Pith. sign in

REVIEW 2 major objections 6 minor 135 references

Recoiling Black Holes I. Burst of Observables

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A recoiling black hole's kick instantly refills its loss cone, producing a burst of tidal disruptions and gravitational-wave captures that could reach roughly 290 offset events per year out to redshift 3.

desk verdict A credible N-body demonstration of a prompt TDE/GW burst from recoiling IMBHs, with headline all-sky rates that are softer than the abstract implies because the γ=1 forecast is an extrapolation of a fit calibrated only at γ=1.75. read the letter →

arxiv 2608.09662 v1 pith:QVRUNPNZ submitted 2026-08-10 astro-ph.HE astro-ph.GA

Erwan Hochart , Simon Portegies Zwart This is my paper · ORCID
classification astro-ph.HEastro-ph.GA
keywords blackholesactivegalacticnucleigravitationalwavesstarclustershigh-redshiftgalaxiestidaldisruptioneventsrecoilinglossconerepopulation
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 argues that the immediate aftermath of a massive black hole binary merger is a burst of activity rather than a quiet ejection. The recoil kick imparted to the merged black hole acts as an impulsive change in the angular momentum of every surrounding star, instantly repopulating the black hole's loss cone and producing a short-lived burst of tidal disruption events (TDEs) and gravitational-wave captures. The burst lasts several orbital periods, not just a single pass, because the kick polarises the orbits of the bound stars into a coherent apsidal alignment whose collective torques keep resupplying disruptive orbits. Using direct N-body simulations of intermediate-mass black holes ($M_\bullet=10^5$ and $4\times10^5\,M_\odot$) kicked at $300$ and $600$ km s$^{-1}$, the paper derives an analytic event-rate law and folds it into cosmological forecasts. If the inner milliparsec of the nuclear star cluster retains the steep Bahcall–Wolf cusp, the forecast reaches $\dot{N}\lesssim290$ observable offset events per year out to $z<3$, whereas a shallow cusp ($\gamma=1$) lowers it to $\dot{N}\lesssim30$ per year.

What carries the argument

The central object is the loss cone: the region of angular momentum below which a star is tidally disrupted or a compact object is captured by the black hole, defined by $L_{\min}\simeq\sqrt{2GM_\bullet R_{\rm tide}}$. The kick repopulates it instantly through the velocity translation $\mathbf{v}\to\mathbf{v}-\mathbf{v}_k$, and the prolonged burst is carried by apsidal alignment: clustered eccentricity vectors make the cluster a mildly triaxial, coherently precessing system whose resonant torques replenish the loss cone on the precession timescale $t_\omega\simeq(M_\bullet/M_{\rm HCSC})P_{\rm orb}$. The quantitative backbone is the fitted rate law $\Gamma=\eta\,A\,B\,C\,D\,E^{-1}e^{-Dt}$, built from the loss-cone filling fraction for a nonspherical potential ($P_{LC}\sim v_k^{-1}$), the scoured-cavity power-law cusp of Equation 5, and the apsidal precession decay.

What would settle it

Survey the sky for offset TDEs and compact-object mergers out to $z\simeq3$ with all-sky X-ray/optical and gravitational-wave instruments: an observed all-sky rate far below the paper's $\gamma=1$ forecast of ~30 yr$^{-1}$ (let alone ~290 yr$^{-1}$), given the assumed intermediate-mass black hole merger rates, would falsify the loss-cone-burst mechanism as quantified here. A more local test is to measure the stellar density slope at milliparsec scales around a post-merger black hole and check whether $\gamma=1.75$ actually holds there.

Watch

Extended reading notes

Core claim

The central claim is that the loss cone of a merged black hole is not left empty: the recoil kick's velocity shift places a substantial fraction of the bound stellar cusp on low-angular-momentum orbits, so the remnant immediately begins disrupting stars and capturing compact objects. This initial burst is extended by apsidal alignment—the eccentricity vectors of the surviving cluster are preferentially oriented relative to the kick direction, making the hyper-compact stellar cluster mildly triaxial—and the coherent torques among aligned orbits drive eccentricity oscillations that keep refilling the loss cone for roughly $10^4$ orbital periods. The paper packages the result as an analytic rate law, $\Gamma(t)\propto M_\bullet^{0.365}\,v_k^{-1}\,e^{-t/t_\omega}$, with a precession timescale $t_\omega\simeq0.045$\,–\,$0.125$ Myr for the simulated configurations, and translates it into all-sky forecasts of $\dot{N}\lesssim290$ yr$^{-1}$ for $\gamma=1.75$ and $\dot{N}\lesssim30$ yr$^{-1}$ for $\gamma=1$ up to $z=3$. Rates are higher for lower kick velocities, larger black hole masses, and steeper cusps—an inverse-kick scaling opposite to the prediction of resonant-relaxation models.

Load-bearing premise

The quantitative forecasts and the burst enhancement assume that the post-merger nuclear star cluster is spherical with a Bahcall–Wolf cusp ($\gamma=1.75$), scoured empty inside the gravitational-wave radius $a_{\rm GW}$, and consists of a single 100-Myr-old stellar population with no primordial mass segregation.

