Eclipse Timing Variations Research Articles

Detection of period variations of eclipsing binaries in the Catalina Sky Survey

ABSTRACT We present 126 eclipsing binary candidates among 4683 Catalina Sky Surveys (CSS) detached and semi-detached eclipsing binary systems (EBs) showing cyclic or quadratic period variations over a 12 yr time span. By using inverse Gaussian profiles of the eclipses coupled with a Markov chain Monte Carlo procedure, times of minima (ToM) were calculated and diagrams with eclipse timing variations (ETVs) were constructed. Numerical tests were performed, involving synthetic EBs with period variations generated by the PHOEBE 2.0 engine and actual data for EBs with well-known period variations from the literature, to verify that the calculation of ToM variations for our CSS systems is reliable. A total of 63 out of the 126 EBs show likely cyclic ETVs, while the remainder present quadratic behaviour instead. Periods, amplitudes, period change rates, and associated errors were determined by using sinusoidal and parabolic models. 12 out of the 63 EBs (19 per cent) that appear to exhibit periodic ETVs are low-mass candidates. Additionally, four out of 126 also have maximum quadrature light variations. The possibility that the cyclic variations are caused by the light traveltime effect due to the presence of a tertiary companion is investigated. The possible nature of the quadratic ETVs is also discussed.

Space observations of AA Doradus provide consistent mass determinations. New HW-Vir systems observed with TESS

ABSTRACT We present an overview of eclipsing systems of the HW-Virginis (HW-Vir) type, based on space observations from the Transiting Exoplanet Survey Satellite (TESS) mission. We perform a detailed analysis of the properties of AA Doradus (AA Dor), which was monitored for almost a full year. This excellent time series data set permitted us to search for both stellar pulsations and eclipse timing variations. In addition, we used the high-precision trigonometric parallax from Gaia Early Data Release 3 to make an independent determination of the fundamental stellar parameters. No convincing pulsations were detected down to a limit of 76 parts per million; however, we detected one peak with false alarm probability of 0.2 per cent. 20 s cadences being collected during Year 3 should confirm or reject our detection. From eclipse timing measurements we were able to confirm that the orbital period is stable, with an upper limit to any period change of 5.75 × 10−13 s s−1. The apparent offset of the secondary eclipse is consistent with the predicted Rømer delay when the primary mass is that of a canonical extended horizontal branch star. Using parallax and a spectral energy distribution corroborates that the mass of the primary in AA Dor is canonical, and its radius and luminosity are consistent with an evolutionary state beyond core helium burning. The mass of the secondary is found to be at the limit of hydrogen burning.

BG Ind: the nearest doubly eclipsing, compact hierarchical quadruple system

ABSTRACT BG Ind is a well-studied, bright, nearby binary consisting of a pair of F stars in a 1.46-d orbit. We have discovered in the TESS light curve for TIC 229804573 (aka BG Ind), a second eclipsing binary in the system with a 0.53-d period. Our subsequent analyses of the recent TESS and archival ground-based photometric and radial velocity (RV) data reveal that the two binaries are gravitationally bound in a 721-d period, moderately eccentric orbit. We present the results of a joint spectro-photodynamical analysis of the eclipse timing variation curves of both binaries based on TESS and ground-based archival data, the TESS light curve, archival RV data, and the spectral energy distribution, coupled with the use of PARSEC stellar isochrones. We confirm prior studies of BG Ind that found that the brighter binary A consists of slightly evolved F-type stars with refined masses of 1.32 and 1.43 M⊙, and radii of 1.59 and 2.34R⊙. The previously unknown binary B has two less massive stars of 0.69 and 0.64 M⊙ and radii of 0.64 and 0.61R⊙. Based on a number of different arguments that we discuss, we conclude that the three orbital planes are likely aligned to within 17○.

