Using the phase shift to asymptotically characterize the dipolar mixed modes in post-main-sequence stars

Mixed modes have been extensively observed in post-main-sequence stars by the Kepler and CoRoT space missions. The mixture of the p and g modes can be measured by the dimensionless coefficient $q$, the so-called coupling strength factor. In this paper we discuss the utility of the phase shifts $\theta$ from the eigenvalue condition for mixed modes as a tool to characterize dipolar mixed modes from the theoretical as well as the practical point of view. Unlike the coupling strength, whose variation in a given star is very small over the relevant frequency range, the phase shifts vary significantly for different modes. The analysis in terms of $\theta$ can also provide a better understanding of the pressure and gravity radial order for a given mixed mode. Observed frequencies of the Kepler red-giant star KIC 3744043 are used to test the method. The results are very promising.