{"id":"6934bd7f-2227-4200-8c78-5f974eae13b3","arxiv_id":"2412.19935","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using high-resolution nuclear density profiles for 91 galaxies, REPTiDE predicts per-galaxy TDE rates that agree with observed rates and peak near black hole mass 10^6.5 solar masses.","lead":"This paper releases a Python package, REPTiDE, that computes tidal disruption event rates from stellar density profiles, and applies it to 91 nearby galaxies. The computed rates agree with observed TDE rates and peak near black holes of a few times 10^6.5 solar masses.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'rate discrepancy resolved' claim rests on comparing an unweighted binned mean of a non-volume-limited, NSC-selected sample to observed population rates; without a selection/weighting correction, the agreement and the 'only sample changed' conclusion are not established.","rationale":"The paper has substantial independent support: REPTiDE is validated against the Stone & Metzger (2016) implementation with a median residual of 0.019 dex, the code is public, the per-galaxy rates are tabulated, and the self-consistency check against MBH growth over a Hubble time is a useful guard against gross errors. The reader's weakest-assumption pick, the Bahcall-Wolf cusp radius for 47/91 galaxies, is a genuine sensitivity, and the paper explicitly acknowledges that rates are quite sensitive to r_relax for steep profiles. However, I do not think it is the single most load-bearing concern for the central claim. Even if the cusp treatment is accepted, the paper's headline conclusion that the historical theory/observation tension is resolved still requires that the sample average be representative of the galaxy population contributing to the observed volumetric/per-galaxy rates. The sample is admittedly not volume-limited and is biased toward nucleated systems; no selection-weighting or completeness correction is applied before comparing binned means to population-averaged observed rates. This affects every galaxy in the comparison, not just the steep unresolved subset, and it is not captured by the quoted per-galaxy uncertainties. The reader flagged this selection issue in the rationale, though not as the weakest assumption, so my agreement is partial. A concrete, feasible test is to redo the binned-mean fits with selection weights or a distance-limited subsample. Because the reader's verdict is already CONDITIONAL and this concern reinforces the need for that condition rather than overturning the paper's technical contribution, I recommend leaving the verdict unchanged.","tokens_in":28692,"tokens_out":7725,"duration_ms":87617,"concrete_test":"Recompute the Figure 3 binned means and double broken power-law fits using selection weights derived from the distance-limited parent samples cited in Paper I (Pechetti et al. 2020 and Hoyer et al. 2023): assign each of the 91 galaxies a weight equal to the inverse probability of entering the sample, or construct a strictly distance-limited subsample with known completeness, then refit. If the volume/selection-weighted mean rate at log(Mgal) ~ 9.5 differs from the nominal unweighted binned mean by more than 0.5 dex, or if the weighted curve no longer overlaps the Yao et al. (2023) rate estimates, the claimed agreement and the 'only sample changed' conclusion are not yet established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central interpretive claim in Section 5 is that past theoretical overprediction of TDE rates is mostly a sample-selection effect: 'the only thing that has changed is the underlying sample of galaxies we average over.' But the sample used for that averaging is not volume-limited (Section 4 states this explicitly) and is focused on nucleated galaxies, with the low-mass end (Mgal < 10^10.5 Msun) composed entirely of NSC hosts. The observed comparison 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, not an unweighted mean over a collection of preferentially nucleated systems. The binned means in Figure 3 use variable bins of 7 galaxies and weight only by rate uncertainties, not by galaxy number density or selection probability. If nucleated, high-density galaxies are overrepresented in the 91-galaxy sample, the binned mean will be biased upward, and the apparent agreement with observations could be produced by the sample construction rather than by an accurate resolution of the historical rate tension. The r_relax/Bahcall-Wolf cusp sensitivity is real, but it is at least partially propagated into the quoted per-galaxy uncertainties; the sample-selection weighting problem is not addressed at all in the population-level comparison.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":29066,"tokens_out":13516,"duration_ms":117482,"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":[{"comment":"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.","section":"Section 4.1, Figure 3, Eq. 17"},{"comment":"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.","section":"Section 3.3, Eq. 15; Section 4; Figure 4"},{"comment":"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.","section":"Section 3.2 vs Section 4"}],"minor_comments":[{"comment":"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.","section":"Eq. 13 and Section 4"},{"comment":"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.","section":"Eq. 16 and Eq. 17"},{"comment":"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.","section":"Table 1"},{"comment":"The name 'Bahcall-Wolf' is misspelled as 'Bachall-Wolf' in several places (e.g., Section 3.3, Table 1 note, Section 4.2).","section":"Throughout"},{"comment":"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.","section":"Section 4.1"},{"comment":"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.","section":"Section 5"},{"comment":"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.","section":"Table 1 note"},{"comment":"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).","section":"Section 4.2"},{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"This paper is in scope for a main journal in this field. The public code and the per-galaxy rate catalog are useful contributions, and the technical validation is solid. The main risk is the unweighted comparison to observed rates: the headline 'rate discrepancy resolved' is not fully supported without a selection correction or a clear framing of the comparison as preliminary, with the rigorous forward-modeling deferred to Paper III. The internal inconsistencies (PDMF upper mass limit, gamma sign convention) should also be fixed before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe headline: this paper gives you a validated, public loss-cone code and the most resolved per-galaxy TDE rate catalog yet assembled; the claim that the old theory/observation rate tension is mostly a sample-selection effect is plausible, but the paper doesn't quite earn that conclusion because the averaging used for comparison is not population-weighted.