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Chapter 8 – Continuous Absorption Physical Processes Definitions Sources of Opacity –Hydrogen bf and ff –H - –H 2 –He –Scattering How does  affect the.

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Presentation on theme: "Chapter 8 – Continuous Absorption Physical Processes Definitions Sources of Opacity –Hydrogen bf and ff –H - –H 2 –He –Scattering How does  affect the."— Presentation transcript:

1 Chapter 8 – Continuous Absorption Physical Processes Definitions Sources of Opacity –Hydrogen bf and ff –H - –H 2 –He –Scattering How does  affect the spectrum? –More continuous absorption, less continuum light at that wavelength –More continuous absorption, lines must form in shallower layers, at lower optical depth –Need  to determine T(  ) relation

2 Many physical processes contribute to opacity 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. Electron Scattering – deflection of a photon from its original path by a particle, without changing its wavelength –Rayleigh scattering – photons scatter off bound electrons. (Varies as -4 ) –Thomson scattering –photons scatter off free electrons (Independent of wavelength) Photodissociation may occur for molecules

3 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

4 Monochromatic Absorption Coefficient Recall d  =   dx. We need to calculate , the absorption coefficient per gram of material First calculate the atomic absorption coefficient  (per absorbing atom or ion) Multiply by number of absorbing atoms or ions per gram of stellar material (this depends on temperature and pressure) MOSTLY HYDROGEN

5 Bound-Bound Transitions Bound-bound transitions produce spectral lines At high temperatures (as in a stellar interior) these may often be neglected. But even at T~10 6 K, the line absorption coefficient can exceed the continuous absorption coefficient at some densities As m > ∞, the transition approaches a bound- free condition. For photons of higher energy, the hydrogen atom is ionized R is the Rydberg Constant, R = 1.1 x Å-1 Remember the hydrogen atom:

6 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 (g bf is not the statistical weight!) (for the nth bound level below the continuum and < n ) where  0 = x 10 –26 for in angstroms and g bf is of order 1 The atomic absorption coefficient  bf (H) has units of cm 2 per neutral H atom

7 Must also consider level populations Back to Boltzman and Saha! g n = 2n 2 is the statistical weight u 0 (T) = 2 is the partition function So, the abs. coef. per neutral H atom is (summing over all levels n):

8 One more step Terms with n > n 0 +2 can be replaced with an integral (according to Unsöld) Plus a little manipulation, gives This is the absorption coefficient per neutral hydrogen atom Here, I is the ionization potential, NOT the intensity!

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10 Model Flux Distributions Sharp edges are the result of sudden drop in bound-free opacities due to ionization

11 Free-Free Absorption from H I Much less than bound free absorption Kramers (1923) + Gaunt (1930) again Absorption coefficient depends on the speed of the electron (slower electrons are more likely to absorb a photon because their encounters with H atoms take longer) Adopt a Maxwell-Boltzman distribution for the speed of electrons Again multiply by the number of neutral hydrogen atoms:

12 Opacity from Neutral Hydrogen Neutral hydrogen (bf and ff) is the dominant source of opacity in stars of B, A, and F spectral type Discussion Questions: –Why is neutral hydrogen not a dominant source of opacity in O stars: –Why not in G, K, and M stars?

13 Opacity from the H - Ion Bound–free and free-free Only one known bound state for bound-free absorption eV binding energy So < 16,500A = 1.65 microns Requires a source of free electrons (ionized metals) Major source of opacity in the Sun’s photosphere Not a source of opacity at higher temperatures because H - becomes too ionized (average e - energy too high)

14 More H - Bound-Free Opacity Per atom absorption coefficient for H- can be parameterized as a polynomial in : Units of cm 2 per neutral hydrogen atom

15 H- Bound-Free Absorption Coefficient Two theoretical calculations Important in the optical and near infrared Peaks at 8500Å

16 H - Free-Free Absorption Coefficient The free-free H- absorption coefficient depends on the speed of the electron Possible because of the imperfect shielding of the hydrogen nucleus by one electron Proportional to  3 Small at optical wavelengths Comparable to H - bf at 1.6 microns Increases to the infrared

