～先端物理学特論～地下実験とガンマ線で迫る暗 …okumura/files/200714DM.pdfderived from observations taken over 10 years of the inner 300 pc of the GC region

[email protected]

～先端物理学特論～

地下実験とガンマ線で迫る暗黒物質の謎奥村曉 1, 2

1宇宙地球環境研究所宇宙線研究部 2素粒子宇宙起源研究所現象解析研究部門

（宇宙線物理学研究室 / CR 研）

2020 年 7 月 14 日

mailto:[email protected]


質問する奴は偉い

2

https://twitter.com/motcho_tw/status/870589211832795136



質問について

皆さんは研究者の卵です（かもしれません） ‣ 何かを疑問に思うことは大切です

‣ 疑問のまま放置しないことも大切です

‣ 何か質問があれば、気軽に、積極的に質問してください ※ Zoom の「手を挙げる」機能かチャットで

あなたが分からないことは、周りの人も分かりません（教員の説明が悪いかも）

あなたが質問すると、他の全員の理解の助けになります

質問で講義を止めることは、迷惑行為ではありません

疑問→質問→答え　の習性がつくと物理や世界はもっと面白くなります ※ 世界の誰にも答えられない疑問があれば、物理学者になろう

この Zoom は 18 時まで開きっぱなしにするので、あとで質問してもらっても大丈夫です（昨年の対面講義では 30 分くらい雑談しました)

さらに質問があれば、[email protected] まで

本日の講義中に（質問のための質問ではない）質問をした学生は、レポートに加点します

3



宇宙素粒子物理学（Astroparticle Physics）

宇宙素粒子物理学とは？ ‣ 宇宙観測から素粒子を調べる

‣ 素粒子検出・素粒子的性質から宇宙を調べる

日本では「宇宙線物理学（cosmic-ray physics)」の研究分野がこれに重なる ‣ 宇宙線（陽子や電子)・ガンマ線・ニュートリノなど

‣ 宇宙線は観測対象でもあり、手段でもある

‣ 宇宙も素粒子も興味のある欲張りな学生向き（個人的経験）

‣ 名大物理では宇宙線物理学研究室（CR 研）4

宇宙線物理学研究室（CR 研）

5

奥村

三宅

伊藤

田島山岡松原山下風間佐藤

毛受

教員 10 名 + 院生 16 名 + 4 年生 6 名の大所帯

より詳しい情報

6

https://www.isee.nagoya-u.ac.jp/CR/



宇宙地球環境研究所 (ISEE) の紹介

Institute for Space‒Earth Environmental Research (ISEE) アイシー

名古屋大学の附置研究所のひとつ（2015 年に開所）

基礎研究部門のうち、宇宙線研究部は物理学教室の宇宙線物理学研究室（CR 研）として 4 年生と大学院生を受け入れ

CR 研では複数の宇宙線実験プロジェクトを行なっている ‣ CTA、Fermi 衛星、LHCf/RHICf、SK/HK、XMASS/XENONnT、太陽中性子望遠鏡、屋久杉 (14C)、などを幅広く (教員 10 名)

‣ https://www.isee.nagoya-u.ac.jp/CR/

宇宙や素粒子に興味のある人はぜひ遊びに来てください7

http://www.isee.nagoya-u.ac.jp/CR/

http://www.isee.nagoya-u.ac.jp/CR/

素粒子宇宙起源研究所（KMI）の紹介

Kobayashi‒Maskawa Institute for the Origin of Particles and the Universe (KMI)

名前の通り、ノーベル賞の後に 2010 年に発足

基礎理論研究部門（理論系）と現象解析研究部門（実験系）に 40 人超が所属（ISEE や物理学教室との兼任含む）

8

講義のスライド

https://www.isee.nagoya-u.ac.jp/~okumura/files/200714DM.pdf

9



可視光で観る人間

10

70 keV の X 線で観る人間（の顎）

波長や粒子が異なると、観える世界が変わってくる相互作用や衝突断面積・散乱弾面積の違い今日の話は、光（電磁波）では観えない暗黒物質について

11

衝突断面積の大雑把な説明

素粒子は大きさを持たないが互いに衝突するどれだけ衝突しやすいかは、相互作用の強さで決まる衝突断面積による学部 3 年あたりの量子力学で、断面積の計算の話が出てくるはずニュートリノなど、電磁相互作用しない粒子は通りぬけやすい 4 つの相互作用：重力・電磁力・弱い力・強い力

12

8

古典力学的な描像

幾何学的な衝突断面積 σ = π(r + r)2

e‒ e‒

半古典的・量子力学的な描像

衝突・散乱する確率分布で重み付けした

実効的な衝突断面積 σ = ∫ drP(r)2πr

遠いと、ほとんど通り抜ける

近いと、衝突・散乱しやすい

※ 粒子の波動性はこの絵に含まれていない

宇宙は何からできているか？

普通の物質 ‣ 直感的な宇宙の構成要素 ‣ 恒星や惑星（太陽、地球など）

‣ 星間ガス（水素、ヘリウムなど）

‣ 陽子や中性子などのバリオンと、電子などのレプトン

暗黒物質 ‣ 電磁放射をしない（= 暗黒） ‣ 様々な観測から存在は確実視 ‣ 正体不明だが、多くの理論により素粒子が提案されている

暗黒エネルギー ‣ 正体は全く不明 ‣ 宇宙を加速膨張させる

13

68.3%

26.8%

4.9%

Planck 衛星による宇宙背景放射の観測より (2013)

暗黒物質

普通の物質

暗黒エネルギー

素粒子標準模型と (普通) の物質 (バリオン)

14

Hhiggs

ggluon

ttop

ccharm

uup

γphoton

bbottom

sstrange

ddown

ZZ boson

τtau

µmuon

eelectron

WW boson

νeelectron neutrino

νµmuon neutrino

ντtau

neutrino

クオーク

レプトン

ゲージボソンスカラーボソン≃ 125.2 GeV/c2 0

0

0

0

1

≃ 173.0 GeV/c2

⅔ ½

≃ 1.27 GeV/c2

⅔ ½

≃ 2.2 MeV/c2

⅔ ½

≃ 4.7 MeV/c2

-⅓

½

≃ 96 MeV/c2

-⅓

½

≃ 4.18 GeV/c2

-⅓

½

0

0

1

≃ 0.511 MeV/c2

-1

½

≃ 105.66 MeV/c2

-1

½

≃ 1.7769 GeV/c2

-1

½

< 2.2 eV/c2 0 ½

< 0.17 MeV/c2 0 ½

< 18.2 MeV/c2 0 ½

≃ 91.19 GeV/c2 0

1

≃ 80.38 GeV/c2 ±1

1

質量

電荷

スピン

udu d

u d陽子中性子

du̅π－中間子

バリオン

γ

γ e+

e‒

電磁相互作用の例

電荷を持つ素粒子は電磁相互作用をすることができるファインマン図 (Feynman diagram) の見方によって、反応が変わる光子 (photon) が媒介粒子

15

<latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit> <latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit> <latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit> <latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit>

時間の向き

電子対生成 (pair production)



16

e+

e‒ <latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit><latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit><latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">AAADMnicnVLLjtMwFHXCawivDizZWFRIHSmq4tAHs0AawYblINGZkdqqchwntcaPyHZGqqJ8Cb/BD7CFL4AdQmLFR+C0gZlOWXHlyNfn+Nx7c32TgjNjo+ir59+4eev2nb27wb37Dx4+6uw/PjGq1IROiOJKnyXYUM4knVhmOT0rNMUi4fQ0OX/T8KcXVBum5Hu7Kuhc4FyyjBFsHbTY9wazhOZMVpnIMsZpXWV0JXONi2UdQHhJbqAeQlE4ig4c5UgHc5rZiqGQxfVfTLN8aSuFQnUFdHG1cClDmClNc61Kmb7qRf3ocIDCMOqPUNxs0Wg0PqibiBduxVtxq2Kp7G6E4XDYKFF82Gzx+IXTO7FC/6eM27JnVKaXPx78Oa6btOh0Xalrg7sOap0uaO140fk5SxUpBZWWcGzMFEWFnVdYW0ZcvGBWGlpgco5zOnWuxIKaebV+3ho+d0jalO4+aeEavaqosDBmJRJ3U2C7NNe5BvwXNy1t9nJeMVmUlkqySZSVHFoFm1mBKdOUWL5yDiaauVohWWKNiXUTtZWlGRpR1IFrDLrehl3nJO4j1/Z3g+7R67ZFe+ApeAZ6AIExOAJvwTGYAOJ98D55n70v/kf/m//d/7G56nut5gnYMv/Xb1Xq96s=</latexit><latexit sha1_base64="1X4BnhgtM5FYlE4mfYKtfzMzcUs=">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</latexit> γ

γ

時間の向き

電子対消滅 (pair annihilation)

e‒e‒



17

γγ <latexit sha1_base64="gYi5O9EjG4qjXIH0AsdRHz3c9Wk=">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</latexit><latexit sha1_base64="gYi5O9EjG4qjXIH0AsdRHz3c9Wk=">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</latexit><latexit sha1_base64="gYi5O9EjG4qjXIH0AsdRHz3c9Wk=">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</latexit><latexit sha1_base64="gYi5O9EjG4qjXIH0AsdRHz3c9Wk=">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</latexit>

時間の向き

コンプトン散乱 (Compton scattering)

e‒

弱い相互作用の例

18

中性子のβ崩壊 (beta decay)

W ν̅e

ud

u

du

d+ ⅔

‒ ⅓

‒ ⅓ ‒ ⅓

+ ⅔

+ ⅔

‒ 1

0n → p + e + ν̅e

<latexit sha1_base64="EQ83Wqi6wzmCkOGYJnBQeoc1rbs=">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</latexit>

弱い相互作用は粒子の種類を変えることができるニュートリノが地球をもすり抜けるのは、相互作用が弱いから W± や Z が媒介粒子相互作用が弱い = 崩壊に時間がかかる or 散乱断面積が小さい

e‒

弱い相互作用の例

弱い相互作用は粒子の種類を変えることができるニュートリノが地球をもすり抜けるのは、相互作用が弱いから W± や Z が媒介粒子相互作用が弱い = 崩壊に時間がかかる or 散乱断面積が小さい

19

電子ニュートリノの散乱(neutrino scattering)

W

νe

ud

u

du

d+ ⅔

‒ ⅓

‒ ⅓ ‒ ⅓

+ ⅔

+ ⅔

‒ 10

<latexit sha1_base64="53fe73Lr//Q2DdJ2KzZ5wqQHwOk=">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</latexit>

νe + n → p + e

課題 1

パイマイナス中間子（π－）が電子（e－）と反電子ニュートリノ（ν̅e）に崩壊するファインマン図を描いてみよ ※写真を送れない学生は、文章で図の概略を説明せよ

ヒント ‣ π－は p14 を見よ

‣ p19 の時間の進行方向を変えると π－はどこに現れるか考えよ

‣ 色々と進行方向を変えても良いことは、p15‒17 を参照せよ

注意 ‣ 実際には π－の崩壊のほとんどは µ－と ν̅µ になる

20

電磁相互作用で観る宇宙（可視光）

21

Mellinger 2008

銀河は星や星間ガス（陽子、中性子、電子）で構成され、　　電磁放射で輝いている（力学的エネルギーを徐々に失う）

電磁相互作用で観る宇宙（可視光）

21

Mellinger 2008

銀河は星や星間ガス（陽子、中性子、電子）で構成され、　　電磁放射で輝いている（力学的エネルギーを徐々に失う）

暗黒星雲 (dark nebula)

電磁相互作用で観る宇宙（電波）

22

Dame et al. 2001

一酸化炭素（CO）の電波輝線（λ = 2.6 mm）観測手段を変えることで、観えないものが観えてくる

電磁相互作用で観る宇宙（ガンマ線）

23

フェルミ衛星（30 MeV‒300 GeV)

我々の銀河（天の川銀河）

24NASA/PS-Caltech/R. Hurt (SSC-Caltech)

※ 想像図です。我々の銀河を上から　見下ろすことはできません。



太陽系

~2.5 万光年




~230 km/s

太陽系

~2.5 万光年


198O

ApJ.

. .23

8. .4

7IR

ROTATIONAL PROPERTIES OF Sc GALAXIES 477

measured velocity, Rf, is listed in column (13), and the ratio of the two, Rf/Rl,b, in column (14). Only for three galaxies is the coverage less than 707o: NGC 753 (55%), 709 (617o), and UGC 2885 (6770). Except for UGC 2885, the largest Sc we have identified, additional observations would add little to our conclusions.

Radial velocities for 13 of these galaxies are listed in RC2. The mean difference |ERC2 — Ehere| = 81 ± 25 km s-1. For NGC 1087, the published velocity differs by +321 from our value. Once again, we stress that large velocity errors permeate existing catalogs.

