{"id":"d2602554-816b-4e1c-8851-06a81cbabffa","arxiv_id":"2412.02082","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"No short-period black hole companions were found among 250 followed-up TESS candidates, giving a 2-sigma upper limit below one such system per 100,000 solar-type stars.","lead":"This paper searched 4.7 million Sun-like stars observed by NASA's TESS satellite for close black hole companions, then followed up the 250 most promising candidates with spectroscopy. Finding none, the authors set a 2-sigma upper limit: fewer than one in 100,000 solar-type stars in the solar neighborhood hosts a black hole on an orbit shorter than about 3 days.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline 2-sigma upper limit is conditioned on an unquantified star-spot selection-efficiency systematic; a factor-of-2 reduction in S' moves the limit qualitatively.","rationale":"The paper is a careful observational upper limit with honest, clearly stated caveats, and the statistical machinery is transparent. The central claim, however, rests on the average selection efficiency S'_Overall, and the paper itself identifies a specific, demonstrated false-negative mechanism—the O'Connell effect causing stars with tidally locked spots to fail the a1>a2 cut—that can only reduce S'. By the authors' own admission, a factor-of-2 reduction would qualitatively change the quoted results, yet no systematic uncertainty is attached to S'_Overall in the headline 2-sigma limit. This is not an external or speculative concern: the paper cites three real systems of the relevant type that were removed by exactly this mechanism. Therefore the specific value '9.5e-6 at 2-sigma' is conditional on an unverified assumption about spot statistics. The strongest, most optimistic theoretical predictions are still robustly excluded even under a factor-of-2 efficiency loss, so rejection of the paper's central methodology is not warranted; however, the claimed 'challenge' to intermediate models at 1-2 sigma depends on the unquantified systematic. A concrete modification of the existing injection-recovery test would settle whether the concern lands. The reader's weakest_assumption identifies the same issue and correctly flags it; I therefore agree with the reader's CONDITIONAL verdict.","tokens_in":25962,"tokens_out":1796,"duration_ms":19328,"concrete_test":"Re-run the Section 6.2 injection-recovery pipeline after removing the a1>a2 cut and/or adding spot-modulated light-curve components calibrated to recover the three known Tucker/Rowan K-dwarf+WD systems as qmin candidates. Recompute S'_Overall and the 1/2/3-sigma fBH limits. If S'_Overall drops by more than ~2 (below ~0.09), the 2-sigma limit moves above ~2e-5 and the claimed tension with intermediate models is no longer significant.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central conversion from zero detections among 250 followed-up candidates to the headline fBH < 9.5e-6 (2-sigma) proceeds through the average selection efficiency S'_Overall = 0.18 (Eqs. 16-17, Table 5). Section 7.3 explicitly concedes that the O'Connell effect caused three real K-dwarf+white-dwarf binaries to fail the Paper I a1>a2 cut, that those systems would have entered the qmin>1 sample, and that a factor-of-2 reduction in S' would 'qualitatively change' the results. The quoted central limit does not include any inflation for this systematic. A reduction of exactly 2 in S' moves the 2-sigma limit from 9.5e-6 to 1.9e-5; a reduction of ~2.4 moves it above 2.3e-5. The most optimistic models (Masuda & Hotokezaka, Mashian & Loeb) are still rejected even with a factor-2 penalty, because they sit 3-7x above the limit; however, the paper's claim to 'challenge' Breivik/Wiktorowicz at 1-2 sigma, and the literal 'one in 10^5' framing, are not robust to this unquantified systematic. The secondary assumption that the observed 250 candidates fairly represent the 457 selected candidates via a single fobserved factor is weaker: follow-up prioritized brightness and mmmr membership, and no quantitative demonstration of representativeness is given, but the primary load-bearing concern remains the star-spot efficiency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper searches TESS light curves of 4.7 million AFGK-type stars from Paper I for ellipsoidal variability indicative of short-period (P_orb < 3 days) dark companions. Two selection methods (a qmin-based mass-function method and the MMMR method of Gomel et al.) produce 457 candidate BH companions. Spectroscopic follow-up of 250 candidates with NTT/INT RVs and Gaia RV data firmly excludes