Eclipse Timing Variations Research Articles

Eclipse timing variation analysis of OGLE-IV eclipsing binaries towards the Galactic Bulge – I. Hierarchical triple system candidates

We report a study of the eclipse timing variation (ETV) of short period ($P_1\le 6^d$) eclipsing binaries (EB) monitored during the photometric survey OGLE-IV. From the 425\,193 EBs we selected approximately 80\,000 binaries that we found suitable for further examination. Among them we identified 992 potential hierarchical triple (or multiple ) system candidates exhibiting light-travel-time effect (LTTE). Besides, we obtained the orbital parameters of these systems and carried out statistical analyses on the properties of these candidates. We found that (i) there is a significant lack of triple systems where the outer period is less than 500 days; (ii) the distribution of the outer eccentricities has a maximum around $e_2\approx0.3$; (iii) the outer mass ratio calculated from an estimated minimum mass of the third component is lower than $q_2\sim 0.5$ for the majority of the sample. We also present some systems that deserve special attention. (i) There are four candidates that show double periodic ETV, which we explain by the presence of a fourth companion. (ii) For two systems the perturbations of the third component are also found to be significant therefore we give a combined dynamical and LTTE ETV solution. (iii) For one system the third component is found to be probably in the substellar mass domain.

High-speed photometry of the eclipsing polar UZ Fornacis

We present 33 new mid-eclipse times spanning approximately eight years of the eclipsing polar UZ Fornacis. We have used our new observations to test the two-planet model previously proposed to explain the variations in its eclipse times measured over the past ~35 yr. We find that the proposed model does indeed follow the general trend of the new eclipse times, however, there are significant departures. In order to accommodate the new eclipse times, the two-planet model requires that one or both of the planets require highly eccentric orbits, that is, e ≥ 0.4. Such multiple planet orbits are considered to be unstable. Whilst our new observations are consistent with two cyclic variations as previously predicted, significant residuals remain. We conclude that either additional cyclic terms, possibly associated with more planets, or other mechanisms, such as the Applegate mechanism are contributing to the eclipse time variations. Further long-term monitoring is required.

Third-body perturbed apsidal motion in eclipsing binaries

Tidally forced apsidal motion in eccentric eclipsing binaries is a key observable of stellar structure studies, and may serve as important probe for different tidal dissipation theories. There are, however, alternative physical processes which result in additional contributions to the observed apsidal motion. Here we mainly concentrate on the perturbing effect of a third, distant stellar companion, forming a hierarchical triple system with the eclipsing pair. First we discuss the mathematical form of the combined third body and tidally forced apsidal motions, and its observational aspects. Then we present a brief description of an eclipse timing variation study (based on the above mentioned analytical formulae) of 26 Kepler spacecraft-discovered 3-rd body perturbation-dominated compact hierarchical triples.

Double eclipsing binary system KIC 3832716

In this paper we analyzed the light curve of the object KIC~3832716 observed during Kepler K1 mission. We showed that this previously known eclipsing binary is in fact quadruple system, in double eclipsing binary configuration on a long period orbit with the mass ratio of eclipsing binaries $0.7 \pm 0.3$. The system consists of eclipsing binary A with the orbital period of $P_A \sim 1.1419$\,d. Eclipsing binary A contains larger but less luminous secondary component in the post main sequence stage of its evolution consistent with an "Algol paradox" which can explain parameters of the components by mass transfer from secondary component after leaving the main sequence. Inspection of the light curve and eclipse time variations of the eclipsing binary A also indicates the presence of spots on the surface of secondary component with $57$\,d period of activity probably induced by longitudonal motion of the spots. The second eclipsing binary B with orbital period $P_B \sim 2.1703$\,d contains very dim secondary component with luminosity below 0.09\,$L_{\odot}$.