Light-time effect detected in fourteen eclipsing binaries

The available minima timings of 14 selected eclipsing binaries (V1297 Cas, HD 24105, KU Aur, GU CMa, GH Mon, AZ Vel, DI Lyn, DK Her, GQ Dra, V624 Her, V1134 Her, KIC 6187893, V1928 Aql, V2486 Cyg) were collected and analyzed. Using the automatic telescopes, surveys, and satellite data, we derived more than 2500 times of eclipses, accompanied with our own ground-based observations. These data were used to detect the period variations in these multiple systems. The eclipse timing variations were described using the third-body hypothesis and the light-time effect. Their respective periods were derived as 2.5, 16.2, 27, 20, 64, 5.6, 22, 115, 27, 42, 6.9, 11.2, 4.1, and 8.4 years for these systems, respectively. The predicted minimal mass of the third body was calculated for each of the systems, and we discuss here their prospective detectability. The light curves of HD 24105, GH Mon, DK Her, V1134 Her, KIC 6187893, V1928 Aql, and V2486 Cyg were analyzed using the PHOEBE program, resulting in physical parameters of the components. Significant fractions of the third light were detected during the light-curve analysis, supporting our hypothesis of the triple-star nature of all these systems. The majority of these systems (nine out of 14) were already known as visual doubles. Our study shifts them to possible quadruples, what makes them even more interesting.

What we can learn from eclipsing binaries in large surveys: The case of EA Catalina systems

With the recent availability of large-scale multi-epoch photometric datasets, we were able to study EBs en masse. Large samples are useful to determine not only statistical properties but for finding strange and curious systems that no one had ever studied before, binaries with peculiarities that may reveal physical significance. We present an updated and more detailed catalog of 4680 Northern EAs in the Catalina Sky Survey (CSS). This work includes, new systems, revised period determination and ephemerides, system morphology classification based on machine learning techniques, computation of principal physical parameters with the EBAI (Eclipsing Binary via Artificial Intelligence) and detection of eclipse timing variations. We identify several groups of interesting systems including those with low mass K and M dwarfs, systems with longterm modulation of the maximum brightness, systems with longterm period modulation, potential triple systems and systems with magnetic activity.

The quest for planets around subdwarfs and white dwarfs fromKeplerspace telescope fields

Context.In this study, we independently test the presence of an exoplanet around the binary KIC 9472174, which is composed of a red dwarf and a pulsating type B subdwarf. We also present the results of our search for Jupiter-mass objects orbiting near to the eclipsing binary KIC 7975824, which is composed of a white dwarf and type B subdwarf, and the pulsating white dwarf KIC 8626021.Aims.The goal is to test analytical techniques and prepare the ground for a larger search for possible substellar survivors on tight orbits around post-common envelope binaries and stars at the end of their evolution, that is, extended horizontal branch stars and white dwarfs. We, therefore, mainly focus on substellar bodies orbiting these stars within the range of the host’s former red-giant or asymptotic-giant phase envelopes. Due to the methods we use, the quest is restricted to single-pulsating type B subdwarf and white dwarf stars and short-period eclipsing binaries containing a white dwarf or a subdwarf component.Methods.Our methods rely on the detection of exoplanetary signals hidden in photometric time series data from theKeplerspace telescope, and they are based on natural clocks within the data itself, such as stellar pulsations and eclipse times. The light curves are analyzed using Fourier transforms, time-delays, and eclipse timing variations.Results.Based on the three objects studied in this paper, we demonstrate that these methods can be used to detect giant exoplanets orbiting around pulsating white dwarf or type B subdwarf stars as well as short-period binary systems, at distances which fall within the range of the former red-giant envelope of a single star or the common envelope of a binary. Using our analysis techniques, we reject the existence of a Jupiter-mass exoplanet around the binary KIC 9472174 at the distance and orbital period previously suggested in the literature. We also found that the eclipse timing variations observed in the binary might depend on the reduction and processing of theKeplerdata. The other two objects analyzed in this work do not have Jupiter mass exoplanets orbiting within 0.7–1.4 AU from them, or larger-mass objects on closer orbits (the given mass limits are minimum masses).Conclusions.Depending on the detection threshold of the time-delay method and the inclination of the exoplanet orbit toward the observer, data from the primaryKeplermission allows for the detection of bodies with a minimum of ~1 Jupiter-mass orbiting these stars at ~1 AU, while data from the K2 mission extends the detection of objects with a minimum mass of ~7 Jupiter-mass on ~0.1 AU orbits. The exoplanet mass and orbital distance limits depend on the length of the available photometric time series.

