{"id":"16d035ec-2069-480c-a77f-346612234184","arxiv_id":"2507.08082","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"SMBH binary-driven TDE rates increase with black hole mass and can explain the elevated rates in post-starburst galaxies, yielding testable redshift-dependent predictions for future surveys.","lead":"We simulated tidal disruption events around pairs of supermassive black holes and found that binaries disrupt stars at rates that rise with black hole mass, unlike single black holes. The result offers a way to infer hidden black hole binaries from TDE surveys like LSST and Roman.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The mass-increasing TDE rate trend for SMBH binaries is demonstrated only for q=100 and m1≤1e7; without a sensitivity scan and high-mass runs, the central demographic dichotomy and PSB match are not established.","rationale":"The paper is a plausible framework, not an established demographic law. The strongest supporting evidence is the OSPE simulation suite from the authors' prior work, but the new mass-dependent claim is constructed from only three primary masses and one mass ratio. The central sentence in Section 3 uses 'binaries' generically, yet Figure 2 and Appendix A restrict the simulated evidence to q=100. This is the least secure link because the enhancement mechanism (EKL plus two-body relaxation) is expected to be configuration-dependent. The reader identified this as the weakest assumption, and I agree. A second issue, that Equation (3) writes Gamma(z) without any redshift dependence in the mass function and may require an unstated evolving mass function, is real but downstream of the mass-rate curve, so I did not make it the primary concern. The correct response is to require a sensitivity scan and high-mass simulations before the claim can be accepted as representative. This leaves the verdict conditional; it does not reject the framework.","tokens_in":21639,"tokens_out":11028,"duration_ms":126399,"concrete_test":"Run the same OSPE setup (1000 systems, e_bin=0.5, a=0.5 Rsph, alpha=1, mstar=0.8) at m1 = 1e6 and 1e7 Msun for q = 1, 3, 10, 30, and 100, and compute the rate ratio gamma(m1=1e7)/gamma(m1=1e6). If the ratio is not >1 for q<100, the mass-increasing claim is an artifact of q=100. Then rerun m1=1e8 with q=100, applying the J_capture >= J_tidal cutoff for solar-type stars, and check whether the 1e8 point still lies in or above the observed PSB band; if it drops, the high-mass PSB agreement is an extrapolation artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Central claim (Section 3): binary TDE rates increase with disrupting SMBH mass, and 'our rate approaches that observed in PSB galaxies' for massive SMBHs. The simulated evidence (Appendix A, Figure 2) is restricted to q=m2/m1=100, e_bin=0.5, separation=0.5 Rsph, alpha=1, and m1=1e5-1e7 Msun. EKL-driven loss-cone refilling depends on companion mass and on the balance between EKL and GR precession, so the mass trend at q=100 need not hold for less extreme mass ratios; yet no sensitivity scan over q (or e_bin, separation, alpha) is reported. The later eta parameter (Section 4) is an envelope that folds in unknown fractions, not a test of the rate-mass curve. In addition, the figure's pink curve is drawn to 1e8 Msun while simulations stop at 1e7, and the text explicitly says the model does not include direct stellar capture; therefore the high-mass approach to the PSB rate is an extrapolation past a known physical cutoff. If real binaries have q~1-10, or if GR precession suppresses EKL at high m1, the claimed increasing-with-mass dichotomy could flatten or reverse.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper argues that TDE rates from SMBH binaries increase with the mass of the disrupting black hole, in contrast to the declining trend for single SMBHs, and that this can explain the elevated TDE rate observed in post-starburst galaxies. The authors use secular three-body simulations (OSPE) of the combined EKL and two-body relaxation mechanisms for a binary configuration with mass ratio q=100, eccentricity e_bin=0.5, separation 0.5 R_sph, and primary masses 1e5, 1e6, and 1e7 M_sun, then extrapolate the resulting rate-mass curve to 1e8 M_sun. They convolve this curve with the Merloni & Heinz (2008) SMBH mass function to predict the redshift-dependent volumetric TDE rate and event counts relevant for LSST and Roman. They also interpret the scatter in TDE light-curve durations as evidence that some TDEs are produced by the less massive member of an unresolved binary.","tokens_in":21969,"tokens_out":5547,"duration_ms":55041,"significance":"If the claimed mass-dependent dichotomy holds, it would provide a new demographic observable for identifying SMBH binaries and would offer a plausible explanation for the PSB TDE excess. The paper makes explicit, falsifiable predictions for upcoming surveys and usefully brings together light-curve timescale data and rate comparisons. However, the central result currently rests on a single simulated configuration and an extrapolation past both the simulated mass range and the direct-capture limit, so the significance is conditional on additional validation. The strong point of the manuscript is that it frames the result as a testable prediction rather than a post-hoc fit.","major_comments":[{"comment":"The pink curve in Figure 