Eclipse Timing Variations Research Articles

Multiply eclipsing candidates from the TESS satellite

We present a catalogue of the Transiting Exoplanet Survey Satellite (TESS) targets that show multiple eclipses. In all of these stars, we detected two sets of eclipses, for which their two distinctive periods can be derived. These multiple stellar systems could either be doubly eclipsing quadruples or triple-star coplanar systems showing eclipses on the outer orbit in addition to the inner eclipses. In total, 116 systems were found to be doubly eclipsing, while 25 stars were identified as triply eclipsing triples. Several confirmed blends of two close sources were not included in our analysis. All these systems were identified by scanning the known eclipsing systems taken from the Variable Star Index database and checking their TESS light curves. The average period of the dominant pair, pair A, is 2.7 days in our sample, while for the second pair, pair B, the average period is 5.3 days. Several systems show evident eclipse timing variation (ETV) changes even from the short interval of the TESS data, indicating possible period changes and short mutual orbit. We also present evidence that the system V0871 Cen is probably a septuple-star system of architecture (Aa-Ab)-B-C-D. Most of the presented systems are adequately bright and show deep enough eclipses for observing, and therefore we call for new ground-based observations for these extremely interesting multiples. Owing to this motivation, we have included also the ephemerides for both pairs of each system, our catalogue also contains their depths of eclipses and the light-curve shapes as extracted from the TESS data. These new ground-based observations would be very useful for further derivation of the mutual movement of both pairs on their orbit via detection of the ETVs of both pairs for example.

Von Zeipel – Lidov – Kozai cycles in action: Kepler triples with eclipse depth variations: KICs 6964043, 5653126, 5731312, and 8023317

ABSTRACT We report the results of the photodynamical analyses of four compact, tight triple stellar systems, KICs 6964043, 5653126, 5731312, and 8023317, based largely on Kepler and TESS data. All systems display remarkable eclipse timing and eclipse depth variations, the latter implying a non-aligned outer orbit. Moreover, KIC 6964043 is also a triply eclipsing system. We combined photometry, ETV curves, and archival spectral energy distribution data to obtain the astrophysical parameters of the constituent stars and the orbital elements with substantial precision. KICs 6964043 and 5653126 were found to be nearly flat with mutual inclinations imut = 4${_{.}^{\circ}}$1 and 12${_{.}^{\circ}}$3, respectively, while KICs 5731312 and 8023317 (imut = 39${_{.}^{\circ}}$4 and 55${_{.}^{\circ}}$7, respectively) are found to lie in the high imut regime of the von Zeipel-Kozai-Lidov (ZKL) theorem. We show that, currently, both high inclination triples exhibit observable unusual retrograde apsidal motion. Moreover, the eclipses will disappear in all but one of the four systems within a few decades. Short-term numerical integrations of the dynamical evolution reveal that both high inclination triples are currently subject to ongoing, large amplitude (Δe ∼ 0.3) inner eccentricity variations on centuries-long time-scales, in accord with the ZKL theorem. Longer-term integrations predict that two of the four systems may become dynamically unstable on ∼ Gyr time-scales, while in the other two triples common envelope phases and stellar mergers may occur. Finally, we investigate the dynamical properties of a sample of 71 KIC/TIC triples statistically, and find that the mutual inclinations and outer mass ratios are anticorrelated at the 4σ level. We discuss the implications for the formation mechanisms of compact triples.

Origin of eclipsing time variations: Contributions of different modes of the dynamo-generated magnetic field

Context. The possibility to detect circumbinary planets and to study stellar magnetic fields through eclipsing time variations (ETVs) in binary stars has sparked an increase of interest in this area of research. Aims. We revisit the connection between stellar magnetic fields and the gravitational quadrupole moment Qxx and compare different dynamo-generated ETV models with our simulations. Methods. We present magnetohydrodynamical simulations of solar mass stars with rotation periods of 8.3, 1.2, and 0.8 days and perform a detailed analysis of the magnetic and quadrupole moment using spherical harmonic decomposition. Results. The extrema of Qxx are associated with changes in the magnetic field structure. This is evident in the simulation with a rotation period of 1.2 days. Its magnetic field has a more complex behavior than in the other models, as the large-scale nonaxisymmetric field dominates throughout the simulation and the axisymmetric component is predominantly hemispheric. This triggers variations in the density field that follow the magnetic field asymmetry with respect to the equator, affecting the zz component of the inertia tensor, and thus modulating Qxx. The magnetic fields of the two other runs are less variable in time and more symmetric with respect to the equator, such that the variations in the density are weaker, and therefore only small variations in Qxx are seen. Conclusions. If interpreted via the classical Applegate mechanism (tidal locking), the quadrupole moment variations obtained in the current simulations are about two orders of magnitude below those deduced from observations of post-common-envelope binaries. However, if no tidal locking is assumed, our results are compatible with the observed ETVs.

