森羅万象2018のコピー

Similar documents
理論懇2014

( ) ,


(Blackbody Radiation) (Stefan-Boltzmann s Law) (Wien s Displacement Law)

The Physics of Atmospheres CAPTER :

総研大恒星進化概要.dvi

GJG160842_O.QXD


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

医系の統計入門第 2 版 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, 第 2 版 1 刷発行時のものです.

橡Taro9-表紙、仕切.PDF

中央大学セミナー.ppt

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

¼§À�ÍýÏÀ – Ê×ÎòÅŻҼ§À�¤È¥¹¥Ô¥ó¤æ¤é¤® - No.7, No.8, No.9

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4

201711grade1ouyou.pdf

1 2 2 (Dielecrics) Maxwell ( ) D H

(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

: , 2.0, 3.0, 2.0, (%) ( 2.

4 1 Ampère 4 2 Ampere 31

I

Part () () Γ Part ,

Hanbury-Brown Twiss (ver. 2.0) van Cittert - Zernike mutual coherence

1 1.1,,,.. (, ),..,. (Fig. 1.1). Macro theory (e.g. Continuum mechanics) Consideration under the simple concept (e.g. ionic radius, bond valence) Stru

(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

Introduction Jones & Palme (2000), Jones & Hood (990), Mueller et al. (988) ρ~3.34g/cm 3, MI~0.39 (<400km) Nakamura et al. (982), Kuskov & Kronrod (99

PDF

Microsoft Word - 章末問題

Note.tex 2008/09/19( )



* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

2 Part A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44, 77, 55, 48 (2) 92, 74, 56, 81, 84, 86, 1, 27,

/ Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiat

meiji_resume_1.PDF

2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n

C el = 3 2 Nk B (2.14) c el = 3k B C el = 3 2 Nk B

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.

Contents 1 Jeans (

数学の基礎訓練I

d > 2 α B(y) y (5.1) s 2 = c z = x d 1+α dx ln u 1 ] 2u ψ(u) c z y 1 d 2 + α c z y t y y t- s 2 2 s 2 > d > 2 T c y T c y = T t c = T c /T 1 (3.

36 th IChO : - 3 ( ) , G O O D L U C K final 1

Outline I. Introduction: II. Pr 2 Ir 2 O 7 Like-charge attraction III.

all.dvi

kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2

³ÎΨÏÀ

磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論

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

磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論



18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α

untitled

I II III IV V

(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a

positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100

7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±

白山羊さんの宿題.PDF

スーパー地球の熱進化と 磁場の寿命 立浪千尋 千秋博紀 井田茂 衛星系形成小研究会 2012 小樽

LLG-R8.Nisus.pdf

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

物性物理学I_2.pptx

t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z

ELECTRONIC IMAGING IN ASTRONOMY Detectors and Instrumentation 5 Instrumentation and detectors

untitled

1: 3.3 1/8000 1/ m m/s v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt kg (


Microsoft Word - 11問題表紙(選択).docx

untitled

太陽系外惑星探査

/02/18

B

TOP URL 1

150518_shin_gakujutsu

2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =

Venkatram and Wyngaard, Lectures on Air Pollution Modeling, m km 6.2 Stull, An Introduction to Boundary Layer Meteorology,

Untitled

u Θ u u u ( λ + ) v Θ v v v ( λ + ) (.) Θ ( λ + ) (.) u + + v (.),, S ( λ + ) uv,, S uv, SH (.8) (.8) S S (.9),

30

ρ(= kg m 3 ), g h P 0 C () [1] 1.3 SI Pa hpa h 100 ( : 100 ) 1m 2 1N 1Pa 1N 1kg 1m s 2 Pa hpa mb hpa 1mm 1mmHg hpa 1mmHg =

. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n

Baker and Schubert (1998) NOTE 1 Baker and Schubert(1998) 1 (subsolar point) 177.4, ( 1). Sp dig subsolar point equator 2.7 dig Np Sun V

A

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

基礎数学I

ポリトロープ、対流と輻射、時間尺度

( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e

系外惑星大気

( )

nm (T = K, p = kP a (1atm( )), 1bar = 10 5 P a = atm) 1 ( ) m / m

001_046_物理化学_解答_責_2刷_Z06.indd

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.

