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Counting the Unseen II: Tidal Disruption Event Rates in Nearby Galaxies with REPTiDE

T0 review · 3 major / 10 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Per-galaxy tidal disruption rates now match observed totals

desk verdict A validated public loss-cone code and the most resolved per-galaxy TDE rate catalog to date, but the 'discrepancy resolved' claim outruns a non-volume-limited sample comparison. read the letter →

arxiv 2412.19935 v1 pith:DIUOVNKD submitted 2024-12-27 astro-ph.GA astro-ph.HE

Christian H. Hannah , Nicholas C. Stone , Anil C. Seth , Sjoert van Velzen This is my paper · ORCID
classification astro-ph.GAastro-ph.HE
keywords tidaldisruptioneventslossconetheorynuclearstarclustersblackholedemographicsintermediate-massholesFokker-PlanckdiffusionTDEratesgalaxystellarmass
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 claims that the long-standing mismatch between theoretical and observed tidal disruption event (TDE) rates disappears when rates are computed from resolved parsec-scale stellar density profiles of a representative sample of 91 nearby galaxies. It introduces REPTiDE, a public Python package implementing the standard loss-cone (two-body relaxation) formalism, and applies it to nuclear density profiles from Paper I. The sample-averaged rates agree with recent ZTF-based observed rates, including for Milky Way-mass galaxies, and the predicted per-galaxy rates peak near galaxy stellar mass $10^{9.5}\,M_\odot$ and black hole mass $10^{6.5}\,M_\odot$. The paper argues that the earlier theoretical/observed discrepancy was mostly a sample-selection effect rather than a failure of loss-cone theory.

What carries the argument

The load-bearing object is the loss cone: the region of orbital angular-momentum space whose stars pass within the tidal radius and are disrupted. REPTiDE solves the orbit-averaged Fokker-Planck diffusion problem in the standard empty/full loss-cone approximation, using the Cohn-Kulsrud flux formula, together with the observed 3D stellar density and black hole mass. For 47 of 91 galaxies with density slopes steeper than a Bahcall-Wolf cusp ($\gamma\ge1.75$), it inserts a $-7/4$ cusp inward of the resolution limit, with the cusp radius fixed by assuming relaxation over a Hubble time (Equation 15). This last step is the main device that prevents divergent rates and sets the steep-profile rates.

What would settle it

Resolve the inner density profiles of steep-slope galaxies below the current few-parsec resolution using JWST or 30-m class adaptive optics; if the measured cusp break radii differ systematically from the Hubble-time relaxation radii given by Equation 15, the REPTiDE rates for those galaxies would need to be recomputed and the turnover mass would move. Alternatively, a sample of several hundred TDEs with host masses showing no peak near $M_\ast\sim10^{9.5}\,M_\odot$ would contradict the claimed turnover.

Watch

Extended reading notes

Core claim

Using the standard steady-state loss-cone framework, REPTiDE computes a TDE rate for each of 91 galaxies from its observed nuclear density profile and central black hole mass, spanning $10^{-7.7}$ to $10^{-2.9}$ yr$^{-1}$. Averaged, these rates match observed optical TDE rates, and the distribution turns over: rates rise toward intermediate-mass black holes and fall again at the low-mass end, so the most probable hosts are galaxies of $\sim10^{9.5}\,M_\odot$ and black holes of $\sim10^{6.5}\,M_\odot$. The same calculation implies that low-mass black holes can acquire a larger fraction of their mass through stellar disruption, which caps their spins at $a_\bullet\approx0.9$ for masses below $\sim10^{5.5}\,M_\odot$.

Load-bearing premise

The calculation depends on replacing the unresolved inner density of 47 steep-cusp galaxies with a Bahcall-Wolf cusp whose starting radius is set by assuming the nucleus has relaxed over a Hubble time; if those cusp radii are wrong, the per-galaxy rates and the location of the turnover shift.

