{"id":"0a8235e7-e2a2-4b40-b39c-232ce9e6d851","arxiv_id":"2603.25065","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Allowing non-parabolic orbits in TDE light-curve fitting changes inferred black-hole masses and yields first eccentricity measurements for 30 ZTF tidal disruption events.","lead":"This paper fits 30 tidal disruption events with a model that lets the disrupted star arrive on any orbit, not only a parabolic one. It finds the inferred black-hole mass shifts by factors that depend on the star's orbital energy, and it uses the fitted orbits to study how the stars originally got close to the black hole.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The M_BH bias and e measurements hinge on Eq. (1), the rigid-shift assumption for dm/dε, which is not tested against hydro simulations; if the shape or width of the debris energy distribution depends on orbital energy or β, the central claim could be a model artifact.","rationale":"Reader's weakest assumption is exactly the one I find most load-bearing. The paper's central claim is that parabolic fits bias M_BH, and that 90% of ZTF-I TDEs are eccentric. Both statements require ε~_orb to be a real physical quantity. That is only true if Eq. (1) correctly captures how orbital energy alters the debris distribution. The rigid shift is a convenient ansatz, not a result. A hydro test would settle whether the ansatz holds; if it fails, the e values and the M_BH bias curve are artifacts, and the conclusions about TDE origins (six outliers, etc.) also collapse. I considered the lack of independent M_BH comparison as an alternative concern, but that test would be secondary: even if non-parabolic masses matched independent estimates, it would not validate the physical interpretation of ε~_orb without the hydro check. Conversely, a failed hydro check would invalidate the central claim regardless of any external agreement. Hence the hydro comparison is the single most load-bearing check. The reader's conditional verdict is appropriate; I do not see grounds to move it.","tokens_in":14351,"tokens_out":9140,"duration_ms":84207,"concrete_test":"Use a hydrodynamics code (e.g., the one used to generate the GR2013 library) to simulate full disruptions (β ≈ 1) of the same stellar model on orbits with ε_orb/Δε = -0.5, -0.25, 0, +0.25. Measure the debris energy distribution dm/dε and compare it to the rigid-shift prediction from the β=1 parabolic run. Quantify differences in the most-bound energy, width, and skewness. If these differences exceed ~10% of Δε — the claimed bias scale from Eq. (9) — the model's e values and M_BH corrections are not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (1) constructs the non-parabolic debris distribution as dm/dε(ε) = [dm/dε]_{e=1}(ε - ε_orb), i.e., a rigid shift of the parabolic distribution with unchanged width and shape. This single assumption feeds everything: the fitted scaled orbital energy ε~_orb, the eccentricities in Table 2, the β values, and the predicted M_BH correction M_BH ∝ (1-ε~_orb)^{17/5}. The paper does not test the assumption against the hydrodynamical simulations from which the parabolic library is drawn, nor against Hayasaki et al. (2018) N-body results. The GR2013 library itself shows that the debris energy distribution depends on the penetration factor β, and the authors acknowledge in §3.1 that β-dependent shape changes are omitted from the scaling argument. If, for a fixed β, the width or asymmetry of dm/dε changes with ε_orb — e.g., because the compression and shock heating at pericenter depend on the incoming orbital energy — then ε~_orb and e are not physical measurements. The 90% eccentricity claim and the direction of the M_BH bias are then properties of the rigid-shift ansatz, not of the observed TDEs. The problem is not that the ansatz is unconventional; it is that the central quantitative claims (bias magnitude and e distribution) inherit its validity, and no independent check is provided.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends a previous fallback-based TDE light-curve model (Zhong 2025) by adding the scaled orbital energy of the disrupted star, tilde_epsilon_orb, as a free parameter. The non-parabolic debris distribution is constructed by rigidly shifting the parabolic dm/dε curve from the Guillochon & Ramirez-Ruiz (2013) library by ε_orb. The model is fit to 30 ZTF-I TDEs and compared with parabolic fits (tilde_epsilon_orb = 0). The authors claim that parabolic models systematically underestimate M_BH for eccentric events and overestimate it for hyperbolic events; that most of the sample (24/30 or ~90%) is on eccentric orbits with e < 1; and that six high-β, e<1 events cannot be explained by two-body relaxation in spherical nuclear star clusters. The paper also derives an analytic mass-biasing relation M_BH ∝ (1−tilde_epsilon_orb)^{17/5}.","tokens_in":14769,"tokens_out":11119,"duration_ms":116209,"significance":"If the rigid-shift assumption and the fits are valid, the paper would establish an important systematic correction for TDE black-hole mass measurements and would open the orbital eccentricity of disrupted stars as a new observable