Hidetaka Okada 21372 Department of Cosmosciences, Graduate School of Science, Hokkaido University 212 2 28
, N 2.,.,.,. N 2, Ar. Ar, N 2, NH 3 N 2.. Kuramoto and Matsui (1994),,., 1 5, 5 K,,., Ar, Ar.,, (Canup and Ward, 22, 26).,,,,., H 2 He, H 2, ( ) ( ) ( ).,
2.,.,.,,,. 3 K,,,.,. 4 W/m 2, 4.,.,.,.,., H 2, He, H 2 O, NH 3. NH 3,., Ar.,, NH 3, N 2 (Atreya et al., 1978). N 2, Ar.
i 1 1 1.1......................... 1 1.2....................... 2 1.3........ 2 1.4................................. 3 2 5 2.1..................................... 5 2.2............................... 5 2.2.1......................... 5 2.2.2......................... 6 2.3..................... 6 2.3.1.................................. 6 2.3.2..................... 8 2.4......................... 12 2.5...................... 12
ii 2.6............................... 16 3 17 3.1............................ 17 3.2............................... 18 3.3............................... 2 4 23 4.1......................... 23 4.2....................... 23 4.3......................... 25 5 27 6 3 6.1 1,.................... 3 6.1.1............................. 3 6.1.2............................ 32
タイタンの原始大気 1 背景と目的 1 背景と目的 1 1.1 タイタンの大気と内部構造 タイタンは 1655 年にホイヘンスによって発見された土星の衛星で, その直径は約 515 km と, 木星の衛星のガニメデに次いで太陽系で二番目に大きい. タイタンの最大の特徴 は, N2 を主成分とする非常に厚い大気をもっていることである. 地表面での大気圧は地球 のおよそ 1.5 倍であり, その主成分は N2 と CH4 である (地表面で N2 95, CH4 5, Niemann et al., 25). これほど厚い大気を持っている衛星は太陽系のなかではタイタン だけである. またカッシーニにより得られた データによると, 慣性能率因子 (慣 性能率を天体の質量と半径の二乗の 積で割ったもの) は.342 であった (Iess et al., 21). この値は, 内部が 完全に分化し金属コアをもつガニメ デの.311 (Anderson, 1996) よりも 大きいが, 一様な球体の慣性能率因 子の値 (.4) よりも小さいため, タイ タンの内部は完全ではないが, 部分 的に分化していると考えられている (図 1). さらにタイタンの自転に関す る観測から液体の海の存在も示唆さ 図1 タイタンの内部構造の想像図 (NASA) れており (Baland et al., 211), タイ タンはその熱史の中で氷が融解する温度を経験したと考えられる. 212 年 2 月 28 日 (岡田英誉)
1 2 1.2 N 2., H 2, He.,.,.,,., H 2, He,.,.,, (Matsui and Abe, 1986).,,.,. N 2,.,, N 2 Ar. 36 Ar/N 2 2.8 1 7 (Niemann, 25), ( 1 1-1 2 ) (Lunine et al., 29), Ar., N 2, N 2 Ar., NH 3 N 2. (Atreya et al., 1978),, (> 15 K). 1.3,,.
1 3,,,. Kuramoto and Matsui (1994),,,.,., 1 5, 5 K.,,., Ar, Ar.,, (Canup and Ward, 22, 26).,..,.,.,. 1.4,,,,,., Canup and Ward (22, 26),.,.,.,
1 4.
