宇宙観測と素粒子物理大栗 真宗(東京大学 RESCEU/物理/カブリIPMU)

2020/9/30 高エネルギー研究者会議勉強会@zoom

宇宙観測による素粒子物理• 様々な空間スケールの密度ゆらぎから調べる
ダークマター

今日の話• 宇宙膨張と密度ゆらぎの時間進化で調べる
ダークエネルギー• 密度ゆらぎで調べるニュートリノ質量 日下氏講演 (?)• 原始ゆらぎで調べるインフレーション物理• 崩壊、対消滅等によるダークマター間接検出• 物理基礎法則、物理定数の普遍性の検証

宇宙論の最近の注目の話題• H0問題 (?)、σ8問題 (??)
ダークエネルギーと関係するかも (?)• いわゆる「小スケール問題」
ダークマターの性質と関係

宇宙膨張とハッブル定数
フリードマン方程式v~H0rr(宇宙のスケールファクターaの時間進化)·a 2 8πG2
H (z) =
=
ρ(z)
(a)
3
含ダークエネルギー

ハッブル定数 (現在の宇宙膨張速度)

H0 = H(z = 0)

線形密度ゆらぎ進化
重力

重力

密度場
ρ(x)
時間進化

線形密度ゆらぎの時間発展
2

d δ
dδ
+
2H(z)
−
4πG
ρ̄δ
=
0
dt 2
dt

ダークエネルギーの効果

ρ − ρ̄
δ≡
(
)
ρ̄
密度ゆらぎ

標準宇宙論の精密検証
CMBからの「外挿」(標準宇宙論を仮定した進化)

無矛盾?

「初期条件」
時間
距離NASA/WMAP science team

CMB観測
→ 宇宙の

宇宙の膨張、ゆらぎの直接観測

H0問題 (?)

Figures:Figure 1: The Current Tension in the Determination of Ho

距離はしご
SH0ES (2019)
H0=74.03±1.42

~5σ!
CMB

P18
H0=67.4±0.5
2020

Freedman 2017

H0問題は何を意味しているか?
• 標準宇宙論の破綻
CMBからのH0は標準宇宙論を仮定した間接的測定• 距離はしごのH0測定の系統誤差
複雑な測定のため系統誤差の見積りは難しい• CMBのH0測定の系統誤差
Planck衛星の測定は正しいか？

標準宇宙論の破綻?

Planck Collaboration: Cosmological pa

H(z)/(1 + z) [km s 1 Mpc 1 ]76
74

Riess et al. (2019)

CMB (planck衛星) H(z)
距離はしごH0

72
70
68
66
64

BOSS DR12

DR14 Ly-

62
60
58

DR14 quasars

56
54
0.0

0.5

1.0

1.5

z

2.0

2.5

(Planck 2018 VI)

標準宇宙論の破綻?

Planck Collaboration: Cosmological pa

late darkenergyIa型超新星観測と合わない

H(z)/(1 + z) [km s 1 Mpc 1 ]76(Benevento+2020)

74

Riess et al. (2019)

72
70
68
66
64

BOSS DR12

DR14 Ly-62

early darkenergy(reduce soundhorizon rs)
σ8問題を

60
58

より深刻に

DR14 quasars

56(Hill+2020)

54
0.0

0.5

1.0

1.5

z

2.0

2.5

(Planck 2018 VI)

パッとした理論モデルがあまり存在しない…

距離はしごの系統誤差?
– 49 –

Type Ia Supernovae → redshift(z)SH0ESチームの結果への「批判」

Cepheids → Type Ia Supernovae

Adam Riess(SH0ES PI)

38(with comments from the SH0ES team)
36

34

SN Ia: m-M (mag)33

Geometry → Cepheids

0.4
0.0

32

-0.4
34

36

38

40

SN Ia: m-M (mag)

31

30

0.4

M31

0.0

25

∆ mag

29

N4258

-0.4
LMC

20

29

30

31

32

33

Cepheid: m-M (mag)Milky Way
10

0.4

0.4
0.2

0.0

0.0
-0.2

-0.4

-0.4
10

G. Efstathiou
Kavli Institute for Cosmology Cambridge and Institute of Astronomy
Madingley Road
Cambridge CB3 OHA
UK
E-mail: gpe@ast.cam.ac.uk

