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The Discovery of Two Quadruple Star Systems with the Second and Third Shortest Outer Periods

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Pith's one-line read TIC 392229331 and TIC 285853156 are proven 2+2 hierarchical quadruple star systems, with outer periods of 144.80 +/- 0.16 days and 151.70 +/- 0.11 days.

desk verdict Solid confirmation of two compact 2+2 quadruples; the core bound-system claim holds, but the long-term stability conclusion for TIC 285853156 is oversold relative to the evidence. read the letter →

arxiv 2504.12239 v1 pith:OWLQEEN3 submitted 2025-04-16 astro-ph.SR

Brian P. Powell , Guillermo Torres , Veselin B. Kostov , Tamás Borkovits , Saul A. Rappaport , Maxwell Moe , David W. Latham , Thomas L. Jacobs
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Robert Gagliano Martti H. K. Kristiansen Mark Omohundro Hans M. Schwengeler Daryll M. LaCourse Ivan A. Terentev Allan R. Schmitt
This is my paper · ORCID
classification astro-ph.SR
keywords eclipsingbinariesquadruplestarsystems2+2hierarchicalquadrupleseclipsetimingvariationsradialvelocitiesphotodynamicalmodelingdynamicalstabilityTESS
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

Two star systems observed by TESS, each showing two independent sets of eclipses, are here claimed to be genuine 2+2 hierarchical quadruples: four stars organised as two close eclipsing binaries that orbit each other on a common outer orbit. By combining all available TESS photometry with new high-resolution spectra, the paper builds a single photodynamical model that fits the light curves, radial velocities, eclipse timing variations, and spectral energy distribution simultaneously. The model finds outer periods of $144.80 \pm 0.16$ days for TIC 392229331 and $151.70 \pm 0.11$ days for TIC 285853156, making them the second and third shortest outer periods known among quadruple systems. The paper also argues that both systems remain dynamically stable for at least a million years despite outer eccentricities of 0.558 and 0.325, and uses that stability to connect these objects to how very compact quadruples form.

What carries the argument

The central machinery is a photodynamical fitter that integrates the gravitational N-body dynamics of a 2+2 quadruple and predicts photometry, eclipse times, and radial velocities at once; it is coupled to stellar evolution tracks and a spectral energy distribution fit. The load-bearing signal in the fit is the common outer orbital period: the same $P_{\rm out}$ must simultaneously explain the slow drift in the radial-velocity residuals of both visible primaries and the anti-correlated eclipse timing variations of the two inner binaries. The distinction between light-travel-time delays and dynamical delays in the eclipse timing variations is what breaks degeneracies and ties the outer orbit to the masses.

What would settle it

Measure the center-of-mass motion of each inner binary with additional radial velocities spanning several outer periods: if the two binaries in either system ever stop tracing a single Keplerian outer orbit, the bound-quadruple interpretation is wrong. A direct test for TIC 285853156 is to search for the predicted outer-orbit eclipses during the windows when the modeled impact parameter drops below unity; their absence would rule out the fitted mutual-inclination geometry.

Watch

Extended reading notes

Core claim

The paper's central claim is that the two previously catalogued quadruple candidates are bound systems, not chance projections, and that they are among the most compact known. The proof rests on coherent outer-orbit motion: after removing each inner binary orbit, the radial velocities of all detected stars in a given system share one common period (about 151.7 days in TIC 285853156 and 144.8 days in TIC 392229331), and the eclipse timing variations of both binaries in each system are reproduced by the same dynamical model, which includes light-travel-time and dynamical delays. The simultaneous photodynamical solution also yields masses, radii, effective temperatures, ages, and mutual inclinations; both systems are nearly coplanar, with the four stars fitting roughly inside the orbit of Venus. Long-term direct N-body integrations show no significant changes in semimajor axes, eccentricities, or inclinations over one million years, so the paper concludes that both systems are dynamically stable even though TIC 285853156 sits close to the analytic stability boundary.