Physics of the Applegate mechanism: Eclipsing time variations from magnetic activity

Since its proposal in 1992, the Applegate mechanism has been discussed as a potential intrinsical mechanism to explain transit-timing variations in various types of close binary systems. Most analytical arguments presented so far focused on the energetic feasibility of the mechanism while applying rather crude one- or two-zone prescriptions to describe the exchange of angular momentum within the star. In this paper, we present the most detailed approach to date to describe the physics giving rise to the modulation period from kinetic and magnetic fluctuations. Assuming moderate levels of stellar parameter fluctuations, we find that the resulting binary period variations are one or two orders of magnitude lower than the observed values in RS-CVn like systems, supporting the conclusion of existing theoretical work that the Applegate mechanism may not suffice to produce the observed variations in these systems. The most promising Applegate candidates are low-mass post-common-envelope binaries with binary separations ≲1 R⊙ and secondary masses in the range of 0.30 M⊙ and 0.36 M⊙.

Photodynamical analysis of the triply eclipsing hierarchical triple system EPIC 249432662

Using Campaign 15 data from the K2 mission, we have discovered a triply-eclipsing triple star system: EPIC 249432662. The inner eclipsing binary system has a period of 8.23 days, with shallow $\sim$3% eclipses. During the entire 80-day campaign, there is also a single eclipse event of a third-body in the system that reaches a depth of nearly 50% and has a total duration of 1.7 days, longer than for any previously known third-body eclipse involving unevolved stars. The binary eclipses exhibit clear eclipse timing variations. A combination of photodynamical modeling of the lightcurve, as well as seven follow-up radial velocity measurements, has led to a prediction of the subsequent eclipses of the third star with a period of 188 days. A campaign of follow-up ground-based photometry was able to capture the subsequent pair of third-body events as well as two further 8-day eclipses. A combined photo-spectro-dynamical analysis then leads to the determination of many of the system parameters. The 8-day binary consists of a pair of M stars, while most of the system light is from a K star around which the pair of M stars orbits.

Applegate mechanism in post-common-envelope binaries: Investigating the role of rotation

Context. Eclipsing time variations are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the observed-minus-calculated (O–C) diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. Aims. In this work we explore the feasibility of driving eclipsing time variations via the Applegate mechanism for a sample of PCEB systems, including a range of different rotation rates. Methods. We used the MESA code to evolve 12 stars with different masses and rotation rates. We applied simple dynamo models to their radial profiles to investigate the scale at which the predicted activity cycle matches the observed modulation period, and quantifiy the uncertainty. We further calculated the required energies to drive the Applegate mechanism. Results. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems. In RX J2130.6+4710, it may be feasible as well considering the uncertainties. We note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star. Conclusions. The results suggest that the ratio of physical to critical rotation rate in the main sequence star is an important indicator for the feasibility of Applegate’s mechanism, but exploring larger samples will be necessary to probe this hypothesis.

The quest for stable circumbinary companions to post-common envelope sdB eclipsing binaries

Context. Period variations have been detected in a number of eclipsing close compact binary subdwarf B stars (sdBs) and these have often been interpreted as being caused by circumbinary massive planets or brown dwarfs. According to canonical binary models, the majority of sdB systems are produced from low mass stars with degenerate cores where helium is ignited in flashes. Various evolutionary scenarios have been proposed for these stars, but a definite mechanism remains to be established. Equally puzzling is the formation of these putative circumbinary objects which must have formed from the remaining post-common envelope circumbinary disk or survived its evolution.Aim. In this paper we review the eclipse time variations (ETVs) exhibited by seven such systems (EC 10246-2707, HS 0705+6700, HS 2231+2441, J08205+0008, NSVS 07826147, NSVS 14256825, and NY Vir) and explore whether there is conclusive evidence that the ETVs observed over the last two decades can reliably predict the presence of one or more circumbinary bodies.Methods. We report 246 new observations of the seven sdB systems made between 2013 September and 2017 July using a worldwide network of telescopes. We combined our new data with previously published measurements to analyse the ETVs of these systems.Results. Our data show that period variations cannot be modelled simply on the basis of circumbinary objects. This implies that more complex processes may be taking place in these systems. These difficulties are compounded by the secondary star not being spectroscopically visible. From ETVs, it has historically been suggested that five of the seven binary systems reported here had circumbinary objects. Based on our recent observations and analysis, only three systems remain serious contenders. We find agreement with other observers that at least a decade of observations is required to establish reliable ephemerides. With longer observational baselines it is quite conceivable that the data will support the circumbinary object hypothesis of these binary systems. Also, we generally agree with other observers that higher values of (O–C) residuals are found with secondary companions of spectral type M5/6 (or possibly earlier as a result of an Applegate type mechanism).

