  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.
