LIFECYCLES OF STARS

M.R. Burleigh 2601/Unit 2

DEPARTMENT OF PHYSICS AND ASTRONOMY

LIFECYCLES OF STARSLIFECYCLES OF STARS

Option 2601Option 2601


Stellar PhysicsStellar Physics

Unit 1 - Observational properties of Unit 1 - Observational properties of starsstars

Unit 2 - Stellar SpectraUnit 2 - Stellar Spectra Unit 3 - The SunUnit 3 - The Sun Unit 4 - Stellar StructureUnit 4 - Stellar Structure Unit 5 - Stellar EvolutionUnit 5 - Stellar Evolution Unit 6 - Stars of particular interestUnit 6 - Stars of particular interest



Unit 2Unit 2

Stellar SpectraStellar Spectra


Unit 1 Slides and NotesUnit 1 Slides and Notes

Reminder, cReminder, can be found at… an be found at… – www.star.le.ac.uk/~mbu/lectures.html

In case of problems see me in lectures In case of problems see me in lectures or email me… [email protected] email me… [email protected]


Book ChaptersBook Chapters

Zeilik and GregoryZeilik and Gregory– Part II, Chapters 8,10-13,Part II, Chapters 8,10-13,– Part III, Chapters 15-18Part III, Chapters 15-18

PhillipsPhillips– Chapters 1-6 Chapters 1-6



Review of atomic physicsReview of atomic physics Absorption and emission processesAbsorption and emission processes Qualitative treatment of spectral line Qualitative treatment of spectral line

formationformation Atmospheric opacityAtmospheric opacity Spectral classification of starsSpectral classification of stars Hertzsprung-Russell diagramHertzsprung-Russell diagram Atmosphere modelsAtmosphere models


Bohr atom – quantized orbitsBohr atom – quantized orbits

Bohr postulate:Bohr postulate:

Energy of orbits:Energy of orbits: NB. It is –ve NB. It is –ve

i.e. boundi.e. bound

As n As n , E , E 0 0

Basic Atomic PhysicsBasic Atomic Physics



Electron transition between orbitsElectron transition between orbits

Emission:Emission: hnEnE ba

Absorption:Absorption: ab nEhnE If nIf naa > n > nbb

Frequency of photon:Frequency of photon:

h

nEnE baab

Quantized RadiationQuantized Radiation

E = hE = h


Quantized RadiationQuantized Radiation

Emission – transition from higher to Emission – transition from higher to lower orbitlower orbit

Absorption – transition from lower to Absorption – transition from lower to higher orbithigher orbit

1 quantum emitted or absorbed1 quantum emitted or absorbed electron can jump over several levelselectron can jump over several levels Can cascade to lower orbit emitting Can cascade to lower orbit emitting

several photons of intermediate energyseveral photons of intermediate energy


Example for hydrogenExample for hydrogen

222

42 1'

12

nR

nh

menE

2222

1111'1

abab

ab

ab nnR

nnchR

c

The Rydberg constant The Rydberg constant (10.96776(10.96776mm-1-1))

Example: Lyman seriesExample: Lyman series

Lyman Lyman ::

41

111

R = 1216= 1216Å (121.6nm)Å (121.6nm)


Important TermsImportant Terms

Bound electrons – in orbits around Bound electrons – in orbits around atomsatoms

Free electrons – not in orbits associated Free electrons – not in orbits associated with individual atomswith individual atoms


ExcitationExcitation

Atoms can be excited (increase in energy)Atoms can be excited (increase in energy) Radiatively – by absorption of a photonRadiatively – by absorption of a photon Collisional – by a free particle Collisional – by a free particle

(electron/atom)...(electron/atom)...– Returns by emitting a photonReturns by emitting a photon

Line formation – decay of radiatively Line formation – decay of radiatively excited statesexcited states


De-excitationDe-excitation

Atoms remain excited for very short Atoms remain excited for very short times (~10times (~10-8-8 seconds) seconds)

Atoms always interacting, cause excited Atoms always interacting, cause excited atom to jump spontaneously to lower atom to jump spontaneously to lower levellevel– Radiative de-excitation – emission of Radiative de-excitation – emission of

photonphoton– Collisional de-excitation – colliding particle Collisional de-excitation – colliding particle

gains gains kinetic energykinetic energy


Liberation of an electron: Liberation of an electron: + energy + energy ++ + e + e--

Energy required = ionisation potentialEnergy required = ionisation potential

e.g. for hydrogen 13.6eV for the ground state:e.g. for hydrogen 13.6eV for the ground state:

eVn

nEEnIP2

6.13

IonizationIonization


Ion notationIon notation

Chemical notation - Chemical notation - + + or or ++ ++ etc.etc.– but but ++++++++ ++++++++ would be silly!would be silly!

