{"id":"f3712fc7-3ce9-4948-b809-0b0ec9ef8b73","arxiv_id":"2610.20719","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":12,"one_line_summary":"Wandering IMBHs from high-redshift star clusters produce off-nuclear TDEs in bursts at z~9-13, with rates up to 4e-2 yr^-1 per galaxy, offering a probe of early cluster conditions.","lead":"This paper predicts that wandering intermediate-mass black holes formed in dense early star clusters produce bursts of off-nuclear tidal disruption events at high redshift, with rates reaching about 1 event per century per massive elliptical galaxy. Such events would offer a new observational window into the properties of the first star clusters, which are otherwise extremely hard to study.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Dependence of TDE rates on the assumed VMS→IMBH conversion efficiency is not independently verified.","rationale":"The reader correctly identifies the IMBH formation model as the weakest assumption. The stress-test finds that within that model, the specific VMS-to-IMBH conversion parameters are uncalibrated and untested against independent simulations or observations. The paper already frames its predictions as bounds, and the reader assigned CONDITIONAL. This concern sharpens that condition—independent calibration of the collapse physics is needed before the rates can be treated as quantitative predictions—but does not warrant a different verdict.","tokens_in":35037,"tokens_out":2281,"duration_ms":23121,"concrete_test":"Run the semi-analytic IMBH formation model (Section 2.4) with the VMS threshold varied from 100 to 500 Msun and the mass conversion factor varied from 0.3 to 1.0, while holding all other cluster parameters fixed. If the peak TDE rate for the maximal model drops below 10^-2 yr^-1 for any plausible combination, the headline result is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of TDE rates up to 4e-2 yr^-1 relies on the assumption that any VMS >200 Msun formed via runaway collisions collapses to an IMBH with 100% mass conversion efficiency, with no mass loss (Section 2.4). This is taken from the authors' own analytic model (Williams+2026a, arXiv:2603.26872), which is not yet independently verified. The model also assumes a fixed metallicity (0.1 Zsun), a single collider mass (1 Msun), and a specific IMF. If the conversion efficiency is lower (e.g., significant mass loss during collapse) or if the threshold mass is higher, the resulting IMBH masses and consequently TDE rates could decrease by an order of magnitude. The paper acknowledges uncertainties in cluster seeding via two models, but does not vary the VMS→IMBH parameters, leaving the rate normalization anchored to uncalibrated cluster physics. While the framework is valuable, the quantitative peak rate is therefore not robust against plausible variations in the VMS collapse physics, and the headline number should be treated as an upper limit modulo this uncertain step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper presents a semi-analytic framework that connects the formation of intermediate-mass black holes (IMBHs) through runaway stellar collisions in high-redshift star clusters to off-nuclear tidal disruption events (TDEs) during galaxy assembly. Using merger trees from TNG50 and two cluster-seeding models (a maximal model from a feedback-free high-resolution simulation and a conservative model calibrated from local scaling relations), the authors follow clusters and their IMBHs through dynamical evolution and compute TDE rates. They predict that off-nuclear TDEs from this channel occur in bursts within 10-100 Myr of IMBH formation, that rates peak at z~9-13 at up to ~4e-2 yr^-1 per massive elliptical galaxy in the maximal model, and that the rates are dominated by the number of clusters per halo and their compactness. The paper also compares the resulting wandering IMBH population with the ASTRID simulation.","tokens_in":35487,"tokens_out":2885,"duration_ms":28432,"significance":"If the results hold, this work provides a direct observational link between the earliest dense star clusters and a potentially detectable population of off-nuclear TDEs, offering a way to constrain cluster formation physics at high redshift that is otherwise inaccessible. The use of two bracketing seeding models gives a useful dynamic range, and the step-by-step decomposition in Appendix B cleanly isolates the dominant uncertainties. The comparison with ASTRID's wandering black hole population is a valuable cross-check. The