KOI-3890: a high-mass-ratio asteroseismic red giant plus M-dwarf eclipsing binary undergoing heartbeat tidal interactions

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-star = 1.04 +/- 0.06M(circle dot) and R-star = 5.8 +/- 0.2R(circle dot), respectively. When combined with transit photometry, the M-dwarf companion is found to have a mass and radius of M-c = 0.23 +/- 0.01M(circle dot) and R-c = 0.256 +/- 0.007R(circle dot). Moreover, through asteroseismology we constrain the age of the system through the red giant primary to be 9.1(-1.7)(+2.4) Gyr. 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(-1.2)(+2.4) 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 psi = 4.2-4.2+2.1 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.