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 ( Delta *D Delta *n) and the frequency of maximum power ( Delta *nmax) 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 Delta *nmax and Delta *D Delta *n 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 Delta *nmax 40-110 Delta *mHz. We measured the small frequency separations Delta *d Delta *n02 and Delta *d Delta *n01 in over 400 stars and Delta *d Delta *n03 in over 40. We present C-D diagrams for l = 1, 2, and 3 and show that the frequency separation ratios Delta *d Delta *n02/ Delta *D Delta *n and Delta *d Delta *n01/ Delta *D Delta *n have opposite trends as a function of Delta *D Delta *n. The data show a narrowing of the l = 1 ridge toward lower Delta *nmax, in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset in the asymptotic relation and find a clear correlation with Delta *D Delta *n, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude- Delta *nmax relation for Kepler red giants. We observe a lack of low-amplitude stars for Delta *nmax 110 Delta *mHz and find that, for a given Delta *nmax between 40 and 110 Delta *mHz, stars with lower Delta *D Delta *n (and consequently higher mass) tend to show lower amplitudes than stars with higher Delta *D Delta *n.