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Summer School High Energy Solar Physics Thermal Radiation

Dive into the fascinating world of solar physics with a focus on thermal radiation in this high-energy summer school session. Understand the basics of physics, thermal continua, line emission, and Chianti v. 5.2. Explore observations, interpretations, and future prospects in this compelling field. Discover the significance of studying thermal radiation, its importance in analyzing energy release processes, and the intricacies of line spectra that offer valuable insights. Uncover the thermal radiation characteristics across various solar spectra, from optical and UV to X-rays, and learn about intensity, flux, and black-body radiation principles. Get a comprehensive overview of solar spectrum variations, Planck's law, and temperature definitions related to thermal emission. Delve into Local Thermodynamic Equilibrium (LTE), chromosphere, corona dynamics, and the solar spectrum's behavior during quiet sun or flares. With a mix of theoretical knowledge and practical applications, this session promises to enhance your understanding of the sun's thermal radiation processes.

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Summer School High Energy Solar Physics Thermal Radiation

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  1. Summer SchoolHigh Energy Solar PhysicsThermal Radiation

  2. Outline • Introduction • Why study thermal radiation • Basic physics • Thermal continua & line emission • Chianti v. 5.2 • Observations • Interpretation • Future Brian Dennis - Thermal Radiation

  3. Introduction • Text Books • Aschwanden – Physics of the Solar Corona • Emslie and Tandberg-Hansen - Solar Flare Physics • Harra & Mason – Space Science • Herzberg – Atomic Spectra & Structure • Thermal Radiation Covered • Optical, UV, EUV, X-rays • Lines & continua • Radio not covered Brian Dennis - Thermal Radiation

  4. Why study thermal radiation? • Negatives • Can’t differentiate between energy release processes All energy release processes produce heat. • Nonthermal products become thermal. • Line spectra complicated. • Positives • Line spectra give lots of information. • Provides context information for high energy processes. • Images, spectra, light curves. • Morphology, temperature, density, abundances. • Magnetic field from Zeeman splitting Optical lines in photosphere IR lines in corona. • Total energy in thermal plasma • Total radiated energy • The best measure of the total flare energy. Brian Dennis - Thermal Radiation

  5. Thermal Radiation • Visible Radiation • Temperature structure of atmosphere • Element abundances (Fraunhofer lines, “curve of growth analysis.” ) • Lower chromosphere (Ha, Ca II H & K optically thick, cores emitted in chromosphere) • Magnetic field • UV & EUV • Chromosphere (H Ly-a, He I & II) • Transition region & corona (1600, 171, 195 Å) • Soft X-rays • Active regions • Flares • Radio Brian Dennis - Thermal Radiation

  6. Intensity & Flux Specific Intensity (erg cm-2 s-1 keV-1 ster-1) Detected Flux (erg cm-2 s-1 keV-1) received intensity (erg cm-2 s-1 keV-1 ster-1) Brian Dennis - Thermal Radiation

  7. Intensity & Flux • Specific Intensity of Source • Units - erg cm-2 s-1 erg-1 ster-1 • Energy emitted by source per unit area of source, time, photon energy, & solid angle. • Photon energy in ergs, Hz, cm-1, or keV • Flux of photons from source detected in space • Units - photons cm-2 s-1 erg-1 • Number of photons detected per unit detector area, time, & photon energy. • Total Intensity of Source • Units - erg cm-2 s-1 erg-1 • = Flux x 2 D2 • D = distance between source and detector (1 AU) • Assumes isotropic emission over upward hemisphere. Brian Dennis - Thermal Radiation

  8. Solar Spectrum Brian Dennis - Thermal Radiation

  9. Black-Body Radiation • Equilibrium between emission & absorption • Applies to photosphere • Kirchhoff’s Law: Є - emission coefficient (erg s-1 cm-3 Hz-1 rad-1) - absorption coefficient (erg s-1 cm-3 Hz-1 rad-1) n - refractive index of the medium B(T) - universal brightness function at temperature T (erg s-1 cm-2 cm-1 steradian-1)  - frequency (Hz) Brian Dennis - Thermal Radiation

  10. Planck’s LawBlackbody Brightness vs.  (or ) and T B(T) – Planck function (erg s-1 cm-2 cm-1 steradian-1) h – Planck’s constant = 6.63 10-27 erg s  – frequency in Hz  – wavelength in cm n– refractive index of the medium c– velocity of light = 3.0 1010 cm s-1 kB– Boltzmann’s constant = 1.38 10-16 erg K-1 T– temperature in K Brian Dennis - Thermal Radiation

