Han Uitenbroek National Solar Observatory/Sacramento Peak Sunspot, USA Hale COLLAGE, Boulder, Feb 18, 216
Today s Lecture How do we get absorption and emission lines in the spectrum? Atomic line- and continuum transitions Non-LTE radiative transfer in atomic models Real world examples: Ca i H& K lines He i 183 nm line
Some History 182 Wollaston was the first to observe dark gaps in spectrum: spectral lines. 1814 Fraunhofer rediscovers lines. Assigns names that we still use, e.g., C (Hα), D (Na i), F (Hβ), G (CH molecules), and H (Ca i).
The spectrum at much better resolution
Remember: Eddington-Barbier approximation a I = S(τ=μ) b Ia > Ib τ=1 τ=μ
Limb Darkening Explained b a θ S ν a I ν a b b h sin θ 1 r/r = sin θ
Can we now explain the Darkening in the Cores of Spectral Lines? Intensity [J m 2 s 1 Hz 1 sr 1 ] 2.5 1 8 2. 1 8 1.5 1 8 1. 1 8 5. 1 9 391 392 393 394 395 396 397 398 399 Wavelength [nm] Intensity [J m 2 s 1 Hz 1 sr 1 ] 4 1 8 3 1 8 2 1 8 1 1 8 588 589 59 591 592 593 594 595 596 Wavelength [nm]
Explanation of Absorption Lines in the Spectrum α ν total τ ν ν ν 1 ν ν 1 ν 1 h I ν Sν ν 1 ν ν h
In the UltraViolet the Spectral Lines are in Emission 1..8 Intensity.6.4.2. 126 128 13 132 134 Wavelength [nm]
Explanation of Emission in Spectral Lines total α ν τ ν ν ν 1 ν ν 1 ν 1 h I ν Sν ν 1 ν ν h
Explanation of the Shape of the CaII Resonance Lines log total α ν h ( ) log τ ν ν ν 1 ν 1 ν ν h h I ν S ν total B ν ν 1 ν ν h
Hα Spectral Line 5 1 8 4 1 8 Intensity [J m 2 s 1 Hz 1 sr 1 ] 3 1 8 2 1 8 1 1 8 Disk center 655.5 656. 656.5 657. Wavelength [nm]
Image of the Sun in the light of Hα
Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ 14 12 1 56 4 3 2 Energy [ev] 8 6 4 2 1
Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ 14 12 1 56 4 3 2 Energy [ev] 8 6 4 2 121.6 12.6 97.3 95. 93.8 1
Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ 14 12 56 4 3 1 656.3 486.1 434. 41.2 2 Energy [ev] 8 6 4 2 121.6 12.6 97.3 95. 93.8 1
Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ 14 12 1875.1 1281.8 193.8 56 4 3 1 656.3 486.1 434. 41.2 2 Energy [ev] 8 6 4 2 121.6 12.6 97.3 95. 93.8 1
Radiative bound bound Transitions E 2 Radiative bound - bound hν ΔE = E 2 - E 1 = hν = hc/λ E 1 absorption hν hν hν hν Spontaneous emission Stimulated emission
Collisional bound bound Transitions E 2 e - E b e - E a Collisional bound - bound E 1 collisional excitation E 2 - E 1 = E b - E a E 2 e - E b e - E a E 1 collisional de-excitation
Radiative bound free Transitions Radiative bound - free e - E e E cont hν E e = hν - (E cont - E 1 ) E 1 radiative ionization e - E e e - E e E cont E cont hν E 1 radiative recombination hν hν E 1 hν stimulated radiative recombination
