Asteroseismology of cool stars: testing scaling laws and detecting signatures of rapid structure variation

First, we investigated the ν max scaling relation, a widely-used equation that states that the frequency of maximum amplitude in a power spectrum scales with a combination of surface gravity and effective temperature. We tested how well the oscillations of cool main-sequence and sub-giant stars follow this relation, using a ensemble of asteroseismic targets observed by Kepler. We then tested seismic scaling relations in a small group of 10 bright red-giant stars observed by Kepler. These giants, some of the brightest observed in the Kepler field, have precise values of parallaxes. We compared the measured distances with inferences made using asteroseismic parameters. We also combined high-quality spectroscopic data with seismic constraints to determine their evolutionary phase. We compared the observed surface abundances of lithium and carbon with models that account for additional mixing processes in redgiants. Finally, we analyzed a group of 13 stars observed by Kepler, and use asteroseismic tools to extract modelindependent information about their internal regions. Our objective is to detect the so-called acoustic glitches, characterized as departures from the uniform frequency spacings predicted by the asymptotic relation. Such departures originate in regions where there is an abrupt change in the stratification of the star