•Sources of energy for Sun •Nuclear fusion •Solar neutrino...

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Solar Interior Sources of energy for Sun Nuclear fusion Solar neutrino problem • Helioseismology

Transcript of •Sources of energy for Sun •Nuclear fusion •Solar neutrino...

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Solar Interior

• Sources of energy for Sun• Nuclear fusion• Solar neutrino problem• Helioseismology

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Solar Atmosphere

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Solar interior

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Solar facts• Luminosity: 3.8x1026 J/s• Mass: 2.0x1030 kg• Composition: 73% Hydrogen, 25%Helium, 2% “heavy elements” (by mass)• Radius: 7.0x108m• Avg Density: 1400 kg/m3

• Teff = (L/(σ4πR2))1/4=5800ºK (How doesthis compare with the average and centraltemperatures?)

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Solar interior

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Solar interior•At avg density of 1400kg/m3 and avg temp of4.5x106K “mean free path”of photon before interactingwith matter is < 1 cm.Optical depth is very high,effective path length is muchlonger than R; time toescape is much longer thanR/c~2 sec

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Solar interior•Timescale for radiation todiffuse out is > few 104 years

• Slow leakage of photonsregulates L

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Solar Energy•Sun is radiating copious amounts of energy• What is the source of this radiation?• What if we just consider the fact that the sunis a ball of hot gas, no additional heat source?• According the ideal gas law, the thermalenergy of a gas at temperature T is:

E=3/2(NkT)(N=# of particles, k=Boltzmann’s constant)

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Solar Energy• (see derivation on board about K-Htimescale)

• Heating from gravitational contraction canonly sustain sun for ~107 years (K-Htimescale)

• Yet we know that the age of the solar systemis ~4.5 billion years

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Radioactive dating• Oldest rocks found so far:

Earth: 3.9 billion yearsMoon: 4.5 billion yearsMars: 4.5 billion yearsMeteorites: 4.6 billion years

• The smaller an object, the faster it coolsand therefore solidifies, the older it isPlanets, moon, meteorites (entire solar system)

formed 4.6 billion years ago (Sun too)

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Solar Energy• (see derivation on board about K-Htimescale)

• Heating from gravitational contraction canonly sustain sun for ~107 years (K-Htimescale)

• Yet we know that the age of the solar systemis ~4.5 billion years

• We need another source of energy: nuclearfusion!

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Fusion &Fission

• Fusion(joining) oflight elementsresults in moretightly boundelementsReleases

energy up toFe

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Fusion &Fission

• Fission (splitting)of heavy elementsresults in moretightly boundelementReleases energy

above Fe

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How does fusion release energy?• So 0.7% of mass of H in Sun is converted into

energy.• Total energy available Enuc= 0.007MSunc2

(compare with Etherm=(3/2)NkT orEgrav=(3/10)GMsun

2/Rsun )• Nuclear lifetime t = Enuc/Lsun = 1011 yrs• Actually, we’ll see drastic things happen to

Sun once H in core exhausted, which is only10% of total

• So Sun “lives” for about 1010 yrs.

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How does fusion happen?• In order for reactionto occur, collidingnuclei must haveenough KE toovercome Coulombrepulsion of likecharges• First, thinkclassically: energyrequired to overcomebarrier is provided bygas thermal energy…

p-p

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How does fusion happen?•Including effects of QMtunneling indicates thatfusion can happen in thecenter of the sun, withT~107 K

• Next, calculate reactionand energy generationrates, which are strongfunctions of temperature.

p-p

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Proton-proton chainMost important reaction in Sun is PPI chain

1H + 1H -> 2H + e+ + ν

2Η + 1Η −> 3Ηe + γ

3He + 3He -> 4He + 1H + 1H

Net result is 4H fused into 4He

e+ = positronν = neutrinoγ = photon

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PPI Chain

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PPII & PPIII• After first 2 steps, 31% of reactions proceedwith 3He+4He 7Be+γ, and further branchbetween:

