Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Then and now: A new look at the eclipse timing variations of hierarchical triple star candidates in the primordial $Kepler$-field, revisited by TESS

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read By extending eclipse-timing curves from Kepler's four years to a 15-year baseline with TESS and ground-based data, this paper establishes 243 hierarchical triple star candidates among Kepler eclipsing binaries, confirming or improving 193…

desk verdict The extended Kepler-TESS ETV baseline delivers a genuinely useful catalog—50 new, longer-period triple candidates and 193 confirmations—but the 243-candidate headline overstates what the uncertain tail and the quadrupole-only model can support. read the letter →

arxiv 2502.09480 v1 pith:DPROQXSJ submitted 2025-02-13 astro-ph.SR

T. Borkovits , S. A. Rappaport , T. Mitnyan , I. B. Bíró , I. Csányi , E. Forgács-Dajka , A. Forró , T. Hajdu
show 4 more authors
B. Seli J. Sztakovics A. Göblyös A. Pál
This is my paper · ORCID
classification astro-ph.SR
keywords eclipsetimingvariationshierarchicaltriplestarseclipsingbinariesKeplermissionTESSlight-travel-timeeffectdynamicalperturbationsstellarmultiplicity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that 243 of the Kepler mission's eclipsing binaries, roughly 9% of the sample, are hierarchical triple star candidates with a third star orbiting the eclipsing pair. The claim is built by extending the eclipse timing variation (ETV) curves from the four-year Kepler baseline to roughly fifteen years, using TESS observations and targeted ground-based eclipse timings. Of the 221 candidates from the authors' earlier study, 193 now have confirmed or improved third-body solutions, while 28 do not, largely because their eclipses have disappeared or are too faint for TESS. The extended baseline also reveals 50 new candidates, most with outer periods longer than the old four-year window could certify. If correct, this more than doubles the number of well-characterized compact triple systems and pushes the detectable outer periods out to several thousand days.

What carries the argument

The load-bearing tool is the analytic ETV model of Eq. (1): a polynomial ephemeris plus three physical terms — the light-travel-time effect (LTTE, a Rømer delay from the binary's revolution about the triple's center of mass), $P_2$-timescale dynamical perturbations from the third body's gravity, and apsidal motion of an eccentric inner binary. For the tightest systems, the code adds the quadrupole-order secular perturbation equations for the orbital elements, and when the 15-year data reveal departures from that approximation, the paper absorbs them with fictitious quadratic or cubic polynomial terms or an extra long-period LTTE-like term. To handle the noisier TESS data, the authors fold and average 5–20 consecutive eclipses into 'normal' minima. The classification into secure, moderately secure, and uncertain follows how many outer periods the data cover and whether TESS points confirm the Kepler-only solution.

What would settle it

A decisive check would be to take the 50 newly identified long-period candidates and the 73 uncertain LTTE systems, measure their radial velocities over a few years, and ask whether the predicted tertiary reflex motion appears with the announced periods and minimum masses. A null result for most of them would falsify the claim that the ETV arcs are third-body signals. Alternatively, a synthetic-recovery test, fitting the same code to simulated ETVs with known $P_2$, $m_C$, and mutual inclination, would settle whether the added quadratic or cubic polynomials systematically distort the recovered parameters on the extended baseline.

Watch

Extended reading notes

Core claim

The central discovery is that the ETV method, when given a baseline three to four times longer than the original Kepler data, turns many tentative or uncertain third-body interpretations into secure ones. The paper reports 63 certain pure light-travel-time (LTTE) systems, 45 moderately certain, and 73 uncertain, plus 37 certain, 7 moderately certain, and 18 uncertain systems in which gravitational (dynamical) perturbations of the third body matter. For the dynamically active systems, the fits yield the mass ratio $m_C/m_{AB}$, the tertiary mass, and the mutual inclination; the paper finds that most such systems are near-coplanar ($\sin i_{\rm mut} < 0.22$ for 44 of 62) but that about nine have mutual inclinations large enough to drive von Zeipel-Lidov-Kozai cycles. The paper also reports outer eccentricities spanning 0 to ~0.9 with median 0.33, an outer-period distribution roughly flat in log space from ~300 to ~5000 days, and 12 systems whose ETVs show a second periodicity consistent with a (2+1)+1 quadruple.

Load-bearing premise

The weakest link is the modeling assumption, stated in Sect. 2.3, that only quadrupole-order analytic perturbation theory is needed, with any leftover 15-year drifts absorbed by fictitious polynomial or extra LTTE terms; if those extra terms soak up part of the real third-body signal, the derived outer periods, masses, and mutual inclinations for the tight LTTE+DE systems would be systematically biased.