Abstract. This is a transcript of a talk that I gave in Cambridge on 17th July 2020 on the‘Hubble tension’, i.e. the discrepancy between traditional distance ladder measurements of the
Hubble constant (which I will refer to as ‘late time measurements’) and the value inferred fromobservations of the cosmic microwave background (CMB) and large-scale structure (‘earlytime measurements’). I review the SH0ES1 analyses by Riess and collaborators and point out
some internal inconsistencies, including a discrepancy between the relative distances inferredfrom Cepheids of two of the primary geometric distance anchors, the Large Magellanic Cloud(LMC) and NGC 4258. I then ask ‘what would it take to make SH0ES compatible with earlytime measurements?’. The answer is a systematic bias of ⇠ 0.1 0.15 mag in the intercept oftheJournal,
Cepheidperiod-luminosity
relationsof SH0ES galaxies. Such a bias resolves
the Hubble
The Astrophysical882:34(29pp), 2019 September
1
https://doi.org/10.3847/1538-4357/ab2f73
tension,Society.
the tension between the distance anchors, and the diﬀerence between SH0ES and© 2019. The American Astronomical
the tip of the red giant branch (TRGB) distance ladder, as measured and calibrated by
Freedman and collaborators. I show that the diﬀerence between the TRGB and SH0ES values
The Carnegie-Chicago
HubbleProgram.
VIII. oﬀset.
An Independent
Determinationof theof H0 is caused mainly
by a systematic
calibration
In the short term,
observational*eﬀortsshould be
focussed onBased
improvingof thedistanceanchors
and nearby
HubbleConstant
onthe
thecalibrations
Tip of the
Red
Giant
Branchgalaxies, 1rather than trying tomeasure distancemoduli to more
supernovae hostgalaxies. I
2
1
3
Wendy L. Freedman, Barry
F. Madore, Dylan
Hatt1 to, Taylor
J. Hoyt, In Sung Jang
, Rachael
L. Beaton4 ,argue that an
independent
distanceestimate
NGC 4258
is particularly
critical.
With such
2567
Christopher
R. Burnsit should, Myung
Lee on ,aAndrew
J. Monson, Jillian R.toNeeley, M.
M. Phillips8 ,observations,beGyoonpossible,
relatively
short timescale,establish
definitively
Jeffrey A. Rich2 , and Mark Seibert2
1whetherthe &Hubbletensionreallyof exists.
Departmentof Astronomy
Astrophysics,
University
Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA; wfreedman@uchicago.edu
2

The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
3
Leibniz-Institut für Astrophysik Potsdam, D-14482 Potsdam, Germany
4
Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ08544, USA
5
Department of Physics & Astronomy, Seoul National University, Gwanak-gu, Seoul 151-742, Republic of Korea
6
Department of Astronomy & Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA
7
Department of Physics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA
8
Carnegie Institution of Washington, Las Campanas Observatory, Casilla 601, Chile
1
April 25;
revisedof2019
22; accepted 2019 July 3; published 2019 August 29
SNe, H0Received, for the2019
Equationof State
darkJuneenergy

15

15

20

25

Geometry: 5 log D [Mpc] + 25

∆ mag

Cepheid: m-M (mag)A Lockdown Perspective on the
Hubble Tension∆ mag
arXiv:2007.10716v2 [astro-ph.CO]
26 Jul 2020

Riess+2016µ (z,H0=73.2,q0,j0)

40

年周視差
→セファイド変光星→Ia型超新星
経験則…

Fig. 10.— Complete distance ladder. The simultaneous agreement of pairs of geometric and

Abstract

We present a new and independent determination of the local value of the Hubble constant based on a calibrationof the tip of the red giant branch (TRGB) applied to Type Ia supernovae (SNeIa). We ﬁnd a value of
H0=69.8±0.8 (±1.1% stat)±1.7 (±2.4% sys) km s−1 Mpc−1. The TRGB method is both precise and accurate
and is parallel to but independent of the Cepheid distance scale. Our value sits midway in the range deﬁned by thecurrent Hubble tension. It agrees at the 1.2σ level with that of the Planck Collaboration et al. estimate and at the1.7σ level with the Hubble Space Telescope (HST) SHoES measurement of H0 based on the Cepheid distance scale.
The TRGB distances have been measured using deep HST Advanced Camera for Surveys imaging of galaxy halos.
The zero-point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of
18.477±0.004 (stat)±0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary stars,
combined with an HST parallax calibration of a 3.6 μm Cepheid Leavitt law based on Spitzer observations. We
anchor the TRGB distances to galaxies that extend our measurement into the Hubble ﬂow using the recently
completed Carnegie Supernova Project I ( CSP-I ) sample containing about 100 well-observed SNeIa . There areseveral advantages of halo TRGB distance measurements relative to Cepheid variables; these include low halo
reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to独立したH0測定の重要性
H0LiCOW XIII: A 2.4% measurement of H01

