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Transcript
Chapter 8 – Continuous Absorption • Physical Processes • Definitions • Sources of Opacity – Hydrogen bf and ff – H– He – Scattering Physical Processes • • • • • Bound-Bound Transitions – absorption or emission of radiation from electrons moving between bound energy levels. Bound-Free Transitions – the energy of the higher level electron state lies in the continuum or is unbound. Free-Free Transitions – change the motion of an electron from one free state to another. Scattering – deflection of a photon from its original path by a particle, without changing wavelength – Rayleigh scattering if the photon’s wavelength is greater than the particle’s resonant wavelength. (Varies as l-4) – Thomson scattering if the photon’s wavelength is much less than the particle’s resonant wavelength. (Independent of wavelength) – Electron scattering is Thomson scattering off an electron Photodissociation may occur for molecules Electron Scattering vs. Free-Free Transition • Electron scattering – the path of the photon is altered, but not the energy • Free-Free transition – the electron emits or absorbs a photon. A freefree transition can only occur in the presence of an associated nucleus. An electron in free space cannot gain the energy of a photon. Why Can’t an Electron Absorb a Photon? • Consider an electron at rest that is encountered by a photon, and let it absorb the photon…. • Conservation of momentum says • Conservation of energy says h mv c m0 2 v v 1 2 c h m0 c 2 (m m0 )c 2 m0 c 2 • Combining these equations gives 1 ( v ) 2 (1 v ) 2 c c • So v=0 (the photon isn’t absorbed) or v=c (not allowed) What can various particles do? • Free electrons – Thomson scattering • Atoms and Ions – – Bound-bound transitions – Bound-free transitions – Free-free transitions • Molecules – – BB, BF, FF transitions – Photodissociation • Most continuous opacity is due to hydrogen in one form or another Monochromatic Absorption Coefficient • Recall dt = krdx. We need to calculate k, the absorption coefficient per gram of material • First calculate the atomic absorption coefficient a (per absorbing atom or ion) • Multiply by number of absorbing atoms or ions per gram of stellar material (this depends on temperature and pressure) Bound-Bound Transitions • These produce spectral lines • At high temperatures (as in a stellar interior) these may often be neglected. • But even at T~106K, the line absorption coefficient can exceed the continuous absorption coefficient at some densities Bound Free Transitions • An expression for the bound-free coefficient was derived by Kramers (1923) using classical physics. • A quantum mechanical correction was introduced by Gaunt (1930), known as the Gaunt factor (gbf – not the statistical weight!) 3 Rg a g l 32 below e bf 0 bf • For the nth bound level the continuum and l a bf (l , n) 3 5 3 n5 < ln 3 3 h n • where a0 = 1.044 x 10–26 for l in Angstroms 2 6 Hydrogen Bound-Free Absorption Coefficient a (cm-2 per atom) x 10^6 3.5E-14 3E-14 2.5E-14 2E-14 Balmer Absorption 1.5E-14 1E-14 5E-15 Lyman Absorption n=1 Paschen Absorption n=3 n=2 0 100 600 1200 2200 3200 4200 5200 6200 7200 8200 9200 Wavelength (A) Converting to the MASS Absorption Coefficient • Multiply by the number of neutral hydrogen atoms per gram in each excitation state n • Back to Boltzman and Saha! Nn g n kT e N u0 (T ) • gn=2n2 is the statistical weight • u0(T)=2 is the partition function 3 n n kT bf n 3 bf n0 n0 aN k (H ) a N l n g e Temperature 20000 HI 16000 12000 8000 4000 H fractional ionization 1.2 1 0.8 0.6 0.4 0.2 0 H II Class Investigation • Compare kbf at l=5000A and level T=Teff for the two models provided • Recall that a 0 g bf l3 a bf (l , n) • and k=1.38x10-16, a0 =1x10-26 • And n5 r P kT • Use the hydrogen ionization chart provided