: 8.2: A group (i.e. a very small cluster) of galaxies superimposed on a x-ray image from the ROSAT satellite

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1 : ( Ω = ρ/ρ c ) (Fukugita, M. et al., APJ 503 (1998) 518) ( 15%) (z 0 ) h h h 1 A h h h 1 A h h h 1 B h h h 1 A h h h 1 A h h h 1.5 A 7a. 1) h h h 1.5 B 7b h h h 1 C h h h 1 B 8. (h= z 0) =7a+7b % ( 8.1) X (Ω B = ρ B /ρ c ) 2% (2 ) ( ) η B = / η B

2 : 8.2: A group (i.e. a very small cluster) of galaxies superimposed on a x-ray image from the ROSAT satellite

3 : η 10 ( / ( η 10 = ) WMAP (η 10 6) ( Three-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Draft: March 16, 2006) η B = n B /n γ η B Ω B = ± (F.Zwicky) (Helv. Phys. Acta, 6 (1933) 110) 19 (HI 21cm ) M/L( ) X (J.Ostriker and P.Peebles: ApJ 186(1973)467) CMBR δt /T 10 5 (z = 1100) δρ/ρ < 10 4 (R 8h 1 Mpc) 1 z=

4 第 8 章 暗黒物質の存在 銀河回転速度より 電波望遠鏡による中性水素分子の出す 21cm 輝線の測定により 銀河の光る円盤をはるかに越えた所まで 水素 分子の回転速度が一定であることが判明した (図 ) ニュートン力学のエネルギー保存則の式を書くと 1 2 M mv Gm = E 2 r r v= 2GM, r v = const. M r (8.1) 銀河回転曲線からは 銀河質量は少なくも見える質量の数倍の物質量を含むことが判明した 図 8.4: (左) アンドロメダ星雲の回転曲線 (右) 暗黒物質は銀河円盤を中心に球状に分布する 中性の水素分子 (HI) の出す 21cm 電波を観測する事により 光らない部分の回転速度も分かる

5 : : ( 8.7 ) E =< K > + < U >= 1 2 < U >, < K >= 1 2 < U > (8.2a) < K > = 1 2 m < v2 >= G Z dm GM (8.2b) 2 r R < K > < U > ( ) M = M > : X X ( 8.7 ) X 10keV ( 1 ) X X 1-5 7% M 2% X

6 第 8 章 暗黒物質の存在 6 図 8.7: 銀河団 MS : 80 億光年 (z=0.831) の彼方にある M > M で さしわたし 3M pc の宇宙 空間に数千もの銀河を含む (左) 銀河団の写真に X 線映像 (青色) を重ねたもの (共に地上で撮影) 右 ハッブル 望遠鏡で撮影した拡大図 演習問題 R = 3M pc の球状分布の銀河団から 一様に X 線が放射されているとしよう X 線を放射するバリ オンの平均運動エネルギーを 1KeV として 式 (8.2b) を使って 銀河団質量 M を計算すれば M M であることを示せ 銀河質量= M とすれば これは大体銀河 3300 個分の質量に相当する 重力レンズ 図 8.8: Abel2218 超銀河団 (20 億光年) の重力レンズ効果による遠方銀河のアーク状映像 ハッブル ケック望遠 鏡合作 青:若く熱い星 黄 白 様々の星 赤 冷たく年老いた星 (右上挿入写真) 一部拡大図 重力レンズに より 30 倍に拡大された非常に遠方 (134 億光年) にある銀河の 2 重像 (矢印) が見える この非常に若い銀河は わずか 106 個の銀河を含むだけであり 初期銀河形成の知識を与える

7 Ω m (M/L) M/L( ) (R) R 1Mpc M = M M/L 300 Ω m = ( 8.9 ) M/L 8.9: ( ) M/L B ( L B ) M /L (R) R 0.3Mpc Ω m ( ) σ 8 Ω m z Cluster Dynamics M/L baryon fraction X (N.A.Bahcall; Physica Scripta T85(2000) 32-36) / < Ω (8.3) (z 6) (Ryα) Ω HI h 1 (8.4) Ryα ( ) Ω B h 2 = ± (8.5)

8 8 8 X X X X X ( ) M M total (0.066 ± 0.003)h 2/ (8.6) ( ) 12% Ω m 0.175h σ 8 8h 1 Mpc σ 8 1 σ 8 1 (z=0) σ 8 Ω 1/2 m 0.5 Ω m σ 8 Ω m z σ 8 Ω 8.9 = Ω m 0.2, σ Ω m ( ) * 1) 8.4 (WMAP ) * 2) (t = t rec 25 ) t = t rec * 3) 1 v s 3 c * 4) ( ) = ( ) n n+1 (n=1) Ω m ( ) ( 2 ) 8.10 WMAP η B * 1) WMAP σ 8 = 0.9 ± 0.1, σ 8 Ω 0.6 m = 0.44 ± 0.1 * 2) Recombination * 3) (X e = ) * 4)