Load-bearing premise

The argument for a bound quadruple assumes that the shared outer-period signal in the radial velocities and eclipse timings comes from one real four-star system, not from two independent binaries that happen to lie along the same line of sight at similar distances.

Editorial extensions

If this is right

  • TIC 392229331 and TIC 285853156 become the second and third confirmed 2+2 quadruples with outer periods under 200 days, after BU CMi, so the known population of extremely compact quadruples now has four members.
  • Both systems' outer eccentricities (0.558 and 0.325) are high for such short outer periods, and the systems' long-term stability implies that high-eccentricity compact quadruples can survive long enough to be observed.
  • TIC 285853156 is predicted to display outer-orbit eclipses for a few years every few decades as apsidal motion carries the stars across the line of sight, giving a concrete test of the model's geometry.
  • The fitted parameters are precise enough that the stars can serve as benchmarks for stellar evolution models at known ages and metallicities.
  • The paper's formation scenario implies that compact quadruples should have systematically larger outer eccentricities than compact triples with similar outer periods.

Reading between the lines

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

  • If the formation picture is right, surveys should find that 2+2 quadruples with $P_{\rm out} \lesssim 200$ days cluster at eccentricities above 0.3 while compact triples cluster below; a larger sample would test the proposed core-fragmentation versus disk-fragmentation split.
  • TIC 285853156 sits just inside the analytic stability boundary yet is 3.8 Gyr old, so continued monitoring of this system could turn it into a calibration point for hierarchical-stability criteria for 2+2 configurations.
  • The predicted outer eclipses of TIC 285853156 offer a concrete time window; observing them, or failing to observe them, would directly check the fitted mutual-inclination geometry in a way the paper does not itself schedule.
  • The slow rotation of the A-type stars in TIC 392229331 may point to tidal spin-orbit misalignment or to chemically peculiar metallic-line stars, and a future abundance analysis could connect these compact quadruples to the broader puzzle of slow rotators in close binaries.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper reports the confirmation of two candidate 2+2 hierarchical quadruple star systems, TIC 285853156 and TIC 392229331, originally identified in TESS data by Kostov et al. (2022, 2024). The authors combine new TRES radial velocities, TESS eclipse timing variations, TESS light curves, archival photometry, and SED data in a simultaneous photodynamical model (Lightcurvefactory) with PARSEC evolutionary tracks, deriving outer periods of 151.70 ± 0.11 days and 144.80 ± 0.16 days and outer eccentricities of 0.325 and 0.558, respectively. They argue that a coherent outer-period signal seen in the RVs of both inner binaries and in the ETVs of both binaries proves that the two binary pairs are gravitationally bound. The paper also presents REBOUND/IAS15 integrations, claiming both systems are long-term dynamically stable for at least one million years, and places the systems as the second and third shortest known 2+2 quadruple outer periods after BU Canis Minoris.

Significance. If the results hold, these systems are valuable additions to the very small sample of compact, well-characterized 2+2 quadruple systems. Their short outer periods and high outer eccentricities provide direct observational constraints on formation and orbital-capture scenarios, and the precision of the fitted masses, radii, and effective temperatures makes them useful tests of stellar evolution models in multiple-star contexts. A particular strength of the paper is the simultaneous fitting of independent data sets (RVs, ETVs, light curves, and SEDs) with MCMC uncertainty estimation, and the use of Sector 86 TESS data as a post-fit predictive check. The bound-system argument is convincing because the same outer period appears coherently in two independent observables, and the fitted mass ratios are internally consistent. However, the long-term stability claim for TIC 285853156 currently rests on a single deterministic integration at parameters that sit near an analytic stability boundary, and the stellar parameter solution contains an unaddressed effective-temperature discrepancy for the dominant star.

