Introduction to Stellar Evolution

1
Introduction toStellar Evolution

• Joyce A. Guzik
• Thermonuclear Applications Group, X-2
• Los Alamos National Laboratory
• April 8, 2002

2
Outline

• Single-star evolution modeling
• stellar structure equations
• physical input and assumptions
• Nuclear Energy Generation
• Evolution of stars of 1/10, 1, and 15 times the
  mass of the Sun
• Star formation and the Initial Mass Function

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Stellar Structure Equations (1)
1)
Mass conservation
Hydrostatic equilibrium
2)
Thermal equilibrium (note time derivative)
3)
4
Stellar Structure Equations (2)
Temperature gradient
4)
radiative diffusion
or, if
convection
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Physical input for stellar models

• Opacities
• LLNL OPAL (Iglesias Rogers 1996) OP (Seaton et
  al. 1996)
• LANL LEDCOP (Magee et al. 1995)
• Low-temperature Opacities
• e.g., Kurucz 1992 Alexander Ferguson 1995
  Neuforge 1993
• Equation of State
• OPAL (Rogers, Swenson Iglesias 1996) MHD
  (Dappen, Mihalas, Hummer, Mihalas 1988) CEFF
  (Christensen-Dalsgaard Dappen 1992) SIREFF
  (Guzik Swenson 1997)
• Nuclear Reaction Rates
• Caughlan Fowler 1988 Bahcall Pinsonneault
  1995 Adelberger et al. 1998 NACRE (Angulo et
  al. 1999)
• Convection Treatment
• Bohm-Vitense 1958 Canuto, Mazzitelli, Goldman
  (1991, 1992, 1996)
• Element Diffusion Treatment
• Burgers 1969 Cox, Guzik Kidman 1988 Thoul,
  Bahcall Loeb 1994

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Assumptions and commonly omitted physics

• 1-dimensional (spherical symmetry)
• hydrostatic and thermal equilibrium
• initial homogeneous composition
• Often omitted
• rotation (solid body or differential)
• B fields
• mass loss and/or accretion
• diffusion and/or radiative levitation
• additional mixing
• convective overshoot
• shear from differential rotation
• meridional circulation
• pulsational instabilities, etc.

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Constraints for solar and stellar models

• For Sun, we have excellent constraints
• Know M, Teff, L, R, age, surface Z/X, surface
  Vrot extremely accurately.
• Because we can resolve the disk, we can observe
  millions of oscillation modes (next weeks
  lecture)
• Can accurately identify all modes
• For other stars
• Know approximately L (Hipparcos parallax),
  surface gravity (M/R2), Teff, surface
  composition M/H, v sin i (not v) from spectrum
  analysis
• Dont know mass, age. Surface composition altered
  by mass loss, accretion, diffusion, levitation.
• Common age and composition often assumed for
  stars in clusters
• Eclipsing spectroscopic binaries extremely useful
  for additional constraints on stellar masses,
  radii, etc.

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Pre-main sequence evolution tracks
Iben fig. reproduced from Bowers Deeming
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Stellar evolution tracks

Iben fig. reproduced from Bowers Deeming
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From Mihalas and Binney 1981
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From Bowers Deeming
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Iben fig. reproduced Bowers Deeming
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Why does a star shine?

• A star shines or radiates energy that we can
  see because
• 1) nuclear fusion reactions are generating energy
  in its core
• 2) it is contracting and/or cooling
• Stars that are forming convert gravitational
  energy to thermal kinetic energy and radiate it
  away.
• white dwarf stars have used up their nuclear
  fuel, and are slowly cooling.
• At its current luminosity, the sun could shine
  for
• 5,000 years (chemical energy source)
• 32 million years (gravitational energy source)
• 10 billion years (nuclear fusion source)

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Figure reproduced from Neuforge et al. ApJ 550,
493 (2001)
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From Clayton 1968
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From Clayton 1968
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From Clayton 1968
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From Phillips, The Physics of Stars
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Nuclear energy generation rates
Proton-Proton Chain
26.2 MeV per He produced
CNO Bi-Cycle
25 MeV per He produced
2.4 MeV per He used
Triple-alpha Process
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Interior structure of main-sequence stars
20,000 Ls 31,000 K, 7 Rs
1 Ms
0.1 Ms
0.7 Ls 5610 K, 0.88 Rs
52,300 K
r0.004
0.0004 Ls 2250 K, 0.15 Rs
15 Ms
r1.5
r30
13 MK, 80 g/cc
4.4 MK, 300 g/cc
34 MK, 6 g/cc
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What happens to a star like the Sun?

• Protostar gravitationally until core hydrogen
  ignites (takes 20 million years).
• Burns hydrogen in core (main-sequence phase) for
  about 11 billion years. (The Sun is now about
  halfway through this phase.)
• When most of core H exhausted, core contracts and
  heats up. Energy released expands envelope, and
  star becomes a red giant with radius 200 x Rs.
• When core temperature reaches 200 million K,
  three He atoms begin to fuse into carbon ( He
  flash). Star contracts and becomes bluer, and
  burns He in core for another billion years.
• When He fuel is exhausted, star expands and
  becomes red again. Outer envelope released as a
  planetary nebula.
• Star becomes Carbon/Oxygen core white dwarf of
  a0.6 Ms, and slowly cools.
• Central density 500,000 g/cc. Radius about 1.5
  REarth

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The Future of the Sun (1)

• Reaches luminosity 1.1 Ls in 1.1 billion years,
  and 1.4 Ls in 3.5 billion years (predict runaway
  greenhouse catastrophes on Earth due to
  additional water vapor in atmosphere)
• As Sun becomes a Red Giant (H shell-burning),
• convective envelope encompasses outer 75 of mass
  (now at only 2.5 of mass), and mixes some of the
  nuclear-processed material to the surface.
• Sun reaches 2300 Ls, and radius of 170 Rs.
  Engulfs Mercury. Sheds 0.275 Ms in strong
  winds.
• Helium Flash fuses He into Carbon in core for
  100 million years.