  11. Black-Body RadiationPlanck’s Function - B(T) Brian Dennis - Thermal Radiation

  12. Planck’s Function - B(T) • Wien Displacement Law Wavelength at which B is maximum • Stefan-Boltzmann Law Total flux - all wavelengths over the visible hemisphere  - Stefan-Boltzmann constant = 5.67 10-5 erg s-1 cm-2 K-4 Brian Dennis - Thermal Radiation

  13. Planck’s Law Approximations Short Wavelengths (X-rays) Wien’s Law kB – Boltzmann’s constant = 1.38 10-16 erg K-1 Long Wavelengths (Radio) Rayleigh-Jeans Law Brian Dennis - Thermal Radiation

  14. Definition of Temperature • From spectrum • Brightness temperature Same flux at a given wavelength as Planck’s Function • Color temperature Distribution of energy in a wavelength range • Effective temperature Same total energy as in Planck’s Function Brian Dennis - Thermal Radiation

  15. LTELocal Thermodynamic Equilibrium • Maxwellian velocity distribution Mean energy = 3/2 k T per particle Fv = • Applies in photosphere • Ionization equilibrium Saha Equation Fraction of ions in k state of ionization Brian Dennis - Thermal Radiation

  16. Chromosphere & Corona Brian Dennis - Thermal Radiation

  17. Solar Spectrum Quiet Sun & Flares - Gamma-rays to Radio Brian Dennis - Thermal Radiation

  18. Chromosphere & Corona Chromospherepartially ionized Coronafully ionized Transition Region Brian Dennis - Thermal Radiation

  19. Chromosphere & Corona • Not black-body • Optically thin in EUV & X-rays • Fraunhofer absorption lines in UV(l > 1900Å) • Line emission from H, He, ionized metals, etc. • Not LTE • Chromosphere partially ionized • Corona is fully ionized Brian Dennis - Thermal Radiation

  20. Principal Radiations • Continuum Emission • Free-free emission (thermal bremsstrahlung) • Free-bound emission • Two-photon • Line Emission • Bound-bound transitions in atoms & ions • Scattered Radiation • Thompson scattering of photospheric emission (LASCO images) Brian Dennis - Thermal Radiation

  21. Thermal Bremsstrahlung Electron in hyperbolic orbit Brian Dennis - Thermal Radiation

  22. Free-Free EmissionThermal Bremsstrahlung • Photon Spectrum Units - keV s-1 cm-2 keV-1 Є - photon energy = h n - electron and ion density V - source volume Brian Dennis - Thermal Radiation

  23. Photon Energy: Є = Ee – EL Electron e- Energy: Ee Nucleus +Ze Energy Level: EL Free-Bound Emission Continuum emission Spectral edges at atomic energy levels Brian Dennis - Thermal Radiation

  24. Two-Photon Continuum • Ion in excited J = 0 state, energy E1 (J is total angular momentum) • De-excites to ground state with J = 0, energy E0 • Single photon cannot be emitted (because photon spin = 1) • 2 photons with opposite spins can be emitted • Photon energies, Є1 + Є2 = E1 – E0 continuum • Important for He-like ions • Lowest excited state is 21S0 Brian Dennis - Thermal Radiation

  25. Atomic Data Bases • Available Codes • Chianti (v. 5..2) • MEKAL (Mewe) • APEC/APED – used in astrophysics • SPEX • Parameters • Temperature 103 – 108 K • Photon wavelength/frequency/energy • Density • Abundances • Ionization equilibrium Brian Dennis - Thermal Radiation

  26. Data Bases Compared APED v. 1.10 APED & SPEX SPEX Chianti v. 4.0 Brian Dennis - Thermal Radiation

  27. CHIANTI (Landi et al., 2005) An Atomic Database for Spectroscopic Diagnostics of Astrophysical Plasmas • In SSW/packages or stand-alone • GUI - IDL >ch_ss • Command-line interface • Great users guide CHIANTI is a collaborative project involving NRL (USA), RAL (UK), and the following Universities: College London (UK), of Cambridge (UK), George Mason (USA), and of Florence (Italy). Brian Dennis - Thermal Radiation

  28. Brian Dennis - Thermal Radiation

  29. Total Free-bound Free-free Thermal Continuum Emission T = 20 MK Coronal Abundances Chianti v. 5.2 Total Free-bound Free-free 2-photon 2-photon 2-photon Brian Dennis - Thermal Radiation