major comments (2)
  1. [Sec. 5.3, Figs. 15-16] The long-term stability claim for TIC 285853156 is not yet adequately supported. The paper states that both the period ratio and semimajor-axis ratio are at only ~95% of the analytic stability criteria in Eqs. (1)-(2), yet the REBOUND/IAS15 integrations appear to be single runs at the median or best-fit parameters, with no sampling over the posterior distribution. Given the quoted uncertainties in the outer eccentricity (0.325 ± 0.003), mutual inclinations (1.15 ± 0.76 and 1.49 ± 0.75 deg), and inner eccentricities, a portion of the posterior volume could plausibly cross the stability boundary. In addition, the 1-Myr integration is a factor of ~4000 shorter than the system's inferred 3.8-Gyr age, so the phrase 'if not for the lifetime of the Galaxy' is not supported by the simulation. The appeal to the 3.8-Gyr age as empirical stability evidence is also not a substitute, because that age is derived from the same photodynamical/PARSEC fit and does not test the orbital evolution over that interval. I recommend running stability integrations over the MCMC posterior (or over a bracketing grid in e_out, mutual inclination, and inner eccentricity) and softening the wording to 'stable for at least 1 Myr under the nominal parameters' unless longer-timescale or posterior-wide survivability is demonstrated.
  2. [Sec. 2.1 vs. Table 7] The adopted spectroscopic effective temperature for the dominant star Aa of TIC 285853156 is Teff = 6280 ± 100 K (Sec. 2.1), while the final photodynamical/evolutionary-track solution in Table 7 gives Teff = 5845 +57/-51 K. This is a discrepancy of roughly 4 sigma. Because Aa contributes ~85.5% of the TESS-band flux and dominates the SED, this tension bears directly on the derived mass, radius, and age of the system, and hence also on the stability discussion that uses the 3.8-Gyr age as empirical evidence. The manuscript does not acknowledge or discuss this inconsistency. Please either quantify the systematic errors that reconcile the two values, or test the sensitivity of the global fit to a prior on Teff from the spectroscopy and report the resulting changes to the stellar and orbital parameters.
minor comments (4)
  1. [Sec. 2.1] The instrument name is spelled 'Tillingast Reflector Echelle Spectrograph' in the text; it should be 'Tillinghast Reflector Echelle Spectrograph'.
  2. [Sec. 2, footnote 3] The footnote for TIC 392229331 lists the same DOI for TESS Sectors 59 and 86; one of these DOIs is likely incorrect.
  3. [Table 6] The archival detection summary is somewhat difficult to parse; it would be clearer to state explicitly, for each source and survey, which inner binary was detected and which was not.
  4. [Sec. 3] The manuscript does not state whether the Lightcurvefactory code will be made public; if not, the reproducibility of the analysis would benefit from a supplementary table of the MCMC priors and proposal distributions used in the fits.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bound-system proof and stability claim rest on new RVs, ETVs, photometry, and an N-body integration, not on the cited candidate catalogs.

full rationale

The paper's central derivation is self-contained against external data. The outer periods are not imposed by the model but were first seen as coherent periodicities in the residuals of preliminary single-lined orbital solutions: 'we eventually discovered that the velocity residuals for the two visible stars (Aa and Ba) showed the same periodicity of about 151.5 days, representing the outer period of the quadruple,' and analogously for TIC 392229331 at ~144.7 days. These outer periods are then fitted jointly with the RVs, ETVs, TESS light curves, and SED in the photodynamical model, so the bound-system conclusion is an inference from multiple independent data sets rather than a definitional tautology. The paper explicitly acknowledges the chance-alignment alternative and identifies RVs or ETVs as the mechanisms that elevate candidates to confirmed status, and the new TRES radial velocities and archival photometry provide exactly that external confirmation. The self-citations to Kostov et al. (2022, 2024a) are used for initial candidate identification, photocenter vetting, and as catalogs being monitored; they are not load-bearing for the new proof of boundness, which rests on new spectroscopic and timing data. The stability claim is supported by REBOUND/IAS15 integrations over one thousand outer orbits and one million years using the fitted parameters, and by the analytic criteria only as a first check; the paper even notes TIC 285853156 fails the analytic criteria and that those criteria are approximate fitting formulae. While one could ask for posterior sampling or longer integrations, that is a robustness/correctness concern, not circularity. The use of the authors' own Lightcurvefactory code is a modeling tool, not an unverified premise that predetermines the result. No predicted quantity reduces by construction to a fitted input, and no load-bearing argument is carried by a self-citation chain. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. It relies on standard stellar evolution models, standard cross-correlation techniques, and a fitting code that has been used in prior publications. The most significant free choices are the adopted spectral parameters for the undetected secondary in TIC 285853156, and the global system parameters (age, metallicity, distance, extinction) that are fit rather than measured. The stability analysis uses the fitted orbital elements as initial conditions, which is not an invented entity but does carry the fit's uncertainties into the stability conclusion.

