Stellar Evolution

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Stellar Evolution

• Interior of a star can be modeled as a series of
  concentric layers (onion skin)
• When in a state of hydrostatic equilibrium,
  weight on each layer is balanced by pressure
  below the layer
• Energy Transport energy flows from hot regions
  to cooler ones
• To fully model stars, need additional concepts
• Conservation of Mass (total mass is the sum of
  all the individual layers)
• Conservation of Energy amount of energy flowing
  out of the top of shell amount of energy
  flowing into the bottom of the shell ( any
  energy generated in the shell)

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• Based on mathematical representations of these 4
  concepts, (Hydrostatic Equilibrium, Energy
  Transport, Conservation of Mass, Conservation of
  Energy) we can create a mathematical model of a
  star -- this works because stars are
  structurally simple

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Main Sequence Stars

• They are in hydrostatic equilibrium
• Energy supplied by nuclear fusion
• Main Sequence is a mass sequence (there is a
  mass/luminosity relationship)
• Masses range from 0.08 50 Msun
• Stars of 100 Msun are unstable generate so much
  energy that outer layers are blown away
• There are a few known very massive stars
  spectra show emission lines (Kirchoffs 2nd Law)

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• Stars with masses lt 0.08 Msun never get hot
  enough in their interiors to ignite fusion
• -- Brown Dwarfs they are warm, due to
  gravitational contraction
• As a star exhausts H, the core contracts. Why?
  then, rate of energy production increases, and
  outer layers expand and cool

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• ZAMS zero age Main Sequence the point when H
  fusion ignites, and star is in hydrostatic
  equilibrium
• Note the Main Sequence is a band on the H-R
  diagram. Position of a star within the Main
  Sequence can change as H gets used up.
• 90 of a stars lifetime is spent on the Main
  Sequence
• For a 25 Msun star 7 x 106 yrs
• For a 0.1 Msun star ( a red dwarf) 200-300 x
  109 yrs
• Can estimate lifetime
• Lifetime M / L, but L proportional to M3.5
• So Lifetime proportional to 1/M2.5

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• Although some mixing occurs due to Convection,
  Hydrogen in outer layers never gets into the
  stars core
• Helium begins to accumulate
• Energy Production decreases
• The Core contracts
• Gravitational energy again converted to thermal
  energy H shell outside core ignites Shell
  Burning
• Energy from contraction and shell burning cause
  stars outer layers to expand
• Star becomes a Giant, highest mass stars become
  SuperGiants

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• Core continues to contract
• Very high density
• In normal gas ? pressure is proportional to
  density times temperature
• At very high density, need Quantum Mechanics to
  describe the gas conditions
• Electrons can only occupy certain energy states
  (or levels
• Two identical electrons cannot occupy the same
  level (they must have different spins)
• In a dense, ionized gas all energy levels are
  filled electron cannot change its energy of
  motion by slowing down (which puts it into a
  lower, filled level). Such a gas is
• Degenerate

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• To compress a degenerate gas, need to add enough
  energy to get the electrons into higher
  (unfilled) energy levels
• As gas heats, energy of motion of electrons
  increases, but only a few may have sufficient
  energy to reach unfilled levels As a result,
  the Pressure may not change much,

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• Lower mass stars may not have degenerate cores
  (at this stage)
• As core contracts, T increases. When T 108 K,
  He nuclei move fast enough to overcome Coulomb
  barrier He fusion begins
• 4He 4He ? 8Be ?
• 8Be 4He ? 12C ?
• He nuclei are called alpha particles so, this
  is referred to as the triple-alpha process

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• Stars of 0.4 3 Msun experience Helium flash
• Cores are degenerate as He ignites, core does
  not expand quickly from the increase in T
  reactions go faster, get a runaway explosion
• If M lt 0.4 Msun , never get He fusion
• If M gt 3 Msun, He ignites before core becomes
  degenerate (so, no flash)
• During Helium flash, L 1014 x Lsun but, star
  is not destroyed (outer layers absorb energy,
  core degeneracy is lifted)

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• He fusion now proceeds, with normal
  pressuretemperature control
• Also H-shell burning continues
• Core expands
• Outer layers contract (get hotter lower L,
  higher T)
• As He-fusion stabilizes, only small changes in L
  surface Temperature increases
• Product of He-fusion, C and O but core not hot
  enough for C, O fusion so ash builds up
• As ash builds up, core contracts, outer layers
  expand (again)

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• M gt 4 Msun T in core reaches 6 x 108 K C fusion
  ignites, followed by O-, Si-fusion (and onward,
  to heavier elements)
• Multiple Shell Burning
• H ? He
• He ? C, O
• C ? Ne, Na, Mg, O
• Ne ? O, Mg
• O ? Si, S, P
• Si ? Ni all the way up to Fe