III. THE ROTATION CURVES

We assume that the emission arises from H n regions which are moving in planar circular orbits about the center of each galaxy. The observed line-of-sight velocities along the major axis can then be projected to velocities in the plane of each galaxy, with V(R) = (Vobs — V0)/sin i. For galaxies for which the major axis (j) is displaced from the position angle of the

spectrum, rç, the circular velocity is given by

i// m ( F°bs - Ko)[sec2 i - tan2 i cos2 (»7 - 0)]1/2 = ^^ — >

sin i cos (rj — 0) R = ¿[sec2 i - tan2 i cos2 (rj - 0)]1/2 ,

where s is the nuclear distance on the plane of the sky and R is the nuclear distance in the plane of the galaxy. Values for 0 and i are listed in columns (7) and (8) of Table 1. The adopted rotation curve is formed from both sides of the major axis. In general, velocities are reasonably symmetrical on both sides of the major axis; the principal exceptions are NGC 3672, 1421, 4321, and 7541. A simple way to determine the symmetry properties of the velocities is to trace a smooth curve through the points in Figure 4, then rotate the tracing paper 180° about the origin and compare the traced line with the plotted points. The adopted rotation curves are plotted in Figure 5, arranged by increasing linear radii, and the velocities are listed in Table 2.

DISTANCE FROM NUCLEUS (kpc) [h= 50 km s'1 Mpc‘]

Fig. 5.—Mean velocities in the plane of the galaxy, as a function of linear distance from the nucleus for 21 Sc galaxies, arranged according to increasing linear radius. Curve drawn is rotation curve formed from mean of velocities on both sides of the major axis. Vertical bar marks the location of Æ25> the isophote of 25 mag arcsec “2 ; those with upper and lower extensions mark Rl b, i.e., R2 5 corrected for inclination and galactic extinction. Dashed line from the nucleus indicates regions in which velocities are not available, due to small scale. Dashed lines at larger R indicates a velocity fall faster than Keplerian.

© American Astronomical Society • Provided by the NASA Astrophysics Data System

1989A&A...223...47B

暗黒物質存在の証拠 (1) 銀河の回転曲線

1980 年代までに、多くの銀河の回転曲線が電波望遠鏡などで観測された電磁波で観測される物質の分布からは説明ができないなんらかの暗黒 (電磁波で見えない) の質量が存在するか、重力相互作用に修正が必要

25

Rubin et al. (1980) Begeman (1989)

速さ一定

速さ一定

表面輝度は半径とともに指数関数的に下がる → 回転曲線は r‒1/2 に比例　（次ページで説明）

F =GM(r)m

r2=

mv2(r)

r<latexit sha1_base64="or35ZIssI8dI88DHkEVISVK7ocE=">AAACJ3icbZDLSgMxFIYz9VbrrerSTbAI1UWZKYJuhKKgboQK9gK9kUkzbWiSGZJMoQzzDr6GL+BW38Cd6NKNz2HaDmJbfwj8fOcczsnvBowqbdufVmppeWV1Lb2e2djc2t7J7u5VlR9KTCrYZ76su0gRRgWpaKoZqQeSIO4yUnMHV+N6bUikor540KOAtDjqCepRjLRBnezJNbyATU8iHN3c5eUxjyPZLsa/kA/bRYMNjTvZnF2wJ4KLxklMDiQqd7Lfza6PQ06Exgwp1XDsQLciJDXFjMSZZqhIgPAA9UjDWIE4Ua1o8qcYHhnShZ4vzRMaTujfiQhxpUbcNZ0c6b6ar43hf7VGqL3zVkRFEGoi8HSRFzKofTgOCHapJFizkTEIS2puhbiPTBbaxDizxSMjwYM4Y4Jx5mNYNNViwbELzv1prnSZRJQGB+AQ5IEDzkAJ3IIyqAAMHsEzeAGv1pP1Zr1bH9PWlJXM7IMZWV8/7JilSw==</latexit><latexit sha1_base64="or35ZIssI8dI88DHkEVISVK7ocE=">AAACJ3icbZDLSgMxFIYz9VbrrerSTbAI1UWZKYJuhKKgboQK9gK9kUkzbWiSGZJMoQzzDr6GL+BW38Cd6NKNz2HaDmJbfwj8fOcczsnvBowqbdufVmppeWV1Lb2e2djc2t7J7u5VlR9KTCrYZ76su0gRRgWpaKoZqQeSIO4yUnMHV+N6bUikor540KOAtDjqCepRjLRBnezJNbyATU8iHN3c5eUxjyPZLsa/kA/bRYMNjTvZnF2wJ4KLxklMDiQqd7Lfza6PQ06Exgwp1XDsQLciJDXFjMSZZqhIgPAA9UjDWIE4Ua1o8qcYHhnShZ4vzRMaTujfiQhxpUbcNZ0c6b6ar43hf7VGqL3zVkRFEGoi8HSRFzKofTgOCHapJFizkTEIS2puhbiPTBbaxDizxSMjwYM4Y4Jx5mNYNNViwbELzv1prnSZRJQGB+AQ5IEDzkAJ3IIyqAAMHsEzeAGv1pP1Zr1bH9PWlJXM7IMZWV8/7JilSw==</latexit><latexit sha1_base64="or35ZIssI8dI88DHkEVISVK7ocE=">AAACJ3icbZDLSgMxFIYz9VbrrerSTbAI1UWZKYJuhKKgboQK9gK9kUkzbWiSGZJMoQzzDr6GL+BW38Cd6NKNz2HaDmJbfwj8fOcczsnvBowqbdufVmppeWV1Lb2e2djc2t7J7u5VlR9KTCrYZ76su0gRRgWpaKoZqQeSIO4yUnMHV+N6bUikor540KOAtDjqCepRjLRBnezJNbyATU8iHN3c5eUxjyPZLsa/kA/bRYMNjTvZnF2wJ4KLxklMDiQqd7Lfza6PQ06Exgwp1XDsQLciJDXFjMSZZqhIgPAA9UjDWIE4Ua1o8qcYHhnShZ4vzRMaTujfiQhxpUbcNZ0c6b6ar43hf7VGqL3zVkRFEGoi8HSRFzKofTgOCHapJFizkTEIS2puhbiPTBbaxDizxSMjwYM4Y4Jx5mNYNNViwbELzv1prnSZRJQGB+AQ5IEDzkAJ3IIyqAAMHsEzeAGv1pP1Zr1bH9PWlJXM7IMZWV8/7JilSw==</latexit><latexit sha1_base64="or35ZIssI8dI88DHkEVISVK7ocE=">AAACJ3icbZDLSgMxFIYz9VbrrerSTbAI1UWZKYJuhKKgboQK9gK9kUkzbWiSGZJMoQzzDr6GL+BW38Cd6NKNz2HaDmJbfwj8fOcczsnvBowqbdufVmppeWV1Lb2e2djc2t7J7u5VlR9KTCrYZ76su0gRRgWpaKoZqQeSIO4yUnMHV+N6bUikor540KOAtDjqCepRjLRBnezJNbyATU8iHN3c5eUxjyPZLsa/kA/bRYMNjTvZnF2wJ4KLxklMDiQqd7Lfza6PQ06Exgwp1XDsQLciJDXFjMSZZqhIgPAA9UjDWIE4Ua1o8qcYHhnShZ4vzRMaTujfiQhxpUbcNZ0c6b6ar43hf7VGqL3zVkRFEGoi8HSRFzKofTgOCHapJFizkTEIS2puhbiPTBbaxDizxSMjwYM4Y4Jx5mNYNNViwbELzv1prnSZRJQGB+AQ5IEDzkAJ3IIyqAAMHsEzeAGv1pP1Zr1bH9PWlJXM7IMZWV8/7JilSw==</latexit>

暗黒物質存在の証拠 (1) 銀河の回転曲線

銀河内の半径 r における力の釣り合い

ある半径で質量分布が途絶えると

もし回転速度が一定であるなら

26

G<latexit sha1_base64="EZo++jhVGmeB9L1ekNM7l9Ghm4U=">AAAB/HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0oMcEzAOSJcxOepMhs7PLzKwQlvgDXvUPvIlX/8Uf8DucJHswiQUNRVU33V1BIrg2rvvtrK1vbG5tF3aKu3v7B4elo+OmjlPFsMFiEat2QDUKLrFhuBHYThTSKBDYCkZ3U7/1hErzWD6acYJ+RAeSh5xRY6X6fa9UdivuDGSVeDkpQ45ar/TT7ccsjVAaJqjWHc9NjJ9RZTgTOCl2U40JZSM6wI6lkkao/Wx26IScW6VPwljZkobM1L8TGY20HkeB7YyoGeplbyr+53VSE974GZdJalCy+aIwFcTEZPo16XOFzIixJZQpbm8lbEgVZcZms7AlxLGMkknRBuMtx7BKmpcVz6149aty9TaPqACncAYX4ME1VOEBatAABggv8ApvzrPz7nw4n/PWNSefOYEFOF+/ujqVSQ==</latexit><latexit sha1_base64="EZo++jhVGmeB9L1ekNM7l9Ghm4U=">AAAB/HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0oMcEzAOSJcxOepMhs7PLzKwQlvgDXvUPvIlX/8Uf8DucJHswiQUNRVU33V1BIrg2rvvtrK1vbG5tF3aKu3v7B4elo+OmjlPFsMFiEat2QDUKLrFhuBHYThTSKBDYCkZ3U7/1hErzWD6acYJ+RAeSh5xRY6X6fa9UdivuDGSVeDkpQ45ar/TT7ccsjVAaJqjWHc9NjJ9RZTgTOCl2U40JZSM6wI6lkkao/Wx26IScW6VPwljZkobM1L8TGY20HkeB7YyoGeplbyr+53VSE974GZdJalCy+aIwFcTEZPo16XOFzIixJZQpbm8lbEgVZcZms7AlxLGMkknRBuMtx7BKmpcVz6149aty9TaPqACncAYX4ME1VOEBatAABggv8ApvzrPz7nw4n/PWNSefOYEFOF+/ujqVSQ==</latexit><latexit sha1_base64="EZo++jhVGmeB9L1ekNM7l9Ghm4U=">AAAB/HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0oMcEzAOSJcxOepMhs7PLzKwQlvgDXvUPvIlX/8Uf8DucJHswiQUNRVU33V1BIrg2rvvtrK1vbG5tF3aKu3v7B4elo+OmjlPFsMFiEat2QDUKLrFhuBHYThTSKBDYCkZ3U7/1hErzWD6acYJ+RAeSh5xRY6X6fa9UdivuDGSVeDkpQ45ar/TT7ccsjVAaJqjWHc9NjJ9RZTgTOCl2U40JZSM6wI6lkkao/Wx26IScW6VPwljZkobM1L8TGY20HkeB7YyoGeplbyr+53VSE974GZdJalCy+aIwFcTEZPo16XOFzIixJZQpbm8lbEgVZcZms7AlxLGMkknRBuMtx7BKmpcVz6149aty9TaPqACncAYX4ME1VOEBatAABggv8ApvzrPz7nw4n/PWNSefOYEFOF+/ujqVSQ==</latexit><latexit sha1_base64="EZo++jhVGmeB9L1ekNM7l9Ghm4U=">AAAB/HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj0oMcEzAOSJcxOepMhs7PLzKwQlvgDXvUPvIlX/8Uf8DucJHswiQUNRVU33V1BIrg2rvvtrK1vbG5tF3aKu3v7B4elo+OmjlPFsMFiEat2QDUKLrFhuBHYThTSKBDYCkZ3U7/1hErzWD6acYJ+RAeSh5xRY6X6fa9UdivuDGSVeDkpQ45ar/TT7ccsjVAaJqjWHc9NjJ9RZTgTOCl2U40JZSM6wI6lkkao/Wx26IScW6VPwljZkobM1L8TGY20HkeB7YyoGeplbyr+53VSE974GZdJalCy+aIwFcTEZPo16XOFzIixJZQpbm8lbEgVZcZms7AlxLGMkknRBuMtx7BKmpcVz6149aty9TaPqACncAYX4ME1VOEBatAABggv8ApvzrPz7nw4n/PWNSefOYEFOF+/ujqVSQ==</latexit>