H0LiCOW XIII. A 2.4% measurement of H0 from lensed
quasars: 5.3 tension between early and late-Universe
probesKenneth C. Wong,1,2? Sherry H. Suyu,3,4,5 Geo↵ C.-F. Chen,6 Cristian E. Rusu,2,7,6
Martin Millon,8 Dominique Sluse,9 Vivien Bonvin,8 Christopher D. Fassnacht,6Stefan Taubenberger,3 Matthew W. Auger,10 Simon Birrer,11 James H. H. Chan,8Frederic Courbin,8 Stefan Hilbert,12,13 Olga Tihhonova,8 Tommaso Treu,11 Adriano Agnello,14 Xuheng Ding,11 Inh Jee,3 Eiichiro Komatsu,3,1 Anowar J. Shajib,11Alessandro Sonnenfeld,15 Roger D. Blandford,16 Léon V. E. Koopmans,17 Philip J.
Marshall,16 and Georges Meylan8
1 Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
2 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
3 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
4 Physik-Department, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany
5 Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), 11F of ASMAB, No.1, Section 4, Roosevelt Road, Taipei 10617,

Taiwan6 Department of Physics, University of California, Davis, CA 95616, USA
7 Subaru Telescope, National Astronomical Observatory of Japan, 650 N Aohoku Pl, Hilo, HI 96720, USA
8 Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290
Versoix, Switzerland
9 STAR Institute, Quartier Agora - Allée du six Août, 19c B-4000 Liège, Belgium
10 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
11 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA
12 Exzellenzcluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany
13 Ludwig-Maximilians-Universität, Universitäts-Sternwarte, Scheinerstr. 1, D-81679 München, Germany
14 DARK, Niels-Bohr Institute, Lyngbyvej 2, 2100 Copenhagen, Denmark
15 Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, the Netherlands
16 Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94035, USA
17 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, NL-9700 AV Groningen, The Netherlands

SH0ESの結果とよく一致(but see also Birrer+2020; Denzel+2020; …)

Accepted XXX. Received YYY; in original form ZZZABSTRACT

We present a measurement of the Hubble constant (H0 ) and other cosmological parameters from ajoint analysis of six gravitationally lensed quasars with measured time delays. All lenses except thefirst are analyzed blindly with respect to the cosmological parameters. In a flat ⇤CDM cosmology,
1
we find H0 = 73.3+1.7
Mpc 1 , a 2.4% precision measurement, in agreement with local
1.8 km smeasurements of H0 from type Ia supernovae calibrated by the distance ladder, but in 3.1 tension
with Planck observations of the cosmic microwave background (CMB). This method is completely

Downloaded from https://academic.oup.com/mnras/article-abstract/doi/10.1093/mnras/stz3094/5849454 by University of Tokyo Library user on 0

• 重力レンズ時間の遅れ• メーザー• 重力波 (標準音源)•…

CMBのH0測定の系統誤差?

ACT+WMAP衛星の結果
Planck衛星の結果

are
pa
ma
na
sta
the
H0
ma
bu
var

T
Aiola+2020

to
ram
do
du
Planck衛星の結果は(結局)正しそう…

密度ゆらぎの規格化σ8P(k, z)[Mpc3]~(σ8)2

CMBで測定する原始ゆらぎ

z=0

時間進化

σ8 ∼ T(k = 1/8 Mpc, z = 0)Ak
伝達関数
(標準宇宙論を仮定し線形ボルツマン方程式を解く)

z~11001/(8 Mpc) k [Mpc−1]

M. Blanton/SDSS

S. Colombi/CFHT

銀河サーベイによるゆらぎ測定

重力レンズ(コズミックシア)

銀河クラスタリング

Stage-III 銀河サーベイ

KiDS (2012-2019) DES (2013-2019) HSC (2014-2021)
1500 deg2, rlim~25 5000 deg2, rlim~25 1400 deg2, rlim~26[すばる望遠鏡]σ8問題 (??)

