Recognition: 2 theorem links
· Lean TheoremThe Delay Time Distribution of Tidal Disruption Events
Pith reviewed 2026-05-10 19:12 UTC · model grok-4.3
The pith
Tidal disruption events occur most often about one billion years after a star formation burst in their host galaxies.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We compile a catalog of 41 TDE host galaxies with optical spectra, model the stellar populations with Bagpipes, and retrieve the age of the most recent burst of star formation to construct the delay time distribution of TDEs. We find that the TDE rate increases with post-burst age to reach a peak at ~1 Gyr relative to a control sample. We compare the observational TDE delay time distribution to theoretical models, which propose overdense stellar nuclei, radial anisotropies in stellar orbits, supermassive black hole binaries, and AGN disks as potential mechanisms that may enhance the TDE rate in post-starburst galaxies. Most models predict a TDE rate that declines with post-burst age, in the
What carries the argument
The observational delay time distribution of TDEs, built by recovering the age of each host galaxy's most recent star-formation burst from Bagpipes fits to optical spectra.
If this is right
- TDEs are more frequent in post-starburst galaxies than in the general galaxy population.
- The TDE rate climbs steadily after a starburst and reaches its highest value near 1 Gyr.
- Most theoretical models for boosted TDE rates predict a steady decline with post-burst age, which does not match the data.
- The supermassive black hole binary model is consistent with the observations at old burst ages, while the stellar overdensity model is consistent at intermediate ages.
Where Pith is reading between the lines
- The observed rise and peak suggest that the mechanism increasing the TDE rate requires roughly a billion years to reach full strength, possibly through gradual orbital diffusion or binary hardening.
- If the distribution is confirmed, TDE detections could serve as a clock for estimating how long ago a galaxy experienced its last major starburst.
- Larger samples at very young and very old post-burst ages would allow a direct test of whether the rate truly turns over after 1 Gyr.
Load-bearing premise
The spectral modeling accurately recovers the true age of the most recent star-formation burst in each TDE host without large systematic bias from dust, metallicity, or burst-duration assumptions.
What would settle it
Finding many TDEs in galaxies whose most recent starburst is either much younger than 500 million years or much older than 2 billion years would contradict the reported peak near 1 Gyr.
Figures
read the original abstract
Tidal disruption events (TDEs) can be observed when stars get too close to supermassive black holes and are torn apart and accreted. The delay time distribution of TDEs, or rate of TDEs as a function of time since a burst of star formation, can be used to determine what mechanisms influence the TDE rate. We compile a catalog of 41 TDE host galaxies with optical spectra, model the stellar populations with Bagpipes, and retrieve the age of the most recent burst of star formation to construct the delay time distribution of TDEs. TDEs occur more frequently in post-starburst galaxies than in other types of galaxies, though the mechanism causing this rate enhancement is unknown. We find that the TDE rate increases with post-burst age to reach a peak at ~1 Gyr relative to a control sample. We compare the observational TDE delay time distribution to theoretical models, which propose overdense stellar nuclei, radial anisotropies in stellar orbits, supermassive black hole binaries, and AGN disks as potential mechanisms that may enhance the TDE rate in post-starburst galaxies. Most models predict a TDE rate that declines with post-burst age, in contrast to our observational results, though some models are still feasible at certain ages (e.g., the black hole binary model matches at old burst ages and the stellar overdensity model matches at intermediate burst ages).
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper compiles a sample of 41 TDE host galaxies with optical spectra, models their stellar populations using Bagpipes to recover the age of the most recent star-formation burst, and constructs an observational delay time distribution (DTD) for TDEs. Relative to a control sample, the TDE rate is found to increase with post-burst age and peak near 1 Gyr. The authors compare this DTD to theoretical models invoking stellar overdensities, orbital anisotropies, SMBH binaries, and AGN disks, noting that most models predict a declining rate with age while the data show the opposite trend.
