ダークマターの観測的制限
大栗真宗(東京大 RESCEU/物理/Kavli IPMU)

2018/8/6 素粒子物理学の進展2018@京大基研

内容• 冷たいダークマターの成功• いわゆる「小スケール問題」• ダークマターはブラックホールか？

• たくさんの状況証拠(銀河回転曲線、銀河団、宇宙の大規模構造、、、)• 観測から「冷たい」
ダークマター (CDM)が示唆• CDMは大規模(=線形)構造から仮定された理論、非線形領域でも正しいかは非自明

密度ゆらぎ線形パワースペクトル

ダークマター

ゆらぎの波数
Tegmark+2004

ダークマターハロー• ダークマターが自己重力により集まってビリアル平衡• 強非線形密度ゆらぎ(δρ/ρ ≫ 1)あ• 銀河、銀河団に対応• N体シミュレーション
によってその構造が詳細に予言される

http://www.mpa-garching.mpg.de/galform/millennium/

CDMが予言するハローの性質• cuspyな動径密度分布
いわゆるNFW分布
ρ(r) ∝ r−1(r+rs)−2 あ• 大きなな非球対称性
銀河団で軸比 ~1:2

• サブストラクチャ「ぶつぶつ」が沢山
http://www.mpa-garching.mpg.de/galform/millennium/

ダークマターの性質と密接な関係

ダークマター性質との関連の一例
2ject in the ΛCDM
In order to simula
we adopt the Mon(2000). We implem
ner. At each timebility for particle icollisionless• self-interacting dark matterあCDMの「小スケール問題」を解決するために導入(Spergel, Steinhardt 2000)• CDM粒子同士の弾性散乱はハローの密度分布を変更– 中心密度低下– より丸い形状
Yoshida+2000

Fig. 1.— Projected mass distributions in a box 15h−1 Mpc ona side. The collision cross-sections per unit mass, core radii, axis
ratios for each model and small panels showing the central region(2h−1 Mpc on a side, enlarged) in a diﬀerent color scale are given tocollisional

where ρi is the loca
the scattering crosis the relative velo
est neighbour, antion is similar to B
rather than the aneck & White (20the scattering rate
tain number of nei
involved in such aties in regions with1986), and so we p
be unbiased even if
small enough to e
nor fraction of its
each collision to b
have a cross-sectio
assumed isotropic
ative velocities are
We carry out sim
by factors of ten.
Most of our sim
high resolution re0.68 × 1010 h−1 M⊙
set to 20h−1 kpc, w
final cluster. We
mass resolution acheck for numerica
start from the sam
cosmology is flat
logical constant Ωkm−1 Mpc−1 . It hso that σ8 = 0.9.
M200 = 7.4 × 1014
the radius R200 =overdensity is 200

The large-scale mlooks very similar.
conditions, the pa
where collisions a
final cluster is mor
radius for larger cial ratios are detematter at densitie
Miralda-Escude (2ダークマター性質との関連の一例• fuzzy dark matter (scalar field DM, wave DM, …)あ
とても軽いボゾンがDMだとドブロイ波長が大きく(~kpc) 小スケール構造を抑制&コア的中心密度分布(e.g., Peebles 2000; Hu+2000; Schive+2014; Hui+2017)

ultra
light
boson

CDM

Schive+2014

Figure 1: Comparison of cosmological large-scale structures formed by standard CDM and by wavelike dark matter, ψ DM. Panel (a) shows the structure created by evolving a single coherent wave function

重力レンズ• 重力場による光の経
路のまがり、天体の形状のゆがみ• ダークマターを含めた全質量を直接測定できるので超便利!

MO, Bayliss, Dahle+ MNRAS 420(2012)3213

重力レンズ信号の大きさ≈動径密度分布

銀河団ダークマターの動径密度分布• 銀河団はダークマ
ターが卓越しているのでN体計算の結果との比較に有用• 多くの銀河団をstack
してS/Nをかせぐ
銀河団中心からの距離• 観測された動径分布はCDMで期待される
NFWと非常に一致

12

CLASH (Umetsu+2015)
Table 5. Summary of stacked tangential shear analysis

25 clusters

Sample

N

⟨z⟩

⟨θE ⟩
(arcsec)

