Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy. PHY 688, Lecture 5 Stanimir Metchev
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1 Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy PHY 688, Lecture 5 Stanimir Metchev
2 Outline Review of previous lecture Stellar atmospheres spectral lines line profiles; broadening Astronomical spectroscopy and spectral types Feb 4, 2009 PHY 688, Lecture 5 2
3 Previously in PHY 688 Feb 4, 2009 PHY 688, Lecture 5 3
4 Internal Equilibrium Equations hydrostatic equilibrium mass continuity conservation of energy dp dr = " GM r# r 2 dm r dr = 4$r2 # dl r dr = 4$r2 #(% "% & ) temperature continuity depends on mode of energy transport Feb 4, 2009 PHY 688, Lecture 5 4
5 Modes of Energy Transport and the Temperature Continuity Equation conduction k: thermal conductivity important only when photon m.f.p. < electron m.f.p. white dwarfs, neutron stars radiation photons absorbed by cooler outer layers efficient in: >1 M Sun star envelopes cores of M Sun stars all stellar photospheres convection adiabatic exponent γ = C P /C V important when radiation inefficient: interiors of brown dwarfs and <0.3 M Sun stars cores of >1 M Sun stars envelopes of ~1 M Sun stars dt dr = " 1 k dt dr = " L r 4#r 2 3$%L r 64#r 2 &T 3 dt dr = ( 1" 1 + * - T ) ', P Feb 4, 2009 PHY 688, Lecture 5 5 dp dr
6 Energy Transport in the Sun Feb 4, 2009 PHY 688, Lecture 5 6
7 stars < 0.25M Sun fully convective all stars have a radiative outer layer: the photosphere Feb 4, 2009 PHY 688, Lecture 5 7
8 Additional Constitutive Equations and Boundary Conditions equation of state equation of energy generation opacity equation P = P (T, ρ, composition) ε = ε (T, ρ, composition) κ = κ (T, ρ, composition) boundary conditions r =0: M 0 = 0, L 0 = 0 r = R: M R = M, T R 0, P R 0 Feb 4, 2009 PHY 688, Lecture 5 8
9 A Special Solution to the E.O.S.: Stars as Polytropes P P(ρ) = Kρ γ, γ = 1+1/n K - constant, n - polytropic index Lane-Emden equations: dimensionless forms of equation of hydrostatic equilibrium solutions: P = P 0 " m +1, # = # 0 " m, T = T 0 " important polytropes: n = 3: normal stars n = 1.5: brown dwarfs, planets, white dwarfs (all are degenerate objects) n = 1: neutron stars n = isothermal proto-stellar clouds 1 d $ " 2 d" " d" ' & 2 ) + # n " % d# ( # " = 0 ( ) = 0 ( ) =1 stellar core $ d# ' & ) % d" ( " = 0 = 0 stellar core Feb 4, 2009 PHY 688, Lecture 5 9
10 Energy Generation: p-p Chain Feb 4, 2009 PHY 688, Lecture 5 10
11 Outline Review of previous lecture Stellar atmospheres spectral lines line profiles; broadening Astronomical spectroscopy and spectral types Feb 4, 2009 PHY 688, Lecture 5 11
12 Stellar Atmospheres higher ionization potential species Feb 4, 2009 PHY 688, Lecture 5 12
13 Line Radiation & h" = #E $ R 1 2 n % 1 ) ( 2 + ' 1 n 2 * Feb 4, 2009 PHY 688, Lecture 5 13
14 Spectral Lines as Photospheric ( Atmospheric) Diagnostics chemical content and abundances mostly H and He, but heavier metals (Z > 2) + molecules are important sources of opacity photospheric temperature individual line strength line ratios photospheric pressure non-zero line width surface gravity g, mass M * stellar rotation Doppler broadening dp dr = " GM r# r 2 = "g# Feb 4, 2009 PHY 688, Lecture 5 14
15 Taking the Stellar Temperature individual line strengths N n " g n e #$ n kt g n statistical weight g n = 2n 2 for hydrogen line ratios N n = g n e # ( $ n #$ m ) kt N m g m Feb 4, 2009 PHY 688, Lecture 5 15
16 Taking the Stellar Temperature T eff (Fe II λ5317 / Fe I λ5328) line ratio decreases with decreasing T eff Feb 4, 2009 PHY 688, Lecture 5 16
17 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 Feb 4, 2009 PHY 688, Lecture 5 17
18 Stark Effect in Hydrogen if external field is chaotic, the energy levels and their differences are smeared line broadening Feb 4, 2009 PHY 688, Lecture 5 18
19 Van der Waals Force: Long-Range Attraction argon Feb 4, 2009 PHY 688, Lecture 5 19
20 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u/c Feb 4, 2009 PHY 688, Lecture 5 20
21 Line Profiles: Rotational Broadening Feb 4, 2009 PHY 688, Lecture 5 21
22 Line Profiles I ν profiles normalized to the same total area ν Feb 4, 2009 PHY 688, Lecture 5 22
23 Line Profiles Natural line width (Lorentzian [a.k.a, Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body Composite line profile: Lorentzian + Gaussian = Voigt profile # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u/c Feb 4, 2009 PHY 688, Lecture 5 23
24 Line Profiles Natural line width (Lorentzian [a.k.a., Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) dipole coupling between pairs of same species (n = 3) dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body Composite line profile: Lorentzian + Gaussian = Voigt profile # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 I " = 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u/c Feb 4, 2009 PHY 688, Lecture 5 24
25 Example: Pressure Broadening of the Na D Fine Structure Doublet Feb 4, 2009 PHY 688, Lecture 5 25
26 Line Profiles: Equivalent Width Feb 4, 2009 PHY 688, Lecture 5 26
27 Outline Review of previous lecture Stellar atmospheres spectral lines line profiles; broadening Astronomical spectroscopy and spectral types Feb 4, 2009 PHY 688, Lecture 5 27
28 Astronomical Spectrograph telescope focus Feb 4, 2009 PHY 688, Lecture 5 28
29 Spectroscopic Bestiary Feb 4, 2009 PHY 688, Lecture 5 29
30 OBAFGKM + LT higher ionization potential species Feb 4, 2009 PHY 688, Lecture 5 30
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