Spectroscopic notation - Spectroscopic notation - (I), (I), (II) (II) etcetc..– e.g. neutral atoms… HI, HeI, CIe.g. neutral atoms… HI, HeI, CI– Singly ionized… HII (HSingly ionized… HII (H++), HeII (He), HeII (He++))– Doubly ionized… CIII (CDoubly ionized… CIII (C++++), NIII), NIII


SpectraSpectra

Bound transitions Bound transitions absorption at absorption at discrete wavelengths discrete wavelengths series limit series limit– e.g. Lyman (n=1), Balmer (n=2), Paschen e.g. Lyman (n=1), Balmer (n=2), Paschen

(n=3), Brackett (n=4), Ffund (n=5)(n=3), Brackett (n=4), Ffund (n=5)– Lyman limit at 13.6eV = 91.2nmLyman limit at 13.6eV = 91.2nm



Spectra of atoms/ionsSpectra of atoms/ions

Very similar except for effects of chargeVery similar except for effects of charge Transitions give rise to emission or Transitions give rise to emission or

absorption features in spectraabsorption features in spectra

222 111

abab nnRZ

Wave numberWave number

Z = value of the ionisation stateZ = value of the ionisation state


Spectra of moleculesSpectra of molecules

Spectra can arise fromSpectra can arise from

1.1. Electronic energy states from Electronic energy states from combined electron cloudcombined electron cloud

2.2. Internuclear distances quantised into Internuclear distances quantised into “vibrational” energy states“vibrational” energy states

3.3. Quantised rotational energyQuantised rotational energy

Appear as Appear as bandsbands in spectra in spectra


Equal areas

Equivalent width

0

Pressure Doppler effects in gas

Spectral line intensities – equivalent widthSpectral line intensities – equivalent width

Line strength Line strength area of the line in the plot (absorption) area of the line in the plot (absorption)

This can be represented by ‘equivalent width’This can be represented by ‘equivalent width’

Spectral LinesSpectral Lines


Mean kinetic energy of a gas particle:Mean kinetic energy of a gas particle:kTmv

23

21 2

Level populations depend upon temperatureLevel populations depend upon temperature

Boltzmann’s equation:Boltzmann’s equation:

kTEE

gg

NN BA

A

B

A

B exp

Excitation equilibriumExcitation equilibrium

NB / NA = excitation ratio

N = number density of state

g = multiplicity

E = energy of level

No of transitions depends on population of energy stateNo of transitions depends on population of energy stateFrom which the transition occursFrom which the transition occurs

Thermal equilibrium Thermal equilibrium mean no of atoms in given states constant mean no of atoms in given states constant


Population of ions also depends on temperaturePopulation of ions also depends on temperature

Saha equation:Saha equation:

kTNkTA

N

N i

ei

i exp

23

1

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

Ionization equilibriumIonization equilibrium


Local thermodynamic equilibriumLocal thermodynamic equilibrium

Combination of Boltzmann & Saha eqCombination of Boltzmann & Saha eqnsns specify state of gas completelyspecify state of gas completely

Iteration for each state and levelIteration for each state and level Plasma where all populations specified Plasma where all populations specified

by T and Nby T and Nee is said to be in Local is said to be in Local Thermodynamic Equilibrium (LTE)Thermodynamic Equilibrium (LTE)

Often assumed as an approximation in Often assumed as an approximation in atmosphere modellingatmosphere modelling


Spectral ClassificationSpectral Classification

Division of stars into groups depending upon Division of stars into groups depending upon features in their spectrafeatures in their spectra

Angelo Secchi (1863) found different types, Angelo Secchi (1863) found different types, but ordering difficultbut ordering difficult

Annie J. Cannon (1910) developed Harvard Annie J. Cannon (1910) developed Harvard scheme scheme H Balmer strengths H Balmer strengths

Later re-arranged in order of decreasing Later re-arranged in order of decreasing temperature (see Saha & Boltzman eqtemperature (see Saha & Boltzman eqnsns))


Harvard schemeHarvard scheme

Seven letters – O B A F G K MSeven letters – O B A F G K M (L T) (L T) Each subdivided from 0 to 9Each subdivided from 0 to 9 e.g. Sun has spectral type G2e.g. Sun has spectral type G2

Mnemonic – Only Bold Astronomers Forge Mnemonic – Only Bold Astronomers Forge Great Knowledgeable MindsGreat Knowledgeable Minds

or the 1950s/Katy Perry versionor the 1950s/Katy Perry version

- Oh Be A Fine Girl Kiss Me- Oh Be A Fine Girl Kiss Me


Harvard SchemeHarvard Scheme


TypeType ColourColour Approximate Approximate surface surface temperature (K)temperature (K)

Main characteristicsMain characteristics ExamplesExamples

OO BlueBlue > 25,000> 25,000 Singly ionised helium lines either in Singly ionised helium lines either in emission or absorption. Strong ultraviolet emission or absorption. Strong ultraviolet continuum.continuum.