16 clusters⟨Mvir ⟩
(1014 h−1 M

⟨cvir

⊙)

all

25

0.469

14.4+10.6−7.0

4.57+0.33−0.31

5.75+0
−0

θE -1
θE -2
θE -3

4
5
7

0.379
0.416
0.471

22.8+4.3−2.8
13.0+2.4−2.8
8.3+2.6−2.4

6.03+0.74−0.72
3.13+0.50−0.50
3.51+0.52−0.52

7.94+1−1
10.23+−
7.08+1−1

Mvir -1
Mvir -2
Mvir -3

5
10
10

0.480
0.472
0.460

17.1+12.9
−6.4
+10.2
14.7−5.7
12.6+9.3−7.8

9.55+1.17
−1.04
+0.61
5.62−0.55
1.97+0.32−0.29

4.90+0−0+05.37−010.59+−

linear dependence on the mass profile. In fact, the redu
shear is defined by g+ ≡ γ+ /(1 − κ), where γ+ and κ
tangential shear and convergence. Thus, the quantity
defin
5
12
Niikura et al.by equation (27) still depends slightly on the source redsh
via the factor 1/(1 − κ), particularly near the halo centFigure 3.Thus,
Upperpanel: Comparisonof modelsto the ensemble-averFigure 6. The stacked tangential shear profile obtained by comin comparison
with theNFW predictions,
we assu100
surface massdensityredshifthh⌃ii (black
obtainedfor theX-ray-selebining the 25 clusters. The average diﬀerential surface density
the sourceof zssquares)= 1.1, whichis thetypicaleﬀectsubsampleof16
clusters.
Models
with
PTE
>
0.05
are
shown
with
⟨∆Σ+ (r)⟩ (see equation 27) is plotted as a function of the phys-M
source redshift for our weak M
lensinganalysis(see Tablegas
500
lines, while those with PTE < 0.05 are shown with dashed lines (seeical radius r. Grey points indicate stacked tangential shear meathesolid
non-linear
dependence
makes
it somewhathalodiﬃc
ble 4). Also
The redcurve shows
the best-fit
two-parametermsurements from weak lensing that are not used for fitting. The
tointerprettheaverage
profile,
and
hence
our
stacked(NFW+LSS (i), Table 4), including the effects of surrounding LSS as at
upper left point with a horizontal error-bar is the constraint fromhalo termgential
assuming
the halobias functionnear
of Tinker
et al. (2010)
in theWM
profilemeasurement
the centre
shouldbe takthe average Einstein radius. The solid line with shading is theseven-year
cosmology.
The
lower
panel
shows
the
deviations(inuniwith caution.
best-fit NFW model with 1σ error range. The lower panel plots)ofthebest-fit profiles with respect to the observed hh⌃ii profile.
10 1 It is known that the matter fluctuations along the li
the stacked profile of the 45◦ rotated component, ⟨∆Σ× (r)⟩.
of-sight contributes to the total error budget (e.g., Hoeks
We quantify
and characterizeensemble-averagedm2003; Hoekstra
et al. 2011; theDodelson
2004; Gruen etbeen successful for constraining mean dark matter distri2011).of
While
have
eﬀect forusing
the analysis
distribution
our weX-ray-selectedsubsample
the hhgas ignored thisbutions of cluster samples (e.g., Mandelbaum et al. 2006b;
clusters
4, herewe take leiprofile individual(Section 5.1).
Topresented
interpret in
theSection
observed
averaged
0.15
Johnston et al. 2007; Leauthaud et al. 2010; Okabe et al.
account
error fromlarge scale structure
fitt
ing signal,
wetheconsiderthetheline-of-sightprojectedin surf
0.102010). Here we conduct stacking analysis of the tanthe stacked
tangential
shearcenter,
profile by including the fullmass density
aroundthe cluster
0.05
gential shear profile for our lensing sample for studyvariance between diﬀerent
Z radial bins (see Oguri & Taka
0.00
ing the mass-concentration relation from another view2011; Umetsu et al. 2011b, for the calculation of the cova
0.05
⌃(R)
= dlcomment⇢(r), that the error of (point. Note that the oﬀ-centreing eﬀect, which has beenance
matrix).
We,
however,
0.10
known to be one of the most significant systematic
large scale structure is subdominant in our analysis, beca
0.15
0101 = cdt
errors in stacked lensing analysis (e.g., Johnston et al.
with of⇢(r)⇢(r) small⇢m10 themassdensity
overdensity,dl
the =relatively
numberof backgroundgal

LoCuSS (Okabe+2013)

LoCuSS+scaling (Niikura+2015)
25 clusters

f NFW

50 clusters(using M )

f NFW

すばる
望遠鏡
貢献大!