Orbital Period Variations in the NY Vir System, Revisited in the Light of New Data

Abstract NY Virginis is an eclipsing binary system with a subdwarf B primary and an M type dwarf secondary. Recent studies (Qian et al. 2012; Lee et al. 2014) suggested the presence of two circumbinary planets with a few Jovian masses within the system. Lee et al. (2014) examined the orbital stabilities of the suggested planets, using the best-fit parameters derived from their eclipse timing variation analysis. They found that the outer companion should be ejected from the system in about 800 000 years. An observational report from Pulley et al. (2016) pointed out that the recent mideclipse times of the binary deviate significantly from the models suggested by Lee et al. (2014). In fact, variations in the orbital period of the system had already been recognized by many authors, but the parameters of these variations vary significantly as new data accumulate. Here, we analyze the eclipse timing variations of the NY Vir system, using new mid-eclipse times that we have obtained together with earlier published measurements in order to understand the nature of the system and constrain its parameters.

The Effects of Barycentric and Asymmetric Transverse Velocities on Eclipse and Transit Times

Abstract It has long been recognized that the finite speed of light can affect the observed time of an event. For example, as a source moves radially toward or away from an observer, the path length and therefore the light travel time to the observer decreases or increases, causing the event to appear earlier or later than otherwise expected, respectively. This light travel time effect has been applied to transits and eclipses for a variety of purposes, including studies of eclipse timing variations and transit timing variations that reveal the presence of additional bodies in the system. Here we highlight another non-relativistic effect on eclipse or transit times arising from the finite speed of light—caused by an asymmetry in the transverse velocity of the two eclipsing objects, relative to the observer. This asymmetry can be due to a non-unity mass ratio or to the presence of external barycentric motion. Although usually constant, this barycentric and asymmetric transverse velocity (BATV) effect can vary between sequential eclipses if either the path length between the two objects or the barycentric transverse velocity varies in time. We discuss this BATV effect and estimate its magnitude for both time-dependent and time-independent cases. For the time-dependent cases, we consider binaries that experience a change in orbital inclination, eccentric systems with and without apsidal motion, and hierarchical triple systems. We also consider the time-independent case which, by affecting the primary and secondary eclipses differently, can influence the inferred system parameters, such as the orbital eccentricity.

KIC 6048106: an Algol-type eclipsing system with long-term magnetic activity and hybrid pulsations – I. Binary modelling

The A-F-type stars and pulsators (δ Scuti-γ Dor) are in a critical regime where they experience a transition from radiative to convective transport of energy in their envelopes. Such stars can pulsate in both gravity and acoustic modes. Hence, the knowledge of their fundamental parameters along with their observed pulsation characteristics can help in improving the stellar models. When residing in a binary system, these pulsators provide more accurate and less model-dependent stellar parameters than in the case of their single counterparts. We present a light-curve model for the eclipsing system KIC 6048106 based on the Kepler photometry and the code phoebe. We aim to obtain accurate physical parameters and tough constraints for the stellar modelling of this intermediate-mass hybrid pulsator. We performed a separate modelling of three light-curve segments which show a distinct behaviour due to a difference in activity. We also analysed the Kepler Eclipse Time Variations (ETVs). KIC 6048106 is an Algol-type binary with F5-K5 components, a near-circular orbit and a 1.56-d period undergoing variations of the order of |$\frac{\Delta P}{P}\simeq 3.60\times 10^{-7}$| in 287 ± 7 d. The primary component is a main-sequence star with M1 = 1.55 ± 0.11 M⊙, R1 = 1.57 ± 0.12 R⊙. The secondary is a much cooler subgiant with M2 = 0.33 ± 0.07 M⊙, R2 = 1.77 ± 0.16 R⊙. Many small near-polar spots are active on its surface. The second quadrature phase shows a brightness modulation on a time-scale 290 ± 7 d, in good agreement with the ETV modulation. This study reveals a stable binary configuration along with clear evidence of a long-term activity of the secondary star.