diagnostic for stellar dynamics in galactic nuclei. The use of a public fallback library, the explicit analytic scaling, and the W-AIC model comparison are useful and transparent elements. However, the central physical claim is conditional on one unvalidated ansatz, and there is a load-bearing algebraic inconsistency in the printed eccentricity mapping. The e−β population discussion is interesting but would need to be re-evaluated after the parameter mapping is fixed.","major_comments":[{"comment":"The printed relation tilde_epsilon_orb = −β(1−e)/(2 q^{1/3}) is algebraically wrong. With r_t = r_*(M/m_*)^{1/3}, Δε = GM r_*/r_t^2, and ε_orb = −GM(1−e)β/(2 r_t), the correct expression is tilde_epsilon_orb = −β(1−e) q^{1/3}/2. Eq. (7) repeats the denominator error. Table 2 confirms the correct numerator form: AT 2018hco has log M=6.98, m_*=0.24, β=0.97, e=0.9983, which under the printed formula would give tilde ~ −2×10^{-6}, not the reported −0.28. The numerical example also states q=100 for a 10^6 M_sun BH and a 1 M_sun star; q should be 10^6. Since e and β are derived from this mapping, this must be corrected and the code/printed formulas reconciled before the fitted eccentricities can be trusted.","section":"§2, Eqs. (4) and (7); Table 2"},{"comment":"The model consists of taking the parabolic debris energy distribution from Guillochon & Ramirez-Ruiz (2013) and rigidly shifting it by ε_orb, preserving the width and shape unchanged. No test from hydrodynamical or N-body simulations is given for how the debris energy distribution changes with the incoming orbital energy at fixed β, even though the same library shows strong β-dependent shape changes. If the width or asymmetry of dm/dε depends on ε_orb — for example because pericenter compression and shock heating depend on orbital energy — then the fitted tilde_epsilon_orb, e, β, and the claimed M_BH bias in §3.1 are properties of the ansatz, not of the observed TDEs. A validation run against existing simulation suites (e.g. Hayasaki et al. 2018) or an explicit controlled test should be added.","section":"§2, Eq. (1)"},{"comment":"The relation M_BH ∝ (1−tilde_epsilon_orb)^{17/5} is derived from the same simplified uniform-dm/dε fallback model family that motivates the fits. The approximate agreement of the 30 data points with this curve in the lower panel of Fig. 2 is therefore partly a self-consistency check of the analytic degeneracy of the assumed fallback model, not independent empirical confirmation of the physical bias. The paper should label this as a model-consistency check and strengthen it with an external test, for example fitting synthetic light curves generated with a known input ε_orb and checking recovery.","section":"§3.1, Eq. (12) and Fig. 2"},{"comment":"The text argues that ε_orb is dynamically fixed and independent of M_BH and m_*, yet the fitting parameter is tilde_epsilon_orb = ε_orb/Δε(M_BH, m_*) with a flat prior. This induces an M- and m-dependent effective prior on ε_orb itself. The inferred eccentricity distribution — including the 90%-e<1 claim in §3.1 — may therefore be prior-driven. Please justify this parameterization or report a robustness test where ε_orb is sampled directly or with a physically motivated prior.","section":"§2, treatment of tilde_epsilon_orb"},{"comment":"The model comparison is presented only through W-AIC scores. The reported W-AIC differences are small for many events, and the paper claims that the non-parabolic model is preferred only for a few objects. In this situation the mass-bias and eccentricity results could be sensitive to the intrinsic scatter term σ, the binning procedure, and the chosen prior ranges. It would strengthen the paper to show posterior distributions or at least a corner-plot example for representative events to demonstrate that the parameters are constrained by the data rather than by prior boundaries.","section":"§3, Tables 2–3 and W-AIC comparison"}],"minor_comments":[{"comment":"The note misidentifies the columns: it says \"the sixth column is the scaled penetration factor b and eighth column is the penetration factor. The eighth column is the W AIC score.\" The table layout shows b, β, and W-AIC in columns 6, 7, and 8; the note should be corrected.","section":"Table 2 note"},{"comment":"For a 10^6 M_sun BH and a 1 M_sun star, q=10^6, not q=100. With the corrected q^{1/3} factor, the stated fractional difference of order 0.1 follows; as printed the numbers do not. Please fix the text and re-check other numerical statements that depend on this example.","section":"§2.1, numerical example"},{"comment":"Eq. (9) should use the corrected q^{1/3} factor from Eq. (4). If the printed Eq. (4) is corrected to q^{1/3} in the numerator, the right-hand side of Eq. (9) must be updated consistently.","section":"Eq. (9)"},{"comment":"There are small formatting issues in the reference list (e.g., \"V .