9 : WMAP (η 10 6) ( Three-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Draft: March 16, 2006)

10 : WMAP ( W.Hu and Dodelson: Cosmic Microwave Background Anisotropies, Annu. Rev. Astron. and Astrophys. 2002) 8.10 Ω m0 Ω total matter h 2 = ± (8.7) Ω B h 2 = ± h = 0.72 Ω B (z 15) ( ) WMAP (htt p : //map.gs f c.nasa.gov/m m m/pub p apers/threeyear.html) 8.12 H 0 = 100h km sec 1 Mpc 1 (h = ± 0.03) t H = H0 1 = h (9.778 Gyr) years 13.7 ± 0.3 Gyears Ω B = h 2 ± / η B = 6.1 ± ( ) Ω m h 2 = ± Ω m = ± 0.03 Ω Λ = ± 0.03 (Ω K = 1 Ω m Ω rad Ω Λ ) Ω K = ± σ ± : 8.5 1)

11 : 2) 1) + 2) 3) 4) Ω DM 0.24 ( ) WIMPS (Weakly Interacting Massive Paricles) (v >> c) (v << c) MACHO: MACHO(MAssive Compact Halo Objiects) - MACHO MACHO MACHO EROS MACHO ( 8.14) 20eV (misaligned) CP ev 2 WIMPS (SUSY) 1/2 (

12 : MACHO 95%CL MACHO MACHO EROS EROS MACHO 10 6 < M < 3M 10% (Astron. Astrophys. 400 (2003) 951; astro-ph/ ) GeV)SUSY R (SUSY ) SUSY SUSY WIMPS(Weakly Interacting Massive Particles) (χ ) Z 1/2 χ a 1 γ + a 2 Z + a 3 H a 4 H 2 0 (8.8a) P > 0.9 gaugino, P < 0.1 higgsino, P = a a 2 2 (8.8b) LEP TECVATRON m χ > 35GeV (MSSM * 5) ) 8.6 1) SUSY WIMPS( ) LEP/TEVATRON m χ > 37GeV 2) WIMP χχ t t, b b, WW, ZZ, γγ e. p, d γ, ν, (8.9) BESS, GLAST, AMS, ISS 3) 2 AMANDA * 5) Minimum Super-symmetric extension of Standard Model

13 8 13 WIMPS 4) WIMPS WIMPS 8.15: DM (isothermal) f (v) e v2 /v 2 0 r (r r α ) ρ 0 ρ DM (r) = 1 + r 2 /r0 2 or ρ s (r/r s ) α (1 + r/r s ) 3 α α 0 1 (8.10a) 1 f (v) = (πv 2 0 )3/2 e v2 /v 2 0 f (v) = 4πv2 (πv 2 0 )3/2 e v2 /v 2 0, (v = v ) (8.10b) 3 ρ 0 0.3GeV /cm 3, v 0 220km/s v rms = 2 v 0 = 2km/s (8.10c) 0.3GeV /cm 3 WIMPS 100GeV 1m cm WIMPS 8.7 K U N ( m k ) r k I = 1 2 N k=1 m k r k 2 (8.11)

14 8 14 n (8.12b) di dt = m k r k ṙ k = r k p k (8.12a) d 2 [ I dt 2 = ṙ k p k + r k dp ] k = 2K + r k F k = 2K r k k U (8.12b) dt U(ar 1,ar 2, ) = a n U r k k U(r 1,r 2, ) = nu (8.13) d 2 I dt 2 = 1 di t dt di t dt, < ( ) >= 1 0 t d 2 I = 2K nu (8.14) dt2 Z t 0 dt( ) (8.15) < K >= 1 2 n < U > (8.16) E = K +U (8.17) < K >= n 2 E, < U >= n + 2 n + 2 E (8.18) N T 3 2 kt = 1 2 < m kv 2 k >= < K > = n < U > = n N 2N 2 < u > (8.19) (8.19) n = 1 < K >= 1 < U >= E (8.20) 2 1/2 1/2 M R < u > = 3 5 GmM R = 1 2 < mv2 > (8.21a) < v 2 > =< v 2 r > + < v 2 θ > + < v2 φ >= 3 < v 2 r > (8.21b) M = M virial 5R < v2 r > G (8.21c)

15 8 15 < v 2 r > < v 2 > R G = (M Pl ) 2 = ( GeV ) 2, hc 1 2 m pv 2 = 1KeV, m p = 0.938GeV, hc = 0.2GeV m (8.22) M = 1 2 m pv 2 R = 1 Gm p 2 m pv 2 R hc MPl 2 3M pc(m) = (1KeV ) m p 0.2GeV m ( GeV ) GeV (8.23) 1Mpc = m, M = kg, 1kg = GeV (8.24) M = M

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2 1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a

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