SGAS (MO+2012)

x

銀河団の
動径密度
質量分布
はNFWと
よく一致

M. Oguri et al.

xpMO, Takada, Okabe, Smith MNRAS 405(2010)2215

非球対称性の観測的検証

重力レンズシア地図+再構築された密度分布

ベストフィット (楕円NFW)

MO, Takada, Okabe, Smith MNRAS 405(2010)2215

銀河団ハローの平均ゆがみ
CDM prediction(Jing, Suto 2002)

18個• 18個の銀河団の重力レンズ信号を解析• ⟨e⟩ = 0.46 ± 0.04

あ

非球対称性を7σ検出(初の直接検出)• CDMモデルの予言ととてもよく一致(e=1−軸比)(see also Evans, Bridle 2009; Oguri+2012;
Clampitt, Jain 2016; van Uitert+2017;
Shin+2018; Umetsu+2018)self-interacting dark matter?
2/g
衝突銀河団からの制限は概ね
σ/m
<
1−3
cm
•

(e.g., Markevitch+2004; Bradac+2008; Randall+2008; Merten+2011)
2/g
マイナー衝突も含めた統計解析
σ/m
<
0.5
cm
•

(Harvey+2015)•

2
銀河団ハローの形状からもおよそ σ/m < 1 cm /g(e.g., Peter+2013)• 銀河団Abell 3827のDM-銀河オフセット→ σ/m ~ 1.7×10−4 cm2/g (Massey+2015) (??)
[w/ restore force σ/m ~ 1.5 cm2/g (Kahlohoefer+2015)]

Abell 3827
Dark matter dynamics in Abell 3827

Ae1

Ag1
Ad1
Ab1

Ah3

Ao1

Aa1

N

Milky Way
star

Ah1

3’’

Af3
Ao3
Ac3
Aa3
Ab3
Ad3

Ac1

N3
N2

3

Ae3

Ag3

N6

Ao7
Ag2

N1
Aa4

Ac4 Ah4

Ae2

Af4
Ac5

Ao5

Ao4

Ao6
Ae4

N4
Ad2

Aa5 Ab5

Af2

Ao2

Ag4

Ah2

Ab2

Ad4

Milky Way
star

Aa2

Ac2

Figure 1. Hubble Space Telescope image of the core of Abell 3827 in F814W (red), F606W (green) and F336W (blue) bands. Light fromtwo foreground stars and five foreground galaxies (labelled in yellow) has been subtracted to reveal the background lens system. The
colour scale is linear. Multiply-imaged components of the background spiral galaxy, identified either in this image or in ALMA/MUSE
data are labelled in white. In our cosmological model, 300 = 5.5 kpc at the redshift of the cluster.

• 同じ著者の重力レンズ再解析によって、DM-銀河
expected from an extrapolation of near-IR emission (a somewhat indirect chain using [Oii] emission to estimate starformation rate and hence far-infrared luminosity, then using the Solomon & Vanden Bout 2005 relation to predict
CO luminosity). Our exposure time was therefore only justsufficient to detect spatial structure in the line emission; no
continuum emission is detected beneath the foregrounds.

Data were reduced using v1.0 of the esorex pipeline,
which extracts the spectra, applies wavelength and flat-fieldcalibration, then forms the data cube. Each hour on sky
included 3⇥ 20 minute exposures, dithered by ⇠1000 . Wealigned the individual exposures by registering the imagesof stars, then removed cosmic rays and pixel defects, andstacked the exposures using the exp combine routine. Flux
calibration was achieved using ESO standard stars whichwere reduced in an identical manner.

オフセットは消え有限断面積も必要なくなった(Massey+2018)

2.3

VLT/MUSE integral field spectroscopy

In June 2016, we obtained a 4 hour integration of Abell 3827
using the Multi-Unit Spectroscopic Explorer (MUSE) Integral Field Unit (IFU) spectrograph (Bacon et al. 2010) on

The background galaxy is visible in emission from the[Oii] 3726.8, 3729.2 line doublet, redshifted to 835.5 nm. In
each spatial pixel, we model the spectrum of foreground con-

銀河団ダークマター分布• 重力レンズを使って銀河団内のダークマター分布を直接、精密に測定できるようになってきた• (無衝突) CDMモデルで予言される動径密度分布、
非球対称性が観測と高い精度で一致• 大規模構造の観測から仮定したシンプルなダーク
マターモデルが強非線形領域でも正しいかどうか
は決して自明ではなく、この高精度の一致はある
意味驚くべきことである

より小スケールへ
密度ゆらぎ

P(k)

ゆらぎ非線形

∝k1

∝k-3

CDM
−1
(~8Mpc)

波数 k

より小スケールへ
密度ゆらぎ

ゆらぎ非線形

P(k)
∝k1

∝k-3

CDM
CMB 大規模構造銀河団

OK!

波数 k

より小スケールへ
密度ゆらぎ

ゆらぎ非線形

P(k)
∝k1

∝k-3

CDM
WDM?
CMB 大規模構造銀河団

OK!

