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Context: The Kepler space mission is reaching continuous observing times longenough to start studying the fine structure of the observed p-mode spectra.Aims: In this paper, we aim to study the signature of stellar evolution on theradial and p-dominated l=2 modes in an ensemble of red giants that showsolar-type oscillations. Results: We find that the phase shift of the centralradial mode (eps_c) is significantly different for red giants at a given largefrequency separation (Dnu_c) but which burn only H in a shell (RGB) than thosethat have already ignited core He burning. Even though not directly probing thestellar core the pair of local seismic observables (Dnu_c, eps_c) can be usedas an evolutionary stage discriminator that turned out to be as reliable as theperiod spacing of the mixed dipole modes. We find a tight correlation betweeneps_c and Dnu_c for RGB stars and no indication that eps_c depends on otherproperties of these stars. It appears that the difference in eps_c between thetwo populations becomes if we use an average of several radial orders, insteadof a local, i.e. only around the central radial mode, Dnu to determine thephase shift. This indicates that the information on the evolutionary stage isencoded locally, in the shape of the radial mode sequence. This shape turns outto be approximately symmetric around the central radial mode for RGB stars butasymmetric for core He burning stars. We computed radial modes for a sequenceof RG models and find them to qualitatively confirm our findings. We also findthat, at least in our models, the local Dnu is an at least as good and mostlybetter proxy for both the asymptotic spacing and the large separation scaledfrom the model density than the average Dnu. Finally, we investigate thesignature of the evolutionary stage on the small frequency separation andquantify the mass dependency of this seismic parameter.

Evolutionary influences on the structure of red-giant acoustic oscillation spectra from 600d of Kepler observations