{"id":"c3095291-d793-4da8-8bcf-3614a54056d6","arxiv_id":"2601.13302","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"About 7.6% of hot Jupiters have a close-in transiting companion, setting a lower limit on the fraction that formed via gentle disk migration or in situ.","lead":"Hot Jupiters are giant planets orbiting very close to their stars; this paper searched thousands of them for small neighboring planets and found about 8% have one. The result helps distinguish gentle disk migration from violent high-eccentricity migration in hot Jupiter formation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline rate is conditional on a Rayleigh(1.8°) mutual-inclination prior; under isotropic mutual inclinations the same six detections imply ~37% rather than 7.6%, and the TTV cross-check is qualitative.","rationale":"The reader identified the mutual-inclination prior as the weakest assumption, and I agree. The paper is transparent about this sensitivity: §5.5 explicitly shows the rate under isotropic versus aligned priors, and the conclusions repeat that the result is highly sensitive to the inclination assumption. However, the quoted headline value is still presented as the occurrence rate, and the abstract's 'likely mostly aligned' claim rests on a qualitative TTV comparison rather than a joint statistical treatment. This is not a fatal flaw—the lower-bound interpretation ('at least 7.6%') is conservative in the sense that allowing misalignment only raises the rate—but it means the numerical claim should not be read as a prior-independent intrinsic occurrence rate. A hierarchical joint analysis of the transit detections and the TTV sample is the natural check. Since the reader's verdict was already CONDITIONAL with medium confidence, my read does not move the verdict; it reinforces the conditionality.","tokens_in":22377,"tokens_out":6294,"duration_ms":76175,"concrete_test":"Implement a hierarchical Bayesian model that jointly constrains η and the mutual-inclination distribution: put a log-uniform hyperprior on Fisher κ over, e.g., [10^-2, 10^4], a uniform prior on η, and compute the likelihood from (a) the six transit detections and non-detections across the 1849 searched hot Jupiter systems and (b) the Kepler TTV sample of Wu et al. (2023), using each method's actual selection function. Report the marginal posterior of η. If the 90% credible interval spans roughly 7%–30% or wider, the 7.6% headline is not robust; if it remains narrow and centered near 7.6%, the prior sensitivity is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central 7.6% occurrence rate is not measured independently of the mutual-inclination prior. Section 5.1 adopts ψ ∼ Rayleigh(1.8°) (Eq. 12c) from Kepler small-planet systems, but hot Jupiters are precisely the population whose dynamical history—and hence mutual inclination distribution—is under test. Section 5.5 shows that the effective sample size changes from n≈89 for well-aligned companions to n≈17 for isotropic mutual inclinations, moving the median rate from 7.4% to 37%. The quoted (7.6 +5.5/−3.8)% is therefore a posterior conditioned on an informative prior, not an intrinsic rate marginalized over the unknown alignment distribution. The §6.2 comparison with the TTV-derived rate (12±6%, Wu et al. 2023) is acknowledged by the authors as 'not directly comparable': the TTV sample is mass-selected over period ratio ≈1.5–4, while this search is radius-selected over 0.25–10 d, so the comparison does not quantitatively pin down the mutual-inclination distribution. Because the headline claim changes by a factor of five across plausible priors, and because the paper itself flags this sensitivity in §5.5 and §7, this is the most load-bearing unaddressed uncertainty.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper searches the first five years of TESS data for short-period transiting companions (0.25 d ≤ P < 10 d, 1 ≤ R_p/R⊕ < 4) to a sample of ~1850 hot Jupiters, using a uniform BLS pipeline, manual vetting, and injection-recovery simulations. From six detections, it derives an occurrence rate of (7.6+5.5/−3.8)% using a beta-binomial posterior with an effective sample size corrected for detection efficiency and false-positive rate. The authors argue this is a lower limit on the fraction of hot Jupiters formed by dynamically quiet mechanisms, compare the rate with a TTV-based estimate to argue that hot Jupiters are mostly aligned with their companions, and assemble evidence that these systems may also host cold outer companions. The paper is careful in its search methodology and completeness treatment, but the headline rate depends strongly on the assumed mutual-inclination prior, and the treatment of known missed companions raises a potential bias.","tokens_in":22780,"tokens_out":8936,"duration_ms":95938,"significance":"If the result holds, this is the largest and most complete measurement of the occurrence rate of nearby companions to hot Jupiters, directly constraining hot Jupiter formation pathways: at least ~8% of hot Jupiters must have formed without dynamically disruptive high-eccentricity migration, and the true fraction could be several times larger after accounting for companion survival. The paper's uniform search, explicit