Editorial extensions

If this is right

  • If the sample-averaged rates are right, surveys like ZTF should see a per-galaxy rate of a few $\times10^{-5}$ yr$^{-1}$ for Milky Way-mass galaxies, consistent with current observed counts.
  • The turnover near $10^{9.5}\,M_\odot$ and $10^{6.5}\,M_\odot$ predicts that most TDE detections should be hosted by galaxies and black holes near those masses, shifting future search strategies.
  • For black holes below about $10^{5.5}\,M_\odot$, repeated TDEs spin them down; a measured spin well above $a_\bullet\approx0.9$ in such a system would require recent coherent accretion rather than TDE-driven growth.
  • The binned mean rates including event-horizon suppression give a double-broken power-law calibration that can be used to convert volumetric observed TDE rates into constraints on black-hole demographics.

Reading between the lines

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

  • If the sample-selection resolution is right, older theoretical rate estimates built on ad hoc archival HST targets overpredicted observed rates, and future rate catalogs should be weighted by representative galaxy samples rather than by available photometry.
  • The convergence of the pinhole fraction to about 0.75 at low black hole mass, attributed to nuclear star cluster densities, implies that partial-disruption TDEs may be rarer in dwarf galaxies than pinhole-dominated models predict; this is testable with the distribution of TDE light-curve shapes.
  • The same loss-cone machinery and density profiles could be used to predict extreme-mass-ratio inspiral rates in these nuclei, since the diffusion calculation is shared.
  • Forward modeling these rates through Rubin and ULTRASAT survey footprints, which the follow-up paper plans, would directly test the predicted host-mass turnover with thousands of events.
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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 / 10 minor

Summary. This paper presents REPTiDE, a public Python package that implements the standard orbit-averaged loss-cone formalism for tidal disruption event (TDE) rates, and applies it to 91 nearby galaxies with resolved pc-scale nuclear density profiles from Hannah et al. (2024, Paper I). The authors compute per-galaxy TDE rates spanning roughly 10^-7.7 to 10^-2.9 yr^-1, find a turnover in the rate as a function of galaxy stellar mass (~10^9.5 Msun) and black hole mass (~10^6.5 Msun), and compare binned means of their sample to observed rates from Yao et al. (2023). They interpret the agreement as resolving the historical tension between theoretical and observed TDE rates, arguing that the main change relative to earlier semi-empirical work is the underlying galaxy sample (Section 5). The paper also presents pinhole fractions, cumulative q distributions, and spin-down constraints for low-mass black holes.

Significance. The public REPTiDE package and the tabulated per-galaxy rate catalog for 91 galaxies are valuable community resources. The validation against Stone & Metzger (2016) with a median residual of 0.019 dex is a strong technical point, as is the use of resolved, non-parametric density profiles that include nuclear star clusters. The finding that rates computed from modern pc-scale density measurements are lower than earlier estimates, and thus closer to observed rates, is physically plausible and important. However, the central comparison to observed population rates currently uses an unweighted mean of a non-volume-limited, NSC-selected sample, so the claim that the rate discrepancy is resolved is not yet fully established. This is a correctable issue, and the rest of the analysis is technically sound.

