2019MNRAS.487...14K

KOI-3890 is a highly eccentric, 153-d period eclipsing, single-lined spectroscopic binary system containing a red giant star showing solar-like oscillations alongside tidal interactions. The combination of transit photometry, radial velocity observations, and asteroseismology has enabled the detailed characterization of both the red giant primary and the M-dwarf companion, along with the tidal interaction and the geometry of the system. The stellar parameters of the red giant primary are determined through the use of asteroseismology and grid-based modelling to give a mass and radius of M_*=1.04±0.06 \textrmM_☉ and R_*=5.8±0.2 \textrmR_☉, respectively. When combined with transit photometry, the M-dwarf companion is found to have a mass and radius of M_c=0.23±0.01 \textrmM_☉ and R_c=0.256±0.007 \textrmR_☉. Moreover, through asteroseismology we constrain the age of the system through the red giant primary to be 9.1^+2.4_–1.7Gyr. This provides a constraint on the age of the M-dwarf secondary, which is difficult to do for other M-dwarf binary systems. In addition, the asteroseismic analysis yields an estimate of the inclination angle of the rotation axis of the red giant star of i=87.6^+2.4_–1.2 degrees. The obliquity of the system - the angle between the stellar rotation axis and the angle normal to the orbital plane - is also derived to give ψ=4.2^+2.1_–4.2 degrees, showing that the system is consistent with alignment. We observe no radius inflation in the M-dwarf companion when compared to current low-mass stellar models.