波数 k

より小スケールへ
dn/dM

小質量

P(k)

M
ハロー質量関数

小スケール

密度ゆらぎ
パワースペクトルkより小スケールへ
dn/dM

小質量

1011M☉ 1013M☉ M
矮小銀河 銀河 銀河団

P(k)

小スケール

密度ゆらぎ
パワースペクトルkバリオン物理: 銀河 (星) 形成• ハローの中でガスが冷えて収縮し星を形成、重たい星は超新星爆発でガスをばらまく• エネルギーの散逸やフィードバックを伴うので分布がダークマターと大きく変わりうる• ダークマター分布もポテンシャルの変化を介して影響を受ける• なので重要

銀河 (星) 形成の効率
Behroozi+2018

M⋆/Mhalo星質量/ハロー質量

10−1

10−2

10−3

10−4 10
10

1011

1012

1013

1014

1015

halo mass Mhalo [M⊙] ハロー質量

銀河 (星) 形成の効率
Behroozi+2018

M⋆/Mhalo星質量/ハロー質量

10−1

矮小銀河

銀河

銀河団

10−2

10−3

10−4 10
10

1011

1012

1013

1014

1015

halo mass Mhalo [M⊙] ハロー質量

銀河 (星) 形成の効率
Behroozi+2018

矮小銀河

銀河

銀河団
冷却時間>宇宙年齢
AGNフィードバック

超新星フィードバック
10−2M⋆/Mhalo星質量/ハロー質量

10−1

10−3

10−4 1010星形成効率最大

1011

1012

1013

1014

1015

halo mass Mhalo [M⊙] ハロー質量

銀河 (星) 形成の効率
Behroozi+2018

矮小銀河

銀河

銀河団
冷却時間>宇宙年齢
AGNフィードバック

超新星フィードバック
10−2M⋆/Mhalo星質量/ハロー質量

10−1

10−3

星形成効率最大バリオン物理の影響が比較的小さい

10−4 10
10

1011

1012

1013

1014

1015

halo mass Mhalo [M⊙] ハロー質量

CDMの小スケール問題 (?)• missing satellites 問題
天の川銀河の周りの矮小銀河の数が観測ではCDMで期待されるより小さい• core/cusp 問題
矮小銀河のダークマター密度分布NFW的ではなく中心にコアを持つ• too big to fail 問題
天の川銀河の周りの重い矮小銀河が観測ではCDMで期待されるより中心密度が低いmissing satellites 問題

TTER SUBSTRUCTURE

Vol. 524

銀河の数 (cumulative)

Moore+1999
シミュレーション

観測

矮小銀河速度 (≈質量)Fig. 2.—Abundance of cosmic substructure within the Milky Way, the Virgo
Cluster, and our models of comparable masses. We plot the cumulative numbersof halos as a function of their circular velocity, vc = (Gmb /rb)1/2, where mb isthe bound mass within the bound radius rb of the substructure, normalized tothe circular velocity, Vglobal, of the parent halo that they inhabit. The dottedcurve shows the distribution of the satellites within the Milky Way’s halo
(Mateo 1998), and the open circles with Poisson errors are data for the Virgo
Cluster (Binggeli et al. 1985). We compare these data with our simulated
galactic mass halo (dashed curves) and cluster halo (solid curve). The second
dashed curve shows data for the galaxy at an earlier epoch, 4 billion years
ago—dynamical evolution has not significantly altered the properties of themissing satellites 問題

TTER SUBSTRUCTURE

Vol. 524

Moore+1999
シミュレーション

シミュレーション102

Nsats > M

銀河の数 (cumulative)

10

Kim+2017

3

101

観測

zre = 9.3
zre = 11.3
zre = 14.4100

矮小銀河速度(≈質量)Fig. 2.—Abundanceof cosmic substructure within
the Milky Way, the Virgo

103

104

105

observed
observed + area cor.
NFW
SIS
ELVIS, stripped
D17
DMO + gal
DMO + gal
+ GK17 stripping

観測
106
107
M (M )

108

109

星質量

Cluster,corrected
and our models ofcomparable masses.
We plot the cumulative
numbers
mpletenessluminosity
functions.
Uncertainties(e.g. from anisotropies) have not been plotted. Tof halos as a function of their circular velocity, v = (Gm /r ) , where m is(black) andonly
radialnormalized
correction;
black dashed) luminosity functions are also shown. L
the boundmass area-corrected
within the bound radius r(i.e.
of the no
substructure,tothe circularvelocity, Vthe
, ofluminosity
the parent halo thatthey inhabit. predicted
The dotted
aded bands
represent
functionsby di↵erent SMHM relations (see Appendix B for detai
curve shows the distribution of the satellites within the Milky Way’s halo
(Mateo1998), isandgenerated
the open circles witherrors areadata
for the Virgo
ge of eachband
by Poisson
assuming
reionization
redshift of zre = 9.3, while the upper edge assumes that
Cluster (Binggeli et al. 1985). We compare these data with our simulatedt a galaxy.
Note
that
thecurves)
Brook
et al.
(Ref.
[49]) relation predicts far fewer and the Behroozi et al. 2013 (Rgalactic
mass halo(dashedand cluster
halo 2014(solid curve).
The second
dashedshows thandata for thethe galaxy
at an earlier epoch,corrected
4 billion years counts. Right: Same as left, except the gray-shaded ba
n predicts
farcurve
morecompleteness• 新しい矮小銀河の発見 (SDSS, DES, HSC, …) および
1/2

