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The observed redshift-dependent rate of tidal disruption events is a sensitive probe of the evolving supermassive black hole mass function at masses 10^5–10^8 M_sun, and a flux-limited LSST sample can constrain the mass function's exponenti

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2026-08-03 04:23 UTC pith:LMIVF3SD

load-bearing objection A useful, transparent forecasting framework for TDE surveys whose strongest quantitative claim — LSST constraining the BHMF evolution slope to ±0.06 — rests on a known, unquantified LF/BHMF inconsistency. the 3 major comments →

arxiv 2602.04947 v2 pith:LMIVF3SD submitted 2026-02-04 astro-ph.HE astro-ph.GA

Tidal disruption event rates across cosmic time: forecasts for LSST, Roman, and JWST and their constraints on the supermassive black hole mass function

Mitchell Karmen , Suvi Gezari , Colin Norman , Muryel Guolo This is my paper
classification astro-ph.HE astro-ph.GA
keywords tidal disruption eventssupermassive black hole mass functionblack hole seeding and growthcosmic noonLSSTRoman HLTDSJWST COSMOS-Websemi-empirical rate model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Tidal disruption events (TDEs)—stars ripped apart by supermassive black holes—offer a rare view of black holes too small and too distant for AGN surveys to census. This paper argues that the observed TDE rate as a function of redshift is governed primarily by the evolution of the 10^5–10^8 M_sun black-hole mass function, and builds a semi-empirical model anchored to the local ZTF rate that adds evolving galaxy densities, mergers, dust, and a possible top-heavy IMF. The model makes the testable prediction that the volumetric TDE rate rises until cosmic noon (z~1–2) and then falls, with forecasts differing by up to a factor of ten at z~3 depending on which black-hole mass function is assumed. For LSST, a flux-limited sample should catch thousands to tens of thousands of TDEs per year, and the paper claims that the yearly yield plus the sample's median redshift can constrain the mass function's exponential slope to ±0.06—sharp enough to distinguish competing models of black-hole seeding and growth. If right, TDE samples become a demographic probe of low-mass black holes across cosmic time, complementary to quasars and AGN.

Core claim

On its own terms, the discovery is that TDEs are not just a local phenomenon: their redshift-dependent rate is dominated by the evolving supply of black holes in the 10^5–10^8 M_sun range, so a flux-limited survey can invert the observed TDE redshift distribution into a constraint on the black-hole mass function. Fitting the density of TDE-capable black holes as an exponential decline N_BH(z) ≈ A e^{α(1+z)}, the paper predicts that LSST's annual TDE yield falls logarithmically with steeper α, while the sample's median redshift moves down; taken together these two summary statistics break the degeneracy with galaxy-scale rate enhancements and recover α to about ±0.06. The two contrasting mass

What carries the argument

The engine of the calculation is the rate integral Γ_TDE = ∫ ε(z) F(z) N_BH(z) R0(z,λ) O(z) dz, where R0 is the local ZTF-measured TDE luminosity function, N_BH(z) is the ratio of the comoving number density of Hills-mass-capable SMBHs (10^5–10^8 M_sun) at redshift z to that locally, F(z) bundles mergers, nuclear stellar density, and IMF evolution, O(z) is the dust-obscuration correction, and ε(z) is survey efficiency (unity for time-domain surveys, estimated via a light-curve visibility time for single-epoch surveys). The key move is normalizing all astrophysical scalings to unity at z=0, so uncertainties enter as multiplicative factors rather than as an absolute first-principles rate, and

Load-bearing premise

The load-bearing assumption is that the shape of the TDE luminosity function (and hence the mapping from black-hole mass to flare brightness) does not evolve with redshift even though the black-hole mass function does; the paper itself acknowledges these are fundamentally incompatible, so the forecast yields and the derived slope constraint inherit any bias from that simplification.