Collisional bound free Transitions Collisional bound - free e - E a E cont e- e - E b E c E a - (E b + E c ) = (E cont - E 1 ) E 1 collisional ionization E a e - E c e - E b E cont E 1 collisional recombination
Absorption and Emission Coefficients for bound-bound Transitions Spontaneous emission j i: j spont ν Stimulated emission j i: = n j (A ji hν ij /4π)φ ν j stim ν = n j (B ji hν ij /4π)φ ν I ν, A ji = (2hν 3 /c 2 )B ji Absorption i j: α ν = n i (B ij hν ij /4π)ϕ ν, g i B ij = g j B ji
Source Function of bound bound Transition Transfer equation: di ν ds = jspont ν + jν stim α ν I ν = n j (A ji hν ij /4π)φ ν hν ij /4πφ ν (n i B ij n j B ji )I ν Source function: S ν = j ν α ν = = 2hν3 ij c 2 n j A ji n i B ij n j B ji n j g j /g i n i n j = (1 ɛ)j + ɛb ν ɛ C ji C ji + A ji + B ji J ; J J ν φ ν dν; B ν 2hν3 c 2 1 e hν/kt 1
Radiative Rates Radiative excitation R ij = B i j hν 4π dν dω hν I νφ ν = B i jj; J 1 4π dω dνi ν φ ν Radiative de-excitation hν R ij = Aji + B ji 4π = A ji + B ji J dν dω hν I νφ ν
Basic Equation: Statistical Equilibrium Consider and atom (or molecule) with levels i =,..., N 1. Statistical equilibrium for level i: 12 N 1 j= n j (Cji + Rji) = CA III 3P6 1SE N 1 j= n i (Cij + Rij) 1 8 Energy [ev] 6 4 CA II 3P6 4P 2 396.85 393.37 CA II 3P6 4S 866.21 849.8 854.21 2SE 2PO 2DE CA II 3P6 3D The set of equations for all levels forms a, generally non-linear, and non-local, set of equations for the population numbers n i
Complicated Termdiagram for Magnesium Energy [ev] 8 6 4 MG II 2P6 3S 2SE 1/2 MG MG I MG 2P6 MG I 2P6 MG 3S I 2P6 3S 1S 9S 2P6 MG I 2P6 MG 3S 8S 2P6 MG 3S 3S I 7S MG 3S I 1P 6S 2P6 MG 9P 8P 2P6 MG 3S I 7P 2P6 MG 3S 6P 2P6 MG 3S I 9D MG 3S 8D 7D 2P6 I 6D 2P6 MG 3S 2P6 MG 3S I 1S 9S 2P6 MG 3S I 5D MG 3S 8S 2P6 MG I 7S 2P6 MG 3S MG I 3S 9P I 8P 2P6 7P 2P6 MG 2P6 MG 3S 3S I 3S 9D 8D 7D 2P6 6D 2P6 MG MG 3S 3S I 9F 8F 7F 2P6 6F 2P6 MG MG 3S 3S I 9G 8G 7G 2P6 6G 2P6 MG MG 3S 3S I 9H 8H 7H 2P6 6H 2P6 MG 3S 3S I 9I 8I 7I 2P6 MG 3S I 9K 8K 2P6 3S 9L 2P6 2P6 3S 6S MG 3S 6P 2P6 MG 3S I 5D 2P6 MG 3S I 5F 2P6 3S 5G MG I 2P6 3S 5P MG I 2P6 MG I 2P6 3S 5S MG I 2P6 3S 4D MG 3S I 5P 2P6 MG 3S I 4D 2P6 3S 4F MG I 2P6 3S 5S MG I 2P6 3S 4P MG I 2P6 MG 3S I 4P 2P6 3S 3D MG I 2P6 3S 3D MG I 2P6 3S 4S MG I 2P6 3S 4S 1999.22 411.55 8871.64 2299.82 5437.63 964.95 129.92 326.84 1154.6 1461.56 6753.38 45.47 9723.86 4177.9 416.51 318.31 2666.11 435.45 473. 3114.92 4649.18 2145.9 1659.57 146.1 1354.56 571.11 1182.82 663.8 729.11 892.36 171.86 2755.4 1469.75 323.35 1594.83 1835.84 44.5 738.7 769.1 12584.33 12368.97 17513.87 7172.84 5187.4 5224.9 11162.53 32892.99 34856.2 43557.27 7244.74 21122.92 21695.93 28591.72 1132.53 4534.33 52449.7 2764.86 1387.2 17948.8 98.48 6462.32 245.1 82.98 1127.15 5474.86 439.29 924.65 3432.83 636. 