R J Rutten Radiation transfer in stellar atmospheres
- Slides: 21
R. J. Rutten ‘Radiation transfer in stellar atmospheres ’ 2. 6 NLTE 2011. 05. 20 Tetsu Anan
2 non-LTE • Non-local thermodynamical equilibrium • ここでは、 ψ: 自然放射の emission 確立分布 Χ : 誘導放射の profile shape φ : extinction profile – Statistical equilibrium ○ – Maxwell distribution ○ – Complete redistribution (Χν=ψν=φν) ○ – Population ≠ local Saha-Boltzmann equilibrium
2. 6. 2 NLTE descriptions 5 Departure coefficients n. LTE : Saha-Boltzmann value Boltzmann distribution NLTEの原因となるいろいろな影響を 丸め込んで表す 定義が定まってないから毎回定義に注意必要 Saha-Boltzmann distribution Bound-bound のsource function、extinction Bound-free のsource function、extinction、emission、 free-free のsource function、extinction、emission をこれから紹介する
2. 6. 2 NLTE descriptions 6 Bound-bound source function ψ: 自然放射の emission 確立分布 Χ : 誘導放射の profile shape φ : extinction profile bl、bu Boltzman distribution Complete redistribution (Χν=ψν=φν )のとき、 Wien regime ( (bl/bu)exp(hν/k. T) >>1 )のとき、 Planck関数
2. 6. 2 NLTE descriptions Bound-bound extinction 7 flu : classical dimensionless oscillator strength αlν= bl、bu Boltzman distribution (2. 65) 散乱断面積表記 (2. 66) Complete redistribution (Χν=ψν=φν )、Wien regimeのとき、 (2. 98) Total line extinction (2. 112) << 1 (W ien )
2. 6. 2 NLTE descriptions 8 Sνl<0 <= ανl <0 (自然放出) Laser = bu/bl T=10000 K Laser regime B u > bl 太陽ではMgⅠ (12 um)など bu/bl 1 ν0
2. 6. 2 NLTE descriptions 9 Bound-free source function 添字 i : ionizing level c : level of the next stage of ionization (usually ground state) 自由電子の衝突捕獲は、Complete redistribution (Χν=ψν=φν ) i i 運動エネルギー => 輻射エネルギー Wien regime (2. 118)
2. 6. 2 NLTE descriptions Bound-free extinction 10 Planck関数 bcはMaxwell分布で~1 Bound-free emission 水素様イオンのσνbf Wien part (hν>>k. T) (2. 74) (水素様イオンだと)〜exp(-hν/k. T) Rayleigh-Jeans part (hν<<k. T) The emissivity is not affected by lasering because the stimulated emission went to α νbf in (2. 119) ?
2. 6. 2 NLTE descriptions Edgeの話 Wien part (hν>>k. T) では、emission edge is much sharper than the extinction edge. Fig. 2. 6 exp(-hν/k. T) ∝水素イオンのJ 11
2. 6. 2 NLTE descriptions Free-free source function, extinction, emission Complete redistribution (Χν=ψν=φν ) Ionのpopulation 他の遷移からの影響 Free-free => 「Maxwell distribution for the kinetic energy => new bremsstrahlung photon」 Source function = Planck function 12
2. 6. 2 NLTE descriptions 13 Formal temperatures 「どのくらいnon. LTEなのか」 指標として種々の温度Txは便利である Excitation temperature Texc General line, complete redistribution TxとTeの違いをみる
2. 6. 2 NLTE descriptions Formal temperatures Ionization temperature Tion Bound-free Radiation temperature Trad Brightness temperature Tb Effective temperature Teff 14
2. 6. 3 Coherent scattering Two-level atoms 16 波長は限定し空間的な非局所性だけ考える permits detailed discussion of spatial non-locality due to photon scattering process without spectral non-locality due to photon conversion processes. Bound-bound process Photon creation Photon scattering Photon destruction 右水平方向が 観測者 詳細は 3. 4. 1で
2. 6. 3 Coherent scattering 17 Coherently scattering medium 単色、bound-boundの吸収係数は、 = photon destruction + photon scattering ちなみに、 連続光の吸収係数= 「(bound or free)-free」 + 「Thomson or Rayleigh scattering」 自由電子や粒子による光の散乱
2. 6. 3 Coherent scattering 18 Destruction probability 吸収(extinction)仮定において光子が破壊(destruction)される確立 吸収(extinction)仮定において光子が散乱される確立
2. 6. 3 Coherent scattering Source function 速度分布がMaxwellianのとき、 単色 two-level line source function = Planck 関数 pure coherent scattering (mean intensity に依存) Bound-free、free-free continuum processも同様 Complete redistribution (Χν=ψν=φν )のとき、 20
2. 6. 3 Coherent scattering 21 Transport equation 媒質がtwo-level atomsのとき、 太陽半径方向に軸対象、半径方向の光学的厚さτνを使うと、 (plane-parallel 大気)
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