2 5 2. 2.1.,. H 2, He (H 2 75 wt, He 25 wt ),..,.,, 3.,. 2.2 2.2.1, (Lunine and Stevenson, 1982). [ 4 dt dr = 3 πg ρr 1 + L vm vap e (P e)r B T C pg eɛ 1 + C pg (P e) ] ( ) 1 + eɛ P e [ C pw L v T + L2 v M rvp (P e)r B T 2 ]. (1), ρ, L v, M rv, C pg, C pw. e,,
2 6 (Weast,1967). 2214 2+(8.771 e = 1.33 1 T ). (2),,. P r = ρ gasg(r) (3) ρ gas.. M gas = P nebm neb + em vap P neb + e, P neb, M neb. (4) 2.2.2,.,,.,,. (3). 2.3 2.3.1,,,.,,
2 7,.,,, κ gas. ( ) 2 ( ) ( ) 1ρH2 1ρH2 1ρHe κ gas ρ gas = α H2 H 2 + α H2He + κ H2 Oρ H2 O (5) µm H2 n µm H2 n m He n, α H2 H 2, α H2 H e Borysow(1985, 1992, 22).,,. 2 Borysow(22) α H2 H 2, α H2 H e. α H2 H2, α H2 H e. α H2 H 2 = 1.328 1 6 + 3.657 1 8 T 1.194 1 1 T 2 + 1.211 1 13 T 3 α H2 He = 1.817 1 8 + 7.95 1 1 T 2.3862 1 11 T 2 + 2.331 1 14 T 3 2.5e-6 alpha coeficient [cm-1 amagat-1] 2e-6 1.5e-6 1e-6 5e-7 5 1 15 2 25 3 35 4 Temperature [K] 2 Borysow(1985), Borysow(1992).. α H2 H 2, α H2 H e.
2 8 2.3.2,,.,,. ν I ν, B ν (T ),,. di ν = κ ν ρ gas (I ν B ν )ds (6) ds, κ ν., r up,,. r up, θ. xy, (,1). (sin θ, cos θ). (, r up )., s (, r up ) + s(sin θ, cos θ). r s. r = (s + r up cos θ) 2 + rup 2 sin 2 θ s = r up cos θ ± r 2 rup 2 sin 2 θ r ds = ± dr r 2 rup 2 sin 2 θ r min = r up sin θ R S,.,,., r min r s (sin θ r S /r up ),
2 9 τ up, I ν,up. RS r τ up = κ ν ρ gas dr r up r 2 rup 2 sin 2 θ I ν,up (r, θ) = B ν (T s )e τ up + τup B ν e τ dτ, r min R S (sin θ R S /r up ), τ up = rmin r κ ν ρ gas dr + r 2 rup 2 sin 2 θ I ν,up (r, θ) = B ν (T )e τ up + rup r κ ν ρ gas dr r min r 2 rup 2 sin 2 θ τup B ν e τ dτ, T s. T, T Hill.. B ν = σt 4 /π, ν. r min R S (sin θ R S /r up ), RS r τ up = κ ν ρ gas dr (7) r up r 2 rup 2 sin 2 θ I up (r, θ) = σt s 4 τup π e τ up + σt 4 (r) e τ dτ (8) π r min R S (sin θ R S /r up ), rmin τ up = r κ ν ρ gas dr + r 2 rup 2 sin 2 θ I up (r, θ) = σt 4 τup π e τ up + rup,. r κ ν ρ gas dr r min r 2 rup 2 sin 2 θ σt 4 (r) e τ dτ π π/2 F up = 2π I up sin θ cos θdθ (9)
2 1. r up τ down, I down, F down. τ down = rup I down (r, θ) = σt 4 τup π e τ down + r κ ν ρ gas dr (1) r 2 rup 2 sin 2 θ σt 4 (r) e τ τ down dτ (11) π π/2 F down = 2π I down sin θ cos θdθ (12), F net. F net = F up F down (13), (τ 1),,., τ > 1. (6), I ν (s) = I ν (s )e τ + ds = τ dz cos θ. 2 B ν τ, B ν (τ ) B ν (τ = τ) + db dτ (τ τ) B ν e τ τ dτ (14)