a high-mass dark companion in every case. Using injection-recovery tests with synthetic BH+MS light curves added to real TESS photometry, the authors measure an average selection efficiency S'_Overall = 0.18 and convert the zero detections into f_BH < 2.4e-6 (1σ), 9.5e-6 (2σ), and 21e-6 (3σ), under stated uniform priors on P_orb and q. They compare this limit to population-synthesis predictions and find that the most optimistic models are ruled out, while more recent, pessimistic models remain consistent with the limit.","tokens_in":26326,"tokens_out":8796,"duration_ms":89654,"significance":"If the headline limit is robust, it is a valuable new empirical constraint on the frequency of short-period dormant black hole companions to Sun-like stars, a quantity that population-synthesis models predict to span several orders of magnitude. The paper's strengths include the use of injection-recovery into real TESS light curves to measure selection efficiency, the cross-check of measured K amplitudes against Gaia RV data, and the presentation of a two-dimensional upper-limit map in M2 and P_orb that avoids some of the assumptions needed for the marginalized headline number. The main limitation is that the quoted one-in-10^5 upper limit is sensitive to an unquantified star-spot systematic that the authors themselves identify in Section 7.3, as well as to the assumed priors on P_orb and q; these issues do not undermine the method or the 2D map, but they require the headline claim to be conditioned or revised.","major_comments":[{"comment":"The paper itself states that the a1 > a2 cut removes genuine binaries exhibiting the O'Connell star-spot effect, that three published active K-dwarf plus white dwarf binaries would have been selected with qmin > 1 in the absence of this cut, and that a reduction of the selection efficiency by a factor of roughly 2 would 'qualitatively change' the results. Nevertheless, the central upper limits in Section 6.1 and the abstract (f_BH < 9.5e-6 at 2σ) do not include any allowance for this systematic. Since the headline claim rests directly on S'_Overall, the limit should be either inflated by a conservative spot-related systematic, presented as a band, or explicitly restated as conditional on the assumption that star spots reduce S' by less than a factor of 2.","section":"§7.3 (and §8)"},{"comment":"The factor fobserved is introduced in Eq. (14) but no value is ever stated; from Table 1 the reader must infer fobserved = 250/457. More importantly, Section 3 describes follow-up priority by MMMR membership and by brightness, so the 250 observed candidates are not demonstrated to be a random subset of the 457 candidates. A single scalar fobserved applied to the combined qmin and MMMR samples may therefore not equal the true observed fraction per selection method or per brightness bin. Please report fobserved explicitly, justify the representativeness assumption (for example by computing S' for the actual observed subset), or marginalize over the unknown fobserved.","section":"§6.1 (Eq. 14)"},{"comment":"The headline upper limit marginalizes over p(P_orb) uniform in 0-3 days and p(q) uniform in 1-30, but S_phys varies by more than an order of magnitude across the period range (Fig. 13 and Table 5). No sensitivity test to these prior choices is presented, so the abstract's 'fewer than one in 10^5' claim is conditioned on untested distributional assumptions. Please add a robustness check (for example a log-uniform P_orb prior or a period distribution matched to the known short-period binary population) and quote the resulting range of f_BH.","section":"§6.1 (Eq. 15)"}],"minor_comments":[{"comment":"The text says 60 targets were observed on NTT and INT, but the NTT and INT rows in Table 2 sum to 61; please correct the count or clarify overlaps.","section":"§3 / Table 2"},{"comment":"The Gaia variable name 'rv_ampltidue_robust' is a typo for 'rv_amplitude_robust'.","section":"§5.2"},{"comment":"The figure label 'Masuda (2019)' is inconsistent with the text citation 'Masuda & Hotokezaka (2019)'.","section":"§7.1 / Fig. 14"},{"comment":"The reference entry 'Mazeh, T., Faigler, S., Mazeh, T., & Faigler, S. 2010' duplicates author names; it should be corrected to cite the actual author list of the 2010 A&A paper.","section":"References"},{"comment":"The colorbar is labeled 'log(1σ upper limit)' while the text and caption describe two-dimensional upper limits more generally; please specify which confidence level is plotted.","section":"Fig. 11"}],"recommendation":"major_revision","confidential_remarks":"The star-spot systematic is acknowledged in the manuscript itself, so the requested revision is feasible without new observations: quoting a spot-inflated limit, reporting fobserved, and adding prior-robustness tests would make the headline claim solid. The paper is within scope for A&A and makes a useful contribution once the central upper limit is conditioned on its own stated systematics."