Photodynamical Modeling of the Compact, Multiply Eclipsing Systems KIC 5255552, KIC 7668648, KIC 10319590, and EPIC 220204960
Authors: Orosz Jerome A. 
Published: December 2023

We present photodynamical models of four eclipsing binary systems that show strong evidence of being members of higher-order multiple systems via their strong eclipse timing variations and/or via the presence of extra eclipse events. Three of these systems are from the main Kepler mission, and the other is from the K2 mission. We provide some ground-based radial velocities measurements for the three Kepler systems and make use of recent light curves from the TESS mission. Our sample consists of two 2 + 1 systems and two 2 + 2 systems. The first 2 + 1 system, KIC 7668648, consists of an eclipsing binary (Pbin = 27.8 days) with late-type stars (M1=0.8403±0.0090M⊙, R1=1.0066±0.0036R⊙ and M2=0.8000±0.0085M⊙, R2=0.8779±0.0032R⊙) with a low-mass star (M3=0.2750±0.0029M⊙, R3=0.2874±0.0010R⊙) on a roughly coplanar outer orbit (P3=208 days). There are several eclipse events involving the third star that allow for the precise determination of the system parameters. The second 2 + 1 system, KIC 10319590, consists of a binary (Pbin=21.3 days) with late-type stars (M1=1.108±0.043M⊙, R1=1.590±0.019R⊙ and M2=0.743±0.023M⊙, R2=0.7180±0.0086R⊙) that stopped eclipsing about a third of the way into the nominal Kepler mission. We show here that the third star in this system is a Sun-like star (M3=1.049±0.038M⊙, R3=1.39±0.11R⊙) on an inclined outer orbit (P3=456 days). In this case, there are no extra eclipse events. We present the first comprehensive solution for KIC 5255552 and demonstrate that it is a 2 + 2 system consisting of an eclipsing binary (Pbin,1=32.5 days) with late-type stars (M1=0.950±0.018M⊙, R1=0.9284±0.0063R⊙ and M2=0.745±0.014M⊙, R2=0.6891±0.0051R⊙) paired with a non-eclipsing binary (Pbin,2=33.7 days) with somewhat lower-mass stars (M3=0.483±0.010M⊙, R3=0.4640±0.0036R⊙ and M4=0.507±0.010M⊙, R4=0.4749±0.0031R⊙). The two binaries, which have nearly coplanar orbits, orbit their common barycenter on a roughly aligned outer orbit (Pout=878 days). There are extra eclipse events involving the component stars of the non-eclipsing binary, which leads to relatively small uncertainties in the system parameters. The second 2 + 2 system, EPIC 220204960, consists of a pair of eclipsing binaries (Pbin,2=13.3 days, Pbin,2=14.4 days) that both consist of two low-mass stars (M1=0.54M⊙, R1=0.46R⊙, M2=0.46M⊙, R2=0.37R⊙ and M3=0.38M⊙, R3=0.40R⊙, M4=0.38M⊙, R4=0.37R⊙) that orbit their common barycenter on a poorly determined outer orbit. Because of the relatively short time span of the observations (≈80 days for the photometry and ≈70 days for the radial velocity measurements), the masses and radii of the four stars in EPIC 220204960 can only be determined with accuracies of ≈10% and ≈5%, respectively. We show that the most likely period of the outer orbit is 957 days, with a 1σ range of 595 to 1674 days. We can only place weak constraints on the mutual inclinations of the orbital planes, and additional radial velocity measurements and/or additional eclipse observations would allow for much tighter constraints on the properties of the outer orbit.