Photodynamical Modeling of the Fascinating Eclipses in the Triple-star System KOI-126

We explore the fascinating eclipses and dynamics of the compact hierarchical triple-star system KOI-126 (KIC 5897826). This system is composed of a pair of M-dwarf stars (KOI-126 B and C) in a 1.74 day orbit that revolve around an F star (KOI-126 A) every 34 days. Complex eclipse shapes are created as the M stars transit the F star, due to two effects: (1) the duration of the eclipse is a significant fraction of the M-star orbital period, so the prograde or retrograde motion of the M stars in their orbit lead to unusually short or long duration eclipses; (2) due to 3-body dynamics, the M-star orbit precesses with an astonishingly quick timescale of 1.74 yr for the periastron (apsidal) precession, and 2.73 yr for the inclination and nodal angle precession. Using the full Kepler data set, supplemented with ground-based photometry, plus 29 radial velocity measurements that span 6 yr, our photodynamical modeling yields masses of M A = 1.2713 ± 0.0047 M ⊙ (0.37%), M B = 0.23529 ± 0.00062 M ⊙ (0.26%), and M C = 0.20739 ± 0.00055 M ⊙ (0.27%) and radii of R A = 1.9984 ± 0.0027 R ⊙ (0.14%), R B = 0.25504 ± 0.00076 R ⊙ (0.3%), and R C = 0.23196 ± 0.00069 R ⊙ (0.3%). We also estimate the apsidal motion constant of the M dwarfs, a parameter that characterizes the internal mass distribution. Although it is not particularly precise, we measure a mean apsidal motion constant, k 2 ¯ , of 0.046 − 0.028 + 0.046 , which is approximately 2σ lower than the theoretical model prediction of 0.150. We explore possible causes for this discrepancy.

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

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.

THE FIRST DETAILED ANALYSIS ON THE ASTROPHYSICAL PROPERTIES OF THE ECCENTRIC BINARY V990 HER

We present accurate physical parameters of the eccentric binary system V990 Her which has an orbital period of P=8.193315±0.000003 days using its photometric and spectroscopic data. The physical parameters of the components were derived as Teff1=8000±200 K, Teff2=7570±200 K, M1=2.01±0.07 Mʘ, M2=1.83±0.03 Mʘ, R1=2.22±0.02 Rʘ, R2=2.12±0.01 Rʘ, log(L1/Lʘ)=1.25±0.04, log(L2/Lʘ)=1.12±0.05. Our findings revealed that both components are slightly evolved from the zero-age main sequence with an age of 6.3×108 years. We estimated an apsidal motion with a period of U=14683±2936 years in the system and the internal structure constants of the components were derived for the first time.

BU CMi as a Quadruple Doubly Eclipsing System

We found that the known spectroscopic binary and variable BU CMi = HD65241 ($$V = 6.4{-} {{6.7}^{{\text{m}}}}$$, A0 V) is a quadruple doubly eclipsing 2+2 system. Both eclipsing binaries are detached systems moving in an eccentric orbits: pair “A” with the period $${{P}_{{\text{A}}}} = {{2}^{{\text{d}}}}.94$$ ($$e = 0.20$$) and pair “B” with the period $${{P}_{{\text{B}}}} = {{3}^{{\text{d}}}}.26$$ ($$e = 0.22$$). All four components have nearly equal sizes, temperatures and masses in the range $$M = 3.1{-} 3.4\,{{M}_{ \odot }}$$, and A0 spectra. We found the mutual orbit of both pairs around the system barycenter with a period of 6.6 years and eccentricity $$e$$ = 0.7. We detected in pairs “A” and “B” the fast apsidal motion with the periods $${{U}_{{\text{A}}}} = 25.4$$ years and UB = 26.3 years, respectively. The orbit of each pair shows small nutation like oscillations in periastron longitude. The system is young and it seems that its components does not yet reached the Zero Age Main Sequence (ZAMS). The photometric parallax calculated from the found parameters coincides perfectly with the GAIA DR2 $$\pi =0.00407'' \pm 0.00006'' $$.

