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Asteroseismic investigations based on the wealth of data now available,inparticular from the CoRoT and Kepler missions, require a good understanding ofthe relation between the observed quantities and the properties of theunderlying stellar structure. Kallinger et al. 2012 found a relation betweentheir determination of the asymptotic phase of radial oscillations in evolvedstars and the evolutionary state, separating ascending-branch red giants fromhelium-burning stars in the `red clump'. Here we provide a detailed analysis ofthis relation, which is found to derive from differences between these twoclasses of stars in the thermodynamic state of the convective envelope. Thereis potential for distinguishing red giants and clump stars based on the phasedetermined from observations that are too short to allow distinction based ondetermination of the period spacing for mixed modes. The analysis of the phasemay also point to a better understanding of the potential for using thehelium-ionization-induced acoustic glitch to determine the helium abundance inthe envelopes of these stars.

On the asymptotic acoustic-mode phase in red-giant stars and its dependence on evolutionary state