paper is clear about most of its limitations and represents a step forward in connecting cluster-scale IMBH formation to cosmological galaxy assembly.","major_comments":[{"comment":"The IMBH formation efficiency is a central, non-negotiable assumption: a VMS with mass >200 M_sun is assumed to collapse to an IMBH with zero mass loss (mass conversion factor = 1). This value is taken from the authors' own semi-analytic model (Williams+2026a) and is not varied or tested. If the actual conversion efficiency is lower (e.g., 30-50% mass loss during collapse, or a higher threshold mass), the resulting IMBH masses and consequently TDE rates could decrease by up to an order of magnitude. While the paper thoroughly tests the sensitivity to cluster seeding (Appendix B), it does not test this equally critical parameter. The central claim of peak rates at 4e-2 yr^-1 is therefore anchored to an uncalibrated step in the physics chain. I request that the authors either (a) vary the conversion efficiency and threshold mass in a dedicated sensitivity test, adding a panel to Figure 3 or a supplementary table, or (b) provide a clear physical argument and literature-based error bar for why the fiducial choice is justified and how it affects the headline rate. Without this, the quantitative predictions remain conditioned on an unverified sub-model.","section":"Section 2.4, Eq. (13) and surrounding text","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The cluster orbit integration neglects tidal stripping and mass loss. The authors acknowledge this in §4.4 but do not estimate the magnitude of the effect on the rates. A brief quantitative estimate (e.g., 'the typical cluster mass-loss fraction per orbit would be X, which would reduce the TDE reservoir by Y%') would strengthen the discussion.","section":"Section 2.5, Eq. (5)-(9)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The TDE rate calculation assumes a fixed stellar density profile (alpha=1.2) after IMBH formation and no loss-cone refilling from outside. The authors note in §4.4 that relaxation would drive the profile toward a Bahcall-Wolf cusp (alpha=7/4), which changes the radial time-dependence of the burst. This is correctly flagged as a simplification, but it would be useful to state explicitly how the total number of TDEs per cluster might change (e.g., if the cusp forms, more stars are initially within r_infl, increasing the reservoir by a factor of ~2).","section":"Section 2.6, Eq. (14)-(17)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The shaded regions show halo-to-halo scatter. The seed-to-seed scatter (Table 5, Appendix C) is reported separately. For the lowest mass bin, the seed-to-seed scatter is 16% and the halo-to-halo range is large. The caption could note that in the lowest mass bin the rates are dominated by small-number statistics to guide the reader.","section":"Figure 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The high-resolution simulation uses a boosted sigma8=1.7. The correction factor f_ST=5 is described but its derivation is only referenced to an earlier paper. A one-sentence summary of how f_ST was estimated (e.g., ratio of Sheth-Tormen mass functions at the relevant mass) would improve self-containedness.","section":"Section 2.2.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper is generally well written, but there are occasional missing spaces (e.g., 'T able' in captions) and minor typographical issues. These can be caught in a final proofread.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The discussion of hostless TDEs at Mpc distances is interesting. The authors should note whether these events could be confused with other known hostless transients (e.g., supernovae or kilonovae) at high redshift, if only briefly.","section":"Section 4.2","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The paper is solid and the semi-analytic framework is a clear advance. The main issue is the lack of any sensitivity test on the VMS→IMBH conversion efficiency, which the skeptic's note flags and which I agree is load-bearing. Adding a simple parameter scan would resolve this and significantly strengthen the paper's robustness claims. The paper otherwise meets the journal's standards for theoretical astrophysics."