Editorial extensions

If this is right

  • The 152 secure-plus-moderately-secure systems give a well-characterized sample of compact triples spanning outer periods from ~45 to ~5000 days, roughly twice the longest periods that four years of Kepler data alone could certify.
  • Because 24 former moderately certain and 7 former uncertain LTTE candidates were upgraded to secure, the paper directly demonstrates that a dataset shorter than the outer period systematically underestimates confidence in third-body solutions.
  • For the 62 LTTE+DE systems, the fits imply that most third-body orbits are nearly coplanar with the inner binary (44 of 62 have $\sin i_{\rm mut} < 0.22$), while about nine are inclined enough to permit von Zeipel-Lidov-Kozai oscillations.
  • The roughly flat log distribution of outer periods from ~300 to ~5000 days, extrapolated to wider separations under a log-flat assumption, suggests that up to about 25% of all binaries may have third companions, not just the ~9% found here.
  • Twelve systems show a second periodicity in their ETVs consistent with a (2+1)+1 quadruple architecture, although the paper treats most of these as mathematical descriptions pending further data.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the secure solutions hold up, the ~9% detection rate among Kepler EBs is a lower bound for compact triples, because systems with very short outer periods or very low ETV amplitudes are hard to detect; a complete census would require combining ETVs with third-body eclipses and radial-velocity surveys.
  • The 12 'four-body' solutions are probably a mix of real outer companions and artifacts of the quadrupole approximation; separating them with higher-order secular theory or long-baseline photometry could turn some fictitious fourth bodies into genuine quadruple systems.
  • Applying the same normal-minima averaging to the full TESS archive, not just the Kepler field, could extend this census to many more eclipsing binaries and test whether the log-flat outer-period distribution is universal.
  • The nine systems whose eclipses vanished between Kepler and TESS provide a clean, independent confirmation of third-body-driven precession, and the same technique could identify new precessing triples in TESS data by their eclipse-depth variations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. Borkovits et al. reanalyze the eclipse timing variation (ETV) curves of 221 previously catalogued Kepler triple-star candidates together with many other Kepler eclipsing binaries, extending the timeline from the ~1470-day Kepler prime mission to ~5500 days using TESS cycles 2-6 eclipse times (from both full-frame and 2-minute-cadence photometry) and targeted ground-based follow-up. The ETVs are fitted with the analytic LTTE plus quadrupole-order dynamical plus apsidal-motion framework of Borkovits et al. (2016), augmented where needed by quadratic/cubic polynomials or extra LTTE terms. The authors report 243 hierarchical triple candidates: 63 certain, 45 moderately certain, and 73 uncertain pure-LTTE solutions, plus 37 certain, 7 moderately certain, and 18 uncertain LTTE+dynamical solutions. They confirm or improve solutions for 193 of the 221 former candidates, cannot recover solutions for 28 (nine because the eclipses have disappeared, sixteen because of sensitivity limits, three because the new data refute the old solutions), and identify 50 new, generally longer-period candidates. The paper includes per-system notes, statistical distributions of outer periods, eccentricities, masses, and mutual inclinations, and plots of all 243 ETV curves with their fits. The authors explicitly acknowledge that the quadrupole-order secular model is inadequate for the tightest systems and that the added polynomial and extra-LTTE terms are mathematical, rather than physical, descriptions.

Significance. If the catalog is accepted, it will become a standard reference for compact hierarchical triples in the Kepler field, and its statistical distributions (P2, e2, q2, imut, apse-nodal timescales) will be widely used. The paper has real strengths: a threefold longer homogeneous baseline; extensive tables (A.2-A.8) and per-system discussion (App. B); an explicit three-tier confidence classification that reserves an 'uncertain' category for 91 systems; agreement with published photodynamical solutions for several robust systems (e.g., KIC 5653126, 5731312, 5952403); and honest reporting of the three systems whose former solutions are refuted by the new data. The 50 newly identified longer-period candidates and the upgrade of 31 former group II/III systems to robust classifications are concrete empirical advances enabled by TESS. The principal risk is not the existence of the third bodies but the quantitative parameters of the LTTE+dynamical solutions: the quadrupole-order-only model, acknowledged in Sect. 2.3, can bias P2, mC, and imut for the tightest systems, so the derived masses and mutual-inclination statistics must be used with the caveats detailed below.

major comments (3)
  1. [Sect. 2.3-2.4, 4.3; Table A.5] The paper states (Sect. 2.3) that the dynamical model applies 'only the lowest, quadrupole-order analytic approximation' and that on the extended ~5500-day baseline 'some substantial departures may and do occur,' which are then 'nicely modeled, at least mathematically' by fictitious quadratic/cubic polynomials or extra LTTE-like terms (Sect. 2.4). This is not purely cosmetic: for systems classified as 'certain' in Table A.5 the paper admits the inadequacy is directly visible. Sect. 4.3 states that KIC 6545018 (P2 = 90.6 d) and 9714358 (P2 = 103.8 d) 'clearly reveal the inadequacy of the applied quadratic order approximations,' and that for KIC 5255552 and 8143170 the added polynomials likely arise from unmodeled octupole or quadrupole-squared perturbations. For KIC 5255552 the fitted cubic coefficient (Table A.5, note a) contributes roughly 0.5 d at the end of the baseline, comparable to the third-body dynamical amplitude itself (A_dyn/A_LTTE = 35). Because the polynomial terms are fitted simultaneously with the LTTE+DE parameters, there is no demonstrated orthogonality between them, so the quoted formal errors understate the true uncertainty in P2, mC, and imut for these systems (e.g., mC = 1.34 ± 0.07 Msun and imut = 3 deg for KIC 5255552). The existence of these third bodies is not in question (KIC 5255552 is triply eclipsing), but the quantitative parameters and the 'certain' classification are not supported for the model-inadequate subset. The authors should provide a systematic-uncertainty estimate (e.g., refits with and without the extra polynomial terms, or with the planned higher-order secular terms), or explicitly reclassify the affected parameters as model-dependent, with the caveat stated in the tables themselves.
  2. [Fig. 10; Table A.3; Sect. 4.2 and 5] The caption of Fig. 10 advises that 'it is wise to require at least two outer orbital cycles before accepting the presence of another body as at least somewhat conclusive.' That standard is not met by a substantial fraction of the 'moderately certain' pure-LTTE solutions in Table A.3: over a ~5500-day dataset, systems with P2 ≳ 2800 d span fewer than two cycles, including KIC 2305372 (P2 = 4859 d), 8081389 (4249 d), 8758161 (4277 d), 6187893 (3901 d), 4758368 (3769 d), 7680593 (3597 d), and 9181877 (3652 d). The stated classification rule for this group ('periods generally longer than one-third of the entire data train, but shorter than the duration of the dataset') explicitly admits such systems, so the category is internally consistent; however, it conflicts with the decisive-acceptance criterion stated in Fig. 10. If 'moderately certain' is meant to imply 'somewhat conclusive,' the placement of these sub-two-cycle systems, and the aggregate count of 152 robust plus moderately secure systems quoted in Sect. 4.5 and Sect. 5, need to be reconciled with that criterion, either by stating an exception (e.g., independent supporting evidence for individual systems) or by reclassification.
  3. [Sect. 2.2] The activation of the dynamical terms depends on the heuristic threshold Adyn/ALTTE ≈ 0.3, computed with an assumed inner-binary total mass of mAB = 2.0 Msun (or an empirical mass-period relation for W UMa stars) and, for the coplanar estimate, an adopted outer eccentricity. Because the assumed mass enters both the threshold decision and the derived minimum masses, systems whose true mAB differs substantially from the assumed value can be fitted with an incomplete model (pure LTTE when a DE component is in fact non-negligible), biasing P2 and the LTTE amplitude even for nominally pure-LTTE solutions. A sensitivity test that varies the assumed mAB over the plausible 1.5-3.5 Msun range and reports how many systems change solution type, or how much fitted parameters shift, would make the catalog's parameter tables more robust; the present text notes the assumption but does not quantify its effect on the threshold decision.
minor comments (5)
  1. [Sect. 5] The extrapolation that 'up to 25% [of Kepler binaries] are triples' assumes a logarithmically flat outer-period distribution over 4.8 decades based on a sample spanning only 1.7 decades; this should be labeled explicitly as a speculative estimate whose main uncertainty is the assumed period distribution.
  2. [Table A.4] Several tabulated formal uncertainties are uninformative as printed (e.g., KIC 10208759, P2 = 11097 ± 26774 d; KIC 10916675, P2 = 9848 ± 2754 d); these entries should be marked as effectively unconstrained rather than quoted with formal errors that formally allow negative periods.
  3. [Sect. 3] The bin sizes used to form the 'normal' minima (5-20 consecutive cycles) are described only qualitatively; since the bin size sets the time resolution and effective noise of the TESS ETV points, the paper should state the bin size per system, at least as a column in a machine-readable table.
  4. [Fig. 10] The three dashed curves that 'go off the scale' are important diagnostics for the model-inadequacy systems discussed in Sect. 4.3; identifying these systems (e.g., in the caption or a zoomed inset) would let the reader connect the figure directly to the quadrupole-order limitation.
  5. [Table A.2; Sect. 4.4] The caption of Table A.2 states that mAB values marked with ':' are 'our own reasonable estimations,' but the basis of these estimates is not given; a brief explanation or a reference to the relevant Appendix B entry would aid reproducibility. Likewise, for the 12 systems with 'four-body' solutions, the paper should provide a machine-readable flag distinguishing the cases considered physically plausible (e.g., KIC 7289157) from those treated as purely mathematical descriptions (e.g., KIC 2715417).