Significance. If the burst-age assignments are robust, the result supplies a direct observational constraint on the TDE DTD that can discriminate among proposed enhancement mechanisms in post-starburst galaxies. The work also demonstrates a practical route for using existing spectroscopic surveys to map TDE rates as a function of stellar population age.
major comments (3)
- [§3] §3 (Stellar population modeling): The manuscript does not quantify the impact of dust-metallicity-burst-duration degeneracies on the recovered burst ages. Post-starburst spectra are known to be sensitive to these parameters; systematic shifts of 0.3–0.5 dex in log(age) would move hosts between the age bins used to construct the DTD and could erase or invert the reported ~1 Gyr peak. A set of robustness tests (varying dust law, metallicity grid, and burst duration) or posterior predictive checks against mock spectra is needed to establish that the functional form of the DTD is not an artifact of modeling assumptions.
- [§4] §4 (DTD construction and control sample): The control sample is modeled with the identical Bagpipes pipeline, yet no differential-bias test is presented. If the TDE hosts and controls differ systematically in dust content or metallicity, the relative rate enhancement could be partly driven by modeling systematics rather than astrophysics. Explicit comparison of the age distributions and a jackknife or bootstrap assessment of bin-to-bin uncertainties are required to support the claim that the observed DTD shape is statistically significant.
- [§5] §5 (Model comparison): The statement that “most models predict a TDE rate that declines with post-burst age” is presented without quantitative overlays of the model predictions on the observed DTD (including uncertainties). Without a figure or table showing the model curves normalized to the same control sample and with the same age binning, it is difficult to assess which models are truly ruled out versus merely disfavored at certain ages.
minor comments (3)
- [Abstract, §1] The abstract and §1 cite 41 TDE hosts but do not state the final number after quality cuts or the redshift range; this information should be added for reproducibility.
- [Figure 3] Figure 3 (or equivalent DTD plot) would benefit from error bars derived from Poisson statistics or bootstrap resampling rather than only the control-sample normalization.
- [§1] A few references to recent TDE host studies (e.g., on post-starburst fractions) appear to be missing from the introduction; adding them would strengthen the context.
Simulated Author's Rebuttal
We thank the referee for their constructive and detailed comments. We address each major point below and will revise the manuscript accordingly to improve the robustness and clarity of our results.
read point-by-point responses
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Referee: [§3] §3 (Stellar population modeling): The manuscript does not quantify the impact of dust-metallicity-burst-duration degeneracies on the recovered burst ages. Post-starburst spectra are known to be sensitive to these parameters; systematic shifts of 0.3–0.5 dex in log(age) would move hosts between the age bins used to construct the DTD and could erase or invert the reported ~1 Gyr peak. A set of robustness tests (varying dust law, metallicity grid, and burst duration) or posterior predictive checks against mock spectra is needed to establish that the functional form of the DTD is not an artifact of modeling assumptions.
Authors: We agree that the current manuscript lacks explicit quantification of these degeneracies. Although Bagpipes was run with standard settings appropriate for post-starburst systems, we did not perform the requested robustness tests. In the revised version we will add a dedicated subsection (or appendix) containing: (i) re-fits varying the dust attenuation law, metallicity grid, and burst-duration prior; (ii) posterior predictive checks on mock spectra with known input ages; and (iii) a demonstration that the recovered burst ages and the resulting DTD shape remain stable within the adopted age bins. These additions will directly address the concern that the ~1 Gyr peak could be an artifact. revision: yes
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Referee: [§4] §4 (DTD construction and control sample): The control sample is modeled with the identical Bagpipes pipeline, yet no differential-bias test is presented. If the TDE hosts and controls differ systematically in dust content or metallicity, the relative rate enhancement could be partly driven by modeling systematics rather than astrophysics. Explicit comparison of the age distributions and a jackknife or bootstrap assessment of bin-to-bin uncertainties are required to support the claim that the observed DTD shape is statistically significant.
Authors: We acknowledge that a differential-bias test was not included. In the revision we will (i) directly compare the posterior distributions of age, dust, and metallicity between the TDE-host and control samples, (ii) apply jackknife and bootstrap resampling to quantify bin-to-bin uncertainties in the DTD, and (iii) report the statistical significance of the observed rise and peak. These tests will confirm that any relative enhancement is not driven by systematic differences in the modeling. revision: yes
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Referee: [§5] §5 (Model comparison): The statement that “most models predict a TDE rate that declines with post-burst age” is presented without quantitative overlays of the model predictions on the observed DTD (including uncertainties). Without a figure or table showing the model curves normalized to the same control sample and with the same age binning, it is difficult to assess which models are truly ruled out versus merely disfavored at certain ages.
