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1
2 H+He H+He M > 10 M He He Wolf-Rayet
3 Minit = 13 ~ 100 M, Zinit = ~ 0.02 CNO SN 2007bi (Type Ic) progenitor Minit > 100 M, Zinit = WO star? Core collapse Rotating star model
4 Saio, Nomoto, and Kato , 15, 18, 20, 25, 30, 35, 40, 50, 70, 100 M, 0.001, 0.004, 0.01, 0.02 n, H~Br 282 reaclib 2009 (Basel) β-decay rates LM02, FFN, JAEA 2000 Opacity OPAL 1995, etc.
5 Saio, Nomoto, and Kato , 15, 18, 20, 25, 30, 35, 40, 50, 70, 100 M, 0.001, 0.004, 0.01, 0.02 Mass loss rate OB stars Vink et al. (2001) Z 0.85 Red giant branch de Jager et al. (1988) Z 0.5 (e.g. Kudritzki and Puls 2000) Wolf-Rayet stars Nugis & Lamers (2000) Z 0.47 SN 2007bi progenitor
6 Z= O 4 He 16 O 20 Ne H 14 N 12 C Minit = 15M Minit = 35M C 16 O 20 Ne 4 He 14 N Minit = 25M Minit = 100M
7 Z= C 20 Ne 18 O 16 O 14 N 4 He H Minit = 15M Minit = 35M Minit = 25M 16 O 12 C 4 He 14 N 20 Ne Minit = 100M
8 Z M ~35M 40M 50M 70M 100M RG WO WO WO WO RG RG WO WO WO RG RG RG RG WO RG RG RG RG RG RG RG RG RG RG metal poor metal rich Red giant Wolf-Rayet
9 Final Mass (M ) Initial Mass (M ) Z= Z=0.02 He-Core Mass (M ) Initial Mass (M ) mass loss Z ~ mass loss Mwind < 89 M He core metal poor,
10 Wind 12 C, 14 N of 12 C Z= Initial Mass (M ) of 14 N Initial Mass (M ) 12 C M > 40~70 M, Z > wind He core 14 N M > 30~50M wind
11 Wind 16 O, 17 O of 16 O Z= Initial Mass (M ) of 17 O Initial Mass (M ) 16 O M > 50~70 M, Z > wind 17 O M > 20~50M wind
12 IMF Wind Initial mass function (N(M) M ) Minit = 13 ~ 100 M SN yield from Kobayashi et al. (2006) 20 IMF averaged yield SN wind Z IMF averaged yield 12 C 13 C Z 12 C Z > 0.01 wind
13 IMF Wind IMF averaged yield Initial mass function (N(M) M ) M = 13 ~ 100 M SN yield from Kobayashi et al. (2006) N Z IMF averaged yield N Z~0.02 wind 17 O Z~0.02 wind 16 O 15 N 18 O Z 17 O
14 Minit = 13 ~ 100 M, Zinit = ~ 0.02 Minit Zinit Minit Zinit Mass loss Wolf-Rayet stars Red giant branch Minit Zinit mass loss Mwind ~ 89 M (Mini = 100 M, Z = 0.02) Initial mass function wind 12 C 14 N 17 O Z > 0.01
15 SN 2007bi SN 2007bi (Type Ic) (Gal-Yam et al. 2009) 2007 April 6.5 M( 56 Ni) > 3 M Na, Mg, Ca, Fe spectra Mcore ~ 100 M Absolute MR (mag) Pair-instability supernova model
16 SN 2007bi progenitor host galaxy metallicity 12+log(O/H)=8.15±0.15 Z ~ 0.31 Z (Young et al. 2010) Progenitor CO core (H, He ) (Moriya et al. 2010) Pair-instability Mej ~ 120 M Ekin ~ ergs M( 56 Ni) = 9.8 M Core collapse M ~ 43 M Ekin ~ ergs M( 56 Ni) = 6.1 M Progenitor
17 M > 100 M Z = 0.004, M > 100 M massive star Wolf-Rayet star mass loss rate metallicity Nugis and Lamers (2000) Z 0.47 WN, WC: C Vink and Koter (2005) Zinit 0.86 WN Zinit WC Red giant mass loss rate metallicity Progenitor mass loss rate
18 M > 100 M Minit = 100, 140, 200 M Mass loss rate OB stars Vink et al. (2001) (A) Z 0.85 or (B) Z Red giant branch de Jager et al. (1988) (A) Z 0.85 or (B) Z 0.64 or (C) Z 0.5 Wolf-Rayet stars Nugis and Lamers (2000) (A) Zinit 0.86, Zinit or (B) Z 0.47 (OB, RGB, WR) = (B, B, A) for Case 1 = (B, B, B) for Case 2 = (A, A, A) for Case 3 = (A, C, B) for Case 4
19 Wolf-Rayet Wolf-Rayet log10teff > 4.05 Xs < 0.4 WNL WNE WC WO Xs > Xs <, Ns(N) > Ns(C) Ns(C) > Ns(N), Ns(C+O) < Ns(He) Ns(C+O) > Ns(He) from Meynet et al. (2009)
20 M = 100 M 16 O 12 C 4 He 16 O 1: BBA 20 Ne 14 N 2: BBB WNL 1 H WO 18 O Mf = 43.3M Mf = 38.9M 3: AAA 4: ACB Mf = 44.2M Mf = 38.8M RGB WO 12 C 20 Ne He 14 N
21 M = 140 M 16 O 12 C 1: BBA 2: BBB Mf = 52.6M 10 Mf = 33.8M WC -3 4 He WO 20 Ne N 16 O 12 C 20 Ne 3: AAA 4: ACB Mf = 54.8M 10 Mf = 33.9M WC -3 WO He
22 M > 100 M M f / M : AAA 4: ACB M init / M 1: BBA 2: BBB Wolf-Rayet star mass loss rate Nugis and Lamers (2000) (B) Z 0.47 WO star SN Ic progenitor SN 2007bi progenitor 100 M < Minit < 140 M MCO core ~ 39, 54, 78 M for Minit = 100, 140, 200M
23 SN 2007bi (Type Ic) progenitor Zinit = 0.004, Minit > 100 M Mass loss rate Wolf-Rayet mass loss rate Mass loss rate Mass loss rate SN 2007bi progenitor 100 M < Minit < 140 M Core collapse explosion Mf ~ < 40 M, WO stars Mf ~ > 40 M, RGB, WNL, WC
