinematicsWojtczak2022
s of blueshifted Continuum
is
of
the
order
of
typicalmagnetosphericsizes.
HWHM
[R
]
18.13
±
3.59
17.36
±
5.10
17.36
±
5.10
7.47
±
0.70
11.32
±
1.61
19.07
±
2.69
10.38
±
1.42
12.64
±
1.04
⇤
tosphericaccretion
scenario,a decreaseof moresize towards
thesignaedges Magnitudes(AS 353, DG
Tau).
This separation
partiallycorresponds
toofthealthough
in
many
cases
the
extentofthesecomplexfortheobservedphotocentre
displacements
areBottom:Br(i.e.
HWHM
versusaccretion
luminosities.
The colour
codingtting a superpo- of
8
1
the
line
highervelocities)
wouldbenaively
expected,
as
<
1·
10
M
yr
,
distinction
betweenweak
accretors
(
Ṁ
Br
HWHM
[R
]
13.32
±
1.16
6.32
±
0.43
5.01
±
0.35
5.13
±
0.33
12.93
±
1.56
5.93
±
0.47
4.36
±
0.75
6.56
±
0.59
acc
⇤
5.1.
Generalresultstures
iswithintheuncertainties.
the
order
of
0.07
au
or
below.
For
multipletargets
theentirecorresponds
to
the
upper
plot.
Table
3.
Resultsforequivalent
widths,mass-accretion
rates,
andsically dividing the gas at the highest velocities should be in free fall close to again DoAr 44 and TW Hya) and the intermediate to strong characteristic sizes of the Br emission region.
Rtr [R⇤ ]point of reference
2.83 - 5.30
- 6.14- 6.61- 12.35 profile
4.50 - across8.42 the10.62- 12.68
3.36 - 6.29
2.86
5.36
An importantin the3.28
searchfor the3.53
originof 8.31
photocentre
line
is sufficiently
compact
to- becomponent and thestar.
In oursample,only 6.47
one radius,
source since(TW
Hya)
clearlyshows
accretors,which
we
indicatedinsuchFig.4
via 2.44
the di↵erent
colours.
Bremissionistheco-rotation
we
know
that
the
within
or
close
to
1
R
,
althoughacompact
concentration
R
[R
]
3.31
3.31
8.89
5.44
5.96
⇤
co
⇤
In
this
sectionwe
firstpresentabreakdownofthegeneralreher these Gaus- this decrease, whereas most of the other objects show either a While the weak accretors do appear to conform to 7.25
theofcoinner
disk
must
be
truncated
insidetheRofphotocentres
does
notnecessarily
correlate
with
the
size
so
that
stablemagこれだけが,観測量
cois alsoreflected
in the equivalentT
widths.
Wedata,computed
the line some
AS353
RU Lup 2018 RU Lup 2021
TW HyaDG TauDoAr 44
S CrA
buted
to specificsults
obtainedfrom
the
GRAVITY
Tauri
introduce
straight
increasewithaminimumatthecentrechannelorevenarotationcriterion
withcompact
emission
regions,thesituation
netospheric
can theform.
If the dominant
driverluminositiesaccretionfor each columns
object fromequivalent
widths andK- the emission region. The photocentre profiles are complex andon top of an ac- mixed
witha decreasing
sizeaccretion,
atfluxlowratio
velocities
andthatthenangiveisFWHM
more
foralthoughobjects
withhigheraccretion
rates,
as peak
there
Notes.
Fprofilethetotal
line2MASStoat expecttheWecentreofusedtheline.
and W10%arethe line
at 50%
and 10%of theL/C is relevant
ただし,
これを空間分解かつスペクトル分解
noteasilyclassified,a widths
broad
distinction
can
be
made
of
Br magnitudes
emissionismagnetosphericwetheadditional
tocontinuum
theinterpretation,andan complex
band
from
(Cutriet al.
2003).
then
Cygni
features, concepts
FL/C
1.91
1.86sizes and the
1.83
1.61
1.29
1.19
1.53
increase
as weregion
move
toposition
higherThese
mixed
profilesis no clear
correlation
betweentheregionflux,
respectively.
µ is thewould
ofvelocities.
thethe
high
(HV)
orthe
low
velocity(LV) component
fromthethatdoubleGaussian
fit torelative
the spectrum.
betweentargets
showquasi-rotational
profiles,featuringBremission
be
of
order
of
co-rotation
the empirical
relationshipfrom
Alcalá
et al.
(2014),
ospheric
accre-over
した点がこの観測の凄さ
1for those
overview
theglobaltrendswewereable
to channel.
identify
acrossTheBr
half-flux
radius
(HWHM)
is
given
for
the
central
R
HWHM,
PA,
and
were targets.
adoptedGravity
Collaboration
could
beindicativeofamulti-componentBremission
region,mass-accretion
rates
FWHM
[km
sarms
] ialigned
233 from
183
121
224
137
175
co , continuum
distinct
blue
and
red
along
a commonaxis,
targets 187
radiusorevenslightly
morecompact.
The
co-rotation
radiusisabsent from the et al. (2021b). Accretion luminosities were estimated from the line luminosities based on the empirical
relationshipin Eq.displacements
1. Theinstantaneous
although
in
many
cases
the! extent
ofsections,thesemore complex
signaMagnitudes
forthes thatobservedphotocentre
are of1
theentiresample.
Inthefollowing
wethenproceedwithcompact
profiles
lack
any
clear
structures,
andcomplexdefinedastheradiusatwhich
theangularvelocityoftherotating
!
]
594
607
420
241
445
274
524
W10%
[km
ts observed at a mass-accretion
rates
were
then
computed
as
in
Eq
2.
R
is
given
based
on
Eq.
4
for
magnetic
field
strengths
between
1
kG
to
3
kG
and
using
the
tr
L
LLinevelocity of the star ⌦⇤ (Bouvier
tures
isacc
withinthe
theangular
uncertainties.
the orderof 0.07or below.
For multiple
targets the entire
which
againau
potentiallyas a superpositionof
diskmatches2013):
1 appear
log
=
a
·
log
+
b
(1) profiles
The
width
and
to go over eachsourceindividuallyindetailandcontextualise
µ
[km
s
]
-97
-55
-50
-183
-273
mass-accretion
rates
derivedfromtheequivalent
widths(EW).
The
asymmetric
error
bars
on
the
absolute
valuesofṀ
represent
the
25th
and
HV profile across the line is sufficiently
acc,inst
An important
pointofreferenceinthesearchfortheoriginofphotocentre
compacttobeLLmultiple components.
In Fig. 5 we give an overview over the
total emission 75th percentiles!1/3of the distribution. Other error bars denote 1 uncertainties.
1[kmtosof1]the
3such
2the
6
1
3
µLV
our
findings
bydrawing
upon
relevantreferences,
if
and
where
Br
emissionistheco-rotation
radius,
since
we
know
that
the
withinorcloseR,althoughacompact
concentrationGM
possiblealignment
photocentre
shiftsacross
line
with
⇤
⇤
e, even between Rco =.
(3) di↵erent
1not necessarily
inner
disk
insidetheRofphotocentres
does
correlatewithsize ofsothatstablemag2must be truncatedaxes.
Toaccounto↵setof the 586
profiles
表3にまとめた残りの物理量は,
計算で推定
co
FWHM
[km
s
] for the520
295 region482
549
HV
Fig.
4.
Relationships
between
Brthe fromemissionsizes and selected⌦available.
Table
3summarises
key
results
concerningthecharugh the overall with a=1.16± 0.07 and b=3.6 ± 0.38, to estimate the accre⇤
theplot
emission
region.
Thephotocentre
