Photodynamical Modeling of the Compact, Multiply Eclipsing Systems KIC 5255552, KIC 7668648, KIC 10319590, and EPIC 220204960

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 circle dot, R1=1.0066 +/- 0.0036R circle dot and M2=0.8000 +/- 0.0085M circle dot, R2=0.8779 +/- 0.0032R circle dot) with a low-mass star (M3=0.2750 +/- 0.0029M circle dot, R3=0.2874 +/- 0.0010R circle dot) 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 circle dot, R1=1.590 +/- 0.019R circle dot and M2=0.743 +/- 0.023M circle dot, R2=0.7180 +/- 0.0086R circle dot) 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 circle dot, R3=1.39 +/- 0.11R circle dot) 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 circle dot, R1=0.9284 +/- 0.0063R circle dot and M2=0.745 +/- 0.014M circle dot, R2=0.6891 +/- 0.0051R circle dot) paired with a non-eclipsing binary (Pbin,2=33.7 days) with somewhat lower-mass stars (M3=0.483 +/- 0.010M circle dot, R3=0.4640 +/- 0.0036R circle dot and M4=0.507 +/- 0.010M circle dot, R4=0.4749 +/- 0.0031R circle dot). 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 circle dot, R1=0.46R circle dot, M2=0.46M circle dot, R2=0.37R circle dot and M3=0.38M circle dot, R3=0.40R circle dot, M4=0.38M circle dot, R4=0.37R circle dot) that orbit their common barycenter on a poorly determined outer orbit. Because of the relatively short time span of the observations (approximate to 80 days for the photometry and approximate to 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 approximate to 10% and approximate to 5%, respectively. We show that the most likely period of the outer orbit is 957 days, with a 1 sigma 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.