The unparalleled photometric data obtained by NASAs Kepler space telescope led to an improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries, exhibiting ellipsoidal modulations, have been detected with Kepler. We aim to study the properties of eccentric binary systems containing a red giant star and derive the parameters of the primary giant component. We apply asteroseismic techniques to determine masses and radii of the primary component of each system. For a selected target, light and radial velocity curve modelling techniques are applied to extract the parameters of the system. The effects of stellar on the binary system are studied. The paper presents the asteroseismic analysis of 18 pulsating red giants in eccentric binary systems, for which masses and radii were constrained. The orbital periods of these systems range from 20 to 440days. From radial velocity measurements we find eccentricities between e=0.2 to 0.76. As a case study we present a detailed analysis of KIC5006817. From seismology we constrain the rotational period of the envelope to be at least 165 d, roughly twice the orbital period. The stellar core rotates 13 times faster than the surface. From the spectrum and radial velocities we expect that the Doppler beaming signal should have a maximum amplitude of 300ppm in the light curve. Through binary modelling, we determine the mass of the secondary component to be 0.29$pm$0.03,$M_odot$. For KIC5006817 we exclude pseudo-synchronous rotation of the red giant with the orbit. The comparison of the results from seismology and modelling of the light curve shows a possible alignment of the rotational and orbital axis at the 2$sigma$ level. Red giant eccentric systems could be progenitors of cataclysmic variables and hot subdwarf B stars.
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