c

b

b

b

b

global銀河-ハロー対応の理解の進展により問題ほぼ消失

ago—dynamical evolution has not significantly altered the properties of thecore/cusp 問題
Oh+2011 Oh et al.

14

ダークマター動径密度分布の冪• N体シミュレーション

core (R0)cusp (R−1)

els which are best fitted to the rotation curves of thgalaxies. From this, we find that the mean value of th
inner density slopes for the galaxies is α=−0.29 ± 0.0(and −0.27 ± 0.07 without Ho I which has a low incli
nation. See Section 3.4 for details). These rather fla
slopes are in very good agreement with the value o
α = −0.2 ± 0.2 found in the earlier work
−1 of de Blok et a
(2001; see also de Blok & Bosma 2002) for a larger num
ber of LSB galaxies. They are, however, in contrast wit
the steep slope of ∼−0.8 predicted by ΛCDM simulation(e.g., Stadel et al. 2009; Navarro et al. 2010) as well athose by the classical simulations (e.g., Navarro, Frenk &White 1996, 1997). This implies that the sample galaxie
show slightly increasing or even constant density profile
towards their centers.
We also examine how the mass model diﬀers when iis based on the hermite h3 rotation curve instead of thbulk one. For this, we use IC 2574 which shows stron
non-circular motions close to the center.
0 As shown in th“Mass density profile” panel of Fig. A.3, the mass den
sity profile derived using the hermite h3 rotation curv
is found to be slightly lower than that from the bulk rotation curve at the central regions. This is mainly duto the lower hermite h3 rotation velocity, resulting ismaller velocity gradients ∂V /∂R in Eq. 15 and thu
smaller densities. The measured inner density slope i
α=0.00 ± 0.19 which is similar, within the error, to tha

はNFW分布を予言(中心でρ(r) ∝ r )• 観測では矮小銀河のダークマター分布はコア的(中心でρ(r) ∝ r )半径

Fig. 8.— The inner slope of the dark matter density profile plotted against the radius of the innermost point. The inner density
slope α is measured by a least squares fit to the inner data point as
described in the small figure. The inner-slopes of the mass density
profiles of the 7 THINGS dwarf galaxies are overplotted with earlier
papers and they are consistent with previous measurements of LSB

バリオン物理の影響
halo (DM)

gas

star

ガスは光を放射することで収縮
でき最終的に星を形成

中心密度増加halo (DM)

gas

star

重たい星は超新星爆発を起こし銀河内のガスを吹き飛ばす

中心密度減少ダークマター分布の力学的反応
Mf

Mi→Mf

Mi
ri

rf

ri

DM粒子

• バリオン物理の影響により内側の質量が突然MiからMfに変化した時のDM粒子軌道の変化
1 2vi
2<latexit sha1_base64="52Nhhp+qHcFrlD5EEloTeFcFATU=">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</latexit>

GMf
1 2
= vf
ri
2

GM
v =
r
2

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GMf
rf<latexit sha1_base64="ZIou80K/5ongN//FJdIqAluekqo=">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</latexit>rf
Mf /Mi=ri
2Mf /Mi 1

ダークマター分布の力学的反応
Mf

Mi→Mf

Mi
ri

rf

ri

DM粒子

• バリオン物理の影響により内側の質量が突然MiからMfに変化した時のDM粒子軌道の変化
rf/ri<latexit sha1_base64="ZIou80K/5ongN//FJdIqAluekqo=">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</latexit>rf
Mf /Mi=ri
2Mf /Mi 1

DM膨張→コア

1

星形成
超新星
爆発

1

DM収縮
→カスプ

Mf/Mi

ダークマター動径密度分布の冪@0.015Rvir

シミュレーション: コア分布を再現
Bullock, Boylan-Kolchin 2017 (sims by Tollet+2016, Fitts+2016, …)