Eclipse time variations in the post-common envelope binary V470 Cam

ABSTRACT Linear or quadratic relations fitted to the time-dependence of post-common envelope binary eclipse times generally give residuals exhibiting a cyclic variation. Among several possible explanations is the presence of one or more orbiting circumbinary objects causing a reflex motion of the binary centre-of-mass, thereby altering the light-travel-time.Twenty new eclipse times for the post-common envelope binary V470 Cam have been obtained; with these and 380 useable eclipse times in the literature, two circumbinary brown dwarfs having orbital periods of 7.87 ± 0.08 and 13.27 ± 0.16 yr were found to give an excellent fit to cyclic residuals resulting from a quadratic ephemeris fit. Irrespective of the excellent fit, it would be premature to claim that the V470 Cam binary is accompanied by two orbiting brown dwarfs; at the very least more eclipse times are needed to confirm the result and other plausible explanations, such as the Applegate mechanism, need eliminating.

Linear and non-linear tidal oscillations and mode identification in the eccentric binary system KIC 3858884

ABSTRACT The phoebe code was used to analyse the Kepler light-curve and to estimate the physical and geometrical parameters of a rare pulsating binary system, KIC 3858884. The analysis indicated that the system is composed of two detached and very similar main-sequence A-type stars, in a highly eccentric orbit with e = 0.47. After disentangling the binarity effect, the residual data were subjected to Fourier frequency decomposition using period04 software. The resulting frequency spectrum consists of two moderately high-amplitude nearby frequencies, F1 = 7.232199 d−1 and $F2=7.472889\, \mathrm{d}^{-1}$, which were attributed to δ Scuti-type pulsations. In addition, 18 frequencies were identified that were exact harmonics of the orbital frequency $f_{\rm orb}= 0.038533\, \mathrm{d}^{-1}$, and also 53 anharmonics. However, it was found that many of these anharmonic frequencies coupled together non-linearly to give harmonic modes of pulsation. Furthermore, some existing theoretical models of the tidal oscillations were numerically verified in general binary systems through estimations of various modal characteristics, for example mode quantum numbers ${n, l, m,}$ energies Ei, threshold energies Ei,th, damping rates γi, growth rates Γi and stability criteria, etc. The evolution of the stars in the binary system was compared with some similar single pulsating stars on the Hertzsprung–Russell diagram and it was concluded that the evolution of a single star is more rapid. Finally, the observed rate of apsidal line displacement was estimated through eclipse timing variation analysis as Uobs = 74745.2 ± 2566 yr. This was compared with the theoretically calculated rate of the line of apsides motion, UTheo = 73588 ± 2298 yr, and found to be in good agreement within errors, hence verifying general relativity theory once again.

TIC 278825952: a triply eclipsing hierarchical triple system with the most intrinsically circular outer orbit

ABSTRACT We report the discovery of a compact triply eclipsing triple star system in the southern continuous viewing zone of the TESS space telescope. TIC 278825952 is a previously known, but unstudied circular eclipsing binary with a period of 4.781 d with a tertiary component in a wider, circular orbit of 235.55-d period that was found from three sets of third-body eclipses and from light travel-time effect dominated eclipse timing variations. We performed a joint photodynamical analysis of the eclipse timing variation curves, photometric data, and the spectral energy distribution, coupled with the use of PARSEC stellar isochrones. We find that the inner binary consists of slightly evolved, near twin stars of masses of 1.12 and 1.09 M⊙ and radii of 1.40 and 1.31 R⊙. The third, less massive star has a mass of 0.75 M⊙ and radius of 0.70 R⊙. The low mutual inclination and eccentricities of the orbits show that the system is highly coplanar and surprisingly circular.