M(r)<latexit sha1_base64="xvzMhMABQISyi0Sy++fMupdAjCQ=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXgRIpgHJEuYnfQmQ2Zml5lZISw5+ANe9Q+8iVc/xR/wO5xN9mASCxqKqm66u4KYM21c99sprK1vbG4Vt0s7u3v7B+XDo5aOEkWhSSMeqU5ANHAmoWmY4dCJFRARcGgH49vMbz+B0iySj2YSgy/IULKQUWIy6b6qzvvliltzZ8CrxMtJBeVo9Ms/vUFEEwHSUE607npubPyUKMMoh2mpl2iICR2TIXQtlUSA9tPZrVN8ZpUBDiNlSxo8U/9OpERoPRGB7RTEjPSyl4n/ed3EhNd+ymScGJB0vihMODYRzh7HA6aAGj6xhFDF7K2Yjogi1Nh4FraEMJEinpZsMN5yDKukdVHz3Jr3cFmp3+QRFdEJOkVV5KErVEd3qIGaiKIRekGv6M15dt6dD+dz3lpw8pljtADn6xdrR5Yw</latexit><latexit sha1_base64="xvzMhMABQISyi0Sy++fMupdAjCQ=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXgRIpgHJEuYnfQmQ2Zml5lZISw5+ANe9Q+8iVc/xR/wO5xN9mASCxqKqm66u4KYM21c99sprK1vbG4Vt0s7u3v7B+XDo5aOEkWhSSMeqU5ANHAmoWmY4dCJFRARcGgH49vMbz+B0iySj2YSgy/IULKQUWIy6b6qzvvliltzZ8CrxMtJBeVo9Ms/vUFEEwHSUE607npubPyUKMMoh2mpl2iICR2TIXQtlUSA9tPZrVN8ZpUBDiNlSxo8U/9OpERoPRGB7RTEjPSyl4n/ed3EhNd+ymScGJB0vihMODYRzh7HA6aAGj6xhFDF7K2Yjogi1Nh4FraEMJEinpZsMN5yDKukdVHz3Jr3cFmp3+QRFdEJOkVV5KErVEd3qIGaiKIRekGv6M15dt6dD+dz3lpw8pljtADn6xdrR5Yw</latexit><latexit sha1_base64="xvzMhMABQISyi0Sy++fMupdAjCQ=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXgRIpgHJEuYnfQmQ2Zml5lZISw5+ANe9Q+8iVc/xR/wO5xN9mASCxqKqm66u4KYM21c99sprK1vbG4Vt0s7u3v7B+XDo5aOEkWhSSMeqU5ANHAmoWmY4dCJFRARcGgH49vMbz+B0iySj2YSgy/IULKQUWIy6b6qzvvliltzZ8CrxMtJBeVo9Ms/vUFEEwHSUE607npubPyUKMMoh2mpl2iICR2TIXQtlUSA9tPZrVN8ZpUBDiNlSxo8U/9OpERoPRGB7RTEjPSyl4n/ed3EhNd+ymScGJB0vihMODYRzh7HA6aAGj6xhFDF7K2Yjogi1Nh4FraEMJEinpZsMN5yDKukdVHz3Jr3cFmp3+QRFdEJOkVV5KErVEd3qIGaiKIRekGv6M15dt6dD+dz3lpw8pljtADn6xdrR5Yw</latexit><latexit sha1_base64="xvzMhMABQISyi0Sy++fMupdAjCQ=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXgRIpgHJEuYnfQmQ2Zml5lZISw5+ANe9Q+8iVc/xR/wO5xN9mASCxqKqm66u4KYM21c99sprK1vbG4Vt0s7u3v7B+XDo5aOEkWhSSMeqU5ANHAmoWmY4dCJFRARcGgH49vMbz+B0iySj2YSgy/IULKQUWIy6b6qzvvliltzZ8CrxMtJBeVo9Ms/vUFEEwHSUE607npubPyUKMMoh2mpl2iICR2TIXQtlUSA9tPZrVN8ZpUBDiNlSxo8U/9OpERoPRGB7RTEjPSyl4n/ed3EhNd+ymScGJB0vihMODYRzh7HA6aAGj6xhFDF7K2Yjogi1Nh4FraEMJEinpZsMN5yDKukdVHz3Jr3cFmp3+QRFdEJOkVV5KErVEd3qIGaiKIRekGv6M15dt6dD+dz3lpw8pljtADn6xdrR5Yw</latexit>

m<latexit sha1_base64="b89D9wJ8VPDrTxC5pIz+e9NeBYo=">AAAB/HicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48JmAckS5id9CZDZmaXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuurvChDNtPO/bKWxsbm3vFHdLe/sHh0fl45OWjlNFsUljHqtOSDRyJrFpmOHYSRQSEXJsh+P7md9+QqVZLB9NlmAgyFCyiFFirNQQ/XLFq3pzuOvEz0kFctT75Z/eIKapQGkoJ1p3fS8xwYQowyjHaamXakwIHZMhdi2VRKAOJvNDp+6FVQZuFCtb0rhz9e/EhAitMxHaTkHMSK96M/E/r5ua6DaYMJmkBiVdLIpS7prYnX3tDphCanhmCaGK2VtdOiKKUGOzWdoSYSZFMi3ZYPzVGNZJ66rqe1W/cV2p3eURFeEMzuESfLiBGjxAHZpAAeEFXuHNeXbenQ/nc9FacPKZU1iC8/UL9sqVbw==</latexit><latexit sha1_base64="b89D9wJ8VPDrTxC5pIz+e9NeBYo=">AAAB/HicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48JmAckS5id9CZDZmaXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuurvChDNtPO/bKWxsbm3vFHdLe/sHh0fl45OWjlNFsUljHqtOSDRyJrFpmOHYSRQSEXJsh+P7md9+QqVZLB9NlmAgyFCyiFFirNQQ/XLFq3pzuOvEz0kFctT75Z/eIKapQGkoJ1p3fS8xwYQowyjHaamXakwIHZMhdi2VRKAOJvNDp+6FVQZuFCtb0rhz9e/EhAitMxHaTkHMSK96M/E/r5ua6DaYMJmkBiVdLIpS7prYnX3tDphCanhmCaGK2VtdOiKKUGOzWdoSYSZFMi3ZYPzVGNZJ66rqe1W/cV2p3eURFeEMzuESfLiBGjxAHZpAAeEFXuHNeXbenQ/nc9FacPKZU1iC8/UL9sqVbw==</latexit><latexit sha1_base64="b89D9wJ8VPDrTxC5pIz+e9NeBYo=">AAAB/HicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48JmAckS5id9CZDZmaXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuurvChDNtPO/bKWxsbm3vFHdLe/sHh0fl45OWjlNFsUljHqtOSDRyJrFpmOHYSRQSEXJsh+P7md9+QqVZLB9NlmAgyFCyiFFirNQQ/XLFq3pzuOvEz0kFctT75Z/eIKapQGkoJ1p3fS8xwYQowyjHaamXakwIHZMhdi2VRKAOJvNDp+6FVQZuFCtb0rhz9e/EhAitMxHaTkHMSK96M/E/r5ua6DaYMJmkBiVdLIpS7prYnX3tDphCanhmCaGK2VtdOiKKUGOzWdoSYSZFMi3ZYPzVGNZJ66rqe1W/cV2p3eURFeEMzuESfLiBGjxAHZpAAeEFXuHNeXbenQ/nc9FacPKZU1iC8/UL9sqVbw==</latexit><latexit sha1_base64="b89D9wJ8VPDrTxC5pIz+e9NeBYo=">AAAB/HicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48JmAckS5id9CZDZmaXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuurvChDNtPO/bKWxsbm3vFHdLe/sHh0fl45OWjlNFsUljHqtOSDRyJrFpmOHYSRQSEXJsh+P7md9+QqVZLB9NlmAgyFCyiFFirNQQ/XLFq3pzuOvEz0kFctT75Z/eIKapQGkoJ1p3fS8xwYQowyjHaamXakwIHZMhdi2VRKAOJvNDp+6FVQZuFCtb0rhz9e/EhAitMxHaTkHMSK96M/E/r5ua6DaYMJmkBiVdLIpS7prYnX3tDphCanhmCaGK2VtdOiKKUGOzWdoSYSZFMi3ZYPzVGNZJ66rqe1W/cV2p3eURFeEMzuESfLiBGjxAHZpAAeEFXuHNeXbenQ/nc9FacPKZU1iC8/UL9sqVbw==</latexit>

r<latexit sha1_base64="iNZq56Seda+Hn0vWhpQL+JOzy3I=">AAAB/HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48JmAckS5id9CZDZmeXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuuruCRHBtXPfbKWxsbm3vFHdLe/sHh0fl45OWjlPFsMliEatOQDUKLrFpuBHYSRTSKBDYDsb3M7/9hErzWD6aLEE/okPJQ86osVJD9csVt+rOQdaJl5MK5Kj3yz+9QczSCKVhgmrd9dzE+BOqDGcCp6VeqjGhbEyH2LVU0gi1P5kfOiUXVhmQMFa2pCFz9e/EhEZaZ1FgOyNqRnrVm4n/ed3UhLf+hMskNSjZYlGYCmJiMvuaDLhCZkRmCWWK21sJG1FFmbHZLG0JMZNRMi3ZYLzVGNZJ66rquVWvcV2p3eURFeEMzuESPLiBGjxAHZrAAOEFXuHNeXbenQ/nc9FacPKZU1iC8/UL/sKVdA==</latexit><latexit sha1_base64="iNZq56Seda+Hn0vWhpQL+JOzy3I=">AAAB/HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48JmAckS5id9CZDZmeXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuuruCRHBtXPfbKWxsbm3vFHdLe/sHh0fl45OWjlPFsMliEatOQDUKLrFpuBHYSRTSKBDYDsb3M7/9hErzWD6aLEE/okPJQ86osVJD9csVt+rOQdaJl5MK5Kj3yz+9QczSCKVhgmrd9dzE+BOqDGcCp6VeqjGhbEyH2LVU0gi1P5kfOiUXVhmQMFa2pCFz9e/EhEZaZ1FgOyNqRnrVm4n/ed3UhLf+hMskNSjZYlGYCmJiMvuaDLhCZkRmCWWK21sJG1FFmbHZLG0JMZNRMi3ZYLzVGNZJ66rquVWvcV2p3eURFeEMzuESPLiBGjxAHZrAAOEFXuHNeXbenQ/nc9FacPKZU1iC8/UL/sKVdA==</latexit><latexit sha1_base64="iNZq56Seda+Hn0vWhpQL+JOzy3I=">AAAB/HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48JmAckS5id9CZDZmeXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuuruCRHBtXPfbKWxsbm3vFHdLe/sHh0fl45OWjlPFsMliEatOQDUKLrFpuBHYSRTSKBDYDsb3M7/9hErzWD6aLEE/okPJQ86osVJD9csVt+rOQdaJl5MK5Kj3yz+9QczSCKVhgmrd9dzE+BOqDGcCp6VeqjGhbEyH2LVU0gi1P5kfOiUXVhmQMFa2pCFz9e/EhEZaZ1FgOyNqRnrVm4n/ed3UhLf+hMskNSjZYlGYCmJiMvuaDLhCZkRmCWWK21sJG1FFmbHZLG0JMZNRMi3ZYLzVGNZJ66rquVWvcV2p3eURFeEMzuESPLiBGjxAHZrAAOEFXuHNeXbenQ/nc9FacPKZU1iC8/UL/sKVdA==</latexit><latexit sha1_base64="iNZq56Seda+Hn0vWhpQL+JOzy3I=">AAAB/HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48JmAckS5id9CZDZmeXmVlhCfEHvOofeBOv/os/4Hc4SfZgEgsaiqpuuruCRHBtXPfbKWxsbm3vFHdLe/sHh0fl45OWjlPFsMliEatOQDUKLrFpuBHYSRTSKBDYDsb3M7/9hErzWD6aLEE/okPJQ86osVJD9csVt+rOQdaJl5MK5Kj3yz+9QczSCKVhgmrd9dzE+BOqDGcCp6VeqjGhbEyH2LVU0gi1P5kfOiUXVhmQMFa2pCFz9e/EhEZaZ1FgOyNqRnrVm4n/ed3UhLf+hMskNSjZYlGYCmJiMvuaDLhCZkRmCWWK21sJG1FFmbHZLG0JMZNRMi3ZYLzVGNZJ66rquVWvcV2p3eURFeEMzuESPLiBGjxAHZrAAOEFXuHNeXbenQ/nc9FacPKZU1iC8/UL/sKVdA==</latexit>