Comprehensive analysis of southern eclipsing systems with pulsating components: The cases of HM Pup, V632 Sco, and TT Vel

This work presents an extensive analysis of the properties of three southern semi-detached eclipsing binaries hosting a pulsating component, namely HM Pup, V632 Sco, and TT Vel. Systematic multi-filtered photometric observations were obtained using telescopes located in Australia and Chile mostly between 2018 and 2021. These observations were combined with data from the Transiting Exoplanet Survey Satellite (TESS) mission for a detailed analysis of pulsations. Spectral types and radial velocities were determined from spectra obtained with the Australian National University’s 2.3 m telescope and Wide Field Spectrograph. The data are modelled and the absolute parameters of all components are derived. The light curve residuals are further analysed using Fourier transformation techniques for the determination of the pulsation frequencies. Using theoretical models, the most probable modes of the principal oscillations are also identified. Eclipse-timing variation analysis is also carried out for all systems and the most likely mechanisms modulating the orbital period are proposed. The physical properties of these systems are compared with other similar cases and the locations of their components are plotted in the Mass-Radius (M−R) and Hertzsprung-Russell diagrams. Finally, the pulsational properties of the oscillating components are compared with currently known systems of this type within the orbital-pulsation period and log g-pulsation period diagrams. These systems are confirmed as oscillating eclipsing Algol-type systems (oEA stars), as the primary components are pulsating stars of δ Scuti type, with evidence of mass flow from the evolved secondary components present in their Na I D spectra.

Eclipse timing variations in post-common envelope binaries: Are they a reliable indicator of circumbinary companions?

ABSTRACT Post-common envelope binary systems evolve when matter is transferred from the primary star at a rate that cannot be accommodated by its secondary companion. A common envelope forms, which is subsequently ejected resulting in a system with a binary period frequently between 2 and 3 h. Where circumbinary companions are predicted, it remains unclear whether they form before or after the common envelope ejection. From observations of eclipse timing variations (ETVs), exoplanet data bases e.g. NASA Exoplanet Archive, list typically a dozen systems with confirmed circumbinary planets. Here, we examine seven of these systems, discuss other possible causes, and consider whether, for these dynamic systems, the ETV methodology is a reliable indicator of planetary companions. The systems selected were those where we could determine precise eclipse timings, free from significant extraneous effects such as pulsations, and present 163 new times of minima permitting us to test existing models. Over 30 circumbinary models have been proposed for these seven systems and note that all, other than the latest model for NY Vir, which remains to be fully tested, fail within a year to accurately predict eclipse times. In examining alternative mechanisms, we find that magnetic effects could contribute significantly in two of the seven systems studied. We conclude that the structure of these dynamic systems, with the extreme temperature differences and small binary separations, is not fully understood and that many factors may contribute to the observed ETVs.

The Photometric Study of Six W UMa Systems and Investigation of the Mass–Radius Relations for Contact Binary Stars

We present the photometric analysis of six short-period systems (EI Oct, V336 TrA, NX Boo, V356 Boo, PS Boo, and V2282 Cyg). This is the first photometric analysis of these systems except for V336 TrA. Observations were conducted for 27 nights at three observatories in the northern and southern hemispheres. We calculated a new ephemeris for each of the systems using our minimum times and additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to determine the eclipse timing variation trends of the systems. We found a likely orbital growth for V336 TrA and PS Boo; four other systems show a linear trend in orbital period changes, which is most likely due to the accumulation of measurement errors in their linear ephemeris parameters. The light curve analysis was performed using the Physics of Eclipsing Binaries (PHOEBE) 2.3.59 version code with the MCMC approach. The absolute parameters of the systems were calculated by using the Gaia Early Data Release 3 (EDR3) parallax. The positions of the systems were also depicted on the Hertzsprung–Russell (H-R) and diagrams. According to a sample, we were able to present relations for the mass–radius (M–R) relationships of contact binary systems. There is also a strong relationship between the mass ratio and the radius ratio in the W UMa systems for which we also provided a new relation. We compared the M–R updated relationships in this study with seven systems in other studies obtained using the spectroscopic method. In addition, we estimated some of the absolute parameters for 1734 EW systems, based on the new relationships.