What would settle it

With two years of flux-limited LSST TDEs (expected to exceed 10^4 events), measure the binned redshift distribution and compare the yield-versus-median-z trend against the band spanned by the two mass-function models and the plausible galaxy-enhancement range; if the observed trend falls outside that band, the constant-luminosity-function assumption fails. A smaller decisive test is to measure the median TDE peak luminosity as a function of redshift—a statistically significant trend would directly falsify luminosity-function shape constancy.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A flux-limited LSST TDE sample yields thousands to tens of thousands of events per year; combining total yield with median redshift constrains the black-hole mass-function slope α to ±0.06, making TDEs a demographic probe of low-mass black holes at z>1.
  • Under the AGN-calibrated mass-function prescription the annual LSST yield is roughly half the simulation-based yield, so even a single-year count discriminates between the two population models.
  • The Roman HLTDS should detect dozens to roughly a hundred TDEs per year with median redshift near z~1 and reach z~2.75, with high-resolution host-galaxy imaging to separate black-hole demographics from galaxy-scale rate enhancements.
  • Single-epoch JWST COSMOS-Web serendipitous discoveries are rare (0–2 TDEs), but multi-epoch monitoring of deep JWST fields provides a path to discovering z>3 TDEs and probing the seeds of the first SMBHs.
  • Current ZTF data cannot distinguish the mass-function models; the limiting factor is sample size and depth, with roughly 400 TDEs at the ZTF magnitude limit needed to see the divergence.
  • The volumetric TDE rate should rise through z~1–2 and then decline, with the turnover redshift depending on which black-hole mass function is correct.
  • Dust obscuration is a minor correction to the overall rate even at high redshift, while nuclear stellar density is the dominant galaxy-scale enhancement at z<3.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If future LSST samples show an excess of high-z TDEs relative to both model families, the first suspect will be the assumed constancy of the TDE luminosity function; the paper's own mass-luminosity scaling suggests the luminosity function should harden with redshift, which would bias the current forecasts.
  • A direct test of the framework would be to use Roman host-galaxy morphologies to estimate nuclear densities and merger signatures, subtract their contribution to the redshift-dependent rate, and then fit the residual as a pure black-hole mass-function probe—bypassing part of the semi-empirical F(z) uncertainty.
  • The claimed ±0.06 constraint assumes the exponential form N_BH(z) ≈ A e^{α(1+z)} and local linearity around the fiducial α; an independent mass estimate from late-time TDE plateaus could break the degeneracy between the black-hole mass function and galaxy-scale enhancements more cleanly.
  • If the low-mass black-hole mass function is considerably more bottom-heavy at z>2 than either tested model, the TDE redshift distribution will peak at lower redshift than predicted—an effect LSST's median-redshift measurement could detect before Roman begins.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper constructs a semi-empirical model for the cosmic evolution of the tidal disruption event (TDE) rate. The calculation starts from the local ZTF g-band TDE luminosity function (Yao et al. 2023) and applies multiplicative redshift-dependent corrections for the evolving supermassive black hole mass function (using Shankar et al. 2009 and ILLUSTRIS), nuclear stellar density, galaxy merger rate, initial mass function, and dust obscuration. The authors forecast annual TDE yields and redshift distributions for Rubin/LSST, Roman HLTDS, and JWST COSMOS-Web, and propose that the total yield plus median redshift of a flux-limited LSST sample can constrain the exponential redshift slope α of the low-mass BHMF to ±0.06. The central assertion is that the observed redshift dependence of the TDE rate is sensitive to the SMBH mass function and its evolution.

Significance. If the forecasts are robust, this work provides a new, observation-driven route to probing the 10^5–10^8 M_sun SMBH population at z > 1, a regime poorly constrained by AGN surveys. The model is transparent and the Monte Carlo propagation of parameter uncertainties is a strength, as is the explicit comparison of two contrasting BHMF models. The survey yield predictions for LSST, Roman, and JWST are useful planning numbers, and the proposed methodology for inverting TDE redshift statistics into a BHMF constraint is a valuable contribution even if the quoted precision needs revision.