123.99 6241.8 314.21 236.45 26.9 1844.27 3396.2 2639.26 398.68 45.75 416.73 435.19 47.3 552.84 966.55 927.34 1436.5 1152.22 131.25 MG I 2P6 3S 3P 88.68 57441.35 13761.24 1852.12 38.13 6442.66 8531.93 342.22 897.31 1834.16 421.84 2121.96 5141.67 1994.13 7932.69 11178.23 5442.85 229.65 2774.8 4388.54 5228.34 899.44 7257.46 11946.51 1812.27 1226.79 2987.29 1668.5 6721.77 4894.27 998.98 253.76 2756.35 3232.88 449.67 11159.32 694.43 6126.76 264.76 269.67 2483.96 534.6 55.96 578.54 277.97 294.2 719.32 1242.82 8874.1 3866.52 2897.16 2495.53 1394.97 147.3 1595.45 1837.44 2456.56 6483.28 422.52 738.77 769.16 821.3 925.57 1942.78 1513.62 1338.32 1245.71 128.34 333.44 631.9 765.84 153.26 517.81 3412.47 1752.19 687.92 1941.13 421.65 11112.27 2598.31 11882.6 2779.41 21475.85 26324.53 169.88 17263.75 3263.3618559.1 1853.97 837.23 2333.2 6624.37 878.7 7121.64 5597. 95.28 3537.48 113.29 718.22 4345.89 3492.12 38.63 1588.29 3679.76 2385.16 1972.87 1775.78 1662.84 83.79847.13 1575.74 196.14 26.52 263.15 267.1 273.5 285. 39.49 383.53 943.58 871.53 85.2 3267.79 1789.4 5922.29 11586.68 192.87 3734.6 5215.19 3459.87 16354.4 4742.14 7656.77 2153.59 34564.63 289.17 4195.18 27335.92 23797.52 4727.91 1345.47 16213.59 1175.25 2654.46 871.41 1436.58 6698.25 5379.42 4362.59 622.1 419.83 3369.33 2999.44 3319.18 228.8 1919.42 174.75 1636.48 MG I 2P6 3S 3P 941.5 873.6 834.61 89.87 1487.78 181.11 329.32 5913.82 11389.9 28526.69 374.83 7547.49 1953.37 26526.46 4676.3 12655.26 18174.53 1968.2 7616.33 11789.51 7269.5 5756.33 717.71 454.82 3639.9 3216.62 3865.54 2541.15 216.9 1895.51 1773.95 594.17 11317.18 27946.63 756.4 19153.72 27459.96 12426.81 18826. 11215.15 1222.25 7439.91 5866.57 7372.8 4615.58 3714.21 3275.65 1134.23 27829.63 1978.35 27678.84 18977.89 11273.1 12319.25 7479.24 5892.13 27798.83 27743.6 1921.76 11289.92 27765.63 2 166.84 168.34 17.71 174.78 182.79 22.58 285.21 456.68 MG I 2P6 3S 3S 1SE 1PO 1DE 3SE 3PO 3DE 3FO 3GE 3HO 3IE 3KO 3LE
We want to Reproduce the Spectrum of the Ca i H&K 3. 1 8 2.5 1 8 Intensity [J m 2 s 1 Hz 1 sr 1 ] 2. 1 8 1.5 1 8 1. 1 8 5. 1 9 Disk center 39 392 394 396 398 Wavelength [nm]
Ingredients for Reproducing the Ca i H&K spectrum Atomic Model: Atmospheric Model: 12 CA III 3P6 1SE 2 1 8 15 Energy [ev] 6 4 2 396.85 393.37 CA II 3P6 4S CA II 3P6 4P 866.21 849.8 854.21 CA II 3P6 3D temperature [1 K] 1 5 2SE 2PO 2DE.1.1.1.1.1 1. 1. log column mass [kg m 2 ] Solve Equations for radiative transfer and statistical equilibrium simultaneously.
