| Abstract
| - Context. Clear power excess in a frequency range typical for solar-type oscillations in red giants has been detected in more than 1000 stars, which have been observed during the first 138 days of the science operation of the NASA Kepler satellite. This sample includes stars in a wide mass and radius range with spectral types G and K, extending in luminosity from the bottom of the giant branch up to high-luminous red giants, including the red bump and clump. The high-precision asteroseismic observations with Kepler provide a perfect source for testing stellar structure and evolutionary models, as well as investigating the stellar population in our Galaxy. Aims. We aim to extract accurate seismic parameters from the Kepler time series and use them to infer asteroseismic fundamental parameters from scaling relations and a comparison with red-giant models. Methods. We fit a global model to the observed power density spectra, which allows us to accurately estimate the granulation background signal and the global oscillation parameters, such as the frequency of maximum oscillation power. We find regular patterns of radial and non-radial oscillation modes and use a new technique to automatically identify the mode degree and the characteristic frequency separations between consecutive modes of the same spherical degree. In most cases, we can also measure the small separation between l = 0, 1, and 2 modes. Subsequently, the seismic parameters are used to estimate stellar masses and radii and to place the stars in an H-R diagram by using an extensive grid of stellar models that covers a wide parameter range. Using Bayesian techniques throughout our entire analysis allows us to determine reliable uncertainties for all parameters. Results. We provide accurate seismic parameters and their uncertainties for a large sample of red giants and determine their asteroseismic fundamental parameters. We investigate the influence of the stars' metallicities on their positions in the H-R diagram. Finally, we study the red-giant populations in the red clump and bump and compare them to a synthetic population. We find a mass and metallicity gradient in the red clump and clear evidence of a secondary-clump population.
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