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the 243-candidate catalog is an empirical fit to independent Kepler/TESS eclipse times, and the model limitations the paper itself discloses are correctness risks rather than circular inputs.

full rationale

The central claim, identification of 243 hierarchical triple candidates, is obtained by fitting an analytic ETV model (Eq. 1, with LTTE in Eq. 2 and dynamical/apsidal terms) to measured Kepler and TESS mid-eclipse times; the third-body parameters P2, e2, omega2, and f(mC) are free fit parameters, not quantities defined in terms of the final candidate list. The analytic machinery is cited to Borkovits et al. (2015, 2016), but that is a parameter-free perturbation derivation with stated assumptions, and the paper notes it has been checked by numerical integrations and against independent photodynamical solutions, so the citation is real evidence rather than a circular premise. The genuinely vulnerable passages are the limitations the paper itself flags: Sect. 2.3 states that the code 'applies only the lowest, quadrupole-order analytic approximation' for secular perturbations, and Sect. 2.4 admits that departures are 'nicely modeled, at least mathematically' by fictitious quadratic/cubic polynomials or extra LTTE-like terms; Sect. 4.3 names KIC 6545018 and 9714358 as systems where the data 'clearly reveal the inadequacy of the applied quadratic order approximations' and KIC 5255552, whose accepted solution required a cubic polynomial attributed to unmodeled octupole or quadrupole-squared perturbations. These are model-accuracy risks that could bias derived masses, periods, or mutual inclinations in tight LTTE+DE systems, but they are not circular steps: the polynomial coefficients are fitted to residual curvature, the third-body parameters are not set equal to those coefficients, and the paper explicitly labels the polynomials as mathematical descriptions rather than physical predictions. The confidence classes are a stated catalog convention, not an output derived from the model definition. The confirmation argument is also empirically anchored: the TESS-era eclipse times sometimes contradict older solutions (e.g., KIC 3338660, 4037163, 4681152), so the identification claim is falsifiable rather than forced. Self-citations are methodological and not load-bearing for the existence of the candidates, and the paper's own caveats strengthen rather than weaken the case that no step in the derivation reduces to its own input.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

The catalog is built on fitted orbital elements rather than first-principles predictions, so most parameters are free. The main external inputs are standard two-body physics, the quadrupole-order perturbation theory from the authors' own prior work, and published binary parameters. The paper introduces no new physical forces, but it does add mathematical 'fourth-body' LTTE components that it itself regards as likely non-physical.