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Star Clusters

• (generally) cannot watch a star evolve, but
• Can use H-R diagram to get snapshot of the
  stage of evolution of a cluster of stars
• Why a Cluster?
• Same age
• Same composition
• Same distance
• Stars will appear different due to masses, rates
  of evolution
• Differences in chemical composition can cause
  differences in relation between L, R, T

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• Can get temperatures from Color Index take
  CCD image of cluster with two different filters
  (very efficient)
• With T, L can plot stars on an H-R diagram
• Most stars will lie along Main Sequence
• There will be some Giants
• Highest mass stars may be missing
• Turn-off Point point at which stars have left
  the Main Sequence (and become Giants) defines
  the age of the cluster

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• Types of star clusters
• Open Clusters 10 few 1000 stars 25 parsecs
  in diameter mostly young to middle age stars
• Globular Clusters 105 106 stars 30 pc in
  diameter old stars
• Main Sequence stars in Globular clusters are
  bluer, fainter than similar stars in Open
  clusters due to lack of elements heavier than
  He (less opacity)
• In Globular Clusters some stars on Horizontal
  Branch
• Stars contract and heat up dramatically after He
  fusion ignites, move to left on H-R diagram
  once He in core is used up, get He-shell burning
  move back to Giant region

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Variable Stars

• Two types eclipsing binaries pulsating stars
• Pulsating stars expand and contract cool and
  heat
• Cepheid variables d Cephei Polaris
• Supergiants (Ib) and Bright Giants (II) spectral
  types F, G
• Vary in brightness 0.5 to more than 1 magnitude,
  over cycles of 2 60 days
• RR Lyrae stars fainter than Cepheids, periods lt
  1 day

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• Period/Luminosity Relationship for Cepheids
  longer period, higher luminosity
• Type I Cepheids sun-like abundance of elements
  heavier than He
• Type II Cepheids small amounts of heavy
  elements they are fainter
• RR Lyrae stars also have small abundances of
  heavy elements

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• Why do these stars pulsate?
• As star moves off Main Sequence
• H shell burning (Giant phase)
• He ignites (back to left of H-R diagram)
• He shell burning star expands again
• Combination of size/temperature results in
  instability Instability Strip
• At this stage, there is an internal zone of
  partially ionized helium (He II) outer layers,
  too cool to ionize He, inner layers get fully
  ionized He
• This zone has large opacity absorbs energy when
  compressed, releases energy when expands

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• Outer layers expands zone gets less ionized,
  energy released, expansion accelerates
• The expansion overshoots star contracts zone
  compressed, ionization increases, energy gets
  absorbed compression overshoots the other way
• And so on the star is not in equilibrium!
• Note if star too cool this zone is too deep
  for expansion to occur if too hot, this zone of
  He II is too close to the surface (dont get
  enough compression)

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Death of Stars

• Most Massive stars live a few x 106 years
• Least Massive stars live 100s of billions of
  years (perhaps.)
• Low Mass Stars
• If lt 0.4 Msun cannot ignite He fusion
• Cores of these stars are convective, so never
  develop He-ash core
• Total lifetime is uncertain (mass loss due to
  strong stellar winds)

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• Intermediate Mass Stars (0.4 4 Msun)
• H exhausted in core
• He ash core (Red Giant stage)
• He fusion ignites but not massive enough for
  Carbon fusion little or no convection in core
• End product? A Carbon/Oxygen core
• Since no fusion core contracts
• Energy released ( energy from shell burning) ?
  Outer envelope expands
• Rapid Mass loss occurs (atmosphere is very cool,
  2000K dust grains form)

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• Periodic eruptions in He-shell ? even more mass
  loss (1 Msun in 105 years)
• Finally, entire outer layers lost in a sudden
  expulsion ? a planetary nebula forms 0.2 3
  light years across gas expands at 10 20 km/sec
• Planetary nebula can last 1000 10,000 yrs
• When outer layers lost, the hot (100,000K) inner
  layers exposed strong UV radiation ionizes the
  expanding nebula
• 10. Eventually, central star cools off ? white
  dwarf

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White Dwarfs

• Along with red dwarfs (low mass, main sequence
  stars), white dwarfs are the most common stars
• No internal energy source
• Degenerate gas C and O ions in a sea of
  degenerate electrons
• Degenerate electron pressure balances gravity
• Near the surface a hot atmosphere heavy ions
  sink, so some have atmosphere of pure H, or He
• Really not a star an example of a compact object

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• Degenerate matter good conductor of thermal
  energy
• Eventually, cools off ? becomes a black dwarf
• Mass Limit 1.4 Msun
• Chandrasekhar Limit
• Note star has lost mass before becoming a white
  dwarf
• If there is more mass, gravity will overcome the
  degenerate electron pressure