  30. Free-Bound Fraction (Chianti) Coronal abundances & Mezzotta et al. ionization equilibrium T = 20 MK T = 40 MK Free-bound Free-free Free-bound Free-free Brian Dennis - Thermal Radiation

  31. Free-Bound FractionCulhane, MNRAS, 144, 375, 1969. Free-bound fraction of total flux Brian Dennis - Thermal Radiation

  32. Line EmissionHydrogen Atom Balmer Series Lyman Series Brian Dennis - Thermal Radiation

  33. Hydrogen Emission Lines Brian Dennis - Thermal Radiation

  34. Quantum Numbers • Principal quantum number n = 1, 2, 3, 4… K, L, M, N,… • Orbital angular momentum l = 0, 1, 2, 3, 4, 5,… s, p, d, f, g, h,… where l < n • Projected angular momentum ml = l, l - 1, l - 2,…-l • Electron spin ms = ±½ Brian Dennis - Thermal Radiation

  35. Electron States Brian Dennis - Thermal Radiation

  36. Spectral Notation • Electron Configuration = n lN • n - principal quantum number • l – orbital angular momentum • N - number of electrons in given configuration • H ground configuration: 1s • Neutral Fe ground configuration 1s22s22p63s23p64s24p6“one s squared…” • Neutral He & Fe XXV ground configuration 1s2 “one s squared…” Brian Dennis - Thermal Radiation

  37. Spectral NotationAtomic or Ionic States • Specification of ion state = 2S+1LJ S = vector sum of all electron spins 2S+1 = number of possible values of J L = vector sum orbital angular momentum of all electrons0,1,2,3,4,5,…S, P. D, F, G, H,… J = vector sum angular momentum of atom= L + S • Fe XXV ground state = 1s21S0 (“one s squared singlet S zero”) • Fe XXVI = 1s 2S1/2 (“one s doublet S half”) Brian Dennis - Thermal Radiation

  38. Ionization equilibrium for Fe – Mazzotta et al. 1.0 0.8 0.6 0.4 0.2 0.0 Ion Fraction 4 5 6 7 8 Log T(K) Chromosphere & CoronaIonization-Recombination Equilibrium • Ions with Complete Outer Shells • Fe IX • Fe XVII • Fe XXV • More stable, • so higher fraction Brian Dennis - Thermal Radiation

  39. Flares Brian Dennis - Thermal Radiation

  40. Highly-ionized Iron - FeXXV • Ion - Fe+24 • Spectrum - FeXXV • 2 electrons remaining in K shell • “helium-like” • Ground state 1s2 (“one s squared”) 1S0 (“singlet S zero”) • Transitions between levels give emission lines Phillips, “The Solar Flare 3.8-10 keV X-Ray Spectrum,” ApJ, 605, 921, 2004. Brian Dennis - Thermal Radiation

  41. Fe-line Complex (~6.7 keV) • Fe xxv w line (“resonance line”) • Energy: 6.699 keV • Wavelength: 1.8508 Å • Transition: 1s2 1S0 – 1s2p 1P1 • Strongest line “quantum mechanically allowed” • Many satellite lines at lower energy • Series 1s – 2p in presence of other electrons • From FeXXV – FeII Kα doublet • FWHM ~ 0.1 keV Brian Dennis - Thermal Radiation

  42. Chianti SpectrumT = 20 MK Coronal Abundances Fe XXV Ca XIX Fe XXVFe XXVINi T = 20 MK Brian Dennis - Thermal Radiation

  43. Fe-line Complex (Chianti v. 5) Brian Dennis - Thermal Radiation

  44. Fe/Ni-line Complex (Chianti v. 5) Brian Dennis - Thermal Radiation

  45. Equivalent Width Definition Area of emission line above continuum = 1.0 x w Brian Dennis - Thermal Radiation

  46. Fe complex at ~6.7 keV Fe-Ni complex at ~8 keV Fe & Fe-Ni Line ComplexesEquivalent Widths vs. Temperature Brian Dennis - Thermal Radiation

  47. Fe Line ComplexesEquivalent Width vs. Temperature 26 April 2003 Brian Dennis - Thermal Radiation

  48. Fe & Fe-Ni Line ComplexesRatio vs. Temperature Equivalent Widths Intensities Brian Dennis - Thermal Radiation

  49. Fe Line Complex (~6.7 keV)Peak Energy vs. T Brian Dennis - Thermal Radiation

  50. Chianti SpectrumFe Line Complex near 6.7 keV Brian Dennis - Thermal Radiation

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