{"id":"ea15a6d9-abe1-4c66-9c20-94891e51d1c6","arxiv_id":"2504.12239","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"TIC 392229331 and TIC 285853156 are confirmed 2+2 quadruple star systems with the second and third shortest outer orbital periods known, 144.8 and 151.7 days.","lead":"Astronomers confirmed two quadruple star systems, each made of two pairs of stars orbiting each other, with the second and third shortest outer orbits known. The work combines space telescope data with ground-based spectroscopy to prove the pairs are truly bound and to measure their orbits precisely.","discovery_kind":"unclear","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stability claim for TIC 285853156 rests on a single 1-Myr REBOUND run of a system that fails the analytic criteria; posterior sampling is needed.","rationale":"The paper's central discovery claim is very strong: the common ~151.7 d and ~144.8 d signals in the RVs of both inner binaries, plus the ETVs, exclude chance alignment, and the fitted masses satisfy Kepler's third law for all three orbits. I do not see a credible threat to the bound-system conclusion, and the undetected secondary in binary B of TIC 285853156 does not undermine the outer-orbit detection because K_B and hence q_out come from Ba's center-of-mass motion. The most defensible objection is to the stability claim for TIC 285853156, which fails the analytic criteria and is checked with a single numerical integration at (presumably) the median parameters. The quoted parameter uncertainties are small, so the risk may be low, but it is unquantified precisely where the system sits near a stability boundary. A posterior-sampling stability test is cheap and would settle it. This leaves the reader's CONDITIONAL verdict unchanged, though for a somewhat different reason than the reader's stated weakest assumption.","tokens_in":27425,"tokens_out":18222,"duration_ms":194344,"concrete_test":"Draw 100 initial conditions for TIC 285853156 from the MCMC posterior summarized in Table 7, varying e_out, mutual inclinations, inner eccentricities, and masses within their quoted uncertainties, and integrate each with REBOUND/IAS15 for at least 10 Myr (or until disruption/ejection), recording the survival fraction and the distribution of Lyapunov times. If any non-negligible fraction, say >5%, of posterior samples disrupt within 10 Myr or show chaotic diffusion on timescales shorter than 1 Gyr, the long-term stability claim in the abstract must be downgraded or explicitly conditioned on the best-fit parameters. For completeness, run the same ensemble for TIC 392229331 to confirm that its stability margin is insensitive to parameter choices.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The discovery and bound-system proof are well supported: the coherent outer-period signal in the RVs of both binaries and in the ETVs effectively rules out chance alignment, and the Keplerian consistency of the fitted masses is an independent check. The load-bearing weakness is in the companion stability claim, specifically for TIC 285853156. Section 5.3 notes that this system has P_out/P_in and a_out/a_in at only ~95% of the analytic stability criteria (Eqs. 1-2), i.e., it sits close to the instability boundary. The long-term stability conclusion is then based on a REBOUND/IAS15 integration, but the paper reports a single run (presumably at the median parameters) for 'one thousand outer orbits' and 'one million years,' without sampling the posterior. Although 1 Myr is ~2.4 million outer orbits, the system is at a boundary where survival can be sensitive to small changes in e_out, mutual inclination, and inner eccentricities, all of which have quoted uncertainties. The later statement that the system is stable 'if not for the lifetime of the Galaxy' is not supported by the simulation, which covers only ~10^-3 of the inferred 3.8 Gyr age. The empirical age is itself derived from the same PARSEC-based fit, so it is not fully independent evidence. If even a small fraction of the posterior volume is unstable on timescales relevant to the system, the abstract's 'long-term dynamically stable' claim would need to be qualified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":27648,"tokens_out":5753,"duration_ms":60557,"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":[{"comment":"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.","section":"Sec. 5.3, Figs. 15-16"},{"comment":"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.","section":"Sec. 2.1 vs. Table 7"}],"minor_comments":[{"comment":"The instrument name is spelled 'Tillingast Reflector Echelle Spectrograph' in the text; it should be 'Tillinghast Reflector Echelle Spectrograph'.","section":"Sec. 2.1"},{"comment":"The footnote for TIC 392229331 lists the same DOI for TESS Sectors 59 and 86; one of these DOIs is likely incorrect.","section":"Sec. 2, footnote 3"},{"comment":"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.","section":"Table 6"},{"comment":"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.","section":"Sec. 3"}],"recommendation":"major_revision","confidential_remarks":"The bound-system confirmation appears solid and the systems are a valuable addition to the compact-quadruple sample. My reservations are the under-supported stability claim in Sec. 5.3 for TIC 285853156 and the unaddressed Teff discrepancy for its dominant star; both are fixable with additional analysis or by tempering the claims. I would support publication after these points are resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this paper does what it says. TIC 392229331 and TIC 285853156 were already candidates; here they become confirmed bound 2+2 quadruples through coherent radial velocities and a global photodynamical fit. The outer periods, 144.80 and 151.70 days, are precise, and the Sector 86 ETV prediction for TIC 392229331 is a real out-of-sample check that passes. That is honest progress for the small catalog of compact quadruples.