QMII_10.dvi

nsg02-13/ky045059301600033210


H.Haken Synergetics 2nd (1978)

II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re

δf = δn I [ ( FI (N I ) N I ) T,V δn I [ ( FI N I ( ) F N T,V ( ) FII (N N I ) + N I ) ( ) FII T,V N II T,V T,V ] ] = 0 = 0 (8.2) = µ (8.3) G


ρ ( ) sgv + ρwgv γ sv + γ wv γ s + γ w e e γ ρ g s s γ s ( ) + γ w( ) Vs + V Vs + V + e + e + e γ γ sa γ e e n( ) + e γ γ s ( n) + γ wn γ s, γ w γ γ +

Transcription:

PD Stellar Irradiation Mineral Atmosphere Na, K, SiO, O 2, O gas (MgO, Al, AlO, FeO etc ) https://www.nasa.gov/topics/universe/features/rocky_planet.html / (2018.5.9) Magma Ocean

Ito et al. (2015) (HRE)

Size: exoplanets.org 10/8/2017 3000 Planetary Radius [Earth Radii] 10 1 Jupiter Neptune > Earth Mars 500 1000 1500 2000 2500 Radiative Equilibrium Temperature[K] NASA/ESA 0.01 0.1 1 Semi-Major Axis [Astronomical Units (AU)]

Rocky Vapor Atmosphere Rocky planet Volatile-rich Atmosphere Water-rich planet *

2002 Hot Jupiter Charbonneau et al. (2002) etc 2010 Hot Neptune Bean et al. (2010) etc 2016 Hot super-earth Demory et al. (2016) etc (TESS-2017 JWST-2020 ) Volatile-rich Atmospheres TESS (2018 ) or H2O+CO2 :Miller-Ricci & Fortney.2010 http://explorers.gsfc.nasa.gov /ex.html#tess GJ1214b JWST (2020 ) GJ1214b De śert et al. (2011)

HRE: Hot Rocky Exoplanet (Super-Earth) > ~1500K (volatile-free) < 0.1AU HRE Ex. CoRoT-7 b (4.8M, 1.7R, T=2500K) Kepler-78 b(1.7m, 1.2R, T=2600K) HRE

HRE Mineral Atmospheres Schaefer & Fegley, (2009) Na, O, O 2, SiO 10 bar 1500K 10 bar 3000K (Schaefer et al., 2012; Volatile-rich) Thibaut & Kristen (2011) 1D - << Y. Ito, M. Ikoma, H. Kawahara, H. Nagahara, Y. Kawashima & T. - Nakamoto (2015)

Ito et al. (2015) Hot Rocky Exoplanet (HRE < 0.1AU HRE

Pressure P vapor 1D atmospheric model (Ito et al. 2015) G-type star(t*=6000k) Stellar Irradiation Rocky vapor compositions Magma ocean Planetary Irradiation Assumptions - Planetary properties 2R earth, 10M earth, R * =R sun, T * =6000K - Magma ocean surface Volatile-free Bulk Silicate Earth (BSE) (McDonough and Sun 1995) - Gas-melt equilibrium composition MELTS model (Ghiorso & Sack 1995) CEA code (Gordon & McBride 1996) - Hydrostatic equilibrium - Local thermal equilibrium - Radiative equilibrium

dp dz = ρg dτ υ dp = κ υ g = σ υ mg z: ρ g τ σ m ( ): Toon et al., (1989) F υ + τ υ F υ τ υ = 7 4 F + υ 1 4 F υ 2π B υ (τ υ ) = 1 4 F + υ 7 4 F υ + 2π B υ (τ υ ) F υ * (τ υ ) = µ * F υ * (τ υ = 0)exp( τ υ / µ * ) ν 100 F ± F * B μ * : Unsold (1955), Gray (1976) a = (γ R +γ W ) / 4πΔυ D, Δυ D = υ 0 σ (υ ) = i, j π 1/2 e 2 g f i exp( E i / kt) i, j m e cδυ D g l exp( E l / kt) l (1 exp( hυ i, j / kt))voigt(υ υ i, j, a) v, v = (2kT c m )1/2 γ R = 0.22 10 14 / λ[nm] 2,γ W =17 C 2/5 6 v 3/5 N

