Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Introduction in Spectroscopy Jiˇ r´ ı Kub´ at Astronomical Institute Ondˇ rejov 6 February 2017
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Outline Introduction 1 Atomic structure 2 Line formation 3 Model atmosphere calculations 4 Synthetic stellar spectra 5 Interesting features 6 7 Conclusions
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Fraunhofer lines D KH G F E C B A b 2–1 h g f e d c a 2–1 Ultra Infrared violet and X-rays Radio Gamma spectrum rays 3900 7500 7600 4500 5500 6500 4000 5000 6000 7000 from Pradhan & Nahar (2011) discovered by Wollaston (1802) independently rediscovered by Fraunhofer (1815) 7594 ˚ A A terrestrial (O 2 ) 6867 ˚ B A terrestrial (O 2 ) 6563 ˚ C A H I H α 5896, 5890 ˚ D1, D2 A Na I 5270 ˚ E A Fe I 4861 ˚ F A H I H β 4300 ˚ G A CH 3968 ˚ H A Ca II 3934 ˚ K A Ca II
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Fraunhofer lines D KH G F E C B A b 2–1 h g f e d c a 2–1 Ultra Infrared violet and X-rays Radio Gamma spectrum rays 3900 7500 7600 4500 5500 6500 4000 5000 6000 7000 from Pradhan & Nahar (2011) discovered by Wollaston (1802) independently rediscovered by Fraunhofer (1815) explained as absorption by atoms first by comparison with emission spectra of gas lamps (Kirchhoff 1860) later consistently using quantum mechanics
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Importance of spectroscopy light is the only information we have How can we predict these lines? Radiation emitted by matter Properties of the emitting matter Structure of atoms Conditions in the radiation emitting region Interaction between radiation and matter Physics involved Atomic physics Statistical physics Radiation transfer Hydrodynamics ...
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Atomic structure solution of the Schr¨ odinger equation ˆ H Ψ = E Ψ � � − h 2 2 µ ∇ 2 + V ( r ) Ψ( � r ) = E Ψ( � r ) solution in spherical coordinates Ψ( � r ) = Ψ( r , θ, φ ) = R ( r ) Y ( θ, φ ) ⇒ quantum numbers: n , l , m l system of discrete energy levels spin, quantum number s
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Hydrogen atom http://skullsinthestars.com
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Hydrogen atom interaction with electron spin fine structure Belluzzi and Trujillo Bueno (2011)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Helium atom Nave (2000)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Metals Asplund et al. (2004, A&A 417, 751)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Metals 2S o 2P o 2D o 2F o 2G o 2P o 2D o 2F o 2G o 2H o 2P o 2S 2P 2D 2F 2S 2P 2D 2F 2G 2S 2D 0 5s’ 4f’ 4f’ 4d’ 4d’ 4f’ 4d’ 4f’ 4d’ 4f’ 3d’’ 5d 5f 5d 5f 5p 5s 4s’ 4d 4f 4d 4f 4d 4f 3d’ 3d’ 3d’ 3d’ 3d’ 3p’’ 4p 4p 4s 3d 1 3d 3d 3p’ 3p’ 3p’ 3s’’ 3p 2p 4 3p 3s’ 3p 2p 4 3s 2 ionization energy (10 −11 erg) 2p 4 3 4 2p 3 5 2p 3 O II doublet 6 2S o 2P o 2D o 2F o 2G o 2P o 2D o 2F o 2G o 2H o 2P o 2S 2P 2D 2F 2S 2P 2D 2F 2G 2S 2D
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Metals Staude (2004)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Metals Kotnik-Karuza et al. (2002, A&A 381, 507)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Metals Gehren et al. (2001, A&A 366, 981)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Transitions between atomic energy levels both collisional and radiative transitions simple transitions bound-bound transitions (excitation, deexcitation) bound-free transitions (ionization, recombination) complex transitions free-free transitions (bremsstrahlung) resonance-line scattering (absorption + emission in the same bound-bound transition) scattering on bound electrons (Rayleigh, Raman) dielectronic recombination photon thermalization autoionization charge transfer transitions Auger effects
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Interaction of radiation and matter continua influence spectral energy distribution sharp ionization edges cross section ∼ ν − 3 lines influence local spectrum many sharp lines cross section rapidly variable with ν , line profiles
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Interaction of radiation and matter continua influence spectral energy distribution sharp ionization edges cross section ∼ ν − 3 resonances for atoms with > 1 electron lines influence local spectrum many sharp lines cross section rapidly variable with ν , line profiles line blanketing
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Spectral lines different shapes weak / strong absorption / emission broad / narrow complex line shapes (shell lines, P Cygni, line blends, ...) HR 7361 Jomaron et al. (1999)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Spectral lines different shapes weak / strong absorption / emission broad / narrow complex line shapes (shell lines, P Cygni, line blends, ...) HR 1847A WR 134 He II 3.0 1.1 TEIDE STRACHAN H α OMM ONDREJOV 2.5 1 DAO LEADBEATER Relative Intensity POTTER NORDIC 0.9 LI AVERAGE NORMALIZED FLUX 2.0 0.8 1.5 0.7 1.0 0.6 0.5 0.5 0.4 0.0 −40 −20 0 20 40 5300 5350 5400 5450 5500 5550 5600 WAVELENGTH (ANGSTROMS) ∆λ (Å) Saad et al. (2006), Aldoretta et al. (2016)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Spectral lines different shapes weak / strong absorption / emission broad / narrow complex line shapes (shell lines, P Cygni, line blends, ...) NLTT 25792 Vennes et al. (2013)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Spectral lines different shapes weak / strong absorption / emission broad / narrow complex line shapes (shell lines, P Cygni, line blends, ...) HD 179343 2 P - 3s 2 S He II 15-5 He II 14-5 He II 13-5 HD 210839 P V 3p He II 6-4 1.5 H α H α 2 Normalized flux Relative Intensity 1.5 1.0 1 0.5 0.5 0.0 6400 6600 −40 −20 0 20 40 1100 1110 1120 1130 1140 o λ / A ∆λ (Å) o λ / A Saad et al. (2006), ˇ Surlan et al. (2013)
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Spectral lines different shapes weak / strong absorption / emission broad / narrow complex line shapes (shell lines, P Cygni, line blends, ...) line opacity (absorption coefficient) χ ( ν ) = n l α lu φ lu ( ν ) n l number density of level l α lu cross section for transition l ↔ u φ lu ( ν ) line profile of transition l ↔ u
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Line cross section for transition l ↔ u α lu = π e 2 m e c f lu = h ν lu 4 π B lu f lu oscillator strength B lu Einstein coefficient for absorption
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Line broadening natural broadening Lorentz profile Γ lu 4 π 2 φ ( ν ) = � Γ lu � 2 ( ν − ν 0 ) 2 + 4 π Γ lu = Γ u + Γ l � � Γ l = [ A li + ✘✘✘ ❳❳❳ B li I ( ν il )] + ✘ ❳❳❳ B li I ( ν li ) ✘ ✘✘✘ ❳ ❳ i < l i > l
Introduction Atomic structure Line formation Model atmosphere Synthetic spectra Interesting features Conclusions Line broadening thermal (Doppler) broadening convolution: natural profile and equilibrium velocity distribution 1 Voigt profile φ ( ν ) = √ π H ( a , x ) ∆ ν D � ∞ e − y 2 d y H ( a , x ) = a ( x − y ) 2 + a 2 π −∞ ∆ ν D = v 0 ν 0 Γ x = ν − ν 0 y = v , a = , , . c 4 π ∆ ν D ∆ ν D v 0 v 0 – most probable velocity
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