profilesare complex
andnetosphericaccretioncolumns
can form.
If thedominant
driver thecentre,we computethe 204di↵erence
vectors
between1 dataing
mass-accretionrates
via (Hartmann
et al.
1998)
We
fittedthevisibility
with
a
2D
Gaussian
in
order
to154
akacteristics
flux ratio and oftion
luminosities
andsubsequently
determinedthecorrespondFWHM
[km
s
]
154
116
170
LV
stellarproperties.
theBremission
regionandaccretion
properties,
Stellarare determinedfrom wemeasurements
noteasilyclassified,althoughabroad
distinction
can
be
made
of
Br angularemissionvelocities
is magnetosphericaccretion,
expect that of
the eachand theradii
centrechannel of(shownas aBrwhitesquare)refind point
the half-flux(HWHM)
the pureemission! 1
EW-19.62± 0.91-16.82± 1.76-13.470.43 -7.11 region± 0.76 of-5.80± 0.35Top:
Fitted
of
the
Br
pure
line±emission
thecen- -2.65 ± 0.38 -8.71 ± 0.66
theFiguresrotational
ofwould
thestar or thethe
vArticlesin(i).
Werefer
to Gravbetween
targets
thatshowHWHM
quasi-rotational
profiles,featuringemissionRperiod
orderof theco-rotation
andthencomputetheminimum
angulardi↵erence
betweenthe
RserveR⇤ number,page
7 of 41 ofrespectively.ṀBr
4
and
5
a
visualoverview
the
gion,
using
the[Å]
inclination
andpositionanglesoftheK-band⇤region⇤ be ofas= or1 even slightly⇡ 1.25L, values radius(2)is angle
acc more
accTheityaccCollaboration
etLal.
(2021b)for therelevantfor ourdistinct
blue
red
arms
aGravity
commonaxis,
targets
radiuscompact.
co-rotationof thedi↵erence
vectoraligned
andNIR
continuum
disk axis[Lchannel] region
3.07the±along0.17
0.98 ±Collaboration
0.12
0.76rate.
± 0.03The
0.03± 0.00is depicted
0.33 ± 0.02in 0.07 ± 0.01 1.74 ± 0.15
Lemission
tral
versusthe
mass-accretion
latteraccandcontinuum
presented
in
R
GM
GM
in
⇤
⇤
sample results
withregards
tothethemost
importantcriteriause
sampleobjects.
The atco-rotation
radii
are
given inofTable
3. Of wepositionangle. toThe
resultingvalue
isa measureofhowcomplex
wellcompact
profilesanyclear
structures,
anddefinedas theradiuswhichangularvelocitytherotating
1
etwithal. log(2021b)constrain
thosetwoparametersin 0.48
our
fit.
The
Ṁacc,inst[Myr that] lack
-6.38±
0.44-6.76bar±-6.87± 0.48 the-8.74range± 0.49 of-7.40
0.47 -8.46 ± 0.49 -6.56 ± 0.44
twoforms:
Once
as
a
grey
which
denotesṀ ±values
course,the best
to determine
thesizeof the2013):
Bren- aligned
thephotocentreo↵setsarerelative
to
the
disk
axis.
The
profiles
which
again
appearpotentiallyasasuperpositionof
diskmatchesthewayangularvelocitybetween
ofwhether
the star⌦⇤gravitational(Bouvier
describes
therelationshiptheto interpret which
ourresults.
HWHMs we obtained
throughthis process
are, across+28.968
1+41.35+20.78the entire +15.79
+0.32
+4.44
+0.38
[10
M
yr
]
41.48
17.31
13.38
0.18
3.95
0.35
27.72
Ṁ
found
in
the
literatureontherespective
source,thenastheinstantaneousemission
regioncorresponds
to
the
size
of
the
magnetosphereacc,inst
plot
can
be
interpretedinameaningfulwaybyconsideringthemultiplecomponents.
In
Fig.
5
we
give
an
overview
over
the
2
0.1
0.19
released !andradiatedaway
by the mass
falling
in from the
8.54
13.57
sample,of the order of less than 0.2120.16
au at their greatest
extent, 6.66
The sampleergy
consistsofmostlystrongBremitters,
withnor1/3in any object
comparesize against
ofdownclustering,
andtheatwhichanglesthe au.
clusteringGM
possiblealignmentofphotocentre
shiftsacrosstheoccurs.
line
with
truncation
radius.
Forbethetorighthand thesideregion
approximation
we thefol- degree
mass-accretion
rate,
which
was
derivedfrom the equivalent width of the⇤ would
rangingtoregions
ascompact
as
0.03
In
terms
of
stel=
.
(3)
R
colinemagnetospherictruncation
directly.
radiusmalised peaktoflux
ratiosbetween
1.91
andAlar1.53
concentrationofin asizes
narrow
angularrange(ASdi↵erent
axes.
Topoints
account
for
the
o↵set
ofup
the
profilesfrom
5 Rtruncation
size
low
the common
conventionradius
of using
Rin ⇡The⇤ as a typicaltoless represents the classification
radii, thecentralchannel
vary
from
to
13
R⇤ 353)⌦2⇤ continuum
GRAVITY
Br
spectra.
The
colourcoding
PA
[
]
173
±
3
99
±
31
101 ± 31130 ± 32
143 ± 12137 ± 41±6cantruncation
be computedfrom stellar parameters, if the strength of the indicatesthatthephotocentre
shift
isalignedalong
asingletheplotcentre,wecomputethedi↵erence
vectors
betweenforradii.
than
5
R,
althoughthemajorityofobjects
show
clustering(see
for six out of
our eight
data
sets and ranging down to 1.19
for⇤ of the sample objects as either weak (green) or intermediate to strong+6+6+6
magnetic
dipolefield
isknown:
axis.
Iftheclustering
range
close
zero, theStellarresults
angularare indeterminedfromaremeasurementsof Figures
each point
andcentrechannelas 16
aphotocentres
whitesquare)These
arevelocities
summarised
Table 3. They
also shown ini [ a] the417 ±2(shown20
14
49 ± 432 ± 427 ± 3
5, 4)
in
range
fromis4 toR⇤to, whichisfairlytypicalfor8
8
14
the weakestFig.
emitter
DoAr
44.
Many
of
the
objects
exhibitline
arealigned
with
the
disk
semi-major
axis,
which
isclusteringsomethingaccretors(red).
Mostof di↵erencetheT Tauristars
clusterin
a 4-7
R⇤ range,whichtherotational
period
of
the
star
or
the
v
sin(i).
We
refer
toGravandthen compute
theminimum
angularbetweenthe4, where4/7
we
presentboththeinstantaneous
mass-accretion
magnetosphericradii(Bouvieretal.
2007).
This
can
12/7
Continuum
HWHM
[au]
0.28
±
0.05
0.21
±
0.06
0.21
±
0.06
0.042
±
0.003
0.13
±
0.01 0.16 ± 0.02 0.17 ± 0.02
B
R
that
would
be
expected
from
a
disk
in
Keplerianrotation.
If
the
ity
Collaboration
et al.based(2021b)forlowest
thean
relevant
valuesforour beangleof theisdi↵erence
vectorandtypicalthemass-accretion
NIRmagnetosphericcontinuum
disk
axissizes.
asasymmetric,
well 3as a 2range
on theandhighestprevious
shapes that rates
featuringexcessofblueshifted
of
the
order
of
observed
acrosstheentire
range
of
rates
of
our
Rare
(4)
tr = 12.6 1/7 2/7 .
Br angle.
HWHM
[au]
0.206
± 0.003
0.076
0.001
0.061
± 0.001 0.029 ± 0.001 0.143 ± 0.004 0.050 ± 0.002 0.071 ± 0.011
clusterat 90, thephotocentres
might
be ±
alignedwithsample objects.
The
co-rotation
radii aregiven
in Table 3.weOf points
positionThe
resulting
value
is
a
measureofhowwellestimates
found
in
the
literature.
Based
on
this