Stability of planetary, single M dwarf, and binary star companions to Kepler detached eclipsing binaries and a possible five-body system

ABSTRACT In this study, we identify 11 Kepler systems (KIC 5255552, 5653126, 5731312, 7670617, 7821010, 8023317, 10268809, 10296163, 11519226, 11558882, and 12356914) with a flip-flop effect in the eclipse timing variations O − C diagrams of the systems, report on what these systems have in common and whether these systems are dynamically stable. These systems have previously reported high eccentric binary stars with highly eccentric third bodies/outer companions. We find that all of the additional bodies in the system are dynamically stable for the configurations previously reported and are therefore likely to exist as described. We also provide additional evidence of KIC 5255552 being a quadruple star system composed of an eclipsing binary pair and non-eclipsing binary pair with the possibility of a fifth body in the system. With the advent of the NASA’s Transiting Exoplanet Survey Satellite (TESS) exoplanet survey, its precision photometric monitoring offers an opportunity to help confirm more local eclipsing binary star companions, including planets.

Eclipse timing variation of GK Vir: evidence of a possible Jupiter-like planet in a circumbinary orbit

ABSTRACT Eclipse timing variation analysis has become a powerful method to discover planets around binary systems. We applied this technique to investigate the eclipse times of GK Vir. This system is a post-common envelope binary with an orbital period of 8.26 h. Here, we present 10 new eclipse times obtained between 2013 and 2020. We calculated the O−C diagram using a linear ephemeris and verified a clear orbital period variation (OPV) with a cyclic behaviour. We investigated if this variation could be explained by the Applegate mechanism, the apsidal motion, or the light travel time (LTT) effect. We found that the Applegate mechanism would hardly explain the OPV with its current theoretical description. We obtained using different approaches that the apsidal motion is a less likely explanation than the LTT effect. We showed that the LTT effect with one circumbinary body is the most likely cause for the OPV, which was reinforced by the orbital stability of the third body. The LTT best solution provided an orbital period of ∼24 yr for the outer body. Under the assumption of coplanarity between the external body and the inner binary, we obtained a Jupiter-like planet around the GK Vir. In this scenario, the planet has one of the longest orbital periods, with a full observational baseline, discovered so far. However, as the observational baseline of GK Vir is smaller than twice the period found in the O−C diagram, the LTT solution must be taken as preliminary.

KIC 12268220: A δ Scuti Pulsating Star and an Active Protohelium White Dwarf in an Eclipsing Binary System

Abstract We present a photometric, spectroscopic, asteroseismic, and evolutionary analysis of the Algol-type eclipsing binary KIC 12268220. We find the O’Connell effect and anticorrelated eclipse timing variations in the Kepler light curve, revealing the presence of large starspots. Radial velocities and atmospheric parameters are obtained from ground-based spectroscopic observations. Combined with the radial velocity measurements and Gaia-derived total luminosity, our light-curve modeling yields the solution of the physical parameters for both the primary and secondary components. We find 14 independent frequencies arising from the δ Scuti primary, and the observed frequencies agree with the frequency range of unstable modes from nonadiabatic calculations. Based on the conclusion from previous literature, we run a grid of models to study the evolution process of our system. The evolutionary tracks of our model suggest that the low-mass ( ∼ 0.23 M ⊙ ) evolved secondary shows a similar evolutionary state to the R CMa-type system, which might evolve to an EL CVn system.

