Near the centre of a solar-mass star the central density is

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Energy transport and the complete stellar model

Problem

Near the centre of a solar-mass star the central density is ρc=1.5×105 kg m−3\rho_c = 1.5\times10^{5}\,\mathrm{kg\,m^{-3}}, the central pressure is Pc=2.30×1016 PaP_c = 2.30\times10^{16}\,\mathrm{Pa}, and the nuclear energy generation rate per unit mass is approximately constant near the centre at ϵc=1.75×10−3 W kg−1\epsilon_c = 1.75\times10^{-3}\,\mathrm{W\,kg^{-1}}. Using the central series expansions r≈(3m4πρc)1/3,L≈ϵcm,P≈Pc−3G8π(4πρc3)4/3m2/3,r \approx \left(\frac{3m}{4\pi\rho_c}\right)^{1/3}, \qquad L \approx \epsilon_c m, \qquad P \approx P_c - \frac{3G}{8\pi}\left(\frac{4\pi\rho_c}{3}\right)^{4/3}m^{2/3}, find rr, LL and PP at the mass shell m=1.0×10−4 M⊙m = 1.0\times10^{-4}\,M_\odot.

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