v(r)<latexit sha1_base64="Io+LoYT29EX8MCZmB1BvwR+xVHo=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QLGF20psMmZldZmYDS8jBH/Cqf+BNvPop/oDf4WyyB5NY0FBUddPdFcScaeO6305hY3Nre6e4W9rbPzg8Kh+ftHSUKApNGvFIdQKigTMJTcMMh06sgIiAQzsY32d+ewJKs0g+mTQGX5ChZCGjxGTSpKou++WKW3PnwOvEy0kF5Wj0yz+9QUQTAdJQTrTuem5s/ClRhlEOs1Iv0RATOiZD6FoqiQDtT+e3zvCFVQY4jJQtafBc/TsxJULrVAS2UxAz0qteJv7ndRMT3vpTJuPEgKSLRWHCsYlw9jgeMAXU8NQSQhWzt2I6IopQY+NZ2hJCKkU8K9lgvNUY1knrqua5Ne/xulK/yyMqojN0jqrIQzeojh5QAzURRSP0gl7Rm/PsvDsfzueiteDkM6doCc7XL60allk=</latexit><latexit sha1_base64="Io+LoYT29EX8MCZmB1BvwR+xVHo=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QLGF20psMmZldZmYDS8jBH/Cqf+BNvPop/oDf4WyyB5NY0FBUddPdFcScaeO6305hY3Nre6e4W9rbPzg8Kh+ftHSUKApNGvFIdQKigTMJTcMMh06sgIiAQzsY32d+ewJKs0g+mTQGX5ChZCGjxGTSpKou++WKW3PnwOvEy0kF5Wj0yz+9QUQTAdJQTrTuem5s/ClRhlEOs1Iv0RATOiZD6FoqiQDtT+e3zvCFVQY4jJQtafBc/TsxJULrVAS2UxAz0qteJv7ndRMT3vpTJuPEgKSLRWHCsYlw9jgeMAXU8NQSQhWzt2I6IopQY+NZ2hJCKkU8K9lgvNUY1knrqua5Ne/xulK/yyMqojN0jqrIQzeojh5QAzURRSP0gl7Rm/PsvDsfzueiteDkM6doCc7XL60allk=</latexit><latexit sha1_base64="Io+LoYT29EX8MCZmB1BvwR+xVHo=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QLGF20psMmZldZmYDS8jBH/Cqf+BNvPop/oDf4WyyB5NY0FBUddPdFcScaeO6305hY3Nre6e4W9rbPzg8Kh+ftHSUKApNGvFIdQKigTMJTcMMh06sgIiAQzsY32d+ewJKs0g+mTQGX5ChZCGjxGTSpKou++WKW3PnwOvEy0kF5Wj0yz+9QUQTAdJQTrTuem5s/ClRhlEOs1Iv0RATOiZD6FoqiQDtT+e3zvCFVQY4jJQtafBc/TsxJULrVAS2UxAz0qteJv7ndRMT3vpTJuPEgKSLRWHCsYlw9jgeMAXU8NQSQhWzt2I6IopQY+NZ2hJCKkU8K9lgvNUY1knrqua5Ne/xulK/yyMqojN0jqrIQzeojh5QAzURRSP0gl7Rm/PsvDsfzueiteDkM6doCc7XL60allk=</latexit><latexit sha1_base64="Io+LoYT29EX8MCZmB1BvwR+xVHo=">AAAB/3icbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QLGF20psMmZldZmYDS8jBH/Cqf+BNvPop/oDf4WyyB5NY0FBUddPdFcScaeO6305hY3Nre6e4W9rbPzg8Kh+ftHSUKApNGvFIdQKigTMJTcMMh06sgIiAQzsY32d+ewJKs0g+mTQGX5ChZCGjxGTSpKou++WKW3PnwOvEy0kF5Wj0yz+9QUQTAdJQTrTuem5s/ClRhlEOs1Iv0RATOiZD6FoqiQDtT+e3zvCFVQY4jJQtafBc/TsxJULrVAS2UxAz0qteJv7ndRMT3vpTJuPEgKSLRWHCsYlw9jgeMAXU8NQSQhWzt2I6IopQY+NZ2hJCKkU8K9lgvNUY1knrqua5Ne/xulK/yyMqojN0jqrIQzeojh5QAzURRSP0gl7Rm/PsvDsfzueiteDkM6doCc7XL60allk=</latexit>

万有引力定数

銀河中心からの距離

半径 r までに含まれる質量

半径 r での回転速度

質点の質量

v(r) = const.<latexit sha1_base64="ezU9gkw6JF76k3fVcJ+fj1D2LSw=">AAACE3icbVDLSsNAFJ3UV62vqODGzWAR6iYkIuhGKLpxWcHWQhvKZDpph85MwsykEGI/wx9wq3/gTtz6Af6A3+GkzcK2HrhwOOde7uEEMaNKu+63VVpZXVvfKG9WtrZ3dvfs/YOWihKJSRNHLJLtACnCqCBNTTUj7VgSxANGHoPRbe4/jolUNBIPOo2Jz9FA0JBipI3Us4/GNXkGr2GXIz2UPMORUNqZ9Oyq67hTwGXiFaQKCjR69k+3H+GEE6ExQ0p1PDfWfoakppiRSaWbKBIjPEID0jFUIE6Un03zT+CpUfowjKQZoeFU/XuRIa5UygOzmcdUi14u/ud1Eh1e+RkVcaKJwLNHYcKgjmBeBuxTSbBmqSEIS2qyQjxEEmFtKpv7EpJU8HhSMcV4izUsk9a547mOd39Rrd8UFZXBMTgBNeCBS1AHd6ABmgCDJ/ACXsGb9Wy9Wx/W52y1ZBU3h2AO1tcvtEKd7Q==</latexit><latexit sha1_base64="ezU9gkw6JF76k3fVcJ+fj1D2LSw=">AAACE3icbVDLSsNAFJ3UV62vqODGzWAR6iYkIuhGKLpxWcHWQhvKZDpph85MwsykEGI/wx9wq3/gTtz6Af6A3+GkzcK2HrhwOOde7uEEMaNKu+63VVpZXVvfKG9WtrZ3dvfs/YOWihKJSRNHLJLtACnCqCBNTTUj7VgSxANGHoPRbe4/jolUNBIPOo2Jz9FA0JBipI3Us4/GNXkGr2GXIz2UPMORUNqZ9Oyq67hTwGXiFaQKCjR69k+3H+GEE6ExQ0p1PDfWfoakppiRSaWbKBIjPEID0jFUIE6Un03zT+CpUfowjKQZoeFU/XuRIa5UygOzmcdUi14u/ud1Eh1e+RkVcaKJwLNHYcKgjmBeBuxTSbBmqSEIS2qyQjxEEmFtKpv7EpJU8HhSMcV4izUsk9a547mOd39Rrd8UFZXBMTgBNeCBS1AHd6ABmgCDJ/ACXsGb9Wy9Wx/W52y1ZBU3h2AO1tcvtEKd7Q==</latexit><latexit sha1_base64="ezU9gkw6JF76k3fVcJ+fj1D2LSw=">AAACE3icbVDLSsNAFJ3UV62vqODGzWAR6iYkIuhGKLpxWcHWQhvKZDpph85MwsykEGI/wx9wq3/gTtz6Af6A3+GkzcK2HrhwOOde7uEEMaNKu+63VVpZXVvfKG9WtrZ3dvfs/YOWihKJSRNHLJLtACnCqCBNTTUj7VgSxANGHoPRbe4/jolUNBIPOo2Jz9FA0JBipI3Us4/GNXkGr2GXIz2UPMORUNqZ9Oyq67hTwGXiFaQKCjR69k+3H+GEE6ExQ0p1PDfWfoakppiRSaWbKBIjPEID0jFUIE6Un03zT+CpUfowjKQZoeFU/XuRIa5UygOzmcdUi14u/ud1Eh1e+RkVcaKJwLNHYcKgjmBeBuxTSbBmqSEIS2qyQjxEEmFtKpv7EpJU8HhSMcV4izUsk9a547mOd39Rrd8UFZXBMTgBNeCBS1AHd6ABmgCDJ/ACXsGb9Wy9Wx/W52y1ZBU3h2AO1tcvtEKd7Q==</latexit><latexit sha1_base64="ezU9gkw6JF76k3fVcJ+fj1D2LSw=">AAACE3icbVDLSsNAFJ3UV62vqODGzWAR6iYkIuhGKLpxWcHWQhvKZDpph85MwsykEGI/wx9wq3/gTtz6Af6A3+GkzcK2HrhwOOde7uEEMaNKu+63VVpZXVvfKG9WtrZ3dvfs/YOWihKJSRNHLJLtACnCqCBNTTUj7VgSxANGHoPRbe4/jolUNBIPOo2Jz9FA0JBipI3Us4/GNXkGr2GXIz2UPMORUNqZ9Oyq67hTwGXiFaQKCjR69k+3H+GEE6ExQ0p1PDfWfoakppiRSaWbKBIjPEID0jFUIE6Un03zT+CpUfowjKQZoeFU/XuRIa5UygOzmcdUi14u/ud1Eh1e+RkVcaKJwLNHYcKgjmBeBuxTSbBmqSEIS2qyQjxEEmFtKpv7EpJU8HhSMcV4izUsk9a547mOd39Rrd8UFZXBMTgBNeCBS1AHd6ABmgCDJ/ACXsGb9Wy9Wx/W52y1ZBU3h2AO1tcvtEKd7Q==</latexit>

M(r) / r<latexit sha1_base64="Tyt3lhMgJ7GFMyqGdVUuAkqq3eQ=">AAACCXicbVBLSgNBEO3xG+Mv6tJNYxDiJsyIoMugGzdCBPOBZAw9nZ6kSf/o7hGGISfwAm71Bu7ErafwAp7DTjILk/ig4PFeFVX1IsWosb7/7a2srq1vbBa2its7u3v7pYPDppGJxqSBJZO6HSFDGBWkYallpK00QTxipBWNbiZ+64loQ6V4sKkiIUcDQWOKkXXS411Fn8Gu0lJZCXWvVPar/hRwmQQ5KYMc9V7pp9uXOOFEWMyQMZ3AVzbMkLYUMzIudhNDFMIjNCAdRwXixITZ9OoxPHVKH8ZSuxIWTtW/ExnixqQ8cp0c2aFZ9Cbif14nsfFVmFGhEksEni2KEwbdi5MIYJ9qgi1LHUFYU3crxEOkEbYuqLktMUkFV+OiCyZYjGGZNM+rgV8N7i/Ktes8ogI4BiegAgJwCWrgFtRBA2CgwQt4BW/es/fufXifs9YVL585AnPwvn4B3EeaRg==</latexit><latexit sha1_base64="Tyt3lhMgJ7GFMyqGdVUuAkqq3eQ=">AAACCXicbVBLSgNBEO3xG+Mv6tJNYxDiJsyIoMugGzdCBPOBZAw9nZ6kSf/o7hGGISfwAm71Bu7ErafwAp7DTjILk/ig4PFeFVX1IsWosb7/7a2srq1vbBa2its7u3v7pYPDppGJxqSBJZO6HSFDGBWkYallpK00QTxipBWNbiZ+64loQ6V4sKkiIUcDQWOKkXXS411Fn8Gu0lJZCXWvVPar/hRwmQQ5KYMc9V7pp9uXOOFEWMyQMZ3AVzbMkLYUMzIudhNDFMIjNCAdRwXixITZ9OoxPHVKH8ZSuxIWTtW/ExnixqQ8cp0c2aFZ9Cbif14nsfFVmFGhEksEni2KEwbdi5MIYJ9qgi1LHUFYU3crxEOkEbYuqLktMUkFV+OiCyZYjGGZNM+rgV8N7i/Ktes8ogI4BiegAgJwCWrgFtRBA2CgwQt4BW/es/fufXifs9YVL585AnPwvn4B3EeaRg==</latexit><latexit sha1_base64="Tyt3lhMgJ7GFMyqGdVUuAkqq3eQ=">AAACCXicbVBLSgNBEO3xG+Mv6tJNYxDiJsyIoMugGzdCBPOBZAw9nZ6kSf/o7hGGISfwAm71Bu7ErafwAp7DTjILk/ig4PFeFVX1IsWosb7/7a2srq1vbBa2its7u3v7pYPDppGJxqSBJZO6HSFDGBWkYallpK00QTxipBWNbiZ+64loQ6V4sKkiIUcDQWOKkXXS411Fn8Gu0lJZCXWvVPar/hRwmQQ5KYMc9V7pp9uXOOFEWMyQMZ3AVzbMkLYUMzIudhNDFMIjNCAdRwXixITZ9OoxPHVKH8ZSuxIWTtW/ExnixqQ8cp0c2aFZ9Cbif14nsfFVmFGhEksEni2KEwbdi5MIYJ9qgi1LHUFYU3crxEOkEbYuqLktMUkFV+OiCyZYjGGZNM+rgV8N7i/Ktes8ogI4BiegAgJwCWrgFtRBA2CgwQt4BW/es/fufXifs9YVL585AnPwvn4B3EeaRg==</latexit><latexit sha1_base64="Tyt3lhMgJ7GFMyqGdVUuAkqq3eQ=">AAACCXicbVBLSgNBEO3xG+Mv6tJNYxDiJsyIoMugGzdCBPOBZAw9nZ6kSf/o7hGGISfwAm71Bu7ErafwAp7DTjILk/ig4PFeFVX1IsWosb7/7a2srq1vbBa2its7u3v7pYPDppGJxqSBJZO6HSFDGBWkYallpK00QTxipBWNbiZ+64loQ6V4sKkiIUcDQWOKkXXS411Fn8Gu0lJZCXWvVPar/hRwmQQ5KYMc9V7pp9uXOOFEWMyQMZ3AVzbMkLYUMzIudhNDFMIjNCAdRwXixITZ9OoxPHVKH8ZSuxIWTtW/ExnixqQ8cp0c2aFZ9Cbif14nsfFVmFGhEksEni2KEwbdi5MIYJ9qgi1LHUFYU3crxEOkEbYuqLktMUkFV+OiCyZYjGGZNM+rgV8N7i/Ktes8ogI4BiegAgJwCWrgFtRBA2CgwQt4BW/es/fufXifs9YVL585AnPwvn4B3EeaRg==</latexit>

v(r) =

rGMtotal

r/ r�1/2

<latexit sha1_base64="ieyt4rJwGWAIFaA4IehAoPaXBjg=">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</latexit><latexit sha1_base64="ieyt4rJwGWAIFaA4IehAoPaXBjg=">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</latexit><latexit sha1_base64="ieyt4rJwGWAIFaA4IehAoPaXBjg=">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</latexit><latexit sha1_base64="ieyt4rJwGWAIFaA4IehAoPaXBjg=">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</latexit>

