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Lecture 3:

Lecture 3:. Microphysics of the radiative transfer. Numerical integration of RT in a simplest case. Local Thermodynamical Equilibrium (LTE, all microprocesses are in detailed balance) Static (no time dependence) Simple geometry (e.g semi-infinit medium) One dimension.

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Lecture 3:

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  1. Lecture 3: Microphysics of the radiative transfer

  2. Numerical integrationof RT in a simplest case • Local Thermodynamical Equilibrium (LTE, all microprocesses are in detailed balance) • Static (no time dependence) • Simple geometry (e.g semi-infinit medium) • One dimension

  3. Equation of radiative transfer (again) Equation of radiative transfer:For the case of semi-infinite medium (e.g. stellar atmosphere) boundary condition is set deep (inside a star): or or

  4. Blu Bul Aul Einstein coefficients • Aul - spontaneous de-excitation. • Blu - radiative excitation. • Bul - stimulated de-excitation. • Einstein relations connect the probabilities: and that lu transition rate match the ul rate:

  5. Blu Bul Aul Absorption/Emission • Energy absorbed: • Energy emitted: • Probability profiles are area normalized:

  6. Absorption/Emission • Absorption coefficient expressed through Einstein probabilities: • Emission coefficient: • LTE (detailed balance for each frequency) means that probability profiles are the same:

  7. Source function • Source function: • LTE (detailed balance for each frequency) means that probability profiles are the same: • Level population in LTE is described by the Boltzmann distribution:

  8. Source function and absorption coefficient in LTE • Source function in LTE is the Planck function: • Absorption coefficient in LTE:

  9. Continuous opacity • Continuous opacity includes b-f (photoionization) and f-f transitions. • Hydrogen is often a dominating source due to its abundance (H, H-). • For b-f transitions only photons with energy larger than the difference between the ionization energy and the energy of a bound level can be absorbed:This produces the absorption edges.

  10. n =  13.6 eV b-f transitions in Hydrogen Paschen,  < 8206 Å 12.1 eV n = 3 Balmer,  < 3647 Å 10.2 eV n = 2 Lyman,  < 912 Å n = 1 0 eV

  11. Total opacity in LTE • b-f and f-f opacities are described by the same expression for opacity coefficient as for b-b. Just Buland the absorption profiles are different. • The source function is still a Planck function. • Total absorption:

  12. Line profile • The last thing left is the absorption probability profile. • Spectral lines are not delta-functions due to three effects: • Damping of radiation • Perturbation of atomic energy level system by neighboring particles • Doppler movements of absorbers/emitters • The convolution the Lorentz and Doppler profile results in Voigt profile: Lorentz Gaussian

  13. Now… we know everything • RT equation: • Boundary condition: • Absorption coefficient: • Absorption profile: • Source function

  14. Practical implementation • Maxwellian velocity distribution: • Boltzmann level population • Saha ionization balance

  15. How good is LTEfor solving RT?

  16. Stellar surfaces Courtesy of Göran Scharmer/Swedish Solar Vacuum Telescope

  17. Energy transport in stars • Radiation • Convection • Particle ejection • Waves Space above surface is not empty! Courtesy of SOHO

  18. Solar corona • Low density: <107 particle/cm3 • Hot: >106 K • Optically thin • Temperature of radiation is very different from the kinetic temperature Courtesy of SOHO

  19. Coronal arcades on the Sun • Heating of the outer layers is part of the energy transport • Magnetic fields play a major role • Coherent motions at the photosphere layers dissipate in the corona making it hot Courtesy of Karel Schrijver/TRACE

  20. How can observe space above solar surface? • At visual spectral range photosphere dominates the total flux • UV lines allow to see chromospheric structures • Going to X-ray is required to observe solar corona Courtesy of Karel Schrijver/TRACE

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