major comments (3)
  1. [§4.2, Eq. (2)] The central forecast that LSST yield and median redshift can constrain the BHMF slope α to ±0.06 rests on a luminosity function whose shape is fixed in redshift while the BHMF evolves. Because peak TDE luminosity correlates with M_BH (Mummery et al. 2024; Yao et al. 2023), a bottom-heavy BHMF at high z should produce a fainter LF, changing both N_TDE and z_med. The paper's statement that this effect is 'a few percent' is not derived from a convolution of an M-dependent L(M) with the evolving BHMF; it is inferred from the difference with Kochanek (2016) at z ≥ 4, outside the LSST redshift range (z ≲ 1.5) that drives the α constraint. If LF evolution shifts z_med by only 0.01–0.02, it can bias α by more than the quoted 0.06. Please provide an explicit estimate with a mass-dependent luminosity relation and observed scatter, or remove the quantitative α precision claim.
  2. [§3.6, Fig. 11] The quoted uncertainty σ_α = 0.06 appears to be only the bootstrap statistical error on the median redshift and Poisson yield scatter. The authors themselves state that N alone gives ±0.6 because of degeneracy with galaxy-scale effects; the 'all enhancements' versus 'dust-only' models differ by ~0.3 dex in N and ~0.05 in z_med. From the right-hand panel, the α–z_med gradient is roughly 8 per unit redshift, so a 0.05 systematic shift corresponds to Δα ≈ 0.4, not 0.06. The α constraint must marginalize over F(z) parameters (E, α_density, IMF slope, obscuration) and report the total error budget; otherwise the headline precision is unsupported.
  3. [§3.5, Fig. 9] The 'reassuring' match to the ZTF cumulative redshift distribution is not an independent validation. The model is normalized to the Y23 local rate, and the shape of R0(z) in Eq. (2) is derived from the same Y23 luminosity function and flux limit. At z ≲ 0.5 the multiplicative corrections F(z)N_BH(z) are within tens of percent, so the CDF shape is essentially the Y23 input. A genuine out-of-sample test would use a flux-limited sample not used in the LF calibration, or hold out part of Y23.
minor comments (5)
  1. [§2.3] Typo: 'observationally confirmed observationally' should be 'observationally confirmed'.
  2. [Table 1 caption] Typo: 'T able' should be 'Table'.
  3. [§4.3 vs §6] The DDT program number is given as 'DDT: 9356' in §4.3 but 'DD: 3956' in the acknowledgments; please reconcile.
  4. [§2.4, Eq. (15)] The definition f_enh = f_pair (t_enh/T_pair) is followed by Eq. (19), which repeats the same ratio explicitly. Since t_enh/T_pair ≈ 1 is adopted, consider simplifying to avoid the impression that f_enh and the ratio are independent.
  5. [Fig. 10] The TNG100/TNG50 fits are shown but not used in the rate forecasts; their role in the argument should be stated more clearly.

Circularity Check

1 steps flagged

Central derivation is independent forward modeling; only the ZTF redshift-CDF check is an in-sample consistency test.

specific steps
  1. fitted input called prediction [§3.5 (Figure 9)]
    "As expected, these align almost exactly because we calibrate all of our rate predictions to the observations from ZTF. However, it is reassuring that the shape of the CDF matches the observed shape, which is not calibrated into our model. This confirms that the only factor influencing the redshift distribution of the ZTF-observed TDEs is the volume probed by the survey."

    The model's predicted cumulative redshift distribution is computed from R0(z) in Eq. (2), which integrates the Y23 g-band luminosity function φ_L(L_g). That luminosity function was fitted to the same ZTF sample whose observed cumulative redshift distribution is displayed in Figure 9. The redshifts and luminosities of that sample are the inputs from which φ_L is derived, so the CDF match is a consistency check built into the construction, not an independent confirmation. The further conclusion that 'the only factor influencing the redshift distribution ... is the volume probed' cannot be established from this in-sample comparison. The paper is transparent that the alignment follows from calibration, so this is a minor validation issue rather than a hidden derivation, and it is not load-bear

full rationale

The main derivation chain is not circular. Equation (1) is a forward model: the local Y23 TDE luminosity function is multiplied by external BHMF models (Shankar+09; Illustris/TNG) and empirically motivated scalings for nuclear density, mergers, IMF, and dust. The BHMF enters as an input through Eqs. (6)-(7), so the claimed sensitivity of the TDE rate to the BHMF is a model prediction obtained by varying external inputs, not a result derived from the conclusion being claimed. The proposed LSST constraint in §3.6 is a forecasting/inversion exercise for future data; the quoted σ_α≈0.06 is a model-based statistical estimate, not a claim that α has already been measured, and it does not reduce to the input by definition. No load-bearing self-citation chain appears: M. Karmen et al. (2025) is cited for JWST detectability and the COSMOS-Web search context, but the rate predictions do not reduce to that citation. The §4.2 limitation—constant LF shape versus evolving BHMF—is explicitly acknowledged as 'fundamentally incompatible,' and the few-percent magnitude is asserted rather than derived; that is a model systematic and correctness risk, not a circular reduction under the hard rules. The only mild circularity is the in-sample ZTF CDF check in §3.5, which is non-independent but transparently acknowledged and does not support the central forecasts.