Apsidal motion in the massive binary HD 152248

Context. Apsidal motion in massive eccentric binaries offers precious information about the internal structure of the stars. This is especially true for twin binaries consisting of two nearly identical stars. Aims. We make use of the tidally induced apsidal motion in the twin binary HD 152248 to infer constraints on the internal structure of the O7.5 III-II stars composing this system. Methods. We build stellar evolution models with the code Clés assuming different prescriptions for the internal mixing occurring inside the stars. We identify the models that best reproduce the observationally determined present-day properties of the components of HD 152248, as well as their internal structure constants, and the apsidal motion rate of the system. We analyse the impact on the results of some poorly constrained input parameters in the models, including overshooting, turbulent diffusion, and metallicity. We further build “single” and “binary” GENEC models that account for stellar rotation to investigate the impacts of binarity and rotation. We discuss some effects that could bias our interpretation of the apsidal motion in terms of the internal structure constant. Results. The analysis of the Clés models reveals that reproducing the observed k2 value and rate of apsidal motion simultaneously with the other stellar parameters requires a significant amount of internal mixing (either turbulent diffusion, overshooting, or rotational mixing) or enhanced mass-loss. The results obtained with the GENEC models suggest that a single-star evolution model is sufficient to describe the physics inside this binary system. We suggest that, qualitatively, the high turbulent diffusion required to reproduce the observations could be partly attributed to stellar rotation. We show that higher-order terms in the apsidal motion are negligible. Only a very severe misalignment of the rotation axes with respect to the normal to the orbital plane could significantly impact the rate of apsidal motion, but such a high misalignment is highly unlikely in such a binary system. Conclusions. We infer an age estimate of 5.15 ± 0.13 Myr for the binary system and initial masses of 32.8 ± 0.6 M⊙ for both stars.

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.

First apsidal motion and light curve analysis of 162 eccentric eclipsing binaries from LMC

We present an extensive study of 162 early-type binary systems located in the LMC galaxy that show apsidal motion and have never been studied before. For the ample systems, we performed light curve and apsidal motion modelling for the first time. These systems have a median orbital period of 2.2 days and typical periods of the apsidal motion were derived to be of the order of decades. We identified two record-breaking systems. The first, OGLE LMC-ECL-22613, shows the shortest known apsidal motion period among systems with main sequence components (6.6 years); it contains a third component with an orbital period of 23 years. The second, OGLE LMC-ECL-17226, is an eccentric system with the shortest known orbital period (0.9879 days) and with quite fast apsidal motion period (11 years). Among the studied systems, 36 new triple-star candidates were identified based on the additional period variations. This represents more than 20% of all studied systems, which is in agreement with the statistics of multiples in our Galaxy. However, the fraction should only be considered as a lower limit of these early-type stars in the LMC because of our method of detection, data coverage, and limited precision of individual times of eclipses.

TESS photometry of the eclipsing δ Scuti star AI Hydrae

AI Hya has been known as an eclipsing binary with a monoperiodic $\delta$ Sct pulsator. We present the results from its TESS (Transiting Exoplanet Survey Satellite) photometry observed during Sector 7. Including our five minimum epochs, the eclipse timing diagram displays the apsidal motion with a rate of $\dot{\omega } = 0.075 \pm 0.031\:$deg$\:$yr$^{-1}$, which corresponds to an apsidal period of $U = 4800\pm 2000\:$yr. The binary star model represents that the smaller, less massive primary component is $427\:$K hotter than the pulsating secondary, and our distance of $612\pm 36\:$pc is in good agreement with the Gaia distance of $644\pm 26\:$pc. We subtracted the binary effects from the observed TESS data and applied a multifrequency analysis to these residuals. The result reveals that AI Hya is multiperiodic in its pulsation. Of 14 signals detected, four ($f_1$, $f_2$, $f_3$, $f_6$) may be considered independent pulsation frequencies. The period ratios of $P_{\rm pul}/P_{\rm orb} = 0.012$–0.021 and the pulsation constants of $Q = 0.30$–0.52 d correspond to $\delta$ Sct pulsations in binaries. We found that the secondary component of AI Hya pulsates in both radial fundamental $F$ modes ($f_2$ and $f_3$) and non-radial $g_1$ modes with a low degree of $\ell = 2$ ($f_1$ and $f_6$).