comparison,ṀM
small sample,
so that a Br
correlation
betweenthoseaccretion
sizes and ac8
0.5
Bottom:HWHM
versusluminosities.
The
colourcodingemission. We
approximate
this
asymmetrybyfittingasuperposome
form
of
polar
outflow
(red
wing
in
DG
Tau).
Anaxis.
even
[au]
0.04
0.08
0.04
0.07
0.04
0.08
0.05
0.07
0.05
- 0.090.09 - 0.11
0.05 - 0.10
course,theourbest
way to determine
whethersize
the Brtralignedrates
theRphotocentreo↵setsarerelative
to
the
disk
The
found
that
mass-accretion
rates tend
to fallthe
intotheofrange
es- cretioncannot be established here. Equally, within our samspreadof points
indicatesinanato
absenceof recognisable
structuresthe
the
upper
plot.
In Gaussian
this notation
wefollow theto
in Hartmannemission
regioncorresponds
thetheof usedthemagnetospheresition of two
functions
toconvention
data,
basically
plotwecaninterpreted
meaningfulwayby0.04
consideringtablishedbypast observations,even
ifsizemostlytowards
the higherdividing
Rcorresponds
[au]
0.10
0.04
0.05
0.06
0.05
0.04
co detectple
dobenota clear correlationofthose
Br sizes withanda random
distribution
ofatphotocentres
(TW
Hya).
The figure
et al.
(2016),
forexample.
We
note
that
Mregionstellarmass
inany
objectwould
betocomparethesizeagainstthedegreeofclustering,
and
which
anglestheclustering
occurs.
end
forthestrongeraccretors.
The
uncertainties
onthecoeffi0.5 is thetheluminosityoftheobjects,as
opposedtothe
NIR
continuum
the feature magnetosphericintoanarrow
centredlowvelocity
component
andclearlyshows the ofpreviously
introduced
distinctionin units,translate
R2 the stellar
radiusin largeunitsof 2 asymmetric
R , Bradius
1/2between
radiusdirectly.
The truncationA
concentration
pointsinanarrow
angular
range
(AS
353)
3 the
cientsa,bofof0.5
Eq.M1truncation
into relatively
andsizes,
which
were
shown
to
correlate
as
per
R
/
L
(Gravity
simplealignments
andcomplexpatterns,
where
we ±
see5.10multipleaFig.
broadero↵sethighvelocity
component.
Whetherthese
Gaussurface
fieldstrengthofthedipolarmagnetic
field
at
the
stellarcanbecomputedfromstellarparameters,
ifthestrengthoftheindicatesthatthephotocentre
shift
isalignedalong
a Fig.
single
error
bars
on
the
absolute
value
of
L
and
consequently
alsoContinuum
HWHM
[R
]
18.13
±
3.59
17.36
17.36
acc
⇤ However, it is apparent from
3. Total and pure line visibilities for an exemplary baseline fromclusters
Collaborationetal.
2021b).
5 ± 5.10 7.47 ± 0.70 11.32 ± 1.61 19.07 ± 2.69 10.38 ± 1.42
(DG
Tau
and
RU
Lup).
equatorindipolekG,
Ṁ
mass-accretion
rate in unitsof specificmagnetic
field
is known:
8 thebeaxis.theIf
theHWHM
clustering
range13.32
isclose
to zero,photocentres
Ṁ
used
aand
Monte-Carloapproach
to determine
the finalisalsoreflected
intheequivalent
widths.
computedtheline 5.93 ± 0.47 4.36 ± 0.75
acc . We
sian
components
cannecessarily
directly
attributedtothat
weakestin the(TW
Hya
andtrack
DoAr
Brtwo[Raccretors±sample1.16
6.32the±0.43
5.01± 0.35 We
5.13± 0.33 12.93± 1.56
the AS353 observation.
⇤]
8
1
It
is
importanttorememberthatthedi↵erential
phases
10 M yr . on
Thetheresultingtruncation
radiusthan
is givenin unitsof 44)
are alsoalignedwiththeclearly
disk semi-major
axis,
which
is something
uncertainties
accretionrate, rather
Gaussian
error
show
most
an
emission
regionsmallerthan3.53
the - 6.61
4/7
12/7
Top: Visibilities
beforethespectralcorrection
wasapplied.
Blueandluminositiesforeach
objectfromtheequivalent
widths
R
[R
]
2.83
5.30
3.28
6.14
8.31 - 12.35
4.50and- 8.42K- 10.62 - 12.68 3.36 - 6.29
physicalphenomena,suchasadditional
outflows
on
top
of
an
acthe
relative
o↵set
of
the
Br
emission
regionfromtheoveralltr⇤
R . The derivationisconceptually
discussed
in
Bessolaz
et
al.
Bnot
R
that
would
be
expected
from
a
disk
in
Keplerianrotation.
Ifthepropagation
applicable
here.
3
2
R
=
12.6
photocentreofthecontinuum.
In Fig.
6, formight
example,the centre
grey
shadedregions
indicatethe.not
uncertainties
onthe totalPand
pure (4)linetr(2008).
R
6.47from
3.31
3.31et al. 2003).
8.89 We then
5.44used
5.96
2.44
band
magnitudes
2MASS(Cutri
1/7 is
2/7
co [R
⇤ ]90
pointsclusterat,thephotocentres
bealignedwithcreting magnetosphere,certain.
InverseCygni
features,ṀM
the plotis of
thepolarcombined
photocentre
ofinthestar
and Another
88 of 41Same
Measurementsof magnetic
fieldbaseline
strengths after
in T Tauristars are ofsome
visibilities, respectively.
Bottom:the correction.
Articlenumber,0.5
page
form
outflow
(red
wing
DG
Tau).
even et al. (2014),
theempirical
relationshipfrom
Alcalá
asEspecially
expected
to
be
seen
when
observingmagnetosphericaccreemitting components such as the dusty disk. If the
scarce,so thatwe computation
cannot rely onofthe
truncation
radiusas a continuumwithrespect
to
the
the
pure
line
visibilities,
spreadofindicates an absence of recognisable structures
In this notation we follow the convention used in Hartmann dusty disk points
isperfectly
centrosymmetric,
itsflux
own
photocentre
誤差推定は,
正規分布仮定にもとづく伝播計算ではなく,MCatapproachprimary
criterion
toinidentify
strongmagnetosphericaccretion
Notes.
F
is
the
total
line
to
continuum
ratio
atThe
the figure
centreof the line. FWHM and W10% are the line widths
50% and 10%
tion
columnsatlow
inclination,aregenerally
absent
from
the
L/C
and
a
randomdistributionofphotocentres
(TW
Hya).
the change
appears
significant
the
red
wing
of
the
signal.
et al. (2016), for example. We note that M0.5 is the stellar mass coincides with that of the star and the overall continuum
cases. Even so, we can still use general estimates of Rtr as
flux, respectively.
is thepositionof the high(HV)or low
velocity (LV) component from the double Gaussian fit to the spectrum.
!
!
clearlyshows the µpreviously
introduced
distinction
betweenunits
of sample,
0.5 M , R2 eventhe stellar
radiusin unitsof 2 Robserved, B3 the photocentre
line profilesin
of
the
for
those
objects
atamatchesLradius
the positionof thestar.
Ifcontinuum
complementary information. Building upon the approach laid
The Brhalf-flux(HWHM)
is given
forthethecentralchannel. Rco , continuum HWHM, PA, and i were adopted from Gravity C
Lwhereacccomplex
Linesimplealignments
andpatterns,
we seemultipleA&A proofs: manuscript no. SpatiallyResolvedKinematicsWojtczak2022