Magnetic field evolution of the K2 dwarf V471 Tau

ABSTRACT Observations of the eclipsing binary system V471 Tau show that the time of the primary eclipses varies in an apparent periodic way. With growing evidence that the magnetically active K2 dwarf component might be responsible for driving the eclipse timing variations (ETVs), it is necessary to monitor the star throughout the predicted ∼35 yr activity cycle that putatively fuels the observed ETVs. We contribute to this goal with this paper by analysing spectropolarimetric data obtained with ESPaDOnS at the Canada–France–Hawaii Telescope in 2014 December and 2015 January. Using Zeeman–Doppler Imaging, we reconstruct the distribution of brightness inhomogeneities and large-scale magnetic field at the surface of the K2 dwarf. Compared to previous tomographic reconstructions of the star carried out with the same code, we probe a new phase of the ETVs cycle, offering new constraints for future works exploring whether a magnetic mechanism operating in the K2 dwarf star is indeed able to induce the observed ETVs of V471 Tau.

Planet Hunters TESS IV: a massive, compact hierarchical triple star system TIC 470710327

ABSTRACTWe report the discovery and analysis of a massive, compact, hierarchical triple system (TIC 470710327) initially identified by citizen scientists in data obtained by NASA’s Transiting Exoplanet Survey Satellite (TESS). Spectroscopic follow-up observations obtained with the hermes spectrograph, combined with eclipse-timing variations (ETVs), confirm that the system is comprised of three OB stars, with a compact 1.10 d eclipsing binary and a non-eclipsing tertiary on a 52.04 d orbit. Dynamical modelling of the system (from radial velocity and ETVs) reveal a rare configuration wherein the tertiary star (O9.5-B0.5V; 14–17 M⊙) is more massive than the combined mass of the inner binary (10.9–13.2 M⊙). Given the high mass of the tertiary, we predict that this system will undergo multiple phases of mass transfer in the future, and likely end up as a double neutron star gravitational wave progenitor or an exotic Thorne–Żytkow object. Further observational characterization of this system promises constraints on both formation scenarios of massive stars as well as their exotic evolutionary end-products.

The first study of four doubly eclipsing systems

We present the discovery and the very first analysis of four stellar systems showing two periods of eclipses, that are the objects classified as doubly eclipsing systems. Some of them were proved to orbit each other thanks to their eclipse-timing-variations (ETVs) of both pairs, hence they really constitute rare quadruples with two eclipsing pairs. Some of them do not, as we are still waiting for more data to detect their mutual movement. Their light curves and period changes were analysed. All of them are detached and near-contact, but none of them contact; moreover, to our knowledge none of these stars can be considered as blend of two spatially unresolved close components on the sky. These systems are CzeV2647 (0.5723296 + 0.9637074 days), proved to orbit with 4.5-year periodicity; CzeV1645 (1.0944877 + 1.6594641 days), with a rather questionable detection of ETV; CzeV3436 (0.6836870 + 0.3833930 days); and, finally, OGLE SMC-ECL-1758 (0.9291925 + 3.7350826 days), proved to move on its 30-year orbit. Even more surprising is the fact that most of these systems show the ratio of their two orbital periods close to coupling near some resonant values of small integers, namely CzeV2647, with only 1% from 3:5 resonance, CzeV1645 1% from 2:3 resonance, and OGLE SMC-ECL-1758 with only 0.49% from 1:4 resonance. The nature of these near-resonant states still remains a mystery.

BEBOP III. Observations and an independent mass measurement of Kepler-16 (AB) b – the first circumbinary planet detected with radial velocities

ABSTRACTThe radial velocity method is amongst the most robust and most established means of detecting exoplanets. Yet, it has so far failed to detect circumbinary planets despite their relatively high occurrence rates. Here, we report velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph, at the Observatoire de Haute-Provence’s 193cm telescope, collected during the BEBOP survey for circumbinary planets. Our measurements mark the first radial velocity detection of a circumbinary planet, independently determining the mass of Kepler-16 (AB) b to be $0.313 \pm 0.039\, {\rm M}_{\rm Jup}$, a value in agreement with eclipse timing variations. Our observations demonstrate the capability to achieve photon-noise precision and accuracy on single-lined binaries, with our final precision reaching $\rm 1.5~m\, s^{-1}$ on the binary and planetary signals. Our analysis paves the way for more circumbinary planet detections using radial velocities which will increase the relatively small sample of currently known systems to statistically relevant numbers, using a method that also provides weaker detection biases. Our data also contain a long-term radial velocity signal, which we associate with the magnetic cycle of the primary star.

