SFN Letters速報ゼミ
April 23, 2021
古屋 玲
#338 21-26担当
14 を参照01 から 06 を参照

HSTデータ解析のシリーズ論⽂

07 から 13 を参照

00

ABSTRACT
Debris disks are tenuous, dusty belts surrounding main sequence stars generated by collisions between
planetesimals. HD 206893 is one of only two stars known to host a directly imaged brown dwarf orbiting
interior to its debris ring, in this case at a projected separation of 10.4 au. Here we resolve structure00
in the debris disk around HD 206893 at an angular resolution of 0. 6 (24 au) and wavelength of 1.3 mm
with the Atacama Large Millimeter/submillimeter Array (ALMA). We observe a broad disk extending+13
from a radius of < 51 au to 194 2 au. We model the disk with a continuous, gapped, and double
power-law model of the surface density profile, and find strong evidence for a local minimum in thesurface density distribution near a radius of 70 au, consistent with a gap in the disk with an inner+8+11radius of 63 16 au and width 31 7 au. Gapped structure has been observed in four other debris disks– essentially every other radially resolved debris disk observed with sufficient angular resolution andsensitivity with ALMA – and could be suggestive of the presence of an additional planetary-masscompanion.
1. INTRODUCTION

bris disks are a common outcome of the star and planet formation process, and serve as a signpost of mtary systems. Bright debris disks are observed around some 25-30% of main sequence stars (Trilling et al.
eau et al. 2014; Montesinos et al. 2016; Sibthorpe et al. 2018). The true incidence is likely to be higher, sintivity of current observations limits our ability to detect debris disks to those systems that are at least an or01

残骸円盤内を褐⾊矮星が公転している系(この系を含め, 2例のみ)；距離 40.8 pc; 中⼼星はF5V型
Hershell 70 μm画像 plus SED解析 ⇨ Rinner ≃ 50 AUは推定されていた; 褐⾊矮星伴星がL5-L9型, ~12 Mjup, age ~ 50 Myrsも推定されていた.
分光観測(Grandjean+2019)から第3の天体(惑星？BD?)の存在も⽰唆されていた.

Figure 1. (Left) Naturally weighted ALMA image of the 1.3 mm continuum emission from the HD 206893 system. (Right)
Same image with a visibility-domain taper of 200 k applied to bring out the large-scale structure of the source. In both panels,
contour levels are [-2,2,4,6]⇥ , where is the rms noise in the image: 5.5 µJy beam 1 for the naturally weighted image and1
6.0 µJy beam
for the image with the taper. The hatched ellipse in the lower left corner represents the size and orientationof the synthesized beam: 0.00 71⇥0.00 58 for the naturally weighted image and 0.00 9⇥1.00 0 for the tapered image. The star symbol
represents the pointing center of the observations, i.e., the expected position of the star including a proper motion correction,and the dot represents the position of the brown dwarf companion directly imaged by Milli et al. (2017).

021 , M. Bonavita11 , B. Lavie22, 12 , A. Zurlo10, 13 , J. Olofsson8, 14 , A. Boccaletti2 ,A. Vigan10 , R. Galicher2 , J.models
Hagelberg
中⼼星の諸元(Saumon & Marley 2008; Madhusudhan et al. 2011;
M0-M5
β/γ/VL-G dwarfs 1
8
1
15
25,
10
22
8
中⼼星と伴星の褐⾊矮星の諸元：先⾏研究からMorleyet al. 2014; Baudino et al.12015). The recent work by
F. Cantalloube , D. MouilletLiu ,et al.G.
Chauvin , F.-J. Hambsch Parameter, M. Langlois, S. Udry , 8T. M6-M9
Henning , J.-L. Beuzit ,(2016) focuses on a sample of substellar objects with
Value
Ref.
L0-L5
known ages and distances and has16
confirmed that low-gravity 24
obL6-L9 18
12
16
8,
17
22
18 ,
V (mag)6.69
Hipparcos
A&A 608, A79 (2017)
jects
populate
an area of NIR colour–magnitude
diagramthatisC.
Mordasini
,
P.
Lucas
,
F.
Marocco,B.
Biller,J.
Carson,A.
Cheetham,E.
Covino,V.
De
CaprioT0-T5
Astronomy
B V (mag)
0.439
Hipparcos
DOI: 10.1051/0004-6361/201731145
distinct from the area occupied by field brown&
dwarfs of the same
10
T6-T8
V I (mag)
0.51
Hipparcos
1
8
7
19
8
8
20
2
spectral type. This study also claims that low-masscompanions>T8
Astrophysics
J
(mag)
5.869
±
0.023
2MASS
A. Delboulbe , M.might
Feldt, J.distinct
Girard, isolated
N. Hubin, HA.-L.
Maire, A. Pavlov , C. Petit , D. Rouan ,have properties
from those of
low-mass(mag)
5.687 ± 0.034 2MASS
objects, while they should have similar gravity, hinting that other(mag)
5.593 ± 0.021222MASS
21 ,K and12parameters might also shape the NIR R.
SED ofRoelfsema
substellar objects.
F.
Wildi
Parallax (mas)24.59 ± 0.26
Gaia DR1
In this light the recent discovery of the very red close-in comTable 1. Stellar parameters of HD 206893.

SpeXprism lib.

c ESO 2017

UScoCTIO 108B
Best et al. 2015

A&A 608, A79 (2017)

CD-352722B

1RXS1609b1In-depth study of moderately young but extremely red, very dusty(Affiliations can be found after the references)
substellar companion HD 206893B