\" with an extra space in several author names). The figures are not embedded in the provided text, so their quality and axis labels could not be checked; please ensure they are complete in the submitted version.","section":"References and figures"}],"recommendation":"major_revision","confidential_remarks":"The paper has a useful idea and an interesting application, but the printed Eq. (4) error is load-bearing because every eccentricity and β posterior uses that mapping. The deeper risk is the unvalidated rigid-shift assumption in Eq. (1); if the debris energy distribution changes shape with ε_orb, the main conclusion becomes a model artifact. I would require either a hydro/N-body validation or a clear repositioning of the results as conditional on the ansatz before accepting. The e−β discussion is worth keeping, but it should be repeated after the parameter mapping is fixed and the prior treatment of tilde_epsilon_orb is clarified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Shiyan,\n\nThe paper is a legitimate extension: it takes the shifted-energy debris model from Zhong (2025), applies it to 30 ZTF TDEs, and gets the first eccentricity measurements for that sample. The e-β plane comparison to the Zhong et al. (2023) boundary is a smart way to use the model, and the analytic scaling M_BH ∝ (1−ε̃_orb)^{17/5} is a useful heuristic. The authors are honest that W AIC doesn't strongly prefer the non-parabolic model for most events.\n\nThe soft spots are real. First, Eq. 4 as printed has q^{1/3} in the denominator; the correct expression (consistent with Eq. 7 and the Table 2 fits) has q^{1/3} in the numerator. That's a typo, but confusing. Second, the central assumption — Eq. 1, that the non-parabolic debris distribution is just the parabolic one shifted by ε_orb — is never tested against hydro simulations. The paper acknowledges the debris shape depends on β, but doesn't check whether the width or shape changes with orbital energy. For a typical event with |ε̃_orb| ~ 0.1 the shift is a modest correction, but for AT2020riz with ε̃_orb ~ −0.9 it's a huge shift, so the inferred e and mass bias could be model artifacts in that regime. Third, the confirmation of the analytic scaling in the fits is partly a check that the fitting code reproduces the model's degeneracy, not an independent physical validation. Fourth, the 'systematically underestimate' language is stronger than the evidence: the comparison is internal to the model, with no independent mass estimates, so the difference is better described as a model-dependent shift than a bias. Fifth, no code or data are released, which makes it hard to reproduce the fits.\n\nDespite these problems, the paper deserves a serious referee. The idea is sensible, the sample application is new, and the e-β diagnostic is worth discussing. A revised version that fixes the typo, tests the shift assumption against simulations (or at least limits the range of validity), adds external M_BH comparisons, and releases fitting code would be a solid contribution. I'd send it to review as is, expecting major revision.","headline":"A useful but incomplete extension of the Zhong (2025) model to 30 ZTF TDEs; the e-β diagnostic is new, but the mass-bias claim rests on an untested rigid-shift assumption and Eq. 4 has a typo.","tokens_in":15264,"tokens_out":9319,"would_cite":true,"duration_ms":79586,"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":"For most tidal disruption events, modeling the star's orbit as parabolic systematically underestimates the host black hole mass.","keywords":["tidal disruption events","black hole masses","orbital eccentricity","mass fallback rate","light curve fitting","supermassive black holes","nuclear star clusters","non-parabolic model"],"falsifier":"Run a hydrodynamical simulation of a star disrupted on an eccentric orbit with known parameters, apply the model's shifted-distribution equation to predict the debris spread, and check whether the recovered scaled orbital energy matches the input. Alternatively, take a TDE with an independently measured host black hole mass: if the event is classified as eccentric, the parabolic-fit mass should be lower than both the non-parabolic mass and the independent mass.","tokens_in":14230,"feed_emoji":"🌌","tokens_out":5163,"duration_ms":56930,"temperature":0.7,"pith_summary":"The paper claims that the standard assumption of a parabolic orbit in tidal disruption event (TDE) light-curve fitting is not just a numerical convenience but a source of systematic error. It constructs a model in which the disrupted star's specific orbital energy is a free parameter, shifting the debris energy distribution, and fits it to 30 optically discovered TDEs. The central result is a bias: parabolic fits underestimate black hole mass for eccentric orbits and overestimate it for hyperbolic orbits, with a derived scaling M_BH proportional to (1 - tilde_epsilon_orb)^(17/5). Most of the sample (27 out of 30) is inferred to be on eccentric orbits, implying that many black hole masses measured with parabolic fits may be too low. The paper also uses the eccentricity-penetration plane to argue that most events are consistent with two-body relaxation, with six outliers suggesting other dynamical channels.","feed_headline":"Eccentric orbits bias black hole masses from tidal disruptions","feed_subtitle":"Including orbital energy as a free parameter changes