Period variations as a probe of exoplanets, multiple star systems and stellar evolution

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2024-06-21

Authors

Ζέρβας, Κωνσταντίνος

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Abstract

In the present work, we study period variations observed in Eclipse Timing Variations (ETVs) as a probe of exoplanets, multiple star systems and stellar evolution. Specifically, we investigate the implications of the Light Travel Time Effect (LTTE), the magnetic activity and mass transfer in ETV diagrams alongside the dynamical stability of the proposed companions in case of multiplicity. The dissertation is divided in two parts. Part I introduces the fundamental concepts, beginning with an overview of multiple stellar and planetary systems (Chapter 1). In Chapter 2 we formulate the ETVs as an O[bserved]-C[alculated] time difference for the effects of LTTE, magnetic activity (Applegate mechanism) and mass transfer. In Chapter 3 we describe the optimization algorithms that was used for the ETV analysis in this study, consisting of a set of global (Genetic Algorithm, Differential Evolution, Simulated Annealing) and local (Nelder-Mead Downhill Simplex, Levenberg-Marquardt, Heuristic Scanning, Markov Chain Monte Carlo sampling) algorithms. These sophisticated methods comprise an effective strategy of finding the best-fitting curve of an ETV diagram in the least-squares sense. Part I is concluded in Chapter 4 with the theory behind the N-body problem within a Hamiltonian framework and the numerical methods used in our case studies for the dynamics and orbital evolution of the resulting configurations. Additionaly, we present the most often-quoted dynamical stability limits based of theoretical, empirical and numerical studies. Finally, in Part II, we present the results of our ETV analysis for two case studies. First, we implement the proposed optimization scheme of global and local search algorithms, together with N-body simulations, for the case of the contact binary TZ Boo as a member of a possible hierarchical quintuple system. Second, a global grid search approach is applied alongside N-body simulations in the case of the Post-Common Envelope Binary (PCEB) NSVS 14256825 as the host of two candidate substellar companions. In the case of TZ Boo, a historically complex and puzzling light curve and period variation was confirmed utilizing the Transiting Exoplanet Survey Satellite (TESS) data. Our ETV analysis, which was the first where both mechanisms, LTTE and Applegate, are assumed to work simultaneously, resulted to the most credible scenario for the ETV variation: two stellar circumbinary companions of minimum masses M_3 = 0.58 M_{\odot}, M_4 = 0.14M_{\odot} with periods P_3 = 38 yr, P_4 = 20 yr alongside with a 24 yr magnetic activity of the secondary component and a long-term period increase (dP/dt = 1.2x10^{-8} d yr^-1), interpreted as a conservative mass transfer from the secondary to the primary component. The TESS light curve data revealed an outer eclipse which we attribute to a detached binary of 9.5 day period in accordance with previously published spectroscopic results. Based on this identification we suggest a hierarchic quintuple architecture of a triple star and an outer binary, which appears to be stable for at least 1 Myr only in the case of a reparameterization of our ETV model with zero eccentricities and an outer retrograde orbit. NSVS 14256825 is a PCEB exhibiting a period variation which is inadequately explained by one LTTE term according to the latest published studies. Here, a grid search optimization scheme is implemented alongside a dynamical stability analysis of N-body simulations, which has not been attempted yet for this system in this extent. Hundreds of stable configurations were identified reaching a lifetime of 1 Myr, with initial conditions derived of Keplerian (kinematic) and Newtonian (N-body) ETV fits. An almost circular inner orbit with period $P_3$ = 7 yr was identified among all solutions and attributed to a circumbinary planet of Jovian mass $M_3$ = 11-14 $M_{Jup}$. In contrast, the outer orbit is unconstrained, with periods ranging from 3:1 to 7:1 Mean Motion Resonance (MMR). As a result, future photometric observations of the system are required to refine and constrain the LTTE solutions.

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Eclipsing binaries, Period variation, Light-time effect (LITE), Magnetic activity (Applegate), Dynamical stability, Optimization methods

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