Axiom & Free-Parameter Ledger

7 free parameters · 7 axioms · 0 invented entities

The model's central inputs are the empirical local TDE rate and external BHMF models; the redshift-dependent factors D, M, I, and O rest on several hand-set or literature-calibrated parameters and extrapolated scaling relations. No new entities are introduced.

free parameters (7)
  • Obscuration fraction logistic parameters (f0, k, fmax) = f0=0.3, k=0.7, fmax=0.9
    Set from the local IR-selected TDE fraction (Masterson+24) and calibrated to AGN obscuration evolution (Gilli+22); enter Eq. 8–9 and set O(z).
  • Nuclear density–TDE rate exponent alpha = uniform prior 1–2
    Bounded by full vs empty loss-cone regimes; enters D(z)=(1+z)^{0.9 alpha} in Eq. 12; the paper adopts the full range as uncertainty.
  • Central density redshift scaling exponent = 0.9
    Adopted from Barro+17/Ormerod+24 central kpc density evolution and extrapolated to z=6; enters D(z).
  • IMF slope alpha_IMF(z) = linear 2.35 (z=0) to 2.081 (z~8)
    Fitted to UV luminosities of high-z galaxies (Finkelstein+24) to set <M_*^2> scaling I(z) in Eq. 21.
  • IMF mass limits Mmin, Mmax = unspecified
    The power-law IMF in Eq. 20 requires Mmin/Mmax to compute <M_*^2>, but the values are not given.
  • Merger rate enhancement E = uniform prior 10–100
    Range from hydro simulations (Pfister+19/21); enters M(z) in Eq. 19.
  • Enhanced-phase duration / pair timescale ratio t_enh/T_pair = 1
    Set by hand from Lotz+11 pair timescales; enters M(z).
axioms (7)
  • domain assumption TDE luminosity function shape is redshift-invariant
    Introduced in §2 and used in Eq. 2 at all z; acknowledged in §4.2 to be fundamentally incompatible with BHMF evolution.
  • domain assumption TDE rate scales as rho^alpha with 1<=alpha<=2
    From loss-cone theory (Lightman & Shapiro 77; Wang & Merritt 04); used to define D(z).
  • domain assumption Central 1 kpc surface density traces density at r_inf with constant profile shape to z=6
    Needed to convert observed size evolution into the nuclear density enhancement D(z); extrapolated from Barro+17/CEERS data.
  • domain assumption AGN obscuration redshift evolution applies to TDE host galaxies
    Used to set O(z) via Eq. 8–9; the paper notes this is phenomenological.
  • domain assumption TDE rate enhancement after mergers follows simulation range E=10–100 for t_enh/T_pair~1
    Used for M(z); based on hydro simulations and observed TDE host preferences.
  • domain assumption Top-heavy IMF inferred from UV-luminous galaxies at high z is real and evolves linearly
    Used for I(z); the linear interpolation is acknowledged to have negligible impact, but the phenomenon itself is speculative.
  • domain assumption Input BHMFs (Shankar+09, ILLUSTRIS) bracket the true BHMF
    The paper selects two contrasting models; all forecasts inherit their validity.

pith-pipeline@v1.3.0-alltime-deepseek · 26883 in / 11678 out tokens · 105909 ms · 2026-08-03T04:23:25.737811+00:00 · methodology

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read the original abstract

Measuring the mass distribution of supermassive black holes (SMBHs) over cosmic time remains particularly challenging for the low mass (M_BH<10^8 M_sun) population at z>1. This population is also the most sensitive to SMBH seeding and early growth models. In this work we construct a semi-empirical model for the redshift evolution of the TDE rate under multiple SMBH mass function prescriptions, and show that the observed redshift-dependent rate of TDEs is very sensitive to the SMBH mass function and its evolution with redshift. We further incorporate galaxy-scale processes that evolve with redshift -- namely, increasing galaxy nuclear stellar densities, enhanced galaxy-galaxy merger rates, dust obscuration, and a possible top-heavy IMF at early cosmic times -- and quantify their combined impact on the TDE rate. We find that including these effects generally results in a volumetric TDE rate that increases with redshift until a maximum near cosmic noon, before declining at higher redshift where SMBHs that can disrupt stars become increasingly scarce. We forecast TDE rates in the Rubin LSST and the Roman High Latitude Time Domain Survey, alongside expectations for serendipitous TDE rates in the JWST COSMOS-Web survey. Finally, we provide a methodology for using a flux-limited survey of TDEs in LSST to directly constrain the redshift evolution of the SMBH mass function.

Figures

Figures reproduced from arXiv: 2602.04947 by Colin Norman, Mitchell Karmen, Muryel Guolo, Suvi Gezari.