free parameters (3)
  • TIC 285853156 star Ba Teff = 5000 K
    The faint secondary in binary B was not measurable in the spectra, so the authors adopted an educated guess of 5000 K under the assumption of spin-orbit alignment and synchronous rotation. This guess enters the photodynamical fit and can bias the derived parameters of binary B.
  • TIC 285853156 star Ba vsini = 20 km/s
    Adopted from the assumption of spin-orbit alignment and synchronous rotation in the 1.77-day orbit, as the star's lines were too weak to measure directly.
  • System age, metallicity, extinction, distance for each system = log(age) 9.584 and 8.014, [M/H] 0.197 and 0.183, E(B-V) 0.257 and 0.301, distances 274 and 607 pc
    These four global parameters per system are fit simultaneously with the orbital and stellar parameters through the SED and PARSEC isochrones. They are not derived from first principles; they are determined by the fit and carry the stellar evolution assumptions.
assumptions (4)
  • domain assumption The four stars in each system formed coevally with the same age and metallicity.
    Section 3 states that the use of PARSEC tracks requires the assumption that all stars evolved coevally with no prior mass transfer. This is a standard assumption for multiple star systems, but it is not independently verified for these targets.
  • domain assumption The two sets of eclipses seen in TESS originate from the same physical source.
    The paper states that K22/K24 confirmed this through photocenter analysis, and the new RV data support it. This is a necessary condition for the quadruple interpretation.
  • standard math The templates and line lists used for TODCOR/TRICOR/QUADCOR provide accurate radial velocities.
    The RV measurement technique is standard in the field and the templates are from Kurucz model atmospheres. The assumption is that the cross-correlation velocities are not systematically biased by the composite spectra.
  • standard math The stability criteria of Equations (1) and (2) apply to these systems.
    The paper uses the Mardling and Aarseth style stability criteria from Borkovits et al. 2022 and notes that TIC 285853156 slightly violates them, which is why they fall back on direct numerical integration.

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Pith. "Pith review of The Discovery of Two Quadruple Star Systems with the Second and Third Shortest Outer Periods." pith.science (2026). https://pith.science/paper/OWLQEEN3

@misc{pith2026250412239,
  author       = {Pith},
  title        = {Pith review of: The Discovery of Two Quadruple Star Systems with the Second and Third Shortest Outer Periods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OWLQEEN3}},
  note         = {Machine review of arXiv:2504.12239}
}
read the original abstract

We present the discovery of two quadruple star systems -- TIC 285853156 and TIC 392229331 -- each consisting of two bound eclipsing binary stars. Among the most compact quadruples known, TIC 392229331 and TIC 285853156 have the second and third shortest outer orbital periods (145 days and 152 days, respectively) after BU Canis Minoris (122 days, Pribulla et al. 2023). We demonstrate that both systems are long-term dynamically stable despite substantial outer orbital eccentricities (0.33 for TIC 285853156 and 0.56 for TIC 392229331). We previously reported these systems in Kostov et al. (2022) and Kostov et al. (2024) as 2+2 hierarchical quadruple candidates producing two sets of primary and secondary eclipses in TESS data, as well as prominent eclipse timing variations on both binary components. We combine all available TESS data and new spectroscopic observations into a comprehensive photodynamical model, proving that the component binary stars are gravitationally bound in both systems and finding accurate stellar and orbital parameters for both systems, including very precise determinations of the outer periods. TIC 285853156 and TIC 392229331 represent the latest addition to the small population of well-characterized proven quadruple systems dynamically interacting on detectable timescales.