\n\nThe modeling is thorough: RVs for three or four stars, ETVs for both binaries, TESS light curves, SEDs, and PARSEC tracks all fit simultaneously, with MCMC uncertainties. The bound-system proof does not rest on a single fragile signal. The outer period appears independently in the RV residuals and in the ETVs, and the fit ties them together with Keplerian consistency. The chance-alignment worry is effectively ruled out.\n\nWhere the paper is softer: the stability claim for TIC 285853156. The system sits at about 95% of the analytic stability criteria, and the long-term stability is inferred from what appears to be a single REBOUND/IAS15 run at the median parameters. No posterior sampling is reported. The abstract's \"long-term dynamically stable\" and the text's \"stable ... if not for the lifetime of the Galaxy\" go beyond a 1-Myr integration, especially when the quoted age of 3.8 Gyr comes from the same fit that produced the orbital parameters. I would ask the authors to either sample the posterior and report the unstable fraction, or tone the claim down to \"stable over at least 1 Myr.\" This is a moderate fix, not a fatal flaw.\n\nThe other weaknesses are minor: the undetected secondary in TIC 285853156 enters the fit with adopted Teff and vsini, and there is no shipped code or machine-readable RV table. Both are standard for this kind of paper and do not threaten the main result.\n\nOverall: this deserves a serious referee and publication after a revision that tightens the stability language and makes the data more accessible. I would cite it if I worked on multiple-star formation.\n\nRecommended verdict: accept with moderate revision.","headline":"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.","tokens_in":28340,"tokens_out":940,"would_cite":true,"duration_ms":11685,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["eclipsing binaries","quadruple star systems","2+2 hierarchical quadruples","eclipse timing variations","radial velocities","photodynamical modeling","dynamical stability","TESS"],"falsifier":"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.","tokens_in":27157,"feed_emoji":"⭐","tokens_out":7478,"duration_ms":70754,"temperature":0.7,"pith_summary":"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.","feed_headline":"Confirmed: two quadruple star systems orbit in 145 and 152 days","feed_subtitle":"New spectra and eclipse timings prove each pair of binaries is one bound four-star system, the second and third tightest ever found.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Catalog that first identified TIC 392229331 as a 2+2 quadruple candidate and supplied the TESS light curves, eclipse timings, and photocenter vetting used here.","marker":"K22"},{"why":"Catalog that first reported TIC 285853156 and its dramatic anti-correlated eclipse timing variations, the starting point for this confirmation.","marker":"K24"},{"why":"Provides the current shortest known 2+2 quadruple outer period (BU CMi), the benchmark against which these periods are ranked.","marker":"Pribulla et al. 2023"},{"why":"Supplies the analytic stability criteria used to test whether the compact outer orbits are stable before numerical integration.","marker":"Borkovits et al. 2022"},{"why":"Provides the N-body integrator used for the long-term stability simulations of both systems.","marker":"Rein & Liu 2012"},{"why":"Provides the high-accuracy integrator used to carry the long-term REBOUND stability simulations.","marker":"Rein & Spiegel 2015"},{"why":"Supplies the two-dimensional cross-correlation method used to measure radial velocities in the blended spectra.","marker":"Zucker & Mazeh 1994"},{"why":"Gives the light-travel-time and dynamical-delay formalism used to separate ETV components and identify the outer period.","marker":"Borkovits 2022"}],"fun_headline_variants":[],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"error":"DeepSeek 429: {\"error\":{\"message\":\"Too many requests. Your current concurrency is 134, which exceeds your concurrency limit of 117 based on your remaining balance. Please top up your balance to restore your concurrency.\",\"type\":\"rate_limit_error\",\"param\":null,\"code\":\"invalid_request_error\"}}"},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:33:13.929054+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"2023, MNRAS, 524, 4220, doi: 10.1093/mnras/stad2015","cited_arxiv_id":null,"evidence_quote":"Provides the current shortest known 2+2 quadruple outer period (BU CMi), the benchmark against which these periods are ranked."}],"review_version":1}