free parameters (5)
  • Outer orbital elements (P2, aAB sin i2, e2, omega2, tau2, f(mC)) for each candidate = Tables A.2-A.7
    Fitted to the ETV data; these are the catalog's central output, not predictions.
  • Extra polynomial coefficients c2 and c3 = Footnotes to Tables A.2-A.7, e.g., c3 = 6.7e-15 d/c2 for KIC 1873918
    Added ad hoc to model unmodeled long-term variations; the paper calls them mathematical descriptions.
  • Assumed inner binary total mass mAB = 2.0 Msun = 2.0 Msun
    Used for pure LTTE systems without RV masses to convert mass function to minimum tertiary mass and to compute Adyn/ALTTE.
  • Dynamical-effect activation threshold = Adyn/ALTTE > 0.3
    Hand-chosen cutoff in Sect. 2.2 to decide when to switch on DE terms.
  • Normal-minima bin size = 5-20 consecutive cycles
    Chosen per target to reduce scatter; can smooth real variations if too large.
assumptions (6)
  • standard math Kepler's laws and the LTTE formula (Eq. 2) exactly describe the outer orbit's effect on eclipse times.
    Used in all LTTE fits; no independent verification needed.
  • domain assumption Quadrupole-order dynamical perturbation theory of Borkovits et al. (2015) is adequate for the 15-year baseline.
    Invoked in Sect. 2.2-2.3; the paper itself notes higher-order departures occur and are absorbed by extra polynomial terms.
  • domain assumption Non-third-body ETV variations can be represented by low-order polynomials without corrupting the LTTE signal.
    Sect. 2.4; 41 of 100 secure fits required such polynomials, so this is load-bearing for the fitted parameters.
  • domain assumption Published inner binary parameters (masses, e1, i1) from Matson et al. 2017, Windemuth et al. 2019, Orosz 2023, etc. are correct.
    Used as fixed inputs in DE fits and mass estimates, e.g., KIC 5255552 and 5095269.
  • standard math Mardling and Aarseth (2001) dynamical stability criterion marks the unstable region.
    Used to define the blue shaded region in Fig. 1.
  • domain assumption Averaging 5-20 consecutive cycles yields unbiased 'normal' eclipse times.
    Used for faint TESS systems; if real ETV variations occur within the bin, the normal times are smeared.
invented entities (2)
  • Fourth-body LTTE components in 12 systems
    purpose: Mathematically model longer-period non-linearities in the ETV residuals of doubly periodic systems
    The paper states in Sect. 4.4 that in most doubly periodic cases one periodicity likely has a non-fourth-body origin and the four-body description should be considered a mathematical approximation.
  • Candidate tertiary stellar companions (243) independent evidence
    purpose: Explain periodic LTTE and/or dynamical ETV signals
    Inferred from ETV data, but many are independently supported by TESS phase confirmation, third-body eclipses (e.g., KIC 5039441 and 5952403), or external RV and photodynamical solutions; they are not ad hoc inventions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Then and now: A new look at the eclipse timing variations of hierarchical triple star candidates in the primordial $Kepler$-field, revisited by TESS." pith.science (2026). https://pith.science/paper/DPROQXSJ

@misc{pith2026250209480,
  author       = {Pith},
  title        = {Pith review of: Then and now: A new look at the eclipse timing variations of hierarchical triple star candidates in the primordial $Kepler$-field, revisited by TESS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DPROQXSJ}},
  note         = {Machine review of arXiv:2502.09480}
}
abstract

In this paper we reanalyze the extended ETV curves of the formerly identified triple star candidates and many other $Kepler$ EBs. Besides the confirmations of the former findings and/or the improvements of the triple systems' orbital properties, the extended time-base allows us to identify several new, longer outer period triple systems, and it also makes possible a more detailed study of the dynamical perturbations in the tightest triple stars. We extend the ETV curves of the $Kepler$ triples with those mid-eclipse times which can be deduced from the TESS observations and, moreover, from targeted ground-based follow up observations for a number of the objects. In general, we use the same methods that were applied for the older studies, which are described in the literature. Due to the lower quality of the TESS observations, however, for the fainter systems we average light curves of the EBs for 5-20 consecutive cycles, and thereby calculate `normal' minima from these averaged light curves. In conclusion, we identified 243 hierarchical triple star candidates in the $Kepler$ sample. This sample strongly overlaps our former, nine-year-old sample, confirming the older results, or providing new solutions for 193 systems of the 2016 sample. For the remaining 28 hierarchical triple candidates of that former study, we were unable to find new solutions either because of the disappearance of the eclipses due to orbital plane precession, or due to instrumental reasons. On the other hand, due to the extended time series, we were able to identify 50 new, longer period triple star candidates, as well. We briefly discuss the main properties of each individual system and present statistical studies of the results, as well.

Figures

Figures reproduced from arXiv: 2502.09480 by the authors.

Figure 1
Figure 1. Locations of the analysed hierarchical triple star candidates, to￾gether with other triply eclipsing triples, detected with space telescopes Kepler and TESS in the P1−P2 plane. Black and red dots and green and orange squares represent the current TESS revisited Kepler candidates. For the black and red systems simple LTTE solutions were satisfac￾tory, while for the green and orange ones, the dynamical effects were al… view at source ↗
Figure 3
Figure 3. The eccentricity of the outer orbit, e2, plotted against the period of the outer orbit, P2. The black circles are all the secure and moderately secure LTTE and LTTE + DE solutions. The faint grey dots are the uncertain systems from both the LTTE and LTTE + DE systems [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Distribution of outer eccentricities, e2. Solid blue portions of the histogram are the secure and moderately secure LTTE and LTTE + DE solutions. The faintly shaded regions are the uncertain systems from both the LTTE and LTTE + DE systems. for any given P2 between ≈ 50−5000 days. It is highly likely that these eccentricities are primordial, and therefore they should ul￾timately tell us something about the formation… view at source ↗
Figures from the paper (3 more)
Figure 7
Figure 7. Figure 7: Mass of the tertiary star, mC, plotted against the binary mass, mAB. Only LTTE + DE solutions were considered - the faint gray circles are the uncertain LTTE + DE systems. The blue line marks the q2 = 1 boundary [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Distribution of sine squared of the mutual inclination angle (imut, i.e., the relative tilt of the planes of the inner binary with respect to that of the outer binary). Only LTTE + DE solutions were considered. (The first bin actually extends off scale to 37 systems.) …
Figure 10
Figure 10. Figure 10: ETV residuals fit to quadratic and cubic polynomials. These are taken from 41 secure LTTE and LTTE+DE fits. They are continuous re￾constructions over a 5000 day interval (spanning the Kepler and current TESS missions) using the polynomial coefficients that were part o…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Maunder Model and Catalog: Stellar Rotation, Bimodal Activity, and Magnetic Braking in Kepler Main-Sequence Stars

    astro-ph.SR 2026-08 conditional novelty 7.0 of 10

    A hybrid self-supervised and consensus-supervised model yields calibrated rotation periods for 148,746 Kepler main-sequence stars and identifies bimodal signals where the longer mode is the true rotation.

