Stellar Interiors – Nuclear EnergyASTR 2120

Sarazin

Fusion – the Key to the Stars

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

Thermal Stability of StarsFusion:

Makes lots of energyVery temperature sensitive

hotter more energy

} explosives

BANG

Thermal Stability of StarsWhy don’t stars explode?Stars have negative heat capacity!

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

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!

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

Fusion – The Key to the Stars

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

Solar Neutrino ExperimentsASTR 2120

Sarazin

Davis Solar Neutrino Experiment

Tests of Stellar Structure Theory

At some level, all of astronomy (rest of this course)

Critical tests?Sun is good since it is close

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

Solar Neutrino Experiments

14 Mev!

Solar Neutrino Experiments

Solar Neutrino Experiments

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

Davis Experiment

Davis Experiment

Davis Experiment

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

Neutrino Oscillations

Three flavors of neutrinos

ne

nµ nt

Neutrino Oscillations

Sudbury Experiment

Super-Kamiokande Experiment

Neutrino Oscillations

Three flavors of neutrinos

ne

nµ nt

Yes!

Nobel Prize 2002

Nobel Prize 2015

Stellar ModelsASTR 2120

Sarazin

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

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* ?

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

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

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

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

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

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

Main Sequence

masslow mass

high mass

Main SequenceHydrogen:

Most abundant elementBest nuclear fuelBurned first

Stars spend most of life on main sequence, only leave it when they start to die

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¤