major comments (3)
  1. [Section 4.1, Figure 3, Eq. 17] The binned means shown in Figure 3 are unweighted averages (weighted only by rate uncertainties) over a sample that is explicitly not volume-limited and is focused on nucleated galaxies, with the low-mass end entirely composed of NSC hosts (Section 4). The observed rates from Yao et al. (2023) are converted from volumetric rates using the Baldry et al. (2012) and Gallo & Sesana (2019) mass functions, so they represent population-averaged per-galaxy rates over all galaxies in each mass bin. Without a correction for the sample selection function or a weighting by the galaxy mass function, the agreement in Figure 3 and the conclusion in Section 5 that 'the only thing that has changed is the underlying sample' are not established. I recommend either weighting the binned means by an appropriate galaxy stellar mass function, forward-modelling the sample selection, or demonstrating explicitly that the sample's mass and NSC-host distribution are representative of the local galaxy population.
  2. [Section 3.3, Eq. 15; Section 4; Figure 4] For 47 of 91 galaxies with density slopes steeper than a Bahcall-Wolf cusp, the unresolved inner profile is replaced by a -7/4 cusp whose radius is set by assuming relaxation over a Hubble time (Eq. 15). The paper notes that the TDE rate is quite sensitive to r_relax, and Figure 4 shows that some of the largest rate uncertainties come from this assumption (e.g., NGC 4592 with an uncertainty of 1.42 dex). This systematic uncertainty is not propagated into the binned means or the broken-power-law fits in Figure 3, which use the nominal rates. If the true dynamical ages (or the cusp radius prescription) differ systematically, both the location of the turnover and the apparent agreement with observed rates could shift. Please present the binned means and fits under alternative cusp-radius assumptions (e.g., applying the cusp at the resolution limit for all steep galaxies) or otherwise propagate this systematic into the population-level comparison.
  3. [Section 3.2 vs Section 4] There is a direct contradiction in the PDMF upper mass limit: Section 3.2 states that 'All TDE rates presented in this work are full rates with minimum and maximum stellar masses of 0.08 Msun and 1 Msun, respectively,' while Section 4 and the Figure 2 caption state that the rates assume a Kroupa PDMF with masses spanning 0.08 to 2 Msun. Since the upper mass cutoff changes the rate enhancement factor (Stone & Metzger 2016), the paper must specify which value was used for Table 1 and all figures, and the text should be made consistent. This affects the exact numerical values compared to observations.
minor comments (10)
  1. [Eq. 13 and Section 4] The sign convention for the power-law index gamma is inconsistent: Eq. 13 and Section 3.3 use gamma as a positive index with rho propto r^{-gamma}, while Section 4 and Table 1 list steep profiles as gamma around -2 to -3 and write 'steeper than a Bahcall-Wolf cusp (gamma < -1.75)'. Please adopt a single convention throughout.
  2. [Eq. 16 and Eq. 17] The relation for the normalization constants reads 'A = B - Mb/Mnorm^{alpha-beta}', which is dimensionally inconsistent and does not match the condition log A + alpha log(Mb/Mnorm) = log B + beta log(Mb/Mnorm). Please correct to log A = log B + (beta - alpha) log(Mb/Mnorm) or equivalent.
  3. [Table 1] The lower uncertainties on log M_BH for NGC 2903, NGC 5457, and NGC 6503 are listed as -7.06, -6.41, and -6.30 respectively; these are clearly typos and should be -0.28, -0.08, and -0.11. Please check all rows for similar errors.
  4. [Throughout] The name 'Bahcall-Wolf' is misspelled as 'Bachall-Wolf' in several places (e.g., Section 3.3, Table 1 note, Section 4.2).
  5. [Section 4.1] The sentence 'We are not the first of recent studies to bring theoretical and observed TDE rates into better agreement, and we include these in Figure 3 for comparison' is ambiguous; 'these' should refer to the results of those studies, and the sentence should be rephrased.
  6. [Section 5] The statement 'the only thing that has changed is the underlying sample of galaxies we average over' overstates the case: the present work also uses resolved pc-scale density profiles, includes nuclear star cluster components, applies the Bahcall-Wolf cusp treatment, and uses updated black hole mass estimates relative to Stone & Metzger (2016). I suggest acknowledging these input differences while noting that the loss-cone treatment itself is unchanged.
  7. [Table 1 note] The column numbering in the table note is off by one: the note refers to columns (11) and (12), but the table has 11 columns, with (10) and (11) being the BW cusp flag and r_BW. Please update the note numbering.
  8. [Section 4.2] It would be helpful to state how asymmetric MBH mass uncertainties were used in the three rate calculations (e.g., whether both the upper and lower 1-sigma values were computed and how they were combined).
  9. [Abstract] The word 'representative' in 'representative sample of 91 nearby galaxies' is not justified given the non-volume-limited, NSC-selected nature of the sample; consider replacing it with 'a sample of 91 nearby galaxies with resolved pc-scale nuclei' or similar.
  10. [Section 4.1] When converting observed volumetric rates to per-galaxy rates with the same mass functions as Yao et al. (2023), the text should explicitly acknowledge the difference between the mass-function-weighted averages and the unweighted binned means of the sample; this is currently only implicit and is closely tied to major comment 1.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; rate predictions are computed from measured density profiles with standard loss-cone theory and compared to external observed rates.