MJsµ↵ (mas yr )94.236 ± 0.044 Gaia DR1
panion HD 206893B (or HIP 107412 b) identified by Milli et al.
1µ (mas yr )0.164 ± 0.031 Gaia DR1(2017), o↵ers the opportunity to explore the physical proper1
RV (km s )–11.92 ± 0.32 this paper? substellar companion
ties of a relatively young mid-L dwarf
1
U (km s )–20.15 ± 0.23 this paper
and to try to understand its atypical properties. We carried out
V (km s 1 )–7.40 ± 0.15,
this paper
1,??
2
1
3
4,
26
2
3
5,
23
a
systematic
study
of
the
debrisdisc-bearing
host
star,
including
1
P. Delorme, T. Schmidt , M. Bonnefoy , S. Desidera , C. Ginski , B. Charnay , C. Lazzoni , V. Christiaens ,W (km s )–3.40 ± 0.26
this paper
new observations,to determine
its age and metallicity(Sect.
2).
6
3
7
8,
9
3
1
1
5,???
S. Messina , V. D’Orazi , J. Milli , J. E. Schlieder , ThroughR. Gratton, L. Rodet, A.-M.
Lagrange, O. Absil
T e↵ (K)6500 ± 100
this paper
the SpHere
INfraredsurveyfor Exoplanets(SHINE) ,22, 12 , A. Zurlo10, 13 , J. Olofsson8, 14 , A. Boccaletti2 ,log g4.45 ± 0.15
this paper
A. Vigan10 , R. Galicher2 , J. Hagelberg1 , M. Bonavita11 , GTO
B. Lavie
large programmewith SPHERE, we obtained additional[Fe/H]+0.04 ± 0.02
this paper
15 , M. observations
22 , T. under1,
resolvedof, thecompanion
very8 ,stable
obF. Cantalloube8 , D. Mouillet1 , G. Chauvin1 , F.-J. Hambsch
Langlois25, 10
S. Udry
Henning
J.-L. Beuzit
EW Li (mÅ)
28.5 ± 7.0
this paper
8, 17 , A. Cheetham
including 22
theC. Mordasini12 , P. Lucas16 , F. Marocco16 , B. Biller24 , J.serving
Carsonconditions,, E.low-resolution
Covino18 , V.spectroscopy
De Caprio18 ,A(Li)2.38 ± 0.10
this paperthat we present 8in Sect. 3. Theseobservations
confirm
that
1
8
7
19
8
20
2
A. Delboulbe , M. Feldt , J. Girard , N. Hubin HD, A.-L.
Maire, A.reddest
Pavlov, C. substellar
Petit , D.
Rouan
[Ba/Fe]0.20 ± 0.20
this paper
206893B
is theknown
object,even, red21
22
R. Roelfsema der, and
F. Wildi
v sin i (km s 1 )32 ± 2
this paperin NIR
than 2M1207 b (admittedly by a slight margin of aplog LX /Lbol–4.80 ±
this paper
proximately, Chauvin et al. 2004) or the recently discovered(Affiliations can be foundafter the1references)log RHK–4.77 ±
this paper
2MASS J223624+4751 (Bowler et al. 2017). Section 4 focusesProt (d)0.996 ± 0.003 this paper
the comparison
HD 206893B with known red L dwarfs.
Received 10 May 2017on/ Accepted
22 July of2017
Age (Myr)
250+450
this paper
Section 5 is dedicated to the characterisation of the atmospheric
これが主題の200
Mstar (M )1.32 ± 0.02
this paper
properties of this atypical young substellar companion, through
ABSTRACT
Rstar (R )1.26 ± 0.02
this paper
atmosphere and substellar evolution models. In Sect. 6 we detail
褐⾊矮星i (deg)30 ± 5this paper
theconstraints
be isderived
from
theH,observed
Fig. 3. Residual images of HD 206893B in
Y, orbital
J, H, and K
bands in linear thatscale. can
The scaleidentical in
Y, J, andbut is 4 timesKewider in K toContext. The substellar companion HD 206893b
hasrecently
been
discoveredbydirectimagingof
its
disc-bearing
host
star
with
the
Spectroaccommodate the brighter speckle residuals
and brightercompanionin theIRDIS K-bandand
image.
plerianmotionof thecompanion
determine that this detected
Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument.
companion cannot shape the colours
observeddisc alone.
Aims. We investigate the atypical properties3.0×10of the companion, which has the reddest near-infraredamong
all known substellar objects,presence of the brown dwarf companion would imply a maxiK1 and K2 filters after TLOCI-ADI reduction. No companion
either orbiting a star or isolated, and we provide a comprehensive characterisation of the host star-disc-companion
system.
was detected even though our detection limits reach respectively
mum
RV semi-amplitude only of the order of 0.15 km s 1 (from00
2.5×10
Methods. We conducted a follow-up of the companion with adaptive optics imaging and spectro-imaging
withof SPHERE,
and a multi-instrument
14.5 and 15.2 mag
contrast for separationsof 0.3 and 0.5
thefamily of orbits fitting the available astrometric data, see
2.
Host
star
properties(seeandFig. 5).
These detection
limits areat
computed
for a2.25
companfollow-up of its host star. We obtain a R = 30 spectrum from 0.95 to 1.64 µm of the companion
additional
photometry
2.11 andµm.
2.0×10Sect. 6.1), which is smaller than our current uncertainties on theion with a uniform contrast and are hence conservative because
We carried out extensive atmosphere model fitting for the companions The
and the
host
star
in
order
to
derive
their
age,
mass,
and
metallicity.
thedeep
absorption
bands
in
the
spectraofreal
substellarcomdetermination of the properties of the substellar object RV of the system and is hence neglected in the kinematic analyResults. We found no additional companion1.5×10
in the system in spite of exquisite observing conditions
resultinginthe
sensitivity
6 MJupdi↵erential(2 MJup )panionsslightly
improvesensitivity toofspectralaround the star depends
sensitivelyontheadoptedstellarpasis.
00
methods (seethe
e.g.possible
Rameau etKeplerianal. 2015). Foran ageof These spectroscopic data also show that HD 206893 is not a
at 0.5 for an age of 300 Myr (50 Myr). We detect orbital motion over more than one year imaging
and characterise
orbits.
We
rameters, and especiallystellarage. Unfortunately,
theage of limits
300on
Myr
(50
limits correspondto detectioninspectroscopic
binary.
1.0×10constrain the age of the system to a minimumof 50 Myr and a maximum of 700 Myr, and determine
thatMyr)thethese
host-star
metallicity
is nearly
solar.
mass, assuming
Bara↵e et al.
(2003) hot-startevolution models, The resulting space velocities of the system are U, V, W =mid-Fstars likeindicates
HD 206893
isdifficultto determine.
The comparisonand photometry to model
atmospheresthat
theparticularlycompanionisanextremely
dusty late L
00 of the companion spectrum5.0×10
ofrespectively
6
and
8
M
(2
and
3
M
).
Jup
Jup
On
the
one
hand,
their
evolutionisslow,
makingisochrone
fit20.15 ± 0.23, 7.40 ± 0.15, 3.40 ± 0.26 km s 1 . We used
dwarf, with an intermediate gravity (log g ⇠ 4.5–5.0) which is compatible with the independent age estimate of the system.
ting Mnot very
constraining
when
close
to is
thealsomain
sequence.with
Ona rangethese kinematics to investigate the possible membership ofConclusions. Though our best fit corresponds to0 a brown dwarf of 15–30
Myr,
our re-detection
analysiscompatible
Jup aged 100–3003.3.
No discin SHINE
data
thetoother
the
based
on rotation
and activity
are HDis 206893 to a young moving group using the BANYAN2
1.0
1.2object
1.4
1.6 indicatorsof masses and ages going from a 50 Myr 12 MJup planetary-mass
a 50hand,
MJup Hyades-age
brown
dwarf.
Even though
this companion
λ(µm)
We
initially
believedthat
ourK-bandIRDIS
SHINE
data showed
more
uncertain
for verycolderstars
due thatto thevery thinconveconline tool (Gagné et al. 2014b). Assuming that HD 206893 isextremely red, we note that it is more probable that it has an intermediate
gravityrather than
than thelowgravityisoften
associatedvery
a re-detection of the faint structure highlighted as witha probable
Fig.
4.
Extracted
spectrumofHD
206893B
through
TLOCI-ADI.
envelope.
et disc,al. (2017)
an
age
range
youngerthan 1 Gyr (see below), we obtain a 13.5% probabilred L dwarfs. We also find that the detected companion cannot shape thetive
observedouterMilli
debrishintingadopted
or extended
severaladditional
planetary
disc
detection
inthatthe oneH broad-band
IRDIS
imagesanalysedby+200
0.2–2.1
Gyr,while
Galicheretal.
(2016)
adopted200
Myrmass objects in the system might be necessary to explain the position of the disc inner edge. Milli et al. (2017). However, given the faintness
ity for membership in the Argus association and 86.5% for the
100 of this signal,
wecheckedwhethertheobserved
extendedstructurewas
indeedfrom X-ray and UV luminosity. Our approach is based on a young field.
the SHINE
Consortium– also
show that thebest
spectral resolution
an astrophysicalsignal or aninteractions
observational bias. Instead of deKey words. brown dwarfs – planets and withinsatellites:
atmospheres
techniques:highangular–severalplanet-disk
comprehensive
evaluationofage
indicators
to the actual paralfidelity, i.e. the ability to retrieve, within the error bars, the spec- rotating our sequence of images accordingfollowing
methods
described
in Desideraal. (2015).
Spectroscopic
trum of an injected fake companion isthebest whenusing only
ADI, lactic
angle of theetobservations,
we applieda de-rotation in the
Jupparameters2.2. Spectroscopic
while the best point-source sensitivityand
is achievedbycombining
opposite
direction,
whichshoulde↵ectively
kill any astrophysphotometric datasets were acquired to gather the required
ADI and SDI. When we probed the possible presence of addi- ical signal. Since the same fuzzy extended structure was still
information.
1. Introduction
the atmospheres
extrasolar
planets(Zurlo et al.
tional companions in the system we used
TLOCI
and PCA using ofvisible,it meant it giant
was causedby an observationalbias,2016;
probJup
Jupthe FEROS spectrograph on
The star was observed with

