Asteroseismology of Red Giants from the First Four Months of Kepler Data: Global Oscillation Parameters for 800 Stars

International audienceWe 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 (Deltanu) and the frequency of maximum power (numax) and show that it is different for red giants than for main-sequence stars, which is consistent with evolutionary models and scaling relations. The distributions of numax and Deltanu 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 sun and numax ~= 40-110 muHz. We measured the small frequency separations deltanu02 and deltanu01 in over 400 stars and deltanu03 in over 40. We present C-D diagrams for l = 1, 2, and 3 and show that the frequency separation ratios deltanu02/Deltanu and deltanu01/Deltanu have opposite trends as a function of Deltanu. The data show a narrowing of the l = 1 ridge toward lower numax, in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset epsilon in the asymptotic relation and find a clear correlation with Deltanu, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-numax relation for Kepler red giants. We observe a lack of low-amplitude stars for numax >~ 110 muHz and find that, for a given numax between 40 and 110 muHz, stars with lower Deltanu (and consequently higher mass) tend to show lower amplitudes than stars with higher Deltanu