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Unformatted text preview: causes this inversion? (b) [15 pts] Plot the mass fractions of 4He, 12C and 16O relative to their photospheric mass fractions (i.e., values at the last radius point) as a function of radius. Describe and explain the origin of any variations (or not) present in the core, radiative zone and convection zone. (c) [15 pts] Reproduce Figure 11.5. You can calculate the derivative dLr/dr numerically (ignoring i=0 and i=max) as: dLr
2 Li − Li−1
Li+1 − Li
ri+1 − ri
ri − ri−1 Where is the maximum of this curve? Why is this the maximum? (d) [15 pts] Calculate and plot the energy production rate ε as a function of radius using Equation 10.36 and verify that it is maximum at the core (be careful at r=0!). (2) [70 pts] Deriving the minimum stellar mass for hydrogen fusion The equation of state for a semi-‐degenerate object, ignoring some constants of order 1, can be written as: 7 5/3 P = 10 ρ η2
1+η N/m2 where ρ is measured in kg/m3 and η is the degeneracy parameter, the ratio of Fermi energy to thermal energy for electrons in the plasma: µe
(3π 2 h3 )2/3 ρNA
¯ 2/3 ≈ 8×10−4 T
ρ2/3 where μe is the number of baryons per electron in a fully ionized gas, a number roughly of or...
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