この予期せぬ質量は何だ？

暗黒物質存在の証拠 (2) 重力レンズ効果

27

NASA & ESA

背景にある遠方の銀河

巨大質量の銀河団とそれに伴う数倍の質量を持った暗黒物質

ハッブル望遠鏡

大きな時空の歪みを生み出し「レンズ」として機能する

⇓

暗黒物質存在の証拠 (2) 銀河団による重力レンズ効果

28

NASA, ESA, M.J. Jee and H. Ford (Johns Hopkins University)

ハッブル望遠鏡による銀河団 Cl 0024+17 の観測

暗黒物質存在の証拠 (2) 銀河団による重力レンズ効果

28


ハッブル望遠鏡による銀河団 Cl 0024+17 の観測

暗黒物質存在の証拠 (2) 重力レンズ効果

29


計算で推定された暗黒物質の質量分布

暗黒物質存在の証拠 (3) 銀河団同士の衝突

30

Optical: NASA/STScI, Magellan/U.Arizona/D.Clowe et al.

http://chandra.harvard.edu/photo/2006/1e0657/more.html

可視光で観た銀河団


30

Optical: NASA/STScI, Magellan/U.Arizona/D.Clowe et al.

http://chandra.harvard.edu/photo/2006/1e0657/more.html

銀河団

銀河団

可視光で観た銀河団


31

Lensing: NASA/STScI, ESO WFI, Magellan/U.Arizona/D.Clowe et al

重力レンズによる質量分布


32

X-ray: NASA/CXC/CfA/M.Markevitch et al.

X 線で観た高温プラズマ (電離した H や He = 物質)

衝突


33

暗黒物質 (銀河団質量の主成分) は衝突することなく、すり抜ける

暗黒物質

暗黒物質

物質

課題 2

銀河団の衝突において、その中に含まれる通常の物質同士は非弾性的に衝突し高温プラズマを生成するが、暗黒物質はすり抜けてしまうことを、相互作用の違いや断面積の違いを踏まえ、定性的に説明せよ

ヒント ‣ p37 の説明を用いて良い

‣ 物質が特定方向に進む運動エネルギーを、ランダムな方向に分布する熱エネルギーに変えるとはどのようなことか考えよ

34

暗黒物質存在の証拠 (4) 宇宙の構造

35

宇宙背景放射 (~2.7 K) の揺らぎ

10-5 ～10-3 程度の揺らぎしかなかった

Planck Collaboration (2015)

暗黒物質存在の証拠 (4) 宇宙の構造

ビッグバン直後のわずかな質量密度分布 (バリオン密度分布) の揺らぎが、大きな揺らぎへと進化暗黒物質の存在がこの進化を説明する暗黒物質の密度揺らぎにより質量が集まり始め、そこにバリオンがさらに集められる背景放射の観測結果などから、宇宙論パラメータが決定される ‣ バリオン密度 ‣ 質量密度 (= バリオン + 暗黒物質)

‣ 真空のエネルギー密度36

https://www.sdss.org/science/

銀河の分布の大規模サーベイ

重力相互作用をする = 質量を持つ

電磁相互作用をしない (銀河団の衝突)

宇宙の構造形成の観点から ‣ ニュートリノではない

‣ 重く暗い天体 (Massive Compact Halo Objects、MACHO) ではない (重力マイクロレンズ観測からも否定)

‣ 相対論的速度 (= 力学的に熱い) 粒子ではない → 冷たい暗黒物質 (cold dark matter、CDM) が支持されている

標準模型を超える新素粒子候補？ ‣ アクシオン (Axion)

‣ 弱い相互作用をする重粒子 (Weakly Interacting Massive Particle、WIMP)

暗黒物質の正体は何か？

37

「弱虫」という意味

arX

iv:h

ep-p

h/05

1100

3v1

31

Oct

200

5

E–WIMPs1

Ki-Young Choi! and Leszek Roszkowski!

!Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK

Abstract. Extremely weakly interacting massive particles (E–WIMPs) are intriguing candidates for cold dark matter inthe Universe. We review two well motivated E–WIMPs, an axino and a gravitino, and point out their cosmological andphenomenological similarities and differences, the latter of which may allow one to distinguishing them in LHC searches forsupersymmetry.

INTRODUCTION

From the particle physics point of view, a WIMP (weaklyinteracting massive particle) looks rather attractive asa candidate for cold dark matter (CDM) in the Uni-verse. In many extensions of the Standard Model (SM)there often exist several new WIMPs, and it is often nottoo difficult to ensure that the lightest of them is sta-ble by means of some discrete symmetry or topologi-cal invariant. (For example, in supersymmetry, one usu-ally invokes R–parity.) In order to meet stringent astro-physical constraints on exotic relics (e.g., anomalous nu-clei), WIMPs must be electrically and (preferably) colorneutral. They can however interact weakly. For WIMPsproduced via a usual freeze–out from an expandingplasma one finds Ωh2 " 1/

!"σann

10#38 cm2

#"v/c0.1

#$. As-

suming a pair–annihilation cross section σann $ σweak $10#38 cm2, and since the relative velocity v at freeze–outis non–relativistic, one often obtainsΩh2 $ 0.1, in agree-ment with current determinations. This has sometimesbeen used as a hint for a deeper connection between weakinteractions and CDM in the Universe.

Contrary to this simple and persuasive argument,CDM particles are not bound to interact with roughly theweak interaction strength. Extremely weakly interactingmassive particles (E–WIMPs) have also been known tobe excellent candidates for CDM. In comparison with“standard” WIMPs, E–WIMP interaction strength withordinary matter is strongly suppressed by some largemass scale, for example the (reduced) Planck scale MP "2.4% 1018 GeV for gravitino or the Peccei–Quinn scalefa $ 1011 GeV for axion and/or axino.

1 Invited plenary talk given by L. Roszkowski at PASCOS–05,Gyeongju, Korea, 30 May – 4 June 2005.

FIGURE 1. A schematic representation of some well–motivated WIMP–type particles for which a priori one can haveΩ $ 1. σint represents a typical order of magnitude of interac-tion strength with ordinary matter. The neutrino provides hotDM which is disfavored. The box marked “WIMP’ stands forseveral possible candidates, e.g., from Kaluza–Klein scenarios.

E–WIMPs are also well motivated from a particle the-orist’s perspective if one takes the point of view thatCDM candidates should appear naturally in some rea-sonable frameworks beyond the SM which have beeninvented to address some other major puzzle in particlephysics. In other words, it would be preferable if a CDMcandidate were not invented for the sole purpose of solv-ing the DM problem.

One way to present well–motivated CDM candidates

AA48CH13-Feng ARI 16 July 2010 22:3

Y

T (GeV)

!X

t (ns)

10–4mX = 100 GeV

10–6

10–8

10–10

10–12

10–14

10–16

100 101 102 103

108

106

104

102

100

10–2

10–4

101 100

Figure 2The comoving number density Y (left) and resulting thermal relic density (right) of a 100-GeV, P-waveannihilating dark matter particle as a function of temperature T (bottom) and time t (top). The solid graycontour is for an annihilation cross section that yields the correct relic density, and the shaded regions are forcross sections that differ by 10, 102, and 103 from this value. The dashed gray contour is the number densityof a particle that remains in thermal equilibrium.

X: General darkmatter candidate

the number of dark matter particles become negligible, but interactions that mediate energyexchange between dark matter and other particles may remain efficient.

This process is described quantitatively by the Boltzmann equation

dndt

= !3H n ! "!Av#(n2 ! n2eq), (5)

where n is the number density of the dark matter particle X, H is the Hubble parameter, "!Av#is the thermally averaged annihilation cross section, and neq is the dark matter number density inthermal equilibrium. On the right-hand side of Equation 5, the first term accounts for dilutionfrom expansion. The n2 term arises from processes XX $ SM SM that destroy X particles, whereSM denotes SM particles, and the n2

eq term arises from the reverse process SM SM $ XX, whichcreates X particles.

The thermal relic density is determined by solving the Boltzmann equation numerically. Arough analysis is highly instructive, however. Defining freeze out to be the time when n"!Av# = H ,we have

n f % (mX T f )3/2e!mX /T f %T 2

f

M Pl"!Av#, (6)

where the subscripts f denote quantities at freeze out. The ratio x f & mX /T f appears in the ex-ponential. It is, therefore, highly insensitive to the dark matter’s properties and may be considereda constant; a typical value is xf % 20. The thermal relic density is, then,

"X = mX n0

#c= mX T 3

0

#c

n0

T 30

% mX T 30

#c

n f

T 3f

% x f T 30

#c M Pl"!Av#!1, (7)

www.annualreviews.org • Dark Matter Candidates 501

Ann

u. R

ev. A

stro

n. A

stro

phys

. 201

0.48

:495

-545

. Dow

nloa

ded

from

ww

w.a

nnua

lrevi

ews.o

rg A

cces

s pro

vide

d by

Nag

oya

Uni

vers

ity o

n 05

/05/

19. F

or p

erso

nal u

se o

nly.

WIMP

100 GeV 程度の質量、<σv> = 3 × 10-26 cm3s-1 の対消滅断面積を持つと期待超対称性理論 (supersymmetry、SUSY) の予言する粒子質量領域と一致宇宙の膨張とともに、温度と密度が下がる途中までは生成と消滅が平衡状態 → その後、生成できなくなる (freeze out)

38

Choi & Roszkowski (2015)質量

反応断面積

Feng (2010)

温度

時間暗黒物質の密度

現在の値

平衡状態

WIMP の反応断面積と速さの積

σが小さいと、近くを通り過ぎてもすり抜けてしまう

v が小さいと、暗黒物質がたくさんあっても平均自由行程を走る時間が長くなってしまう

それぞれを単独で観測することは困難

もし対消滅でなんらかの粒子を放射し、それを観測できるなら、その明るさから積の平均値 <σv> が求められる

39

χ

χv：WIMP の速さ (cm/s)

σ：衝突に寄与する WIMP の実効的な大きさ (cm2)

消滅と生成の平衡状態

40

SMχ

χ SM

<latexit sha1_base64="qeth/vLJtbb7g+pbPegPBX7feXA=">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</latexit><latexit sha1_base64="qeth/vLJtbb7g+pbPegPBX7feXA=">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</latexit><latexit sha1_base64="qeth/vLJtbb7g+pbPegPBX7feXA=">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</latexit><latexit sha1_base64="qeth/vLJtbb7g+pbPegPBX7feXA=">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</latexit>

SM

SM

χ

χ

χ

<latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit>

消滅

生成

χの密度と断面積が十分小さいと、対消滅はほとんど起きなくなる？

？

WIMP 標準模型粒子

WIMP の探し方 (ただし暗黒物質が WIMP だった場合)

粒子加速器による暗黒物質の生成 ‣ CERN の Large Hadron Collider (LHC)

‣ 加速エネルギーで、生成可能な質量が決まる

‣ 現在のところ観測されていない

暗黒物質を地上検出器に衝突させる直接探査 ‣ 暗黒物質がたまたま原子核に衝突するのを待つ

‣ 液体キセノンを使った観測手法が代表的

‣ 現在のところ観測されていない

暗黒物質同士の衝突痕跡を探す間接探査 ‣ 標準模型粒子が生成・崩壊しガンマ線を出す

‣ 宇宙および地上のガンマ線望遠鏡で探査

‣ 直接探査と相補的、将来計画 (’20 年代) に期待41

SMχ

χ SM


？

SM

SM

χ

χ

<latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit><latexit sha1_base64="lfbdm+Mkv3rP7I96bKv9NKdogj4=">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</latexit>