MELTS & CEA: P vapor (T ground ), χ (T n, P n ) No No σ ν (T n,p n,χ) :(Toon et al., 1989) F n = F ν,n σ ν,χ, P n )dν F n =const Yes : P ground =P vapor (T ground ), χ (T n, P n )=χ n Yes σ ν (T n,p n,χ) No T n =T n +ΔT n T: P ν P vapor χ F σ n : n ground : Database HITRAN2012 : Kurucz(1992) Yes

H, C, N, S, Cl Log(Total Pressure [bar]) 0-1 -2-3 -4-5 -6-7 1500 2000 2500 3000 Temperature [K] Log (Molar fractoin) 0-1 -2-3 -4 1500 2000 2500 3000 Temperature [K] SiO O2 Na K O SiO 2 Mg MgO TiO 2 CrO Fe FeO NaO KO P Na( ), O 2, O, K, SiO etc. 10-7 - 10-1 bar (1500-3000K)

O Fe Na K T=3000K, P= 10-2 bar SiO Si O 2 Fe / Na K /FUV SiO

T eq = T p R /a Teq=1800K Teq=2000K Teq=2300K Teq=2500K Teq=3000K SiO Si + O 10 P[bar] Log P P[bar] -8 10-7 -6 10-8 10-7 10-6 Si Teq=3000K SiO Fe O 2 10-5 SiO O2 10-4 Na K 10-3 O Si -2 10-2 Fe 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 fraction Log Molar fraction K O Na 10-6 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0-8 -5 Teq=1800K Molar fraction SiO Si + O -8-6 -4-2 0 Teq<2000K : () Teq>2300K : SiO FUV SiO

MELTS & CEA: P vapor (T ground ), χ (T n, P n ) No No σ ν (T n,p n,χ) :(Toon et al., 1989) F n = F ν,n σ ν,χ, P n )dν F n =const Yes : P ground =P vapor (T ground ), χ (T n, P n )=χ n Yes σ ν (T n,p n,χ) No T n =T n +ΔT n T: P ν P vapor χ F σ n : n ground : Database HITRAN2012 : Kurucz(1992) Yes

F P (λ) ( L * / L P ) P ε( λ)= L P L * R P R * T 2 F P F * λ ( ) ( λ)

/ Na, K, Fe SiO R * =R sun R p =2R earth =0.02Rsun Teq>2300K : Hot Rocky Exoplanet Na K Fe 4,10,100μm SiO

5m 10h 100pc HRE(Teq=3000K) / R * =R sun R p =2R earth =0.02Rsun Na K SiO SiO Photon noise limit S/ N = N P N * (JWST 2020 ) SiO Na K

3 Teq=2300K [ ] 1 0.1 Hot Rocky Super-Earth / Detectable Mineral Atmosphere [AU] G Teq>2300K :r=0.5% (Howard et al.2012) G :N Gstar =26(d/10pc) 3 dmax(s/n): 5m(JWST) HRE : N = rn [d (S/ N)] 3 70planets 80 HRSE Gstar max

55 Cnc e (8.1Me,2Re,0.015AU) 55 Cnc e (Mp=8.1Me, Rp=2Re, a=0.015 AU, Teq=2700K) 55 Cnc e Water planets region Hot Rocky Exoplanet region Gillon et al.(2012)

55 Cnc e (8.1Me,2Re,0.015AU) 2700K 1300K 3370 K 2240 K (μ=2-7, P>10-3 bar) 1220 K (Demory et al., 2016) (Rp/Rs) 2 ~10% (Tsiaras et al., 2016) [um] ~1Myr

55 Cnc e (8.1Me,2Re,0.015AU) (Demory et al., 2016) (Kite et al.2016) (Tsiaras et al., 2016)

Summary 背景 主星近傍の岩石惑星は 高温であるためミネラル大気を持つ 本研究の結果 1, 大気構造 温度逆転構造 Teq>2300K 2, 二次食スペクトル Na, K, SiO由来の観測可能な特徴 近い将来展望 JWSTによるミネラル大気の検出 観測的課題 大気組成 温度分布の詳細測定 理論的課題 現在 過去 進化 に対する 内部混合 大気循環 大気散逸の影響推定(システム理解)