みどりは共動半径
⾚は2μm連続波

J. A. Wojtczak et al.: Spatially resolved kinematics of hot hydrogen gas

matic depiction of the innermost parts of the circumstellar disk of a T Tauri star. Br emission in T Tauri stars is associated with theagnetospheric accretion, but outflows caused by certain types of disk or stellar winds (dashed lines) can heat the hydrogen gas totemperatures to produce Br emission as well. Di↵erent origin mechanisms can be tied to di↵erent spatial scales. Magnetosphericws (depicted in red) can only stably form in a compact region within the co-rotation radius Rco , where the gaseous disk rotates at thevelocity ⌦ as the star. Spatially extended Br emission from outside Rco cannot be attributed to magnetospheric accretion and mustsome other emission component.
ecifically shows the common case of a non-axisymmetric magnetosphere, featuring a tilt between the stellar rotational axis ⌦⇤ anddipole µ. The obliquity of the magnetosphere leads to the formation of two accretion columns, which funnel gas from a wide arc at
radius onto one primary hot spot per hemisphere, as first suggested in Bertout et al. (1988) and Calvet & Hartmann (1992). The
physical quantities relevant for the determination of the co-rotation radius Rco and the magnetic truncation radius Rtr are discussed
For the equations used to estimate the sublimation radius Rsub , which indicates the area at which the disk becomes sufficiently hot torains, we refer to Gravity Collaboration et al. (2021b).

weaker mass-accretion rates, but also exhibits sig- plane is almost completely evacuated from gas particles (Bounetic field strengths of 1-2 kG due their convective vier et al. 2007). Instead of further spiralling inwards, the gas
Johns-Krull 2007). This substantial di↵erence in the particles can only move freely along the field lines, which e↵ecFig.activity
5. Sample
overview
for emission
region sizesof
andphotocenter
shifts.
netic
hasgiven riseto the paradigm
magtively
serve as funnels that channel the gas onto the star. As the
Top: Br half-flux radii (yellow), compared to K-band NIR continuum half-flux radii (red) and co-rotation radii (green) across the sample. We
accretion.
As a theory concerning accretion in low- gas impacts the stellar surface at high latitudes, it creates heatednote that Br region and continuum HWHMs are based on a Gaussian disk and a Gaussian ring model, respectively, which should approximately
it reflect
has attained
preeminence
due to itsof ability
to recshockareregions
the poles (Hartmann
etrate.
al. 2016).
the di↵erencesin the morphology
both regions.
The objects
given incloseorder toof descending
mass-accretion
tionBottom:
properties
with the ofpresenceof stellar
hotacrossspotsthe line
The distribution
photocentre
shift angles
for the entire
sample.lines
The x-axis
the minimumdi↵erenceangle between
Hydrogenemissionserveshows
as tracers
for thekinematics
ofthe relative
shift vectorline
and thepositionangle of the continuum
disk. The white channel serves as the point of reference for the relative shift vector.
rvationsof hydrogen
profiles(Camenzind
1990; thehot gas in the inner star-disk system. In particular the nearAn angleof 0 means
photocentre shift
is aligned
the disk axis, as would for example be expected for a disk in rotation. A di↵erence
artmann1992).
It hasthesuperseded
the vector
earliertheorywithinfrared(NIR)
Br lineat 2.16is directly
relevant
angle of 90 indicates that the shift vector is perpendicular to the disk axis.
A clusteringof points
closeµm,
to a which
certain di↵erence
angle
indicates anlayeraccretion,
which
is
still
thought
togovernthework,requiresthe gas ofto photocentres,
be at temperaturesof 8000
tomorealignment of the photocentre shifts along a preferential axis. VVfor
CrAthisshows
a monoaxial
distribution
while for othertargets
mass
accretioninmagneticallyweakintermediate
complex profiles with multiple alignments are indicated. The number
in brackets afterthe(1998a),
object namegives the averageon the angle
10000stated
K (Muzerolle
et al.
Tambovtseva
et erroral. (2016))
Ae/Be
type
YSOs
(Mendigutía2020).
for the five central channels.
in order to produce strong emission. A heated gaseous disk inof magnetospheric accretion, it is proposed that the↑ Brγ
￼ 輝線は, どこから放射しているのだろうか？

まずはサイズ⽐較（上から降着率順）

R Lupでは, 2018?9?から2021にかけての変動も検出.

灰⾊直線は, 円盤単軸の向き
灰⾊影は, その不定性
⻩⾊⽮印線(ここでは左下向き)は,blue jetの向き; ⻩⾊影は不定性
⾚の楕円は星の位置の不定性
Fig. 7. Spectrum (top), size (middle), and photocentre shift (bottom) profiles for the two epochs of RU Lup in 2019 and 2021. Shaded regions
indicate uncertainties.

ただし, R Lup星の半径￼R* ≃ 2.6R⊙

⻩⾊⽮印線(ここでは左下向き)は,blue jetの向き; ⻩⾊影は不定性

⾚の楕円は星の位置の不定性

灰⾊直線は, 円盤単軸の向き

ただし, R Lup星の半径￼R* ≃ 2.6R⊙

灰⾊影は, その不定性

Fig. 7. Spectrum (top), size (middle), and photocentre shift (bottom) profiles for the two epochs of RU Lup in 2019 and 2021. Shaded regions
indicate uncertainties.

Br wavelengths is small, it is reasonable to assert th
the maximum shiftHydraof 0.009
au and an average shift ofpole-onで⾒ているはずのTW(残念ながら１エポックのみ)
0.003 for the central channels compared to a stellar
0.006 au, the Br photocentre across the line coincides• 他の天体と⽐べ、コンパクトな領域に集中
position of the central star. This suggests that most of t
• ポールオン＆１回の観測なので、このデータだけから⾔えることは
ent photocentre velocity components of Br emission,
少ないが、⾮対称分布であることから…………???のモデルと合う.
almost pole-on, are well centred on the stellar positio
can be inferred directly from such a distribution. At ver
clination, any centrosymmetric brightness distribution
to lead to a similarly compact profile centred on zero,
only in combination with more conclusive evidence, as p
above, does it support the magnetospheric accretion sc
is still noticeable that the distribution, and indeed the diphase signals at the individual baselines, appear to show
larger shifts in the red wing of the line. In the case
⾚の楕円は星の位置の不定性
clined magnetosphere with two accretion columns, theただし, TW Hの星半径￼R* ≃ 1.21R⊙
could be naively expected in a pole-on configuration, as
灰⾊直線は, 円盤単軸の向き
gas
at
the
far
side
of
the
star
at
the
highestblueshiftedv
灰⾊影は, その不定性
would be blocked by the star itself, which should leadaway from the centre for the blue components. The abs
stronger shift in the blue arm could indicate that the ction of the magnetic field in TW Hya is close to an axisy
scenario with a small obliquity angle between dipole
tional axes. Such a case would be in line with the relativ
di↵erence in inclination between the inner NIR continu
Fig. 10. Spectrum (top), size (middle), and photocentre shift (bottom) and the outer disk and also the lack of blueshifted ab
profiles for TW Hya. Shaded regions indicate uncertainties.
However, a previous study by Johnstone et al. (2014)

