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 (ν_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 ν_max 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 ≳ 2M_⊙ and ν_max ≃ 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 δν ₀₂/Δν and δν₀₁/Δν have opposite trends as a function of Δν. The data show a narrowing of the l=1 ridge toward lower ν_max, 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 Δν, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-vmax 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 and 110 νHz, stars with lower Δν (and consequently higher mass) tend to show lower amplitudes than stars with higher Δν.