A red giant on the way up the red giant branch has a degenerate helium core of mass

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

Stars from the Inside, Ch Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters

Problem

A red giant on the way up the red giant branch has a degenerate helium core of mass Mc=0.45 M⊙M_c = 0.45\,M_\odot, still below the ignition mass of 0.47 M⊙0.47\,M_\odot at which the helium flash occurs. Use the Refsdal-Weigert core-mass-luminosity relation L≈2.3×105 L⊙(McM⊙)6L \approx 2.3\times10^{5}\,L_\odot\left(\frac{M_c}{M_\odot}\right)^{6} (fitted for 0.150.15 to 0.45 M⊙0.45\,M_\odot and extended slightly to the ignition mass). ((a)) Estimate this star's luminosity. ((b)) Estimate the luminosity at the ignition core mass 0.47 M⊙0.47\,M_\odot (the tip of the red giant branch) and state the factor by which the tip is brighter than the 0.45 M⊙0.45\,M_\odot star.

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