Detection of two additional circumbinary planets around Kepler-451

ABSTRACT We announce the detection of two new planetary-mass companions around Kepler-451 binary system in addition to the one detected previously based on eclipse timing variation analysis. We found that an inner planet with 43 d period with a minimum mass of 1.76 Mjup and an outer one with a ∼1800 d orbital period with a minimum mass of 1.61 Mjup can explain the periodic variations in the residuals of the one-planet fit of the eclipse timings. We updated the orbital period of the middle planet as 406 d, and determined its eccentricity as 0.33. The newly discovered outer planet is also on an eccentric orbit (0.29), while the innermost planet was assumed to have a circular orbit. All three Jovian planets have similar masses, and our dynamical stability test yields that the system is stable.

Triply eclipsing triple stars in the northern TESS fields: TICs 193993801, 388459317, and 52041148

ABSTRACT In this work we report the discovery and analysis of three new triply eclipsing triple star systems found with the TESS mission during its observations of the northern skies: TICs 193993801, 388459317, and 52041148. We utilized the TESS precision photometry of the binary eclipses and third-body eclipsing events, ground-based archival and follow-up photometric data, eclipse timing variations, archival spectral energy distributions, as well as theoretical evolution tracks in a joint photodynamical analysis to deduce the system masses and orbital parameters of both the inner and outer orbits. In one case (TIC 193993801) we also obtained radial velocity measurements of all three stars. This enabled us to ‘calibrate’ our analysis approach with and without ‘truth’ (i.e. RV) data. We find that the masses are good to 1–3 per cent accuracy with RV data and 3–10 per cent without the use of RV data. In all three systems we were able to find the outer orbital period before doing any detailed analysis by searching for a longer-term periodicity in the ASAS-SN archival photometry data – just a few thousand ASAS-SN points enabled us to find the outer periods of 49.28 d, 89.86 d, and 177.0 d, respectively. From our full photodynamical analysis we find that all three systems are coplanar to within 1°−3°. The outer eccentricities of the three systems are 0.003, 0.10, and 0.62, respectively (i.e. spanning a factor of 200). The masses of the three stars {Aa, Ab, and B} in the three systems are: {1.31, 1.19, 1.34}, {1.82, 1.73, 2.19}, and {1.62, 1.48, 2.74} M⊙, respectively.

The Measurement of Dynamic Tidal Contribution to Apsidal Motion in Heartbeat Star KIC 4544587

Abstract Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high-quality observations. KIC 4544587 with tidally excited oscillations has been observed by Kepler high-precision photometric data based on long-time-baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as 19.05 ± 1.70 mrad yr−1 via tracking the orbital phase shifts of tidally excited oscillations. We also calculate the procession rate of the orbit due to the Newtonian and general relativistic contribution as 21.49 ± 2.8 and 2.4 ± 0.06 mrad yr−1, respectively. The sum of these three factors is in excellent agreement with the total observational rate of apsidal motion 42.97 ± 0.18 mrad yr−1 measured by eclipse timing variations. The tidal effect accounts for about 44% of the overall observed apsidal motion and is comparable to that of the Newtonian term. Dynamic tides have a significant contribution to the apsidal motion. The analysis method mentioned in this paper presents an alternative approach to measuring the contribution of the dynamic tides quantitatively.

Eclipse timing variation analysis of OGLE-IV eclipsing binaries towards the Galactic Bulge – II. Short periodic triple stellar systems

ABSTRACT We report an eclipse timing variations (ETV) study to identify close, stellar mass companions to the eclipsing binaries monitored during the photometric survey Optical Gravitational Lensing Experiment-IV. We also present an alternative automatic way to determine the first and last contacts of an eclipse. Applying the phase dispersion minimization method to identify potential triples, we find close third components with outer periods in less than 1500 d in 23 systems. We present outer orbit solution for 21 of 23 systems. For the 10 tightest triples, we find that the ETV can only be modelled with the combination of the light-travel-time effect (LTTE) and third-body perturbations, while in case of another 11 systems, pure LTTE solutions are found to be satisfactory. In the remaining two systems, we identify extra eclipses connected to the outer component, but for the incomplete and noisy ETV curves, we are unable to find realistic three-body solutions. Therefore, in these cases we give only the outer period.

Searching for orbital decay in a heartbeat star system KIC 3766353

ABSTRACT Theory suggests that the orbits of a large fraction of binary systems, including planet–star binary systems, shrink by a few orders of magnitude after formation. But so far, only one hot Jupiter with tidally driven orbital decay has been found by transit timing variations. We propose to search for orbital decay companions in heartbeat star systems because the orbital angular momentum is effectively transferred to the host star, causing tidal dissipation. KIC 3766353 is one of the heartbeat stars with tidally excited oscillations. We acquired the primary and the secondary eclipse time variations from the Kepler photometric light curves. Timing analysis shows that KIC 3766353 is a hierarchical triple system with a hidden third body and a red dwarf (mass 0.35 M⊙, radius 0.34 R⊙) in its inner orbit. The minimum mass of the third body is ∼0.26 M⊙, and the distance from the inner orbital is ∼111.4 R⊙. The period decay rate of the red dwarf is approximately 358 ms yr−1. The combined effects of the light-traveltime and the orbital decay lead to the observed timing variations. Future monitoring with long-time baseline observations is required to delve into the contributions of these two effects.