The Kepler Eclipsing Binary V2281 Cygni with Twin Stars

Abstract We present the physical properties of the eclipsing binary V2281 Cyg, which shows a light-time effect due to a supposed tertiary component from its eclipse timing variation according to the Kepler observations. The high-resolution spectra and BVR photometric data of the system were obtained at Bohyunsan Optical Astronomy Observatory and Mount Lemmon Optical Astronomy Observatory, respectively. To determine the fundamental parameters of the eclipsing pair and its circumbinary object, we simultaneously analyzed the radial velocities, light curves, and eclipse times including the Kepler data. The masses and radii for the primary and secondary stars were determined with accuracy levels of approximately 2% and 1%, respectively, as follows: and , and . If its orbit is coplanar with the eclipsing binary, the period and semimajor axis of the third body were calculated to be years and , respectively, and its mass is . The evolutionary state of the system was investigated by comparing the masses and radii with theoretical models. The results demonstrate that V2281 Cyg is a detached eclipsing binary, which consists of twin main-sequence stars with an age of 1.5 Gyr.

Radial Velocities of 41 Kepler Eclipsing Binaries

Abstract Eclipsing binaries are vital for directly determining stellar parameters without reliance on models or scaling relations. Spectroscopically derived parameters of detached and semi-detached binaries allow us to determine component masses that can inform theories of stellar and binary evolution. Here we present moderate resolution ground-based spectra of stars in close binary systems with and without (detected) tertiary companions observed by NASA’s Kepler mission and analyzed for eclipse timing variations. We obtain radial velocities and spectroscopic orbits for five single-lined and 35 double-lined systems, and confirm one false positive eclipsing binary. For the double-lined spectroscopic binaries, we also determine individual component masses and examine the mass ratio distribution, which is dominated by binaries with like-mass pairs and semi-detached classical Algol systems that have undergone mass transfer. Finally, we constrain the mass of the tertiary component for five double-lined binaries with previously detected companions.

A search for tight hierarchical triple systems amongst the eclipsing binaries in the CoRoT fields

We report a comprehensive search for hierarchical triple stellar system candidates amongst eclipsing binaries (EB) observed by the CoRoT spacecraft. We calculate and check eclipse timing variation (ETV) diagrams for almost 1500 EBs in an automated manner. We identify five relatively short-period Algol systems for which our combined light curve and complex ETV analyses (including both the light-travel time effect and short-term dynamical third-body perturbations) resulted in consistent third-body solutions. The computed periods of the outer bodies are between 82 and 272 days, (with an alternative solution of 831 days for one of the targets). We find that the inner and outer orbits are near coplanar in all but one case. The dynamical masses of the outer subsystems determined from the ETV analyses are consistent with both the results of our light curve analyses and the spectroscopic information available in the literature. One of our candidate systems exhibits outer eclipsing events as well, the locations of which are in good agreement with the ETV solution. We also report another certain triply eclipsing triple system which, however, is lacking a reliable ETV solution due to the very short time range of the data, and four new blended systems (composite light curves of 2 eclipsing binaries each), where we cannot decide whether the components are gravitationally binded or not. Amongst these blended systems we identify the longest period and highest eccentricity eclipsing binary in the entire CoRoT sample.