A&A proofs: manuscript
no. SpatiallyResolvedKinematicsWojtczak2022
J. A. Wojtczak
et al.: Spatially resolved kinematics of hot hydrogen gas

matic depiction of the innermost parts of the circumstellar disk of a T Tauri star. Br emission in T Tauri stars is associated with theagnetospheric accretion, but outflows caused by certain types of disk or stellar winds (dashed lines) can heat the hydrogen gas totemperatures to produce Br emission as well. Di↵erent origin mechanisms can be tied to di↵erent spatial scales. Magnetosphericws (depicted in red) can only stably form in a compact region within the co-rotation radius Rco , where the gaseous disk rotates at thevelocity ⌦ as the star. Spatially extended Br emission from outside Rco cannot be attributed to magnetospheric accretion and mustsome other emission component.
ecifically shows the common case of a non-axisymmetric magnetosphere, featuring a tilt between the stellar rotational axis ⌦⇤ anddipole µ. The obliquity of the magnetosphere leads to the formation of two accretion columns, which funnel gas from a wide arc at
radius onto one primary hot spot per hemisphere, as first suggested in Bertout et al. (1988) and Calvet & Hartmann (1992). The
physical quantities relevant for the determination of the co-rotation radius Rco and the magnetic truncation radius Rtr are discussed
For the equations used to estimate the sublimation radius Rsub , which indicates the area at which the disk becomes sufficiently hot torains, we refer to Gravity Collaboration et al. (2021b).

weaker mass-accretion rates, but also exhibits sig- plane is almost completely evacuated from gas particles (Bounetic field strengths of 1-2 kG due their convective vier et al. 2007). Instead of further spiralling inwards, the gas
Johns-Krull 2007). This substantial di↵erence in the particles can only move freely along the field lines, which e↵ecnetic activity has given rise to the paradigm of mag- tively serve as funnels that channel the gas onto the star. As theaccretion. As a theory concerning accretion in low- gas impacts the stellar surface at high latitudes, it creates heatedit has attained preeminence due to its ability to rec- shock regions close to the poles (Hartmann et al. 2016).
Fig.properties
15. Modelwith
imagesderivedofquantitiesof spots
the Br emission region.
tion
the andpresencestellar hot
Hydrogenemissionlinesimage
serveat as
tracers
for thekinematics
The three
the profiles
left show(Camenzind
the continuum-subtracted
Br emission
regionthree
di↵erent
velocities,
while ofthe two columns onrvationsof columns
hydrogenonline
1990; the hot
gas
in
the
inner
star-disk
system.
In
particularthenearthe right1992).
show thephotocentre
shift theprofileand thesize profile across all velocity components of the Br line, for a range of inclinations between
artmann
It hassuperseded
earliertheoryinfraredred(NIR)
Br marked
line atwith
2.16a µm,
is directly
relevant
5 and 67 . The model images correspond to the blue, whitechannelsbold which
black outline,
and thephotocentres and region
layeraccretion, which is still thought to govern the for and
this
work,
requires
the
gas
to
be
at
temperaturesof8000
sizes in those particular channels are defined by the red dots and the semi-major axes of the red ellipses, respectively. Only thetosemi-major axis ofmassaccretion in magnetically weak intermediate 10000theK approach(Muzerolleet withal. (1998a),
Tambovtseva
et al.16(2016))
the ellipse is left as a free parameter of the fit, which emulates
taken
the observational
data. Fig.
shows the corresponding
Ae/Be
type
YSOs
(Mendigutía2020).
in orderstrong emission. A heated gaseous disk in
profiles if inclination and position angle are also free parametersof totheproduce
fit.
of magnetospheric accretion, it is proposed that theFig. 9. Spectrum (top), size (middle), and photocentre shift (bottom)
profiles for DG Tau. Shaded regions indicate uncertainties.

16

Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale Aldo Moro 2, I-00185, Rome, Italy
17 Department of Physics
The &
Star
Formation
Rateofof
the Milky
Way as seen
byCalgary,
Herschel
Astronomy,
University
Calgary,
2500 University
Dr. NW,
AB, T2N1N4, Canada

D. Elia,1 S. Molinari,1 E. Schisano,1 J. D. Soler,1 M. Merello,2 D. Russeil,3 M. Veneziani,4 A. Zavagno,3, 5 A. Noriega-Crespo,6 L. Olmi,7M. Benedettini,1 P. Hennebelle,8 R. S. Klessen,9, 10 S. Leurini,11 R. Paladini,12 S. Pezzuto,1 A. Traficante,1 D. J. Eden,13, 14 P. G. Martin,15
Submitted
to
9
1, 16
8
17ApJ
M. Sormani, A. Coletta,
T. Colman, R. Plume, Y. Maruccia,1 C. Mininni,1 and S. J. Liu1
1 INAF - Istituto di Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere 100, I-00133 Roma, Italy

ABSTRACT

2 Departamento de Astronomı́a, Universidad de Chile, Casilla 36-D, Correo Central, Santiago, Chile

We present a new derivation3 Aixof Marseillethe Milky
current
star
formation
Univ.,Way’s
CNRS, CNES,
LAM,
Marseille,
Francerate (SFR) based on the data of
4 Science
the Hi-GAL Galactic
plane& survey.
estimateOlof
thePalmestraat
distribution
of LR
theDelft,
SFR
the Galactic plane fromTechnologyWe
Corporation,
14, 2616
Theacross
Netherlands
Universitairede France,
France the total SFR from the sum of their
the star-forming clumps identified in5 Institut
the Hi-GAL
surveyandParis,
calculate
6 Space Telescope Science Institute, 3700 San Martin Dr., Baltimore,−1MD 21218, USA−1
contributions. The estimate of the global SFR amounts to 2.0 ± 0.7 M! yr , of which 1.7 ± 0.6 M! yr coming
7 INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Firenze, Italy
from clumps with8reliable heliocentric distance assignment. This value is in general agreement with estimates
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France
found
in
the
literatureof
last
decades.
The
profileofSFR
density
averagedin
Galactocentric
rings
is
found
9 Universität Heidelberg, Zentrum für Astronomie, Institut für theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germanytobe qualitatively
similartootherspreviously
computed,
with
a
peak
corresponding
totheCentral
Molecular
10 Universität
Heidelberg, Interdiszipliäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany∼ Scienza
5 kpc,5, followedby anexponential
decrease as
Zone and another11 INAF
one -around
Galactocentric
galdellaOsservatorio
Astronomico di radius
Cagliari, R
Via
I-09047 Selargius
(CA),
Italy
−2
−1
12
kpc Processing]) = a RAnalysis+ b,with aInstitute= −0.28± 0.01.Pasadena,
In thisCAregard,
the fraction of SFR
log(ΣSFR /[M! yr Infrared
gal /[kpc]Center,California
of Technology,
91125, USA
13 Astrophysics
producedwithinandInstitute,outsidethe Solar
84% and16%,
respectively;
theUK
far
Research
LiverpoolJohncircle
Mooresis
University,
IC2,
Liverpool
Science Park,the146fraction
Brownlowcorresponding
Hill, Liverpool, L3to
5RF,
14 Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DB, UK
outer Galaxy (Rgal > 13.5 kpc) is only 1%. We also find that, for Rgal > 3 kpc, our data follow a power law as a
15 Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
function of density, similarly to the Kennicutt-Schmidt relation. Finally, we compare the distribution of the SFR
16
Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale Aldo Moro 2, I-00185, Rome, Italy
density acrosstheface-onGalactic
plane
and
those
of
medianparameters,suchastemperature,luminosity/mass
17 Department of Physics & Astronomy, University of Calgary, 2500 University Dr. NW, Calgary, AB, T2N1N4, Canada
ratio and bolometric temperature, describing the evolutionary stage of Hi-GAL clumps. We found no clear
correlation between the SFR and the clump evolutionary stage.
Submitted to ApJ