detection-efficiency calibration, and sensitivity analysis are valuable contributions. The main strengths are the large sample (1849 systems), the injection-recovery-based completeness characterization, and the transparent exploration of the mutual-inclination dependence (Section 5.5). The principal weakness is that the headline number is conditional on an externally adopted prior (Rayleigh(1.8°)) that is not independently constrained for hot Jupiters; under an isotropic prior the same detections imply 37%. The paper also excludes known real companions from the detection list because the pipeline missed them, which biases the numerator. These issues must be addressed before the result can be taken at face value.","major_comments":[{"comment":"The headline occurrence rate (7.6+5.5/−3.8)% is conditional on the mutual-inclination prior ψ∼Rayleigh(1.8°) in Eq. (12c). Section 5.5 shows that replacing this with an isotropic Fisher prior (κ→0) changes the effective sample size from n≈89 to n≈17 and the inferred rate to (37+19/−17)%. Because hot Jupiters are the population whose dynamical history is under test, adopting the alignment distribution from Kepler small-planet systems is not a benign assumption. The abstract and §5.4 quote the conditional number as the occurrence rate, while §7 acknowledges the sensitivity. The TTV comparison in §6.2 is explicitly 'not directly comparable' (mass-selected, period ratio 1.5–4), so it does not independently pin down the alignment distribution. Please either marginalize over the mutual-inclination parameter (e.g., with a hyperprior) or present the headline as conditional and move the sensitivi","section":"§5.1, §5.5, Fig. 7"},{"comment":"WASP-47 e/d and TOI-4468.02 are real nearby companions in sample hosts (WASP-47 b and TOI-4468.01) that were not detected by the pipeline, and the paper states they 'will not count as detections.' This is not a neutral choice. If these planets fall within the search's period (0.25–10 d) and radius (1–4 R⊕) bounds, they should contribute to the numerator s in Eq. (11). Their exclusion biases the occurrence rate low, and the pipeline's failure to recover them is a direct calibration point for the detection efficiency in §3.4 that should be folded into the completeness estimate. Please re-run the analysis with known companions counted as detections (and the missed-known-companion rate used to validate or revise the gamma-CDF), or provide a quantitative justification for their exclusion.","section":"§4"},{"comment":"The gamma-CDF parameters in Eq. (10) are quoted to 8 decimal places with no uncertainties, and the ESS=92.50 in §5.3 is treated as fixed in the beta posterior Eq. (11). The detection efficiency at low S/N is steep and estimated from a finite number of injections; the fit uncertainty should propagate into the final credible interval. As written, the quoted 90% interval is conditional on the efficiency curve being known exactly. Please propagate the injection-recovery uncertainty (e.g., via bootstrap or MCMC over the gamma parameters) or demonstrate quantitatively that it is negligible compared with the binomial uncertainty.","section":"§3.4, §5.3, Eq. (10)"},{"comment":"The abstract states that comparing with TTV-derived rates 'suggests that hot jupiters are likely mostly aligned with their nearby companions,' but §6.2 acknowledges the TTV rate 'is not directly comparable' because it is mass-selected over period ratio ≈1.5–4 while this search is radius-selected over 0.25–10 d. The two rates can differ substantially even for a fixed intrinsic alignment distribution because of these selection differences. Since this comparison is the only quantitative argument against the isotropic-prior case (37%), the conclusion of alignment is stronger than the evidence. Please either develop a joint likelihood that accounts for the different selection functions or temper the abstract and conclusions accordingly.","section":"§6.2, Abstract"}],"minor_comments":[{"comment":"The parameters α, θ, C are given to eight decimal places and described as 'machine precision.' Report them with meaningful significant figures and uncertainties.","section":"Eq. (10)"},{"comment":"Typo: 'alerted on or before ut 2024 May 30' should be 'UTC 2024 May 30.'","section":"§2.1"},{"comment":"The subtraction of N_FP from both numerator and denominator assumes all eliminated targets are true false positives; this is reasonable but the uncertainty in the inferred FPR_HJ is not propagated. A simple sensitivity test would be useful.","section":"§2.2, Eq. (2)"},{"comment":"The grazing-transit analysis assumes R_p=1 R_J for all four grazing planets because their radii are poorly constrained. Since the conclusion is only a mild hint (Pr≈7.5%), this is acceptable, but the assumption should be stated as a potential source of systematic uncertainty in the p_i calculation.","section":"§6.3"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the scope of AJ and presents a substantial observational effort. The self-citations are numerous but appear to be used appropriately; they do not drive the result. The editor should ensure the authors address the conditional nature of the headline rate and the treatment of known non-detections, as these are load-bearing. The current abstract overstates the robustness of the 7.6% value and the alignment conclusion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is the largest uniform search to date for short-period transiting companions to hot Jupiters, and it mostly delivers what it promises. The sample is roughly ten times larger than the earlier Hord et al. estimate, the BLS search and injection-recovery are described carefully, and the beta-binomial framework is a sensible way to turn six detections into a rate. The new mutual-inclination sensitivity analysis and the grazing-transit hint are genuinely useful additions. I believe the central measurement is real and an improvement over what we had.