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper delivers the first statistically grounded upper limit on short-period black hole companions to solar-type stars, and the core work is solid. From 4.7 million TESS targets the authors select 457 ellipsoidal candidates, follow up 250 with RVs (NTT/INT plus Gaia), find none consistent with a black hole, and then use injection-recovery through their actual BEER pipeline to turn that null into a completeness-corrected limit. The selection-function estimation is the real contribution: adding synthetic BH light curves to real TESS data and measuring how many survive each cut is the right way to make such a limit credible. The comparison to population-synthesis predictions in Fig. 14, with explicit caveats about converting literature predictions to a common metric, is fairly done. The authors also deserve credit for flagging their own main weakness in Section 7.3 rather than burying it.\n\nThe soft spots are real but not disqualifying. The star-spot systematic is the load-bearing one. The paper admits that a factor-of-2 reduction in selection efficiency S' would qualitatively change the results, yet the quoted 2-sigma limit of 9.5e-6 does not include any systematic inflation. A factor of exactly 2 moves that limit to 1.9e-5, which changes the \"one in 10^5\" headline to about one in 50,000. That is not a fatal flaw for the paper's central conclusion: even with a factor-2 penalty, the most optimistic models (Masuda & Hotokezaka, Mashian & Loeb) are still ruled out, and intermediate models are challenged at roughly the 1-sigma level rather than 1-2 sigma. But the headline number should be restated with this uncertainty built in, or the systematic should be quantified. The second issue is the follow-up completeness factor fobserved: 250 of 457 candidates were observed, with priority given to brightness and mmmr membership, and the paper does not demonstrate that the observed subset is representative. This is probably a minor effect, but it deserves a sentence or two more than it gets.\n\nI do not see circularity here. The priors on Porb and q are explicit modeling choices, and the limit is inverted from an observed null via a measured selection function. That is the standard logic. The paper is honest, clearly written, and the data products (RV tables, light-curve injections) are reproducible in principle.\n\nWho is this for? Anyone working on BH binary populations, TESS variability selection, or survey completeness methodology. It deserves a serious referee. My recommendation: accept after major revision, with the authors either quantifying the star-spot effect on S' or presenting the headline limit with an explicit systematic term. The science is good; the presentation of the central number needs to catch up with the caveats the authors already know about.","headline":"Careful upper-limit measurement; the headline 'one in 10^5' needs a systematic inflation before it is robust.","tokens_in":26863,"tokens_out":2773,"would_cite":true,"duration_ms":29691,"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":"Short-period black holes around Sun-like stars are rarer than optimistic models predict, the paper claims.","keywords":["black hole companions","ellipsoidal variability","TESS","solar-type stars","upper limits","stellar binaries","dormant black holes","population synthesis"],"falsifier":"A single confirmed short-period black-hole companion among the 207 unobserved candidates, or in a re-run of the same selection on the full 4.7-million-star TESS sample, would directly violate the limit at the claimed confidence. Conversely, an injection-recovery calculation that includes O'Connell-effect star spots and finds the selection efficiency drops by more than a factor of two would invalidate the $9.5\\times10^{-6}$ number.","tokens_in":25758,"feed_emoji":"🕳️","tokens_out":8412,"duration_ms":78082,"temperature":0.7,"pith_summary":"The paper tries to answer a census question: how often do Sun-like stars have a black hole companion on a very short orbit, under about three days? It argues that the answer is almost never: after hunting through TESS light curves of 4.7 million AFGK-type stars for the tidal 'ellipsoidal' distortion a dark