In the Sun's core ( , )

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Nuclear astrophysics and applications · Nuclear astrophysics and applications

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

Problem

In the Sun's core (

\rho_c = 150\,\mathrm{g\,cm^{-3}}

X_c = 0.34

), a proton waits about

7\times10^{9}\,\mathrm{yr}

before reacting by the

p+p

reaction. A younger, still-contracting solar-mass star has the same central temperature but a core with

\rho_c = 100\,\mathrm{g\,cm^{-3}}

and

X_c = 0.70

(hydrogen not yet depleted). Estimate the proton lifetime against

p+p

fusion in this younger core.