Young/Dusty/VL-G

14
HN Peg B

Received 10 May 2017 / Accepted 22 July 201716

Mace et al. 2013
2M1207b51 Eri b

これが主題の褐⾊矮星

18

ABSTRACTInterstellar (R=3.1)
0.5 µm forsterite

HIP 107412b

20-1
0 star 1with the
2 Spectro3
Context. The substellar companion HD 206893b has recently been discovered by direct imaging of its disc-bearing
host
J -K1

Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument.
Fig. 7. Placement of the IRDIS photometry of HD 206893B (HIP 107412
Aims. We investigate the atypical properties of the companion, which has the reddest near-infrared colours
among
all known
substellar
to thereddening vector
caused by forsterite
grains withobjects,
mean size 0.5 µm
parameter R = 3.1).
either orbiting a star or isolated, and we provide a comprehensive characterisation of the host star-disc-companion system.
Methods. We conducted a follow-up of the companion with adaptive optics imaging and spectro-imaging with50SPHERE,
and a multi-instrument
No correlated noise
follow-up of its host star. We obtain a R = 30 spectrum from 0.95 to 1.64 µm of the companion and additional photometry at 2.11 and 2.25 µm.
40
We carried out extensive atmosphere model fitting for the companions and the host star in order to derive their age,mass, and metallicity.
Results. We found no additional companion in the system in spite of exquisite observing conditions resulting in sensitivity to 6 MJup (2 MJup )30
at 0.5 for an age of 300 Myr (50 Myr). We detect orbital motion over more than one year and characterise the possible Keplerian orbits. We
constrain the age of the system to a minimum of 50 Myr and a maximum of 700 Myr, and determine that the host-starmetallicity is nearly solar.
20
The comparison of the companion spectrum and photometry to model atmospheres indicates that the companion is an extremely dusty late L
10dwarf, with an intermediate gravity (log g ⇠ 4.5–5.0) which is compatible with the independent age estimate of the system.
0 is also compatible with a range
Conclusions. Though our best fit corresponds to a brown dwarf of 15–30 M aged 100–300 Myr, our analysis
M5
L0
L5
T0
T5
Y0
of masses and ages going from a 50 Myr 12 M planetary-mass object to a 50 M Hyades-age brown dwarf. Even thoughthistypecompanion isSpectral
Bonnefoy et al. 2016; Vigan et al. 2016; De Rosa et al. 2016;2008 November 13 as part of the preparatory program for the
The discovery of young
giant planets
high- Chilcote
extremely
red,extrasolar
we notethatfound
it withis moreprobable
that
it
has
an
intermediate
thantheset-up
very
low gravity
that isof often
associated
with
very
et al.
2017).and young groups membership
SPHEREgravity
GTO survey. rather
Details on the
instrument
and reFig.
8.
Comparison
theNIR
spectrumandphotometryofHD
206893b to
2.1.
Kinematic
analysiscontrast imaging techniques (Chauvin et al. 2004; Marois et al.
ductionprocedure
are
given
in
Desideraetal.
(2015).
These previous
studies have shownthat while
young theexo- observed outer debris disc, hinting correlationnoiseorof theIFS spectrum;on the right, itplanetary
does.
red
dwarfs.
WeRameaualsoet al.findthecompanion
cannot
shape
that
one
severaladditional
2008; L
Lagrange
et al. 2010;2013;that
Delormeet al.detected
HDplanets
206893haveis included
in
Gaia
DR1
and
we
adoptedGaia
a spectral signature quite distinct from field brownAs done in our previous investigations (see e.g. Vigan et al.
2013; Bailey et al. 2014; Macintosh et al. 2015; Gauza et al.DR1 trigonometricparallax and proper motion (using a corre- 2016, for GJ 758 B) we derived spectroscopic parameters usdwarfsofequivalente↵ectivetemperature,theyhave many atmass
objectsinthesystemmight
benecessary
toexplainthepositionof the disc inner edge.
032015) o↵ers the opportunity to directly probe the proper-sponding distance of 40.6
pc; see Table 1),
unlikeMilli et al. ing
mospheric properties in common with isolated brown dwarfsthe code MOOG by Sneden (1973, 2014) and the Kurucz
s

−16

−16

−16

−16

−17

this combined “ASDI” approach with IFS data. Figure 3 shows
the resulting residuals maps in the Y, J, H, and K bands. The
Y, J, and H are a stack of the IFS channels after TLOCI-ASDI
reduction that have a wavelength corresponding to each photometric band, while the K-band image is a stack of the IRDIS
A79, page 6 of 25

ably the wind extending the coronagraphic halo along a privileged direction. As a sanity check, we also applied this procedure to the H-band data analysed by Milli et al. (2017), and weshow that as expected for an astrophysical disc signal, applying
an incorrect de-rotation angle destroys the signal in this case.
+0.5
0.4

G

Flux (Wm2µm−1)−16

PSO057+15

ULASJ2227-00

o↵set of the disk center from the star position (and indeed, the assumption is verified a posteriori by the lack of
2. Azimuthallyradial intensity
profileof thenaturally
weighted
image,
deprojectedalongcontours
2 elliptical1
residuals after Figure
the best-fit
model isaveraged
subtracted
from thedata).
We
assumeadust
opacityof
2.3
cmg(Beckwith
Nederlander
et andal. position angle of 60 . The blue shaded region
assuming a circular geometry and an inclination to the lineof sight of 45
et al. 1990), yielding
opticallythinerror
emissiontheall bin,of themodelswithindeviation
the parameter
space
byrepresents
the standardof the formean
fordusteach inradialwhere
the standard
is calculated
for explored
all pixels within
the MCMC chains.
densitytemperaturearethedegenerate
for opticallyemission,
we assume
that
these
the bin Since
and thendividedandby thesquare root of
number of beams
sampled. thin
The sizeof the synthesized
beam
is indicatedgray Gaussian
marked “Beam.”
The central
10.4 au projected
206893B (Milli
et al. 2017)
large grains arebyintheblackbody
equilibriumwith thestar andseparation
calculateof aHD
dust
grain
temperature
ofis marked with avertical dashed line.
✓
◆1/4
L⇤
Tdust =
(1)
1
2
The surface brightness of the central peak, 19.7
16⇡± 5.5
R µJy beam , is approximately consistent with the expected
flux density of 12.6 µJy for a star with a temperature of 6500 K and radius 1.26 R (Delorme et al. 2017), when
Nederlander
et al. constant, and R is the distance of thewhere L⇤ is thebolometricluminosity
of
the
star,
is
the
Stefan-Boltzmann
approximating the star as a blackbody (in this case, the systematic flux uncertainty provides the largest source ofdust grain fromerror
theincentral
star. We adopt
stellarluminosity
ofaat
L= 2.83
L wavelengths
forこれは中⼼星の光度HD206893 (Delorme et al. 2017).
⇤millimeter
theWhileatheproperties
stars
Forcomparison).
example, the surface
densityin the diskof
follows
power-lawdistribution
whereare not well understood, and can
We assumed several
possiblefunctional
for thedensityof the disk;
the functional
forms
for thedeviate di↵erent
significantly
from theexpectedforms
blackbodyfluxsurface
for a varietyof reasons
includingchromosphericemissionandp= ⌃cthisR estimate provides a ballpark figure to guide(2) our
surface densityflaring
are summarized(Cranmer etinal.Table
2013; 4.
White et al. 2018, 2019,⌃(R)
2020),
interpretation
the ofemission
demonstrateforin theSection4 below,a statisticallysignificant
betweenofradii
R andmorphology.
R , where ⌃Asis wea normalization
total dust
mass there
in the isdisk,M(see Table
4
in