2, which carries the central claim, is not derived or tabulated in this paper; the simulations described in Appendix A cover only m1 = 1e5, 1e6, 1e7 M_sun with q=100, e_bin=0.5, separation=0.5 R_sph, alpha=1, and the curve is drawn to 1e8 M_sun. No sensitivity study over q, e_bin, separation, or alpha is presented, and the text states that the model does not include direct stellar capture. Because the EKL-driven rate depends on the balance between companion perturbations and general relativistic precession, the increasing-with-mass trend at q=100 need not hold for less extreme mass ratios or at high m1 where GR precession suppresses high-eccentricity excitations. The claim in Section 3 that the binary rate 'approaches that observed in PSB galaxies' for massive SMBHs is therefore an extrapolation past both the simulated mass range and a known physical cutoff. At minimum, the paper should tabulate the rate curve, justify the power-law extrapolation to 1e8 M_sun, and test the mass trend against variations in q and the other fixed parameters.","section":"Section 3, Appendix A, Figure 2"},{"comment":"The convolution in Equation (3), Gamma(z) = integral of (d2N/dV dlnM) gamma(M) dlnM, does not contain a binary fraction or a factor specifying what fraction of SMBHs are in binaries of the simulated configuration. As written, it appears to assume that every SMBH of mass M produces TDEs at the binary rate gamma(M), which is the eta=1 upper limit introduced only later in Section 4. The 'upper limit' interpretation of Figures 3 and 4 depends on this normalization; without a clear definition of gamma(M) (per binary? per unit SMBH? per galaxy?) and its relation to eta, the volumetric rates and cumulative event numbers are not uniquely defined. Please revise Equation (3) to include the binary fraction explicitly or state that the plotted curves are the eta=1 limit.","section":"Section 3, Equation (3)"},{"comment":"The parameter eta is introduced as an envelope that folds in unknown binary fractions and binary properties, but it does not test the rate-mass curve: the pink curve at eta=1 is simply the extrapolated curve from Figure 2, and the light blue line is a linear interpolation anchored at that point. The alignment with observed PSB fractions is therefore not independent evidence for the mass-dependent dichotomy. To make the PSB match convincing, the paper would need a scan over the simulation parameters (q, e_bin, separation, alpha) or a physical argument for why the chosen configuration is representative of the post-merger binary population.","section":"Section 4, Figure 4"}],"minor_comments":[{"comment":"The sentence stating that the binary-driven rates show 'only a modest difference between 10^7 M⊙ and 10^7 M⊙' appears to contain a typo; it should presumably read 'between 10^7 M⊙ and 10^8 M⊙.'","section":"Section 3"},{"comment":"The text refers to 'Equation B, in Appendix A' when presenting the single-SMBH rate; the reference should be to Equation (B1).","section":"Appendix B"},{"comment":"The pink curve is described as a 'predicted upper-limit TDE rate,' but the text does not define whether this is an upper limit per binary, per SMBH, or per galaxy; please clarify the normalization in the caption or in Section 3.","section":"Figure 2 caption"},{"comment":"The discussion of the asymmetric scatter in light-curve timescales would benefit from a quantitative statement of the fraction of TDEs falling in the blue-shaded region and a simple statistical test of whether that asymmetry is expected under the binary hypothesis.","section":"Section 2, Figures 1 and 5"},{"comment":"The tables have several formatting inconsistencies, including repeated reference entries and incomplete journal information for some references, which should be cleaned up before publication.","section":"Tables 1 and 2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript builds heavily on the authors' own prior work (Naoz et al. 2022; Melchor et al. 2024) for the central rate curve. This is legitimate, but the current paper should make the provenance of the pink curve in Figure 2 explicit and provide the underlying data or a fitting formula so that readers can assess the extrapolation. The extrapolation and lack of sensitivity analysis are substantial concerns that are addressable with additional simulations or a careful parameter scan; I therefore recommend major revision rather than rejection. The paper is within the journal's scope and the forward-looking predictions are valuable if the validation can be supplied."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The genuinely new piece is the demographic wrapper: convolving the binary-driven TDE rate with a SMBH mass function to get redshift-dependent predictions, and the eta framework that maps PSB fractions onto binary-fraction constraints. The underlying rate enhancement and its mass scaling come from the authors' earlier work (Melchor et al. 2024), and the paper says so. The light-curve asymmetry argument—short t1/2 and tau for masses derived from host scaling relations—is a useful observational handle and is the part I find most convincing.