starsdns/frs126/star.struct.pdf · 2012-06-21 · earth: 3.9 billion years moon: 4.5 billion years...
TRANSCRIPT
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Stars
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Nearest stars are almost all low mass stars
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Stellar Census• Luminous stars are very rare:
High-mass main-sequence stars (O stars) arefewer than 1 in a million
Supergiants are similarly rare• Since they are rare, most are very far away.• Most stars seen with naked eye are
intrinsically luminous = Malmquist bias
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Stellar Census
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Stellar Physics and Interiors
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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•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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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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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 observatories•
•Sudbury NeutrinoObs.
•Super-Kamiokande
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Helioseismology• Vibrations of solar
atmospheremeasured byDoppler shifts
• Pattern ofobservedfrequencies tells usabout sun’sinterior (e.g. soundspeed)
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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.
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But fundamentally, they all have thesame structure – they are just giant ballsof gas, mostly H and He.
Stars come in all different masses and sizes…
Stars of different masses differ primarily in• Internal energy transport mechanism• Primary H fusion network
• PP chain in low mass stars• CNO cycle in high mass stars
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Energy Transport in stars•Radiation: energy is carried towardssurface via photons
•Convection: energy transported via hotbuoyant mass elements rising outwardswhile cool elements fall inwards
•Conduction: energy transported viacollisions through particles
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Photosphere:Radiates tospace
Energy Transport in Sun
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Solar Convection:
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Energy Transport in other stars
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Energy Transport in other stars•High-mass stars (M>1.2-1.3 Msun):convective core, radiative envelope
•Low-mass stars (M<1.2-1.3 Msun): radiativecore, convective envelope
•Really low-mass stars (M<0.3 Msun): entirelyconvective
•Relative importance of convection andradiation, depends on opacity and temperaturegradient
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How can we calculate conditions inside Sun
and Stars?…(M, L, T, P, ρ)
…using equations of stellar structure.
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Luminosity increases with Mass
• Bigger mass means higher gravity• Higher gravity means higher pressure in core• Higher pressure means higher T and density• This means MUCH more nuclear fusion• This means star is MUCH more luminous• This means mass determines luminosity
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Mass – Luminosity RelationOn the main sequence
high-mass stars areMUCH moreluminous thanlow-mass stars:
0.1 Msun 0.0005 Lsun
40 Msun 400,000 Lsun
Whitedwarfs
Main sequencestars
L ∝ M3.5