？

SM

χ

<latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="4miLyAx6p6t5RquYQ9AkM/HLRVc=">AAAB7XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwf5AO5RM5k4bmmSGJCMMY1/ArW/gTnwiX8DnMP1ZWOuBwOGchHvzxbngxgbBl1fb2d3bP6gf+kcN//jktNnomazQDLssE5kexNSg4Aq7lluBg1wjlbHAfjy7X/T9Z9SGZ+rJljlGkk4UTzmj1kWdcbMVtIOlyLYJ16YFa42b36MkY4VEZZmgxgzDILdRRbXlTODcHxUGc8pmdIJDZxWVaKJqueacXLokIWmm3VGWLNPfLyoqjSll7G5Kaqfmb7cI/+uGhU1vo4qrvLCo2GpQWghiM7L4M0m4RmZF6QxlmrtdCZtSTZl1ZDampFgqmc99xyX8S2Hb9K7bYdAOHwOowzlcwBWEcAN38AAd6AKDBF7hzXvx3r2PFb+atwZ5BhvyPn8A3biSog==</latexit><latexit sha1_base64="jpm/2qoR3jz8uafo9e9MIS1COT8=">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</latexit><latexit sha1_base64="jpm/2qoR3jz8uafo9e9MIS1COT8=">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</latexit><latexit sha1_base64="Vj86w8P0x2bxVtl+7KUJu/DiW3c=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">AAADa3icpVJda9swFJXjbuu8r3R92/ZgFgopmGB5TbI+DMr2sscOlraQhCDLsiOqDyPJgWD8L/eyP7C3/YE9TXKy9Wsw2C4IXZ2jc+/lcNOSUW3i+KvX8Xfu3X+w+zB49PjJ02fdvednWlYKkwmWTKqLFGnCqCATQw0jF6UiiKeMnKeXHxx/viJKUyk+m3VJ5hwVguYUI2OhxZ7HZykpqKhznueUkabOyVoUCpXLJgjDK3ID9SGMo1F8aClLWpiR3NQURjRpfmOKFktTSxjJa6Ctq7htGYW5VKRQshLZu348GA6HURQPYHLsrmT85rBx9Vbw79L4+Ag60Qgm7opHo7ETJ/8hXv370E7a9p0RkV05Fvx6tu4uuj3bq43wbgK3SQ9s43TR/TbLJK44EQYzpPUUxqWZ10gZim29YFZpUiJ8iQoytalAnOh53e5FEx5YJHOj2yNM2KLXFTXiWq95an9yZJb6NufAP3HTyuRv5zUVZWWIwJtGecVCI0O3ZGFGFcGGrW2CsKJ21hAvkULY2FW80cVtGy+bwBoDb9twNzlLBtDa/umod/J+a9EueAlegz6AYAxOwEdwCiYAe1+8Hx2/s9P57u/7L/xXm68db6vZBzfCP/gJmQwElA==</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit><latexit sha1_base64="MCLIENe3lfcspaSmo1RDD8BRYFs=">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</latexit>SM

χ

？

陽子

陽子生成

原子核

散乱

反跳

対消滅生成

地下実験

42

WIMP と原子核の衝突

太陽系は (= 地球は) 銀河中心のまわりを ~230 km/s で移動している ~0.3 GeV/c2/cm3 の質量密度で WIMP が存在 WIMP 質量を 100 GeV/c2 とすると、69,000 個/cm2/s の WIMP が地球に向かって、すり抜けていくたまに原子核に衝突するので、辛抱強くその痕跡を探せば良いただし、宇宙線や検出器中自体から出る放射線も原子核に衝突する

43

χごく稀に散乱

反跳

液体キセノンを使った WIMP 検出原理

大量の液体キセノンへの WIMP の衝突散乱された原子核が周辺の原子核を励起・電離 178 nm (真空紫外) の蛍光を発する地下に設置し、宇宙線の影響を取り除く不純物や放射線同位体をできる限り除去して使用比較的高い沸点－108℃ A = 131 と大きく、衝突断面積 (∝A2) が大きい Z = 54 でガンマ線をタンク外周部でよく遮蔽する 3 次元で衝突位置が分かる

44

LUX-ZEPLIN (LZ) Collaboration / SLAC National Accelerator Laboratory

光検出器

光検出器

液体キセノン

電離した電子電離した電子を電場で集める

蛍光

蛍光

XENON 実験

XENON10 (14 kg)、XENON100 (62 kg)、ZENON1T (2 ton) と進み、XENONnT (5.9 ton) が 2020 年秋に稼働予定現在、WIMP の間接探査で世界最高感度 (= キセノンの量が多く、放射線除去が良い) 名古屋大学も宇宙線物理学研究室 (CR 研) が参加

45

1 10 100 1000 10410 50

10 49

10 48

10 47

10 46

10 45

10 44

10 43

10 42

10 41

10 40

10 39

WIMP Mass GeV c2

WIMPnucleoncrosssectioncm

2

7BeNeutrinos

NEUTRINO C OHER ENT SCATTERING

NEUTRINO COHERENT SCATTERING

8BNeutrinos

Atmospheric and DSNB Neutrinos

CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)

ZEPLIN-III (2012)COUPP (2012)

SuperCDMS Soudan Low ThresholdSuperCDMS Soudan CDMS-lite

XENON 10 S2 (2013)CDMS-II Ge Low Threshold (2011)

SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

WIMP‒核子の衝突断面積の上限値競争

46

Cushman et al. (2013)

1 10 100 1000 10410 50

10 49

10 48

10 47

10 46

10 45

10 44

10 43

10 42

10 41

10 40

10 39

WIMP Mass GeV c2

WIMPnucleoncrosssectioncm

2

7BeNeutrinos

NEUTRINO C OHER ENT SCATTERING

NEUTRINO COHERENT SCATTERING

8BNeutrinos

Atmospheric and DSNB Neutrinos

CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)

ZEPLIN-III (2012)COUPP (2012)

SuperCDMS Soudan Low ThresholdSuperCDMS Soudan CDMS-lite

XENON 10 S2 (2013)CDMS-II Ge Low Threshold (2011)

SuperCDMS Soudan

Xenon1T

LUXDarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

DarkSide G2

LZ

WIMP‒核子の衝突断面積の上限値競争

47

XENON Collaboration (2018)

XENON1T (

2018)PandaX-II (

2017)

LUX (2017)

ニュートリノ

が邪魔となる

観測限界

2-4 keV

Time (day)

Res

idua

ls (c

pd/k

g/ke

V) DAMA/NaI (0.29 ton×yr)

(target mass = 87.3 kg)DAMA/LIBRA (0.53 ton×yr)

(target mass = 232.8 kg)

2-5 keV

Time (day)

Res

idua

ls (c

pd/k

g/ke




2-6 keV

Time (day)

Res

idua

ls (c

pd/k

g/ke




Figure 2: Model-independent residual rate of the single-hit scintillation events, mea-sured by the new DAMA/LIBRA experiment in the (2 – 4), (2 – 5) and (2 – 6) keVenergy intervals as a function of the time. The residuals measured by DAMA/NaI andalready published in ref. [4, 5] are also shown. The zero of the time scale is January1st of the first year of data taking of the former DAMA/NaI experiment. The exper-imental points present the errors as vertical bars and the associated time bin widthas horizontal bars. The superimposed curves represent the cosinusoidal functions be-haviours A cos!(t ! t0) with a period T = 2!

" = 1 yr, with a phase t0 = 152.5 day(June 2nd) and with modulation amplitudes, A, equal to the central values obtained bybest fit over the whole data, that is: (0.0215± 0.0026) cpd/kg/keV, (0.0176± 0.0020)cpd/kg/keV and (0.0129±0.0016) cpd/kg/keV for the (2 – 4) keV, for the (2 – 5) keVand for the (2 – 6) keV energy intervals, respectively. See text. The dashed verticallines correspond to the maximum of the signal (June 2nd), while the dotted verticallines correspond to the minimum. The total exposure is 0.82 ton"yr.

8

結晶シンチレータ実験による暗黒物質の「発見」

6 月のほうが地球と WIMP の相対速度が大きく、反跳エネルギーが大きい

検出のしやすさが季節変動するため、放射線などの引き算が楽 (証拠として出しやすい)

DAMA/NaI および DAMA/LIBRA 実験によって、検出された何らかの粒子検出数の季節変動が発見された

48

🌏

🌞

230 km/s

12 月

6 月

Bernabei et al. (2008)

χ

LETTER RESEARCH

probability density functions within their uncertainties. We also con-sider the possibility of correlated rate and shape uncertainties and the uncorrelated bin-by-bin statistical uncertainties (Methods). To calculate the expected 90% confidence level upper limits on WIMP–nucleon scat-tering cross-sections, we performed 1,000 simulated experiments with the expected backgrounds and no dark-matter signal.

Data were fitted to each of the 18 WIMP masses. An example of a maximum-likelihood fit with a 10!GeV!c!2 WIMP signal is presented in Fig.!3 (see also Extended Data Fig.!5). The summed event spec-trum for the six crystals is shown together with the best-fit result. For comparison, the expected signal for a 10!GeV!c!2 WIMP with a spin- independent cross-section of 2.35 " 10!40!cm2—the central value of the DAMA/LIBRA-phase1 signal interpreted as a WIMP–sodium interaction—is overlaid in red. No excess of events that could be attrib-uted to standard-halo WIMP interactions are found for the 18 WIMP masses considered. The posterior probabilities of the existence of a WIMP-induced signal are consistent with zero in all cases; we deter-mined 90% confidence level limits. In Fig.!4 we show the 3! contours of the allowed WIMP mass and the cross-sections that are associated with the DAMA/LIBRA-phase1 signal10, together with the 90% confidence level upper limits from the COSINE-100 data.

Despite strong evidence for its existence, the identity of dark matter remains a mystery. COSINE-100 continues to collect data, and sev-eral years of data will be necessary to fully confirm or refute DAMA’s results. However, the first 59.5 days of background data show that the annual modulation in the signal observed by DAMA is inconsistent with spin-independent interactions between WIMPs and sodium or iodine in the context of the standard halo model.

Online contentAny Methods, including any statements of data availability and Nature Research reporting summaries, along with any additional references and Source Data files, are available in the online version of the paper at https://doi.org/10.1038/s41586-018-0739-1.

Received: 27 April 2018; Accepted: 13 September 2018; Published online 5 December 2018.

1. Clowe, D. et al. A direct empirical proof of the existence of dark matter. Astrophys. J. 648, L109–L113 (2006).

2. Ade, P. A. R. et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016).

3. Baer, H., Choi, K.-Y., Kim, J. E. & Roszkowski, L. Dark matter production in the early Universe: beyond the thermal WIMP paradigm. Phys. Rep. 555, 1–60 (2015).

4. Lee, B. W. & Weinberg, S. Cosmological lower bound on heavy-neutrino masses. Phys. Rev. Lett. 39, 165–168 (1977).

5. Goodman, M. W. & Witten, E. Detectability of certain dark matter candidates. Phys. Rev. D 31, 3059–3063 (1985).

6. Battaglieri, M. et al. US cosmic visions: new ideas in dark matter 2017: community report. Preprint at https://arxiv.org/abs/1707.04591 (2017).

7. Bernabei, R. et al. Searching for WIMPs by the annual modulation signature. Phys. Lett. B 424, 195–201 (1998).

8. Bernabei, R. et al. Final model independent result of DAMA/LIBRA-phase1. Eur. Phys. J. C 73, 2648 (2013).

9. Bernabei, R. et al. First model independent results from DAMA/LIBRA-phase2. Preprint at https://arxiv.org/abs/1805.10486 (2018).

10. Savage, C., Gelmini, G., Gondolo, P. & Freese, K. Compatibility of DAMA/LIBRA dark matter detection with other searches. J. Cosmol. Astropart. Phys. 4, 10 (2009).

11. Baum, S., Freese, K. & Kelso, C. Dark matter implications of DAMA/LIBRA-phase2 results. Preprint at https://arxiv.org/abs/1804.01231 (2018).

12. Kang, S., Scopel, S., Tomar, G. & Yoon, J.-H. DAMA/LIBRA-phase2 in WIMP e!ective models. J. Cosmol. Astropart. Phys. 7, 16 (2018).

13. Barbosa de Souza, E. et al. First search for a dark matter annual modulation signal with NaI(Tl) in the Southern Hemisphere by DM-Ice17. Phys. Rev. D 95, 032006 (2017).

14. Amaré, J. et al. Status of the ANAIS dark matter project at the Canfranc Underground Laboratory. J. Phys. Conf. Ser. 718, 042052 (2016).

15. Fushimi, K. et al. Dark matter search project PICO-LON. J. Phys. Conf. Ser. 718, 042022 (2016).

16. Xu, J., Calaprice, F., Froborg, F., Shields, E. & Suerfu, B. SABRE – a test of DAMA with high-purity NaI(Tl) crystals. AIP Conf. Proc. 1672, 040001 (2015).

17. Adhikari, P. et al. Understanding internal backgrounds in NaI(Tl) crystals toward a 200 kg array for the KIMS-NaI experiment. Eur. Phys. J. C 76, 185 (2016).

