We have studied solar-like oscillations in ∼ 800 red-giant stars using Kepler long-cadence photometry. The sample includes stars ranging in evolution from the lower part of the red-giant branch to the Helium main sequence. We investigate the relation between the large frequency separation (∆ν) and the frequency of maximum power (ν max ) and show that it is different for red giants than for mainsequence stars, which is consistent with evolutionary models and scaling relations. The distributions of ν max and ∆ν are in qualitative agreement with a simple stellar population model of the Kepler field, including the first evidence for a secondary clump population characterized by M 2 M ⊙ and ν max ≃ 40−110 µHz. We measured the small frequency separations δν 02 and δν 01 in over 400 stars and δν 03 in over 40. We present C-D diagrams for l = 1, 2 and 3 and show that the frequency separation ratios δν 02 /∆ν and δν 01 /∆ν have opposite trends as a function of ∆ν. The data show a narrowing of the l = 1 ridge towards lower ν max , in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset ǫ in the asymptotic relation and find a clear correlation with ∆ν, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-ν max relation for Kepler red giants. We observe a lack of low-amplitude stars for ν max 110 µHz and find that, for a given ν max between 40 − 110 µHz, stars with lower ∆ν (and consequently higher mass) tend to show lower amplitudes than stars with higher ∆ν.

We have measured solar-like oscillations in red giants using time-series photometry from the first 34 days of science operations of the Kepler Mission. The light curves, obtained with 30 minute sampling, reveal clear oscillations in a large sample of G and K giants, extending in luminosity from the red clump down to the bottom of the giant branch. We confirm a strong correlation between the large separation of the oscillations (Δν) and the frequency of maximum power (ν max ). We focus on a sample of 50 low-luminosity stars (ν max > 100 μHz, L 30 L ) having high signal-to-noise ratios and showing the unambiguous signature of solar-like oscillations. These are H-shellburning stars, whose oscillations should be valuable for testing models of stellar evolution and for constraining the star formation rate in the local disk. We use a new technique to compare stars on a singleéchelle diagram by scaling their frequencies and find well-defined ridges corresponding to radial and non-radial oscillations, including clear evidence for modes with angular degree l = 3. Measuring the small separation between l = 0 and l = 2 allows us to plot the so-called C-D diagram of δν 02 versus Δν. The small separation δν 01 of l = 1 from the midpoint of adjacent l = 0 modes is negative, contrary to the Sun and solar-type stars. The ridge for l = 1 is notably broadened, which we attribute to mixed modes, confirming theoretical predictions for low-luminosity giants. Overall, the results demonstrate the tremendous potential of Kepler data for asteroseismology of red giants.

Mass estimates of K giants are generally very uncertain. Traditionally, stellar masses of single field stars are determined by comparing their location in the Hertzsprung-Russell diagram with stellar evolutionary models. Applying an additional method to determine the mass is therefore of significant interest for understanding stellar evolution. We present the time series analysis of 11 K giants recently observed with the WIRE satellite. With this comprehensive sample, we report the first confirmation that the characteristic acoustic frequency, , can n max be predicted for K giants by scaling from the solar acoustic cutoff frequency. We are further able to utilize our measurements of to determine an asteroseismic mass for each star with a lower uncertainty compared to the n max traditional method, for most stars in our sample. This indicates good prospects for the application of our method on the vast amounts of data that will soon come from the COROT and Kepler space missions.