out

c

disk

for definition), and p is a power law index that we initially set to a value of 1.0. While the value of p is interestingfrom the perspective of debris disk evolution, there is a well-known degeneracy between p and the location of theouter radius Rout (see, e.g., section 4.2.2. of Ricarte et al. 2013) and our data are of sufficiently limited sensitivity
and angular resolution that we chose to focus on Rout rather than p. We chose a value of 1 as a middle-of-the-road
estimate bounded by theoretical predictions of 0 for collisional evolution models that assume a collisional lifetime ofaged radial intensity profile of the naturally weighted image, deprojected alongRellipticalcontours
Routを知りたいので,
p=1を仮定outとpは縮退していることが知られていること,
thelargest planetesimal longer than the age of the system(Schüppler et al. 2016;
Marino et al. 2017), and 7/3 fory and an inclination to the line of sight of 45 and position angle of 60 . The blue shaded region
those that assume the opposite (Kennedy & Wyatt 2010).
r of the mean for each radial bin, where the standard deviation is calculated for all pixels within
As it became clear that the local minimum and maximum evident in the radial surface density profile (Figure 2)
the square root of the number of beams sampled. The size of the synthesized beam is indicatedwould require a more complex radial surface density distribution than the initial flat disk model, we explored two
d “Beam.” The 10.4 au projected separation of HD 206893 B (Milli et al. 2017) is marked with afamilies of more complicated models: models with broken power laws that switched power law indices at one or two
transition radii within the inner and outer radius of the disk, and models that included a sharp radial gap in the surface
density profile at a particular radius. When analyzing surface brightness features with modest signal-to-noise, it is1of the central peak, 19.7 ± 5.5 µJy beam , is approximately consistent withoftenthenotexpected
possible to determine the exact shape of the feature, but broken power laws and sharp gaps are both common
or a star with a temperature of 6500 K and radius 1.26 R (Delorme et families
al. 2017),
when assumed in the literature (see, e.g., Ricci et al. 2015) and adequately represent the extremes of anof solutions
abrupt anddeepofgap vs. a broad and shallow gap.
a blackbody (in this case, the systematic flux uncertainty provides the largest
sourceAfter generating
While the properties of stars at millimeter wavelengths are not well understood,
and can the sky-projected images, we apply a primary beam correction (multiplying by the primary beam)and emission
then convert
the expected blackbody flux for a variety of reasons including chromosphericandthe model image into synthetic model visibilities using the MIRIAD task uvmodel (Sault et al. 1995),
2
which
we
then
compare
with
the
data
in
the
uv
plane
to
calculateavalue as a goodness-of-fit test. Comparing
13; White et al. 2018, 2019, 2020), this estimate provides a ballpark figure to guide ourdata in the uv plane is desirable both because uncertainties are well characterized in the uv plane (unlike in the image
sion morphology. As we demonstrate in Section 4 below, there is a statisticallysignificant
domain, where the uncertainties are unknown and correlated between pixels, and nonlinearities can be introduced
Figure3. Ellipticallyaveragedvisibilityitprofile
comparingdata of(blue
points)with the best-fit
flat disk(redline),
by the CLEAN
process),
and because
is agnostic
to thethechoiceimaging
parameters
and allows
us to
take
fulldouble
power-lawa gap(greenline) andtriple sampled.
power-law (orange line) models. The top panel shows the real part of the visibilities
advantage withof therange
of baseline
lengthswhilebottompanel
the imaginary
part of the visibilities.
visibilities
have been
deprojected
an inclination
We thefit themodelstoshows
the data
using an affine-invariant
MCMCThesampler(Goodman& Weare2010)assuming
implemented
inof
44 andpositionangle
of 60 ,emcee
the best-fit
values for theetdoublepower-law
Pythonin athesoftwarepackage(Foreman-Mackey
al. 2013).
The model.
goodness of a fit between the synthetic
Nederlander et al.

1 https://github.com/kevin-flaherty/disk model3

2

04

5.
DISCUSSION
Nederlander et al.

5.1. Disk Structure Constraints
by Grandjean et al. (2019), as well as the 30 ± 5 inclination of the stellar po
The results of our MCMC fits demonstrate
残骸円盤の全体像 that the HD 206893 disk is wellInterestingly,
theversionoftheGrandjeanetal.
(2019)
dynamical
MCMC
ana
+13
内径
<
51
AU；外径
~194
AU
(表の
)⇨
褐⾊矮星まわりの残骸円盤
R+
ΔR•
distribution extending from radii of < 51 au to 194 2 in au (this constraint on. (Left) Naturally weighted ALMA image of the 1.3 mm continuum emission from the HD 206893 system, withaとして最⼤(と⾔ってもサンプル数⼩)
fromdistribution
radialvelocity,
astrometry,stellarpropermotion,anddirectimaging
resul
00 k applied to bring out the large-scale
structure of the source.
(CenterLeft)
Fullresolution
model
image
for
a
of
R
=
R
+
R,
which
is
not
shown
in
Figure
8),
with
a
ga
out
in
Resolved
DebrisDiskaround206893Right) Model image sampled at thehowing the structure of the disk
with a stellar
flux
equal
to zero.HD(Centersame+5• ⽅位⻆⽅向平均操作は妥当だった.
+11ofcompanionof
45±
3
engths and orientations asinclination
the ALMA data, showing
thethebest-fit model
without a gap in the
middleof thedust
disk.and a mass of 10 4 MJup , though they
anda width of 31 7 symbols
au.• mmサイズのダストが中⼼There are no ≲statisticallysignificant (> 3
Table from
3.exhibiting
MCMC
Fitting
Results
esidual image after subtracting the modelthe data
in thevisibility domain. Contour levels andare as37 AUに存在しないと輝度分布を説明できな
1.
data
is
six
times
higher
than
when
they
do
not
includethestellarpropermotio
い.
Parameter
Flat Disk
Double Power Law
withwell
Gap
Triple Power Law
observationsaredescribed
by an azimuthally symmetric and circular distribBest FitMedianBest FitMedianBest FitMedianmayratio
be someinconsistency
intheability
of
their
model
to
reproduce
both
the
R
of the data (the brightest parts
of
the
dust
disk
are
approximately
atthePlanetesimal belt (邦訳は微惑星帯？)
R (au)
9
< 44
21
< 51
35
29
perhaps
providing
additional
supportforthepresenceofanothercompanionin
残骸円盤円盤⾯とのなす⻆が⼤きい可能性を排除できない.
out
local
(or
point-to-point)
spatialvariations
in
flux
of
&
50%
on
spatial
scale
•
R(au)
155
151
176
166
159
164
Log(M ) (M )
-1.66
1.63
-1.61
1.63
-1.74
1.74
cannotrule
outmutualinclination
for the star and brown dwarf companion, copl
⇠30
au or
F (µJy)16
19
17 larger.
18
14
15
PA ( )
66
63
60
59
60
63
When wecompareourderiveddisk size to the sample of spatially resolved disk
i( )
47
47
45
44
43
47
x( )
0.11
0.14
0.16
0.11
0.11
0.09
we
that theof R0.06for HD 206893
accordingto thedefinition
laid out i
y( )
0.05
0.04 note 0.04
0.03 value0.05
5.2.
Gap
DetectionandImplications
R
(au)
67
63
115 au. 32Of theirsample of ten F stars, only one (HR 8799) has a larger radi
R
(au)
31
pp1
-2.0
1.1
-2.7
1.2 between the best-fit models provide strong evid
The AIC andBIC
comparisonギャップ
pp2
4.7 that> 0.23
unusual 2.8 Boo 3.0
spectrumis in some
ways
more
consistent
with
an
A
star
spec
• 図2-4の解析から, R~63 AUに幅30+/-10AUのギャップが 存在することは確実
pp3-3.7
3.0 of 80 au.
thesurfacedensityneararadius
This
marks
the
fourthdetection
of
a
ra
Rt1
97
102
71
is therefore
amongthe73 largest
known
debrisdisks around F stars, although co(⇦ 古屋疑問— Gapの幅、こんなに⼤きいのはBDまわりの残骸円盤だから？)
Rt2
113
115
HD
107146(Riccietal.
2015;
Marinoetal.
2018),HD
15115(MacGregoretal.
• ギャップの「今の姿」を説明するためには, 惑星による形成が⾃然で, ガスの運
Ln prob-10733015.1 (Sepulveda-10732991.8et al. 2019).
-10732995.1
動, 化学進化によるみかけ上のギャップ形成説や磁気流体不安定性による形成
Note— The inner radius2019).
is unresolved inWhile
the models without
a gap,
so the best-fit sizevalue of 9is
au ornot
21 au is large,
thesample
there
are
only
a
coupleofotherdebrismakes
not meaningful. The upper limit of 44Our
au or 51 aumodel
represents the 99.7th
percentileseveralof the posterior simplifying assumptions that may or may not be説を積極的に⽀持する証拠はない.
distribution.
05
belts that have been imaged with sufficient resolution and sensitivity at millimeter
Figure 4. (Left) Naturally weighted ALMA image of the 1.3 mm continuum emission from the HD 206893 system, with ataper of 200 k applied to bring out the large-scale structure of the source. (Center Left) Full resolution model image for aflat disk showing the structure of the disk with a stellar flux equal to zero. (Center Right) Model image sampled at the samebaseline lengths and orientations as the ALMA data, showing the best-fit model without a gap in the middle of the dust disk.
(Right) Residual image after subtracting the model from the data in the visibility domain. Contour levels and symbols are as
in Figure 1.