Reference graph

Works this paper leans on

160 extracted references · 80 canonical work pages · cited by 1 Pith paper

  1. [1]

    et al., 2016, , 151, 101

    Abdul-Masih, M. et al., 2016, , 151, 101

    2016

  2. [2]

    Ali c avu s , F., Soydugan, F., 2017, in AIP Conf. Proc. Vol. 1815, Turkish Physical Society 32nd International Physics Congress (TPS32). Am. Inst. Phys., New York, p. 080004

    2017

  3. [3]

    H., 1992, , 385, 621

    Applegate, J. H., 1992, , 385, 621

    1992

  4. [4]

    J., Pollacco, D., Snterne, A., 2017, , 465, 2634

    Armstrong, D. J., Pollacco, D., Snterne, A., 2017, , 465, 2634

    2017

  5. [5]

    Auvergne. M. et al., 2009, , 506, A411

    2009

  6. [6]

    M., & Rappaport, S., 2015, , 448, 429

    Balaji, Bh., Croll, B., Levine, A. M., & Rappaport, S., 2015, , 448, 429

    2015

  7. [7]

    A., 2017, , 467, 1830

    Balona, L. A., 2017, , 467, 1830

    2017

  8. [8]

    Belopolski, A., 1911, Pulkova Mitt., 4, 171

    1911

Show all 160 references
  1. [9]

    Belopolski, A., 1906, Pulkova Mitt., 1, 101

    1906

  2. [10]

    Bienas, J., B\'odi, A., Forr\'o, A., Hajdu, T., Szab\'o, R., 2021, , 256, 11

    2021

  3. [11]

    S., 1973, , 27, 249

    Biermann, P., Hall, D. S., 1973, , 27, 249

    1973

  4. [12]

    Borkovits, T., 2022, Galaxies, 10, 9

    2022

  5. [13]

    Borkovits, T., Mitnyan, T., 2023, Universe, 9, 485

    2023

  6. [14]

    & Kov\'acs, T., 2003, , 398, 1091

    Borkovits, T., \'Erdi, B., Forg\'acs-Dajka, E. & Kov\'acs, T., 2003, , 398, 1091

    2003

  7. [15]

    M., Csizmadia, Sz., Nuspl, J., B\' r\'o, I

    Borkovits, T., Elkhateeb, M. M., Csizmadia, Sz., Nuspl, J., B\' r\'o, I. B., Heged\"us, T., Csorv\'asi, R., 2005, , 441, 1087

    2005

  8. [16]

    L., Kir\'aly, A., Forg\'acs-Dajka, E., B\' r\'o, I

    Borkovits, T., Derekas, A., Kiss, L. L., Kir\'aly, A., Forg\'acs-Dajka, E., B\' r\'o, I. B., Bedding, T. R., Bryson, S. T., Huber, D. & Szab\'o, R., 2013, , 428, 1656

    2013

  9. [17]

    Borkovits, T., Derekas, A., Fuller, J., et al., 2014, , 443, 3068

    2014

  10. [18]

    Borkovits, T., Rappaport, S., Hajdu, T., & Sztakovics, J., 2015, , 448, 946

    2015

  11. [19]

    B., & Klagyivik, P., 2016, , 455, 4136

    Borkovits, T., Hajdu, T., Sztakovics, J., Rappaport, S., Levine, A., B\' r\'o, I. B., & Klagyivik, P., 2016, , 455, 4136

    2016

  12. [20]

    A., 2019a, EAS Publ

    Borkovits, T., Forg\'acs-Dajka, E., Rappaport, S. A., 2019a, EAS Publ. Ser., 82, 99

  13. [21]

    W., Cs\'anyi, I., Hajdu, T., Moln\'ar, L., 2019b, , 487, 4631

    Borkovits, T., Sperauskas, J., Tokovinin, A., Latham, D. W., Cs\'anyi, I., Hajdu, T., Moln\'ar, L., 2019b, , 487, 4631

  14. [22]

    Borkovits, T., et al., 2020, , 493, 5005

    2020

  15. [23]

    Borkovits, T., et al., 2020b, , 496, 4624

  16. [24]

    Borkovits, T., et al., 2022a, , 510, 1352

  17. [25]

    A., Toonens, S., Moe, M., Mitnyan, T., Cs\'anyi, I

    Borkovits, T., Rappaport, S. A., Toonens, S., Moe, M., Mitnyan, T., Cs\'anyi, I. 2022b, , 515, 3773

  18. [26]

    J., et al., 2010, Science, 327, 977

    Borucki, W. J., et al., 2010, Science, 327, 977

    2010

  19. [27]

    N., et al., 2016, , 151, 66

    Brewer, L. N., et al., 2016, , 151, 66

    2016

  20. [28]

    Chandler, S.C., 1892, , 11, 113

  21. [29]

    Chen, X., et al., 2022, , 263, 34

    2022

  22. [30]

    E., Pr s a, A., Stassun, K

    Conroy, K. E., Pr s a, A., Stassun, K. G., Orosz, J. A., Fabrycky, D. C., & Welsh, W. F. 2014, , 147, 45

    2014

  23. [31]

    F., Garrido, H

    Cruz, P., Aguilar, J. F., Garrido, H. E., Diaz, M. P., Solano, E., 2022, , 515, 1416

    2022

  24. [32]

    H., 1908, , 28, 150

    Curtiss, R. H., 1908, , 28, 150

    1908

  25. [33]

    R., Borkovits, T., Mitnyan, T., Rappaport, S

    Czavalinga, D. R., Borkovits, T., Mitnyan, T., Rappaport, S. A., P\'al, A., 2023a, , 526, 2830

  26. [34]

    R., et al., 2023b, , 670, A75

    Czavalinga, D. R., et al., 2023b, , 670, A75

  27. [35]

    F., Schneider, P

    Czesla, S., Huber, K. F., Schneider, P. C., Schmitt, J. H. M. M., 2014, , 570, A115

    2014

  28. [36]

    et al., 2011, Science, 332, 216

    Derekas, A. et al., 2011, Science, 332, 216

    2011

  29. [37]

    Diethelm, R., 2014, IBVS, 6093, 1

    2014

  30. [38]

    G., Struve, O., 1956, , 124, 507

    Ebbighausen, E. G., Struve, O., 1956, , 124, 507

    1956

  31. [39]

    Felce, C., Fuller, J., 2023, , 526, 6168

    2023

  32. [40]

    Fuller, J., Felce, C., 2024, , 527, L103

    2024

  33. [41]

