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 similar to 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 nu) and the frequency of maximum power (nu(max)) 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 nu(max) and Delta nu 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 greater than or similar to 2M(circle dot) and nu(max) similar or equal to 40-110 mu Hz. We measured the small frequency separations delta nu(02) and delta nu(01) in over 400 stars and delta nu(03) in over 40. We present C-D diagrams for l = 1, 2, and 3 and show that the frequency separation ratios delta nu(02)/Delta nu and delta nu(01)/Delta nu have opposite trends as a function of Delta nu The data show a narrowing of the l = 1 ridge toward lower nu(max), in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset is an element of in the asymptotic relation and find a clear correlation with.., demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-nu(max) relation for Kepler red giants. We observe a lack of low-amplitude stars for nu(max) greater than or similar to 110 mu Hz and find that, for a given nu(max) between 40 and 110 mu Hz, stars with lower Delta nu (and consequently higher mass) tend to show lower amplitudes than stars with higher Delta nu.