Transcript Document
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, c an be found at… – www.star.le.ac.uk/~mbu/lectures.html
In case of problems see me in lectures or email me… [email protected]
M.R. Burleigh 2601/Unit 2
Book Chapters
Zeilik and Gregory – Part II, Chapters 8,10-13, – Part III, Chapters 15-18 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
Basic Atomic Physics
Bohr atom – quantized orbits
Bohr postulate: Energy of orbits:
mvr
=
n
è
h
2 p ø = 2 p 2
me
4
Z
2
n
2
h
2 As n , E 0 NB. It is –ve i.e. bound M.R. Burleigh 2601/Unit 2
M.R. Burleigh 2601/Unit 2
Quantized Radiation
Electron transition between orbits
Emission:
E
a
E
b
h
E = h If n a > n b Absorption:
E
b
Frequency of photon:
h
ab
E E
a
h E
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
E
2 2
me
4
h
2 1
n
2
R
' 1
n
2 1
ab
ab c
R ch
' 1
n b
2 1
n a
2
R
1
n b
2 1
n a
2 Example: Lyman series Lyman : 1
R
1 1 1 4 The Rydberg constant (10.96776
m -1 ) = 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
Ionization
Liberation of an electron: + energy + + e Energy required = ionisation potential e.g. for hydrogen 13.6eV for the ground state:
IP
E
E
13 .
6
eV n
2 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
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 1
ab
RZ
2 1
n b
2 1
n a
2 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.
3.
Internuclear distances quantised into “vibrational” energy states Quantised rotational energy Appear as
bands
in spectra M.R. Burleigh 2601/Unit 2
Spectral Lines
Spectral line intensities – equivalent width
Line strength area of the line in the plot (absorption) This can be represented by ‘equivalent width’ Pressure Doppler effects in gas 0 Equal areas Equivalent width M.R. Burleigh 2601/Unit 2
Excitation equilibrium
No of transitions depends on population of energy state From which the transition occurs Level populations depend upon temperature Mean kinetic energy of a gas particle: 1 2
mv
2 3 2
kT
Thermal equilibrium mean no of atoms in given states constant Boltzmann’s equation: N B / N A = excitation ratio
N B N A
g B g A
exp
E A
g = multiplicity
kT E B
N = number density of state E = energy of level M.R. Burleigh 2601/Unit 2
Ionization equilibrium
Population of ions also depends on temperature Saha equation:
N i
1
N i
A
3 2
N e
exp
i kT
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 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
A F G K B Type O
Harvard spectral classifications
Colour Blue Approximate surface temperature (K) > 25,000 Main characteristics Blue 11,000 – 25,000 Singly ionised helium lines either in emission or absorption. Strong ultraviolet continuum.
Neutral helium lines in absorption.
Examples 10 Lacertra Rigel, Spica M Blue 7,500 – 11,000 Blue to white 6,000 – 7,500 White to yellow 5,000 – 6,000 Orange to red 3,500 – 5,000 Red < 3,500 Hydrogen lines at maximum strength for A0 stars, decreasing thereafter.
Metallic lines become noticeable.
Sirius, Vega Canopus, Procyon Solar-type spectra. Absorption lines of neutral metallic atoms and ions (e.g. once ionised calcium) grow in strength.
Metallic lines dominate. Weak blue continuum.
Sun, Capella Arcturus, Aldebaran Molecular bands of titanium oxide noticeable.
Betelgeuse, Antares M.R. Burleigh 2601/Unit 2
G K M O B A F
Absorption spectra
M.R. Burleigh 2601/Unit 2
Stellar spectra
M.R. Burleigh 2601/Unit 2
Stellar Spectra
M.R. Burleigh 2601/Unit 2
Spectral Type
The Sun Vega
M.R. Burleigh 2601/Unit 2
Luminosity Classification
Observers noted differences in spectral line shapes Narrow lines classes star more luminous Morgan & Keenan 6 luminosity e.g. Sun is a G2 V star M.R. Burleigh 2601/Unit 2
Morgan-Keenan luminosity classes
Ia Ib II III IV V M.R. Burleigh 2601/Unit 2 Most luminous supergiants.
Less luminous supergiants.
Luminous giants.
Normal giants.
Subgiants.
Main sequence stars (dwarfs).
Stellar Spectra
M.R. Burleigh 2601/Unit 2
Luminosity Class
Colour/Magnitude diagram
Hertzsprung-Russell (H-R) diagram 1.
2.
– Plot luminosity vs. spectral type Plot magnitude vs. colour… same idea but different parameters Colour measures changes in spectral shape M.R. Burleigh 2601/Unit 2
M.R. Burleigh 2601/Unit 2
H-R diagram
Important equations
Bohr postulate: Energy of orbits: Transition wavelength:
mvr
n h
2 n = 1, 2, 3
E
2 2
me
4
Z
2
n
2
h
2 1
ab
R
1
n b
2 1
n a
2 R = Rydberg constant = 10.96776
m -1 M.R. Burleigh 2601/Unit 2
Boltzmann’s equation: N = number density of state g = multiplicity
N B N A
g B g A
exp
E A
kT E B
E = energy of level Saha equation:
N i
1
N i
A
3 2
N e
exp N i+1 = number density of the higher ion
i kT
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
Atmosphere Models
Flux is constant:
F
4
T
eff
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:
L
3 64
r
2
T
3
dT dr
= Rosseland mean opacity M.R. Burleigh 2601/Unit 2
Flux equation:
c dP d
T
4
d
t = k
dh
= optical depth h > 0 d > 0 = 0 h = 0 M.R. Burleigh 2601/Unit 2 > 0
Flux is constant so we can integrate:
P
c T eff
4
q
Constant Calculate q from the boundary conditions: P(r) = P(r = surface) at = 0
q
c
4
T
eff
P
surface
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.
P
surface
2 3
c T
4
eff
q
2 3 and:
T
4 3 4 4
T eff
2 3 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 and 2) T(0) = T eff / 2 1/4 = 0.841 T eff Surface M.R. Burleigh 2601/Unit 2
To complete the model add hydrostatic equilibrium to find pressure and density distribution:
dP dh
GM
2
r
Variation in h is small compared to R M atm << M M(r) = M and r = R
dP dh
MG R
2
g
And dividing by gives: Surface gravity M.R. Burleigh 2601/Unit 2
dP d
g
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 DETERMINE NEW TEMPERATURE STRUCTURE SOLVE EQUATION OF HYDROSTATIC EQUILIBRIUM COMPARE NEW MODEL WITH OLD If differences are small END M.R. Burleigh 2601/Unit 2 LOOP BACK If differences are large i.e. > some limit
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 M.R. Burleigh 2601/Unit 2