The compact triply eclipsing triple star TIC 209409435 discovered with TESS

ABSTRACT We report the discovery in TESS Sectors 3 and 4 of a compact triply eclipsing triple star system. TIC 209409435 is a previously unknown eclipsing binary with a period of 5.717 d, and the presence of a third star in an outer eccentric orbit of 121.872-d period was found from two sets of third-body eclipses and from eclipse timing variations. The latter exhibits signatures of strong third-body perturbations. After the discovery, we obtained follow-up ground-based photometric observations of several binary eclipses as well as another of the third-body eclipses. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of TESS and ground-based light curves (including both archival WASP data, and our own follow-up measurements), as well as eclipse timing variation curves. Also, we have included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones. We find that the inner binary consists of near twin stars of mass 0.90 M⊙ and radius 0.88 R⊙. The third star is just 9 per cent more massive and 18 per cent larger in radius. The inner binary has a rather small eccentricity, while the outer orbit has e = 0.40. The inner binary and outer orbit have inclination angles within 0.1° and 0.2° of 90°, respectively. The mutual inclination angle is ≲1/4°. All of these results were obtained without radial velocity observations.

TICs 167692429 and 220397947: the first compact hierarchical triple stars discovered with TESS

ABSTRACT We report the discovery and complex analyses of the first two compact hierarchical triple star systems discovered with TESS in or near its southern continuous viewing zone during Year 1. Both TICs 167692429 and 220397947 were previously unknown eclipsing binaries, and the presence of a third companion star was inferred from eclipse timing variations exhibiting signatures of strong third-body perturbations and, in the first system, also from eclipse depth variations. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of TESS and archival ground-based WASP light curves, as well as eclipse timing variation curves. Also, for the first time, we included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones, taking into account Gaia DR2 parallaxes and catalogued metallicities. We find that both systems have twin F-star binaries and a lower mass tertiary star. In the TIC 167692429 system, the inner binary is moderately inclined (imut = 27°) with respect to the outer orbit, and the binary versus outer (triple) orbital periods are 10.3 versus 331 d, respectively. The mutually inclined orbits cause a driven precession of the binary orbital plane that leads to the disappearance of binary eclipses for long intervals. In the case of TIC 220397947, the two orbital planes are more nearly aligned and the inner versus outer orbital periods are 3.5 and 77 d, respectively. In the absence of radial velocity observations, we were unable to calculate highly accurate masses and ages for the two systems. According to stellar isochrones TIC 167692429 might be either a pre-main sequence (MS) or an older post-MS system. In the case of TIC 220397947, our solution prefers a young pre-MS scenario.

Kepler-1661 b: A Neptune-sized Kepler Transiting Circumbinary Planet around a Grazing Eclipsing Binary

Abstract We report the discovery of a Neptune-sized ( ) transiting circumbinary planet, Kepler-1661 b, found in the Kepler photometry. The planet has a period of ∼175 days and its orbit precesses with a period of only 35 yr. The precession causes the alignment of the orbital planes to vary, and the planet is in a transiting configuration only ∼7% of the time as seen from Earth. As with several other Kepler circumbinary planets, Kepler-1661 b orbits close to the stability radius, and is near the (hot) edge of the habitable zone. The planet orbits a single-lined, grazing eclipsing binary, containing a 0.84 and 0.26 pair of stars in a mildly eccentric (e = 0.11), 28.2 day orbit. The system is fairly young, with an estimated age of ∼1–3 Gyr, and exhibits significant starspot modulations. The grazing eclipse configuration means the system is very sensitive to changes in the binary inclination, which manifests itself as a change in the eclipse depth. The starspots contaminate the eclipse photometry, but not in the usual way of inducing spurious eclipse timing variations. Rather, the starspots alter the normalization of the light curve, and hence the eclipse depths. This can lead to spurious eclipse depth variations, which are then incorrectly ascribed to binary orbital precession.