    R., Kiss, L

    Fuller, J., Derekas, A., Borkovits, T., Huber, D., Bedding, T. R., Kiss, L. L., 2013, , 429, 2425

    2013

  34. [42]

    Non-single stars, https://ui.adsabs.harvard.edu/abs/2022yCat.1357....0G

    Gaia Collaboration, 2022, VizieR Online Data Catalog I/357: Gaia DR3 Part 3. Non-single stars, https://ui.adsabs.harvard.edu/abs/2022yCat.1357....0G

    2022

  35. [43]

    A., 2019, , 630, A106

    Gaulme, P., & Guizk, J. A., 2019, , 630, A106

    2019

  36. [44]

    L., Jackiewicz, J., Mosser, B., Guzik, J

    Gaulme, P., McKeever, J., Rawls, M. L., Jackiewicz, J., Mosser, B., Guzik, J. A., 2013, , 767, 82

    2013

  37. [45]

    Gaulme, P., et al., 2020, , 639, A63

    2020

  38. [46]

    Gaulme, P., et al., 2022, , 668, A173

    2022

  39. [47]

    Gazeas, K., St e pie \'n , K., , 390, 1577

  40. [48]

    K., Carter, B., King, R., O'Toole, S., 2017, , 468, 2932

    Getley, A. K., Carter, B., King, R., O'Toole, S., 2017, , 468, 2932

    2017

  41. [49]

    K., Carter, B., King, R., O'Toole, S., 2020, , 498, 4356

    Getley, A. K., Carter, B., King, R., O'Toole, S., 2020, , 498, 4356

    2020

  42. [50]

    R., Williams, S

    Gies, D. R., Williams, S. J., Matson, R. A., Guo, Z., Thomas, S. M., Orosz, J. A., Peters, G. J., 2012, , 143, 137

    2012

  43. [51]

    R., Matson, R

    Gies, D. R., Matson, R. A., Guo, Z., Lester, K. V., Orosz, J. A., Peters, G. J., 2015, , 150, 178

    2015

  44. [52]

    M., 1983, , 92, 203

    Gim\'enez, A., Garcia-Pelayo, J. M., 1983, , 92, 203

    1983

  45. [53]

    V., Albrecht, S., Deeg, H

    Goldberg, M., Fabrycky, D., Martin, D. V., Albrecht, S., Deeg, H. J., Nowak, G., 2023, , 525, 4628

    2023

  46. [54]

    Guo, Zh., Li, G., 2019, , 882, L5

    2019

  47. [55]

    et al., 2017, , 471, 1230

    Hajdu T. et al., 2017, , 471, 1230

    2017

  48. [56]

    2019, , 485, 2562

    Hajdu T., Borkovits, T., Forg \'a cs-Dajka, E., Sztakovics, J., Marschalk \'o , G., Kutrov \'a tz, G. 2019, , 485, 2562

    2019

  49. [57]

    S., 1989, SpaceSci.Rev., 50, 219

    Hall, D. S., 1989, SpaceSci.Rev., 50, 219

    1989

  50. [58]

    W., Mahadevan, S., Bender, Ch

    Hambleton, K., Pr sa, A., Fleming, S. W., Mahadevan, S., Bender, Ch. F., 2022, , 931, 75

    2022

  51. [59]

    D., Bakos, G., Stanek, K

    Hartman, J. D., Bakos, G., Stanek, K. Z., Noyes, R. W., 2004, , 128, 1761

    2004

  52. [60]

    G., et al., 2016, , 461, 2896

    He miniak, K. G., et al., 2016, , 461, 2896

    2016

  53. [61]

    G., et al., 2017a, , 602, A30

    He miniak, K. G., et al., 2017a, , 602, A30

  54. [62]

    G., et al., 2017b, , 468, 2726

    He miniak, K. G., et al., 2017b, , 468, 2726

  55. [63]

    G., et al., 2019, , 484, 451

    He miniak, K. G., et al., 2019, , 484, 451

    2019

  56. [64]

    Hubscher, J., Lehmann, P, B., Walter, F., 2012, IBVS, 6010, 1

    2012

  57. [65]

    Hubscher, J., Lehmann, P, B., 2015, IBVS, 6149, 1

    2015

  58. [66]

    In \'a cio, J. R. P., et al., 2024, , 529, 2967

    2024

  59. [67]

    B., 1952, , 116, 211

    Irwin, J. B., 1952, , 116, 211

    1952

  60. [68]

    Jeffries, M. W. Jr., et al., 2013, , 146, 58

    2013

  61. [69]

    A., Borkovits, T., Handler, G., Kurtz, D

    Jennings, Z., Southworth, J., Rappaport, S. A., Borkovits, T., Handler, G., Kurtz, D. W., 2024, , 533, 2705

    2024

  62. [70]

    et al., 2020, , 160, 120

    J\"onsson, H. et al., 2020, , 160, 120

    2020

  63. [71]

    Kalimeris, A., Rovithis-Livaniou, H., Rovithis, P., 2002, , 387, 969

    2002

  64. [72]

    Kjurkchieva, D., Atanasova, T., 2016, , 49, 17

    2016

  65. [73]

    Kjurkchieva, D., Vasileva, D., 2018, , 58, 10

    2018

  66. [74]

    Kjurkchieva, D., Vasileva, D., Atanasova, T., 2017, , 154, 105

    2017

  67. [75]

    et al., 2016, , 151, 68

    Kirk, B. et al., 2016, , 151, 68

    2016

  68. [76]

    A., Molnar, L

    Kobulnicky, H. A., Molnar, L. A., Cook, E. M., Henderson, L. E., 2022, , 262, 12

    2022

  69. [77]

    W., Hong, K., 2017, , 154, 235

    Koo, J.-R., Lee, J. W., Hong, K., 2017, , 154, 235

    2017

  70. [78]

    Kostov, V. B. et al., 2024, , 974, 25

    2024

  71. [79]

    Hartman, J

    Kov\'acs, G. Hartman, J. D., Bakos, G. \'A., 2019, , 631, A126

    2019

  72. [80]