-2

15

15

10

10

-180

5

5

-120

0

-60

0

60

120

180

0

Galactic latitude [deg]Log(ΣSFR/[MO•deed generally dominated by the Galacticbar(Binney et al.
Elia
et
al.
0.03
1991; Ellsworth-Bowers et al. 2015; Li et al. 2016). As ex0.02
+2
-3
-1.40
plainedby Mège et al. (2021) and Elia et al.Elia(2021),
only in8
et al.
0.01
cases of small deviations, the distance of the corresponding
0
-1.40
-4
10 is assigned to sources, which can therefore betangent point
involved in the calculationof the SFR. Additionally, in the
10-2longitude range corresponding to the void lobe in the fourth
0.00
100
SFR [M yr ]
0.08
-2.10
5
quadrant, Mège
et al. (2021) found a relatively high occur1.5-2.10
5 original spectral survey data which in
rence
of
noise
in
the
0.06
80
many cases prevented an estimation of the radial velocity and0.04
hence of thekinematic distance. In any case, since the two
0
60
0
1.0
0.02
void areas are oriented approximately along Galactocentric
0.00
-2.80
radial directions, their influence is distributed over a certain
-2.80
40
+180
+120
+60
0
-60
-120
-180
number of rings (andtherefore attenuated).
-5
Galactic longitude [deg]
-5
0.5
The
dip
in the SFR density profile is followed by another
20
Figure 4. Top: Star formation rate (SFR) toward the Galactic plane in 3◦ × 0.2◦ bins in Galactic longitude and latitude, respectively. It is tolocal peak at around 5 kpc. A peak in this position was prenotice that in the outer Galaxy the Hi-GAL latitude coverage follows the variations in the midplane position, or Galactic warp (Westerhout
dicted by Krumholz-10 & McKee (2005) as a consequence of1957). For a better rendering of the image dynamic range, the color scale follows0.0
a power law with exponent 0.4. The dotted lines indicate the0-3.50
location of the three most prominent SFR peaks. Bottom: SFR as a function of longitude, estimated from the sum of the results reported in the-10 of the molecular gas surface density, and was-3.50
the distribution
The
SFR
of
the
Milky
Way
as
seen
by
Herschel
9
0
5
10
15
top panel across Galactic latitude.
Crux-Scutum
Galactocentric radius [kpc]found also by Portinari& Chiosi (1999) and Chiappini et al.
lar, in these areas absolute values of radial velocity are exNorma (Outer)Milky Way:NGC 6946:
Crux-Scutum-15
0(2001),
but
at
∼
4
kpc.
It should correspond to the soTable 2. Star
formation rate estimates for the Central Molecular Zone
−1
This work
Schruba et al. (2011)
Carina-Sagittarius(Ellsworth-Bowers
al.
pectedbe larger
100 km srate
Figure6. toTop:
Starthanformation(SFR) density etprofile
estiNorma(Outer)Guesten & Mezger (1982)
calledMolecularRing(which is, more realistically, an efPerseus
-15
2015,
their
Fig.
1),
while
most
of
sources
observed
inthecormated
fromthe
Hi-GALobservations
in
0.5-kpc-wide
concentric
Lee et al. (2016)-4.20-1
Carina-Sagittarius
MethodArea boundaries
SFRCMZ (lit.) Reference
SFRCMZ (this work)
responding
longitude
rangesshow
lower
values.
The
kinefectofspiralarm
arrangement,
see
Dobbs
&
Burkert2012;
rings aroundMtheyr−1Galactic center, shown in black
filled circles. Fit-15
-10
-5
0
5
10
15
PerseusM# yr−1#
matics
of
the
Milky
Way
along
these
lines
of
sight
is
in-4.20
Roman-Duval et al. 2016; Miville-Deschênes
et al. 2017),
ting the relation
2 to theat 0.04
Rgal± 0.02
≥ 5 kpc givesx[kpc]-2counts (Spitzer)
YSO|!| < 1◦ , |b| < 10%
0.14 in Eq.
Yusef-Zadeh
et al.portion(2009)
deed generally dominated by the Galactic bar (Binney et al.
= −0.30± 0.16. The fit
is±plotted
as a black
Continuum emission at 60, 100 µm (IRAS)|!| < 3◦ , |b| < 1◦ a a = −0.28 ± 0.01
0.12 and b
Crocker
et al. (2011)
0.12
0.05
but it does notpeak of source-15mirror exactly-10 the -5
0 number5 dis- 10
15
1991;
Ellsworth-Bowers
et
al.
2015;
Li
et
al.
2016).
As
exContinuum
emission at 60, 100 µm (IRAS)|!| < 0.8◦ , |b| < 0.3◦ dashed line. The
0.08 green
Crocker
etshowsal. (2011)the results
0.04of± 0.02line
theonlyvisible-band-3
x [kpc]% 6 kpc. Finally,
tribution found by Elia et al. (2017) at Rgal
plained
by
Mège
et
al.
(2021)
and
Elia
et
al.
(2021),
in◦◦Figure
5.
Map
of
the
decimallogarithmofSFR
density(dividedbyM yr kpc ), across the Galactic plane. The spatial bins are of 0.5 × 0.5
YSO counts (Spitzer)|!| < 1.5 , |b| < 0.5 observations considered
0.08
Immer
et
al.
(2012)
0.08
±
0.03
in
Guesten&Mezger(1982),
re-scaledbysmall deviations,corresponding
a exponentiating
systematicde- logarithm, and then multiplying by a factor
at larger
distances,ΣSFR
the absolute SFR
insidedefinitely
each pixel can beshows
obtained by
the displayed
kpc , so that
Ionization
rate from radio free-free
2.5◦ < ! < 3.5◦ , |b| < 0.5◦ cases of 0.035
Longmorethe
et al.distance(2013) of the0.11± 0.04 −1-4Kennicutt& point
Evansis (2012)
totothetotal SFR
1.9therefore
M# yr bereported
4 kpc . The Galactic center is at the [0,0] position, while the gray X symbol indicates the position of the Sun. Gray dashed lines mark Galactic
tangent
assignedsources,whichofcan
Ionization rate from radio free-free
as above, but |b| < 1◦ for |!| <1◦
0.06
Longmoreetal.
(2013)
0.12±
0.05
crease.
 (2011). The blue line corresponds to theoctants. Four spiral arms according to the prescription of Hou et al. (2009)
are overplottedwith four different tones of green; the correspondence−1−2in
Chomiuk&
Povich◦◦
involved
inthecalculation
of
the
SFR.
Additionally,inthe
Figure
5.
Map
of
the
decimallogarithmofSFR
density(divided
by
M
yr
kpc
),
acrossthe Galactic plane. The spatial bins are of 0.5 ×!
Continuum emission at 24 µm (Spitzer)|!| < 1 , |b| < 0.5
0.09 ± 0.02 
betweenarms andbehavior
colors is explainedin the legend at the bottom
left corner.
This
globalisqualitatively
similar
to
those
shown
2