Figure 1
Figure 1. Figure 1: The two SMBH mass functions used in this work at z ∼ 0 through z = 6. The solid line is the semi-empirical model from F. Shankar et al. (2009) and the dashed line is the ILLUSTRIS simulation (S. Genel et al. 2014). 0 1 2 3 4 5 6 7 8 z 0.3 0.4 0.5 0.6 0.7 0.8 0.9 fobscured AGN (Gilli+22, θtorus = 60◦) TDEs [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of galaxy central surface density as a function of redshift. Lines are solid where measured, and dashed where G. Barro et al. (2017) is extrapolated to higher redshifts. It can be seen that the extrapolation of the star-forming sample is a good prediction of what is later observed in the CEERS (K. Ormerod et al. 2024; S. L. Finkelstein et al. 2023) data taken with JWST. The quiescent extrapolatio… view at source ↗
Figure 4
Figure 4. Figure 4: Scalings of all rate modifications as a function of redshift. On the left y-axis, a value of 1 is equivalent to the local value. All values at 1 is the local TDE rate. On the right y-axis, we show the volumetric TDE rate. low-mass end of the SMBH mass function. We focus here on the Legacy Survey of Space and Time (LSST, Z. Ivezi´c et al. ˇ 2019) conducted using the Vera C. Rubin Observatory (hereafter Rubi… view at source ↗
Figure 5
Figure 5. Figure 5: Volumetric rate of TDEs as a function of redshift after applying all redshift-dependent rate modifications. The red line uses the F. Shankar et al. (2009) BHMF model and the blue uses the ILLUSTRIS simulation. The shaded regions are the 1σ confidence intervals using Monte Carlo sampling of all uncertain parameters. Previous calculations also using the F. Shankar et al. (2009) BHMF were done in C. S. Kochan… view at source ↗
Figure 6
Figure 6. Figure 6: Predicted observed rates of TDEs in the Vera Rubin Observatory LSST. The left two panels show rates assuming a F. Shankar et al. (2009) BHMF, and the right two use the ILLUSTRIS simulation BHMF. The top two panels show TDEs per redshift bin, and the bottom two show the total cumulative TDEs up to redshift z. Each line shows a different single redshift-dependent rate modification (including the BHMF), and t… view at source ↗
Figure 7
Figure 7. Figure 7: Predicted observed rates of TDEs in the Roman High Latitude Time Domain Survey, as described in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Predicted observed rates of TDEs in the JWST COSMOS-Web survey. Rates are as described in [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative redshift distribution of TDEs as observed by ZTF. The black line is the observed TDEs from the ∼ 3 year ZTF flux-limited sample in Y23, and the surrounding shaded region is the Poisson uncertainty. The filled curves are our TDE rates models, scaled using the loss factor of ZTF. While the models differ slightly, they all fall within the ZTF uncertainty region rendering them indistinguishable. tha… view at source ↗
Figure 10
Figure 10. Figure 10: Exponential approximations for the black hole mass function “slope”, colored by exponent α (Equation 22). The semi-empirical BHMF (F. Shankar et al. 2009) is well-approximated by the exponential downsizing with red￾shift, while the simulated BHMFs behave more stochasti￾cally. heads, weather, moon phase, etc. Ideally the survey efficiency will be well-measured and corrected for, thus we can put a first con… view at source ↗
Figure 11
Figure 11. Figure 11: Left: The number of TDEs detected in a flux-limited survey conducted with LSST vs the exponent index of the mass function evolution (Equation 22, see [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. TDEs on FIRE: Illuminating the Cosmic Evolution of Tidal Disruption Rates

    astro-ph.HE 2026-06 unverdicted novelty 7.0

    FIRE-2 simulations show per-galaxy tidal disruption rates peak near z=2.5 at 4e-4 per year, correlate with SFR and central density, and remain high in satellite galaxies at early times.

  2. TDE 2025abcr: A Tidal Disruption Event in the Outskirts of a Massive Galaxy

    astro-ph.HE 2026-02 conditional novelty 6.0

    TDE 2025abcr is the first optical tidal disruption event found more than 30,000 light-years from its host galaxy's center, implying a wandering black hole.

  3. The Lazuli Space Observatory: Opportunities for time-domain and multi-messenger astronomy

    astro-ph.IM 2026-06 unverdicted novelty 4.0

    Lazuli is proposed as a space observatory combining flagship sensitivity with response times one to two orders of magnitude faster than current large facilities to enable new time-domain and multi-messenger science.

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