    M., Kim, Ch.-H., Nha, I.-S., 2001, An atlas of O-C diagrams of eclipsing binary stars , Wydawnictwo Naukowe Akademii Pedagogicznej, Cracow, Poland

    Kreiner, J. M., Kim, Ch.-H., Nha, I.-S., 2001, An atlas of O-C diagrams of eclipsing binary stars , Wydawnictwo Naukowe Akademii Pedagogicznej, Cracow, Poland

    2001

  73. [81]

    F., Rodon\`o, M., 1999, , 349, 887

    Lanza, A. F., Rodon\`o, M., 1999, , 349, 887

    1999

  74. [82]

    W., Hong, K., Hinse, T

    Lee, J. W., Hong, K., Hinse, T. C., 2015, , 149, 93

    2015

  75. [83]

    W., Hong, K., Koo, J.-R., Park, J.-H., 2016, , 820, 1

    Lee, J. W., Hong, K., Koo, J.-R., Park, J.-H., 2016, , 820, 1

    2016

  76. [84]

    W., Hong, K., Koo, J.-R., Park, J.-H., 2020, , 159, 24

    Lee, J. W., Hong, K., Koo, J.-R., Park, J.-H., 2020, , 159, 24

    2020

  77. [85]

    A., Ngo, H., Mawet, D., Csizmadia, Sz., Forg\'acs-Dajka, E., 2016, , 819, 33

    Lehmann, H., Borkovits, T., Rappaport, S. A., Ngo, H., Mawet, D., Csizmadia, Sz., Forg\'acs-Dajka, E., 2016, , 819, 33

    2016

  78. [86]

    Li, G., et al., 2020, , 497, 4363

    2020

  79. [87]

    Li, X.-Z., Liu, L., 2021, , 161, 35

    2021

  80. [88]

    Liakos, A., 2017, , 607, A85

    2017

  81. [89]

    Liakos, A., 2018, , 616, A130

    2018

  82. [90]

    Liakos, A., 2020, , 642, A91

    2020

  83. [91]

    Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C. et al., 2018, Astrophysics Source Code Library, ascl 1812.013

    2018

  84. [92]

    Lurie, J. C. et al., 2017, , 154, 250

    2017

  85. [93]

    Mahadevan, S., et al., 2019, , 884, 126

    2019

  86. [94]

    Marcadon, F., Pr s a, A., 2024, , 976, 242

    2024

  87. [95]

    A., Aarseth, S

    Mardling, R. A., Aarseth, S. J., 2001, , 321, 398

    2001

  88. [96]

    Mart\' nez-Palomera, J., Hedges, C., Dotson, J., 2023, , 166, 265

    2023

  89. [97]

    Masuda, K., Uehara, Sh., Kawahara, H., 2015, , 806, L37

    2015

  90. [98]

    A., Gies, D

    Matson, R. A., Gies, D. R., Guo, Zh., Williams, S. J., 2017, , 154, 216

    2017

  91. [99]

    Maxted, P. F. L., Hill, G., Hilditch, R. W., 1994, , 282, 821

    1994

  92. [100]

    Mayer, P., 1983, BAICz, 34, 335

    1983

  93. [101]

    Mayer, P., 1990, BAICz, 41, 231

    1990

  94. [102]

    A., P\'al, A., Maxted, P

    Mitnyan, T., Borkovits, T., Rappaport, S. A., P\'al, A., Maxted, P. F. L., 2020, , 498, 6034

    2020

  95. [103]

    A., P\'al, A., Powell, B

    Mitnyan, T., Borkovits, T., Czavalinga, D., Rappaport, S. A., P\'al, A., Powell, B. P., Hajdu, T., 2024, , 685, A43

    2024

  96. [104]

    G., Marcadon, F., Pawar, T., Konacki, M., Ukita, N., Kambe, E., Maehara, H., 2023, , 521, 1908

    Moharana, A., He miniak, K. G., Marcadon, F., Pawar, T., Konacki, M., Ukita, N., Kambe, E., Maehara, H., 2023, , 521, 1908

    2023

  97. [105]

    Molnar, L. A. et al., 2017, , 840, 1

    2017

  98. [106]

    J., Moe, M., Kurtz, D

    Murphy, S. J., Moe, M., Kurtz, D. W., Bedding, T. R., Shibahashi, H., Boffin, H. M. J., 2018, , 474, 4322

    2018

  99. [107]

    Nanouris, N., Kalimeris, A., Antonopoulou, E., & Rovithis-Livaniou, H., 2011, , 535, A126

    2011

  100. [108]

    Nanouris, N., Kalimeris, A., Antonopoulou, E., & Rovithis-Livaniou, H., 2015, , 575, A64

    2015

  101. [109]

    NegmEldin, M. A. F., Essam Elsayed, A, Yousef, S. M, 2019, Res. A&Ap, 19, 025

    2019

  102. [110]

    W., Rix, H

    Ness, M., Hogg, D. W., Rix, H. -W., Martig, M., Pinsonneault, M, H., Ho, A. Y. Q., 2016, , 823, 114

    2016

  103. [111]

    Ochsenbein F., Bauer P., Marcout J., 2000, , 143, 23

    2000

  104. [112]

    A., 2015, ASPC, 496, 55

    Orosz, J. A., 2015, ASPC, 496, 55

    2015

  105. [113]

    A., 2023, Universe, 9, 505

    Orosz, J. A., 2023, Universe, 9, 505

    2023

  106. [114]

    A., 2017, , 34, e017

    \"Ozdarcan, O., Dal, H. A., 2017, , 34, e017

    2017

  107. [115]

    \"Ozdarcan, O., 2023, , 166, 215

    2023

  108. [116]

    P\'al, A., 2012, , 421, 1825

    2012

  109. [117]

    Pollacco, D. L. et al., 2006, , 118, 1407

    2006

  110. [118]

    Powell, B. P. et al., 2022, , 938, 133

    2022

  111. [119]

    M., 2008, , 386, 377

    Pribulla, T., Rucinski, S. M., 2008, , 386, 377

    2008

  112. [120]

