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Wandering intermediate-mass black holes and off-nuclear tidal disruption events from early star clusters

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Claire E. Williams, Smadar Naoz, Yihao Zhou, Tatsuya Akiba-Lewis, Mark Vogelsberger, Blakesley Burkhart, Naoki Yoshida, Avi Chen
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Kyle Kremer, William Lake, Federico Marinacci, Shyam H. Menon

Astrophysics of Galaxies · Submitted 14 Oct 2026 · 300 references

Pith's verdict: 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.

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arXiv ID2610.20719 (version 1)
Pith IDGIVDQRD3, Pith's permanent record of this paper and its review
CitationAvi Chen, Blakesley Burkhart, Claire E. Williams, Federico Marinacci, Kyle Kremer, Mark Vogelsberger, Naoki Yoshida, Shyam H. Menon, Smadar Naoz, Tatsuya Akiba-Lewis, William Lake, Yihao Zhou. "Wandering intermediate-mass black holes and off-nuclear tidal disruption events from early star clusters." arXiv:2610.20719 (2026). https://pith.science/paper/GIVDQRD3
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The paper

The paper claims

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.

The reading

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.

What carries the argument

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.

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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).

Reading between the lines

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

  • 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.
Original abstract

Off-nuclear tidal disruption events (TDEs) reveal evidence for massive black holes outside galactic centers, but the origins of this wandering population remain uncertain. We investigate wandering intermediate-mass black holes (IMBHs) formed through runaway stellar collisions in dense, high-redshift star clusters and predict their TDE signatures across cosmic time. Our semi-analytic model samples clusters associated with low-mass subhalos at $7<z<20$ and uses merger trees from the IllustrisTNG TNG50 simulation to follow the assembly of 15 elliptical galaxies with stellar masses of $10^9-10^{11}~M_\odot$. We compare two models for high-redshift cluster formation: a maximal model taken from a high-resolution simulation and a conservative model calibrated from local cluster relations. Off-nuclear TDEs produced through this mechanism occur in bursts within 10-100 Myr of IMBH formation as the loss-cone surrounding the black hole is depleted. We estimate the rate of off-nuclear TDEs expected across time per galaxy, and characterize these events as typically occurring between $10-10^3$ kpc from their host galaxy centers. Event rates increase with galaxy mass; in the maximal model, the progenitors of the most massive galaxies reach peak off-nuclear TDE rates of approximately $5\times10^{-4}-4\times10^{-2}~\mathrm{yr}^{-1}$ per galaxy at $7\lesssim z\lesssim13$. This work provides a framework for constraining the early population of star clusters that form IMBHs through runaway collapse via their contribution to the rate of off-nuclear TDEs in the high redshift Universe.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-16: 1 request, 6,665 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.53 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Off-nuclear tidal disruption events (TDEs) reveal evidence for massive black holes outside galactic centers, but the origins of this wandering population remain uncertain. We investigate wandering intermediate-mass black holes (IMBHs) formed through runaway stellar collisions in dense, high-redshift star clusters and predict their TDE signatures across cosmic time. Our semi-analytic model samples clusters associated with low-mass subhalos at $7<z<20$ and uses merger trees from the IllustrisTNG TNG50 simulation to follow the assembly of 15 elliptical galaxies with stellar masses of $10^9-10^{11}~M_\odot$. We compare two models for high-redshift cluster formation: a maximal model taken from a high-resolution simulation and a conservative model calibrated from local cluster relations. Off-nuclear TDEs produced through this mechanism occur in bursts within 10-100 Myr of IMBH formation as the loss-cone surrounding the black hole is depleted. We estimate the rate of off-nuclear TDEs expected across time per galaxy, and characterize these events as typically occurring between $10-10^3$ kpc from their host galaxy centers. Event rates increase with galaxy mass; in the maximal model, the progenitors of the most massive galaxies reach peak off-nuclear TDE rates of approximately $5\times10^{-4}-4\times10^{-2}~\mathrm{yr}^{-1}$ per galaxy at $7\lesssim z\lesssim13$. This work provides a framework for constraining the early population of star clusters that form IMBHs through runaway collapse via their contribution to the rate of off-nuclear TDEs in the high redshift Universe.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Off-nuclear tidal disruption events (TDEs) reveal evidence for massive black holes outside galactic centers, but the origins of this wandering population remain uncertain. background 0.57 0.06 0.04 asserted 0.84
s1 We investigate wandering intermediate-mass black holes (IMBHs) formed through runaway stellar collisions in dense, high-redshift star clusters and predict their TDE signatures across cosmic time. contribution 1.00 0.91 0.09 asserted 0.90
s2 Our semi-analytic model samples clusters associated with low-mass subhalos at $7<z<20$ and uses merger trees from the IllustrisTNG TNG50 simulation to follow the assembly of 15 elliptical galaxies with stellar masses of $10^9-10^{11}~M_\odot$. method 1.00 0.91 0.03 asserted 0.98
s3 We compare two models for high-redshift cluster formation: a maximal model taken from a high-resolution simulation and a conservative model calibrated from local cluster relations. method 0.99 0.77 0.03 asserted 0.88
s4 Off-nuclear TDEs produced through this mechanism occur in bursts within 10-100 Myr of IMBH formation as the loss-cone surrounding the black hole is depleted. result 0.98 0.75 0.13 asserted 1.00
s5 We estimate the rate of off-nuclear TDEs expected across time per galaxy, and characterize these events as typically occurring between $10-10^3$ kpc from their host galaxy centers. result 0.96 0.93 0.10 asserted 0.94
s6 Event rates increase with galaxy mass; in the maximal model, the progenitors of the most massive galaxies reach peak off-nuclear TDE rates of approximately $5\times10^{-4}-4\times10^{-2}~\mathrm{yr}^{-1}$ per galaxy at $7\lesssim z\lesssim13$. result 1.00 0.92 0.20 asserted 0.99
s7 This work provides a framework for constraining the early population of star clusters that form IMBHs through runaway collapse via their contribution to the rate of off-nuclear TDEs in the high redshift Universe. contribution 0.47 0.78 0.54 asserted 0.69