DM膨張→コア的星質量が小さいと影響小さい

DM収縮
→より
cuspy
log10(星質量/ハロー質量)

too big to fail 問題
Boylan-Kolchin+2012, modified
シミュレーション

回転速度

天の川銀河内の比較的重めの矮小銀河の内部構造の問題

半径• core/cusp問題と同様にバリオン物理によるDM

Figure 10

The Too-Big-to-Fail Problem. Left: Data points show the circular velocities of classical Milky
Way satellite galaxies with M? ' 105 7 M measured at their half-light radii r1/2 . The magentalines show the circular velocity curves of subhalos from one of the (dark matter only) Aquarius
simulations. These are specifically the subhalos of a Milky Way-size host that have peakmaximum circular velocities Vmax > 30 km s 1 at some point in their histories. Halos that are thismassive are likely resistant to strong star formation suppression by reionization and thus naively
too big to have failed to form stars (modified from Boylan-Kolchin, Bullock & Kaplinghat 2012).
The existence of a large population of such satellites with greater central masses than any of the
Milky Way’s dwarf spheroidals is the original Too-Big-to-Fail problem. Right: The same problem

密度分布変化+天の川銀河との潮汐相互作用で説明できる (e.g., Wetzel+2016)

CDMの小スケール問題 (?) の現状• 観測の進展、銀河形成物理の理解の進展により明確に問題だといえるものはないのが現状• 一方で、伝統的な無衝突CDM以外の可能性を理論的、観測的に追求することは理解を深める
上で依然としてとても重要• 特に、より小スケールまで詳しく調べることが大切より小スケールへ• ハロー質量で• 星を持たない「ダーク」ハローを検出できればCDM理論の強力な検証 (holy grail!)10−2星質量/ハロー質量 M⋆/Mhalo

109M☉以下まで
行けばバリオン
物理の影響はかなり小さい

Behroozi+2018

10−1

10−3

≲109Msun

10−4

バリオン物理影響ほぼなし

10−5
−6

10

←ultra faint dwarfs
108

109

1010

1011

1012

1013

halo mass Mhalo [M⊙]

1014

ハロー質量

1015

超低光度矮小銀河 (ultra faint dwarfs)

12

Errani et al.

cuspy

Cusp “ = 1Core “ = 0

コア

10

≠3

§

8

x ,0

密度 lg ÈÍ(< r)Í / M kpc

M ma

1

0.1

x/

0.0

M ma

9

/Mmax,0

0.1

1.0

Mmax

1.0

0.0

7

6

5
0.01

0.1

r / kpc

1

半径

0.01

0.1

r / kpc1

半径1

Sagittarius dSph
Fornax
Leo I
Sculptor
Leo II
Sextans (I)CarinaUrsa Minor
Draco
Canes Venatici (I)Crater 2
Leo T
HerculesBootes (I)
Leo IVUrsa Major (I)
Leo V
Canes Venatici II
Ursa Major II
Coma Berenices
Bootes II
Willman 1
Segue II
Segue (I)

Errani+2018• 個々の超低光度矮小銀河で密度分布を測るのはFigure 9. Mean densities r(< 1.8 Rh ) within 1.8 half-light radii Rh of Milky Way dSphs, estimated using the minimum-variance mass estimator (equation 17).
Grey curves show the mean density profiles of cuspy (g = 1, left panel) and cored (g = 0, right panel) haloes of the controlled cosmological simulations
introduced in section 3.2. These curves assume {a, b , g} = {1, 5, g} profiles with {rmax , vmax } as fitted to the simulated haloes. Note that the ultra-faint Milky
Way dwarfs are too dense to be compatible with any of the simulated cored DM haloes.

困難、ただ統計的にはNFW的な密度分布を支持しているようである (see also e.g., Hayashi, Chiba 2015)

球状星団 (globular cluster)
6M 程度の星の集団、ダーク10☉•

マターが付随していない (??)
(e.g., Moore 1996; Conroy+2011)• 力学的摩擦が効いてない (??)
(e.g, Tremaine 1976)• 原因はきちんと理解されてない、
例の小スケール問題より問題？
(fuzzy dark matterを支持？ Hui+2017;
Broadhurst, private communication)

wikipedia

「ダーク」ハローの検出に向けて
dn/dlogM ハロー質量関数
DM理

UFD 銀河、銀河団論に依存「ダーク」ハロー?
10−10?

107-8 109

M/M☉

• CDMでは星なし小質量ハローが大量に存在
CDMの究極の検証 & DM理論の強力なテスト

「ダーク」ハロー検出方法• 強い重力レンズ
小ハローにより重力レンズ像の位置や明るさが摂動を受ける• 潮汐ストリーム
銀河内で潮汐相互作用で破壊された星団などのストリームが小ハローにより摂動をうける• その他?
PTAによる小ハロー接近検出 (Kashiyama, MO 2018)

強い重力レンズ

global VLBI imaging of MG J0751+2716

3

VLBI: 分解能0.04mas (!)