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"This paper does something genuinely new: it connects a semi-analytic model of IMBH formation in high-redshift star clusters to galaxy merger trees and computes off-nuclear TDE rates as a function of host mass and redshift. The combination of ingredients (cluster seeding from a feedback-free simulation and from local scaling relations, orbit integration with dynamical friction, and a relaxation-driven TDE burst calculation) has not been done before. The step-by-step decomposition in Appendix B showing which ingredients drive the factor-of-20 difference between models is a model of transparency.\n\nThe authors are unusually honest about limitations. They acknowledge the uncertain VMS-to-IMBH conversion, the fixed stellar density profile, the neglect of tidal stripping, loss-cone refilling, and cluster evolution. They state flatly that the simulation-based seeding model is a maximal case within LambdaCDM. The paper's internal logic is sound, and the two bounding models bracket the plausible range.\n\nThe soft spot is the one the stress-test note flags: the IMBH formation model (Williams+2026a) is taken without independent verification. The assumption that any VMS >200 Msun collapses to an IMBH with 100% efficiency is a single-parameter choice that directly anchors the TDE rate normalization. If the threshold is higher or mass loss significant, the peak rate in the maximal model could drop by an order of magnitude, moving it closer to the conservative model's rate. The paper does not vary these parameters, so the upper bound is softer than the factor-of-20 spread between models suggests. The reader's circularity concern (3/10) is fair but partially mitigated by the two seeding models and the transparent appendix.\n\nThis paper is for two audiences: observers planning high-redshift transient surveys (it gives a target rate and radial distribution) and theorists working on IMBH formation and cluster dynamics. It deserves a serious referee—the framework is reusable and the limitations are stated. The headline numbers should be treated as exploratory upper limits until the VMS-to-IMBH efficiency is independently constrained.","headline":"A credible framework for off-nuclear TDEs from cluster-born IMBHs, but the headline rates are upper limits due to unverified VMS-to-IMBH efficiency.","tokens_in":36558,"tokens_out":778,"would_cite":false,"duration_ms":21458,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"Off-nuclear tidal disruption events from wandering intermediate-mass black holes are predicted to peak at high redshifts and rates up to ~4e-2 yr^{-1} in massive elliptical galaxies, with the rate tracing star cluster density and abundance.","keywords":["Intermediate-mass black holes","Star clusters","Tidal disruption events","Galaxy formation","Elliptical galaxies","High-redshift universe","Runaway stellar collisions","Dynamical friction"],"falsifier":"A deep, wide-field time-domain survey at z~9–13 (e.g., with JWST extended mission or a dedicated Roman survey) that finds no off-nuclear TDEs at rates above ~$10^{{-3}}$ $yr^{{-1}}$ for massive (M_*>$10^{{11}}$ M_⊙) galaxies would rule out the maximal cluster seeding model, implying that early star clusters are either much less numerous or much less dense than the feedback-free simulation suggests.","tokens_in":36555,"feed_emoji":"🕳️","tokens_out":3729,"duration_ms":36010,"temperature":0.7,"pith_summary":"This paper argues that intermediate-mass black holes (IMBHs) born via runaway stellar collisions in the dense star clusters of the early Universe will produce bursts of off-nuclear tidal disruption events (TDEs) as they deplete the stars within their gravitational sphere of influence. The authors build a semi-analytic model that places star clusters into the merger trees of 15 simulated elliptical galaxies, follows the clusters' orbits under dynamical friction, and calculates when and how many stars each cluster-born IMBH disrupts. They find that the TDE activity is not a steady trickle but a rapid burst lasting 10–100 million years after the IMBH forms, because the stellar reservoir is not replenished. The peak rate per galaxy scales strongly with galaxy mass and the compactness of the seeding clusters: in a maximal scenario drawn from a feedback-free high-redshift simulation, the most massive ellipticals (stellar mass >$10^{{11}}$ M_⊙) reach ~4e-2 $yr^{{-1}}$ at z~9–13, while a conservative scenario based on local globular cluster relations gives rates about two orders of magnitude lower. The work matters because if true, it predicts a population of high-redshift off-nuclear TDEs that could be detectable with JWST or future surveys, offering a direct probe of the density and abundance of the Universe's first