Period-luminosity relations in evolved red giants explained by solar-like oscillations

Context. Solar-like oscillations in red giants have been investigated with the space-borne missions CoRoT and Kepler, while pulsations in more evolved M giants have been studied with ground-based microlensing surveys. After 3.1 years of observation with Kepler, it is now possible to link these different observations of semi-regular variables. Aims. We aim to identify period-luminosity sequences in evolved red giants identified as semi-regular variables and to interpret them in terms of solar-like oscillations. Then, we investigate the consequences of the comparison of ground-based and space-borne observations. Methods. We first measured global oscillation parameters of evolved red giants observed with Kepler with the envelope autocorrelation function method. We then used an extended form of the universal red giant oscillation pattern, extrapolated to very low frequency, to fully identify their oscillations. The comparison with ground-based results was then used to express the period-luminosity relation as a relation between the large frequency separation and the stellar luminosity. Results. From the link between red giant oscillations observed by Kepler and period-luminosity sequences, we have identified these relations in evolved red giants as radial and non-radial solar-like oscillations. We were able to expand scaling relations at very low frequency ( periods as long as 100 days and large frequency separation less than 0.05 mu Hz). This helped us identify the different sequences of period-luminosity relations, and allowed us to propose a calibration of the K magnitude with the observed large frequency separation. Conclusions. Interpreting period-luminosity relations in red giants in terms of solar-like oscillations allows us to investigate the time series obtained from ground-based microlensing surveys with a firm physical basis. This can be done with an analytical expression that describes the low-frequency oscillation spectra. The different behavior of oscillations at low frequency, with frequency separations scaling only approximately with the square root of the mean stellar density, can be used to precisely address the physics of the semi-regular variables. This will allow improved distance measurements and opens the way to extragalactic asteroseismology with the observations of M giants in the Magellanic Clouds.