The Main Sequence

1
The Main Sequence
2
Projects

• Evolve from initial model to establishment of H
  burning shell after core H exhaustion
• At minimum do z0, z0.1solar, zsolar, z2solar
• for z2solar use hetoz 2.0 and 3.0 (see genex)
• Note features in the HR diagram and identify with
  physical processes
• Compare results from different metallicity and YHe

3
What should a star spend most of its time doing?
fuel q(erg g-1) T/109
1H 5-8e18 0.01
4He 7e17 0.2
12C 5e17 0.8
20Ne 1.1e17 1.5
16O 5e17 2
28Si 0-3e17 3.5
56Ni -8e18 6-10

• 1H?4He qgt10xq for any other stage, lowest
  threshold T, largest amount of available fuel

4
The PP Chain

• Actually three reaction branches
• PPI
• p(p,e,?)d
• d(p,?)3He
• 3He(3He,2p)4He
• PPII
• 3He(4He, ?)7Be
• 7Be(e-,?)7Li
• 7Li(p,?)4He
• PPIII
• 7Be(p,?)8B
• 8B(e ? decay)24He
• PPII/III dominate at high T, high Yhe
• Sun predominantly PPII

5
CNO Cycle

• CN
• 12C(p,?)13N
• 13N(??)13C ? decays are weak rather
  than strong rxns - longer
• 13C(p,?)14N timescales, produce
  bottlenecks
• 14N(p,?)15O
• 15O(??)15N
• 15N(p,?)12C
• 15N(p,?)16O
• NO Higher coulomb
  barriers - higher T
• 16O(p,?)17F
• 17F(??)17O
• 17O(p,?)14N
• OF
• 17O(p,?)18F
• 18F(?-,?)18O
• 18O(p,?)19F
• 19F(p,?)16O

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CNO vs. PP Chain

• Equate CNO and PP energy production to find where
  each dominates
• T 1.7x107(XH/50XCN)1/12.1
• Crossover point occurs at 1.1 M? for Pop I
• At z0 must reach He burning T and produce CNO
  catalysts
• ?(PP)?X2H?0(T/T0)4.6 ?(CNO)
  ?XHXCNOfN?0(T/T0)16.7
• PP and CNO have to produce same luminosity to
  support a given mass but CNO works over much
  narrower T range
• ? Energy from CNO deposited in very small radius
  - too much to carry by radiation
• 1st physical division of stellar types PP
  dominated with no convective core and CNO
  dominated with convective core at 1.1 M?

7
CNO vs. PP Chain
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Problems of convective cores

• Convective core size determines
• Luminosity
• Entropy of burning
• progress of later burning stages yields
• How do we measure core size?
• Indirectly
• Binaries (esp. double lined eclipsing binaries)
  give precise masses and radii. If predicted core
  size too small model is underluminous. Radius
  also too small since central condensation ?
  fluffy exterior
• Cluster ages - turnoff ages lower than ages
  determined by independent means like Li depletion
  in brown dwarfs
• Width of the main sequence - centrally condensed
  stars evolve further to the red
• Directly - apsidal motion of binaries - stars not
  point masses tidal torques cause line of apsides
  of orbit to precess. Rate of precession depends
  on central condensation

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Problems of convective cores
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Problems of convective cores
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Problems of convective cores

• Apsidal motion - stars not point masses so tidal
  torques cause precession of the line of apsides
  of the orbit
• Rate of precession depends on central
  condensation of star
• Stars with larger convective cores more centrally
  condensed

12
Problems of convective cores

• Mixing length models always predict core sizes
  too small
• Posit convective overshooting and say material
  mixed some arbitrary distance outside core
• Various levels of sophistication, but always
  observationally calibrated
• Amount of overshooting needed varies with mass -
  calibration for one star wont work for different
  ones

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Convection

• Bouyant force per unit volume
• If the signs of fB and ?r are opposite fB is a
  restoring force
• implies harmonic motion of the form
• where N is the Brünt-Väisälä frequency N2-Ag
• N2lt0 implies and exponentially growing
  displacement - unstable
• N2gt0 oscillatory motion - g-mode/internal waves
• Locally the acceleration is

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Convection

• Deceleration of plumes occurs in a region
  formally stable against convection
• Region may still be mixed turbulently if energy
  in shear gt potential across region established by
  stratification
• If less, material displaced by plume, not
  engulfed or continuing to accelerate, and returns
  to original position - harmonic lagrangian motion
• Richardson number characterizes stability of
  stratification to energy deposited in shear -
  real criterion for bulk fluid flow
• Stars dominated by radiation pressure have less
  restoring force - effect of waves boundary
  stability INCREASES WITH MASS

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Convection

• Richardson number characterizes stability of
  stratification to energy deposited in shear -
  real criterion for bulk fluid flow
• Rilt0.25 fully turbulent, shear from plume
  spreading nonlinear waves
• Rilt1.0 non-linear waves break mix
• Rigt1.0 linear internal waves

16
Convection

• Richardson number characterizes stability of
  stratification to energy deposited in shear -
  real criterion for bulk fluid flow
• Rilt0.25 fully turbulent, shear from plume
  spreading nonlinear waves
• Rilt1.0 non-linear waves break mix
• Rigt1.0 linear internal waves

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The Convective Boundary

• Boundary characterized by Richardson number Ri
  N2 / (?u/?r)2 Ratio of potential energy across
  a layer to energy in shear
• Ri 0.25
• Boundary region. Impact of plumes deposits
  energy through Lagrangian displacement of
  overlying fluid. Internal waves propagate from
  impacts. Rilt0.25 turbulent.
• Conversion of convective motion to wave motion.
  Shear instabilities, nonlinear waves mix
  efficiently, large luminosity carried by waves.