b voidobtainedin Barnes
Lee etet al.
(2016)
bylobecombining
YSO NIR kpc , so that the absolute SFR inside each pixel can be obtained by exponentiating the displayed logarithm, and then multiplying by a fa
longitude
tothein
thecfourth
0.06± 0.020.5◦ estimates
0.10 range± 0.02 correspondingal. (2017)
Continuum emission at 70 µm (Spitzer)|!| < 1◦ , |b| < 100
5 of
one canappreciate
that,dashedwith respect
to the
3.2.
SFR
Galactocentric
profile2
byGalactic
Kennicutt&
Evans(2012)(startingfrom indicates
theIn Figure
data
center isat the[0,0]position,while
the gray X symbol
the positionof theSun. Graylines markGal
quadrant,
etal.
(2021) foundrelatively highandMège
cloud
properties
fromamillimeterline occurobservations. 4 kpc . The
Cont. emission at 5.8-500 µm (Spitzer, Herschel) |!| < 1◦ , |b| < 0.5◦ photometry
0.09± 0.03Galactic
center(towhich
weassignthe[0,0]position),
the
Using
informationabout
the heliocentric
a are overplotted with four different tones of green; the correspondoctants. Four spiralarmstheaccording
to theprescriptionof Hou distance,
et al. (2009)
1.5
rence
of
noise
in
the
original
spectralsurvey
data
which
in
Guesten&Mezger
1982)
and
Lee
et
al.
(2016):
an absolute
The red line shows the SFR profile of the galaxy NGC 6946, pre- between arms andSFRshows a certain degree of circular symmetry.
80
pole-onviewofSFR density
in legend
the MilkyWay,mappedoncorner.
acolorsis
explained
in
the
at
the
bottomleft
a Differently from other rectangular areas quoted in the table, this one has an elliptical
many
cases
analong
estimationof theradialvelocity and& Evans
It makessense, therefore, to analyze the behavior of theshapewithprevented
axesaligned! andand b,adapted
andsemi-axesofsentedin
Schrubaetal.
(2011)
byKennicutt
built.
This
is a simplified
grid of 0.5 ×
0.5-kpc2 pixels, can be
maximum
corresponding
to
the
CMZ,
followedbyalocal
in concentric
500-pcrings, toSFRdensity5ΣSFR
3◦ and 1◦ , respectively.
In
Figureone, averaged
can appreciatethat,withwide
respect
3.2.representation
SFR Galactocentric
profilehenceof pink-shaded
the kinematic area
distance.
In region
any case,since theby
twothe mod2-Dof the Galactic
disk which has a structure60(2012).
Theistheoccupied
5 kpc,
minimumand by another local peak at Rgal =1. In Figure
6, toppanel,
vsand
the Galactocentric
radiuswe
Rgalb In 1.0
along the third dimension, an idea of which can be taken from
Galactic
center(to whichassignthe[0,0]position),
voidtheareas
approximately
Galactocentric
Barnes et al. (2011), their Table 2, a further list of SFRCMZ estimates derived withinsameareareaoriented
from monochromatic
fluxes oralong
bolometric
2
Using
the
information
about
the
heliocentric
distance,aels of omitEvansetin al.
(2022).
Bottom:Cumulative SFR profile as aa peakcorresponding to the inner circle is followed by a
Figure 4. The designofathedecreasing
Hi-GAL survey took
into accountrespectively,
withbehavior
atlargerGalactoluminosities available in the literature from 1998 to 2011 are quoted (see text). Weradial
them
this
table
for
the
sake
of
brevity.
SFRshows
a certain degree of circular symmetry.
directions,
theirinfluenceisdistributedoveracertainpole-onviewofSFR
density
in
the
Milky
Way,
mappedona40functionof theGalactocentric
radius,also expressed as a percentthe warp of far-infared emission already observed by IRAS
c The three SFR
It makes sense, therefore, to analyze the behavior of
2
number
of
rings
(and
therefore
attenuated).
centric
distances.
This
generalbehavior
was successfully
estimatesbyBarnesetal.
(2017)
arederivedwithin
the
same
area
in
the
sky
throughdifferent
methods;
obviously,
for
the
CMZ
pixels,canbebuilt.
This
is aissimplified
grid of 0.5 × 0.5-kpc
towards
theouterGalaxy,which
howeverlessprominent
0.5
To correctly compare this plot with Figure 5, it must be considered that inage with
respect
to thetotal
SFR(y-axison the byright-handside).
,density
averagedin concentric 500-pc wide ri
SFRdensityΣi)SFRsame area we can provide only one estimate.
The
dip
in
the
SFR
density
profileisfollowed
another2-D
representationoftheGalactic
disk
which
has
a
structure
this case theSFR
is obtained by dividing by the ring area, proporthan the by
Galactic
warp etobserved
in atomic bygas (Westerhout
modeledEvansal.
(2022)
takingintoaccounta
20
The verticaldottedlines 5indicate,frominleft
right, wasthe GalactocenFigurepa
Galactocentric
radiusRgal . Inconsists
to R , while in Figure
5 the denominatorof a 6,
localtoparea exlocal peakat aroundkpc. A peakthistoposition
preSoler et al.
2022),
correspondingtoGalactocentric
dis- vs thetional
along thedependence
third1957;
dimension,
an
idea
of
which
can
be
taken
from
respectively. The former one is about 3 times larger thanmates from the literature collected in Table 2. The authorsof theby conversion
factorfrom
CO aluminosity
to kpc . Also
2 in Section 2.2.1, thenoticethat, as discussed
tendingover 0.25
tric
radii
corresponding
to
50%,
90%,
and
99%
of
the
total
SFR,
is followed b
peakcorresponding
to
the
inner
circle!
16
kpc,
tancesnotachieved
objectsinoursample(R
dictedbyKrumholz&
McKee(2005)
asaconsequenceofgal
Figure 4. The design of the Hi-GAL survey took into accountdistribution in longitude of sources without a distance assignment shows athat0.0
of Longmore et al. (2013), and not compatible with it0
indeed suggest that the choice of the assumed IMF, which
Voskes& Butler2006).
),
mass
on Burton
metallicity(whichbyinIRAS
turn dependsremarkableon Rgalrespectively.
distributionof thepeculiar
molecular
gas surface
density, and wasconcentration
at 0 " ! " 20 . Assigning the distance of the
5
10
15 of
the warpcloudof far-infaredemissionalready observed
within 0the associated error
bar. Of course,
the estimate
did notthe
account
for possible
conditionsof the CMZ,
Galactic center to all of them would turn out in an even higher value for
Galactocentric radius [kpc]found also by Portinari & Chiosi (1999) and Chiappini et al.
and ii) a dependence of the star formation efficiency
on the8-1Log(ΣSFR/[MO• yr-1 kpc-2])

y [kpc]y [kpc]

!