17 H - Free Free Absorption Coefficient H - ff is important in the infrared combining H - bf and ff gives an opacity minimum at 1.6 microns H - ff parameterized as the f’s are functions of log and  is 5040/T Units are cm 2 per neutral H atom

18 Molecular H 2, H 2 +, H 2 - Opacities H 2 is more common than H in stars cooler than mid-M spectral type (think brown dwarfs!!) Recall that these are important in L and T dwarfs! Also in cool white dwarfs… Not important in optical region (H 2 + less than 10% of H - in the optical) H 2 in the infrared H 2 + in the UV, H 2 - has no stable bound state, but ff absorption is important in cooler stars

19 Collision induced opacity of molecular hydrogen H2 has no dipole moment - no rotation or vibration-rotation spectrum Collisions with (H 2, He, H) can induce transient dipole moments Fundamental VR band at 4162 cm -1 (2.4 microns). First overtone VR band at 8089 cm -1 (1.2 microns). Second overtone VR band at cm -1 (0.2 microns). Collisions are fast - individual spectral lines broad and overlap H2CIO is important for computing the temperature structure of brown dwarfs because it is a near-continuous opacity source that fills in the opacity gaps between the molecular absorption lines. Linsky/JILA

20 Helium Absorption He in hot stars only, O and early B stars –  1 =19.7eV, I 1 =24.6 eV, I 2 =54.4 eV –He I absorption mimics H –He II also mimics H, but x4 in energy, ¼ in  Bound-free He - absorption is negligible (excitation potential of 19 eV!) Free-free He - can be important in cool stars in the IR BF and FF absorption by He is important in the hottest stars (O and early B)

21 Electron Scattering vs. Free-Free Transition Electron scattering (Thomson scattering) – the path of the photon is altered, but not the energy Free-Free transition – the electron emits or absorbs a photon. A free-free transition can only occur in the presence of an associated nucleus. An electron in free space cannot gain the energy of a photon.

22 Why Can’t a Lone 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 Combining these equations gives So v=0 (the photon isn’t absorbed) or v=c (not allowed)

23 Electron Scattering Thomson scattering (photons scatters off a free electron, no change in, just direction): Independent of wavelength In hot stars (O and early B) where hydrogen is ionized (P e ~0.5P g ),  (e)/P e is small unless P e is small In cool stars, e - scattering is small compared to other absorbers for main sequence star but is more important for higher luminosity stars

24 Rayleigh Scattering Photons scatter off bound electrons (varies as -4 ) Generally can be neglected But – since it depends on  4, it is important as a UV opacity source in cool stars with molecules in their atmospheres. H 2 can be an important scattering agent

25 Other Sources Metals: C, Si, Al, Mg, Fe produce bound- free opacity in the UV Line Opacity: Combined effect of millions of weak lines –Detailed tabulation of lines –Opacity distribution functions –Statistical sampling of the absorption Molecules: CN -, C 2 -, H 2 0 -, CH 3, TiO are important in late and/or very late stars

26 Sources of Opacity for Teff=4500 Log g = 1.5

27 Opacity Sources at 5143K

28 Opacity at 6429 K

29 Opacity at 7715 K

30 Opacity at K

31 Opacity vs. Spectral Type Main Sequence Supergiants

32 Dominant Opacity vs. Spectra Type O B A F G K M H-Neutral H H- Electron scattering (H and He are too highly ionized) He+He Electron Pressure High Low (high pressure forces more H - ) Low pressure – less H -, lower opacity

33 Class Exercise – Electron Scattering Estimate the absorption coefficient for electron scattering for the models provided at a level where T=Teff Recall that and with  in AMU and k=1.38x How does  e compare to  Rosseland

34 Class Investigation Compare  bf at =5000A and level T=Teff for the two models provided Recall that and k=1.38x10 -16, a 0 =1x And Use the hydrogen ionization chart from your homework.


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