Publications of the Astronomical Society of Jap
A&A proofs: manuscript no. KiDS_1000_3x2pt

Hikage,MO+2019
ferred cosmologicalparameters when using different two-point3.1. Comparison with weak lensing surveys

BOSS+KV450 (Tröster et al. 2020)
DES Y1 3 ⇥ 2pt (DES Collaboration 2018)
KiDS-1000 3 ⇥ 2pt
Planck 2018 TTTEEE+lowE

1.0

CMB

0.9
8

statistics which exhibit an excellent goodness-of-fit. As such, we
could be subject to an unlucky noise fluctuation that particularly
impacts the band power estimator in Eq. (1). Cautiously inspecting Fig. 1, as ‘ -by-eye’ is particularly dangerous with correlated
data points, we nevertheless note a handful of outlying points,
for example the low `-scales in the fifth tomographic bin. We
also note that Giblin et al. (2020) document a significant but lowlevel PSF residual systematic in the KiDS-1000 fourth and fifth
tomographic bins that was shown to reduce the overall goodnessof-fit in a cosmic shear analysis, but not bias the recovered cosmological parameters (see the discussion in Amara & Réfrégier
2008). Future work to remove these low-level residual distortions is therefore expected to further improve the goodness-offit.

Heymans+2020

1.1

0.8

~2-3σ

0.7

銀河サーベイ

重力レンズ

0.
35

0.
30

0.
25

0.
20

Our results are consistent with weak lensing constraints in theliterature. We limit our discussion in this section to published0.6
3⇥2pt analyses, referring the reader to Asgari et al. (2020b) who
discuss how the KiDS-1000 cosmic shear results compare withother weak lensing surveys. We note that direct comparisons of⌦mcosmological parameters should be approached with some caution, as the priors adopted by different surveys and analyses
are often informative (see section 6.1 in Joachimi et al. 2020). Fig. 8: Marginalised posterior distribution in the 8 -⌦mnalized posterior
contoursin the!mshear–σ 8 analyses,
plane (left)
and in plane,
the !comparing
plane(right),where S8and(α) ≡the0.45)3 ⇥ 2pt
analysesfrom KiDS-1000
m –S8 (α =Homogenisingpriors forcosmicfor example,
DES Y1 (Abbott et al. 2018) with the CMB constraints fromhasandbeen 95%
showncredible
to lead to different
whenForassessingel. Both 68%
levels conclusions
are shown.
comparison,
we plot cosmic shear results from KiDS-4
inter-survey consistency (Chang et al. 2019; Joudaki et al. 2020; Planck Collaboration et al. (2018). The KiDS-1000 3 ⇥ 2pt result canbe compared
our previous
analy- etors (Hildebrandt
2017) and with quadratic estimators (QE)
(Kalsoöhlinger
et al.to 2017)
and KV450-BOSSDES Y1 (Troxel
Asgari etetal.al.
2020c).
sis from Tröster et al. (2020).

重力レンズ+銀河クラスタリング

σ8問題は何を意味しているか?
• 単なる統計的ばらつき
銀河サーベイの進展ではっきりするはず• 重力レンズ解析の系統誤差
測光的赤方偏移、銀河形状測定、バリオン効果、…

• 標準宇宙論の破綻
ダークエネルギー?? 修正重力理論??
あと数年でもうちょっと状況がはっきり見えてくるはず撮像銀河サーベイの将来計画
stage-IIIstage-IV
LSST (チリ) 参加模索中
Euclid衛星

HSC

日本の参加決定 (PI: 大栗)

DES
KiDS
2020

2025

2030

H0問題とσ8問題: まとめ• CMBの初期宇宙からの測定と近傍宇宙を観測する後期宇宙からの測定との食い違い• 額面でH0の違いは~5σ、σ8の違いは~2-3σ• 本当なら標準宇宙論の修正が必要だがこれといった理論モデルは (今のところ) あまりない• 様々な観測、解析の相互比較による系統誤差の慎重な見積もりが重要

小スケール: 非線形密度ゆらぎ
密度場
ρ(x)