massive companion would imprint, and following up 250 of the 457 most promising candidates with spectroscopy, none is consistent with a black hole. From this non-detection the paper derives a 2-$\\sigma$ upper limit of $9.5\\times10^{-6}$ on the fraction of solar-type stars with such a companion, tightening to about $1\\times10^{-6}$ near one-day orbits. If correct, this rules out the most optimistic population models and shows that short-period dormant black holes are not hiding in large numbers around Sun-like stars.","feed_headline":"Fewer than one in 100,000 Sun-like stars host close black holes","feed_subtitle":"Spectroscopic follow-up of 250 TESS candidates found none, ruling out optimistic predictions.","key_machinery":"The engine is the ellipsoidal amplitude $A_\\mathrm{ell}$: the photometric variation at twice the orbital period caused by tidal distortion. Under the assumption that all light comes from the primary star, the amplitude formula links $A_\\mathrm{ell}$ to the mass ratio $q=M_2/M_1$, and the ellipsoidal mass function $\\mathcal{M}_\\mathrm{ell}=\\sin^2 i\\, q/(q+1)$ yields a lower limit $q_\\mathrm{min}$ that can exceed unity only for a dark, high-mass companion. Candidate selection used $q_\\mathrm{min}>1$ for periods above one day and the alternative MMMR statistic for shorter periods, with by-eye eclipse checks to remove contact binaries. The calculation is carried by injection-recovery simulations that add synthetic black-hole binary light curves to real TESS light curves, measuring an average selection efficiency $\\bar{S}'=0.18$; the upper limit then follows from inverting the expected number and applying a Wilson score interval.","core_discovery":"The central discovery is a null result with a number attached. For orbital periods below three days, black hole companions to AFGK main-sequence stars exist in at most $9.5\\times10^{-6}$ of such stars at 2-$\\sigma$ confidence, and at most $1\\times10^{-6}$ when the period is close to one day, under the paper's fiducial priors on companion mass and period. The claim is established by combining the photometric selection of ellipsoidal binaries (the tidal deformation of the visible star where a compact companion's gravity modulates its projected area) with a measured selection efficiency from injection-recovery simulations, and then using the absence of any innocent explanation among 250 spectroscopically observed candidates to invert the expected count. The paper presents this as the strongest direct constraint yet in this period range, and notes it is in tension with predictions as high as one in $10^{4-5}$ stars.","pith_inferences":["Editorial inference: if this limit survives, binary population synthesis must be tuned so that the vast majority of massive stars with low-mass companions either merge, are disrupted, or avoid shrinking to $P<3$ days; the bottleneck is the survival fraction, not the survey volume.","Editorial inference: the star-spot caveat cuts both ways; a future injection-recovery calculation that includes explicit O'Connell-effect spot signals could find that the true sensitivity is lower than $\\bar{S}'=0.18$, which would push the upper limit upward.","Editorial inference: the same TESS dataset could be re-mined with the $q_\\mathrm{min}$ method extended below one day and with less aggressive amplitude cuts; any recovered candidates would directly test the limit rather than assuming it.","Editorial inference: the comparison to X-ray binaries implies that the detached, pre-mass-transfer phase of black-hole low-mass binaries is not enormously longer than the accreting phase, otherwise more non-accreting systems would have been found."],"forward_implications":["The most optimistic published population models, predicting $10^{-4}$ to $10^{-5}$ short-period black-hole companions per solar-type star, are excluded at the 2-3 sigma level.","More pessimistic recent models at $10^{-7}$ to $10^{-8}$ remain consistent but untestable with current data; reaching them would need a survey 30 to 100 times larger than the 4.7 million stars processed here.","The space density of non-accreting short-period binaries cannot exceed the space density of accreting low-mass X-ray binaries by more than about two orders of magnitude.","At periods near one day the limit tightens to $\\lesssim 10^{-6}$, so the absence is most severe exactly where the ellipsoidal signal is strongest.","Future searches should focus on the $q_\\mathrm{min}$ method and on less strict harmonic cuts, because the MMMR method has very low completeness for black-hole companions."],"supporting_citations":[{"why":"Supplies