ALMA: 分解能30mas~109M☉
Hezaveh+2016 (see also Inoue+2016)•

Spingola+2018現在108−9M☉、近い将来106M☉のハローまで検出

Figure 1. Global VLBI imaging of MG J0751+2716 at 1.65 GHz obtained by using uniform weights and multi-scale cleaning in wsclean. The o↵-source rms
is 41 µJy beam 1 and the peak surface brightness is 2.9 mJy beam 1 . The restored beam is 5.5 ⇥ 1.8 mas2 at a position angle 9.8 deg, and is shown within
the white box in the bottom left hand corner.

24 antennas from the European VLBI Network (EVN) and the VeryLong Baseline Array (VLBA), and included the large (> 50 m)
Lovell, E↵elsberg, Robledo and Green Bank telescopes. The scanson the target were about 3 min in duration, which were interleavedby scans of about 2 min on the phase-reference source J0746+273.
Several observations of the bright calibrator sources 4C39.25 andDA193 were taken throughout the run for fringe finding during correlation and for the bandpass calibration at the data reduction stage.
The data were recorded at 512 Mbits s 1 and correlated at the Joint

および数密度の制限ができる(IFs) with 8 MHz bandwidth and 32 channels each, through both
circular polarizations (RR, LL). A visibility averaging time of 2 s
was used. This time and channel resolution limited the e↵ective
field-of-view of the observations to about 16 and 10 arcsec, respectively, from the phase centre, which easily encompassed all of the
expected structure of the target.
The dataset was initially edited, calibrated and reduced using
the EVN pipeline and the Astronomical Image Processing Software

天の川銀河内の潮汐ストリーム
Discovery of the Pal 5 stream perturbations 17
1
N-body
Data

)
2 (

0
1
2

Erkal+2017

Perturbation by subhaloes
Leading

Trailing

3
4Linear Density(arcmin 1 )5⇠ 106 M8

⇠ 107.7 M

flyby

flyby

6
4
2
0
12

20

15

10

5

0
1 ( )

5

10

15

20

6M のハローを検出できる!
ギャップによって~10☉•

Figure 9. Comparison between the measured stream properties and the model of the Pal 5 stream in the MWPotential2014 potentialfrom Bovy (2015) perturbed by two subhalo fly-bys. As in Fig. 7, the stream track, debris density, stream width, radial velocity andGalactocentric radius are shown. Details of the panels are described in the caption of Fig. 7. The vertical dotted lines show the approximate
locations of the centers of the two gaps produced as a result of interaction with dark matter subhaloes. The gap in the leading arm (left)
is created by a 106 M subhalo while the gap in the trailing arm (right) is created by a 5 ⇥ 107 M subhalo. In an apparent contrast
to Fig. 7, there is a good match between the measured and modelled stream density. In addition, the trailing tail now has a roughly
constant width until 1 ⇠ 10 , providing a better match to the observations.

• 他の可能性 (バー回転, GMC, …) もあるので注意

stream (Bernard et al. 2014) and found a dramatic e↵ect

cused on the importance of orbital chaos, a topic which will

天の川銀河内の潮汐ストリーム
CDM

boson 10−22eV• DMが軽いボゾ
ンだと対応する特徴的なス
ケールでおおきなゆらぎ• ストリームを力学的に温めて太くする• 暫定的制限
Amorisco, Loeb 2018−22
m>1.5×10 eV

e 2. The density distributions of identical GC streams (rc = 4.4 kpc, j = 0.9) evolved for 3
TheWaydensityof decreasing
identical GC(rc =panels
4.4 kpc,= 0.9) evolved
for 3
n. Milkysized distributions
FDM haloes withaxionstreams
mass. Upper
showjprojectionsinダークマターは素粒子か？

• 何らかの素粒子を仮定した直接、間接検出
実験は今のところ成果なし• ひょっとしたら素粒子ではない?
• 他の可能性として (原始) ブラックホールも検討されている原始ブラックホール (PBH)

wikipedia• インフレーション中に作られた大きなゆらぎが重力崩壊しブラックホール生成 (モデルによる)2016年2月11日

Saul Loeb/Getty Images

nonlinear dynamics of highly disturbed black holes.
II. OBSERVATION

gravitational-wave transients [41] and was reported within
three Abbott
minutes ofetdata[43]. Subsequently,al., acquisition
PRL 116(2016)061102
matched-filter analyses that use relativistic models of compact binary waveforms [44] recovered GW150914 as themost significant event from each detector for the observations reported here. Occurring within the 10-ms intersite

重力波ついに発見!