KIC 4150611: a rare multi-eclipsing quintuple with a hybrid pulsator

We present the results of our analysis of KIC 4150611 (HD 181469) - an interesting, bright quintuple system that includes a hybrid $\delta$ Sct/$\gamma$ Dor pulsator. Four periods of eclipses - 94.2, 8.65, 1.52 and 1.43 d - have been observed by the Kepler satellite, and three point sources (A, B, and C) are seen in high angular resolution images. From spectroscopic observations made with the HIDES spectrograph attached to the 1.88-m telescope of the Okayama Astrophysical Observatory (OAO), for the first time we calculated radial velocities (RVs) of the component B - a pair of G-type stars - and combined them with Kepler photometry in order to obtain absolute physical parameters of this pair. We also managed to directly measure RVs of the pulsator, also for the first time. Additionally, we modelled the light curves of the 1.52 and 1.43-day pairs, and measured their eclipse timing variations (ETVs). We also performed relative astrometry and photometry of three sources seen on the images taken with the NIRC2 camera of the Keck II telescope. Finally, we compared our results with theoretical isochrones. The brightest component Aa is the hybrid pulsator, transited every 94.2 days by a pair of K/M-type stars (Ab1+Ab2), which themselves form a 1.52-day eclipsing binary. The components Ba and Bb are late G-type stars, forming another eclipsing pair with a 8.65 day period. Their masses and radii are $M_{Ba}=0.894\pm0.010$ M$_\odot$, $R_{Ba}=0.802\pm0.044$ R$_\odot$ for the primary, and $M_{Bb}=0.888\pm0.010$ M$_\odot$, $R_{Bb}=0.856\pm0.038$ R$_\odot$ for the secondary. The remaining period of 1.43 days is possibly related to a faint third star C, which itself is most likely a background object. The system's properties are well-represented by a 35 Myr isochrone. There are also hints of additional bodies in the system.

Evidence for a planetary mass third body orbiting the binary star KIC 5095269

In this paper, we report the evidence for a planetary mass body orbiting the close binary star KIC 5095269. This detection arose from a search for eclipse timing variations among the more than 2,000 eclipsing binaries observed by Kepler. Light curve and periodic eclipse time variations have been analysed using Systemic and a custom Binary Eclipse Timings code based on the Transit Analysis Package which indicates a $7.70\pm0.08M_{Jup}$ object orbiting every $237.7\pm0.1d$ around a $1.2M_\odot$ primary and $0.51M_\odot$ secondary in an 18.6d orbit. A dynamical integration over $10^7$ years suggests a stable orbital configuration. Radial velocity observations are recommended to confirm the properties of the binary star components and the planetary mass of the companion.

TEE, an estimator for the precision of eclipse and transit minimum times

Context: Transit or eclipse timing variations have proven to be a valuable tool in exoplanet research. However, no simple way to estimate the potential precision of such timing measures has been presented yet, nor are guidelines available regarding the relation between timing errors and sampling rate. Aims: A `timing error estimator' (TEE) equation is presented that requires only basic transit parameters as input. With the TEE, it is straightforward to estimate timing precisions both for actual data as well as for future instruments, such as the TESS and PLATO space missions. Methods: A derivation of the timing error based on a trapezoidal transit shape is given. We also verify the TEE on realistically modeled transits using Monte Carlo simulations and determine its validity range, exploring in particular the interplay between ingress/egress times and sampling rates. Results: The simulations show that the TEE gives timing errors very close to the correct value, as long as the temporal sampling is faster than transit ingress/egress durations and transits with very low S/N are avoided. Conclusions: The TEE is a useful tool to estimate eclipse or transit timing errors in actual and future data-sets. In combination with an equation to estimate period errors (Deeg 2015), predictions for the ephemeris precision of long-coverage observations are possible as well. The tests for the TEE's validity-range led also to implications for instrumental design: Temporal sampling has to be faster than transit in- or egress durations, or a loss in timing-precision will occur. An application to the TESS mission shows that transits close to its detection limit will have timing uncertainties that exceed 1 hour within a few months after their acquisition. Prompt follow-up observations will be needed to avoid a `loosing' of their ephemeris.