a

in

disk

⇤

00

00

in,Gap
Gap

+14
11
+0.03
0.03
+6
6
+3
3
+2
2
+0.07
0.07
+0.06
0.06

a

a

+20
16
+0.03
0.02
+5
5
+3
3
+3
3
+0.07
0.09
+0.05
0.05
+8
16
+11
7
+1.1
0.8
+1.0
0.9
+16
17

a

+7
20
+18
14
+0.07
0.07
+5
6
+3
3
+3
3
+0.08
0.09
+0.11
0.07

+0.8
1.1

+1.3
1.0
+9
33
+8
7

5.3. N-body Simulations of the Star, Brown Dwarf, and Putative Planeteory on which
baseWidth
our andestimateof Varying
planetBrown
massDwarf
is fundamentallya 3-body result, but adding
Tablewe
5. GapDepth withParameters
ce of the brown dwarf (e↵ectively treating the central star as a low-µ binary system) makes they a 4-body problem. We therefore conducted N-body simulations with and without the brown
BD Mass (MJup ) BD Eccentricity BD Inclination( ) Gap Width (au) Gap Depth (%)
erify that
the
gap
depth
and
width
were
not
Nederlander
etal.significantly a↵ected by the presence of the brown
12
0
0
34
95
whetherproperties
of
the
brown
dwarf
have
a
detectable
impact
on
the
width
of
the
15 the orbital
0
0
35
94
Table 6. Gap Width and Depth with Varying Planet Parameters

30
0
0
35
97
e gravitational
interaction between
the star,
50
00 brown dwarf,
34 putative planet,
96 and dust particles
PlanetMass (M ) Planet Eccentricity
Planet Inclination( ) Gap 34
Width (AU) Gap 98
Depth (%)
50
0.03
0he N-body software REBOUND (Rein & Liu 2012) with hybrid integrator MERCURIUS (Rein et al.
0.5
00
Gap Undetectable
0.1
0particle comes 34
96 distance of a massive
from1 a50fixed to variable timestep
when
any
withinacertain
0
0
740
表5, 6にまとめた解析から
50
0.3
0
35
99
to •beradii. We chosethe fixed timestep
to be 4% 11of the brown dwarf’s
initial period,
5three =Hill0051
褐⾊矮星質量15 Mjup,,,,,,
50
0
5
34
95
of everywhen the simulation
begins. Dust
particles are
10 dust particle’s period001358 treated in the test
50
0
10
34
97
議論の焦点(のひとつ)/明らかにしたいこと：Gapped
structureの起源
15
0
0
15
62
No
BD
34
98
原始惑星系円盤期から成⻑してきたものか？あるいは
thesystem(
残骸円盤期と意訳してよい？)になってから形成されたものか？
≃• (この残骸円盤中の巨⼤な)ギャップは,
20
0
0
16
60

y randomly distributed with a uniform distribution of semimajor axes between 8 and 158 au, a
本研究だけからは定かでない.
• ⇨ 2500
16
59
of eccentricity
from
0
to
0.02,
and
a
uniform
distributionofinclination
from
0
to
10
.
We
30
0
0
18
64
cles,
adequatetosample
the
150
au
span
of
the
disk
and
smooth
of
the
final
disk
⇠6 systems
that haveso far beensurveyedatsufficient
resolution
and recoversensitivity
to detectimages
such
a gap.
35
00
18
66
論⽂タイトルをみたとき&読み始めの段階で, 私が知りたかったこと
originofgappedstructureis
stillunclear,
in
this
case
the
low
limit
on
the
gas
mass
in
the
systemrendersWe• 褐⾊矮星を含む残骸円盤の初めてのALMA撮像観測なので,assumedastellar
mass
of
1.32
M
and
a
stellarradiusof
1.26
R(Delorme
et al. 2017). The
40
0
0
19
71
惑星だけを含む残骸円盤(統計が無理であれば代表的なもの)との⽐較コメントを読みたかった(それほど意味のな
adientsdue
toresidual
disk
gas
an
unlikely
explanation,
so
the
gap
must
eitherhave
beeninheritedfrom
惑星に⽐べ,
輻射場は強いのであろうから,ダストの性質(1mm帯のみの観測だからβの議論は無理だが,NIRと合わせて何か議論できる？)に与える影響,ガ
0 axis 10.4 au
0 assumed to have
20 a radius of
71 RJup . We assumed
danetary
onいことなのか？),
a45orbitwithsemimajor
and
1.3
disk
phase
or
carved
by
one
or
more
additional,
unseencompanionsatlargerseparationinthe
ス・ダスト⽐(COが検出できなかった上限値は強い制限にならなかったのか？)の議論など.
⇨ 今後の研究に期待
350
0020 on a circular
72 orbit at 80 au. We
M
and
a
bulk
density
of
1.3
g
cm
.
We
placedtheplanettheJupgap is carved by a single planet on a circular orbit, chaotic zone theory predicts that it should have a
06
100

0

0

24

86

(a)いくつかの銀河では, ⾮対称的なガス分布(必然的に⾮対称性のある星形成率分布) ⇨ CMZ全域にわたって離⼼率の⼤きい
楕円軌道となり, ~10 Myrはつづく爆発的星形成(b)それ以外び銀河では, 滑らかなガス分布(同, 星形成率分布)07

Table 2. Physics & Numerics Explored in This Paper (and Papers II & III)

今回, 解析したシュミレーション：先⾏研究から

Physics/Numerics§

Effects in FIRE-2 Simulations

Guidelines / Default Choice

Resolution:
Mon. Not. R. Astron. Soc. 000, 000–000 (0000)

Printed 13 November 2018

(MN LATEX style file v2.2)

Mass Resolution

4.1

Collisionless (DM/Stellar)
Force Softening
Gas Force Softening

4.2

FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation
4

1 TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
2 Carnegie Observatories, Pasadena, CA 91101, USA

3 Department of Physics, University of California, Davis, CA 95616, USA

11

FIRE-15 Department of PhysicsFIRE-2
and Astronomy and CIERA, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA

Conduction, Viscosity
Metal Diffusion(sub-resolution mixing)

4.2
4.3

10

6 Department of Astronomy and Theoretical Astrophysics Center, University of California Berkeley, Berkeley, CA 94720

56F
7.2 & F

9

alo
M
o

f
=
⇤
M

ry

ba
9 Center for Computational Astrophysics,
Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

8

10 Institute for Computational Science, University of Zurich, Zurich CH-8057, Switzerland
11 Department of Physics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

7

12 Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics, Stanford University, Stanford, CA, USA
13 Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA

6

14 Department of Astronomy, University of Florida, Gainesville, FL 32611, USA

Molecular Chemistry/Cooling

7&B

Low-Temperature Cooling(T ⌧ 104 K)
Metal-Line Cooling(T & 104 K)
Photo-Heating (Background)

7&B

Observed (abundance matching):
Self-Gravity (Virial) Criterion
5
Moster+ 2013
ABSTRACTBrook+ 2014
Density Threshold
4
Garrison-Kimmel+
The Feedback In Realistic Environments (FIRE)
project explores2016
feedback in cosmological galaxy formation simulations.
by the devel3 Previous FIRE simulations used an identical source code (“FIRE-1”) for consistency. MotivatedJeans-Instability
Criterion
opment8.5of moreaccuratehydrodynamic
softening, and supernova coupling
9.0
9.5numerics
10.0– including
10.5 11.0
11.5 solvers,
12.0 gravitational
12.5
algorithms – and exploration of new physics (e.g. magnetic fields), we introduce “FIRE-2”, an updated numerical imlog(Mhalo )code.
[M We] run a suite of simulations and compare against
Self-shielding/Molecular
plementation of FIRE physics for the GIZMO
FIRE-1: overall,Criterion
Figureimprovements
7. Stellar mass-halo
mass relationchange
for FIRE-2
simulations(coloredWe pursue an extensive study of numerics
FIRE-2
do not qualitatively
galaxy-scale
properties.
“Efficiency”(Rate)
versusphysics.
of thestar-formation
algorithm,
physics,
providedthat
points)at z =Details
0. Stellar
massesand halo virial
massescoolingare defined
as inandTa-chemistry have weak effects,
Resolution
Limit
weble
includecoolingand star formation
at higher-than-meandensities. We present new atresolution
criteria
1, formetal-line
all resolved,
uncontaminatedhalos occurs(116 galaxies
total; see text,for§high-resolution
galaxyMost(mostgalaxy-scale
are robust3). Large points
showsimulations.
the “primary”
massive)properties
galaxy within
the to numerics we test, provided: (1) Toomre
masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved.
StellarContinuous Mass-Losszoom-in region, in each simulation (different point styles). Grey triangles
masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followedby prop(OB & AGB)
show
FIRE-1
simulations.
Whileindividual
galaxiesmaydifferinmass,erties of winds and circum-galactic media (CGM). Central (⇠kpc) mass concentrations in massive (> L⇤ ) galaxies are
Supernovae (Ia & II)
the effects
are primarily
stochastic: the twoofagree
well
on average.
We comsensitive
to numerics(via trapping/recyclingwinds
in hothalos). Multiple
feedback mechanisms play key roles: super(“How to Couple”)
pare regulate
observationalas labeled;dottedfuelslineslateshow
obser- radiative feedback suppresses
novae
stellarestimates
masses/winds;
stellarblackmass-loss
startheformation;accretion
onto
dwarfs andinstantaneous
formationin disks.
We provide
conditions and numerical algorithms used.
vationallyestimated⇠ 95%star
intrinsic
scatter(see text).
Within all
theinitial
scatter
Radiative Feedback
andsystematic
variations
betweenfits,
thesimulations
agree
well
with
the
Key words: galaxies: formation — galaxies: evolution — galaxies: active — stars: formation — cosmology:
theory&—(Photo-Heating
observations
at all masses.
methods:
numerical
Radiation Pressure)

Submitted to MNRAS, February 2017

Irrelevant for dwarfs. Important for massive galaxies with hot halos.
SPH may suppress cooling & artificially allows clumpy winds to vent
Unimportant unless set too large, then prevents real fragmentation.
Double-counts “sub-grid” treatment of fragmentation with SF model
Weak effects on sub-galactic scales (dense gas, morphology, turbulent ISM)
(Not studied here, but in Su et al. 2017; effects in CGM could be larger)
Small effects on galaxy properties & dynamics,
but potentially important for abundance distributions of stars

Newer methods recommended
Do not use with
self-gravity based SF models
See Su et al. (2017)
Best practice depends
on numerical hydro method

Cooling:

7 Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USAh8 Canadian Institute for Theoretical Astrophysics,
n
60 St. George Street, University of Toronto, ON M5S 3H8, Canada

Resolution criteria in§ 4.1.3 (Eq. 5-7)
Optimal range of valuesin § 4.2.2
Fully-adaptive softenings(matching gas) should be used
Standard limiters + Stellar (Eq. 12)+ Adaptive softening (Eq. 13)(Magneto)-Hydrodynamics:

4 Department of Physics, Center for Astrophysics and Space Science, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USAlog(M⇤ ) [M ]arXiv:1702.06148v2 [astro-ph.GA] 11 Nov 2018

1,2,3

Philip F. Hopkins , Andrew Wetzel †, Dušan Kereš , Claude-André FaucherCriteria
Giguère5 , Eliot Quataert6 , Michael Boylan-Kolchin7 , Norman Murray8Timestep, Christopher
C. Hayward9 , Shea Garrison-Kimmel1 , Cameron Hummels1 , Robert Feldmann6,10 ,1Paul Torrey11 , Xiangcheng Ma1 , Daniel Anglés-Alcázar5 , Kung-Yi Su1 , Matthew
Hydro MethodOrr ,1 vs. SPH)
(MFM
Denise Schmitz1 , Ivanna Escala1 , Robyn Sanderson1 , Michael Y. Grudić
, Zachary
Artificial Pressure 4
Hafen5 , Ji-Hoon Kim12 , Alex Fitts7 , James S. Bullock13 , Coral Wheeler1 , “Floors”
T. K. Chan ,Magnetic Fields,
Oliver D. Elbert13 , Desika Narayanan14?1

Most results robust after resolving the Toomre scale, some (e.g.
massive galaxy morphology) depend on resolved winds/hot gas
Irrelevant unless extremely small or very large values used,adaptive collisionless softenings require additional timestep limiters
Forcing fixed softening generally has no effect, unless too large,
then fragmentation & SF are artificially suppressed
Provided that standard stability criteria are met, this has no effect.
Additional limiters needed for stellar evolution & adaptive softening

7&B
7&B

No effect on galaxy properties or star formation (just a tracer).
Not important star formation criterion if fragmentation is resolved
Details have no dynamical effects because tcool ⌧ tdyn in cold gas
to opacity limit (⇠ 0.01 M ). Relevant for observables in cold phase
Dominates cooling in metal-rich centers of “hot halos” around massive
galaxies, and of individual SNe blastwaves
Significantly suppresses star formation in small (Mhalo . 1010 M ) dwarfs

May be relevant at [Z/H] ⌧ 3, can beimportant for observational tracers
Some needed to form cold clouds,
details dynamically irrelevant
Needed: important insuper-bubbles & “hot halos”
Needed: dwarfs & CGM/IGM

Star Formation:
8&C
8&C
8&C
8&C
8&C

Negligible effect on galaxy properties (SF is feedback-regulated). Moreaccurately identifies collapsing regions in high-dynamic range situations
Negligible effect on galaxy properties (SF is feedback-regulated)
Can be arbitrarily high with adaptive gas softenings
Negligible effect on galaxy properties (SF is feedback-regulated).
Automatically satisfied in high-density, self-gravitating gas
Negligible effect on galaxy properties (SF is feedback-regulated).
Automatically satisfied in high-density, self-gravitating gas
Negligible effect on galaxy properties (SF is feedback-regulated).
If artificially lowered, more dense gas “piles up” until same SFR achieved

Recommended;
see Appendix C for implementation
Should exceed galactic mean density;
ideally, highest resolved densities
Not necessary
Not necessary⇠ 100% per free-fallin locally-self-gravitating gas

Stellar Feedback:
9&A
A&D
Paper II
A&E
Paper IIIPrimarily important as a late-time fuel source for SF
Relatively weak “primary” feedback effects on galactic scales
Type-II: Dominant FB mechanism on cosmological scales. Need to accountfor PdV work if Sedov phase un-resolved. Subgrid models should reproduce
exact solutions, conserve mass, energy, & momentum, and converge“Smooths” SF in dwarfs (less bursty) & suppresses SF in dense gas.
UV background dominates in dwarfs. Photo-electric heating unimportant.
IR multiple-scattering effects weak, except in massive galaxy nuclei.

