Examination of the third body hypothesis in the eclipsing binary AV CMi K.Karpouzas , A.Tsiaras , D.Mislis , A.Liakos Aristotle University of Thessaloniki Departement of Astrophysics, Astronomy and Mechanics National Observatory of Athens

Purpose of this work In this work we re-analyzed the data of Liakos and Niarchos and our own, in a different manner. We present the revised physical parameters for the system and also the O-C diagrams. Finally we proove that a new transit event is allowed to happen thanks to the dynamics of the orbits.

Observations and analysis The data, was a collaboration of the Holomon Astronomical Station (H.A.S) at Mt. Holomon, Halkidiki and the National Observatory of Athens (N.O.A). The observations took place between the years 2008-2011 in N.O.A and between the years 2013-2014 in H.A.S . We analyzed 7 transit lightcurves from N.O.A. obtained and corrected by Alexios Liakos. From H.A.S we obtained and analyzed 4 more transit lightcurves (11 in total) , alongside with various observations near the primary and secondary minima of the system, which we use and present in this work. The data were analyzed using aperture photometry, while the physical parameters were obtained through a more or less classical MCMC fit.

Lightcurve analysis In the following table we summarize the results of the fitting process and compare cases A and B using the Pal transit model, Pal et al 2008 Mean values Case A Case B i (deg.) 52.118 72.228 Radius (Rj) 4.810 4.207 chi square 2.663 2.826

TTV [min] Left : case A Right : case B

Inclination [deg] Left : case A Right : case B

Radius [ jupiter radii ] Left : case A Right : case B

Discussion From the previous analysis, we can support that case A is the more dominant case because of the systematically bigger chi square. Although some lightcurves were better fitted through case B, we believe that this was due to the dependance of the chi square on the (supposed) Gaussian noise of the ligthcurve. We can proove the latter by computing the difference in chi square, between the two cases/models, using various noise patterns (bootsrap analysis). This kind of analysis belongs to our future work.

An alternative method There is an even more straightforward way to decide who the host star is. That is by observing the transit of the third body during a primary or secondary minima of the system. For example let's assume that the primary is the host star (case A), then if a transit happened during a primary minima of the system, then the third body would have to be exactly in the middle of the two stars, from the observer's point of view, and thus it could be implied that the transit would not be visible.

Case A during a primary minimum The red sphere represents the primary component ,which is the host star for this case.

Case B during a primary minimum Here, the green sphere represents the secondary component which is the host star for this case

Observation of a transit during a primary minimum We observed a primary minima of the system while a transit of the third body was expected at the same time. Then we subtracted the contribution of the binary to check if a transit signal actually existed.

The orbital problem Although we managed to observe a transit of the third body during a primary minima, we can not directly assume that the secondary is the host star, and that is due to the fact that we don't know the difference between the longitudes of the ascending node of the two orbits

Explaining the observation through case A Phase 1 : = 0

Explaining the observation through case A Phase 1 : = 60

Explaining the observation through case A Phase 1 : = 90

Explaining the observation through case A Phase 1 : = 130

Explaining the observation through case A Phase 1 : = 180

Limits for the parameter [deg] Given that case A is the most propable senario so far, we defined the lower and upper limit for the and found that 122 340

Why is AV CMi special ? The previous analysis, raises a simple question. Since we prooved that for certain values of the non-host star can “block” the view of the transit, the projected spheres of the non-host and the third body should be able to overlap. So, is it possible to have a second transit event were the eclipsed body is the non-host star? The answer is YES. We call this event “strange transit” because both of the overlapping bodies are moving around their own barycenters, making it difficult to imagine how such a singal would look like.

The strange transit Here we can see a 3D animation of a strange transit event, as seen by the observer on earth (the projection on the celestia sphere)

The strange transit We constructed the analytic relation for the projected distance between the centers of the third body and the non-host component and then using the Pal transit model, we simulated various time series for this phenomenon. We did not directly observe such a signal yet, due to the limited observations, but it still is interesting from a theoretical point of view.

Modeling the strange transit The projected distance : were ,

Modeling the strange transit We must stress, that the main difference between the strange transit model and a normal transit model, is the existence of the parameter in the formula for the projected distance, whereas in the classical transit this factor disappears . This extra parameter, is enough to complicate the phenomenon.

Simulated time series This is how often a strange transit would be visible in the same time scale as the observations we undertaken between 2013-2014 1.1 mmag 33 mmag

shape of the lightcurve A closer look on the two former parts of the time series

How would the strange transit look on a real lightcurve of the binary? If such a phenomenon is observed, we can define if it is a third body or a blend, as proposed by Liska et al 2012

Conclusions We analyzed all the existing transit lightcurves and confirmed that case A is still the best senario. We found an upper and lower limit for the parameter and prooved that it can be calculated solely from optical photometry. We proposed and analyzed the properties of a second transit event that is possible. We prooved that the “strange transit” is observable and that an actual observation could not only yield quite accurate values for but show us if it is actually a third body or a blended system. If observed, it could also help ensure that case A is the true orbital senario.