The Eddington standard model (an polytrope) of Chapter 5 gives the central…

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Thermonuclear energy generation: reaction rates, burning stages and the elements they make

Problem

The Eddington standard model (an

n=3

polytrope) of Chapter 5 gives the central temperature

T_c = \frac{\mu m_H GM}{1.171\,k_BR}

for a star of mass

M

, radius

R

and mean molecular weight

\mu

(fully ionised gas, no radiation pressure correction). ((a)) Evaluate

T_c

for

M = M_\odot

R = R_\odot

and

\mu = 0.62

. ((b)) At the true solar centre,

T=1.57\times10^{7}\,\mathrm{K}

, the pp reaction has

\tau = 13.5

and

\nu = 3.8

. Using

\tau \propto T^{-1/3}

, find

\nu

for the pp reaction at the polytrope's central temperature found in part (a), and comment on the sign of the change.