Couple as Appendix D.
Rates given in § A
Couple as Appendix D.
Validation & convergence tests& criteria in Paper II
Need photo-heating & singlescattering rad. pressure (Paper III).
Rad.-hydro algorithm sub-dominant08

Low-mass “dwarf” galaxies represent the most signiﬁcant challenges to the cold dark matter (CDM) model of
今回, 解析したシュミレーション：先⾏研究から
cosmological structure formation. Because these faint galaxies are (best) observed within the Local Group (LG) of
the Milky Way (MW) and Andromeda (M31), understanding their formation in such an environment is critical. We
The Astrophysical Journal Letters, 827:L23 (6pp), 2016 August 20
doi:10.3847/2041-8205/827/2/L23
present ﬁrst results from the Latte Project: the Milky Way on Feedback in Realistic Environments (FIRE). This
simulation models the formation of an MW-mass galaxy to z  0 within ΛCDM cosmology, including dark
RECONCILING DWARF GALAXIES WITH ΛCDM COSMOLOGY: SIMULATING A REALISTIC POPULATION
OF SATELLITES AROUND A MILKY WAY–MASS GALAXY
matter, gas, and stars at unprecedented resolution: baryon particle mass of 7070 M: with gas kernel/softening that
Andrew R. Wetzel, Philip F. Hopkins , Ji-hoon Kim, Claude-André Faucher-Giguère ,adapts down to 1 pc (with a median of 25–60 pc at z  0 ). Latte was simulated using the GIZMO code with aDušan Kereš , and Eliot Quataert
TAPIR, California Institute of Technology, Pasadena, CA, USA
mesh-free method for accurate hydrodynamics and the FIRE-2 model for star formation and explicit feedback
Carnegie Observatories, Pasadena, CA, USA
Department of Physics, University of California, Davis, CA, USAwithin a multi-phase interstellar medium. For the ﬁrst time, Latte self-consistently resolves the spatial scales
Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics, Stanford University, Stanford, CA, USA
Department of Physics and Astronomy and CIERA, Northwestern University, Evanston, IL, USA
5M .
Department of Physics, Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, CA, USAM
210
correspondingtohalf-light
radii
of
dwarf
galaxiesthat
formaroundan
MW-mass
host
down
to
star
:
Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, CA, USA
Received 2016 February 18; revised 2016 July 17; accepted 2016 July 29; published 2016 August 12
Latte’s population of dwarf galaxies agrees with the LG across a broad range of properties: (1) distributions of
ABSTRACT
stellar masses and stellar velocity dispersions (dynamical masses), including their joint relation; (2) 5the mass–
Low-mass “dwarf” galaxies represent the most signiﬁcant challenges to the cold dark matter (CDM) model of
Figure 2. Left: proﬁles of circular velocity, vcirc (r )  Gm total (r ) r at z  0 . Points show observed satellites of the MW with Mstar  2 q 10  2 q 107 M:
cosmological structure formation. Because these faint galaxies are (best) observed within the Local Group (LG) of
metallicity
relation;and(3)diverserange
of star simulation
formation
histories,
including
their
mass
dependence.
Thus,(light
Latte
d

300
kpc
(Wolf
et
al.
2010).
Curvesshow
the19
subhalosinthedark-matter-onlyatwithdensities
as
low
as
Ursa
Minor.
Twosubhalosblue)
host
the Milky Way (MW) and Andromeda (M31), understanding their formation in such an environment is critical. We
5
are denser
than all observed
satellites.
Allowing oneofto hostthe SMCand noting
ﬁve 2
othersUrsanot
Minor,
Draco,from
Sculptor,
LeoI,and Leo II
Mstar
10 areMconsistentpresent ﬁrst results from the Latte Project: the Milky Way on Feedback in Realistic Environments (FIRE). Thisdoes
sufferthe“missing
producesa realistic
population
dwarf
galaxies
at that: that withsimulation models the formation of an MW-mass galaxy to z  0 within ΛCDM cosmology, including darkleads satellites”
to 13 that are too
to fail”
problem). Right:
proﬁles of stellar
3D velocity
dispersion for
the 13satellite galaxies
in the baryonicsimulation.
Allor dense“too(thebig“too
tobig
fail”
problemsof small-scale
structureformation.
We
concludethatbaryonic
physics
canmatter, gas, and stars at unprecedented resolution: baryon particle mass of 7070 M with gas kernel/softening that
proﬁles are nearly ﬂat with radius. One satellite has high dispersion, closer to the SMC’s 48 km s1; all others are broadly consistent with the MW.
adapts down to 1 pc (with a median of 25–60 pc at z  0 ). Latte was simulated using the GIZMO code with areconcile observed dwarf galaxies with standard ΛCDM cosmology.
mesh-free method for accurate hydrodynamics and the FIRE-2 model for star formation and explicit feedback
within a multi-phase interstellar medium. For the ﬁrst time, Latte self-consistently resolves the spatial scales
corresponding to half-light radii of dwarf galaxies that form around an MW-mass host down to M 2 10 M .
Key words: cosmology: theory – galaxies: dwarf – galaxies: formation – galaxies: star formation – Local Group –Latte’s population of dwarf galaxies agrees with the LG across a broad range of properties: (1) distributions ofstellar masses and stellar velocity dispersions (dynamical masses), including their joint relation; (2) the mass–
methods: numericalmetallicity relation; and (3) diverse range of star formation histories, including their mass dependence. Thus, Latte© 2016. The American Astronomical Society. All rights reserved.

1,2,3,8,9

1

6

1,4,10

5

7

1

2

3

4

5

6

7

:

star

5

:

produces a realistic population of dwarf galaxies at Mstar 2 10 5 M: that does not suffer from the “missing
satellites” or “too big to fail” problems of small-scale structure formation. We conclude that baryonic physics canreconcile observed dwarf galaxies with standard ΛCDM cosmology.
Key words: cosmology: theory – galaxies: dwarf – galaxies: formation – galaxies: star formation – Local Group –methods: numerical