Figures

Figures reproduced from arXiv: 2504.12239 by the authors.

Figure 1
Figure 1. TESS Full-Frame Image eleanor(Feinstein et al. 2019) light curves for TIC 285853156 from Sectors 43 (upper left), 44 (upper right), 45 (lower left), and 71 (lower right) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. TESS Full-Frame Image eleanor(Feinstein et al. 2019) light curves for TIC 392229331 from Sectors 19 (upper left), 59 (upper right), and 86 (bottom). following Torres et al. (2002). For the brighter star in TIC 285853156 (star Aa), we determined Teff = 6280 ± 100 K and v sin i = 7 ± 2 km s−1 . The faintness of the other star (Ba) prevented us from determining its properties reliably. We therefore adopted educated gue… view at source ↗
Figure 3
Figure 3. Radial velocity data vs. time and model fits for TIC 285853156 binaries A (upper panel) and B (lower panel) shown over the full duration of the collected spectra (see [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Measured ETV points and the corresponding model fits for TIC 285853156. The results for binary A and binary B are displayed in the top panel and bottom panel, respectively. The ETVs and for the primary and secondary eclipses are shown with red circles and blue squares,…
Figure 7
Figure 7. Figure 7: SED data points and model fit for TIC 285853156. The SED measurements are shown as red circles, while the model contributions from stars Aa (blue), Ab (green), Ba (orange), Bb (purple), and the total system (black) are shown superposed on the data. The system age is 3.…
Figure 8
Figure 8. Figure 8: Radial velocity measurements and model fits vs. time for TIC 392229331. The upper and lower panels show the RVs for binary A and binary B, respectively. All other descriptors are the same as given in the caption to Fig￾ure 3 for TIC 285853156. based on the most recent …
Figure 10
Figure 10. Figure 10: ETV points and model curves for TIC 392229331. The top and bottom panels are for binary A and binary B, respectively, with the red circles indicating the primary eclipses and blue squares the secondary eclipses. The smooth curves of the corresponding colors are the mo…
Figure 9
Figure 9. Figure 9: Radial velocity measurements and model fits vs. orbital phase for the three binary orbits in TIC 392229331. These are the binary A components in A’s center of mass (top panel), binary B components in B’s center of mass (middle panel), and binaries A and B orbiting the …
Figure 11
Figure 11. Figure 11: Lightcurve segments from TESS sectors 19 (top), sector 59 (middle), and sector 86 (bottom) for TIC 392229331. Lightcurve data points (blue circles) are com￾pared to the model lightcurve (red line). Residuals of the data points from the model fit are shown in the botto…
Figure 12
Figure 12. Figure 12: SED data points and model fit for TIC 392229331. The SED measurements are shown as red cir￾cles, while the model contributions from stars Aa (blue), Ab (green), Ba (orange), Bb (purple), and the total system (black) are shown superposed on the data. The system age is …
Figure 13
Figure 13. Figure 13: Impact parameter (centroid distance divided by the sum of the radii) of pairs of stars in TIC 285853156 (top panel) and TIC 392229331 (bottom panel) for a one thousand year duration. We should expect a pair of stars to produce eclipses on the outer orbit when the impa…
Figure 14
Figure 14. Figure 14: Orbital motions in TIC 285853156 (top panel) and in TIC 392229331 (bottom panel), as seen from a vantage point above the orbital plane. The actual observational view direction from the Earth is along the +y axis. A compari￾son between the sizes of these orbits with th…
Figure 15
Figure 15. Figure 15: For TIC 285853156, orbital parameters of binary A (red), binary B (blue), and quadruple AB (green). The top row shows one thousand orbits of the semi-major axes (top left), the eccentricities (top middle), and the inclinations (top right). The bottom row shows a zoome…
Figure 16
Figure 16. Figure 16: For TIC 392229331, orbital parameters of binary A (red), binary B (blue), and quadruple AB (green). The top row shows one thousand orbits of the semi-major axes (top left), the eccentricities (top middle), and the inclinations (top right). The bottom row shows a zoome…

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

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