black hole mass estimates for 30 events.","key_machinery":"The central object is the shifted debris mass distribution, written as dm/depsilon(epsilon) = (dm/depsilon)_parabolic(epsilon - epsilon_orb). The paper parameterizes this using the scaled orbital energy tilde_epsilon_orb = epsilon_orb / Delta_epsilon, where Delta_epsilon is the typical half-width of the parabolic debris energy spread. This shift changes the fraction of bound debris and the timescale of the most-bound debris; by requiring the mass fallback rate to have the same peak and timescale under both models, the paper derives the scaling M_BH proportional to (1 - tilde_epsilon_orb)^(17/5).","core_discovery":"On the paper's own terms, the discovery is that the orbital energy of the disrupted star must be included in TDE light-curve modeling if black hole masses are to be trusted. The non-parabolic model replaces the parabolic debris mass distribution with a shifted version, adding the scaled orbital energy tilde_epsilon_orb as a fitting parameter. Applied to 30 events, the recovered black hole masses depend strongly on this parameter, following the analytic relation M_BH proportional to (1 - tilde_epsilon_orb)^(17/5); eccentric-orbit events need larger masses than parabolic fits give, while hyperbolic events need smaller ones. Since 90% of the sample has eccentricity less than unity, with deviati","pith_inferences":["Extending the paper's logic, previously published TDE-based black hole mass scaling relations may be systematically underestimated if TDEs are preferentially drawn from slightly bound orbits.","The same shifted-distribution machinery could unify single and repeated partial TDEs by treating orbital energy as a continuous parameter rather than fixing parabolicity.","A direct check would combine this model with independently measured host black hole masses for a few events: for an eccentric event, the parabolic mass should fall below the independent mass while the non-parabolic mass should agree.","If future hydrodynamic simulations show that the debris energy spread or shape depends on orbital energy or penetration depth, the recovered tilde_epsilon_orb values would become model artifacts rather than physical measurements."],"forward_implications":["Parabolic-fit black hole masses for eccentric TDEs are biased low, with a correction factor on the order of (1 - tilde_epsilon_orb)^(-17/5).","If most TDEs are on slightly eccentric orbits, population-level black hole mass estimates from TDE light curves are likely shifted downward.","TDE light-curve fitting can now deliver orbital eccentricity measurements, opening a new observational window into loss-cone dynamics.","The eccentricity-penetration plane can separate standard two-body relaxation production from other mechanisms; the six high-penetration outliers motivate alternative formation channels.","For hyperbolic-orbit events, parabolic fits overestimate the black hole mass, so the sign of the bias depends on whether the star was bound or unbound."],"fun_headline_variants":["Orbital energy shifts black hole masses in tidal disruption fits","Parabolic fits bias black hole masses from tidal disruptions","New model corrects black hole masses for eccentric star orbits","Tidal disruption masses depend on star's orbital energy","Star's orbit changes black hole mass estimates in 30 events"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire analysis rests on the assumption that the mass distribution of debris from a non-parabolic disruption is exactly the parabolic distribution shifted rigidly by the star's orbital energy, with unchanged width and shape; if the energy spread or shape actually changes with orbital energy or penetration depth, the inferred orbital energies, eccentricities, and black hole mass biases would not be physical.","fun_headline_variants_meta":{"raw":{"variants":["Orbital energy shifts black hole masses in tidal disruption fits","Parabolic fits bias black hole masses from tidal disruptions","New model corrects black hole masses for eccentric star orbits","Tidal disruption masses depend on star's orbital energy","Star's orbit changes black hole mass estimates in 30 events"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000587,"raw_usage":{"total_tokens":2617,"prompt_tokens":790,"completion_tokens":1827,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":534,"completion_tokens_details":{"reasoning_tokens":1746}},"tokens_in":534,"tokens_out":1827,"duration_ms":14446,"temperature":1.0,"reasoning_tokens":1746,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T17:24:41.374849+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a hydrodynamical simulation of a star disrupted on an eccentric orbit with known parameters, apply the model's shifted-distribution equation to predict the debris spread, and check whether the recovered scaled orbital energy matches the input. Alternatively, take a TDE with an independently measured host black hole mass: if the event is classified as eccentric, the parabolic-fit mass should be lower than both the non-parabolic mass and the independent mass.","supporting_citations":[],"review_version":1}