HIDES spectroscopy of bright detached eclipsing binaries from the Kepler field – II. Double- and triple-lined objects

We present the results of our spectroscopic observations of eight detached eclipsing binaries (DEBs), selected from the $Kepler$ Eclipsing Binary Catalog. Radial velocities (RVs) were calculated from high resolution spectra obtained with the HIDES pectrograph, attached to the 1.88-m telescope of the Okayama Astrophysical Observatory, and were used to characterize the targets in combination with the $Kepler$ light curves. For each binary we obtained a full set of orbital and physical parameters, reaching precision below 3% in masses and radii for 5 pairs. By comparing our results with theoretical models, we assess the distance, age and evolutionary status of the researched objects. We also study eclipse timing variations of selected objects, and identify a new system with a $\gamma$Dor pulsator. Two systems are triples, and show lines coming from three components. In one case the motion of the outer star and the perturbation in the RVs of the inner binary are clearly visible and periodical, which allows us to directly calculate the mass of the third star, and inclination of the outer orbit. In the second case we only see a clear motion of the tertiary, and investigate two scenarios: that it is a linear trend coming from the orbital motion around the inner binary, and that it is caused by a planetary mass companion. When possible, we also compare our results with the literature, and conclude that only by combining photometry with RVs it is possible to obtain correct physical parameters of both components of a DEB.

KIC 11401845: An Eclipsing Binary with Multiperiodic Pulsations and Light-travel Time

Abstract We report the photometry of KIC 11401845 displaying multiperiodic pulsations, superimposed on binary effects. Light-curve synthesis shows that the binary star is a short-period detached system with a very low mass ratio of q = 0.070 and filling factors of F 1 = 45% and F 2 = 99%. Multiple-frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the observed data. We detected 23 frequencies with signal-to-noise ratios larger than 4.0, of which the orbital harmonics (f 4, f 6, f 9, f 15) in the low-frequency domain may originate from tidally excited modes. For the high frequencies of 13.7–23.8 day−1, the period ratios and pulsation constants are in the ranges of and Q = 0.018–0.031 days, respectively. These values and the position on the Hertzsprung–Russell diagram demonstrate that the primary component is a δ Sct pulsating star. We examined the eclipse timing variation of KIC 11401845 from the pulsation-subtracted data and found a delay of 56 ± 17 s in the arrival times of the secondary eclipses relative to the primary eclipses. A possible explanation of the time shift may be some combination of a light-travel-time delay of about 34 s and a very small eccentricity of . This result represents the first measurement of the Rømer delay in noncompact binaries.

How eclipse time variations, eclipse duration variations, and radial velocities can reveal S-type planets in close eclipsing binaries

While about a dozen transiting planets have been found in wide orbits around an inner, close stellar binary (so-called "P-type planets"), no planet has yet been detected orbiting only one star (a so-called "S-type planet") in an eclipsing binary. This is despite a large number of eclipsing binary systems discovered with the Kepler telescope. Here we propose a new detection method for these S-type planets, which uses a correlation between the stellar radial velocities (RVs), eclipse timing variations (ETVs), and eclipse duration variations (EDVs). We test the capability of this technique by simulating a realistic benchmark system and demonstrate its detectability with existing high-accuracy RV and photometry instruments. We illustrate that, with a small number of RV observations, the RV-ETV diagrams allows us to distinguish between prograde and retrograde planetary orbits and also the planetary mass can be estimated if the stellar cross-correlation functions can be disentangled. We also identify a new (though minimal) contribution of S-type planets to the Rossiter-McLaughlin effect in eclipsing stellar binaries. We finally explore possible detection of exomoons around transiting luminous giant planets and find that the precision required to detect moons in the RV curves of their host planets is of the order of ${\rm cm\,s}^{-1}$ and therefore not accessible with current instruments.