Transcript The Main Sequence - University of Arizona

The Main Sequence
Projects
• Evolve from initial model to establishment of H
burning shell after core H exhaustion
• At minimum do z=0, z=0.1solar, z=solar, z=2solar
– for z=2solar 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
What should a star spend most of its time doing?
fuel
1H
4He
12C
20Ne
16O
28Si
56Ni
•
1H4He
q(erg g-1)
5-8e18
7e17
5e17
1.1e17
5e17
0-3e17
-8e18
T/109
0.01
0.2
0.8
1.5
2
3.5
6-10
q>10xq for any other stage, lowest threshold T, largest
amount of available fuel
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
CNO Cycle
CN:
12C(p,)13N
13N(+)13C
13C(p,)14N
 decays are weak rather than strong rxns - longer
timescales, produce bottlenecks
14N(p,)15O
15O(+)15N
15N(p,)12C
15N(p,)16O
NO:
16O(p,)17F
17F(+)17O
17O(p,)14N
OF:
17O(p,)18F
18F(-,)18O
18O(p,)19F
19F(p,)16O
Higher coulomb barriers - higher T
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 z=0 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
CNO vs. PP Chain
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
Problems of convective cores
Problems of convective cores
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
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 won’t work for different ones
Convection
Bouyant force per unit volume f B  g  gAr
If the signs of fB and r are opposite fB is a restoring force
d 2r
f B   2  gA r
dt

implies harmonic motionof the form r  e iNt
where N is the Brünt-Väisälä frequency N2=-Ag
N2<0 implies and exponentially growing displacement unstable

N2>0 oscillatory motion - g-mode/internal waves
Locally the acceleration is
d 2r
2

N
r
2
dt
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Convection
• Deceleration of plumes occurs in a region formally
stable against convection
• Region may still be mixed turbulently if energy in
shear > 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
N
ofRi stratification
to energy deposited in shear - real
u
r
criterion for bulk fluid flow
 •
Stars dominated by radiation pressure have less
restoring force - effect of waves & boundary stability
INCREASES WITH MASS
2
2
2
shear
Convection
Ri 

N2
 2 ushear r 2
• Richardson number
characterizes stability of
stratification to energy deposited
in shear - real criterion for bulk
fluid flow
• Ri<0.25 fully turbulent, shear
from plume spreading &
nonlinear waves
• Ri<1.0 non-linear waves break &
mix
• Ri>1.0 linear internal waves
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Convection
Ri 

N2
 2 ushear r 2
• Richardson number
characterizes stability of
stratification to energy deposited
in shear - real criterion for bulk
fluid flow
• Ri<0.25 fully turbulent, shear
from plume spreading &
nonlinear waves
• Ri<1.0 non-linear waves break &
mix
• Ri>1.0 linear internal waves
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. Ri<0.25 turbulent.
•Conversion of convective motion to wave motion. Shear instabilities,
nonlinear waves mix efficiently, large luminosity carried by waves.
Vorticity
XH
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are needed to see this picture.
Velocity
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. Ri<0.25 turbulent.
•Conversion of convective motion to wave motion. Shear instabilities,
nonlinear waves mix efficiently, large luminosity carried by waves.
Vorticity
XH
Velocity
The Convective Boundary
•Ri > 0.25-1: Linear internal wave
spectrum.
•Internal waves propagate
throughout radiative region
Baroclinic
generation term
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YUV420 codec decompressor
are needed to see this picture.
•Radiative damping of waves
generates vorticity (Kelvin’s
theorem)
•Slow compositional mixing
•Energy transport changes
gradients; generates an
effective opacity
QuickTime™ and a
YUV420 codec decompressor
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Vorticity
The Convective Boundary
•Ri > 0.25-1: Linear internal wave
spectrum.
•Internal waves propagate
throughout radiative region
•Radiative damping of waves
generates vorticity (Kelvin’s
theorem)
•Slow compositional mixing
•Energy transport changes
gradients; generates an
effective opacity
Baroclinic
generation term
Vorticity

Internal Waves
• Ri>1.0 linear internal (g-mode) mode waves

 T  S
t
Kelvin’s 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
(Fewer) Problems of convective cores
(Fewer) Problems of convective cores
(Fewer) Problems of convective cores
(Fewer) Problems of convective cores
(Fewer) Problems of convective cores
• Cluster ages match Li depletion
ages
• Width of main sequence
reproduced
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
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
Mass luminosity relations again
M
0.08
1
40
150
t(yr)
1012
1010
3x106
3x106
L
~10-4
1
>105
>105
Mass luminosity relations again
23 M
1 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
Understanding the Mass-Luminosity Relation
Relation of pressure to luminosity
Pgas  nkT
Prad 
a 4
T
3
L T4


Pgas
Ptotal
At low masses ~1
Gm
P
dm

3
  dm  const 
HSE requires fg=-fp T  r
doubling M requires doubling T, so L16L
LM4 (ignoring changes
in radius with mass &

degeneracy)
M
M
M
0
0
0
Tdm
Understanding the Mass-Luminosity Relation
Relation of pressure to luminosity
Pgas  nkT
a
Prad  T 4 ; u  aT4
3
L T4


Pgas
Ptotal
4
At high masses 0
M Gm
M
M aT
HSE requires fg=-fp T4  0 r dm    0 udm    0  dm
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

Opacity sources
• Thompson scattering (non-relativistic limit of Klein-Nishina)
8 re2
 
 0.2(1 X H ) e = mean molecular weight per free e-, mu in AMU
3 e mu
for h > 0.1mec2 (T~108 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
X i Zi2  7 2
22
 ff  3.8 10 (1 X)(X  Y)  
T

i
Ai 
Bound-free - ionization
Bound-bound - level transitions
H- -free e- from metal atoms weakly bound to H - important in sun
Conduction
1
1
1 energy transport by e- collisions - important under degenerate conditions 

  rad  cond note the mantle of the sun is mildly degenerate
Mass loss
• Steady mass loss (neither of the cases pictured above)
usually driven by absorption of photons in bound-bound
transitions of metal lines
Ý is metallicity dependent
– most transitions in metal atoms, so M
– depends on current surface z, so self enrichment important
– depends on rotation - higher temperatures and increased radiative flux
Ý and asymmetry
 - higher M
increase mass loss at poles
– 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