重力

重力

時間進化

非線形
δρ/ρ ≫ 1

時間進化ダークマターハロー• 密度ゆらぎが非線形成長
しビリアル平衡http://www.mpa-garching.mpg.de/galform/millennium/• ゆらぎスケール ➞ 質量
• 数値シミュレーションによる性質の詳細な予言
非線形δρ/ρ ≫ 1

数値シミュレーション

ダークマターハロー内の星形成
Behroozi+2018

星質量/ハロー質量
M!/Mhalo

10−1

10−2

10−3

10−4 10
10

1011

1012

1013

1014

1015

halo mass Mhalo [M!] ハロー質量

ダークマターハロー内の星形成
Behroozi+2018

星質量/ハロー質量
M!/Mhalo

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

ダークマターハロー内の星形成
Behroozi+2018

星質量/ハロー質量
M!/Mhalo

10−1

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
−2
10

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

ダークマターハロー内の星形成
Behroozi+2018

星質量/ハロー質量
M!/Mhalo

10−1

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−210星形成効率最大

10−3

−4

10

バリオン物理の影響が比較的小さい

1010

1011

1012

1013

1014

1015

halo mass Mhalo [M!] ハロー質量

ダークマターの小スケール問題
L20
DARK MATTER SUBSTRUCTURE
矮小銀河に関する様々な問題(e.g., Klypin+1999; Moore+1999)• core/cups問題(e.g., Flores, Primack 1994)• too-big-to-fail問題(e.g., Boylan-Kolchin+2011)

素粒子研究の動機としてもしばしば引用される

Moore+1999
銀河の数 (cumulative)• missing satellite問題

Vol. 524

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 dottedダークマター候補
Ultralight DM(e.g., axion-like particle)

10−18 eV10−9 eV

Light DM WIMP

(e.g., sterile ν)

1 eV

1 GeV

PBH

mass
1017 g• 非常に多岐にわたる• いくつかは「小スケール問題」を解決可能であり注目されている

小スケール問題の現状• 様々な面での進展がある− 矮小銀河観測の進展− 銀河形成理論の発展− 小スケール観測の他の手段の開発• これらの進展を簡単にレビューする

Missing satellite問題• 理論予言に比べて天の川銀河周りの観測された矮小銀河の数が少なすぎる問題• 問題が提唱された~2000年頃に比べて色々な進展がある− SDSS、Pan-STARRS、DES、HSCなどなどのサーベイ観測による新しい矮小銀河の発見− 観測された銀河の明るさとダークマター
質量の対応の理解の進展

最近の理論と観測の比較

Publications of the Astronomical Society of Japan (2019), Vol. 71

PHYSICAL REVIEW LETTERS 121, 211302 (2018)

理論と一致する数

Kim+2018

Homma+2019

incompleteness
補正の違い

矮小銀河数

観測

理論 (incompleteness考慮)

矮小銀河明るさ
矮小銀河数FIG. 2. The number of completeness corrected luminous satellites (left)oflinethe showslowest mass
subhalo hostinga
Fig.and
11. the
Theinfall
blackmasssolid
the cumulative
luminosity
distribu-

L > 340 L⊙ galaxy (right). Colors match those in Fig. 1; the dark red denotes results based on D17. The light colored bands denote thetion of all visible satellites obtained from the study of Newton et al.
uncertainty due to anisotropy (based on Ref. [15]). Left: The gray-shaded region shows the+40
predicted number of luminous satellites
line
accounts for the(2018), If
namely124−27 for MV ≤ 0. The
expected for the MW based on the calculation described below [Eqs. (7)–(9)].
the completeness-corrected
countblue
fallssolid
withinthese, of the HSC-SSP
correction
relatedthe ð1–2Þ
sky coverage,
HSClight
bounds, there is no MSP. Right: The width of the dark bands is set by theuncertainty
on theonly
MWtomass,
× 1012 M ⊙f!,
. The
surveyandmass
the redsolidandlinetheaccounts
all thebands denote uncertainties due to anisotropy. The bottom axis shows thesubhaloat infall,
top axisforshows
thecorrections
average associatedcorresponding subhalo mass today [90].
with the HSC-SSP survey. Dotted lines above and below each of the• 観測された矮小銀河むしろ多すぎ (?)

