The core of a main-sequence star has central temperature and central total pressure

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · Radiation, radiative transfer and stellar atmospheres

Stars from the Inside, Ch Radiative transfer solved: the grey atmosphere, the diffusion limit and the curve of growth

Problem

The core of a 3 M⊙3\,M_\odot main-sequence star has central temperature Tc=2.3×107 KT_c = 2.3\times10^{7}\,\mathrm{K} and central total pressure Pc=4.5×1016 PaP_c = 4.5\times10^{16}\,\mathrm{Pa}. Treat the radiation field at the centre as isotropic. ((a)) Find the radiation pressure PradP_{\rm rad} at the centre, using Prad=13aTc4P_{\rm rad} = \tfrac{1}{3}aT_c^4 with a=7.566×10−16 J m−3 K−4a = 7.566\times10^{-16}\,\mathrm{J\,m^{-3}\,K^{-4}}. ((b)) Express PradP_{\rm rad} as a fraction of PcP_c.

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