\n\nThe soft spot is load-bearing. The central rate-mass curve (pink line in Figure 2) is inherited, not derived or tabulated here, and rests on simulations at only three masses (1e5–1e7 Msun) with a fixed mass ratio q=100. The curve is then drawn to 1e8 Msun, past the point where the model itself says direct capture suppresses TDEs. No sensitivity scan over q, eccentricity, separation, or density slope is reported, so we have no way to know whether the increasing-with-mass trend survives for less extreme mass ratios. The text notes that the less-massive-primary configuration is chosen to avoid GR precession suppression, which makes q=100 a designed limit rather than a typical case. If the trend flattens or reverses for q~1–10, the claimed dichotomy and the PSB match both weaken.\n\nThe convolution in Equation (3) also uses the Merloni & Heinz (2008) mass function, which is a local measurement. The paper restricts to z<=2 but does not specify how the mass function evolves with redshift; that is a mismatch worth fixing. The eta parameter is honestly described as an envelope for unknown fractions, but it is a tuning knob, not a test.\n\nAll that said, the paper is transparent about its upper-limit framing and about the plunge cutoff, and the comparison with observed PSB rates is interesting even without error bars. The reader's conditional verdict is about right. This deserves a serious referee; the fixes are straightforward: show the underlying rate data, run a sensitivity scan over binary parameters, and either adopt an evolving mass function or justify the local one. For TDE theorists and survey forecasters, this is a useful framework to have on the record.","headline":"A useful demographic wrapper around an inherited binary-TDE rate curve whose mass dependence is only demonstrated for one extreme configuration; deserves review, but needs sensitivity analysis and an evolving mass function.","tokens_in":22477,"tokens_out":4058,"would_cite":true,"duration_ms":39759,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that tidal disruption event demographics can reveal hidden supermassive black hole binaries, because in binary systems the disruption rate rises with black hole mass while single black holes show the opposite trend.","keywords":["tidal disruption events","supermassive black hole binaries","eccentric Kozai-Lidov mechanism","TDE rates","post-starburst galaxies","redshift evolution","SMBH mass function","LSST"],"falsifier":"Measure the TDE rate as a function of host-derived SMBH mass in an LSST sample where binary companions have been independently identified: the paper predicts a plateau or rise from $10^6$ to $10^7\\,M_\\odot$ for binary hosts while single-SMBH models fall, so a monotonically declining rate in that range would falsify the central claim.","tokens_in":21425,"feed_emoji":"🕳️","tokens_out":4567,"duration_ms":48855,"temperature":0.7,"pith_summary":"This paper argues that the demographics of tidal disruption events can reveal whether a galaxy hosts a supermassive black hole binary. Using simulations of binaries that combine the eccentric Kozai-Lidov mechanism with two-body relaxation, it finds that binary systems disrupt stars at a rate that rises with the disrupting black hole's mass, opposite to the falling trend for single black holes. Convolving those mass-dependent rates with the supermassive black hole mass function yields redshift-dependent volumetric TDE rates, and the binary rates match the elevated rates observed in post-starburst galaxies. If correct, the mass and redshift dependence of TDEs becomes a testable demographic probe of unresolved black hole binaries for wide-field surveys.","feed_headline":"Binary black holes flip the TDE rate trend with mass","feed_subtitle":"Simulations predict more tidal disruptions around massive binaries, matching post-starburst galaxy rates and giving surveys a new probe.","key_machinery":"The central mechanism is the combined eccentric Kozai-Lidov plus two-body relaxation channel in an SMBH binary with a fixed extreme mass ratio ($q=100$), moderate eccentricity $e_{\\rm bin}=0.5$, separation set to half the primary's sphere of influence, and a core-like stellar density slope $\\alpha=1$. The companion's torque drives stellar orbits to high eccentricity, refilling the loss cone and producing TDEs from the primary; the rate curve from 1000 simulated systems per mass configuration is then used as $\\gamma(M)$ in the convolution $\\Gamma(z)=\\int (d^2N/dV\\,d\\ln M)\\,\\gamma(M)\\,d\\ln M$ with the Merloni & Heinz (2008) SMBH mass function. This convolution, together with the $(1+z)^{-1}$ time-dilation factor and comoving volume, converts the simulated per-mass rates into the redshift-dependent volumetric rates and cumulative TDE counts shown for $z\\le2$.","core_discovery":"The paper's central claim is a mass-dependent dichotomy: in a supermassive black hole binary, with the primary (less massive) black hole acting as the disruptor, the per-black-hole TDE rate increases with disrupting black hole mass from $10^5$ to $10^7\\,M_\\odot$, whereas single-SMBH rates decline over the same range. This reversed trend is attributed to the companion's eccentric Kozai-Lidov perturbations keeping loss-cone refilling efficient where two-body relaxation alone is not. The authors convolve the simulated rate curve with the Merloni & Heinz (2008) SMBH mass function to predict the volumetric TDE rate and cumulative counts for $z\\le 2$, presenting them as upper limits. They further report that binary-driven rates approach the observed TDE rate in post-starburst galaxies for $M_{\\rm BH}\\gtrsim$ a few $\\times 10^6\\,M_\\odot$, and interpret the asymmetric scatter of TDE light-curve durations around the $t_{1/2}\\propto M_{\\rm BH}^{1/2}$ relation as evidence that some high-host-mass TDEs are disruptions by the less massive member of a binary.","pith_inferences":["Inference beyond the paper: if the mass-dependent dichotomy survives, the ratio of TDE rates at high versus low host mass could itself serve as a binary-fraction estimator, independent of the overall volumetric normalization that the paper keeps as an upper limit.","Inference beyond the paper: the model's omission of direct stellar capture above roughly $10^8\\,M_\\odot$ means the predicted high-mass rates are optimistic; a survey that resolves the location of the high-mass cutoff in the rate curve could separate the binary and single channels cleanly.","Inference beyond the paper: the fixed $q=100$, fixed-separation configuration may not represent the real binary population; running the same mass-function convolution on simulated rate curves for smaller mass ratios or different separations would be a natural sensitivity test of the PSB-rate match."],"forward_implications":["If binary-driven TDE rates rise with disrupting black hole mass, then a measured TDE rate that flattens or climbs toward $10^7$-$10^8\\,M_\\odot$, where single-SMBH models fall, would indicate a population of unresolved binaries.","The match between binary-model rates and the observed post-starburst galaxy TDE rate suggests that a subset of PSB TDE hosts may contain SMBH binaries with a disrupting black hole in the few $\\times 10^6$-$10^8\\,M_\\odot$ range.","The computed volumetric rates imply substantially more TDEs per unit redshift from the binary channel than from two-body relaxation alone, giving LSST and Roman upper-limit rate predictions to test.","Short-duration TDEs whose inferred black hole mass is systematically lower than host-galaxy scaling relations predict can be targeted as candidate binary disruptions.","The redshift-dependent TDE counts, scaled by a tuning parameter $\\eta$ representing the binary fraction, provide a route to constrain the SMBH binary fraction from future photometric surveys."],"supporting_citations":[{"why":"Provides the simulated binary TDE rates from combined eccentric Kozai-Lidov and two-body relaxation that this paper extends across mass and redshift.","marker":"Melchor et al. 2024"},{"why":"Supplies the $t_{1/2}$ light-curve durations, black hole mass estimates, and the best-fit $t_{1/2}\\propto M_{\\rm BH}^{1/2}$ relation whose asymmetric scatter motivates the binary-interpretation.","marker":"Yao et al. 2023"},{"why":"Gives the observed TDE rate in post-starburst galaxies that the binary model is compared against and matches.","marker":"French et al. 2020a"},{"why":"Provides the average observed TDE rate baseline and the observed PSB overrepresentation context for the rate comparison.","marker":"van Velzen et al. 2020"},{"why":"Supplies the supermassive black hole mass function used to convolve the mass-dependent TDE rates into volumetric and redshift-dependent rates.","marker":"Merloni & Heinz 2008"},{"why":"Supports the scenario in which TDEs around the less massive SMBH in a binary yield systematically underestimated masses relative to host-galaxy expectations.","marker":"Mockler et al. 2023"},{"why":"Establishes the binary-driven TDE rate framework combining eccentric Kozai-Lidov oscillations and two-body relaxation that the simulations build on.","marker":"Naoz et al. 2022"},{"why":"Supplies the core-like stellar density profile assumption used in the simulation setup for post-starburst environments.","marker":"Stone & Metzger 2016"}],"fun_headline_variants":["TDE rates climb with mass in SMBH binaries","Binary black holes reverse TDE mass trend","Cosmic TDE demographics from binary SMBHs","Binary SMBHs boost tidal disruption rates"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions assume that the simulated binary configuration, with a companion 100 times more massive than the disruptor at half the sphere of influence, eccentricity 0.5, and a core-like density slope, represents the real post-merger SMBH binary population, and that the simulated rate curve can be extrapolated and convolved with the mass function at all redshifts.","fun_headline_variants_meta":{"raw":{"variants":["TDE rates climb with mass in SMBH binaries","Binary black holes reverse TDE mass trend","Cosmic TDE demographics from binary SMBHs","Binary SMBHs boost tidal disruption rates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000207,"raw_usage":{"total_tokens":1439,"prompt_tokens":1020,"completion_tokens":419,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":636,"completion_tokens_details":{"reasoning_tokens":359}},"tokens_in":636,"tokens_out":419,"duration_ms":5164,"temperature":1.0,"reasoning_tokens":359,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:27:57.853024+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the TDE rate as a function of host-derived SMBH mass in an LSST sample where binary companions have been independently identified: the paper predicts a plateau or rise from $10^6$ to $10^7\\,M_\\odot$ for binary hosts while single-SMBH models fall, so a monotonically declining rate in that range would falsify the central claim.","supporting_citations":[],"review_version":1}