LIFECYCLES OF STARS

1. LIFECYCLES OF STARS Option 2601

2. Stellar Physics • Unit 1 - Observational properties of stars • Unit 2 - Stellar Spectra • Unit 3 - The Sun • Unit 4 - Stellar Structure • Unit 5 - Stellar Evolution • Unit 6 - Stars of particular interest

3. Unit 2 Stellar Spectra

4. Unit 1 Slides and Notes • Reminder, can be found at… • www.star.le.ac.uk/~mbu/lectures.html • In case of problems see me in lectures or email me… mbu@star.le.ac.uk

5. Book Chapters • Zeilik and Gregory • Part II, Chapters 8,10-13, • Part III, Chapters 15-18 • Phillips • Chapters 1-6

6. Stellar Spectra • Review of atomic physics • Absorption and emission processes • Qualitative treatment of spectral line formation • Atmospheric opacity • Spectral classification of stars • Hertzsprung-Russell diagram • Atmosphere models

7. Bohr postulate: Energy of orbits: Basic Atomic Physics Bohr atom – quantized orbits NB. It is –ve i.e. bound As n  , E  0

9. E = h Emission: Absorption: Frequency of photon: Quantized Radiation Electron transition between orbits If na > nb

10. Quantized Radiation • Emission – transition from higher to lower orbit • Absorption – transition from lower to higher orbit • 1 quantum emitted or absorbed • electron can jump over several levels • Can cascade to lower orbit emitting several photons of intermediate energy

11. The Rydberg constant (10.96776m-1) Lyman : Example for hydrogen Example: Lyman series   = 1216Å (121.6nm)

12. Important Terms • Bound electrons – in orbits around atoms • Free electrons – not in orbits associated with individual atoms

13. Excitation Atoms can be excited (increase in energy) • Radiatively – by absorption of a photon • Collisional – by a free particle (electron/atom)... • Returns by emitting a photon • Line formation – decay of radiatively excited states

14. De-excitation • Atoms remain excited for very short times (~10-8 seconds) • Atoms always interacting, cause excited atom to jump spontaneously to lower level • Radiative de-excitation – emission of photon • Collisional de-excitation – colliding particle gains kinetic energy

15. Ionization Liberation of an electron:  + energy  + + e- Energy required = ionisation potential e.g. for hydrogen 13.6eV for the ground state:

16. Ion notation • Chemical notation - + or ++ etc. • but ++++++++ would be silly! • Spectroscopic notation - (I), (II) etc. • e.g. neutral atoms… HI, HeI, CI • Singly ionized… HII (H+), HeII (He+) • Doubly ionized… CIII (C++), NIII

17. Spectra • Bound transitions  absorption at discrete wavelengths  series limit • e.g. Lyman (n=1), Balmer (n=2), Paschen (n=3), Brackett (n=4), Ffund (n=5) • Lyman limit at 13.6eV = 91.2nm

19. Wave number Spectra of atoms/ions • Very similar except for effects of charge • Transitions give rise to emission or absorption features in spectra Z = value of the ionisation state

20. Spectra of molecules Spectra can arise from • Electronic energy states from combined electron cloud • Internuclear distances quantised into “vibrational” energy states • Quantised rotational energy Appear as bands in spectra

21. Equivalent width Pressure Doppler effects in gas Equal areas 0 Spectral Lines Spectral line intensities – equivalent width Line strength  area of the line in the plot (absorption) This can be represented by ‘equivalent width’

22. Mean kinetic energy of a gas particle: Boltzmann’s equation: NB / NA = excitation ratio N = number density of state g = multiplicity E = energy of level Excitation equilibrium No of transitions depends on population of energy state From which the transition occurs Level populations depend upon temperature Thermal equilibrium  mean no of atoms in given states constant

23. Saha equation: Ionization equilibrium Population of ions also depends on temperature Ni+1 = higher ion number density Ni = lower ion number density A = constant incorporating atomic data i = ionisation potential of ion i Ne = electron density

24. Local thermodynamic equilibrium • Combination of Boltzmann & Saha eqns specify state of gas completely • Iteration for each state and level • Plasma where all populations specified by T and Ne is said to be in Local Thermodynamic Equilibrium (LTE) • Often assumed as an approximation in atmosphere modelling

25. Spectral Classification Division of stars into groups depending upon features in their spectra • Angelo Secchi (1863) found different types, but ordering difficult • Annie J. Cannon (1910) developed Harvard scheme  H Balmer strengths • Later re-arranged in order of decreasing temperature (see Saha & Boltzman eqns)

26. Harvard scheme • Seven letters – O B A F G K M (L T) • Each subdivided from 0 to 9 • e.g. Sun has spectral type G2 Mnemonic – Only Bold Astronomers Forge Great Knowledgeable Minds or the 1950s/Katy Perry version - Oh Be A Fine Girl Kiss Me

27. Harvard Scheme

28. Harvard spectral classifications

29. O B A F G K M Absorption spectra

30. Stellar spectra

31. Stellar Spectra Spectral Type

32. The Sun Vega

33. Luminosity Classification Observers noted differences in spectral line shapes • Narrow lines  star more luminous • Morgan & Keenan  6 luminosity classes • e.g. Sun is a G2 V star

34. Morgan-Keenan luminosity classes

35. Stellar Spectra Luminosity Class

36. Colour/Magnitude diagram Hertzsprung-Russell (H-R) diagram • Plot luminosity vs. spectral type • Plot magnitude vs. colour… same idea but different parameters • Colour measures changes in spectral shape

37. H-R diagram

38. Important equations Bohr postulate: n = 1, 2, 3 Energy of orbits: Transition wavelength: R = Rydberg constant = 10.96776m-1

39. Boltzmann’s equation: N = number density of state g = multiplicity E = energy of level Saha equation: Ni+1 = number density of the higher ion Ni = number density of the lower ion A = constant incorporating atomic data i = ionisation potential of ion I Ne = electron density

40.  = Rosseland mean opacity Atmosphere Models Flux is constant: Scale height of the atmosphere is << R*, so we can represent the atmosphere as a plane parallel layer of infinite extent Equation of radiative transfer:

41.  = optical depth h > 0  = 0 d > 0 h = 0  > 0 Flux equation:

42. Constant Flux is constant so we can integrate: Calculate q from the boundary conditions: P(r) = P(r = surface) at  = 0

43. Surface Assume that locally the radiation field is a Planck function. At the stellar surface, radiation outflow is in one direction – outwards.  Surface radiation pressure is half that given by the Planck formula. and: 1st simple model equation This gives T as a function of  (Rosseland mean optical depth)

44. Surface gravity And dividing by  gives: To complete the model add hydrostatic equilibrium to find pressure and density distribution: Variation in h is small compared to R Matm << M  M(r) = M and r = R

45. Schematic model atmosphere calculation INITIAL MODEL e.g. Grey approximation T,  structure CALCULATE ION AND LEVEL POPULATIONS i.e. solve Saha-Boltzmann equations CALCULATE RADIATIVE TRANSFER LOOP BACK DETERMINE NEW TEMPERATURE STRUCTURE If differences are large i.e. > some limit SOLVE EQUATION OF HYDROSTATIC EQUILIBRIUM COMPARE NEW MODEL WITH OLD If differences are small END

46. Stellar Spectra • Review of atomic physics • Absorption and emission processes • Qualitative treatment of spectral line formation • Atmospheric opacity • Spectral classification of stars • Hertzsprung-Russell diagram • Atmosphere models

47. Unit 2 Stellar Spectra

48. LIFECYCLES OF STARS Option 2601