\n\nThe soft spot is the one you already spotted: the headline 7.6% is not a direct measurement; it is a posterior conditioned on a Rayleigh(1.8 deg) mutual-inclination prior borrowed from Kepler small-planet systems. The paper itself shows in §5.5 that the effective sample size drops from 89 to 17 under isotropic mutual inclinations, and the rate jumps to 37%. It does not hide this, and the TTV comparison in §6.2 gives a qualitative argument against maximal misalignment. But that comparison is not directly comparable, as the authors admit—different period ranges, mass-selected versus radius-selected. So the reader walks away with one number, and that number is prior-dominated.\n\nA few smaller issues. The gamma-CDF completeness fit in Eq. (10) is quoted to many decimals with no uncertainty, and ESS=92.50 is treated as exact; these propagate directly into the credibility interval. The injection-recovery uses automatic ephemeris matching while the real search used manual vetting; the paper notes this but does not quantify how much the mismatch might bias the detection efficiency. And the FPR correction, though reasonable, relies on a single early estimate.\n\nNone of this is fatal. The paper's real contribution—the sample size and the careful completeness treatment—stands. The authors would need to either reframe the result as a function of the mutual-inclination prior, or marginalize over a wider range of priors and report the uncertainty that introduces. A referee should require that.\n\nYes, send this to peer review. It deserves serious refereeing, and the prior sensitivity is addressable rather than disqualifying. I would bring it to a reading group and likely cite it, at least for the new constraints and sample.","headline":"A careful, much larger TESS search for close-in companions to hot Jupiters gives a 7.6% occurrence rate, but the headline number is conditional on a well-aligned mutual-inclination prior—the same six detections imply ~37% under isotropic inclinations.","tokens_in":23389,"tokens_out":1314,"would_cite":true,"duration_ms":15826,"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":"At least about 8% of hot Jupiters carry a nearby small companion, implying a comparable fraction formed via calm disk migration or in situ rather than violent high-eccentricity migration.","keywords":["Hot Jupiters","exoplanet companions","occurrence rate","transit search","TESS","exoplanet migration","mutual inclination","planet formation"],"falsifier":"A transit-timing-variation survey of a complete, well-characterized sample of TESS hot Jupiters that measures the nearby-companion rate independently of transit geometry—or directly constrains the mutual-inclination distribution—would settle the claim. If such a survey found the true rate is consistent with ~7.6% only under an isotropic (maximally misaligned) inclination prior rather than the Rayleigh prior, the headline rate and its formation-channel interpretation would need revision.","tokens_in":22283,"feed_emoji":"🪐","tokens_out":4149,"duration_ms":42301,"temperature":0.7,"pith_summary":"Hot Jupiters were long thought to be loners: a close-in giant planet should eject any smaller neighbors during violent high-eccentricity migration. This paper searches five years of TESS light curves for small transiting planets near roughly 1,850 hot Jupiters, finds six such companions, and corrects for how many would be missed. The authors report an intrinsic occurrence rate of (7.6 +5.5/-3.8)% for nearby companions with periods 0.25–10 days and radii 1–4 Earth radii. Because high-eccentricity migration would destroy such companions, this rate is a strict lower limit on the fraction of hot Jupiters formed by disk migration or in situ assembly. The result matters because it turns a decades-old 'loneliness' argument—previously read as evidence for violent migration—into a quantitative formation-channel constraint.","feed_headline":"8% of hot Jupiters keep a nearby companion planet","feed_subtitle":"The rate is a floor on the share of hot Jupiters that formed quietly rather than by violent high-eccentricity migration.","key_machinery":"The analysis rests on a uniform BLS transit search whose detection probability is calibrated by injecting simulated planets into real TESS light curves and fitting the recovery fraction as a scaled gamma cumulative distribution function of transit signal-to-noise. Each hot Jupiter is treated as a Bernoulli trial; simulated companions drawn from priors on radius, period, and mutual inclination (Rayleigh with scale 1.8°, adopted from Kepler multi-planet systems) determine whether a companion would transit and be detected, yielding an effective sample size. The beta-binomial posterior then converts the six detections and effective sample size into the occurrence rate. The assumed mutual-inclina","core_discovery":"Using a uniform box least-squares search of TESS photometry (sectors 1–69) for transiting companions in 1,849 hot Jupiter systems, the paper detects six companions and models each hot Jupiter as a Bernoulli trial. After accounting for transit geometry, pipeline detection efficiency (from injection–recovery), and a ~6% false-positive rate among hot Jupiter candidates, the effective sample size is 87 trials. The resulting beta posterior gives a median occurrence rate of 7.6% with a 90% credible interval +5.5/-3.8 percentage points. The rate depends strongly on the assumed mutual inclination between the hot Jupiter and its companion: it rises to ~37% if companions are isotropically oriented and","pith_inferences":["If the mutual-inclination prior is ever measured directly—say, via combined transit-timing and Doppler data on the six systems—the same detections could yield a rate anywhere from ~7% to ~37%; the headline number is therefore as much a constraint on hot Jupiter–companion alignment as on formation fraction.","The grazing-transit signal, if confirmed with a larger sample, would suggest a population of hot Jupiters that experienced mild dynamical stirring—enough to tilt companion orbits slightly but not enough to eject them—fitting a 'gentle' high-eccentricity migration variant rather than pure disk migration.","A targeted search for ultra-short-period planets (P < 1 day) with a relaxed radius cut could test whether the companion population extends to very close-in, tidally evolved orbits, sharpening the formation-channel interpretation.","Applying the same uniform search to the full TESS dataset beyond sector 69 and to the extended mission should roughly halve the statistical uncertainty, since the current 90% interval is dominated by the small number of detections."],"forward_implications":["At least ~8% of hot Jupiters (about one in thirteen) must have formed by dynamically quiet pathways such as disk migration or in situ assembly, since high-eccentricity migration would remove inner companions.","Because disk-migration simulations suggest only about one-third of close companions survive, the observed rate is consistent with roughly 20% of hot Jupiters forming by disk migration—making quiet formation several times more common than the raw count implies.","The transit-based rate and the TTV-based rate can be reconciled only if hot Jupiters and their nearby companions are mostly mutually aligned, ruling out formation scenarios that produce nearly perpendicular orbits.","The apparent excess of grazing transits among the nine known hot Jupiter systems with nearby companions hints at a small systematic misalignment, possibly a dynamical remnant of migration.","Hot Jupiters with nearby companions appear to host cold outer companions at a rate similar to the general hot Jupiter population, complicating the simple picture that outer companions trigger high-eccentricity migration."],"fun_headline_variants":["7.6% of hot Jupiters host a nearby companion","Hot Jupiters with neighbors formed quietly, not violently","TESS survey: 7.6% of hot Jupiters have close companions","Rare companions reveal calm birth of some hot Jupiters","Nearby companions imply disk migration for 7.6% of hot Jupiters"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The headline 7.6% rate assumes the mutual inclination between a hot Jupiter and its nearby companion follows a narrow Rayleigh distribution with scale 1.8°, borrowed from Kepler's small-planet systems; if real hot Jupiter companions are more misaligned, the same detections imply a rate as high as ~37%.","fun_headline_variants_meta":{"raw":{"variants":["7.6% of hot Jupiters host a nearby companion","Hot Jupiters with neighbors formed quietly, not violently","TESS survey: 7.6% of hot Jupiters have close companions","Rare companions reveal calm birth of some hot Jupiters","Nearby companions imply disk migration for 7.6% of hot Jupiters"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000245,"raw_usage":{"total_tokens":1403,"prompt_tokens":803,"completion_tokens":600,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":547,"completion_tokens_details":{"reasoning_tokens":504}},"tokens_in":547,"tokens_out":600,"duration_ms":7480,"temperature":1.0,"reasoning_tokens":504,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T09:34:45.541065+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A transit-timing-variation survey of a complete, well-characterized sample of TESS hot Jupiters that measures the nearby-companion rate independently of transit geometry—or directly constrains the mutual-inclination distribution—would settle the claim. If such a survey found the true rate is consistent with ~7.6% only under an isotropic (maximally misaligned) inclination prior rather than the Rayleigh prior, the headline rate and its formation-channel interpretation would need revision.","supporting_citations":[],"review_version":1}