\n\nWhat's actually new: REPTiDE, an observer-friendly Python implementation of the standard Cohn-Kulsrud loss-cone formalism, checked against Stone & Metzger (2016) with a median residual of 0.019 dex; and its application to 91 galaxies from Paper I with resolved nuclear densities inside 5 pc. The per-galaxy rates, the turnover near Mgal ~ 10^9.5 / MBH ~ 10^6.5, the pinhole-fraction plateau near 0.75, and the spin limits for low-mass MBHs are all new. The agreement with Chang et al. (2024) on the IMBH rollover, from a very different sample, is a nice independent cross-check. The code and tables are real products; this isn't a paper that hides its machinery.\n\nSoft spots. First, the central comparison. The sample is not volume-limited and is heavily nucleated. The binned means in Figure 3 use 7 galaxies per bin and weight only by rate uncertainties; the Yao et al. (2023) rates are converted from volumetric rates using mass functions, so they represent population averages over all galaxies, not unweighted means over a preferentially nucleated set. The paper's line that 'the only thing that has changed is the underlying sample' is therefore an interpretation, not a demonstrated result. A selection-function or weighting correction, or a forward model like the planned Paper III, is needed to make the 'resolved' claim stick. Second, there is a minor internal contradiction: Section 3.2 states all rates use PDMF masses 0.08-1 Msun, while Section 4 says 0.08-2 Msun. Easy fix, but it should be fixed. Third, the r_relax dependence for the 47 steep galaxies is real and is honestly propagated into per-galaxy uncertainties (sometimes >1 dex, as for NGC 4592), but the turnover position and the low-mass end of the rate-mass relation will shift if those cusp radii are wrong. I'd want that caveat front and center in the abstract or conclusions.\n\nBottom line: this is a serious piece of work, clearly argued, with genuine deliverables. The rate discrepancy claim needs to be toned down or re-derived with selection weighting, but the catalog and code are worth having. Send it to a good referee; it will come back stronger.","headline":"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.","tokens_in":29576,"tokens_out":3168,"would_cite":true,"duration_ms":30566,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Per-galaxy tidal disruption rates now match observed totals","keywords":["tidal disruption events","loss cone theory","nuclear star clusters","black hole demographics","intermediate-mass black holes","Fokker-Planck diffusion","TDE rates","galaxy stellar mass"],"falsifier":"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.","tokens_in":28507,"feed_emoji":"🌠","tokens_out":5251,"duration_ms":52003,"temperature":0.7,"pith_summary":"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.","feed_headline":"Per-galaxy TDE rates now match observed flare counts","feed_subtitle":"Rates computed from resolved stellar cores peak at 10^9.5 solar masses and explain the old theory-observation gap.","key_machinery":"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.","core_discovery":"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 $\\sim10^{5.5}\\,M_\\odot$.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the resolved 3D nuclear density profiles and scaling relations for the 91-galaxy sample used as input to REPTiDE.","marker":"Paper I"},{"why":"Provides the baseline semi-empirical loss-cone implementation whose outputs REPTiDE is validated against, and whose higher rates are the previous comparison point.","marker":"Stone & Metzger (2016)"},{"why":"Establishes the steady-state loss-cone formalism applied here to observed galactic nuclei.","marker":"Wang & Merritt (2004)"},{"why":"Supplies the analytic flux formula and the $R_0(\\epsilon)$ approximation that sets the empty and full loss-cone regimes.","marker":"Cohn & Kulsrud (1978)"},{"why":"Supplies the theoretical $-7/4$ cusp profile used to replace unresolved inner density profiles in steep galaxies.","marker":"Bahcall & Wolf (1976)"},{"why":"Provides the observed ZTF TDE rates and mass functions used to convert volumetric rates to per-galaxy comparisons.","marker":"Yao et al. (2023)"},{"why":"Supplies the black hole mass measurements and scaling relations used for most galaxies in the sample.","marker":"Greene et al. (2020)"},{"why":"Gives an independent recent TDE rate calculation whose IMBH rollover is compared with the turnover found here.","marker":"Chang et al. (2024)"}],"fun_headline_variants":["TDE rates turn over at 10^9.5 solar mass galaxies","TDE growth caps black hole spins at 0.9","REPTiDE computes TDE rates for 91 nearby galaxies","Stellar cores yield TDE rates matching observed flares","TDE rates from 91 galaxies match observed flares"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["TDE rates turn over at 10^9.5 solar mass galaxies","TDE growth caps black hole spins at 0.9","REPTiDE computes TDE rates for 91 nearby galaxies","Stellar cores yield TDE rates matching observed flares","TDE rates from 91 galaxies match observed flares"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001297,"raw_usage":{"total_tokens":5340,"prompt_tokens":1040,"completion_tokens":4300,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":656,"completion_tokens_details":{"reasoning_tokens":4214}},"tokens_in":656,"tokens_out":4300,"duration_ms":29661,"temperature":1.0,"reasoning_tokens":4214,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:46:16.892754+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}