star clusters.","feed_headline":"Wandering IMBHs cause TDE bursts at 4e-2 yr^{-1} at z~9–13","feed_subtitle":"First prediction of off-nuclear TDE rates from cluster-born IMBHs, linking early star cluster density to observable transients.","key_machinery":"The machinery is a semi-analytic model that combines: (i) a calibration catalog of star clusters extracted from a feedback-free, high-resolution cosmological hydrodynamical simulation (Williams et al. 2025) or, alternatively, empirical scaling relations for globular cluster systems (Burkert & Forbes 2020; Marks & Kroupa 2012); (ii) the SubLink merger trees of 15 dispersion-dominated (elliptical) galaxies from the Illustris TNG50-1 simulation; (iii) an analytic IMBH formation prescription (Williams et al. 2026a) that follows runaway stellar collisions and the collapse of a very massive star when the cluster is dense enough; (iv) an orbit integrator that evolves each cluster through the merger tree under the combined gravitational potential of its host dark-matter halo (NFW profile) and dynamical friction (Chandrasekhar 1943); and (v) a loss-cone TDE rate calculation that assumes the stellar density profile is fixed after IMBH formation and that stars are fed into the loss cone by two-body relaxation on the local relaxation timescale. The key unifying object is the star cluster itself: its internal density sets the IMBH mass, its orbital decay sets the spatial distribution of TDEs, and its stellar mass limits the total number of TDEs per cluster.","core_discovery":"The central claim is that off-nuclear tidal disruption events are a natural, time-delayed consequence of IMBH formation in dense, high-redshift star clusters. Because the IMBH is built from the cluster's own stars and the surrounding stellar population is not replenished, each IMBH produces a prompt burst of TDEs—typically within 10–100 Myr of its formation—rather than a sustained rate over cosmic time. The galaxy-integrated TDE rate therefore tracks the formation rate of IMBH-hosting clusters in its progenitor halos. Using merger trees from Illustris TNG50-1 and two contrasting models for seeding early star clusters, the authors predict that the progenitors of the most massive elliptical galaxies experience peak off-nuclear TDE rates of approximately 5×$10^{{-4}}$–4×$10^{{-2}}$ $yr^{{-1}}$ per galaxy at 7≲z≲13, with events occurring at separations of 10–$10^{3}$ kpc from the eventual galaxy center. The difference between the maximal and conservative models (roughly a factor of 20 in integrated TDE number) is driven primarily by the number of clusters per halo (factor ~10) and their compactness (factor 2–3), showing that the off-nuclear TDE rate is a sensitive diagnostic of early cluster formation conditions.","pith_inferences":["If the maximal model is correct, then high-redshift surveys should find a population of transient flares not associated with any obvious host galaxy, located tens to hundreds of kiloparsecs from massive ellipticals. A non-detection at the predicted rates would falsify the assumption that feedback-free high-resolution simulations accurately represent star cluster formation in the early Universe.","The predicted burst-like nature of these TDEs (10–100 Myr) means that the event rate at any fixed redshift is strongly non-stationary: individual clusters are invisible most of the time and bright only during their brief TDE phase. Stacking or wide-field time-domain surveys may be required to catch the population.","The semi-analytic framework could be extended to other feedback models or cosmological simulations to test the robustness of the rate predictions. In particular, including stellar feedback and metal enrichment in the high-resolution simulation would lower cluster densities and reduce the maximal rate, narrowing the gap with the conservative model.","The comparison with ASTRID's wandering black hole population (Figure 6) suggests that traditional halo-based seeding misses a large population of low-mass IMBHs formed in multiple star clusters per halo. This could have consequences for gravitational-wave event rates from IMBH mergers and for the seeding of supermassive black holes at high redshift."],"forward_implications":["If dense star clusters commonly form IMBHs via runaway collisions, then the progenitors of massive elliptical galaxies should produce a burst of off-nuclear TDEs at z~9–13, potentially observable with next-generation facilities like JWST, Roman, or future X-ray observatories.","The off-nuclear TDE rate