M.R. Burleigh 2601/Unit 2 DEPARTMENT OF PHYSICS AND ASTRONOMY LIFECYCLES OF STARS Option 2601

M.R. Burleigh 2601/Unit 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

M.R. Burleigh 2601/Unit 2 DEPARTMENT OF PHYSICS AND ASTRONOMY Unit 2 Stellar Spectra

M.R. Burleigh 2601/Unit 2 Unit 1 Slides and Notes  Reminder, can be found at… –  In case of problems see me in lectures or me…

M.R. Burleigh 2601/Unit 2 Book Chapters  Zeilik and Gregory –Part II, Chapters 8,10-13, –Part III, Chapters  Phillips –Chapters 1-6

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 Bohr atom – quantized orbits Bohr postulate: Energy of orbits: NB. It is –ve i.e. bound As n  , E  0 Basic Atomic Physics

M.R. Burleigh 2601/Unit 2

Electron transition between orbits Emission: Absorption: If n a > n b Frequency of photon: Quantized Radiation E = h E = h

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 Example for hydrogen The Rydberg constant (  m -1 ) Example: Lyman series Lyman  :  = 1216Å (121.6nm)

M.R. Burleigh 2601/Unit 2 Important Terms  Bound electrons – in orbits around atoms  Free electrons – not in orbits associated with individual atoms

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 Liberation of an electron:  + energy   + + e - Energy required = ionisation potential e.g. for hydrogen 13.6eV for the ground state: Ionization

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2

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

M.R. Burleigh 2601/Unit 2 Spectra of molecules Spectra can arise from 1.Electronic energy states from combined electron cloud 2.Internuclear distances quantised into “vibrational” energy states 3.Quantised rotational energy Appear as bands in spectra

M.R. Burleigh 2601/Unit 2 Equal areas Equivalent width 0 Pressure Doppler effects in gas Spectral line intensities – equivalent width Line strength  area of the line in the plot (absorption) This can be represented by ‘equivalent width’ Spectral Lines

M.R. Burleigh 2601/Unit 2 Mean kinetic energy of a gas particle: Level populations depend upon temperature Boltzmann’s equation: Excitation equilibrium N B / N A = excitation ratio N = number density of state g = multiplicity E = energy of level No of transitions depends on population of energy state From which the transition occurs Thermal equilibrium  mean no of atoms in given states constant

M.R. Burleigh 2601/Unit 2 Population of ions also depends on temperature Saha equation: N i+1 = higher ion number density N i = lower ion number density A = constant incorporating atomic data  i = ionisation potential of ion i N e = electron density Ionization equilibrium

M.R. Burleigh 2601/Unit 2 Local thermodynamic equilibrium  Combination of Boltzmann & Saha eq ns specify state of gas completely  Iteration for each state and level  Plasma where all populations specified by T and N e is said to be in Local Thermodynamic Equilibrium (LTE)  Often assumed as an approximation in atmosphere modelling

M.R. Burleigh 2601/Unit 2 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 eq ns )

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 Harvard Scheme

M.R. Burleigh 2601/Unit 2 TypeColour Approximate surface temperature (K) Main characteristics Examples OBlue > 25,000 Singly ionised helium lines either in emission or absorption. Strong ultraviolet continuum. 10 Lacertra BBlue 11,000 – 25,000 Neutral helium lines in absorption. Rigel, Spica ABlue 7,500 – 11,000 Hydrogen lines at maximum strength for A0 stars, decreasing thereafter. Sirius, Vega F Blue to white 6,000 – 7,500 Metallic lines become noticeable. Canopus, Procyon G White to yellow 5,000 – 6,000 Solar-type spectra. Absorption lines of neutral metallic atoms and ions (e.g. once- ionised calcium) grow in strength. Sun, Capella K Orange to red 3,500 – 5,000 Metallic lines dominate. Weak blue continuum. Arcturus, Aldebaran MRed < 3,500 Molecular bands of titanium oxide noticeable. Betelgeuse, Antares Harvard spectral classifications

M.R. Burleigh 2601/Unit 2 OBAFGKMOBAFGKM Absorption spectra

M.R. Burleigh 2601/Unit 2 Stellar spectra

M.R. Burleigh 2601/Unit 2 StellarSpectra SpectralType

The Sun Vega

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 Morgan-Keenan luminosity classes Ia Most luminous supergiants. Ib Less luminous supergiants. II Luminous giants. III Normal giants. IVSubgiants. V Main sequence stars (dwarfs).

M.R. Burleigh 2601/Unit 2 StellarSpectra LuminosityClass

Colour/Magnitude diagram Hertzsprung-Russell (H-R) diagram 1.Plot luminosity vs. spectral type 2.Plot magnitude vs. colour… same idea but different parameters –Colour measures changes in spectral shape

M.R. Burleigh 2601/Unit 2 H-R diagram

M.R. Burleigh 2601/Unit 2 Bohr postulate:n = 1, 2, 3 Energy of orbits: Transition wavelength: R = Rydberg constant =  m -1 Important equations

M.R. Burleigh 2601/Unit 2 Boltzmann’s equation: N = number density of state g = multiplicity E = energy of level Saha equation: N i+1 = number density of the higher ion N i = number density of the lower ion A = constant incorporating atomic data  i = ionisation potential of ion I N e = electron density

M.R. Burleigh 2601/Unit 2 Flux is constant: Equation of radiative transfer:  = Rosseland mean opacity Scale height of the atmosphere is << R *, so we can represent the atmosphere as a plane parallel layer of infinite extent Atmosphere Models

M.R. Burleigh 2601/Unit 2 Flux equation:  = optical depth h > 0 h = 0  = 0  > 0 d  > 0

M.R. Burleigh 2601/Unit 2 Flux is constant so we can integrate: Constant Calculate q from the boundary conditions: P(r) = P(r = surface) at  = 0

M.R. Burleigh 2601/Unit 2 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:1 st simple model equation This gives T as a function of  (Rosseland mean optical depth)Note:1) T eff is T at  = 2/3 and2) T(0) = T eff / 2 1/4 = T eff Surface

M.R. Burleigh 2601/Unit 2 To complete the model add hydrostatic equilibrium to find pressure and density distribution: Variation in h is small compared to R M atm << M  M(r) = M and r = R Surface gravity And dividing by  gives:

M.R. Burleigh 2601/Unit 2 INITIAL MODEL e.g. Grey approximation CALCULATE ION AND LEVEL POPULATIONS i.e. solve Saha-Boltzmann equations CALCULATE RADIATIVE TRANSFER DETERMINE NEW TEMPERATURE STRUCTURE SOLVE EQUATION OF HYDROSTATIC EQUILIBRIUM COMPARE NEW MODEL WITH OLD LOOP BACK END Schematic model atmosphere calculation T,  structure If differences are small If differences are large i.e. > some limit

M.R. Burleigh 2601/Unit 2 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

M.R. Burleigh 2601/Unit 2 DEPARTMENT OF PHYSICS AND ASTRONOMY Unit 2 Stellar Spectra

M.R. Burleigh 2601/Unit 2 DEPARTMENT OF PHYSICS AND ASTRONOMY LIFECYCLES OF STARS Option 2601