Vorticity
XH
Velocity
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The Convective Boundary

• Boundary characterized by Richardson number Ri
  N2 / (?u/?r)2 Ratio of potential energy across
  a layer to energy in shear
• Ri 0.25
• Boundary region. Impact of plumes deposits
  energy through Lagrangian displacement of
  overlying fluid. Internal waves propagate from
  impacts. Rilt0.25 turbulent.
• Conversion of convective motion to wave motion.
  Shear instabilities, nonlinear waves mix
  efficiently, large luminosity carried by waves.

Vorticity
XH
Velocity
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The Convective Boundary

• Ri gt 0.25-1 Linear internal wave spectrum.
• Internal waves propagate throughout radiative
  region
• Radiative damping of waves generates vorticity
  (Kelvins theorem)
• Slow compositional mixing
• Energy transport changes gradients generates an
  effective opacity

Baroclinic generation term
Vorticity
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The Convective Boundary

• Ri gt 0.25-1 Linear internal wave spectrum.
• Internal waves propagate throughout radiative
  region
• Radiative damping of waves generates vorticity
  (Kelvins theorem)
• Slow compositional mixing
• Energy transport changes gradients generates an
  effective opacity

Baroclinic generation term
Vorticity
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Internal Waves

• Rigt1.0 linear internal (g-mode) mode waves
• Kelvins theorem lagranigian displacement and
  oscillatory motion is irrotational unless there
  is damping
• Dissipation of waves by radiative damping
  generates vorticity - mechanism for mixing in
  radiative regions

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(Fewer) Problems of convective cores
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(Fewer) Problems of convective cores
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(Fewer) Problems of convective cores
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(Fewer) Problems of convective cores
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(Fewer) Problems of convective cores

• Cluster ages match Li depletion ages
• Width of main sequence reproduced

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Rotation

• Changes stellar structure in several ways
• Centripedal accelerations mean isobars not
  parallel with equipotential surfaces
• star is oblate
• star is hotter at poles than equator (cetripedal
  acceleration counters some gravity so pressure
  support can be less)
• ?T has non-radial components - meridional
  circulation which transports angular momentum and
  material
• Turbulent diffusion along isobars radiative
  losses during meridional circulation wave
  motion transport J - setting up shear gradients
  and diffusing composition
• evaluating stability against shear gradients
  back to Richardson
• Coupled strongly with waves since waves transport
  J
• not well modeled
• waves probably have more effect on core sizes,
  rotation better at transporting material through
  radiative region

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Other outstanding issues in stellar observations

• Observations potential solutions
• Weird nucleosynthesis on RGB/AGB - Li,N,13C
  enhancements, s process - waves ( rotation)
• He enhancements in O stars, He,N enhancements in
  blue supergiants - rotation (waves)
• Blue/red supergiant demographics - waves
  (rotation)?
• Primary nitrogen production in early massive
  stars - waves (rotation)
• Young massive stellar populations, I.e. terrible
  starburst models - waves rotation
• eruptions in very massive stars - waves
  radiation hydro (radiative levitation?)
• mass loss leading to Wolf-Rayet demographics
  rotation waves

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Mass luminosity relations again
M? 0.08 1 40 150
t(yr) 1012 1010 3x106 3x106
L ? 10-4 1 gt105 gt105
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Mass luminosity relations again
23 M?
52 M?

• 104 change in energy generation rate between 1
  and 23 M?
• 1.5 change in energy generation rate between 23
  and 52 M?

1 M?
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Understanding the Mass-Luminosity Relation
Relation of pressure to luminosity At low
masses ?1 HSE requires fg-fp? ?T ?doubling M
requires doubling T, so L?16L ?L?M4 (ignoring
changes in radius with mass degeneracy)
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Understanding the Mass-Luminosity Relation
Relation of pressure to luminosity At high
masses ??0 HSE requires fg-fp? ?T4 ?doubling M
requires doubling P, T?21/4T ?L?2L ?L?M t?L/M
?t ?M-3 at low mass and t ? const at high mass
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Opacity sources

• Thompson scattering (non-relativistic limit of
  Klein-Nishina)
• ?e
  mean molecular weight per free e-, mu in AMU
• for h? gt 0.1mec2 (T108 K) must account for
  compton scattering
• Dominates for completely ionized material
• During H burning Ye goes from 0.72 ? 0.4994
  fewer e- per nucleon, so scattering diminished.
  Opacity drops so convective cores shrink on the
  main sequence
• Free-free
• Bound-free - ionization
• Bound-bound - level transitions
• H- - free e- from metal atoms weakly bound to H -
  important in sun
• Conduction
• energy transport by e-
  collisions - important under degenerate
  conditions - note the mantle of
  the sun is mildly degenerate

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Mass loss

• Steady mass loss (neither of the cases pictured
  above) usually driven by absorption of photons in
  bound-bound transitions of metal lines
• most transitions in metal atoms, so is
  metallicity dependent
• depends on current surface z, so self enrichment
  important
• depends on rotation - higher temperatures and
  increased radiative flux increase mass loss at
  poles - higher and asymmetry
• Kinematic luminosity of O star wind integrated
  over lifetime can be 1051 erg - comparable to
  supernovae
• Eruptions in sun driven by magnetic reconnection
• To be explored later
• eruptions in massive stars (pulsational and
  supereddington instability)
• dust driven and pulsational mass loss in AGB
  stars
• continuum ? driven winds in Wolf-Rayet stars