Magneto-hydrodynamical origin of eclipsing time variations in post-common-envelope binaries for solar mass secondaries

Abstract Eclipsing time variations have been observed for a wide range of binary systems, including post-common-envelope binaries. A frequently proposed explanation, apart from the possibility of having a third body, is the effect of magnetic activity, which may alter the internal structure of the secondary star, particularly its quadrupole moment, and thereby cause quasi-periodic oscillations. Here we present two compressible non-ideal magneto-hydrodynamical (MHD) simulations of the magnetic dynamo in a solar mass star, one of them with three times the solar rotation rate (“slow rotator”), the other one with twenty times the solar rotation rate (“rapid rotator”), to account for the high rotational velocities in close binary systems. For the slow rotator, we find that both the magnetic field and the stellar quadrupole moment change in a quasi-periodic manner, leading to O-C (observed - corrected times of the eclipse) variations of ∼0.025 s. For the rapid rotator, the behavior of the magnetic field as well as the quadrupole moment changes become considerably more complex, due to the less coherent dynamo solution. The resulting O-C variations are of the order 0.13 s. The observed system V471 Tau shows two modes of eclipsing time variations, with amplitudes of 151 s and 20 s, respectively. However, the current simulations may not capture all relevant effects due to the neglect of the centrifugal force and self-gravity. Considering the model limitations and that the rotation of V471 Tau is still a factor of 2.5 faster than our rapid rotator, it may be conceivable to reach the observed magnitudes.

Doubly eclipsing systems

Context. Only several doubly eclipsing quadruple stellar systems are known to date, and no dedicated effort to characterize population properties of these interesting objects has yet been made. Aims. Our first goal was to increase number of known doubly eclipsing systems such that the resulting dataset would allow us to study this category of objects via statistical means. In order to minimize biases, we used long-lasting, homogeneous, and well-documented photometric surveys. Second, a common problem of basically all known doubly eclipsing systems is the lack of proof that they constitute gravitationally bound quadruple system in the 2+2 architecture (as opposed to two unrelated binaries that are projected onto the same location in the sky by chance). When possible, we thus sought evidence for the relative motion of the two binaries. In that case, we tried to determine the relevant orbital periods and other parameters. Methods. We analysed photometric data for eclipsing binaries provided by the OGLE survey and we focused on the LMC fields. We found a large number of new doubly eclipsing systems (our discoveries are three times more numerous than the previously known cases in this dataset). In order to prove relative motion of the binaries about a common centre of mass, we made use of the fact that OGLE photometry covers several years. With a typical orbital period of days for the observed binaries, we sought eclipse time variations (ETVs) on the timescale comparable to a decade (this is the same method used for an archetype of the doubly eclipsing system, namely V994 Her). In the cases where we were able to detect the ETV period, the difference between the inner and outer periods in the quadruple system is large enough. This allows us to interpret ETVs primarily as the light-time effect, thus providing an interesting constraint on masses of the binaries. Results. In addition to significantly enlarging the database of known doubly eclipsing systems, we performed a thorough analysis of 72 cases. ETVs for 28 of them (39% of the studied cases) showed evidence of relative motion. Among these individual systems, we note OGLE BLG-ECL-145467, by far the most interesting case; it is bright (12.6 mag in I filter), consists of two detached binaries with periods of ≃3.3 d and ≃4.9 d (making it a candidate for a 3:2 resonant system) revolving about each other in only ≃1538 d. Distribution of the orbital period ratio PA/PB of binaries in 2+2 quadruples shows statistically significant excess at ≃1 and ≃1.5. The former is likely a natural statistical preference in weakly interacting systems with periods within the same range. The latter is thought to be evidence of a capture in the 3:2 mean motion resonance of the two binaries. This sets important constraints on evolutionary channels in these systems. Conclusions. The total number of doubly eclipsing systems increased to 146, more than 90% of which are at low declinations on the southern sky. This motivates us to use southern hemisphere facilities to further characterize these systems, and to seek possibilities to complement this dataset with northern sky systems.