Collisional and Radiative Excitation in a realistic Case Photosphere Chromosphere e - hν e - hν deep high deep high
Source function Ca i K line (Non-LTE) 1 6 1 6 S total S total S active S backgr B Planck J 1 7 S active S backgr B Planck J S, J [J m 2 s 1 Hz 1 sr 1 ] 1 7 1 8 392.8 392.9 393. 393.1 393.2 393.3 λ[nm] S, J [J m 2 s 1 Hz 1 sr 1 ] 1 8 393.1 393.2 393.3 393.4 393.5 393.6 λ[nm] 1 9 1 9.1.1.1.1 1. 1. 1. Column Mass [kg m 2 ] 1 1.1.1.1.1 1. 1. 1. Column Mass [kg m 2 ] 1 6 S total 1 6 S total S active S active S backgr S backgr 1 7 B Planck J 1 7 B Planck J S, J [J m 2 s 1 Hz 1 sr 1 ] 1 8 393.1 393.2 393.3 393.4 393.5 393.6 λ[nm] S, J [J m 2 s 1 Hz 1 sr 1 ] 1 8 393.1 393.2 393.3 393.4 393.5 393.6 λ[nm] 1 9 1 9 1 1.1.1.1.1 1. 1. 1. Column Mass [kg m 2 ] 1 1.1.1.1.1 1. 1. 1. Column Mass [kg m 2 ]
Full disk images of He i equivalent width and B
Full disk images of He i EQW and Fe xii 19.3 nm
Line profiles of the He i 183 nm triplet 1 7 4.6 1 8 4.4 1 8 Intensity [J m 2 s 1 Hz 1 sr 1 ] Intensity [J m 2 s 1 Hz 1 sr 1 ] 4.2 1 8 4. 1 8 3.98 1 8 Disk center 3.96 1 8 Disk center 1 8 182.6 182.8 183. 183.2 183.4 Wavelength [nm] 3.94 1 8 182.6 182.8 183. 183.2 183.4 Wavelength [nm]
The He i 183. nm line: chromospheric? Courtesy Bernhard Fleck
The He i 183. nm termdiagram HE III HE II 3S HE II 3P HE II 3D 164.5 164.4 HE II 2S 164.4 HE II 2P 6 Energy [ev] 4 25.63 3.38 2 HE I 1S 3S 4SHE I 1S 3P HE I 1S 3D 4DHE II 1S HE I 1S 2SHE 1S 2P 54.77 2113.2 728.13 7435.48 258.13 51.57 9576.17 198.93 667.81 492.19 HE I 1S 3S 4S HE I 1S 3PHE 4PHE I 1S 3D 4D HE I 1S 2S HE I 1S 2P 471.31 76.52 4294.78 1252.75 183.2 183.3 388.86 318.77 182.91 1954.31 2112. 18617.44 1879.16 43957.16 17.24 587.56 447.15 587.56 587.56 587.56 587.56 587.6 53.7 58.43 HE I 1S2 1SE 1PO 1DE 2SE 2PO 2DE 3SE 3PO 3DE
The He i 183. nm termdiagram, triplet system 587.6 24 HE I 1S 4S 1879.16 43957.16 2112. 1954.31 HE I 1S 4P 587.56 HE I 1S 4D 587.56 Energy [ev] 23 22 471.31 1252.75 4294.78 HE I 1S 3S 76.52 17.24 HE I 1S 3P 18617.44 587.56 587.56 HE I 1S 3D 21 2 318.77 388.86 183.3 183.2 HE I 1S 2S 182.91 447.15 587.56 HE I 1S 2P 3SE 3PO 3DE
EUV irradiation from Corona populates triplet levels
The He i 183. nm contribution function Height [km] 2 15 1 5 182.6 182.8 183. 183.2 183.4 Wavelength [nm] 3. 1 1 2.5 1 1 2. 1 1 1.5 1 1 1. 1 1 5. 1 11 Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Contribution function: τ dτ C S(τ)e dh
He i Line contribution function Height [km] 2 15 1 5 8 1 13 6 1 13 4 1 13 2 1 13 Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Line contribution function: 182.6 182.8 183. 183.2 183.4 Wavelength [nm] S tot = (η l + η c ) (χ l + χ c ) [ C = η l (χ l + χ c ) + η c (χ l + χ c ) ] τ dτ e dh
He i Line contribution function with irradiation 1x 1x Height [km] 2 15 1 5 1.4 1 12 1.2 1 12 1. 1 12 8. 1 13 6. 1 13 4. 1 13 2. 1 13 Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Height [km] 2 15 1 5 6 1 12 4 1 12 2 1 12 Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] 182.6 182.8 183. 183.2 183.4 Wavelength [nm] 182.6 182.8 183. 183.2 183.4 Wavelength [nm]
Next lecture: Molecular line formation
Details of the CaII K line 1.2 1 8 1. 1 8 Intensity [J m 2 s 1 Hz 1 sr 1 ] 8. 1 9 6. 1 9 4. 1 9 2. 1 9 393. 393.2 393.4 393.6 393.8 394. Wavelength [nm] Back
Voigt Functions log H(a, v) / sqrt(π) 1 1 2 1 4 1 6 a = 1.E 4 1.E 3 5.E 3 1.E 2 1.E 1 H(a, v) φ(ν ν ) = π νd ν D ν 2kT c m Γ a = 4π ν D 1 8 1 5 5 1 v [Doppler units] Back