TIC 454140642: A Compact, Coplanar, Quadruple-lined Quadruple Star System Consisting of Two Eclipsing Binaries

Abstract We report the discovery of a compact, coplanar, quadruple-lined, eclipsing quadruple star system from Transiting Exoplanet Survey Satellite data, TIC 454140642, also known as TYC 0074-01254-1. The target was first detected in Sector 5 with a 30-minute cadence in full-frame images and then observed in Sector 32 with a 2-minute cadence. The light curve exhibits two sets of primary and secondary eclipses with periods of P A = 13.624 days (binary A) and P B = 10.393 days (binary B). Analysis of archival and follow-up data shows clear eclipse-timing variations and divergent radial velocities, indicating dynamical interactions between the two binaries and confirming that they form a gravitationally bound quadruple system with a 2 + 2 hierarchy. The Aa+Ab binary, Ba+Bb binary, and A-B system are aligned with respect to each other within a fraction of a degree: the respective mutual orbital inclinations are 0.°25 (A versus B), 0.°37 (A versus A-B), and 0.°47 (B versus A-B). The A-B system has an orbital period of 432 days—the second shortest of the confirmed quadruple systems—and an orbital eccentricity of 0.3.

Catalog of W UMa type binary systems with additional components based on eclipsing time variations

A catalog of W UMa type eclipsing binary systems with tertiary components based on eclipse timing diagrams is presented listing the physical and orbital parameters (including third body parameters) of 150 W UMa type eclipsing binaries.In this study, the (O–C) diagrams of nine sample W UMa type eclipsing binary systems, based on the most reliable timings of minima in the literature, are analyzed to obtain the third-body parameters and significant statistical results are presented from the data in the catalog.

A new photometric and dynamical study of the eclipsing binary star HW Virginis

ABSTRACT A growing number of eclipsing binary systems of the ‘HW Virginis’ (HW Vir) kind (i.e. composed by a subdwarf-B/O primary star and an M dwarf secondary) show variations in their orbital period, also called eclipse time variations (ETVs). Their physical origin is not yet known with certainty: While some ETVs have been claimed to arise from dynamical perturbations due to the presence of circumbinary planetary companions, other authors suggest that the Applegate effect or other unknown stellar mechanisms could be responsible for them. In this work, we present 28 unpublished high-precision light curves of one of the most controversial of these systems, the prototype HW Vir. We homogeneously analysed the new eclipse timings together with historical data obtained between 1983 and 2012, demonstrating that the planetary models previously claimed do not fit the new photometric data, besides being dynamically unstable. In an effort to find a new model able to fit all the available data, we developed a new approach based on a global-search genetic algorithm and eventually found two new distinct families of solutions that fit the observed timings very well, yet dynamically unstable at the 105-yr time-scale. This serves as a cautionary tale on the existence of formal solutions that apparently explain ETVs but are not physically meaningful, and on the need of carefully testing their stability. On the other hand, our data confirm the presence of an ETV on HW Vir that known stellar mechanisms are unable to explain, pushing towards further observing and modeling efforts.

The detectability of binary star planetary and brown dwarf companions from eclipse timing variations

ABSTRACT In this paper, we determine the detectability of eclipsing binary star companions from eclipse timing variations using the Kepler mission data set. Extensive and precise stellar time-series photometry from space-based missions enable searches for binary star companions. However, due to the large data sets and computational resources involved, these searches would benefit from guidance from detection simulations. Our simulations start with and benefit from the use of empirical Kepler mission data, into which we inject third bodies to predict the resulting timing of binary star eclipses. We find that the orbital eccentricity of the third body and the orbital period of the host binary star are the key factors in detecting companions. Target brightness is also likely to be a factor in detecting companions. Detectable third body masses and periods can be efficiently bound using just two equations. Our results enable the setting of realistic expectations when planning searches for eclipsing binary star planetary and brown dwarf companions. Our results also suggest the brown dwarf desert is real rather than observational selection.

Erratum: Magnetohydrodynamical origin of eclipsing time variations in post-common-envelope binaries for solar mass secondaries

Erratum: Magnetohydrodynamical origin of eclipsing time variations in post-common-envelope binaries for solar mass secondaries