Finding invisible exoplanets

M. D. MELITA; D. D. CARPINTERO

Cartagena de Indias

Congreso; XV Reunión Regional Latinoamericana de Astronomía; 2016

Universidad de Colombia

We show that, given the non-periodic transits of aexoplanet and assuming that the lack of periodicityis due to another, non transiting planet, it is possibleto recover the six orbital elements of both planets, aswell as their masses and the mass of the star. Theseelements and masses, when used as initial conditionsto integrate the equations of motion, allow to recoverall the observed transits. The searching forthe masses and elements is based on a genetic algorithm,which is an ideal tool for optimization inmany-dimensional spaces. As required by any geneticalgorithm, we developed a suitable fitness function,which, starting from a set of initial guesses ofall the elements and masses, compares the observedtransits against the transits obtained with all theguesses, ranking the results. The algorithm itselfsearches for new guesses based on this ranking; theiteration of this scheme leads to a convergence to thedesired solution.We applied our algorithm to the case of exoplanetsKepler 419b and c. We obtained orbital elementsand masses that, when integrated, allow to recoverall the observed transits with a precision of abouta minute. In contrast, the solution given by Dawsonet al. (2014, ApJ, 791, 89), when integrated,has a cummulative drift in the transits of about fivehours per period of the transiting planet. We alsoobtain, with our solution, the observed Transit TimingVariations (TTVs), as well as the observed radialvelocities of the star.