full rationale

The paper's central per-galaxy TDE rates are computed from observed nuclear density profiles and MBH masses using the standard loss-cone formalism, with no TDE rate fitted to observed counts. The comparison to Yao et al. (2023) uses external observed rates and externally derived mass functions, and the code validation against Stone & Metzger (2016) is a numerical cross-check of a standard method, not a rate-tuned output. The dependence on Paper I is for measured density profiles and scaling relations, which are observational inputs rather than outputs of the present rate calculation; the fact that Paper I shares authors does not make the measured densities circular. The Bahcall-Wolf cusp treatment and the Hubble-time relaxation assumption are stated modeling assumptions, and the paper explicitly propagates the resulting sensitivity into the quoted uncertainties (Section 4.2). The broken power-law fits describe the model outputs themselves, so they cannot independently validate the turnover, but this is self-description rather than circular reasoning. The sample-selection weighting concern about comparing an unweighted binned mean to population-averaged observed rates is a statistical and interpretational caveat, not a definitional reduction of the prediction to its inputs. No load-bearing step was found in which a result is equivalent by construction to a fitted parameter or to a self-citation chain.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The code's main inputs are measured density profiles and MBH masses from Paper I and catalogs; these are inherited, not fitted here. The free choices in this paper are the PDMF limits, the inner cusp treatment for steep galaxies, and the descriptive broken power-law fits. No new physical entities are introduced; REPTiDE is a software implementation.

free parameters (4)
  • Kroupa PDMF minimum and maximum stellar masses = M_min=0.08 Msun; M_max stated as 1 Msun in Section 3.2 and as 2 Msun in Section 4
    Chosen by hand rather than fit; sets the rate normalization through <M*> and <M*^2> and affects the spin cap. The inconsistent statement of M_max is a red flag.
  • Bahcall-Wolf cusp slope = gamma_BW = 7/4
    Fixed theoretical value imposed inward of the resolution limit for 47/91 galaxies; the central density extrapolation, and thus the rates, depend on it.
  • Inward cusp radius r_relax for steep galaxies = Set by Eq. 15 with t_relax = Hubble time; for 12/47 galaxies capped at the resolution limit
    The paper treats this as an uncertainty source, but the choice is effectively a free modeling parameter; rates are highly sensitive to it.
  • Broken power-law fit parameters for N_TDE(Mgal) and N_TDE(MBH) = log(A)=-4.23, alpha=1.19, beta=-0.88, log(Mb)=9.45 for Mgal; analogous for MBH
    These are descriptive fits to the computed model rates, not physical inputs, but they encode the claimed turnover and are presented as observer-friendly results.
assumptions (7)
  • domain assumption Spherically symmetric, approximately isotropic galactic nuclei.
    The density deprojection and Eddington-inversion DF (Eq. 4) assume spherical symmetry and isotropy; the authors note they neglect asphericity and anisotropy. Section 2, Eqs. 3-4.
  • domain assumption Steady-state, orbit-averaged loss-cone formalism with energy diffusion neglected.
    The code follows Magorrian & Tremaine 1999, Wang & Merritt 2004, and Stone & Metzger 2016, assuming angular-momentum diffusion dominates energy diffusion. Section 2, after Eq. 5.
  • domain assumption Bahcall-Wolf cusp with slope -7/4 replaces unresolved density profiles for galaxies with gamma >= 1.75, with cusp radius set by relaxation over a Hubble time.
    Applied to 47/91 galaxies; the paper states rates are sensitive to r_relax. Section 3.3 and Section 4.
  • domain assumption Kroupa present-day stellar mass function with adopted minimum and maximum stellar masses.
    PDMF sets the rate normalization through <M*> and <M*^2>; the text is inconsistent about the maximum mass (1 vs 2 Msun). Section 3.2 and Section 4.
  • domain assumption MBH masses from scaling relations (Greene+20) are valid down to the IMBH regime for galaxies lacking dynamical masses.
    61/91 galaxies get MBH from scaling relations, with large uncertainties; the rate-mass turnover depends on these masses. Section 4, Table 1.
  • domain assumption TDEs are modeled as stars disrupted outside the horizon with Newtonian Hills mass; spin and giant-star disruptions neglected.
    Authors explicitly neglect spin corrections and giant disruptions. Section 2, Hills mass paragraph.
  • ad hoc to paper For spin limits, a constant TDE rate over a Hubble time and half the stellar mass accreted (Eq. 18).
    The simplified spin-down calculation in Section 4.5 is an estimate, not a full growth history; the authors note it is simplified.