2 11 e τ, I ν (s), B ν db ν dτ τ = B ν [ e τ τ ] τ B ν (τ = τ)e τ τ dτ + db dτ + db ν dτ [ = B ν B ν e τ + τe τ db ν dτ τ (τ τ)e τ τ ] τ (τ τ)e τ τ dτ db ν dτ db [ ] ν dτ e τ τ τ = B ν Bνe τ + db ν dτ ( τe τ 1 + e τ ) I ν = B ν (T ) cos θ db ν (T ) κρ gas dz. F ν,net = I ν cos θdω τ e τ τ dτ (15) (16) =, 2π π = 2π π I ν cos θ sin θdθdφ B ν cos θ sin θdθ = π 2 [ B ν cos 2θ] π 2π B ν 3κρ gas dz = 4π db ν 3κρ gas dz F net = = 4π 3 2π db ν κρ gas dz π [ cos 3 θ ] 1 1 cos 2 θ sin θdθ (17) F ν dν 1 db ν dν κρ gas dz (18) κ,,., 1 κ R ρ gas = 1 κρ F net = 16σT 3 3ρκ R db ν dt dν dbν dt dν (19) dt dz (2)
2 12 dbν dt dν = 4σT 3 π (21) 2.4 m. U = GM Sm r R S, (22) m = 4/3πr 3 ρ.,, E acc. E acc = GM s r 4 3 πr3 ρ 1 4πr 2 τ acc = GρM s 3τ acc (22) 2.5,.,,,., T disk. σ SB Tdisk 4 = 1 [( 1 + 3 2 16 τ R + 1 ) 2τ P E ν + ( 1 + 1 ) ( E 2τ in + P ] E P ) + σ SB Tneb 4, σ SB, τ R, τ P, T neb. E ν, E in, E P,,,. E ν = 9 4 σ GνΩ 2, E in = GM P 2r F πrc 2, E P = 9 ( ) 2 4 σ SBTP 4 RP ( cs ) r rω (23) (24)
2 13, r, G, Ω, M P, F, r c, T P, R P, c s (= γr B T disk /µ mol, γ γ = 1.4), σ G. ν α (Shakura and Sunyaev, 1973), ν = αc s H = αc 2 s/ω. (25), α, H. σ G, 2.,,. σ G t = 1 Ṁ 2πr r + F in = (26), Ṁ r, Ṁ = 2πrσ G v r. v r., g vis. g vis Ṁ. g vis r = Ṁ h r. (27) g vis = 3πσ G hν (28), h, h = r 2 Ω. (26), (27),. σ G = 4F 15πν [ 5 4 ( rc r d ) 2 1 ( ) ] 2 r 4 r c (29), r d. σ G, P disk, ρ disk. P disk = ρ disk µ mol R B T disk ρ disk = σ G 2H.
2 14 3 (Canup and Ward, 22) F,., α (1 4 α 1 2 )., D ( 2.11 R saturn, R saturn ) F, α. α 5. 1 3, 1 3, 1 4 3, F., (r = 2.273R saturn ),., H 2 O, 99 wt, : 1 wt. 4, 5,. F, α.,.,. 4, 5 5-9 K,.1 -.1 Pa.,,., 5 K,.1 Pa 1 Pa.
2 15 35 3 Disk temperature [K] 25 2 15 1 5 5 1 15 2 25 3 Distance from Saturn [Saturn radius] 4.. T P = 4K (Burrows et al., 1997), κ P (= τ P /σ G ) κ R (= τ R /σ G ).1 m 2 /kg (Semenov, 23). F, α,,,, α = 5 1 3 (F = 3.5 1 1 M saturn ), 1 3 (4.1 1 1 M saturn ), 1 4 (1.9 1 1 M saturn ). 1 1 1 Disk pressure [Pa] 1.1.1.1.1 5 5 1 15 2 25 3 Distance from Saturn [Saturn radius]. 4.
2 16 2.6.,. 1 ρ 1.88 1 3 [kg m 3 ] C pn H-He 1.2 1 4 [J kg 1 K 1 ] L v 2.26 1 6 [J kg 1 ] C pv 2.5 1 3 [J kg 1 K 1 ] C pw 4.3 1 3 [J kg 1 K 1 ] κ neb 1 4 ρ neb [m 2 kg 1 ] κ vap 1 5 e [m 2 kg 1 ] M neb 2.5 1 3 [kg mol 1 ]
3 17 3 3.1, ( ), ( 6).,,.,,.,,., 5 K,. 1e+25 1e+2 1e+15 Optical depth 1e+1 1 1 1e-5 1e-1 5 1 15 2 25 3 Disk Temperature [K] 6..,,,, 1 Pa, 1 Pa, 1 Pa,.1 Pa.
