Stellar Interiors –Nuclear Energy ASTR 2120 Sarazincls7i/Classes/astr2120/... · ASTR 2120...
Transcript of Stellar Interiors –Nuclear Energy ASTR 2120 Sarazincls7i/Classes/astr2120/... · ASTR 2120...
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Stellar Interiors – Nuclear EnergyASTR 2120
Sarazin
Fusion – the Key to the Stars
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Fusion Reactions
log T (K)
Sun
log
ε (e
rg/s
/gm
)
7 7.5
0
8-2
2
4
6
pp
CNO 3αC burning
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Thermal Stability of StarsFusion:
Makes lots of energyVery temperature sensitive
hotter more energy
} explosives
BANG
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Thermal Stability of StarsWhy don’t stars explode?Stars have negative heat capacity!
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Stars have negative heat capacityIf you add energy (heat), they get cooler!!
Energies is Stars
PE = −2 TE
E = − TE 0
TE
E
PE
0
TE
E
PE
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Thermal Stability of StarsWhy don’t stars explode?Stars have negative heat capacity!
Add energy, get coolerAdd energy, pressure increases, gas expands, gas
gets coolerCooler è less fusion è less energy
Fusion in stars è perfect thermostat!Stars are incredibly stable!
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Thermal Stability of StarsExceptions:1. Virial theorem applies to whole of star
Parts of star exchange energy è pulsations
2. Thermal gas pressure onlyKE = − EKE = (3/2) PV = (3/2) NkT only if P = Pgas
Degeneracy pressure, KE = (3/2) Pdeg V, butPdeg = func. of density only, not temperature
Fusion in degenerate regions è explosion
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Fusion – The Key to the Stars
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Fusion – The Key to the Stars• Make stellar energy, provide source of light
• Make all heavy elements (C, N, O, Fe, …)
• Make stars stable (or unstable)
• Change composition of stars → they evolve
• Set lifetime of stars, t = Enucl / L
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Solar Neutrino ExperimentsASTR 2120
Sarazin
Davis Solar Neutrino Experiment
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Tests of Stellar Structure Theory
At some level, all of astronomy (rest of this course)
Critical tests?Sun is good since it is close
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Solar Neutrino Experiments
Test idea: Fusion powers starsCannot see into Solar core with light, but
neutrinos should escapeUnfortunately, main neutrinos made by pp
reaction are very low energy, hard to detect
Detect side reactions
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Solar Neutrino Experiments
14 Mev!
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Solar Neutrino Experiments
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Solar Neutrino Experiments
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Davis Experiment
Mainly detect 8B n’sn + 37Cl ® 37Ar + e-
Normal chlorine - use 100,000 gal of C2Cl4 (dry-cleaning fluid)
Argon inert, bubble out of tank37Ar decays (beta decay), detect every
single atom!Homestead Gold Mine, South Dakota
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Davis Experiment
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Davis Experiment
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Davis Experiment
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Davis Experiment
Predict ~ 5.6 SNU (solar neutrino units)Observe only 1.8 ± 0.3 SNUs ~ 1/3
expectedWhat is wrong?
1. Experiment wrong - No2. Nuclear reaction rates wrong - No3. Astronomy wrong (solar model incorrect)
- No4. Physics wrong - Yes!
Neutrinos are NOT mass-less and stable
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Neutrino Oscillations
Three flavors of neutrinos
ne
nµ nt
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Neutrino Oscillations
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Sudbury Experiment
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Super-Kamiokande Experiment
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Neutrino Oscillations
Three flavors of neutrinos
ne
nµ nt
Yes!
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Nobel Prize 2002
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Nobel Prize 2015
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Stellar ModelsASTR 2120
Sarazin
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Five EquationsdPdr
= −GM (r)ρ
r2 Hydrostatic equilibrium
dMdr
= 4πr2ρ Mass
dLdr
= 4πr2ερ Thermal equilibirum
dTdr
= −min
3κρ64πσ r2
1T 3 L(r) radiation
25TPdPdr
convection
"
#$$
%$$
Energy transport
P = ρkTµmp
+Prad +Pdeg Equation of state
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Boundary ConditionsTake radius r as independent variableP(r), T (r), ρ(r), L(r), M (r) 0 ≤ r ≤ R*
Boundary Conditions:Center (r = 0): M (0) = 0, L(0) = 0Surface (r = R*): M (R*) =M*, P(R*) = 0, ρ(R*) = 0Two Problems: 4 differential equations, 5 boundary conditions What is R* ?
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Boundary ConditionsChange independent variable to mass Mr(M ), P(M ), T (M ), ρ(M ), L(M ), 0 ≤M ≤M*
dMdr
= 4πr2ρ ⇒ drdM
=1
4πr2ρ
dXdM
=dXdr
drdM
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Five (New) EquationsdrdM
=1
4πr2ρ radius (formerly mass)
dPdM
= −GM (r)4πr4 Hydrostatic equilibrium
dLdM
= ε Thermal equilibirum
dTdM
= −min
3κ256π 2σ r4
1T 3 L(r) radiation
25TPdPdM
convection
"
#$$
%$$
Energy transport
P = ρkTµmp
+Prad +Pdeg Equation of state
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Boundary ConditionsCenter (M = 0): r(0) = 0, L(0) = 0Surface (M =M*): P(M*) = 0, ρ(M*) = 0Better! 4 differential equations⇔ 4 boundary conditions R* is derived
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Vogt-Russell TheoremNecessary inputs:
Mass of star M*
Mean particle mass μ , opacity κ, energy production εDepend on ρ, T, composition
Vogt-Russell Theorem:Star is uniquely determined by mass M* &
composition
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Solar Model
T (K3)
ρ (gm/cm3)
ρc = 147 gm/cm3
Tc = 15 million K
Burning hydrogen in core ~ 20% of radius
Radiative zone ~ inner 85% of radiusConvective zone ~ outer 15% of radius
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Main SequenceChoice of composition:
Try mainly hydrogen and heliumSurface of Sun and most other starsInterstellar gas è what stars form from
Vary mass M*
Reproduce main sequence (normal stars)All burning H in their coresMain Sequence = stars made of hydrogen
burning H in their cores
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Main Sequence
masslow mass
high mass
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Main SequenceHydrogen:
Most abundant elementBest nuclear fuelBurned first
Stars spend most of life on main sequence, only leave it when they start to die
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Sub-Stellar ObjectsStars Brown Dwarfs Planets
Mass M ≥ 0.075≥ 78 MJ
0.012 ≤ M ≤ 0.07513 MJ ≤ M ≤ 78 MJ
M ≤ 0.012≤ 13 MJ
Fusion? Burn HLater He, C, …
Burn D = 2H deuteriumShort time, then coolDegeneracy pressure
No fusion
M¤ M¤M¤ M¤
Define “star” as self gravitating object which burns hydrogen in its early life
Star M ≥ 100 è blown apart by radiation pressure while forming?
M¤