Absolute Dimensions of a Flat Hierarchical Triple System KIC 6543674 from the Kepler Photometry

Abstract

Many of the Kepler close binaries are suggested to constitute hierarchical triple systems through their eclipse timing variations (ETVs). Eclipses by the third body in those systems, if observed, provide precise constraints on its physical and orbital properties, which are otherwise difficult to obtain. In this Letter, we analyze such a "tertiary event" observed only once in the KIC 6543674 system. The system consists of a short-period ($2.4\,\mathrm{days}$) inner eclipsing binary and a third body on a wide ($1100\,\mathrm{days}$) and eccentric ($e\simeq0.6$) orbit. Analysis of three tertiary eclipses around a single inferior conjunction of the third body yields the mutual inclination between the inner and outer binary planes to be $3.3^\circ\pm0.6^\circ$, indicating an extremely flat geometry. Furthermore, combining the timings and shapes of the tertiary eclipses with the phase curve and ETVs of the inner binary, we determine the mass and radius ratios of all three bodies in the system using the Kepler photometry alone. With the primary mass and temperature from the Kepler Input Catalog, the absolute masses, radii, and effective temperatures of the three stars are obtained as follows: $M_\mathrm{A}=1.2\pm0.3\,M_\odot$, $R_\mathrm{A}=1.8\pm0.1\,R_\odot$, $M_\mathrm{B}=1.1_{-0.2}^{+0.3}\,M_\odot$, $R_\mathrm{B}=1.4\pm0.1\,R_\odot$, $M_\mathrm{C}=0.50_{-0.08}^{+0.07}\,M_\odot$, $R_\mathrm{C}=0.50\pm0.04\,R_\odot$, $T_\mathrm{A} \simeq T_\mathrm{B}\simeq 6100\,\mathrm{K}$, and $T_\mathrm{C}<5000\,\mathrm{K}$. Implication for the formation scenario of close binaries is briefly discussed.