Material [31] for a detailed discussion of anisotropies). In
agreement with Refs. [8,16], we find that the correction isblack, blue, and red solid lines correspond to the 68% confidence range
Segue
I itselfwith
accountsfor ∼40%the solid
correction;
associatedthese estimates.
Theofgreen
line corresponds toaccounting for even fainter galaxies will increase the total

Core/cusp問題
ダークマター動径密度分布の冪14Oh+2011Oh et al.

core (R0)• 数値シミュレーション

els which are best fitted to the rotation curves of thegalaxies. From this, we find that the mean value of theinner density slopes for the galaxies is α=−0.29 ± 0.07
(and −0.27 ± 0.07 without Ho I which has a low inclination. See Section 3.4 for details). These rather flat
slopes are in very good agreement with the value of
α = −0.2 ± 0.2 found in the earlier work of de Blok et al.
(2001; see also de Blok & Bosma 2002)−1
for a larger number of LSB galaxies. They are, however, in contrast withthe steep slope of ∼−0.8 predicted by ΛCDM simulations(e.g., Stadel et al. 2009; Navarro et al. 2010) as well as
those by the classical simulations (e.g., Navarro, Frenk &White 1996, 1997). This implies that the sample galaxies
show slightly increasing or even constant density profiles
towards their centers.
We also examine how the mass model differs when it
is based on the hermite h3 rotation curve instead of the
0 shows strong
bulk one. For this, we use IC 2574 which
non-circular motions close to the center. As shown in the“Mass density profile” panel of Fig. A.3, the mass density profile derived using the hermite h3 rotation curve
is found to be slightly lower than that from the bulk rotation curve at the central regions. This is mainly due
to the lower hermite h3 rotation velocity, resulting insmaller velocity gradients ∂V /∂R in Eq. 15 and thus
smaller densities. The measured inner density slope is
α=0.00 ± 0.19 which is similar, within the error, to that
(α=0.13 ± 0.07) based on the bulk rotation curve. This
supports earlier studies that suggest that the effect of

はNFW分布を予言(中心でρ(r) ∝ r )cusp (R−1)• 観測の矮小銀河のダー

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
galaxies. The pseudo-isothermal model is preferred over the NFW

バリオン物理の影響
halo (DM)

gas

star

ガスは光を放射し収縮して星を形成

中心密度増加halo (DM)

gas

star

重い星の超新星
爆発で銀河内のガスが吹き飛ぶ中心密度減少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

Simulationでのコア分布の再現
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)

矮小銀河とダークマター• 現状では標準宇宙論モデル (無衝突冷たいダー
クマター) と明確に矛盾する観測結果はないと言ってよいより小スケールへ
ダークマター卓越

星形成影響大星なし
ダークマター 矮小銀河
ハロー？
107

109

1011

銀河

1013

ダークマター卓越

銀河団

1015
太陽質量

小質量ダークマターハロー• ハローの質量が 108-9太陽質量まで小さくなると内部で星がほとんどできなくなる• そのような星なしダークマターハローの観測
は標準宇宙論モデルの非線形領域での究極のテスト• ダークマターモデルにも非常に強い制限• 検出法はいくつかある

例: 強い重力レンズ• 強い重力レンズ系の摂動から小質量
ハローを検出可能~109M☉
Hezaveh+2016 (see also Inoue+2016)

現在の制限冷たいダークマターとconsistent (mDM>5.2keV)

8太陽質量まで標準宇~10•

宙論 (無衝突冷たいダーク
事後分布マター) と無矛盾最小ハロー質量 [太陽質量]
Gilman+2020

6太陽質量く
近い将来~10•
らいまでいけるだろう例: 天の川銀河の潮汐ストリーム
dynamical evidence of a dark halo substructure

Bonaca+2019

wikipedia• 球状星団が銀河の潮汐力で破壊

Figure 1. (Top) Likely members of the GD-1 stellar stream, cleanly selected using Gaia proper motions and PanSTA
photometry, reveal two significant gaps located at 1 ⇡ 20 and 1 ⇡ 40 , and dubbed G-20 and G-40, respectively. T
is a long, thin spur extending for ⇡ 10 from the G-40 gap. (Bottom) An idealized model of GD-1, whose progenitor disru
at 1 ⇡ 20 to produce the G-20 gap, and which has been perturbed by a compact, massive object to produce the G-40
The orbital structure of stars closest to the passing perturber is distorted into a loop of stars that after 0.5 Gyr appears
underdensity coinciding with the observed gap, and extends out of the stream similar to the observed spur.