3 18 3.2 7, 8, 9 1 Pa,,..,,,.,,.,,,. 22 Distance from center of satellite [satellite radius] 2 18 16 14 12 1 8 6 4 2 5 1 15 2 25 3 Temperature [K] 7... 1 Pa.,,,,,, 1 Pa
3 19 22 Distance from center of satellite [satellite radius] 2 18 16 14 12 1 8 6 4 2 1 1 1 1 1 1 1e+6 1e+7 Pressure [Pa] 8. 7 11 Distance from center of satellite [satellite radius] 1 9 8 7 6 5 4 3 2 1 1e-6 1e-5.1.1.1.1 1 1 1 1 1 Optical depth 9. 7
3 2 3.3 1..,,.,.,.,,,. 33 3 Temperature of satellite surface [K] 27 24 21 18 15 12 9 6 3 5 1 15 2 height of tropopause [satellite radius] 1...,,,, 1 Pa, 1 Pa, 1 Pa,.1 Pa. 11 1 Pa..,.,.,,.,
3 21.,,. 22 Distance from centr of satellite [satellite radius 2 18 16 14 12 1 8 6 4 2 11.1.1 1 1 1 1 Net radiation flux [W m-2]. 7 12..,,.,,,., 1,, 2 K., 1 Pa.,,,., 1 Pa 4 W/m 2, 4.,., 1. Ar. Ar, Ar.
3 22 12 Net radiation flux from upper of atmosphere [W m-2] 5 4 3 2 1 5 1 15 2 25 3 Suraface Temperature [K].,. 1.,., 4, 5, 1.
4 23 4 4.1,,,.,,..,.,,. 6,.,. 4.2, F, α., (9.384 R Jupiter, R Jupiter ). 13, 14,.,.,, 12 K,.1 Pa - 1 Pa.
4 24 35 3 Disk temperature [K] 25 2 15 1 5 5 1 15 2 25 3 Distance from Jupiter [Jupiter radius] 13.. T P = 5K (Burrows et al., 1997), 4. 1 1 Disk pressure [Pa] 1 1 1.1.1 14 5 1 15 2 25 3 Distance from Jupiter [Jupiter radius]. 13.
4 25 4.3 15., 3 K. 35 Temperature of satellite surface [K] 3 25 2 15 1 5 2 4 6 8 1 12 height of tropopause [satellite radius] 15... 1. 16.,.,.,.,.,,,,.
4 26,. Net radiation flux from upper of atmosphere [W m-2] 8 7 6 5 4 3 2 1 15 2 25 3 Suraface Temperature [K] 16.., 3, 5, 1. 12.
5 27 5,,.,.,,,,.,,,., 1, 2 K., 1 Pa.,., 1 Pa, 5 K 4 W/m 2, 4.,,..,., H 2, He, H 2 O, NH 3. NH 3,.,, Kuramoto and Matsui (1994), Ar.,, NH 3, N 2 (Atreya et al., 1978). N 2, Ar.
5 28,.,..,.
5 29,..,,.,..,,,.,.,,,,,..,,,,,.,,..,,.
6 3 6 6.1 1, 6.1.1 Nakamoto and Nakagawa (1994)..,,,, T s. σ SB Ts 4 = 1 ( E ν + E 2 s + E ) P + σ SB Tcloud 4 (3), Ėν, (2). E ν,, h E ν = 2 F (z)dz = 32σ SB (Tm 4 Ts 4 ) 3τ R T 4 s = T 4 m 3τ R 32σ SB E ν, σ SB T 4 m = 1 2 ( ) 3 16 τ RE ν + E ν + E s + E P + σ SB Tcloud 4 (31)., dτ = κ ν ρds, ds = dz/ cos θ,, cos θ di ν dτ ν = I ν + B ν. I ν (τ ν, θ) = I ν (, θ)e τ ν/ cos θ + (1 e τ ν/ cos θ )B ν.
