1 / 17

Radiation Transfer

0. Radiation Transfer. z. I l. d W. d q. d f. q. y. dA. x. 0. Radiation Transfer. Emission → j l. I l 0. Absorption → k l. 0. Special Cases. Radiation Transfer. I l ( t l ) = I l (0) e - t l + S l (1 – e - t l ). I l ( t l ) = I l (0) e - t l. 1) Absorption spectra.

rue
Télécharger la présentation

Radiation Transfer

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 0 Radiation Transfer z Il dW dq df q y dA x

  2. 0 Radiation Transfer Emission → jl Il0 Absorption → kl

  3. 0 Special Cases Radiation Transfer Il (tl) = Il(0) e-tl + Sl (1 – e-tl) Il (tl) = Il(0) e-tl 1) Absorption spectra Bright background source behind a cold absorber (Sl ≈ 0)

  4. 0 Special Cases Radiation Transfer (III) Il (tl) = Il(0) e-tl + Sl (1 – e-tl) Il (tl) = Sl (1 – e-tl) Il (tl) = Sl 2) Emission spectra No significant background source (Il (0)≈ 0) I) Optically thick emission: (tl >> 1)

  5. 0 Special Cases Radiation Transfer (IV) Il (tl) = Il(0) e-tl + Sl (1 – e-tl) Il (tl) ≈ Sltl ≈ jl r Ds 2) Emission spectra No significant background source (Il (0)≈ 0) II) Optically thin emission: (tl << 1)

  6. 0 Einstein Coefficients E2 = E1 + hn0 E1 1) Prompt emission→ A21

  7. 0 Einstein Coefficients E2 = E1 + hn0 E1 1) Prompt emission→ A21 2) Absorption→ B12

  8. 0 Einstein Coefficients E2 = E1 + hn0 E1 1) Prompt emission→ A21 2) Absorption→ B12 3) Stimulated Emission→ B21

  9. 0 1) Bound-Bound transitions (lines) Radiation Mechanisms (I) Get A21 = spontaneous transition probability per unit time, from quantum mechanics. 2) Bound-Free transitions (recombination / photoionization) Characteristic absorption edges: sabs ~ l3 ~ n-3 jn ~ (ehn/kT – 1) -1 hnthr = c In n

  10. 0 3) Free-free transitions (bremsstrahlung) Radiation Mechanisms (II) jn ~ e-(hn/kT) In Opt. thin Opt. thick ~ n2 n

  11. 0 4) Cyclotron/synchrotron Radiation Mechanisms (III) Cyclotron frequency: ncy = eB/(2pmec) ~ 2.8*106 (B/G) Hz Magnetic field B Nonrelativistic electrons Cyclotron radiation In Harmonics: In ~ (v/c)n ncy n

  12. 0 Synchrotron Radiation Radiation Mechanisms (III) Relativistic electrons: nsy ~ 3.4*106 (B/G) g2 Hz e-n/nsy In n1/3 n nsy

  13. 0 Synchrotron Radiation Radiation Mechanisms (III) Power-law distribution of relativistic electrons: Ne(g) ~ g-p jn ~ n-a a = (p-1)/2 kn ~ n-b b = (p+4)/2 Opt. thick In Opt. thin n5/2 n-(p-1)/2 n

  14. 0 5) Electron scattering Radiation Mechanisms (IV) Most important in very hot (relativistic) plasmas Determined by Thomson cross section: sT = 6.65*10-25 cm2 Power-law distribution of relativistic electrons: Ne(g) ~ g-p jn ~ n-a a = (p-1)/2

  15. 0 Plane Parallel Approximation z tl = tl,vsecq tl,v s = zsecq q

  16. 0 Rosseland Mean Opacity Kramer’s Opacity Law aR ~ r T-7/2 log(aR [cm-1]) Gas fully ionized; opacity dominated by free-free absorption Gas gradually becoming ionized 104 105 106 107 Temperature [K]

  17. 0 Limb Darkening

More Related