Hidetaka Okada Department of Cosmosciences, Graduate School of Science, Hokkaido University

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1 Hidetaka Okada Department of Cosmosciences, Graduate School of Science, Hokkaido University

2 , 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, ( ) ( ) ( ).,

3 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.

4 i

5 ii ,

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.

6 タイタンの原始大気 1 背景と目的 1 背景と目的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)

7 N 2., H 2, He.,.,.,,., H 2, He,.,.,, (Matsui and Abe, 1986).,,.,. N 2,.,, N 2 Ar. 36 Ar/N (Niemann, 25), ( ) (Lunine et al., 29), Ar., N 2, N 2 Ar., NH 3 N 2. (Atreya et al., 1978),, (> 15 K). 1.3,,.

8 1 3,,,. Kuramoto and Matsui (1994),,,.,., 1 5, 5 K.,,., Ar, Ar.,, (Canup and Ward, 22, 26).,..,.,.,. 1.4,,,,,., Canup and Ward (22, 26),.,.,.,

9 1 4.

10 ,. H 2, He (H 2 75 wt, He 25 wt ),..,.,, 3., , (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,,

11 2 6 (Weast,1967) (8.771 e = 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) ,,,.,,

12 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 = T T T 3 α H2 He = T T T 3 2.5e-6 alpha coeficient [cm-1 amagat-1] 2e-6 1.5e-6 1e-6 5e Temperature [K] 2 Borysow(1985), Borysow(1992).. α H2 H 2, α H2 H e.

13 ,,.,,. 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 ),

14 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)

15 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)

16 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)

17 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 [( τ R + 1 ) 2τ P E ν + ( ) ( 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)

18 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.

19 (Canup and Ward, 22) F,., α (1 4 α 1 2 )., D ( 2.11 R saturn, R saturn ) F, α. α , 1 3, 1 4 3, F., (r = 2.273R saturn ),., H 2 O, 99 wt, : 1 wt. 4, 5,. F, α.,.,. 4, K, Pa.,,., 5 K,.1 Pa 1 Pa.

20 Disk temperature [K] 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 = (F = M saturn ), 1 3 ( M saturn ), 1 4 ( M saturn ) Disk pressure [Pa] Distance from Saturn [Saturn radius]. 4.

21 ,. 1 ρ [kg m 3 ] C pn H-He [J kg 1 K 1 ] L v [J kg 1 ] C pv [J kg 1 K 1 ] C pw [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 [kg mol 1 ]

22 , ( ), ( 6).,,.,,.,,., 5 K,. 1e+25 1e+2 1e+15 Optical depth 1e e-5 1e Disk Temperature [K] 6..,,,, 1 Pa, 1 Pa, 1 Pa,.1 Pa.

23 , 8, 9 1 Pa,,..,,,.,,.,,,. 22 Distance from center of satellite [satellite radius] Temperature [K] Pa.,,,,,, 1 Pa

24 Distance from center of satellite [satellite radius] e+6 1e+7 Pressure [Pa] Distance from center of satellite [satellite radius] e-6 1e Optical depth 9. 7

25 ,,.,.,.,,, Temperature of satellite surface [K] height of tropopause [satellite radius] 1...,,,, 1 Pa, 1 Pa, 1 Pa,.1 Pa Pa..,.,.,,.,

26 3 21.,,. 22 Distance from centr of satellite [satellite radius Net radiation flux [W m-2] ,,.,,,., 1,, 2 K., 1 Pa.,,,., 1 Pa 4 W/m 2, 4.,., 1. Ar. Ar, Ar.

27 Net radiation flux from upper of atmosphere [W m-2] Suraface Temperature [K].,. 1.,., 4, 5, 1.

28 ,,,.,,..,.,,. 6,.,. 4.2, F, α., (9.384 R Jupiter, R Jupiter ). 13, 14,.,.,, 12 K,.1 Pa - 1 Pa.

29 Disk temperature [K] Distance from Jupiter [Jupiter radius] 13.. T P = 5K (Burrows et al., 1997), Disk pressure [Pa] Distance from Jupiter [Jupiter radius]. 13.

30 , 3 K. 35 Temperature of satellite surface [K] height of tropopause [satellite radius] ,.,.,.,.,,,,.

31 4 26,. Net radiation flux from upper of atmosphere [W m-2] Suraface Temperature [K] 16.., 3, 5,

32 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.

33 5 28,.,..,.

34 5 29,..,,.,..,,,.,.,,,,,..,,,,,.,,..,,.

35 , 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.

36 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

37 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 [( τ R + 1 ) ( Ė ν ) ( 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)

38 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 πf inr 5/2 p 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/ ( rp r c ) ] [ 2 (rd ) ] 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

39 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

40 6 35 Anderson et al., 1996, Gravitational constraints on the internal structure of Ganymede, Nature, Volume 384, Issue 669, p Baland et al., 211, Titan s obliquity as evidence of a subsurface ocean?, Astronomy and Astrophysics, Volume 53, id.a141 Borysow et al., 1985, Modeling of pressure-induced far-infrared absorption spectra. Molecular hydrogen pairs Astrophysical Journal, Volume 296, p Borysow et al., 1992, New model of collision-induced infrared absorption spectra of H2-He pairs in the micrometer region at temperatures from 2 to 3K: An update, Icarus, Volume 96, p Canup, Robin M., Ward, William R., 22, Formation of the Galilean Satellites: Conditions of Accretion., The Astronomical Journal, Volume 124, Issue 6, p Canup, Robin M., Ward, William R., 26, A common mass scaling for satellite systems of gaseous planets., Nature, Volume 441, Issue 795, p Gautier and Raulin, 1997, Chemical Composition of Titan s Atmosphere, Huygens: Science, Payload and Mission, Proceedings of an ESA conference. Edited by A. Wilson., p. 359 Houghton, 1977, The Physics of Atmosphere, Cambridge University Press, New York Kuramoto and Matsui, 1994, Formation of a hot proto-atmosphere on the accreting giant icy satellite: Implications for the origin and evolution of Titan, Ganymede, and Callisto, Journal of Geophysical Research, Volume 99, Nomber E1, p

41 6 36 Luciano et al., 21, Gravity Field, Shape, and Moment of Inertia of Titan, Science, Volume 327, p Lunine and Stevenson, 1982, Formation of the Galilean satellitres in a gaseous nebula, Icarus, Volume 52, p Lunine et al., 29, Titan from Cassini-Huygens Mizuno, 198, Formation of the Giant Planets, Progress of Theoretical Phydics, Volume 64, Nomber 2, p Mosqueira, Ignacio., Estrada, Paul R., 23, Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites. Icarus, Volume 163, Issue 1, p Niemann et al., 25, The abundances of constituents of Titan s atmosphere from the GCMS instrument on the Huygens probe, Nature, Volume 438, issue 769, p Sohl et al., 22, Implications from Galileo Observations on the Interior Structure and Chemistry of the Galilean Satellites, Icarus, Volume 157, issue, 1, p Semenov et al., 23, Rosseland and Planck mean opacities for protoplanetary discs, Astronomy and Astrophysics, Volume 41, p Sekine et al., 211, Replacement and late formation of atmospheric N 2 on undifferentiated Titan by impacts, Nature Geoscience Shakura, N. I., Sunyaev, R. A., 1973,Black holes in binary systems. Observational appearance. Astron. Astrophys., Volume 24, p Weast, 1967, Handbook of Chemistory and Physics, 48th ed. Chemical Rubber Co., Cleveland., 27,..

Formation process of regular satellites on the circumplanetary disk Hidetaka Okada Department of Earth Sciences, Undergraduate school of Scie

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