CoRoT and Kepler observations of red giants reveal a large variety of spectra of nonradial solar-like oscillations. So far, we understood pretty well the link between the global properties of the star (radius, mass, evolutionary state) and the properties of the oscillation spectrum (Δν, νmax, period spacing). We are interested here in the theoretical predictions of two other components of a power spectrum, the mode linewidths and heights. The study of the energy of the oscillations is of great importance to predict the peak parameters in the power spectrum. We will discuss circumstances under which mixed modes are detectable for red-giant stellar models from 1 to 2 M⊙, with emphasis on the effect of the evolutionary status of the star along the red-giant branch on theoretical power spectra.

We present an absolute magnitude calibration for red giants with the colour–magnitude diagrams of six Galactic clusters with different metallicities, i.e. M92, M13, M3, M71, NGC 6791, and NGC 2158. The combination of the absolute magnitudes of the red giant sequences with the corresponding metallicities provides calibration for absolute magnitude estimation for red giants for a given (g − r)0 colour. The calibration is defined in the colour interval 0.45 ≤ (g − r)0 ≤ 1.30 mag and it covers the metallicity interval −2.15≤[Fe/H]≤ +0.37 dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the interval −0.28 < ΔM ≤ +0.43 mag. However, the range of 94% of the residuals is shorter, −0.1 < ΔM ≤ +0.4 mag. The mean and the standard deviation of (all) residuals are 0.169 and 0.140 mag, respectively. The derived relations are applicable to stars older than 2 Gyr, the age of the youngest calibrating cluster.

We present two absolute magnitude calibrations, MJ and MKs, for red giants with the colour–magnitude diagrams of five Galactic clusters with different metallicities, i.e. M92, M13, M71, M67, and NGC 6791. The combination of the absolute magnitudes of the red giant sequences with the corresponding metallicities provides calibration for absolute magnitude estimation for red giants for a given colour. The calibrations for MJ and MKs are defined in the colour intervals 1.3≤(V−J)0≤2.8 and 1.75≤(V−Ks)0≤3.80 mag, respectively, and they cover the metallicity interval −2.15≤[Fe/H]≤+0.37 dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the intervals −0.08<ΔMJ≤+0.34 and -0.10< Δ MKs≤ +0.27 mag for MJ and MKs, respectively. The means and standard deviations of the residuals are 〈ΔMJ〉=0.137 and σMJ=0.080, and $〈 Δ MKs〉 =0.109 and σMKs=0.123 mag. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster.

We present our ongoing survey of ∼1000 GK-giants with the 9.2-m Hobby-Eberly Telescope in search for planets around evolved stars. The stars selected for this survey are brighter than 11 mag and are located in the section of the HR-diagram, which is approximately delimited by the main sequence, the instability strip, and the coronal dividing line. We use the High Resolution Spectrograph to obtain stellar spectra for radial velocity measurements with a 4-6 m s−1 precision. So far, the survey has discovered a planetary-mass companion to the K0-giant HD 17092, and it has produced a number of plausible planet candidates around other stars. Together with other similar efforts, our program provides information on planet formation around intermediate mass main sequence-progenitors and it will create the experimental basis with which to study dynamics of planetary systems around evolving stars.