1

Mass Statistics• Add mass for main

sequence to our plot• Masses vary little• Model: Stars are the

same: mass determines rest

• Heavy stars hot, luminous

2

Mass-Luminosity Relation• Find approximately

• Borne out by models: Mass compresses star increasing rate of fusion

• If amount of Hydrogen available for fusion is near constant fraction, big stars run out sooner

• OB stars are young!

3

Main Sequence Stars• Stellar modeling matched to data tells us

about how stars work• Main-Sequence stars fuse Hydrogen to Helium

in core• Hydrostatic Equilibrium determines rate of

fusion and density profile from mass

4

CNO Chain• In large stars

core hot and CNO chain dominates fusion

• Rate rises rapidly with temperature

5

Size Matters• Mechanisms of heat

transfer depend on mass• In small stars, entire

volume convective so all available to fuse in core

• In large stars, radiation and convection zones inverted

6

Expansion by Contraction• As a main sequence star ages core

enriched in Helium• Rate of fusion decreases –

temperature and radiation pressure decrease

• Number of particles decreases – thermodynamic pressure decreases

• Core contracts and heats• Fusing region grows• Luminosity increases• Envelope expands

• Sun now 25% brighter than when it formed

• Core now 60% Helium• Continues to brighten –

heating Earth• In 1-3Gy could be

uninhabitable?• Orbit stable out to 1Gy?

7

Questions• For 90% of stars we have a good

understanding of how they work• This comes from careful observation and

detailed modeling• Where do the rest come from?• What happens when core is all Helium??

8

Modelling Collapse• Model a cloud of mass• Within a few Ky form opaque radiating photosphere

of dust and later H-

• Photosphere contracts from to at constant fueled by

Kelvin-Helmholtz and deuterium fusion over 600Ky

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Pre-Main Sequence• Initial photosphere contracts at

constant T decreasing L• Rising ionization in center

reduces opacity creating radiative zone increasing L

• When fusion begins L decreases initially as core expands

• In 40My settle down to MS equilibrium: KH time!

• Larger stars go faster

105

106

107

10

Too Small• Below effective

fusion does not occur• is a brown dwarf type L,

T, Y• How Many? 1:1? 1:5?

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Too Big?• Models suggest that collapse with fails as radiation pressure fragments cloud• Recent record

12

On the Main Sequence• Hydrogen fusion in core

supports envelope by thermal and radiation pressure

• Luminosity, surface temperature determined by mass, composition, rotation, close binary partner, atmospheric and interstellar effects

• Main Sequence thickened by variations in these

• Over time core contracts and heats

• Fusion rate increases • Envelope expands slowly

with little change in temperature

• Evolutionary track turns away from Main Sequence

13

Running Out of Gas • Inner 3% inert Helium

core is isothermal• Hydrogen fusion in shell

exceeds previous core luminosity

• Envelope expands and cools

• Inert core grows

14

Sub-Giant Branch• In isothermal core pressure

gradient maintained by density gradient

• If core too large cannot support outer layers.• Core collapses rapidly (KH scale)• Gravitational energy expands

envelope• Temperature decreases• Sub-Giant Branch

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Red Giant• Core collapses• Compression heats shell

increasing luminosity• Envelope expands and cools,

H- opacity creates deep convection

• First dredge-up brings fusion products to atmosphere

• Mass loss up to 28%

16

Then What?• Core does not collapse due to

electron degeneracy pressure• Quantum effect of Pauli

exclusion principle• Squeezing electrons into small

space requires occupying higher energy states

• Produces temperature-independent contribution to pressure

• This is smaller than thermal pressure in Hydrogen core today

• In compressed inert Helium core degeneracy pressure stops collapse

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Helium Core Flash• When core temperature reaches

108K Helium fusion via triple-α process occurs explosively in degenerate core

• For a few seconds produce galactic luminosity absorbed in atmosphere, possibly leading to mass loss

• Expands shell decreasing output• Envelope contracts and heats

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Horizontal Branch• Deep convection rises• Convective core fusing

Helium to Carbon, Oxygen• Shell fusing Hydrogen to

Helium• Core contracts• Envelope contracting and

heating

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Early Asymptotic Giant Branch• Inert CO core collapses to

degeneracy• Helium fusion in shell• Hydrogen shell nearly inactive• Envelope expands and cools• Convective envelope

deepens: second dredge-up• Mass loss in outer layer

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Thermal Pulse AGB• Hydrogen shell reignites• Helium shell flashes intermittently• Flash expands Hydrogen shell, luminosity

drops and envelope contracts heats• Hydrogen reignition increases luminosity

envelope expands cools• Convection between shells and deep

convective envelope: third dredge-up and Carbon stars

• Rapid mass loss to superwind• s-process neutron capture

nucleosynthesis produces heavier elements

21

The End• Pulses eject envelope

exposing inert degenerate CO core

• Initially hot core cools• Expanding envelope ionized

by UV radiation of white dwarf glows as ephemeral planetary nebula

22

M57

23

Ghost of Jupiter (NGC 3242)

24

Cat’s Eye

25

Hubble 5

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NGC-2392 (Eskimo)

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Clusters and the Model• Model predicts how clusters will evolve• Massive stars evolve faster• Later stages of evolution rapid• Can find cluster age from Main-Sequence turnoff• Main Sequence Matching leads to distance:

Spectroscopic Parallax and other cluster distance measures

28

Does it Work?• IC 1795 – OB Association • NGC 2264 8My

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Older• Orion Nebula Cluster 12My • M45 130My

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And Older• NGC6494 300My • M44 800My

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Oldest• M67 3.5Gy • M13 12Gy

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Blue Stragglers• Some MS stars found

past turnoff point• Mechanism:– Mass Transfer in close

binary– Collision and Merger

• Likely both

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Populations• Astronomers distinguished

Population II from Population I stars based on peculiar motion

• Differ in metallicity: Population II metal-poor formed early

• Globular Clusters are Population II

• Population III: Conjectured first stars – essentially metal free

34

Variable Stars• Some Giants and

Hypergiants exhibit regular periodic change in luminosity

• Mira (Fabricius 1595) changes by factor of 100 with period of 332d

• LPV like Mira not well modelled

35

Instability Strip• A nearly vertical region traversed

by most massive stars on HB • RR Lyrae: PII HB stars with

periods of hours. Luminosity varies little (!)

• Cepheids (PI) , W Virginis (PII) periods of days.

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Why They Pulse• Cepheids oscillate in size (radial oscillation)• Temperature and luminosity peak during rapid

expansion• Eddington: Compression increases opacity in layer

trapping energy and propelling layer up where it expands, releases energy

• Problem: compression reduces opacity due to heating

• Solution: compression ionizes Helium so less heating. Expansion reduces ionization – κ-mechanism

• Instability strip has partially ionized Helium at suitable depth

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Why We Care• Leavitt 1908: Period-Luminosity

Relation for SMC cepheids• Luminous cepheids have longer

periods• With calibration in globular clusters

cepheids become standard candles

• Later: W Virginis PLR less luminous for same period

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Discovery• Bessel 1844: Sirius wobbles: a

binary• Pup hard to find. Clark 1846

• Orbits:

• Spectrum (Adams 1915):

• Surface Gravity

• Spectrum: Very broad Hydrogen absorption lines

• Estimate:

• No Hydrogen else fusion

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Degenerate Matter• White dwarves are the

degenerate cores of stars with

• Composition is Carbon Oxygen

• Masses• Significant mass loss

• Chandrasekhar:

• Relativity:

40

Mass-Radius