Atomic Spectral Lines

Transcription

1 Han Uitenbroek National Solar Observatory/Sacramento Peak Sunspot, USA Hale COLLAGE, Boulder, Feb 18, 216

2 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

3 Some History 182 Wollaston was the first to observe dark gaps in spectrum: spectral lines 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).

4 The spectrum at much better resolution

5 Remember: Eddington-Barbier approximation a I = S(τ=μ) b Ia > Ib τ=1 τ=μ

6 Limb Darkening Explained b a θ S ν a I ν a b b h sin θ 1 r/r = sin θ

7 Can we now explain the Darkening in the Cores of Spectral Lines? Intensity [J m 2 s 1 Hz 1 sr 1 ] Wavelength [nm] Intensity [J m 2 s 1 Hz 1 sr 1 ] Wavelength [nm]

8 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

9 In the UltraViolet the Spectral Lines are in Emission 1..8 Intensity Wavelength [nm]

10 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

11 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

12 Hα Spectral Line Intensity [J m 2 s 1 Hz 1 sr 1 ] Disk center Wavelength [nm]

13 Image of the Sun in the light of Hα

14 Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ Energy [ev]

15 Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ Energy [ev]

16 Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ Energy [ev]

17 Energy Levels and Transitions in Hydrogen Atom E = hν = hc λ Energy [ev]

18 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

19 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

20 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

21 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

22 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

23 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

24 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

25 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 CA II 3P6 4S SE 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

26 Complicated Termdiagram for Magnesium Energy [ev] 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 MG I 2P6 3S 3P MG I 2P6 3S 3P MG I 2P6 3S 3S 1SE 1PO 1DE 3SE 3PO 3DE 3FO 3GE 3HO 3IE 3KO 3LE

27 We want to Reproduce the Spectrum of the Ca i H&K Intensity [J m 2 s 1 Hz 1 sr 1 ] Disk center Wavelength [nm]

28 Ingredients for Reproducing the Ca i H&K spectrum Atomic Model: Atmospheric Model: 12 CA III 3P6 1SE Energy [ev] CA II 3P6 4S CA II 3P6 4P CA II 3P6 3D temperature [1 K] 1 5 2SE 2PO 2DE log column mass [kg m 2 ] Solve Equations for radiative transfer and statistical equilibrium simultaneously.

29 Collisional and Radiative Excitation in a realistic Case Photosphere Chromosphere e - hν e - hν deep high deep high

30 Source function Ca i K line (Non-LTE) 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 ] λ[nm] S, J [J m 2 s 1 Hz 1 sr 1 ] λ[nm] Column Mass [kg m 2 ] 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 ] λ[nm] S, J [J m 2 s 1 Hz 1 sr 1 ] λ[nm] Column Mass [kg m 2 ] Column Mass [kg m 2 ]

31 Full disk images of He i equivalent width and B

32 Full disk images of He i EQW and Fe xii 19.3 nm

33 Line profiles of the He i 183 nm triplet Intensity [J m 2 s 1 Hz 1 sr 1 ] Intensity [J m 2 s 1 Hz 1 sr 1 ] Disk center Disk center Wavelength [nm] Wavelength [nm]

34 The He i 183. nm line: chromospheric? Courtesy Bernhard Fleck

35 The He i 183. nm termdiagram HE III HE II 3S HE II 3P HE II 3D HE II 2S HE II 2P 6 Energy [ev] HE I 1S 3S 4SHE I 1S 3P HE I 1S 3D 4DHE II 1S HE I 1S 2SHE 1S 2P HE I 1S 3S 4S HE I 1S 3PHE 4PHE I 1S 3D 4D HE I 1S 2S HE I 1S 2P HE I 1S2 1SE 1PO 1DE 2SE 2PO 2DE 3SE 3PO 3DE

36 The He i 183. nm termdiagram, triplet system HE I 1S 4S HE I 1S 4P HE I 1S 4D Energy [ev] HE I 1S 3S HE I 1S 3P HE I 1S 3D HE I 1S 2S HE I 1S 2P 3SE 3PO 3DE

37 EUV irradiation from Corona populates triplet levels

38 The He i 183. nm contribution function Height [km] Wavelength [nm] Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Contribution function: τ dτ C S(τ)e dh

39 He i Line contribution function Height [km] Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Line contribution function: 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

40 He i Line contribution function with irradiation 1x 1x Height [km] Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Height [km] Contribution function [J m 2 s 1 Hz 1 sr 1 km 1 ] Wavelength [nm] Wavelength [nm]

41 Next lecture: Molecular line formation

42 Details of the CaII K line Intensity [J m 2 s 1 Hz 1 sr 1 ] Wavelength [nm] Back

43 Voigt Functions log H(a, v) / sqrt(π) 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 v [Doppler units] Back