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7 - Stellar Structure and Evolution

# 7 - Stellar Structure and Evolution - Main Sequence phase...

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Main Sequence phase of stellar evolution -- phase in which H fuses in the core of the star the sun and most other stars doing this ! Main Sequence

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central pressure = GM ρ /2R M sun = 1.989 x 10 33 gr , R sun =6.96 x 10 10 cm ==> < ρ > = 1.41 gr / cm -3 , ρ center = 150 ==> P center ~ 10 17 dynes/cm 2 central temperature = P / n k = = > T center ~ 12 x 10 6 K
sun not heating up or cooling down ==> thermal equilibrium L sun = 3.8 x 10 33 ergs/sec = 3.8 x 10 26 watts source of this energy ? gravity : (3/5) (GM 2 /R) (1/2) => thermal => 15 x 10 6 yrs chemical : few ev per reaction (not enough) fusion (nuclear) : 4H He + Δ E 4 p + => 4(1.0078) = 4.0312 AMU He => 4.0026 AMU => Δ m = 0.0286 x 1.6 x 10 -24 gr Δ E = Δ m c 2 = 4.27 x 10 -5 ergs/4H = 27 Mev How long can sun shine w/ nuclear energy ? # 4H nuclei = 2x10 33 gr / 4x1.6x10 -24 gr = 3x10 56 ==> 12x10 51 ergs ==> 3x10 18 sec ==> 10 11 yr

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Stellar Structure Equations : use concentric spherical shells 1) Δ P / Δ r = -GM r ρ / r 2 <= press.-grav. equil. 2) ΔΜ r / Δ r = 4 π r 2 ρ <= mass conserv. 3) Δ T / Δ r = -(3 κ / 64 πσ ) ρ L r / (r 2 T 3 ) <= radiative energy transport 4) Δ L / Δ r = 4 π r 2 ερ <= ε = nuclear energy release using perfect gas law, P = k ρ T / (m H ) , 4 equat. for P, T, L, M as functions of r Δ r gas press.
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