Identifying Transiting Circumbinary Planets

arXiv:0807.0527v1 [astro-ph] 3 Jul 2008 Transiting Planets Proceedings IAU Symposium No. 253, 2008 A.C. Editor, B.D. Editor & C.E. Editor, eds. c⃝2008 International Astronomical Union DOI: 00.0000/X000000000000000X Identifying Transiting Circumbinary Planets Aviv Ofir1 1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel email: avivofir@wise.tau.ac.il Abstract. Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit, making BLS [Kov´acs et al. 2002] almost ineffective. Therefore, a modified version for the identification of CB planets was developed - CB-BLS. We show that using CB-BLS it is possible to find CB planets in the residuals of light curves of eclipsing binaries (EBs) that have noise levels of 1% or more. Using CB-BLS will allow to easily harness the massive ground- and space- based photometric surveys to look for these objects. Detecting transiting CB planets is expected to have a wide range of implications, for e.g.: The frequency of CB planets depend on the planetary formation mechanism - and planets in close pairs of stars provides a most restrictive constraint on planet formation models. Furthermore, understanding very high precision light curves is limited by stellar parameters - and since for EBs the stellar parameters are much better determined, the resultant planetary structure models will have significantly smaller error bars, maybe even small enough to challenge theory. Keywords. methods: data analysis binaries: eclipsing planetary systems occultations - binaries : close 1. The Challenge Light curves (LCs) of transiting planets around single stars have precise depths, du- rations and epochs - and changes in any of these tell us something about the system. Light curves of transiting CB planets are expected to have very different photometric and temporal characteristics (Fig. 1), where none of these properties hold. In general, photometric signal = blocked flux / total flux, but for CB planets neither is constant: the total flux changes all the time because of ellipsoidal variation and binary eclipses. The blocked flux varies according to the surface brightness of the binary component being transited. The temporal characteristics arise from the fact the transits are not periodic, and that their duration is highly variable - depending more on the transversal velocity of the binary components than on the planetary motion (the binary components can move either in parallel or anti-parallel to the planet’s motion, enabling long and short transits, respectively). 2. Solution: CB-BLS We assume the EB is solved as usual (PB, T0, e, ω, iB, R1,2), and normalize the LC and EB model to max(model flux)=1. We then first deal with the photometric characteristics and then with the temporal characteristics. Photometric characteristics: regularizing all depths is done simply by multiplying each point on the residuals LC by its corresponding model value - making all transits well- defined as the depth against full binary flux. We define the CB-BLS statistic by gener- alizing the BLS statistic to a two-box fit to allow for different surface brightness of the 1 2 Aviv Ofir binary components: s2 r(1 −r) → (s1 + s2)2 1 −(r1 + r2) + s2 1 r1 + s2 2 r2 (2.1) Where the left side is the usual BLS statistic and the right side is the new CB-BLS statistic. Similarly to BLS, s1 and r1 are a weighted sum and a sum of weights of points in-transit of component 1, and similarly for s2, r2. Temporal −→Geometric characteristics: transits are not a function of time, but of ge- ometry: the alignment of celestial bodies. We will therefore search not in time or phase, but rather in orbital parameters space: for a given test planetary (and binary) orbit the projected distances between the planet and each of the stars is known, and occurrence of a transit is exactly true or false at each point in time (ignoring planetary ingress/egress). One can then, similarly to BLS, fit a discrete-valued function to the data - where all the in-transit and out-of-transit points are already separated, using the CB-BLS statistic above (see Fig. 2). The output is a multi-dimensional ”periodogram” - where the peak value corresponds to the best fit not only in orbital period, but also all other tested orbital elements. More intuitively, it allows to fold the LC not in orbital phase, but in projected sep- aration - where, ideally, all points closer to component 1 than R1 will be in-transit (of component 1), and similarly for component 2 (see Fig. 2). 3. Tests on Simulated Data We simulated several systems - starting from 3D 3-body interaction, through LC gen- eration, and to CB-BLS analysis. We varied different system parameters in order to explore the properties of CB-BLS, and each system was realized 50 time

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