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The Future of the Sun (2)

• After core Helium exhausted, Sun progresses to
  the Asymptotic Giant Branch (AGB). Begins
  thermal pulses. Reaches luminosity 5200 Ls.
  Stronger winds reduce Suns mass further.
• Sun spends 20 million years on AGB, and 400,000
  years thermally pulsing.
• Suns radius increases to 213 Rs (0.99 AU), or
  about the radius of the Earths present orbit,
  but by this time Venus and Earth have moved out
  to 1.22 and 1.69 AU, respectively
• Results for fate of Venus and Earth strongly
  depend on mass loss rate if Sun loses less
  mass, could engulf Venus and Earth

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The Future of the Sun (3)

• Suns rate of mass loss accelerates, and it
  spends last 100,000 years ejecting outer envelope
  as a planetary nebula.
• Material in envelope, including some processed in
  core of sun that has been mixed to the surface,
  is expelled in the strong winds to enrich the
  interstellar medium.
• Sun ends up as a Carbon-Oxygen core white dwarf
  of mass 0.541 Ms. Suns radius then only 1.5 x
  the radius of Earth. Orbits of Venus and Earth
  shifted to 1.34 and 1.85 AU, respectively.

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From Sackmann et al., ApJ 418, 457 (1993)
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What happens to a star only 1/10the mass of the
Sun?

• Protostar gravitationally contracts until core
  hydrogen ignites (this takes 2 billion years!).
• Burns hydrogen in core for about six trillion
  years (450 x longer than current age of
  universe!).
• After 6 trillion years, core becomes radiative
  and burns hydrogen more rapidly. Hydrogen starts
  to burn in shell around core, and core begins to
  contract.
• Core becomes degenerate and stops contracting.
  Star never becomes a red giant.
• Hydrogen shell burning dies out, and star cools
  as a Helium-core white dwarf with radius a few x
  REarth.
• (Very efficient use of H fuel--the final envelope
  H mass fraction is only 15.5, and final overall
  H fraction is only 1)

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From Laughlin et al. ApJ, 482, 420 (1997)
0.1 Ms evolution
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From Laughlin et al. ApJ, 482, 420 (1997)
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What happens to a star 15 timesas massive as the
Sun?

• Protostar gravitationally contracts until core
  hydrogen ignites (takes only 100,000 years).
• Burns hydrogen in core for about 10 million
  years.
• When core H exhausted and core T reaches 200
  million K, He burns in core for about 1 million
  years. Core shrinks and star evolves to the red.
• After core He is exhausted, burns C to Ne, Ne to
  O and Si, O to Si, and Si to Fe. Stages are
  progressively shorter, and Si burning takes only
  2 days!
• After Fe core produced, any further nuclear
  reactions consume energy instead of producing it.
  Core loses support and collapses, releasing
  gravitational energy. Outer layers are expelled,
  creating a Type II supernova.
• Remnant of core is a neutron star of at most a
  few Ms
• density 100 million tons/cc radius only 15 km
  . May see as a pulsar

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From Brunish Truran, ApJ 256, 247 (1982)
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Mass Breakpoints

Process Mass (Ms) D
burning gt0.012 H burning gt0.07 end as He
WD lt 0.8 Conv. Core on MS gt1.2 He
flash 0.8-2.25 Ends as CO WD 0.8-9 Ends as
NeOMg WD 9.-11 Ends as Type II SN/Neutron
Star 11.-50 Ends as Type Ib SN/black hole gt50
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Star formation considerations (1)
Jeans critical mass for gravitational instability
For normal interstellar matter, density 1
atom/cc,
3000 Ms for T 10 K 100,000 Ms for T 100 K
For cold dense molecular clouds 102 - 104
atom/cc,
300 Ms for T 10 K
As a cloud contracts, if it cannot lose heat to
its surroundings, it will reach a limit to
contraction.
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Star formation considerations (2)

• Radiative cooling from molecules and dust grains
  important (higher µ)
• As subclouds become Jeans unstable they will
  start to contract separately (fragmentation)
• External heating by cosmic rays and x-rays
• Role of initial angular momentum/rotation in
  resisting collapse?
• Role of magnetic fields?
• Role of turbulence (turbulent pressure)?
• Role of observed mass outflows in forming stars?
• Role of disk formation (more efficient cooling)
• Massive stars contract more quickly, but if they
  form first might heat surroundings and disrupt
  formation of low mass stars.
• How universal is initial mass function--dependen
  ce on metallicity, low mass cutoff?

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Number of stars of different masses

• Initial Mass Function N(m?m) µ m-1.35
• Mass (Ms) Number
• 49 - 50 1
• 14 - 15 20
• 4.5 - 5 100
• 0.9 - 1 1000
• 0.45 - 0.5 3000
• 0.09 - 0.1 24,000

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Stellar Recycling

• Stars can eject some of their mass at various
  stages, in winds, in pulses while red giants, in
  the helium flash, as planetary nebulae while
  becoming white dwarfs, or in supernova
  explosions.
• All elements except the light elements H, He, Li,
  Be, and B are produced in stars. These elements
  on earth (and in your body) have been processed
  through several generations of stars.
• hydrogen and helium Big Bang
• lithium, beryllium, boron Big Bang, cosmic rays
• nitrogen and some helium hydrogen-burning
• carbon, oxygen, neon helium-burning
• neon, magnesium, aluminum, sodium
  carbon-burning
• silicon, sulfur, argon, calcium
  oxygen-burning
• iron, nickel, heavier elements supernovae, red
  giants