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Cite this review

Pith. "Pith review of Counting the Unseen II: Tidal Disruption Event Rates in Nearby Galaxies with REPTiDE." pith.science (2026). https://pith.science/paper/DIUOVNKD

@misc{pith2026241219935,
  author       = {Pith},
  title        = {Pith review of: Counting the Unseen II: Tidal Disruption Event Rates in Nearby Galaxies with REPTiDE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIUOVNKD}},
  note         = {Machine review of arXiv:2412.19935}
}
abstract

Tidal disruption events (TDEs) are a class of transients that occur when a star is destroyed by the tides of a massive black hole (MBH). Their rates encode valuable MBH demographic information, but this can only be extracted if accurate TDE rate predictions are available for comparisons with observed rates. In this work, we present a new, observer-friendly Python package called REPTiDE, which implements a standard loss cone model for computing TDE rates given a stellar density distribution and an MBH mass. We apply this software to a representative sample of 91 nearby galaxies over a wide range of stellar masses with high-resolution nuclear density measurements from arXiv:2407.10911. We measure per-galaxy TDE rates ranging between 10$^{-7.7}$ and 10$^{-2.9}$ per year and find that the sample-averaged rates agree well with observations. We find a turnover in the TDE rate as a function of both galaxy stellar mass and black hole mass, with the peak rates being observed in galaxies at a galaxy mass of $10^{9.5}$ M$_\odot$ and a black hole mass of $10^{6.5}$ M$_\odot$. Despite the lower TDE rates inferred for intermediate-mass black holes, we find that they have gained a higher fraction of their mass through TDEs when compared to higher mass black holes. This growth of lower mass black holes through TDEs can enable us to place interesting constraints on their spins; we find maximum spins of $a_\bullet \approx 0.9$ for black holes with masses below $\sim10^{5.5}$ M$_\odot$.

Figures

Figures reproduced from arXiv: 2412.19935 by the authors.

Figure 1
Figure 1. Top: One-to-one comparison of TDE rates for the Stone & Metzger (2016) galaxy sample with REPTiDE using identical density profiles and black hole masses (dashed line shows the one-to-one line). Bottom: Loss-cone flux curve for NGC 4551 from Stone & Metzger (2016) (red dashed) compared to the same flux curve computed by REPTiDE (black). where κ = 0.34 (Binney & Tremaine 2008) and M(rrelax) = 4π(3 − γ) −1ρ5pc(5 pc)γ r… view at source ↗
Figure 2
Figure 2. Per-galaxy TDE rates for our sample galaxies as functions of galaxy mass (left) and MBH mass (right), colored by galaxy-type. The symbol sizes specify the uncertainty on the rates and the shape indicates the origin of the MBH mass measurement. The solid black lines give the best-fit broken power-laws to the data with the scatter (derived separately above and below the break radius) shown as the gray shaded regions. … view at source ↗
Figure 3
Figure 3. Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: TDE rate uncertainties plotted as a function of MBH mass where the colors indicate the dominate source of error (out of the four explored). While most uncertainties are dominated by errors in MBH mass, the largest uncertainties are due to the sensitivity of steep power…
Figure 5
Figure 5. Figure 5: Pinhole fraction (fpinhole) for our sample galaxies as a function of MBH mass along with the best-fit relations from Stone & Metzger (2016) (black dashed) and Chang et al. (2024) (green) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Cumulative q distributions for our sample galax￾ies highlight the increased contribution to TDEs from the full loss cone regime (q > 1) in lower mass galaxies. The black dashed line gives the q = 1 line. this investigation a step further by deriving the normal￾ized cum…
Figure 7
Figure 7. Figure 7: Maximum dimensionless MBH spin values (amax) shown as a function of MBH mass, with the theoretical maximum value for thin disk accretion 0.997 (Thorne 1974) marked by the black dashed line. The gray crosses represent current SMBH spin measurements from Reynolds (2021).…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.