された星のストリームの観測

To highlight the complex structure of the GD-1
stream, we present the distribution of likely stream
members at the top of Figure 1. As a first step in finding likely members, we followed Price-Whelan & Bonaca(2018) in selecting stars consistent with an old andmetal-poor population at a distance of 8 kpc, and moving retrograde with respect to the Galactic disk, withproper motions in the GD-1 reference frame (µ 1 , µ 2 ) ⇡( 7, 0) mas yr 1 . The spatial distribution of these stars
in the 2 direction (i.e. perpendicular to the stream) is

pmem > 0.5, with larger and darker points represenstars with a higher membership probability.
Most likely GD-1 members trace a thin stream, w
width varies between⇡ 100 and 300 . As note
Price-Whelan & Bonaca (2018), the stellar density athe stream is not uniform, and there are two sig
cant underdensities, or gaps, located at 1 ⇡ 40
20 , which we refer to as G-40 and G-20, res
1 ⇡tively. The main focus of this work are structures reto the G-40 gap, so if not specified, the gap refers t• 小質量ハローの重力的な摂動でストリームが非一様に

現在の制限12classical Milky Way satellites.

10

mWDM/keV

Banik+2019 (but see also Ibata+2020)

1C.

DM onlyincl. baryonic disruption

Including classical Milky Way satellites.

1.4

mWDM
> 4.6
keV (95%)
We haveso farperformed
a conservative
analysis of theconstraints on the mass function of dark matter subhalos
1.2> study
3.6 keV(95 %) perturbations in MilkyWDMthe
潮汐ストリームによる制限
arisingmfromof density
Way streams only. We explore now the consequences of103
also taking into account the measurement of the high1.0
mass end of the mass function using observations of classical Milky Way satellites. For this, we use the compila2
0.8
10tion of properties of the classical satellites (with stellar
mass M⇤ > 105 M ) within 300 kpc from Ref. [83] (these
are the LMC, SMC, Sagittarius, Fornax, Sculptor, Leo I
0.6
and II, Sextans, Ursa Minor, Carina, Draco, and Canes
101
Venatici I). We assign dark-halo masses for all of these
0.4
satellites using the stellar-mass vs. halo-mass relation
for satellites given in Ref. [84], obtained from abundance
100
matching,
GD-1 ⇥ Pal 5
0.2
Streams (Banik et al. 2019; this paper)
✓
◆
✓
GD-1◆
M
M
Classical MW satellitesh⇤
Pal 5 . (5)
log10
=
0.468
log
10
11 M
8M
6
7
8
9
10
11
12
10
3
⇥
10
10
10
10
10
10
10
10
0.0
0.00
0.25
0.50
0.75
1.00
1.25
1.50
Mh/M
We then compute themass function bylogclassical-satellite
10 (mWDM /keV)
counting the number of satellites in log10 Mh /M bins
ハロー質量 [太陽質量]of width 0.5 between
the lower limit in stellar mass of
ダークマター質量and 11.4; PDF
the uncertainty
on thesenumbersis PoisFIG. 10. Measuring the subhalo mass function using the comFIG. 8.9.4Posterior
for the thermal
WDM
particlemass,
bined statistics of Pal 5 and GD-1 streams. The black solid
son distributed. The dark-matter subhalos probed byobtained by comparing the power spectrum in the observed
line indicate the subhalo mass function in the fiducial CDM
our stream measurements live within ⇡ 20 kpc from theGD-1(blue)and Pal 5 (red) linear density, with that arising
only model. The gray shaded region shows mass function
Galactic center. To be able to combine these stream mea-

PDF

事後分布

dN/d log10 M

ハローの数

104

• 標準宇宙論 (無衝突冷たいダークマター) と無矛盾

他の超小質量ハロー検出法• パルサータイミングアレイによるハロー
接近検出 (e.g., Kashiyama, MO 2018; Dror+2019)• 近傍弱重力レンズ (e.g., Mondino+2020)• 重力波の弱重力レンズ効果の周波数依存性(e.g., MO, Takahashi 2020)•…

「小スケール問題」: まとめ• 標準宇宙論モデル (無衝突冷たいダークマター)の枠内で色々な観測は問題なく説明でき、明確な「問題」は今のところない• ダークマターモデルに強い制限• 理論 (バリオン効果) の理解の進展も一つの鍵• より小質量のダークマターハローの調査が重要なフロンティア、活発な研究が進行中