Using phase shift to numerically characterize the mixed modes in post–main sequence stars
Chen Jiang (Instituto de Astrofísica e Ciências do Espaço, U.Porto), Joergen Christensen-Dalsgaard (SAC), Margarida Cunha (IA)

Mixed modes have been largely observed in post–main sequence stars by the Kepler and CoRoT space missions. The mixed nature of pressure and gravity modes leads to variations of some observable parameters of the oscillation modes, such as the mode frequency and amplitude. The level of the mixture of the p and g modes can be measured by the dimensionless coefficient q, the so-called cou- pling strength. Although the coupling strength varies with the mode frequencies, the difference between them is normally small within a star. Therefor, q is not optimal to characterize the behaviour of mixed modes. We discuss the utility of the phase shift θ as a tool to distinguish mixed modes from the theoretical as well as the practical point of view. The theoretical calculation of θ is very sensitive to the wave number K which is computed through series of approximations, nevertheless, it works well for high-radial-order mixed modes. Observed frequencies of a Kepler red giant star KIC 3744043 are used to test the method. We use the large frequency separation and the period spacing, which can be extracted from the power spectrum, to replace the theoretical integrals of K over different oscillatory cavities. The result is also very promising. Aside from the use of characterizing mixed modes, the computation of θ can also provide us better understanding of the pressure and gravity radial order of the mixed modes.