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

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 (Δν) and the frequency of maximum power (νmax) 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 νmax and Δν 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 νmax ~= 40-110 μHz. We measured the small frequency separations δν02 and δν01 in over 400 stars and δν03 in over 40. We present C-D diagrams for l = 1, 2, and 3 and show that the frequency separation ratios δν02/Δν and δν01/Δν have opposite trends as a function of Δν. The data show a narrowing of the l = 1 ridge toward lower νmax, 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 Δν, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-νmax relation for Kepler red giants. We observe a lack of low-amplitude stars for νmax >~ 110 μHz and find that, for a given νmax between 40 and 110 μHz, stars with lower Δν (and consequently higher mass) tend to show lower amplitudes than stars with higher Δν.