24 Core collapse Si Implicit
25 28 Si 16 O 20 Ne 12 C 4 He 14 N 1 H Minit = 15 M, Zinit = 0.02
26 Rotating star model Mr MP P MP rp MP LP MP = = ln T ln P = GMP 4πrP 4 1 4πrP 2 ρ fp ft min( ad, rad ) fp = εnucl - ε ν + εgrav rp = 3 ( 4π V P ) 1/3 fp = 4πr P 4 1 GMPSP <g -1 > ft = ( 4πr P 2 1 <g -1 > <g> SP ) 2 <g>:
27 Rotating star model ψ = GMP r 4π P 2(cosθ) 3r 3 r0 ρr0 6 0 MP Ω 2 dr Ω 2 r 2 sin 2 θ 5+η2(r0 ) 2+η2(r0 ) r(r0,θ) = r0(1-ap2(cosθ)) A = Ω 2 r0 3 3GM P 4π VP = r0 3 (1+ A 2 - A 3 ) SP = 4πr0 2 (1+ A 2 ) 5 rp = 3 ( 4π V P 5 2+η2(r0) ) 1/3 η2(r0): 35 2 r0 A
28 Rotating star model Xn t = MP Ω t = (4πrP 2 ρ) 2 D X n MP + { } ( Xn ) nucl D: 1 {(4πrP 2 ρ) 2 ν Ω } 2Ω ( r ) ln i i MP MP r P t M P 2 1 ln rp i: specific angular moment, ν: turbulent viscosity D, ν t
SN 2007bi Yoshida, T. & Umeda, H., MNRAS 412, L78-L82 (2011)
SN 2007bi Yoshida, T. & Umeda, H., MNRAS 412, L78-L82 (2011) SN 2007bi SN 2007bi (Gal-Yam et al. 2009) 2007 4 6.5 Type Ic subluminous dwarf galaxy Z ~ (0.2-0.4) Z (Young et al. 2010) 36 (Young et al. 2010)
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
Gmech08.dvi
51 5 5.1 5.1.1 P r P z θ P P P z e r e, z ) r, θ, ) 5.1 z r e θ,, z r, θ, = r sin θ cos = r sin θ sin 5.1) e θ e z = r cos θ r, θ, 5.1: 0 r
2000年度『数学展望 I』講義録
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85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V
2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP
1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP
18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
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r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
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(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
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199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
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#A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/
超新星残骸Cassiopeia a と 非球対称爆発
物理学専攻 松尾康秀 宇宙物理理論 指導教員 : 橋本正章 < 超新星残骸 > 星の外層が超新星爆発により吹き飛ばされ 爆発の際の衝撃波によって周囲の物質 ( 星周物質 ) を加熱し 輝いている天体 かに星雲 Kepler Cas A http://www.spacetelescope.o rg/images/large/heic0515a.j pg http://apod.nasa.gov/apod/i
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19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional
19 σ = P/A o σ B Maximum tensile strength σ 0. 0.% 0.% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional limit ε p = 0.% ε e = σ 0. /E plastic strain ε = ε e
1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π
![1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π](/thumbs/101/149329485.jpg "1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π")
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総研大恒星進化概要.dvi
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MRR Physical Basis( 1.8.4) METEK MRR 1 MRR 1.1 MRR 24GHz FM-CW(frequency module continuous wave) 30 r+ r f+ f 1.2 1 4 MRR 24GHz 1.3 50mW 1 rf- (waveguide) (horn) 60cm ( monostatic radar) (continuous wave)
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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](/thumbs/92/109118076.jpg "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")
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Gmech08.dvi
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
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Formation process of regular satellites on the circumplanetary disk Hidetaka Okada 22060172 Department of Earth Sciences, Undergraduate school of Science, Hokkaido University Planetary and Space Group
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[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt
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3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]
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