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•69% of the time, H fusion occurs via PPI chainin Sun

•31% of the time, PPII chain occurs1H + 1H -> 2H + e+ + ν2Η + 1Η −> 3Ηe + γ3He + 4He -> 7Be + γ7Βe + e- -> 7Li + ν7Li + 1H -> 2 4He

•Other chains (CNO cycle) are negligible, butimportant in other stars

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CNO Cycle

•H can also be converted to4He through the CNO cycle

• Carbon, Nitrogen, Oxygenused as catalysts

•Much more T-dependentthan P-P chain, CNO cycleoccurs in stars slightly moremassive than the Sun

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CNO cycle: stars with M > 1.2MSun

Uses C, N, and Onuclei to catalyzefusion of H intoHe

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Solar neutrino problem• 4 fundamental forces:gravitational, electromagnetic,strong, weak• Elementary particlesLeptons (electrons, muons,taus, 3 neutrinos) participatein weak and EM interactionsQuarks, 3 at a time make upprotons and neutrons(baryons), participate instrong, weak, EM interactionsBoth leptons and quarks areacted on by gravity

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Solar neutrino problem• Neutrinos: zero charge, non-zero mass, eachtype νe, νµ, ντ, is associated with a chargedparticle (electron, muon, tau)• Rarely interact with matter: 1011 neutrinos passthrough your thumb every second. For every1011 neutrinos from the sun that pass through theearth, only one interacts with terrestrial material

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Solar neutrino problem• Spectacular confrontation of solar andtheoretical particle physics

• Background: the P-P chain predicts theproduction of neutrinos along the way toforming 4He, e.g.:

8B8Be + e+ + νe

Ultimately results in:4 1H 4He + 2e+ + 2 νe + 2γ

(e+ positrons, γ photons, νe neutrinos)

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Energy spectrum of neutrinosproduced in different reactions

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In 1970, in theunderground Homestake

Gold Mine in SD,physicists startedmeasuring solar

neutrino flux producedby p-p chain

•Underground tank of 615,000 kg of C2Cl4

•Detects 37Ar produced by reaction between 37Cl and ν•Sensitive to production of few Ar atoms per month

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Solar neutrino results• Measured rate was ~1/3 predicted rate fromstandard solar model = “solar neutrinoproblem”

• Physicistsblamed this onSolar models

• But experimentsmeasured onlyelectron neutrinos...

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Solar neutrino solutions?3 possibilities:1. Predicted # of ν from the solar interaction, or predicted

# of argon incorrect

2. Experimental data wrong

3. Theory of neutrinos incorrect: in terms of behaviorwhile traversing large distances

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Solar neutrino results• For 30 years, measured rate was ~1/3 predicted

rate from standard solar model = “solarneutrino problem”

• 3 possibilities:1. Predicted # of ν from the solar interaction, or predicted

# of argon incorrect

2. Experimental data wrong

3. Theory of neutrinos incorrect: in terms of behaviorwhile traversing large distances

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Solar neutrino results• The problem was not with the solar model, but

our understanding of particle physics!

• Solution: while traveling from the sun at close tothe speed of light, electron neutrinos change“flavor” to muon or tau neutrinos. Detector isonly sensitive to electron neutrinos, hence thelower detection rate than expected

• Verified this model with recent observations of(Superkamiokande, Sudbury Neutrinoobservatory)

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Solar neutrino observatories•

•Sudbury NeutrinoObs.

•Super-Kamiokande

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Helioseismology• Vibrations of

solar atmospheremeasured byDoppler shifts

• Pattern ofobservedfrequencies tellsus about sun’sinterior (e.g.sound speed)

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Measured vs. predicted soundspeed in Sun

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Internal rotation rate of Sunmeasured through helioseismology

Convection andradiative zonesrotate at differentratesPerhaps leads togeneration ofmagnetic field

Red = fast rot.Blue = slow rot.