−1

−2

2

%

15

15

10

10

5

5

0

2

0

∫0Rgal SFR(r) dr [MO• yr-1]%∫0Rgal SFR(r) dr [MO• yr-1]

SFR [MO• yr-1]

•
O

2

2
gal

2

◦

◦

Milky Way:NGC 6946:

This work
Guesten & Mezger (1982)
Lee et al. (2016)

Schruba et al. (2011)

-2
-3

15

15

10

10

5

5

0

-4

100

1.5

80
60

1.0

%

∫0Rgal SFR(r) dr [MO• yr-1]

lar, in these areas absolute values of radial velocity are ex- 15
pected10-2to be larger than 100 km s−1 (Ellsworth-Bowers et al.
2015, their Fig. 1), while most of sources observed in the corresponding longitude ranges show lower values. The kinematics
10-3of the Milky Way along these lines of sight is in- 10
deed generally dominated by the Galactic bar (Binney et al.
1991; Ellsworth-Bowers et al. 2015; Li et al. 2016). As explained
10-4by Mège et al. (2021) and Elia et al. (2021), only incases of small deviations, the distance of the corresponding 5
tangent point is assigned to sources, which can therefore be
involved
10-5 in the calculation of the SFR. Additionally, in thelongitude range corresponding to the void lobe in the fourth
quadrant, Mège et al. (2021) found a relatively high occur- 0-1
rence of noise in the
spectralgal
10original
100 survey data
101 which inR[kpc]-2 radial velocity andmany cases prevented an estimationof theΣH2 [MO• pc]
hence of the kinematic distance. In any case, since the twovoid areas
approximately
Galactocentric
Figure7. areStaroriented
formation
rate (SFR) along
estimatedfrom the HiGAL
versusthe averagemolecularover
gas asurface
radialobservations
directions, theirinfluenceis distributed
certaindensity(fromofMiville-Deschênes
et al.
2017) in 1-kpc-wide concentric
numberrings (and therefore
attenuated).
rings
aroundcenter profile
whose central
radiusbyis anotherindicated byThe
dip inthe
theGalactic
SFR density
is followed≤ 3position
kpc, andwas
Rgalpre> 3 kpc
thecolors.
bins corresponding
to R
local
peakTheat around
5 kpc. A peakingalthisaremarkedwith square
circle(2005)
symbols,
dictedby Krumholz
&and
McKee
as arespectively.
consequenceTheof dotted
the dashedindicate thefit density,
to the SFR
theanddistributionof lines
the moleculargaslinearsurfaceandestimates
wasatfound
Rgal ≥
3 kpc(with slope
n = 1.14± 0.07),and the KSetrelation
also
by Portinari&
Chiosi(1999)
and
Chiappinial.
−4 1.4(Σ
10∼ Σ4gaskpc.
), respectively.
SFR = 2.5
(2001),
but× at
It should correspond to the socalled Molecular Ring (which is, more realistically, an effect of spiralarrangement,
see that
Dobbs
Burkert2012;
Boissier
et al.arm(2003),
who found
the&KS
relationis satRoman-Duvalet al. 42016;
al. 2017),≤ 15 kpc with eta slopeof 2.06,
isfiedin the range≤ RgalMiville-Deschênes
but itindoes
not mirror
exactly
the whopeak obtainedof source number
andMisiriotis
et al.
(2006),
a slope disof 2.18
tribution found by Elia et al. (2017) at Rgal % 6 kpc. Finally,
across the entire range of Rgal .
at larger distances, ΣSFR definitely shows a systematic deTo do that, for the x axis we use the molecucrease.
averagedoverGalactocentricbins
of 1shownkpc bylarThisΣH2global
behavior
is qualitatively
similarto those
Miville-Deschênes
et al.(2012)(2017),
startingfrom
fromthethe data
CO survey
by Kennicutt & Evans(startingofassembledby Dameet al.and(2001),
and(2016):
the atomic
ΣHi from
Guesten & Mezger
1982)
Lee et al.
an absolute
Nakanishi
Sofue (2016).
Therefore,
for consistency,
maximum &corresponding
to theCMZ, followed
by a local werecalculated
densityin theat samebins
and(which
5 kpc, areminimum andthe
by SFR
another
local peakRgal =1
respectively,
with thosea decreasing
at3 .larger Galactotwice
wider thanused forbehavior
Figure 6)
centric
distances.
This generalΣH2 successfully
is shown. DifIn Figure
7 the log-log
plot ofbehavior
ΣSFR vswas
modeled fromby Evans
et al. (2022)
by takinginto accounti) a gas
ferently
the plots
built withthe atomic
and total
dependence
the conversion
luminosity
todensity(see ofAppendixB), a factor
linearfrom
trendCOcanbe recognized
cloudexcept
mass on(which in turntodepends
on Rgal ),radii.
here,
formetallicity
points corresponding
the innermost

ΣSFR [MO• yr-1 kpc-2]-10

Log(ΣSFR/[MO• yr-1 kpc-2])

0

40

0.5
20

0.0

0

0

5
10
Galactocentric radius [kpc]15

Figure 6. Top: Star formation rate (SFR) density profile estimated from the Hi-GAL observations in 0.5-kpc-wide concentricrings around the Galactic center, shown in black filled circles. Fitting the relation in Eq. 2 to the portion at Rgal ≥ 5 kpc givesa = −0.28 ± 0.01 and b = −0.30 ± 0.16. The fit is plotted as a black
dashed line. The green line shows the results of the visible-band
observations considered in Guesten & Mezger (1982), re-scaled by
Kennicutt & Evans (2012) to the total SFR of 1.9 M# yr−1 reported
in Chomiuk & Povich (2011). The blue line corresponds to theestimates obtained in Lee et al. (2016) by combining YSO NIR
photometry and cloud properties from millimeter line observations.
The red line shows the SFR profile of the galaxy NGC 6946, presented in Schruba et al. (2011) and adapted by Kennicutt & Evans(2012). The pink-shaded area is the region occupied by the models of Evans et al. (2022). Bottom: Cumulative SFR profile as afunction of the Galactocentric radius, also expressed as a percentage with respect to the total SFR (y-axis on the right-hand side).
The vertical dotted lines indicate, from left to right, the Galactocentric radii corresponding to 50%, 90%, and 99% of the total SFR,
respectively.

First of all, from the qualitative point of view, it is important to confirm that the largest part of the Milky Way disk
follows a power-law behavior, testifying a direct and clear
connection between the availability of molecular gas and therate of its conversion into stars.
The slope n we found appears in good agreement withthose derived by Luna et al. (2006) and Sofue & Nakanishi(2017), while it is shallower than those found by
Boissier et al. (2003) and Misiriotis et al. (2006). Furthermore, we note the agreement of our result with that obtainedby Onodera et al. (2010) for the M33 galaxy (n = 1.18 ±0.11). The comparison with the classic slope of Kennicutt(1998), instead, makes little sense, since it refers to the total
Σgas .
Actually, it is known that a variety of slopes is generally found for the KS relation (see, e.g., Kennicutt & Evans2012, and references therein). Furthermore, it is not difficult to figure out how varying some assumptions made incalculating the plotted variables can produce a change ofthe slope (even though preserving the global power-law behavior). For example, surface densities were computed byMiville-Deschênes et al. (2017) by converting CO to H2 byusing the constant factor XCO = 1020 cm−2 (K km s−1 )−1 .
However, if an increasing trend of XCO at increasing Rgal was
adopted (e.g., Nakanishi & Sofue 2006; Pineda et al. 2013),
the plot in Figure 7 would get steeper (see also Boissier et al.
2003). Moreover, the masses used here as input for the
SFR calculation were derived by Elia et al. (2021) by assuming a constant gas-to-dust ratio of 100. However, a possible increase of this ratio at increasing Rgal is suggested
by Giannetti et al. (2017), and invoked by Elia et al. (2021)
themselves to better explain the Galactocentric behavior of
the surface density of Hi-GAL clumps. Taking into accountsuch dependence would produce a flattening of our ΣSFR vs
ΣH2 plot.