What kind of paper the classifier reports this is: simulation study 0.59 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Distributions of star cluster properties, split by host halo mass. Each color corresponds to one halo mass bin (legend). The top row shows cluster stellar mass, cluster half-mass radius, and three-dimensional distance from the halo center in physical kpc. The bottom row shows the magnitude of each cluster’s velocity relative to its host halo, the number of associated clusters per halo, and the cluster–halo separation in units of the halo virial radius, Rvir. the mass of the halo that hosts j. We adopt its stel￾lar mass Mcl, half-mass radius rh, host-centric distance in units of its…
Figure 2. shows the IMBH mass–cluster mass relation for all of our runs. Because our IMBH formation model does not depend on the properties of the host galaxy, the relations for the different mass bins lie on top of one another. The plot shows the central difference be￾tween our models–the increased number of dense clus￾ters seeded in the maximal model leads to a boosted IMBH mass function, driving additional TDEs. In Ap￾pendix B, we show that the dominant impact on the number of IMBH-hosting clusters per galaxy is simply the number of clusters seeded per subhalo, rather than the increased…
Figure 3. Average off-nuclear TDE rate per galaxy among the sample, smoothed over 100 Myr, as a function of redshift for the maximal model (left) and the conservative model (right). The colored lines correspond to stellar mass bins (stellar mass of the Illustris TNG-50 host galaxy at z = 0). The top panels show the TDE rate of events occurring within 3R200c of the host, and the bottom shows the rate occurring outside. Shaded regions show the spread across the five galaxies in each mass bin. present at high redshift drops in the final redshift bin as those clusters are subsumed into the main…
Figure 4. Radial distribution of off-nuclear TDEs about the central galaxy, in five redshift windows (panels). Each curve shows the rate of TDEs per dex of separation, dN˙ TDE/d log10 r, where r is the separation of the TDE-producing IMBH’s host cluster from the main progenitor of the z = 0 galaxy. For each halo, the rate is averaged over the time spanned by the redshift window and smoothed in log10 r with a Gaussian kernel of 0.2 dex FWHM. Colors denote bins of stellar mass at z = 0, solid lines are the mean over the five halos in each bin, and shaded regions span the full halo-to-halo range
Figure 5. ). In the conservative model, every cluster starts deep inside (Re = 0.03R200) and bound to its birth halo. Es￾cape in this model must therefore be driven by the hier￾archical assembly itself. Two processes can do this: the loss of the host subhalo’s mass as it is tidally stripped, which lowers the binding energy of its clusters, and the orbital energy carried by the host subhalo when it is absorbed into a larger halo, which is inherited by its clusters at the hand-off. In the maximal model, a large fraction of clusters additionally begin at 1–5 R200 of their minihalo (
Figure 6. Radial distribution at z = 0 of the IMBHs in our model, compared with the wandering black holes in ASTRID. Each panel shows the number of black holes per galaxy per dex of distance from the center of the central galaxy. The left column gives the physical distance rBH and the right column the distance in units of the central’s R200c at z = 0. Colors give the z = 0 stellar-mass bin. Thick solid and dashed lines are the maximal and conservative models, respectively, averaged over the five galaxies in each bin (
Figure 7. Three-dimensional distributions of star clusters around twelve example dark matter halos. Each row is a halo mass bin, labeled at left, and each column is a halo drawn at random from that bin among halos with at least one associated cluster. In each panel, the black star marks the halo center and the red points are the positions of the halo’s associated clusters relative to the center, in physical kpc. The gray sphere shows the halo’s virial radius, R200. Blue arrows give each cluster’s velocity relative to the halo. Each panel shows the halo mass and the number of associated…
Figure 8. Average TDE rate per galaxy as a function of redshift, as the conservative model (Section 2.3) is converted into the maximal model (Section 2.2.1) one ingredient at a time. Each panel is one z = 0 stellar-mass bin (
Figure 9. Summary of the model sequence in
Figure 10. Smoothed TDE rate per galaxy versus redshift depicting six independent realizations for each halo in our sample. All runs are the maximal model, and only the TDEs that occur beyond 3R200c are shown (see

Figures reproduced from arXiv:2610.20719 by the authors.

References

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