the 4.7-million-star input sample, the BEER selection of about 15,000 ellipsoidal binaries, and the completeness and purity estimates on which the efficiency calculation builds.","marker":"Paper I (Green et al. 2023)"},{"why":"Introduces the BEER algorithm that fits beaming, ellipsoidal, and reflection signals; the ellipsoidal amplitudes analyzed here come from this algorithm.","marker":"Faigler & Mazeh (2011)"},{"why":"Derives the ellipsoidal amplitude formula used in Equation 1 to relate photometric amplitude to mass ratio.","marker":"Morris & Naftilan (1993)"},{"why":"Defines the MMMR statistic and the C-factor correction; the second candidate-selection channel and the discussion of qmin limitations rest on this work.","marker":"Gomel et al. (2021b)"},{"why":"Provides the stellar parameter tables used to convert effective temperature into mass and radius for the qmin calculation and for simulated host stars.","marker":"Pecaut & Mamajek (2013)"},{"why":"TESS Input Catalogue version 8 supplies the effective temperatures and magnitudes for the input sample and the followed-up targets.","marker":"Stassun et al. (2019)"},{"why":"Three active K-dwarfs with white-dwarf companions were removed by the a1>a2 cut, demonstrating the O'Connell-effect false-negative channel that could suppress the selection efficiency.","marker":"Tucker et al. (2024); Rowan et al. (2024)"},{"why":"Predicts 400-450 detectable black-hole low-mass binaries in TESS; its optimistic rate is the main comparison model ruled out by the limit.","marker":"Masuda & Hotokezaka (2019)"},{"why":"Provides the score-interval counts (1.0, 3.9, 8.7) used to convert the zero detections into 1, 2, and 3 sigma upper limits.","marker":"Wilson (1927)"},{"why":"Gives the space density of black-hole low-mass X-ray binaries used to bound the non-accreting-to-accreting ratio.","marker":"Corral-Santana et al. (2016)"}],"fun_headline_variants":["No close black holes around Sun-like stars: <1 in 100,000","Upper limit on close black holes: <0.001% of Sun-like stars","Sun-like stars with black hole companions: <1 per 100,000","TESS null: fewer than 1 in 100,000 Sun-like stars host black holes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quoted upper limit assumes that unmodeled star-spot variability does not reduce the measured selection efficiency by more than about a factor of two, and that the 250 candidates actually followed up fairly represent the 457 selected candidates; if either assumption fails, the limit is too strong.","fun_headline_variants_meta":{"raw":{"variants":["No close black holes around Sun-like stars: <1 in 100,000","Upper limit on close black holes: <0.001% of Sun-like stars","Sun-like stars with black hole companions: <1 per 100,000","TESS null: fewer than 1 in 100,000 Sun-like stars host black holes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001282,"raw_usage":{"total_tokens":5271,"prompt_tokens":1005,"completion_tokens":4266,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":621,"completion_tokens_details":{"reasoning_tokens":4177}},"tokens_in":621,"tokens_out":4266,"duration_ms":28652,"temperature":1.0,"reasoning_tokens":4177,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:51:37.420392+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A single confirmed short-period black-hole companion among the 207 unobserved candidates, or in a re-run of the same selection on the full 4.7-million-star TESS sample, would directly violate the limit at the claimed confidence. Conversely, an injection-recovery calculation that includes O'Connell-effect star spots and finds the selection efficiency drops by more than a factor of two would invalidate the $9.5\\times10^{-6}$ number.","supporting_citations":[{"cited_title":"& Mazeh, T","cited_arxiv_id":null,"evidence_quote":"Introduces the BEER algorithm that fits beaming, ellipsoidal, and reflection signals; the ellipsoidal amplitudes analyzed here come from this algorithm."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the ellipsoidal amplitude formula used in Equation 1 to relate photometric amplitude to mass ratio."},{"cited_title":"& Hotokezaka, K","cited_arxiv_id":null,"evidence_quote":"Predicts 400-450 detectable black-hole low-mass binaries in TESS; its optimistic rate is the main comparison model ruled out by the limit."},{"cited_title":"1927, Journal of the American Statistical Association, 22, 209","cited_arxiv_id":null,"evidence_quote":"Provides the score-interval counts (1.0, 3.9, 8.7) used to convert the zero detections into 1, 2, and 3 sigma upper limits."}],"review_version":1}