KIC 4247791 is listed as an EA+EA in VSX. The paper 2012arXiv1202.6552L indicates that there are 2 eclipsing binary signals (SB4), though the authors could not conclusively tell whether the 2 eclipsing binary systems are physically connected (or just 2 systems coincidentally aligned).
The system has a dominant EB signal with 4.10 d period, and a much shallower EB signal with ~4.05 d period. From the 2012 paper:
I think I have found the a strong sign that the 2 eclipsing systems are indeed physically connected. Specifically, there are signs of non-linear eclipse timing variations (ETV), in the time scale of decades.
The following is the O-C plot [*] of Kepler, TESS and other archival data for the primary eclipse of the 4.10 d EB signal (secondary eclipses follow a similar trend).
It looks to me that the plot suggests there is some ETV. The period is too long for us to tell, based the data with a baseline of ~17 years.
Thoughts?
[*] A small caveat: The O-C plot above did not account for any distortion caused by the second EB (P: ~4.05 d). The impact is minimal, however, as the second EB is much shallower. I redid TESS portion of the O-C by masking out the eclipses of the second EB, and found no significant change.
See also: the details at Kepler EBs .
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The hypothesis implies that, with a much longer time base in the future, the O-C diagram would be described by a sinusoidal function.
An alternative hypothesis would be a decreasing period of the binary system at a constant rate, which could for example be caused by mass transfer from the more massive to the less massive component.
A third possibility is that both of the above processes could be occurring.
My interpretation of the O-C plot suggests that change in period is nonlinear. The O-C between 2007 - 2013 (Kepler and SuperWASP data) is largely constant (about +1 minute). It starts to trend downwards at some point after 2013.
Zoom-in of the Kepler portion (2009 - 2013) of the O-C:
Having said that, another consideration is that in calculating the O-C, I use the epoch/period from Kepler EB. So there is some chance the adopted period overfits Kepler data, distorting the O-C results.
The first sentence in the above quote could be tested statistically, by determining whether a linear or quadratic function was a better fit for that subset of the data.
Looking at the entire O-C diagram if the quadratic model represents reality the direction of the apparent change in period is a decrease, and the rate of change is constant.
Here is an O-C plot that has both the linear model and the quadratic model for comparison.
The quadratic model fits the actual O-C better than that of the linear model.
A linear relationship in an O-C plot means the period you used to calculate is off by a constant amount from the actual period (each orbit adds a fixed amount to the O-C difference).
A quadratic relationship in an O-C plot means the actual period is linearly changing in time (each orbit adds a time-varying amount to the O-C difference).
-Kenneth
