HW 8 Written solns 1. Ionization fraction in log T vs. log plane, overplotted with strucure for Present, RG, and HB phases of sun a, b: sec. 14.2, Saha eqn.: Let i = 0, so that f ≡ f 1 ≡ n 1 n H = n e / n H , and n 0 = n H (1-f). Then Saha eqn. can be rewritten: f 2 1f = g + g 0 2 m p ( 2 m e k h 2 ) 32 T 32 ΔE i kT = 4.0 × 10 6 T 32 ρ 1.6 10 5 T ≡ b[,T] Fom the quadratic formula, we then have:
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HW 8 - Bartol Research Instituteowocki/phys633/HW8-solns.pdf · HW 8 Written solns 1. Ionization fraction in log T vs. log ! plane, overplotted with strucure for Present, RG, and
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HW 8 Written solns
1. Ionization fraction in log T vs. log ρ𝜌 plane, overplotted with strucure for Present, RG, and HB phases of sun
a, b:
sec. 14.2, Saha eqn.:
Let i = 0, so that f ≡ f1≡ n1 /∕nH= ne/ nH, and n0= nH (1-f). Then Saha eqn. can be rewritten:
f 2
1-−f = g+
g0 2mp (
2π𝜋 me kh2 )3/∕2 T
3/∕2
ρ𝜌 ⅇ-−ΔEi/∕kT = 4.0 × 10-−6 T32
ρⅇ-−1.6 105T ≡ b[ρ𝜌,T]
Fom the quadratic formula, we then have:
f = (1/2) (-b + b2 + 4 b )
sec. 14.2, Saha eqn.:
Let i = 0, so that f ≡ f1≡ n1 /∕nH= ne/ nH, and n0= nH (1-f). Then Saha eqn. can be rewritten:
e. Red dotted line, which has slope 3 in log-log plot that is predicted by scaling analysis in sec. 16.2, fits the points quite well.For Mass-Radius plot, the 3 lines are for slopes of 0.5, 0.75 and 1. The steepest, unit-slope line nearly fits the data for lower-mas stars with M<1 Msun.The shallowest, 1/2-slope line near fits the data for higher-mass stars with M > 1 Msun.