Authors: We agree that a quantitative overlay is needed for a rigorous comparison. The revised manuscript will include a new figure (and accompanying table) that normalizes each theoretical model (stellar overdensity, orbital anisotropy, SMBH binary, AGN disk) to the control sample, applies the identical age binning, and displays the model curves together with the observed DTD and its uncertainties. This will allow readers to evaluate consistency or tension at each age. revision: yes
Circularity Check
No circularity: observational DTD from external Bagpipes fits and control comparison
full rationale
The paper compiles 41 TDE host spectra, applies the external Bagpipes stellar population code to recover the age of the most recent star-formation burst, bins the resulting ages, and computes the TDE rate as a function of post-burst age relative to a control sample modeled identically. This produces an empirical delay time distribution that is then contrasted with independent theoretical models. No equations, fitted parameters, or self-citations reduce the reported ~1 Gyr peak to a quantity defined by the same data or prior author work; the central result remains a direct measurement whose functional form is not forced by construction.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Bagpipes stellar population synthesis models accurately recover the age of the most recent star-formation burst from optical spectra
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We compile a catalog of 41 TDE host galaxies with optical spectra, model the stellar populations with Bagpipes, and retrieve the age of the most recent burst of star formation to construct the delay time distribution of TDEs.
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We find that the TDE rate increases with post-burst age to reach a peak at ~1 Gyr relative to a control sample.
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 1 Pith paper
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JWST and Keck observations of the off-nuclear tidal disruption event TDE 2025abcr: An evolving reprocessing layer
New JWST and Keck data on off-nuclear TDE 2025abcr show shifting emission-line velocities from a changing reprocessing layer and an IR power-law slope of -2.13 that is consistent with either reprocessing gas or a youn...
Reference graph
Works this paper leans on
-
[1]
2011, , 193, 29, 10.1088/0067-0049/193/2/29
Aihara, H., Allende Prieto, C., An, D., et al. 2011, ApJS, 193, 29, doi: 10.1088/0067-0049/193/2/29 Alexander, K. D., Berger, E., Guillochon, J., Zauderer, B. A., & Williams, P. K. G. 2016, ApJL, 819, L25, doi: 10.3847/2041-8205/819/2/L25 Almaini, O., Wild, V., Maltby, D., et al. 2025, MNRAS, 539, 3568, doi: 10.1093/mnras/staf659 Alush, Y., & Stone, N. C....
-
[2]
# Falling slope index , taken from Carnall +2019 a 14dblplaw [ " a l p h a _ p r i o r " ] = " log_10 " 34 Figure A1.The age of the burst modeled as an exponential function versus the age of the burst modeled as a double power law function, for all TDE hosts in the sample. The differently-colored markers represent burst mass fraction classifications in on...
work page 2019
-
[3]
The subset with broad lines is similar to the fiducial rate, with a less pronounced peak at 1 Gyr. D.INFORMATIONAL TABLES 36 TDE namet burst σt M∗,burst σM∗,burst M∗,old σM∗,old M∗,burst/M∗,tot α σ α Gyr Gyr log 10(M⊙) log 10(M⊙) log 10(M⊙) log 10(M⊙) AT 2023clx 0.131 0.014 6.989 0.059 9.274 0.045 0.005 895 90 AT 2022dyt 0.077 0.006 8.245 0.027 10.425 0.0...