On September 14, 2015 at 09:50:45 UTC, the LIGO
Hanford, WA, and Livingston, LA, observatories detectedweek ending
12 FEBRUARY 2016

REVIEW LETTERS

重力波GW150914
FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, rightUTC. Forvisualization,
all time series are filtered
~30M
の質量の
of column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45☉
a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject
ed, withfilters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain.
ect GW150914 arrived first at L1 and 6.9 ms later at H1; for a visual comparison,
ブラックホール合体
the H1 data are also shown, shifted in time by this

to-

þ0.5
−0.4

nal amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each

LIGOによる重力波発見
重力波で発見されたブラックホール• ~30M☉ BHが思っ

太陽質量

たよりたくさん存在• その起源は不明• もしかしてPBH?
(Bird+ 2016; あSasaki+ 2016)
https://www.ligo.caltech.edu

ダークマター=ブラックホール説が脚光をあびる

PBHの観測的制限• 重力マイクロレンズ (microlensing)
遠方天体の手前をPBHが通過した際の増光からPBHを検出• ホーキング放射
軽いPBHは蒸発し高エネルギー光子を放出• 宇宙背景放射PBH周りの高温ガスがCMBをゆがめる• その他、動力学的制限など

ダークマターに占めるPBHの割合

観測的制限 (存在量の上限) の現状
Accretion(X-ray)
OGLE

WD

WB

KeplerNS

重力レンズ
NSWD破壊Caustic

Femtolensing

HSC

wave+finite source effects?

Eri-II

ガス降着
銀河動力学

EROS
Accretion(Radio)UFDsMillilensing

Accretion(X-ray-II)

Accretion disk
(CMB)
Accretion disk
(CMB-II)

DF
Accretion(CMB)

Sasaki+2018

PBH質量• ほとんどのPBH質量で fPBH=1が棄却されている

gure 11: Upper limit on fPBH = ⌦PBH/⌦DM −12for various PBH mass (assuming monochro−13(windowaround
~10
−10
M
☉ ?)
atic mass function). Blue curves represent lensing constraints by EROS [116], OGLE [119],Kelly, …, MO+ Nat. Ast. 2(2018)334

最遠方の単独の星「イカロス」の発見• z=1.5の単独の星のマイクロレンズ増光Kelly, …, MO+ Nat. Ast. 2(2018)334

最遠方の単独の星「イカロス」の発見
増光

明るさ Flux

0.5

0.0

2012

2014

Year

2016

観測した年

• 速い増光と減光 → 半径~200R☉ の青色超巨星• 銀河団のダークマター+星の「二重レンズ」で最大~4000倍の増光を達成

MO, Diego, Kaiser+ PRD 97(2018)023518

イカロスによるPBHダークマターの制限
ダークマターに占めるPBHの割合

DM
=
PBHだと
•
重力波で発見されたブラックホール

PBHによる多重the robust interpretation
clue may be obtained b
散乱で増光抑制
curves before and after•
イカロス観測によって棄却

in order to obtain robu
~30M
PBHが全
matter☉fromobservation
ray-tracing simulations t
DMである可能compact dark matter, a
tracing simulations are h
性を棄却kind light curves such co• 広がった質量関VII. SUMMAR
数をもった場合
積分したfにhave
In this paper,
PBHwe

PBHの質量model that consists of a
適用可
(およそ)
convergenceand shear fi
ing properties of a poinZumalacarregui, Seljak, arXiv:1712.02240

Ia型超新星爆発の重力マイクロレンズ
るIa型超新星の光度分布ゆがみ

Eridanos II

0.9

SNe lensing(this work)

0.7• ~30M☉ PBHが全

0.6)
Planck (photo

0.5
0.4
0.3

EROS
LIGO BHs

0.2
0.1
0.0
10 4

10 3

10 2

10 1

100
101
MPBH [M ]102

DMである可能性を棄却

Planck (coll)(95% c.l.)0.8↵ ⌘ ⌦PBH /⌦M

全質量に占めるPBHの割合• PBH lensingによ103• 広がった質量関104

PBHの質量FIG. 1: Bounds on the abundance of PBHs as a function of
the mass (95 % confidence level). The analysis of SNe lensing
using the JLA (solid) and Union 2.1 compilations (dashed)

数をもった場合
積分したfPBHに

FIG. 2: E↵ects of the PBH
probability density function (objects and cosmological larg

適用可 (およそ)

今後のPBH制限• ~30M☉ PBH (重力波BH)
すばる望遠鏡HSCを用いたM31の長期モニター(PI: M. Takada) → fPBH<0.01 (95%CL) まで制限可−13−10−12M PBH (f~10
PBH=1可能?)•☉

アイデア募集中、、、

まとめ• CDMは今のところ成功しており、はっきり矛盾する観測はいまのところない• バリオン物理を正しく考慮することが重要• バリオン物理が (あまり) 効かない小質量ハローが現在のフロンティアのひとつ• ダークマターはなかなか尻尾を出さないが、観測的制限は今後数年でさらにおおきく進展する見込みなので乞うご期待