Observational Detection of Higher Order Secular Perturbations in Tight Hierarchical Triple Stars

In this work, we search for observational evidence of higher-order secular perturbations in three eclipsing binaries. These are slightly eccentric binaries, and they form the inner pairs of tight, compact, hierarchical triple star systems. We analyze simultaneously the high precision satellite ($Kepler$ and $TESS$) light curves, eclipse timing variations, combined spectral energy distributions (through catalog passband magnitudes) and, where available, radial velocities of KICs 9714358, 5771589 and TIC 219885468. Besides the determination of robust astrophysical and dynamical properties of the three systems, we find evidence that the observed unusual eclipse timing variations of KIC 9714358 are a direct consequence of the octupole-order secular eccentricity perturbations forced by an unusual, resonant behaviour between the lines of the apsides of the inner and outer orbital ellipses. We also show that, despite its evident cyclic eclipse depth variations, KIC~5771589 is an almost perfectly coplanar system (to within $0.3^\circ$), and we explain the rapid eclipse depth variations with the grazing nature of the eclipses. Finally, we find that the inner pair of TIC~219885468 consists of two twin stars and, hence, in this triple there are no octupole order three-body perturbations. Moreover, we show that this triple is also coplanar on the same level as the former one, but due to its deep eclipses, it does not exhibit eclipse depth variations. We intend to follow this work up with further analyses and a quantitative comparison of the theoretical and the observed perturbations.Comment: Accepted for publication in the journal Universe, special issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets, 33 page

Transit timing variations in eccentric hierarchical triple exoplanetary systems. I. Perturbations on the time-scale of the orbital period of the perturber

We study the long-term time-scale (i.e. period comaprable to the orbital period of the outer perturber object) transit timing variations in transiting exoplanetary systems which contain a further, more distant (a_2>>a_1) either planetary, or stellar companion. We give an analytical form of the O-C diagram (which describes such TTV-s) in trigonometric series, valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. We show that the dependence of the O-C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the real physical parameters (i.e. masses, separations, periods) of a concrete system, and depend only on dimensionless orbital elements, and so, can be analyzed in general. We analyze these dimensionless amplitudes for different arbitrary initial parameters, as well as for two particular systems CoRoT-9b and HD 80606b. We find in general, that while the shape of the O-C strongly varies with the angular orbital elements, the net amplitude (departing from some specific configurations) depends only weakly on these elements, but strongly on the eccentricities. As an application, we illustrate how the formulae work for the weakly eccentric CoRoT-9b, and the highly eccentric HD 80606b. We consider also the question of detection, as well as the correct identification of such perturbations. Finally, we illustrate the operation and effectiveness of Kozai cycles with tidal friction (KCTF) in the case of HD 80606b.Comment: Submitted to Astronomy and Astrophysics; Revised versio

EPIC 219217635: A Doubly Eclipsing Quadruple System Containing an Evolved Binary

We have discovered a doubly eclipsing, bound, quadruple star system in the field of K2 Campaign 7. EPIC 219217635 is a stellar image with Kp = 12.7 that contains an eclipsing binary (`EB') with PA = 3.59470 d and a second EB with PB = 0.61825 d. We have obtained followup radial-velocity (`RV') spectroscopy observations, adaptive optics imaging, as well as ground-based photometric observations. From our analysis of all the observations, we derive good estimates for a number of the system parameters. We conclude that (1) both binaries are bound in a quadruple star system; (2) a linear trend to the RV curve of binary A is found over a 2-year interval, corresponding to an acceleration, \dot{γ }= 0.0024 ± 0.0007 cm s-2; (3) small irregular variations are seen in the eclipse- timing variations (`ETVs') detected over the same interval; (4) the orbital separation of the quadruple system is probably in the range of 8-25 AU; and (5) the orbital planes of the two binaries must be inclined with respect to each other by at least 25°. In addition, we find that binary B is evolved, and the cooler and currently less massive star has transferred much of its envelope to the currently more massive star. We have also demonstrated that the system is sufficiently bright that the eclipses can be followed using small ground-based telescopes, and that this system may be profitably studied over the next decade when the outer orbit of the quadruple is expected to manifest itself in the ETV and/or RV curves

Four New Compact Triply Eclipsing Triples found with Gaia and TESS

This paper presents a comprehensive analysis of four triply eclipsing triple star systems, namely TIC 88206187, TIC 14839347, TIC 298714297, and TIC 66893949. The four systems with third-body eclipses were found in the TESS lightcurves from among a sample of ~400 matches between known eclipsing binaries and the Gaia DR3 Non-Single Star (NSS; Gaia Collaboration 2022; Pourbaix et al. 2022) solution database. We combined photometric lightcurves, eclipse timing variations, archival spectral energy distributions, and theoretical evolution tracks in a robust photodynamical analysis to determine the orbital and system parameters. The triples have outer periods of 52.9, 85.5, 117, and 471 days, respectively. All dozen stars have masses $\lesssim$ 2.6 M$_\odot$. The systems are quite flat with mutual inclination angles between the inner and outer orbital planes that are all $\lesssim 4^\circ$. The outer mass ratios range from 0.39--0.76, consistent with our earlier collection of compact triply eclipsing triples. TIC 88206187 exhibits a fractional radius of the outer tertiary component $(r_B \equiv R_B/a_{\rm out})$ exceeding 0.1 (only the third such system known), and we consider its future evolution. Finally, we compare our photodynamical analysis results and the orbital parameters given in the Gaia DR3 NSS solutions, indicating decent agreement, but with the photodynamical results being more accurate.Comment: 16 pages, 8 figures. Accepted for publication in MNRA

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

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

Surface activity of the G dwarf primary in the quaternary star system V815 Her

We investigate the magnetic activity of the G dwarf primary star in the multiple system V815 Herculis. Recently, TESS Sector 26 data have revealed that V815 Her is in fact a four-star system consisting of two close binaries in a long-period orbit. We give preliminary orbital solution for the long-known but unseen "third body" V815 Her `B', which is itself a close eclipsing binary of two M dwarfs. Long-term spot activity of the G dwarf is presented along with the very first Doppler image reconstructions of its spotted surface.Comment: 3 pages, poster paper presented at the 21th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (Toulouse, France) in 202

A comprehensive study of the Kepler triples via eclipse timing

We produce and analyse eclipse time variation (ETV) curves for some 2600 Kepler binaries. We find good to excellent evidence for a third body in 222 systems via either the light-travel-time (LTTE) or dynamical effect delays. Approximately half of these systems have been discussed in previous work, while the rest are newly reported here. Via detailed analysis of the ETV curves using high-level analytic approximations, we are able to extract system masses and information about the three-dimensional characteristics of the triple for 62 systems which exhibit both LTTE and dynamical delays; for the remaining 160 systems, we give improved LTTE solutions. New techniques of pre-processing the flux time series are applied to eliminate false positive triples and to enhance the ETV curves. The set of triples with outer orbital periods shorter than ˜2000 d is now sufficiently numerous for meaningful statistical analysis. We find that (i) there is a peak near im ≃ 40° in the distribution of the triple versus inner binary mutual inclination angles that provides strong confirmation of the operation of Kozai-Lidov cycles with tidal friction; (ii) the median eccentricity of the third-body orbits is e2 = 0.35; (iii) there is a deficit of triple systems with binary periods ≲1 d and outer periods between ˜50 and 200 d which might help guide the refinement of theories of the formation and evolution of close binaries; and (iv) the substantial fraction of Kepler binaries which have third-body companions is consistent with a very large fraction of all binaries being part of triples

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