encodes the abundance and internal density of early star clusters: measuring it (or obtaining upper limits) would discriminate between the maximal and conservative seeding scenarios, thereby constraining the physics of the first star clusters.","A large fraction of these TDEs would appear at >3R_{200c} from the host galaxy, often in separate low-mass halos, leading to apparently hostless transients that could be misattributed to other phenomena or overlooked.","The absence of a high-redshift TDE burst would rule out the efficient formation of IMBHs in dense star clusters as a major channel, placing strong limits on the cluster densities at z>7.","At low redshift (z<3), the model predicts negligible off-nuclear TDEs from this channel if cluster formation stops at z~7, but a continued rate at ~10^{-5}–10^{-4} yr^{-1} if clusters keep forming—potentially contributing to the off-nuclear TDE candidates observed locally by e.g., Guolo (2026)."],"supporting_citations":[{"why":"Supplies the analytic model for IMBH formation through runaway stellar collisions and very massive star collapse, which is the core of our IMBH production pipeline.","marker":"Williams et al. 2026a"},{"why":"Provides the high-resolution cosmological simulation calibration catalog of star clusters used as the maximal model for the initial cluster population.","marker":"Williams et al. 2025"},{"why":"Describes the Illustris TNG50-1 simulation whose merger trees and halo catalogs are used to follow the hierarchical assembly of the 15 elliptical galaxies in our sample.","marker":"Nelson et al. 2019"},{"why":"Establishes the M_vir–N_GC relation used in the conservative star cluster model to set the number of clusters per progenitor halo.","marker":"Burkert & Forbes 2020"},{"why":"Provides the birth mass–radius relation for embedded clusters used in the conservative model to assign half-mass radii.","marker":"Marks & Kroupa 2012"},{"why":"Supplies the dynamical friction formula used to integrate cluster orbits through the merger tree.","marker":"Chandrasekhar 1943"},{"why":"Compiles a sample of four off-nuclear TDE candidates at low redshift, which our model attempts to explain for the case of continued cluster formation.","marker":"Guolo 2026"}],"fun_headline_variants":["Cluster-born IMBHs spark off-nuclear TDE bursts at z~7–13","Off-nuclear TDE rate from wandering IMBHs peaks at 4e−2 yr^{-1}","Bursty off-nuclear TDEs reveal IMBHs from early star clusters","IMBHs formed in high-z clusters produce prompt TDE outbursts","Wandering IMBHs from dense clusters cause TDE bursts within 100 Myr"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The IMBH formation model (runaway collisions to a very massive star that collapses directly to an IMBH) is taken from the authors' own semi-analytic work without independent verification, and the maximal cluster seeding model is derived from a simulation that lacks stellar feedback, which could significantly reduce cluster densities and numbers.","fun_headline_variants_meta":{"raw":{"variants":["Cluster-born IMBHs spark off-nuclear TDE bursts at z~7–13","Off-nuclear TDE rate from wandering IMBHs peaks at 4e−2 yr^{-1}","Bursty off-nuclear TDEs reveal IMBHs from early star clusters","IMBHs formed in high-z clusters produce prompt TDE outbursts","Wandering IMBHs from dense clusters cause TDE bursts within 100 Myr"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000351,"raw_usage":{"cost":0.000351439788,"is_byok":false,"cost_details":{"upstream_inference_cost":0.000351439788,"upstream_inference_prompt_cost":4.2612108e-05,"upstream_inference_completions_cost":0.00030882768},"total_tokens":4589,"prompt_tokens":1153,"completion_tokens":3436,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":256,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":3321}},"tokens_in":1153,"tokens_out":3436,"cost_source":"openrouter_usage","duration_ms":31786,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":3321,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-16T18:03:26.806594+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"A deep, wide-field time-domain survey at z~9–13 (e.g., with JWST extended mission or a dedicated Roman survey) that finds no off-nuclear TDEs at rates above ~$10^{{-3}}$ $yr^{{-1}}$ for massive (M_*>$10^{{11}}$ M_⊙) galaxies would rule out the maximal cluster seeding model, implying that early star clusters are either much less numerous or much less dense than the feedback-free simulation suggests.","supporting_citations":[],"review_version":1}