Modelling Kepler eclipsing binaries: homogeneous inference of orbital and stellar properties

Abstract We report on the properties of eclipsing binaries (EBs) from the Kepler mission with a newly developed photometric modelling code, which uses the light curve, spectral energy distribution of each binary, and stellar evolution models to infer stellar masses without the need for radial velocity (RV) measurements. We present solutions and posteriors to orbital and stellar parameters for 728 systems, forming the largest homogeneous catalogue of full Kepler binary parameter estimates to date. Using comparisons to published RV measurements, we demonstrate that the inferred properties (e.g. masses) are reliable for well-detached main-sequence (MS) binaries, which make up the majority of our sample. The fidelity of our inferred parameters degrades for a subset of systems not well described by input isochrones, such as short-period binaries that have undergone interactions, or binaries with post-MS components. Additionally, we identify 35 new systems which show evidence of eclipse timing variations, perhaps from apsidal motion due to binary tides or tertiary companions. We plan to subsequently use these models to search for and constrain the presence of circumbinary planets in Kepler EB systems.

Distinguishing Polar and Coplanar Circumbinary Exoplanets by Eclipse Timing Variations

Abstract Circumbinary planets (CBPs) can be misaligned with their host binary stars. Orbital dynamics, simulations, and recent observations of protoplanetary disks all suggest that the planet can stably orbit in a plane perpendicular to that of an eccentric host binary star (i.e., a polar orbit). No solid claim of detection of such a configuration has been made; the nine systems detected by the transit technique are nearly coplanar, but their discovery is also biased toward that configuration. Here, we develop eclipse timing variations (ETVs) as a method to detect misaligned CBPs. We find that because the apsidal motion (periastron precession) of the host binary is prograde for a coplanar planet and retrograde for a polar planet, the mean eclipse periods of primary and secondary eclipses differ in a way that distinguishes those configurations. Second, the eclipse duration variations vary in a way that can confirm that inference, over and against a polar model. Third, the relative phasing of primary and secondary ETVs on the planet’s orbital timescale also distinguishes the two configurations, which we explain analytically and quantify through a grid of numerical models. We apply these methods to Kepler-34, a transiting planet known to be nearly coplanar by detailed photodynamic modeling. In this system, we find that the binary eclipse times alone suffice to distinguish these orbital configurations, using the effects introduced here. Our work provides a tool for discovering potential polar CBPs, or misaligned CBPs of milder inclinations, from the existing ETV data set of the Kepler, as well as future observations by TESS or PLATO.

Orbital Period Variation of KIC 10544976: Applegate Mechanism versus Light Travel Time Effect

Abstract In recent years, several close post-common-envelope eclipsing binaries have been found to show cyclic eclipse timing variations (ETVs). This effect is usually interpreted either as the gravitational interaction among circumbinary bodies and the host binary—known as the light travel time (LTT) effect—or as the quadrupole moment variations in one magnetic active component—known as the Applegate mechanism. In this study, we present an analysis of the ETV and the magnetic cycle of the close binary KIC 10544976. This system is composed of a white dwarf and a red dwarf in a short orbital period (0.35 days) and was monitored by ground-based telescopes between 2005 and 2017 and by the Kepler satellite between 2009 and 2013. Using the Kepler data, we derived the magnetic cycle of the red dwarf by two ways: the rate and energy of flares and the variability due to spots. Both methods resulted in a cycle of ∼600 days, which is in agreement with magnetic cycles measured for single low-mass stars. The orbital period of KIC 10544976 shows only one long-term variation which can be fitted by an LTT effect with period of ∼16.8 yr. Hence, one possible explanation for the ETVs is the presence of a circumbinary body with a minimal mass of ∼13.4 M Jup. In the particular scenario of coplanarity between the external body and the inner binary, the third body mass is also ∼13.4 M Jup. In this case, the circumbinary planet must either have survived the evolution of the host binary or have been formed as a consequence of its evolution.