10 Lacertra10 Lacertra

BB BlueBlue 11,000 – 25,00011,000 – 25,000 Neutral helium lines in absorption.Neutral helium lines in absorption. Rigel, SpicaRigel, Spica

AA BlueBlue 7,500 – 11,0007,500 – 11,000 Hydrogen lines at maximum strength for Hydrogen lines at maximum strength for A0 stars, decreasing thereafter.A0 stars, decreasing thereafter.

Sirius, VegaSirius, Vega

FF Blue to Blue to whitewhite

6,000 – 7,5006,000 – 7,500 Metallic lines become noticeable.Metallic lines become noticeable. Canopus, ProcyonCanopus, Procyon

GG White White to to yellowyellow

5,000 – 6,0005,000 – 6,000 Solar-type spectra. Absorption lines of Solar-type spectra. Absorption lines of neutral metallic atoms and ions (e.g. once-neutral metallic atoms and ions (e.g. once-ionised calcium) grow in strength.ionised calcium) grow in strength.

Sun, CapellaSun, Capella

KK OranOrangge e to redto red

3,500 – 5,0003,500 – 5,000 Metallic lines dominate. Weak blue Metallic lines dominate. Weak blue continuum.continuum.

Arcturus, Arcturus, AldebaranAldebaran

MM RedRed < 3,500< 3,500 Molecular bands of titanium oxide Molecular bands of titanium oxide noticeable.noticeable.

Betelgeuse, Betelgeuse, AntaresAntares

Harvard spectral classificationsHarvard spectral classifications


O

B

A

F

G

K

M

Absorption spectraAbsorption spectra


Stellar spectraStellar spectra


StellarStellarSpectraSpectra

SpectralSpectralTypeType


The SunThe Sun

VegaVega


Luminosity ClassificationLuminosity Classification

Observers noted differences in spectral Observers noted differences in spectral line shapesline shapes

Narrow lines Narrow lines star more luminous star more luminous Morgan & Keenan Morgan & Keenan 6 luminosity 6 luminosity

classesclasses e.g. Sun is a G2 V stare.g. Sun is a G2 V star


Morgan-Keenan luminosity classesMorgan-Keenan luminosity classes

IaIa Most luminous supergiants.Most luminous supergiants.

IbIb Less luminous supergiants.Less luminous supergiants.

IIII Luminous giants.Luminous giants.

IIIIII Normal giants.Normal giants.

IVIV Subgiants.Subgiants.

VV Main sequence stars Main sequence stars (dwarfs).(dwarfs).


StellarStellarSpectraSpectra

Luminosity Luminosity ClassClass


Colour/Magnitude diagramColour/Magnitude diagram

Hertzsprung-Russell (H-R) diagramHertzsprung-Russell (H-R) diagram

1.1. Plot luminosity vs. spectral typePlot luminosity vs. spectral type

2.2. Plot magnitude vs. colour… same idea Plot magnitude vs. colour… same idea but different parametersbut different parameters

– Colour measures changes in spectral Colour measures changes in spectral shapeshape


H-R diagramH-R diagram


Bohr postulate: n = 1, 2, 3

Energy of orbits:

Transition wavelength:

R = Rydberg constant = 10.96776m-1

2h

nmvr

22

2422

hn

ZmenE

22

111

abab nnR

Important equationsImportant equations


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

kTEE

gg

NN BA

A

B

A

B exp

kTNkTA

N

N i

ei

i exp

23

1


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

4effTF

dr

dTTr

rrrL 32

364

Atmosphere ModelsAtmosphere Models


Flux equation: 4Td

rdPc

= optical depth

h > 0

h = 0

= 0

> 0

d > 0


Flux is constant so we can integrate:

qTc

rP eff 4

Constant

Calculate q from the boundary conditions:

P(r) = P(r = surface) at = 0

surfacePT

cq

eff4


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.

32

32 4 qTc

surfaceP eff

and: 1st simple model equation

32

43 44 effTT

This gives T as a function of (Rosseland mean optical depth)

Note:Note: 1)1) TTeffeff is T at is T at = 2/3 = 2/3

andand 2)2) T(0) = TT(0) = Teffeff / 2 / 21/41/4 = 0.841 T = 0.841 Teffeff

Surface


To complete the model add hydrostatic equilibrium to find pressure and density distribution:

2r

rGMdhdP

Variation in h is small compared to R

Matm << M M(r) = M and r = R

gR

MGdhdP

2

Surface gravityAnd dividing by gives:

g

ddP


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



Review of atomic physicsReview of atomic physics Absorption and emission processesAbsorption and emission processes Qualitative treatment of spectral line Qualitative treatment of spectral line

formationformation Atmospheric opacityAtmospheric opacity Spectral classification of starsSpectral classification of stars Hertzsprung-Russell diagramHertzsprung-Russell diagram Atmosphere modelsAtmosphere models



Unit 2Unit 2




LIFECYCLES OF STARSLIFECYCLES OF STARS

Option 2601Option 2601

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LIFECYCLES OF STARS