KOI-3890: A high-mass-ratio asteroseismic red giant+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 theM-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 ± 0.06M⊙ and R⊙ = 5.8 ± 0.2R⊙, respectively. When combined with transit photometry, the M-dwarf companion is found to have a mass and radius of Mc = 0.23 ± 0.01M⊙ and Rc = 0.256 ± 0.007R⊙. Moreover, through asteroseismology we constrain the age of the system through the red giant primary to be 9.1+2.4-1.7 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+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.