    Pribulla, T., Balu d ansk \'y , D., Dubovsk \'y , P., Kudzej, I., Parimucha, S ., Siwak, M., Va n ko, M., 2008, , 390, 798

    2008

  113. [121]

    et al., 2023, , 524, 4220

    Pribulla, T. et al., 2023, , 524, 4220

    2023

  114. [122]

    Qian, Sh.-B., 2001, , 328, 914

    2001

  115. [123]

    Qian, Sh.-B., et al., 2018, , 235, 5

    2018

  116. [124]

    Rappaport, S., Deck, K., Levine, A., Borkovits, T., Carter, J., El Mellah, I., Sanchis-Ojeda, R., & Kalomeni, B., 2013, , 768, 33

    2013

  117. [125]

    A., et al., 2022, , 513, 4341

    Rappaport, S. A., et al., 2022, , 513, 4341

    2022

  118. [126]

    A., et al., 2023, , 521, 558

    Rappaport, S. A., et al., 2023, , 521, 558

    2023

  119. [127]

    A., et al., 2024, , 686, A27

    Rappaport, S. A., et al., 2024, , 686, A27

    2024

  120. [128]

    Ricker, G.R., et al., 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, id. 014003

    2015

  121. [129]

    Y., Pazhouhesh, R., 2022, Res A&Ap, 22, 025013

    Roobiat, K. Y., Pazhouhesh, R., 2022, Res A&Ap, 22, 025013

    2022

  122. [130]

    Schwamb, M. E. et al., 2013, , 768, 127

    2013

  123. [131]

    et al., 2020, , 643, A162

    Sekaran, S. et al., 2020, , 643, A162

    2020

  124. [132]

    Shi, F., Zhang, H., Fu, J., Kurtz, D., Xiang, M., 2023, , 943, 147

    2023

  125. [133]

    R., Orosz, J, A., Windmiller, G., Welsh, W

    Short, D. R., Orosz, J, A., Windmiller, G., Welsh, W. F., 2018, ,156, 297

    2018

  126. [134]

    Slawson, R. W. et al., 2011, , 142, 160

    2011

  127. [135]

    Socia, Q. J. et al., 2018, , 864, L32

    2018

  128. [136]

    S\"oderhjelm, S., 1975, , 42, 229

    1975

  129. [137]

    L., M\'esz\'aros, Sz., Vink\'o, J., Csizmadia, Sz., 2007, , 465, 943

    Szalai, T., Kiss, L. L., M\'esz\'aros, Sz., Vink\'o, J., Csizmadia, Sz., 2007, , 465, 943

    2007

  130. [138]

    H., Quinn, S

    Steffen, J. H., Quinn, S. N., Borucki, W. J. et al., 2011, , 417, L31

    2011

  131. [139]

    2005, The O-C Diagram: Basic Procedures

    Sterken, C. 2005, The O-C Diagram: Basic Procedures. In The Light-Time Effect in Astrophysics: Causes and Cures of the O-C Diagram; Sterken, C., Ed.; ASPacific Conf. Ser., 335, 3

    2005

  132. [140]

    Tal-Or, L., Faigler, S., Mazeh, T., 2015, , 580, A21

    2015

  133. [141]

    2012, , 753, 86

    Thompson, S.E., Everett, M., Mullally, F., et al. 2012, , 753, 86

    2012

  134. [142]

    Tokovinin, A., 2008, , 389, 925

    2008

  135. [143]

    Tokovinin, A., 2014a, , 147, 86

  136. [144]

    Tokovinin, A., 2014b, , 147, 87

  137. [145]

    Tokovinin, A., 2021, Universe, 7, 32

    2021

  138. [146]

    S., Bandopadhyay, D., 2020, , 640, A16

    Toonen, S., Portegies Zwart, S., Hamers, A. S., Bandopadhyay, D., 2020, , 640, A16

    2020

  139. [147]

    Toonen, S., Boekholt, T. C. N., Portegies Zwart, S., 2022, , 661, A61

    2022

  140. [148]

    Tran, K., Levine, A., Rappaport, S., Borkovits, T., Csizmadia, Sz., & Kalomeni, B., 2013, , 774, 81

    2013

  141. [149]

    E., 2007, , 661, 1129

    Van Hamme, W., Wilson, R. E., 2007, , 661, 1129

    2007

  142. [150]

    & Han, Z., 2010, , 715, 51

    van Kerkwijk, M.H., Rappaport, S., Breton, R.P., Justham, S., Podsiadlowski, Ph. & Han, Z., 2010, , 715, 51

    2010

  143. [151]

    V\"olschow, M., Schleicher, D. R. G., Banerjee, R., Schmitt, J. H. M., M., 2018, , 620, A42

    2018

  144. [152]

    2019, , 489, 1644

    Windemuth, D., Agol, E., Ali, A., Kiefer, F. 2019, , 489, 1644

    2019

  145. [153]

    Yang, Y.-G., Dai, J.-M., Yin, X.-G., Xiang, F.-Y., 2007, , 134, 179

    2007

  146. [154]

    Zasche, P., Wolf, M., Ku c \'akov\'a, H., Vra s til, J., Jury s ek, J., Ma se k, M., Jel\' nek, M., 2015, , 149, 197

    2015

  147. [155]

    Zasche, P., Wolf, M., Vra s til, J., 2017, , 472, 2241

    2017

  148. [156]

    Zasche, P., Uhla r , R., Svobova, P., Caga s , P., Ma s ek, M., 2020, , 643, 130

    2020

  149. [157]

    Zhang, J., Qian, Sh.-B., Wu, Y., Zhou, X., 2019, , 244, 43

    2019

  150. [158]

    B., Fu, J

    Zhang, X. B., Fu, J. N., Luo, C. Q., Ren, A. B., Yan, Z. Z., 2018, , 865, 115

    2018

  151. [159]

    Zhang, X., Chen, X., Zhang, H., Fu, J., Li, Y., 2020, , 895, 124

    2020

  152. [160]

    Zola, S., Baran, A., Debski, B., Jableka, D., 2017, , 466, 2488

    2017

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.