6 31 τ ν / cos θ 1,, ( I ν (τ ν, θ) 1 τ ν cos θ ) I ν (, ν) + I. I(τ ν, θ) = = I(, θ) I ν (τ ν, θ)dν [( 1 τ ν cos θ ) I ν (, θ) + τ ν cos θ I ν(, θ)dν + τ ν cos θ B ν(t m ). τ ] ν cos θ B ν(t m ) dν τ ν cos θ B ν(t m )dν (32) z = h (τ ν = ) T cloud, I(, θ) = B ν (T cloud )dν = σ SB π T 4 cloud., (τ P = κ P σ g ), τ ν cos θ I ν(, ν)dν = τ ν cos θ B ν(t cloud )dν = τ ν cos θ B ν(t m )dν = τ P σ SB cos θ π T m 4 τ P σ SB cos θ π T cloud 4 τ P = τ ν B ν (T )dν B ν (T )dν (32), I ν (h, θ) = ( 1 τ ) P σt 4 cloud cos θ π + τ P σtm 4 cos θ π. z = h, F + = I cos θdω π/2 = 2π I(h, θ) cos θ sin θdθ dω = sin θdθdφ = 2π sin θdθ
6 32, π/2 F + = 2π = σt 4 cloud = σt 4 cloud [ (cos θ τ p ) σ π T 4 cloud + τ p σ π/2 sin 2θdθ 2τ p σt 4 cloud [ 1 cos 2θ 2 ] π/2 = σt 4 cloud 2τ p σt 4 cloud + 2τ p σt 4 m π T 4 m π/2 ] sin θdθ sin θdθ + 2τ p σt 4 m π/2 + 2τ p σtcloud 4 [cos θ] π/2 2τ p σtm 4 [cos θ] π/2 sin θdθ z = h F (h) = σt 4 cloud,, z = h F (h) = 2τ p σ(t 4 m T 4 cloud)., 2F (h) = Ėν + Ės σ SB T 4 m = 4τ p σ SB (T 4 m T 4 cloud) = Ėν + Ės 1 ( T 4 4τ p σ m T 4 ) cloud + σsb Tcloud 4 (33) SB (31), (33), σ SB T 4 m = 1 [( 1 + 3 2 16 τ R + 1 ) ( Ė ν + 1 + 1 ) ( E s + 2τ p 2τ ) ] E J + σ SB Tcloud 4 (34) p 6.1.2, (26), (27),. g vis (r = r P ) (r = r d ) (g vis,d = g vis,p = ). r c < r < r d,, F in =. (26), Ṁ r (Ṁ = Ṁ = const). (27) r c r d, Ṁ (h h d ) = (g vis g vis,d ) = g vis. (35)
6 33 r < r c. (27) hdṁ/dr,, Ṁdh/dr = d(ṁh)/dr hṁ(r) + g(r) = 4 5 πf in(r 2 ch c r 2 ph p ) + Ṁph p 4 5 πf inr 2 ph p. (36), h c = r c 2 Ω c, h d = r d 2 Ω d, r P. r = r c., Ṁ = Ṁ, r = r c, h c Ṁ + Ṁ(h d h c ) = 4 5 πr c 2 h c F in + Ṁph p 4 5 πf inr p 2 h p, (37) Ṁ h d Ṁph p = 4 5 πf in(r c 2 h c r p 2 h p ). (38),,,., Ṁp, r d Ṁ,., (38), (39), Ṁp + Ṁ = Ṁ πf inr p 2. (39) Ṁ h d (πf in r c 2 πf in r p 2 + Ṁ)h p = 4 5 πf in(r c 2 h c r p 2 h p ). (4), h p = r p 2 Ω p,, Ω d =, GM GM r 3 d, Ω c = r 3 c, Ω p = GM r 3 p, Ṁ (r 1/2 d r 1/2 p ) = πf in r 2 c r 1/2 p + 1 5 πf inr 5/2 p + 5 4 πf inr 5/2 c, (41) [ ( ) 1/2 2 4 rc Ṁ = πf in r c + 1 ( ) ] [ 2 (rd ) ] 1/2 1 rp 1 1. (42) 5 5 r p r c r p Ṁ(r > r c ) = Ṁ, = πf in r c 2 [ 4 5 ( rc r p ) 1/2 + 1 5 ( rp r c ) ] [ 2 (rd ) ] 1/2 1 1 1. r p (43) rc Ṁ(r < r c) = 2πrF in dr Ṁ, (44) r [ ( ) ] 2 2 r = πf in r c 1 (4/5)(r c/r p ) 1/2 + (1/5)(r p /r c ) 2 1.(45) (r d /r p ) 1/2 1 r c
6 34,,, (R p /r c ) 2 1, (r d /R p ) 1/2 1, [ 4 Ṁ(r > r c ) = Ṁ Ṁ 5 [ ( r Ṁ(r < r c ) Ṁ 1,. ( rc r c r d ) 1/2 ] ) 2 4 5, (46) ( rc r d ) 1/2 ]. (47) (r > r c ), (r < r c ), [ σ G (r) 4Ṁ rc 15πν r σ G (r) 4Ṁ 15πν rc r d ]. (48) [ 5 4 rc 1 ( ) ] 2 r. (49) r d 4 r c
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