Helium Ignition in the Cores of Low-Mass Stars

Abstract: In stars with $M_\ast \lesssim 2 M_\odot$, nuclear burning of helium starts under degenerate conditions and, depending on the efficiency of neutrino cooling, more or less off-center. The behavior of the centers of low-mass stars undergoing core helium ignition on the $\log\rho - \log T$ plane is not thoroughly explained in the textbooks on stellar evolution and the appropriate discussions remain scattered throughout the primary research literature. Therefore, in the following exposition we collect the available knowledge, we make use of computational data obtained with the open-source star-modeling package MESA, and we compare them with the results in the existing literature. The line of presentation follows essentially that of Thomas (1967) who was the first who outlined correctly the stellar behavior during the off-center helium flashes that lead to central helium burning. The exposition does not contain novel research results; it is intended to be a pedagogically oriented, edifying compilation of pertinent physical aspects which help to \emph{understand} the nature of the stars.