1. INTRODUCTION

outﬂows that generate signiﬁcant dark-matter cores ingalaxies (e.g., Read & Gilmore 2005; Mashchenko et al.
galaxies (Mstar 1 109 M:) provide the smallest-scale
1. INTRODUCTION
outﬂows that generate signiﬁcant dark-matter cores Dwarf
in dwarf
Pontzen & Governato 2012; Di Cintio et al. 2014;
galaxies (e.g., Read & Gilmore 2005; Mashchenko et al. 2008;
Dwarf galaxies (M 1 10 M ) provide the smallest-scale
2014; Chan of cosmological structure formation and thus are
Pontzen & Governato 2012; Di Cintio et al.probes
probes of cosmological structure formation and thus are
et al. 2015). Almost all baryonic simulations have m
et al. 2015). Almost all baryonic simulations have modeled
compelling laboratories to test the cold dark matter (CDM)
compelling
laboratories
to
test
the
cold
dark
matter(CDM)
isolated dwarf galaxies, which are computationally tractable atframework. However, observed dwarf galaxies in the Local
isolated dwarf galaxies, which are computationally tract
the necessary resolution. However, faint dwarf galaxies areGroup (LG) of the Milky Way (MW) and Andromeda (M31)framework.
However,observeddwarf
galaxies
in
the
Local
(most robustly) observed near the MW/M31. Thus, modelingpresent signiﬁcant challenges to CDM. First, the “missing
the necessary resolution. However, faint dwarf galax
dwarf-galaxy formation within such a host-halo environment issatellites” problem: far fewer luminous satellites appear to be
Group
(LG)
of
the
Milky
Way
(MW)
and
Andromeda(M31)
critical, both to understand the role of this environment in theirobserved around the MW than dark-matter-only models predict(most robustly) observed near the MW/M31. Thus, moformation and to provide the proper environment to compare(Klypin et al. 1999; Moore et al. 1999). More concretely, thepresent
signiﬁcantchallenges
to
CDM.
First,
the“missing
statistical properties of the population against the LG.
“too big to fail” problem: dark-matter-only simulations predict
dwarf-galaxy formation within such a host-halo environm
Cosmological simulations of MW-mass galaxies havetoo many massive dense subhalos compared with satellites
satellites”
problem:far
fewer
luminous
satellites
appeartobeprogressed at increasing resolution and with more realistic
around the MW (Read et al. 2006; Boylan-Kolchin et al. 2011).
critical, both to understand the role of this environment istellar physics (e.g., Hopkins et al. 2014; Agertz & KravtRelatedly, the “core–cusp” problem: the inner density proﬁles
observedaroundtheMWthandark-matter-onlymodelspredict
sov 2015; Mollitor et al. 2015), and some simulations haveof dwarf galaxies appear to be cored, rather than cuspy as CDM
formation and to provide the proper environment to costarted to resolve the more massive satellite galaxies withinpredicts (e.g., Flores & Primack 1994; Moore 1994; Simon(Klypin
et
al.
1999;
Moore
et
al.
1999).
More
concretely,theMW-mass halos, with promising results (e.g., Brooks &et al. 2005; Oh et al. 2011).
statistical properties of the population against the LG.
Zolotov 2014; Sawala et al. 2016). However, such simulations
Many works have explored modiﬁcations to standard CDM,
“too
big
to
fail”
problem:dark-matter-only
simulations
predict
have not yet achieved sufﬁciently high spatial resolution
such as warm (e.g., Lovell et al. 2014) or self-interacting (e.g.,
Cosmological simulations of MW-mass galaxies(comparable to simulations of isolated dwarf too
galaxies)toRocha et al. 2013) dark matter. However, one must account formany
massivedense
subhaloscomparedwithsatellites
robustly resolve the half-light radii of such satellites, as smallbaryonic physics as well, and many theoretical studies haveprogressed at increasing resolution and with more r
as _200 pc.
shown that stellar feedback can drive strong gas inﬂows/
around
the
MW
(Read
et
al.
2006;
Boylan-Kolchinetal.
2011).
In this Letter, we introduce the Latte Project: the Milky Way
Figure 3. Cumulative number of satellites at z  0 above a given stellar mass (left) andstellar physics
3D velocity(e.g.,
dispersion(right) in et
the al.
Latte2014;
simulation(blue) andstellarHopkins
Agertz&on Feedback in Realistic Environments (FIRE). Our
goal is to
Moore Prize Fellow.
Relatedly,
the“core–cusp”
problem:theinnerdensity
proﬁles
observed around the Milky Way (MW; dashed) and Andromeda (M31; dotted), excluding the LMC, M33, and Sagittarius. For both Mstar and σ, Latte’s satellites lie
simulate a series of MW-mass galaxies to z  0 within ΛCDM
Carnegie Fellow in Theoretical Astrophysics.
2015; Mollitor et al. 2015), and some simulation
cosmology at sufﬁcient resolution to resolve boththe host
Einstein Fellow.
entirely
between the
MW andso Latterather
does notthan
suffercuspy
from theas“missing
or “too big to fail” problems. Thin curves (right) show Vcirc,max for all darkof dwarf
galaxies
appearto M31,be cored,
CDMsatellites”sov
starteddemonstrating
to resolvethemore massive
satellite
3q reduction
from baryonicphysics. galaxies
matter(e.g.,subhalosin the baryonic(light blue)and dark-matter-only(DMO;orange) simulations,the x
1predicts
Flores& Primack
1994;
Moore 1994;
Simon
MW-mass halos, with promising results (e.g., Broo
et al. 2005; Oh et al. 2011).
star

9

:

8
9

10

proﬁles. Figure 3 compares directly against observed disper-

09

Next, we further demonstrate that Latte’s dwarf galaxies

考慮していない現象

時間分解能

空間分解能

ガス塊を星に置き換える条件考慮した現象10結果(a)いくつかの銀河では, ⾮対称的なガス分布(必然的に⾮対称性のある星形成率分布) ⇨ CMZ全域にわたって離⼼率の⼤きい楕円軌道となり, ~10 Myrはつづく爆発的星形成

星形成率の⾯密度
Msun yr-1 kpc-2

ガスの⾯密度Msun pc-2

天の川のCMZと⽐べるとき,
R<145 pc を⾒てください。
( | l | ≲ 1∘ at d of ~8.2 kpc)

星形成率の⾯密度
Msun yr-1 kpc-2

ガスの⾯密度Msun pc-2

どちらのタイプの渦巻銀河でも⻑寿命のリング構
造は確認されず(b)それ以外び銀河では, 滑らかなガス分布(同, 星形成率分布)

緑は上のタイプの銀河,
茶⾊は下のタイプの銀河
古屋納得しきれていない点「滑らか」と⾔われても緑と茶⾊の銀河での差は, ⽬でみた範囲ではわからない(定量化してほしい).
古屋理解しきれていない点
中段パネルの点線は明らかに灰⾊帯(天の川CMZ)より上にある. これが渦巻銀河中⼼部の通常の姿という主張か？
⼀時的に低減することは, 緑の破線からわかる. しかし, 本⽂でいうstarburstはここではみられない.

11

結果

天の川のCMZと⽐べるとき,
R<145 pc を⾒てください。
( | l | ≲ 1∘ at d of ~8.2 kpc)

ガスの枯渇時間 = ガスの平均⾯密度を星形成率⾯密度を10 Myrsにわたって積分したもので除した.
Myrs
灰⾊帯は天の川CMZ

古屋理解しきれていない点
緑の破線の振る舞い(⼿書きメモ箇所). ガスが枯渇したあともSFR密度があがったままの銀河あるのは, なぜ？

12

結果

最後にKS則と合っていることを⽰したいらしい
⽔⾊とピンクの帯は, 天の川銀河CMZ
少なくとも解析した7つの銀河の値は, 帯の交差部分付近にくる(⇦それってすでにFigs.1&2で⽰したことじゃないの？. さらにその時間変化の軌跡は, KS則と⼤きな⽭盾はない.
議論に付⾔されていたこと
バーエンドでの星形成率↑は, 定常的で⼤きく時間変化しない.

素⼈のツッコミ, 解釈
KS則と⽐較するためには, ガス⾯密度⽅向のダイナミックレンジが⼩さすぎる.
KS則との整合性の⽂脈でみるよりかは, むしろ, 帯の交差部分よりもシミュレーション点がひろがっていることや(緑の線に⾒られるように)KS則からずれた軌跡を描く中⼼領域が多いことは, KS則成⽴はあくまでも, いわゆる円盤部だけでは？ ⇨ むしろ星形成のモードの議論へのヒントになるのでは？
SMBHフィードバック、特にsuperwindなどを考慮しないでも, ある程度, 説明できるのですね.
銀河シュミレーションの結果という意味では, 私の知る限りでは, 特段新しい知⾒(物理の提案)はなかった. この論⽂がApJ Lettersに受理された⼤きな理由は, cosmologicalなシュミレーションから出発して, z = 0の銀河の中⼼領域の振る舞いをそれなりにそれなりの分解能で(Δt~2Myrs, 数100 pc = JCMTで数Mpcの銀河を観測する分解能)再現できたことではないか？

13

Gemini Northで2008年に取得した⾯分光データのトモグラフィ plus PCA再解析導出された, 科学的な結果はそれほど画期的ではないかもしれないが, ⼿法がユニークで”変数分離”に成功 ⇨ PC n成分ごとに何らかの天体構造の抽出に成功(n=5まで析している.)

14