1. Line Broadening Chap 9, part 9.3

2. ‘Natural’ Line Width For quantum-mechanical reasons (which we can express in terms of the Heisenberg uncertainty principle), no emission [or absorption] feature can be arbitrarily ‘thin’ – i.e. it cannot be essentially monochromatic or monoenergetic. (Think in terms of ΔE Δt ≥ h/4π)

3. As Here [See Appendix D]

4. Lorentzian Profile The natural emission profile is a function called the Lorentzian. Note the scale: this is for Ly α, for which ν o is ~2.5 x 10 15 Hz. The natural width is very narrow.

5. Other Effects Broaden the Lines 1.Doppler Broadening In real astrophysical situations, emitting atoms in a gas cloud (or absorbers in a stellar atmosphere) will have thermal motions, with varied line-of-sight velocities. This broadens the observed line by different Doppler shifts.

6. As Shown Here

7. What is the Resultant Profile? Remember the Maxwellian velocity distribution for a cloud in thermal equilibrium! If the gas is optically thin, we see all the atoms along the line of sight, and they contribute individually according to n(v) at the appropriate Doppler-shifted wavelength (or frequency) corresponding to that velocity v.

8. The Net Effect The profile is Gausssian, with a half-width that can be fairly straightforwardly expressed in terms of the temperature of the gas (see pp 291-293 for the details) – but remember that as T  0, the line-width approaches the natural width, not getting infinitesimally narrow.

9. For Example

10. Doppler-Broadened vs Lorentz

11. Complicating Effects Systematic motions – like a whole cloud moving. But these merely displace line centres. Turbulence on different scales (e.g. ‘microturbulence’) broaden the lines yet again, in a way that is the convolution of the two effects.

12. Turbulence

13. …and Others Rotational broadening (i.e. the whole star rotates) – again, a Doppler effect, but not characterized by a temperature Other coherent (non-random) motions on various scales (think about GONG in the Sun)

14. The Solar Surface

15. Convective Motions (Small-scale)

16. A Direct Probe: GONG visit http://gong.nso.edu/

17. Methodology Measure Doppler shifts (vertical motions) at umpteen points on the surface of the Sun. Consider overtones, as in music: many vibrational modes may be happening at once. The sun ‘rings like a bell.’

18. A Special Vantage Point

19. Modes of Very High Order Here’s a simulation: https://www.youtube.com/watch?v=YxUsr4vp3yM

20. Back to Doppler Broadening: The Usefulness Rather obviously, the half-width of a line gives an upper limit to the gas temperature.

21. 2. Pressure Broadening An atom does not typically undergo transitions in complete isolation: it will be surrounded by other particles (electrons, various ions in various states of excitation and ionization, neutrals). The consequent E-fields perturb the transitions and broaden the line.

22. Perhaps Surprisingly… The net effect of this “collisional broadening” is a line with a Lorentzian profile, but larger than its natural profile. This allows us to discriminate between Doppler (thermal) broadening and this inter-particle effect.

23. If Both are Present? Convolving the Doppler broadening profile with the collisional broadening profile yields what is known as the Voigt profile – in a sense, a Doppler core with Lorentzian wings. Other terms for this include Stark broadening and pressure broadening.

24. Like so…

25. Some Expectations The inter-atomic effects should be more pronounced in denser gases, so we expect to see different line profiles in giants (diffuse, low- density atmospheres) and dwarfs (main sequence stars) even of the same surface temperature / spectral type. Lines that show this are said to be gravity sensitive.

26. Telling Giants from Dwarfs

27. Digression: Ancient Terminology In early spectroscopic studies, stars with very narrow lines were annotated “c” Eventually this was understood in terms of the low particle density, and the stars acting this way were clearly giants or supergiants Oddly, the inappropriate term “cD” came to be used for giant galaxies, like M87 at the core of the Virgo Cluster. “D” means diffuse. (Most astronomers now assume that it comes from “central dominant.” T’aint so!)

28. M87: My Fave