18. Adhikari, G. et al. Initial performance of the COSINE-100 experiment. Eur. Phys. J. C 78, 107 (2018).

19. Adhikari, P. et al. Background model for the NaI(Tl) crystals in COSINE-100. Eur. Phys. J. C 78, 490 (2018).

20. Tanabashi, M. et al. The review of particle physics. Phys. Rev. D 98, 030001 (2018).

21. Drukier, A. K., Freese, K. & Spergel, D. N. Detecting cold dark-matter candidates. Phys. Rev. D 33, 3495–3508 (1986).

22. Freese, K., Frieman, J. A. & Gould, A. Signal modulation in cold dark matter detection. Phys. Rev. D 37, 3388–3405 (1988).

23. Lewin, J. & Smith, P. Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil. Astropart. Phys. 6, 87–112 (1996).

24. Park, J. S. et al. Performance of a prototype active veto system using liquid scintillator for a dark matter search experiment. Nucl. Instrum. Methods A 851, 103–107 (2017).

25. Prihtiadi, H. et al. Muon detector for the COSINE-100 experiment. J. Instrum. 13, T02007 (2018).

26. Friedman, J. H. Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001).

27. Agostinelli, S. et al. GEANT4: a simulation toolkit. Nucl. Instrum. Methods A 506, 250–303 (2003).

28. Swiderski, L. Response of doped alkali iodides measured with gamma-ray absorption and Compton electrons. Nucl. Instrum. Methods A 705, 42–46 (2013).

29. Caldwell, A., Kollár, D. & Kröninger, K. BAT – the Bayesian analysis toolkit. Comput. Phys. Commun. 180, 2197–2209 (2009).

30. Alner, G. J. et al. Limits on WIMP cross-sections from the NAIAD experiment at the Boulby Underground Laboratory. Phys. Lett. B 616, 17–24 (2005).

Acknowledgements We thank the Korea Hydro and Nuclear Power (KHNP) Company for providing underground laboratory space at Yangyang. This work is supported by: the Institute for Basic Science (IBS) under project code IBS-R016-A1 and NRF-2016R1A2B3008343, South Korea; UIUC campus research board, the Alfred P. Sloan Foundation Fellowship, NSF grant numbers PHY-1151795, PHY-1457995, DGE-1122492 and DGE-1256259, WIPAC, the Wisconsin Alumni Research Foundation, Yale University and DOE/NNSA grant number DE-FC52-08NA28752, USA; STFC grants ST/N000277/1 and ST/K001337/1, UK; and CNPq and grant number 2017/02952-0 FAPESP, Brazil.

Reviewer information Nature thanks B. Sadoulet and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author contributions Y.K., H.S.L., R.H.M. and N.J.C.S. conceived the COSINE-100 experiment. Its design and installation were led by K.P. and C.H.H. and carried out by all members of the collaboration. Operation and maintenance were organized by C.H.H. with support from on-site crews, W.G.K., B.K. and S.H.Y. Jaison Lee, J.P., J.H.J., G.A., P.A., H. Prihtiadi, C.H.H., W.G.T., E.B.d.S., H.S.L. and K.K. contributed to data acquisition, production and verification. H.J., Hyeonseo Park and K.K. provided nuclear recoil data. P.A., G.A., J.P., K.K., H. Prihtiadi, N.Y.K. and C.H.H. performed the source calibrations. Hyounggyu Kim, N.Y.K., C.H.H. and H.S.L. developed the slow

WIMP mass (GeV c–2)101 102 103 104

WIM

P–n

ucle

on s

pin-

inde

pend

ent

cros

s-se

ctio

n (c

m2 )

10!43

10!42

10!41

10!40

10!39

10!38NAIADDAMA, sodium (3V)DAMA, iodine (3V)COSINE-100 1VCOSINE-100 2VCOSINE-100 observed limit(90% con!dence level)

Fig. 4 | Exclusion limits on the WIMP–nucleon spin-independent cross-section. The 90% confidence level exclusion limits on the WIMP–nucleon spin-independent cross-section determined from the data from the first 59.5 days of the COSINE-100 experiment (filled circles and black solid line; total exposure of 6,303.9!kg!d) are shown together with their 68% (grey shading) and 95% (blue shading) probability bands assuming the background-only hypothesis. Our exclusion limits are compared with 3! allowed regions of the WIMP mass and the cross-section associated with the DAMA/LIBRA-phase1 signal for the WIMP–sodium (red dotted contour) and the WIMP–iodine (blue dotted contour) scattering hypothesis10. The limit from NAIAD30—the only other sodium-iodide-based experiment to set a competitive limit—is shown in purple.

6 D E C E M B E R 2 0 1 8 | V O L 5 6 4 | N A T U R E | 8 5© 2018 Springer Nature Limited. All rights reserved.

同様の実験による否定的な結果

COSINE-100 実験による最近の結果は、DAMA の結果より厳しい上限「先端物理学」だとよくある話

49

Adhikari et al. (2018)

XENON1T による謎の超過事象の発見

低エネルギー（~2.3 keV）に予期されぬ信号を発見暗黒物質ではないが、太陽からのアクシオンなどの可能性を示唆 KMI のプレスリリースも参照（2020/6/18）

50

https://www.kmi.nagoya-u.ac.jp/blog/2020/06/18/%E6%9A%97%E9%BB%92%E7%89%A9%E8%B3%AA%E7%9B%B4%E6%8E%A5%E6%8E%A2%E7%B4%A2%E5%AE%9F%E9%A8%93xenon1t%E3%81%8C%E9%9B%BB%E5%AD%90%E6%95%A3%E4%B9%B1/

https://www.kmi.nagoya-u.ac.jp/blog/2020/06/18/%E6%9A%97%E9%BB%92%E7%89%A9%E8%B3%AA%E7%9B%B4%E6%8E%A5%E6%8E%A2%E7%B4%A2%E5%AE%9F%E9%A8%93xenon1t%E3%81%8C%E9%9B%BB%E5%AD%90%E6%95%A3%E4%B9%B1/

ガンマ線観測

51

WIMP 対消滅による標準模型粒子の生成

52

SMχ

χ SM


？WIMP ~100 GeV/c2

W-/Z/q

W+/Z/q̅

ガンマ線ニュートリノ陽電子/反陽子　などをさらに生成

d��

dE�(E� ,�, ✓) =

1

4⇡

< �v >

2m2WIMP

X

f

dN�,f

dE�Bf

⇥Z

�⌦(�,✓)d⌦0

Z

l.o.s.⇢2(r(l,�0))dl(r,�0)

<latexit sha1_base64="5HiaqvYXvVppQE5W0abypUat4Qo=">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</latexit><latexit sha1_base64="5HiaqvYXvVppQE5W0abypUat4Qo=">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</latexit><latexit sha1_base64="5HiaqvYXvVppQE5W0abypUat4Qo=">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</latexit><latexit sha1_base64="5HiaqvYXvVppQE5W0abypUat4Qo=">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</latexit>

単位エネルギーあたりのガンマ線放射量

密度の二乗に比例

どのような終状態でどれだけガンマ線を出すか素粒子物理の計算

暗黒物質の空間分布

縮退している

課題 3

WIMP の対消滅で期待されるガンマ線の放射強度は、なぜ WIMP 密度の 2 乗に比例するかを、定性的に説明せよ

53

ガンマ線で観た宇宙

数千におよぶ高エネルギー天体 (点源) からのガンマ線放射星間ガスと宇宙線陽子の衝突で生じるパイ中間子の崩壊によるガンマ線放射 WIMP 由来のガンマ線が簡単に観えるほど、宇宙はガンマ線で暗くない

54

フェルミ衛星 7 年間の観測 (> 1 GeV)

暗黒物質の分布推定

銀河中心：高密度の WIMP と高いガンマ線強度が期待、ただし他天体や銀河面からのガンマ線混入が多い銀河ハロー：比較的高密度だが、銀河面からのガンマ線混入が多い矮小楕円体銀河：密度は低いが、自身のガンマ線放射が非常に小さく銀河面からも離れている

55

銀河ハロー

銀河中心

矮小楕円体銀河

Pieri et al. (2011)

フェルミ宇宙ガンマ線望遠鏡

2008 年に NASA によって打ち上げられた人工衛星大面積望遠鏡 (Large Area Telescope、LAT) とガンマ線バーストモニター (Gamma-ray Burst Monitor、GBM) の 2 種類を搭載 LAT は 20 MeV～300 GeV のガンマ線を全天サーベイ観測する日米欧の国際共同

56

NASA

LAT

GBM

incoming gamma ray

e+e-

electrton-positron pair

0.72 m

1.8 m1.8 m

Calorimeter

Anticoincidencedetector

Tracker

Large Area Telescope (LAT)

ガンマ線が検出器中の原子核 (の周りの仮想光子) に衝突し、電子・陽電子対を生成する電子・陽電子の飛跡をシリコン半導体検出器が記録し、ガンマ線の入射方向を決定結晶シンチレータの熱量計 (カロリメータ) でエネルギーを光に変換し、エネルギーを決定

57

入射ガンマ線　　　　　　

電子・陽電子対　　　　

飛跡検出器

　　熱量計

荷電粒子検出器

the bb̄ and !!!! channels with expectation bands derivedfrom the analysis of 300 randomly selected sets of blankfields. Sets of blank fields are generated by choosingrandom sky positions with jbj > 30° that are centered atleast 0.5° from 3FGL catalog sources. We additionallyrequire fields within each set to be separated by at least7°. Our expected limit bands are evaluated with the 3FGL

source catalog based on four years of PASS7 REPROCESSED

data and account for the influence of new sources present inthe six-year PASS8 data set.Comparing with the results of Ackermann et al. [13], we

find a factor of 3–5 improvement in the limits for allchannels using six years of PASS8 data and the same sampleof 15 dSphs. The larger data set as well as the gains in the

LAT instrument performance enabled by PASS8 bothcontribute to the increased sensitivity of the presentanalysis. An additional 30%–40% improvement in thelimit can be attributed to the modified functional formchosen for the J factor likelihood (3). Statistical fluctua-tions in the PASS8 data set also play a substantial role.Because the PASS8 six-year and PASS7 REPROCESSED

four-year event samples have a shared fraction of only20%–40%, the two analyses are nearly statistically inde-pendent. For masses below 100 GeV, the upper limits ofAckermann et al. [13] were near the 95% upper bound ofthe expected sensitivity band while the limits in the presentanalysis are within 1 standard deviation of the medianexpectation value.

FIG. 1 (color). Constraints on the DM annihilation cross section at the 95% CL for the bb̄ (left) and !!!! (right) channels derived froma combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by repeating the same analysis on 300 randomlyselected sets of high-Galactic-latitude blank fields in the LAT data. The dashed line shows the median expected sensitivity while thebands represent the 68% and 95% quantiles. For each set of random locations, nominal J factors are randomized in accord with theirmeasurement uncertainties. The solid blue curve shows the limits derived from a previous analysis of four years of PASS7 REPROCESSED

data and the same sample of 15 dSphs [13]. The dashed gray curve in this and subsequent figures corresponds to the thermal relic crosssection from Steigman et al. [5].

FIG. 2 (color). Comparison of constraints on the DM annihilation cross section for the bb̄ (left) and !!!! (right) channels from thiswork with previously published constraints from LAT analysis of the Milky Way halo (3" limit) [57], 112 hours of observations of theGalactic center with H.E.S.S. [58], and 157.9 hours of observations of Segue 1 with MAGIC [59]. Pure annihilation channel limits forthe Galactic center H.E.S.S. observations are taken from Abazajian and Harding [60] and assume an Einasto Milky Way density profilewith #! " 0.389 GeV cm"3. Closed contours and the marker with error bars show the best-fit cross section and mass from severalinterpretations of the Galactic center excess [16–19].

PRL 115, 231301 (2015) P HY S I CA L R EV I EW LE T T ER Sweek ending

4 DECEMBER 2015

231301-6

LAT による WIMP 対消滅断面積の上限

15 の矮小楕円体銀河からは有意なガンマ線放射が検出されなかった (対消滅断面積の上限値を与えた) WIMP の正体が謎のため、最終的にどのようにガンマ線に行くかが分からない bb̅、τ+τ－の終状態の場合などに分けて上限をつけるすでに、100 GeV/c2 以下の質量範囲では <σv> = 3 × 10-26 cm3s-1 より強い制限

58the bb̄ and !!!! channels with expectation bands derivedfrom the analysis of 300 randomly selected sets of blankfields. Sets of blank fields are generated by choosingrandom sky positions with jbj > 30° that are centered atleast 0.5° from 3FGL catalog sources. We additionallyrequire fields within each set to be separated by at least7°. Our expected limit bands are evaluated with the 3FGL

source catalog based on four years of PASS7 REPROCESSED

data and account for the influence of new sources present inthe six-year PASS8 data set.Comparing with the results of Ackermann et al. [13], we

find a factor of 3–5 improvement in the limits for allchannels using six years of PASS8 data and the same sampleof 15 dSphs. The larger data set as well as the gains in the

LAT instrument performance enabled by PASS8 bothcontribute to the increased sensitivity of the presentanalysis. An additional 30%–40% improvement in thelimit can be attributed to the modified functional formchosen for the J factor likelihood (3). Statistical fluctua-tions in the PASS8 data set also play a substantial role.Because the PASS8 six-year and PASS7 REPROCESSED

four-year event samples have a shared fraction of only20%–40%, the two analyses are nearly statistically inde-pendent. For masses below 100 GeV, the upper limits ofAckermann et al. [13] were near the 95% upper bound ofthe expected sensitivity band while the limits in the presentanalysis are within 1 standard deviation of the medianexpectation value.

