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 1
Feb 24, 2016
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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
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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!
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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
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CNO Chain• In large stars
core hot and CNO chain dominates fusion
• Rate rises rapidly with temperature
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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
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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?
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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??
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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
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106
107
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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
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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
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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
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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%
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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
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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
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M57
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Ghost of Jupiter (NGC 3242)
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Cat’s Eye
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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
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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
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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
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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:
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Mass-Radius