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 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± 0.06 M_{⊙} and R_{\star }=5.8± 0.2 R_{⊙}, 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 M_{⊙} and R_c=0.256± 0.007 R_{⊙}. 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.