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REVIEW 3 major objections 5 minor 129 references

Tidal Disruption Event Demographics in Supermassive Black Hole Binaries Over Cosmic Times

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2507.08082 v1 pith:4NWT7ZAS submitted 2025-07-10 astro-ph.GA astro-ph.HE

Denyz Melchor , Smadar Naoz , Suvi Gezari , Brenna Mockler This is my paper · ORCID
classification astro-ph.GAastro-ph.HE
keywords tidaldisruptioneventssupermassiveblackholebinarieseccentricKozai-LidovmechanismTDEratespost-starburstgalaxiesredshiftevolutionSMBHmassfunctionLSST
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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 $z\le2$.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Section 3, Appendix A, Figure 2] 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.
  2. [Section 3, Equation (3)] 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.
  3. [Section 4, Figure 4] 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.
minor comments (5)
  1. [Section 3] 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⊙.'
  2. [Appendix B] The text refers to 'Equation B, in Appendix A' when presenting the single-SMBH rate; the reference should be to Equation (B1).
  3. [Figure 2 caption] 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.
  4. [Section 2, Figures 1 and 5] 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.
  5. [Tables 1 and 2] The tables have several formatting inconsistencies, including repeated reference entries and incomplete journal information for some references, which should be cleaned up before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the binary TDE rate curve is a simulation output from the authors' prior work, and the demographic predictions are convolutions with external functions, not fitted to the targets they claim to match.

full rationale

The paper's central mass-dependent binary TDE rate is not derived from the observed PSB rate or from the redshift-dependent predictions; it is taken from the authors' own previous numerical simulations (Naoz et al. 2022; Melchor et al. 2024), which are code-based, externally checkable results with stated assumptions rather than fitted parameters. The single-SMBH comparison rates are computed from the standard two-body relaxation formalism in Appendix B, and the redshift evolution is obtained by convolving the simulated rate with the independent Merloni & Heinz (2008) mass function, so the redshift curves are not forced to match observed counts. The short-duration TDE discussion is offered as a consistency argument, not as a derivation, and the 'approach' to the PSB rate band is a comparison of a simulated upper limit to an observed band, not a fit. Self-citations are frequent, but they support the framework with prior simulation work; the load-bearing claim of an increasing binary TDE rate with mass is a simulation result that could fail in other parts of parameter space, which is a robustness concern rather than circularity. The paper therefore does not reduce its predictions to its inputs by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a chain of modeling choices inherited from earlier work by the same group. The binary TDE rate is not independently benchmarked here, and the redshift convolution depends on an unspecified evolution of the SMBH mass function. The eta parameter is a free tuning knob.

free parameters (6)
  • binary mass ratio q = 100
    Fixed to 100 in Appendix A; chosen by hand, not sampled or fitted, and the paper does not study sensitivity to q.
  • binary eccentricity e_bin = 0.5
    Fixed to 0.5 in Appendix A to represent moderate post-merger eccentricity; not varied.
  • binary separation a_bin = 0.5 R_sph
    Set to half the primary's sphere of influence (Appendix A), following Merritt & Milosavljevic (2005).
  • stellar density slope alpha = 1 (core-like)
    Adopted in Appendix A as a core-like profile; single-SMBH comparisons use alpha=2 (cusp-like).
  • stellar mass m_star = 0.8 M_sun
    Fixed in Appendix A following Melchor et al. (2024).
  • tuning parameter eta = not fixed
    Introduced in Section 4 to scale the binary contribution; eta=1 means all TDEs are binary-driven, eta->0 means negligible. The paper uses observed PSB fractions to infer plausible eta values, effectively allowing the model normalization to adjust to observation.
assumptions (6)
  • standard math The loss-cone two-body relaxation formalism (Eq. B1) gives the single-SMBH TDE rate within the sphere of influence.
    Used to compute single-SMBH rates in Figure 2; based on Frank & Rees (1976) and subsequent standard treatments.
  • domain assumption The OSPE secular three-body code correctly models EKL-driven orbital evolution in SMBH binaries.
    The binary TDE rates in Figure 2 are inherited from Melchor et al. (2024), which uses OSPE; no validation or code is provided in this draft.
  • ad hoc to paper The binary configuration (q=100, e_bin=0.5, separation 0.5 R_sph, alpha=1, m_star=0.8 M_sun) represents typical post-merger SMBH binaries.
    These parameter choices are fixed in Appendix A without a sensitivity study; the mass-dependent rate curve in Figure 2 depends on them.
  • domain assumption The stellar density profile follows the M-sigma relation normalization (M0=1e8 M_sun, sigma0=200 km/s) with a power-law slope alpha.
    Equation (B4) derives the number density from the M-sigma relation; the paper does not quantify the uncertainty in this relation.
  • domain assumption The SMBH mass function from Merloni & Heinz (2008), with an implicit redshift dependence, can be integrated against TDE rates.
    Equation (3) uses this mass function, but its z-dependence is not described; Figure 3 shows a redshift-evolving Gamma(z).
  • domain assumption A steady-state stellar cusp surrounds each SMBH in the binary.
    The paper acknowledges this is 'often used, although not always justified' (Section 3) and applies it to both binary and single cases.

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Cite this review

Pith. "Pith review of Tidal Disruption Event Demographics in Supermassive Black Hole Binaries Over Cosmic Times." pith.science (2026). https://pith.science/paper/4NWT7ZAS

@misc{pith2026250708082,
  author       = {Pith},
  title        = {Pith review of: Tidal Disruption Event Demographics in Supermassive Black Hole Binaries Over Cosmic Times},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4NWT7ZAS}},
  note         = {Machine review of arXiv:2507.08082}
}
read the original abstract

Tidal disruption events (TDEs) offer a unique probe of supermassive black hole (SMBH) demographics, but their observed rates remain difficult to reconcile with standard single-SMBH models. In this work, we use simulations of SMBH binaries, including the combined effects of eccentric Kozai-Lidov oscillations and two-body relaxation, to explore how TDE rates scale with SMBH mass and redshift. We find that binary systems exhibit increasing TDE rates with mass, in contrast to the declining trend expected for single SMBHs. These binary-driven rates match those observed in post-starburst galaxies, suggesting that a subset of TDE hosts may contain SMBH binaries. TDE light curves in some massive galaxies exhibit unexpectedly short durations, suggesting that the disrupting SMBH may be less massive than implied by host galaxy scaling relations, consistent with disruptions by the less massive black hole in a binary. By convolving our mass-dependent rates with the SMBH mass function, we predict redshift-dependent TDE rates, which we show can be used to constrain the supermassive black hole binary fraction. Our results provide a testable framework for interpreting TDE demographics in upcoming wide-field surveys such as LSST and Roman.

Figures

Figures reproduced from arXiv: 2507.08082 by the authors.

Figure 1
Figure 1. Correlation between TDE light curves and black hole mass. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Projected TDE rate per SMBH mass. The pink curve shows the predicted upper-limit TDE rate as a function of disrupting SMBH mass for a binary with fixed mass ratio (q = 100) and a core-like stellar density profile. The solid and dashed black lines show single-SMBH TDE rates from two-body relaxation assuming core-like and cusp-like profiles, respectively. The orange line represents the TDE rate estimated by Rom & Sari… view at source ↗
Figure 3
Figure 3. Upper limit TDE redshift evolution. Top panel: [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Number of TDEs from an SMBH binary: Uncertainty at [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Correlation between TDE light curves and black hole mass. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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