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Planet WS Berlin 12/2003 Transit detecion on eclipsing binary systems Hans J. Deeg Instituto de Astrofísica de Canarias 1.Transit observations in eclipsing binary systems, why and how 2.Transit detection algorithms for EB's 3.Considerations for computing requirements

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Planet WS Berlin 12/2003 Why are EB transits of interest to be observed The probability to detect planets around EB's with transits is higher: Since the EB plane is aligned with the observer, the planetary one is it likely as well ->higher probability for correct alignement Non-aligned planetary planes would precess around EB rotation axis, and cause periodically transits as well (Schneider, 1994) Detection of circumbinary planets would be a very significant extension to the variety of known planets.

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Planet WS Berlin 12/2003 EB Transit lightcurves 1 Time and duration of transits depends on phase of EB during transit.

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Planet WS Berlin 12/2003 EB transit lightcurves 2: after removal of binary eclipse 'Normal' case: planet transits one component complicated shapes: planetary transit during binary eclipse A detection algorithm needs to model these curves by considering all possible periods AND phases of EB at planet crossing P=9d P=36d For longer periodic planets v pl << v EB : trains of several irregularly spaced transits per EB crossing v p l < v EB v pl > v EB

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Planet WS Berlin 12/2003 EB Transit detection algorithm (TDA) development Jenkins,Doyle & Cullers 1996: propose a matching filter TDA.The detection statistics C is obtained from a scalar multiplication of the vectors representing model-lc and observed data. Jenkins et al. present this TDA in the context of the transit detection of EBs TEP project (1994-2000; Deeg et al 1998,Doyle et al 2000.) detection statistics is obtained from a comparison of hypotheses transit-present vs transit-absent.

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Planet WS Berlin 12/2003 EB transit detecion algorithm, general There is nothing special about them, except for the first step: i) removal of binary eclipses from lightcurve. Use fit obtained from several good observations of eclipses. ii) model signal for Planet(E i,P i,{R pl,ecc}) E: Epoch [E 0,..,E 0 +P] (or phase [0..2 ]) iii) compare model to data -> detection statistical value C(E i,P i ) within search space [E 0,..,E 0 +P], and [Pmin..Pmax], (R pl, ecc), repeat steps ii) and iii) for all values of E, P that generate significantly different model signals

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Planet WS Berlin 12/2003 EB transit detecion vs single star TD Difference of EB algorithms is in the generation of model transits and in finding an efficient way to compare them to the data. -> EB transit detection is a much larger computational problem than single star TD on the order of the number of epoch steps needed For single star transits: Transits are strictly periodic. Transit shape, duration is invariant against Epoch (slowly varying if eccentric) EB transits: Transits are semi-periodic and shapes/durations depend strongly on planet's epoch

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Planet WS Berlin 12/2003 The TEP project 1994-2000, Doyle, Deeg, Schneider, Jenkins et al. Observed CM Dra for 1000hrs (Deeg et al 1998, Doyle et al 2000) TDA: searched data from 1994-98 for P=7-60 days over all phases of CM Dra ~ 2 month computing time with Sun Ultra5 (300MHz) a list of planet candidates was published. Follow-up observations 1999-2001 at predicted transit times did rule out all of them

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Planet WS Berlin 12/2003 Algorithm used in TEP Adapted for analysis of ground based data with unknown extinction slope: Compares data to two models: -one with transits (E,P) and extinction fits to all nights (H1) -one without transit, only extinction fit to all nights (H0) Detection stat. C is difference between residuals: C(E,P) = |resid H0 | – |resid H1 | This algorithm is NOT specific for eclipsing binaries – but for problematic ground-based data! Doyle et al. 2000

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Planet WS Berlin 12/2003 A transit candidate with P ≈ 11d Doyle et al. 2000

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Planet WS Berlin 12/2003 Computational Requirements: TD stepsize Minimum TD step sizes to not miss a transit (Jenkins et al. 1996): If a planet (E,P) is tested by a detection test with (P± P,E) or (P,E± E), its detection statistics is reduced 'signficantly' (to 1/2 in case of correlation). Planet (E,P) Model (E,P) c=1 Model (E+ E,P), E=t d /2 tdtd P t obs c=1/2 Model (E,P+ P), P=P t d /t obs c=1/2 detc. stat.