work page 2023
-
[4]
1.65 Brimacombe et al. (2015); Holoien et al. (2016) RX J1242-A 190.65375−11.3263889 0.05 10.3 Wevers et al. (2019a)
work page 2015
-
[5]
1.5 Komossa & Greiner (1999) RX J1624 246.2360833 75.9155806 0.0636 10.4 Wevers et al. (2019a)
work page 1999
-
[6]
(1999) TDE2 350.9525833−1.1362056 0.2515 10.6 French et al
1.7 Grupe et al. (1999) TDE2 350.9525833−1.1362056 0.2515 10.6 French et al. (2020)
work page 1999
-
[7]
(2011) XMM J0740 115.0337083−85.6586944 0.0173 10.8 *
1.5 van Velzen et al. (2011) XMM J0740 115.0337083−85.6586944 0.0173 10.8 *
work page 2011
-
[8]
(2017) PS1-10jh 242.3678333 53.6733306 0.1696 9.2
4.8 Saxton et al. (2017) PS1-10jh 242.3678333 53.6733306 0.1696 9.2
work page 2017
-
[9]
(2012) PTF09axc 223.3045 22.2422972 0.1146 9.8
1.0 Gezari et al. (2012) PTF09axc 223.3045 22.2422972 0.1146 9.8
work page 2012
-
[10]
(2014) PTF09djl 248.4832083 30.2379583 0.184 9.9
1.0 Arcavi et al. (2014) PTF09djl 248.4832083 30.2379583 0.184 9.9
work page 2014
-
[11]
(2014) AT 2018fyk 342.56723−44.86457 0.06 9.7 WISeREP
1.0 Arcavi et al. (2014) AT 2018fyk 342.56723−44.86457 0.06 9.7 WISeREP
work page 2014
-
[12]
(2019) iPTF16fnl 7.4875417 32.8936778 0.0163 9.6
2.0 Holoien et al. (2019) iPTF16fnl 7.4875417 32.8936778 0.0163 9.6
work page 2019
-
[13]
(2016) AT 2019dsg 314.2623917 14.20440556 0.0512 10.6
2.0 Gezari et al. (2016) AT 2019dsg 314.2623917 14.20440556 0.0512 10.6
work page 2016
-
[14]
(2021) iPTF15af 132.11726 22.059315 0.079 10.3 SDSS
2.0 Cannizzaro et al. (2021) iPTF15af 132.11726 22.059315 0.079 10.3 SDSS
work page 2021
-
[15]
(2016) ASASSN-14ae 167.16716 34.097847 0.0436 9.8 SDSS
2.0 French et al. (2016) ASASSN-14ae 167.16716 34.097847 0.0436 9.8 SDSS
work page 2016
-
[16]
(2014) AT 2018bsi 123.860919 45.592208 0.051 10.6
2.0 Holoien et al. (2014) AT 2018bsi 123.860919 45.592208 0.051 10.6
work page 2014
-
[17]
2.5 [3], Reynolds (2018) AT 2019qiz 71.657851−10.2263679 0.0151 10.0
work page 2018
-
[18]
(2019) F01004 15.7133333−22.3641667 0.1178 9.8 French et al
2.5 [3], Siebert et al. (2019) F01004 15.7133333−22.3641667 0.1178 9.8 French et al. (2020)
work page 2019
-
[19]
(2024) AT 2020nov 254.554042 2.117511 0.0826 10.4 Earl et al
1.2 Heikkila (2016); Sun et al. (2024) AT 2020nov 254.554042 2.117511 0.0826 10.4 Earl et al. (2025) MOSTn/aDahiwale & Fremling (2020b) T able D1.TDE and associated host galaxy information Note—* indicates that the stellar mass was calculated from the 2MASS K-band magnitude. Galaxies with spectra from WISeREP or MOST did not have available slit dimensions
work page 2016
-
[20]
Hammerstein et al. (2023)
work page 2023
-
[21]
Tadhunter et al. (2021) 38 TDE name HαHαuncertainty HδHδuncertainty Broad lines Galaxy label ˚A ˚A ˚A ˚A AT 2023clx 3.37 0.35 0.52 0.39 1 SF AT 2022dyt 4.36 0.31 1.22 0.66 1 SF AT 2022bdw 9.41 0.33 1.61 0.56 1 SF AT 2021nwa 0.64 0.19 0.55 1.0 1 Quiescent AT 2020wey 0.08 0.15 2.92 0.69 1 QBS AT 2020vwl 0.04 0.2 0.2 1.22 1 Quiescent AT 2020ohl 0.68 0.06−0.9...
work page 2021
discussion (0)
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