FIG. 1 (color). Constraints on the DM annihilation cross section at the 95% CL for the bb̄ (left) and !!!! (right) channels derived froma combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by repeating the same analysis on 300 randomlyselected sets of high-Galactic-latitude blank fields in the LAT data. The dashed line shows the median expected sensitivity while thebands represent the 68% and 95% quantiles. For each set of random locations, nominal J factors are randomized in accord with theirmeasurement uncertainties. The solid blue curve shows the limits derived from a previous analysis of four years of PASS7 REPROCESSED

data and the same sample of 15 dSphs [13]. The dashed gray curve in this and subsequent figures corresponds to the thermal relic crosssection from Steigman et al. [5].

FIG. 2 (color). Comparison of constraints on the DM annihilation cross section for the bb̄ (left) and !!!! (right) channels from thiswork with previously published constraints from LAT analysis of the Milky Way halo (3" limit) [57], 112 hours of observations of theGalactic center with H.E.S.S. [58], and 157.9 hours of observations of Segue 1 with MAGIC [59]. Pure annihilation channel limits forthe Galactic center H.E.S.S. observations are taken from Abazajian and Harding [60] and assume an Einasto Milky Way density profilewith #! " 0.389 GeV cm"3. Closed contours and the marker with error bars show the best-fit cross section and mass from severalinterpretations of the Galactic center excess [16–19].


4 DECEMBER 2015

231301-6

Ackermann et al. (2015)

解像型大気チェレンコフ望遠鏡 (Imaging atmospheric Cherenkov Tel.)

超高エネルギーガンマ線が大気中で生じる電磁カスケード (電子・陽電子対とガンマ線で構成、空気シャワー) を観測する

空気シャワー中で生じる 300～500 nm の紫外・可視光を巨大望遠鏡で撮影

大型のものは HESS 望遠鏡 (4 + 1 台)、MAGIC 望遠鏡 (2 台)、VERITAS 望遠鏡 (4 台) が稼働中59

28 m

12 m

HESS 望遠鏡 @ ナミビア Stefan Klepser

from 0.3° to 0.9° in radial distance from the GC, hereafterreferred to as the ON regions. In order to minimizecontamination from the above-mentioned astrophysicalemission, a band of !0.3° in Galactic latitude is excludedalong the Galactic plane. (Interestingly, this enablesus to derive constraints that do not strongly depend onthe central DM density distribution, which is poorly knownin the innermost few tens of parsecs of the GC.) Thebackground events are selected in OFF regions defined foreach observation as annuli symmetric to the ON regionswith respect to the pointing position (see Fig. 1 in theSupplemental Material [16]). The OFF regions are expectedto contain signal events as well, which decreases anypotential excess in the ON regions. The OFF regions arealways taken sufficiently far from the ON regions to obtaina significant contrast in the DM annihilation signal betweenthe ON and OFF regions. [This analysis method is unableto probe cored profiles (such as isothermal or Burkertprofiles). A dedicated observation strategy is required asshown in Ref. [12]]. We considered here the above-mentioned DM profiles for which the OFF regions containalways fewer DM events than the ON regions. A Galacticdiffuse emission has been detected by the Fermi satellite[19,20] and H.E.S.S. [21]. Any potential !-ray contributionfrom the Galactic diffuse emission is considered as partof the signal, which makes the analysis conservative aslong as no signal is detected.We perform a 2D binned Poisson maximum likelihood

analysis, which takes full advantage of the spatial and

spectral characteristics of the DM signal with respect to thebackground. We use 70 logarithmically spaced energy binsfrom 160 GeV to 70 TeV, and seven spatial bins corre-sponding to ROIs defined as the above-mentioned annuli of0.1° width. For a given DM mass mDM and annihilationchannel, the joint likelihood is obtained by the product ofthe individual Poisson likelihoods over the spatial bins iand the energy bins j. It reads

L"mDM; h"vi# $Y

i;j

Lij;

with Lij"NS;NBjNON;NOFF;!#

$"NS;ij % NB;ij#NON;ij

NON;ij!e!"NS;ij%NB;ij#: "3#

NS;ij % NB;ij is the expected total number of events inthe spatial bin i and spectral bin j of the ON regions.The expected number of signal events NS;ij is obtainedby folding the theoretical number of DM events by theinstrument response function of H.E.S.S. for this data set.NB;ij is the number of background events expected inthe spatial bin i and spectral bin j. NON;ij and NOFF;ij

are the number of observed events in the ON and OFFregions, respectively.NB;ij is extracted from theOFF regionsand given by NB;ij $ #iNOFF;ij. The parameter #i $!"i=!"OFF refers to the ratio between the angular sizeof the ON region i and the OFF region. In our case, this ratio

(TeV)DMm0.05 0.1 0.2 1 2 3 4 5 10 20 30

)-1 s3

(cm

! v"#

-2710

-2610

-2510

-2410

-2310

-2210

Observed, this workExpected68% Containment95% ContainmentH.E.S.S 112h (2011)

Thermal relic density

-W+ W$254h, DM DM

Einasto profile

(TeV)DMm0.05 0.1 0.2 1 2 3 4 5 10 20 30

)-1 s3

(cm

! v"#

-2710

-2610

-2510

-2410

-2310

-2210

Observed, this workExpected

68% Containment95% Containment

Thermal relic density

-%+%$254h, DM DM

Einasto profile

FIG. 1. Constraints on the velocity-weighted annihilation cross section h"vi for theW%W! (left panel) and $%$! (right panel) channelsderived from observations taken over 10 years of the inner 300 pc of the GC region with H.E.S.S. The constraints for the bb̄, tt̄, and%%%! channels are given in Fig. 4 in Supplemental Material [16]. The constraints are expressed as 95% C.L. upper limits as a function ofthe DM mass mDM. The observed limit is shown as a black solid line. The expectations are obtained from 1000 Poisson realizations ofthe background measured in blank-field observations at high Galactic latitudes. The mean expected limit (black dotted line) togetherwith the 68% (green band) and 95% (yellow band) C.L. containment bands are shown. The blue solid line corresponds to the limitsderived in a previous analysis of 4 years (112 h of live time) of GC observations by H.E.S.S. [10]. The horizontal black long-dashed linecorresponds to the thermal relic velocity-weighted annihilation cross section (natural scale).


9 SEPTEMBER 2016

111301-4

HESS 望遠鏡による WIMP 対消滅断面積の上限

ポインティング観測のため、フェルミ衛星ほど多数の矮小楕円体銀河を観測できない → 銀河中心ハローを長時間観測 TeV/c2 の質量領域で、<σv> = 3 × 10-26 cm3s-1 に迫るフェルミ衛星の結果と合わせると、1 TeV/c2 以上の質量が残る領域か？

60

HESS Collaboration (2016)

チェレンコフ望遠鏡アレイ (Cherenkov Telescope Array、CTA)

61

cherenkov telescope array

Image Credit: G. Pérez, IAC, SMM

チェレンコフ望遠鏡アレイ (Cherenkov Telescope Array、CTA)

62

電磁カスケード (対生成、制動放射)

超高エネルギーガンマ線 (20 GeV ～300 TeV)

大気チェレンコフ光の光量 ∝ 入射エネルギー (300～600 nm, 5‒20 ns)

R ~150 mK. Bernlöhr

✤ 1桁以上の感度向上が期待される ❖フェルミ衛星の観測時間の蓄積と解析対象の矮小楕円銀河の追加•改良された検出技術で新しい矮小楕円銀河が次々に発見

❖フェルミ衛星の銀河中心データにおけるバックグラウンドの理解が進めば、暗黒物質を検出できる可能性

❖次世代ガンマ線観測装置によるTeV質量領域における感度向上

/34ガンマ線観測と地下実験で探る暗黒物質の正体先端物理学特論, 名古屋大学 2018/6/5

将来のガンマ線観測によるWIMP探査

33

101 102 103 104

DM Mass (GeV/c2)

10!27

10!26

10!25

10!24

10!23

!v(cm

3s!

1 )Pass 8 Combined dSphsFermi-LAT MW HaloH.E.S.S. GC HaloMAGIC Segue 1Abazajian et al. 2014 (1")

Daylan et al. 2014 (2")Calore et al. 2015 (2")

LAT dSph (15 yrs 60 dSphs)CTA GC Halo 500h (Lefranc+2015)CTA MW Halo 500h (Carr+2015) stat. only

Thermal Relic Cross Section(Steigman et al. 2012)

bb

Gordon & Macias 2013 (2")

–

H.E.S.S. 2016

CTA で期待される WIMP の発見

フェルミ衛星の継続的な観測と、CTA の長時間観測によって、10 TeV/c2 の質量範囲まで高感度 WIMP 探査が可能になる (2020 年代) CTA では現行の望遠鏡よりおよそ 1 桁感度が向上近年、矮小楕円体銀河も新たに発見され続けている WIMP 以外のガンマ線放射の定量的理解が、特に銀河中心周辺で重要

63

CTA

Fermi/LAT

CR 研での CTA 開発

1400 人、31 カ国の国際共同研究名古屋大学 CR 研では、焦点面カメラの開発 (光検出器、ソフトウェア、エレクトロニクス)、光学系の開発などを担当 (奥村、田島) 3 種類の異なる口径の望遠鏡開発に参加

64

望遠鏡試作機の完成式典

10 億分の 1 秒ごとの動画を撮る技術

5～20 ナノ秒 (ns) しか継続しない大気チェレンコフ光を撮像するには、10 億分の 1 秒 (1 ns) ごとに 1 フレームを撮影できる高速カメラが必要多チャンネルの半導体光検出器と独自開発の集積回路の組み合わせ https://www.isee.nagoya-u.ac.jp/CR/result/2019/06/28/CHEC-S-First-Light.html （リンクをクリックすると、CR 研のウェブサイトで動画を観られます）

65

Photo by C. Föhr

試作カメラでのチェレンコフ光撮影例

https://www.isee.nagoya-u.ac.jp/CR/result/2019/06/28/CHEC-S-First-Light.html


10 億分の 1 秒ごとの動画を撮る技術

5～20 ナノ秒 (ns) しか継続しない大気チェレンコフ光を撮像するには、10 億分の 1 秒 (1 ns) ごとに 1 フレームを撮影できる高速カメラが必要多チャンネルの半導体光検出器と独自開発の集積回路の組み合わせ https://www.isee.nagoya-u.ac.jp/CR/result/2019/06/28/CHEC-S-First-Light.html （リンクをクリックすると、CR 研のウェブサイトで動画を観られます）

65

Photo by C. Föhr

試作カメラでのチェレンコフ光撮影例



CTA 大口径望遠鏡 (23 m)

低エネルギー（と言っても 20 GeV 以上）のガンマ線を観測するすでに 1 台がカナリア諸島に完成し、2～4 台目の建設準備中 https://www.isee.nagoya-u.ac.jp/CR/result/2018/11/05/LST-Inauguration.html

66

https://www.isee.nagoya-u.ac.jp/CR/result/2018/11/05/LST-Inauguration.html

https://www.isee.nagoya-u.ac.jp/CR/result/2018/11/05/LST-Inauguration.html

レポート課題

途中に示した課題 1～3（p20、p34、p53）を全て提出せよ（採点対象） ‣ あまり難しく考える必要はない

‣ 合計で 20 分以下の所要時間を想定

講義中に質問をした人は、念のためそのことを記しておいてください（加点対象）

講義の感想（採点対象外） ‣ 書かなくても良い

‣ ネガティブなものも大歓迎 (改善点、分かりにくかった点など)

‣ コロナ禍での大学対応の不満や（本科目を含む）講義形式の不満でも良い

‣ 活発な質問が出る講義にするにはどうすれば良いか

‣ 質問したいことがあっても講義中の質問に躊躇してしまう人がいれば、どのようにしたら良いかの提案など

提出期限：7 月 14 日 (火) 23:59

67

Documents

～先端物理学特論～ 地下実験とガンマ線で迫る 暗 …okumura/files/200714DM.pdfderived from observations taken over 10 years of the inner 300 pc of the GC region

～先端物理学特論～地下実験とガンマ線で迫る暗 …okumura/files/200714DM.pdfderived from observations taken over 10 years of the inner 300 pc of the GC region