The space-borne missions CoRoT and Kepler opened up a new opportunity for better understanding stellar evolution by probing stellar interiors with unrivalled high-precision photometric data. Kepler has observed stellar oscillation for four years, which gave access to excellent frequency resolution that enables deciphering the oscillation spectrum of evolved red giant branch and asymptotic giant branch stars. The internal structure of stars in the upper parts of the red and asymptotic giant branches is poorly constrained, which makes the distinction between red and asymptotic giants difficult. We perform a thorough seismic analysis to address the physical conditions inside these stars and to distinguish them. We studied the oscillation mode properties of about 2.000 evolved giants in a model described by the asymptotic pressure-mode pattern of red giants, which includes the signature of the helium second-ionisation zone. We extracted the mode properties up to the degree l = 3 and investigated their dependence on stellar mass, metallicity, and evolutionary status. We identify a clear difference in the signature of the helium second-ionisation zone between red and asymptotic giants. We also detect a clear shortage of the energy of l = 1 modes after the core-He-burning phase. Furthermore, we note that the mode damping observed on the asymptotic giant branch is similar to that observed on the red giant branch. We highlight that the signature of the helium second-ionisation zone varies with stellar evolution. This provides us with a physical basis for distinguishing red giant branch stars from asymptotic giants. Here, our investigation of stellar oscillations allows us to constrain the physical processes and the key events that occur during the advanced stages of stellar evolution, with emphasis on the ascent along the asymptotic giant branch, including the asymptotic giant branch bump.
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