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Planet WS Berlin 12/2003 Computational Requirements 1 Number of epoch and period steps in TDA: t obs : duration of observations t d : duration of transit ( fundamental mesh size) P : period of planet in Epoch: E=t d /2 -> N E = P / E = 2 P /t d in Period: P=P t d /t obs -> N P = (t obs /t d ) ln(P max /P min ) total: N step ≈ 2 t obs t d - 2 (P max - P min ) Ignored here is a weak dependency of t d ~ P 1/3

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Planet WS Berlin 12/2003 Computational Requirements 2 Total Number of operations of TDA: N op = k N step N pts, = k 2 t obs t d - 2 (P max - P min ) N pts where k is a factor depending on the TDA used (k might be < 1), N pts is the number of data pts. For equidistant points: N pts = t obs /t inc and then: N op = k 2 t d -2 (P max -P min ) t obs 2 t inc -1 (1) Examples: (k =1, P min =7d, P max =60d, t d =0.0139d = 20min) TEP: N op ≈ 2. 10 13 (t obs = 1526d, N pts =24 874) COROT: N op ≈ 1.1. 10 12 (t obs =150d, N pts =13 500, t inc =16min) Kepler/Eddi: N op ≈ 1.0. 10 14 ( t obs =1100d, N pts = 158 000, t inc =10min)

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Planet WS Berlin 12/2003 Slicing the lightcurve: saving computing steps Principle: running a TDA on shorter sections of a lightcurve, and co-adding detection statistics from individual sections. If a lightcurve of N pts points is divided into n s sections of N pts,s points, of length t obs,s, the computing requirement N op,s for each section is: N op,s = k 2 t d -2 (P max -P min ) t obs,s N pts,s. The total number of operations is then given by: N op = n s N op,s = k 2 t d -2 (P max -P min ) t obs,s N pts (2) i.e. N op is reduced by t obs /t obs,s against (1) This scheme was used by TEP project, dividing the observations of t obs =1529d into 5 sections corresponding to the yearly (1994-1998) observing seasons, using t obs = 200d for each of them (mid-march to october). Savings: 1526/200 ≈ 7.6 Only this made the computation feasable with a CPU time of 2 months

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Planet WS Berlin 12/2003 Slicing: Adding of detection statistics 1994 (186h) 1995 (185h) 1996 (246h) 1997 (250h) 94-96 P E maps C(E,P) of small region around a candidate with P ≈ 36d, using t d = 20min, t obs =200d 94-97 epoch E is an offset {0..P} from reference Epoch JD 0 =2450000 (9 Oct 1995) Bright: high C(E,P) 36,1d 36,7d JD 0 +0JD 0 +3 dominant lines are caused by individual features in lightcurve coadded C(E,P) arrays: Once maxima in C(E i,T i ) map are found, TDA needs to be rerun with a finer mesh (t d,fine ≈ 1/4 t d ) in small area in E,P around all maximum to find best value of C in (E,P) space. In TEP, this fine-mesh search was performed around the 5000 highest maxima -> final list of planet candidates, subject to follow-up observations

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Planet WS Berlin 12/2003 Slicing for equidistant data starting from (2) : N op = k 2 t d -2 (P max -P min ) t obs,s N pts with N pts = t obs /t inc the total number of computations is: N op = k 2 t d -2 (P max -P min ) t obs,s t obs t inc -1 (3) now, N op t obs, instead of N op t obs 2 without 'slicing'. Savings from slicing is n s.. Drawbacks: added complexity. Slicing allows running the TDA on shorter sections of data, with the possiblitity to add matrizes C of later data at any time (useful for missions with long t obs )

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Planet WS Berlin 12/2003 Analysis of COROT EB data vs TEP -data span only 150 days, not 5 years as in TEP -homogenous noise characteristics in data set -no atmosphere with ‘unkown’ extinction -computers became faster With O(100) EB's to analyze in COROT fields, no serious computing obstacles are expected. Selection of best TDA-kernel (matched filter, BLS,..) is TBD and requires lightcurves with realistic noise simulations.

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Planet WS Berlin 12/2003 Summary 1. algorithms to analyze EB lightcurves: fundamentally similar to single stars; need to model more complex transits; more 'tricky' to obtain efficient transit detection, as there are fewer invariants in transit lightcurves. 2. Slicing the data into smaller sections improves computational efficiency of TDA, adding complexity. Also, allows efficient adding of additional data. ¿How useful may this method be to single star TD? - TBD 3. COROT EB analysis is not expected to cause serious difficulties. Selection of best TDA is TBD

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Planet WS Berlin 12/2003 References Deeg, H.J., et al.1998, A&A 338, 479 Doyle, L.R., et al. 2000, ApJ, 535, 338 Jenkins, J. M.; Doyle, L. R.; Cullers, D. K. 1996, Icarus 119, 244 Schneider, J. 1994, Planet Space Sci. 42, 539

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