Editorial extensions

If this is right

  • With the steep Bahcall–Wolf cusp, recoiling intermediate-mass black holes ejected from their hosts yield up to ~290 observable offset tidal-disruption and gravitational-wave events per year out to redshift 3; with a shallow cusp ($\gamma=1$) the same calculation gives $\dot{N}\lesssim30$ yr$^{-1}$.
  • The burst phase extends well beyond the first orbital pass: apsidal alignment keeps the loss cone refilled for several orbital periods, boosting rates by roughly 7–20 times relative to a static black hole for $\gamma=1.75$ and 30–100 times for $\gamma=2$.
  • Because the event rate is so sensitive to the inner density slope $\gamma$, observed counts (or non-detections) of offset transients become a probe of the milliparsec-scale stellar distribution at the moment of black hole merger.
  • Rates increase for lower kick velocities and larger black hole masses, and the inverse scaling of the burst rate with $v_k$ distinguishes this mechanism from resonant-relaxation-driven models, which predict rates that grow with kick speed.

Reading between the lines

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

  • If nuclear star clusters are mass-segregated before merger, the inner ~10 mpc could be dominated by stellar-mass black holes rather than stars; the burst would then shift toward EMRI-type gravitational-wave captures and away from optical/UV tidal disruptions, changing the observable mix.
  • A few years of all-sky transient surveys with no offset TDEs would not uniquely falsify the idea, because rare intermediate-mass black hole mergers, low nuclear-star-cluster occupancy, or a shallow cusp could each suppress the rate; the paper's two density-slope cases bracket this degeneracy.
  • Extending the same mechanism to sub-escape kicks, which the paper only briefly mentions, would add a factor ~10–20 to the rates; the resulting sources would not appear as offsets but as returning transients.
  • Adding post-Newtonian terms to the integrator is a natural next step; the paper argues their omission underestimates EMRI occurrence and strains, so the frequency–strain map shown for the simulated events is likely a lower bound.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper uses 25 direct N-body simulations (AMUSE/Ph4, 4th-order Hermite, no softening, stellar evolution with SeBa) of an intermediate-mass black hole (M_sun = 10^5 and 4x10^5) embedded in a Bahcall-Wolf (gamma=1.75) nuclear star cluster, subjected to a recoil kick v_k = 300 or 600 km/s, and integrated for 0.1 Myr. The principal claims are: (i) the kick instantaneously refills the loss cone, producing a burst of tidal disruptions and gravitational-wave events; (ii) the post-kick apsidal alignment of the bound (HCSC) population sustains this burst on the t_omega ~ 45-65 kyr precession timescale; (iii) rates scale as v_k^-1, M^0.365, and increase with gamma; and (iv) after calibrating the analytic rate formula (Eq. 12) to the simulations and convolving with cosmological IMBH merger histories, the all-sky observable rate is ~290/yr for gamma=1.75 and ~30/yr for gamma=1 out to z=3, dominated by TDEs. The paper is explicitly framed as a burst-phase extension of Komossa & Merritt (2008) and Stone & Loeb (2012), and it repeatedly discloses its main simplifications: Newtonian-only dynamics with EMRI proxies, a lower-limit scoured cavity a_GW, and single-gamma initial conditions.

Significance. If the burst mechanism is confirmed, the paper delivers a falsifiable, observationally timely prediction: an early post-merger phase whose rates exceed RR-based forecasts by factors of 5-180, with a v_k dependence opposite to the RR regime - a distinctive signature for Rubin/eROSITA and LISA-era surveys. Credit is due for the mechanics of the study: event counts are directly visible in the simulations; the fit is anchored to a publicly available, standard N-body stack (AMUSE/Ph4/SeBa/AGAMA); and the limitation statements are unusually thorough (PN omission, cavity overestimate, limited mass/kick range, NSC occupancy). The headline 290/yr is an upper limit; the paper's own acknowledged factors (NSC occupancy 0.3-0.6, mean stellar mass of 2 M_sun, wider cavity, mass segregation) can individually reduce it by factors of 2-5, so the robust takeaway is 'of order tens to a few hundred events per year, TDE-dominated.' The gamma=1 branch, which is the more realistic one for massive post-merger galaxies per the paper's own citation of Merritt & Milosavljevic (2005), is the least supported and needs direct testing before the forecast stands as a quantitative prediction.

major comments (2)
  1. [Sec. 4.1.1-4.1.2; Eq. 12] The gamma=1.0 forecast of ~30/yr is an untested extrapolation of constants calibrated only at gamma=1.75. All 25 runs in Table 1 use gamma=1.75, and the best-fit eta~8.7e4, alpha~6.4e-4, beta~9.55 (Section 3.1.1) are inserted into Eq. 12 for gamma=1.0 without any check that these constants are gamma-independent; the passage at the end of Section 3.1.1 describes them as encapsulating the mass of the apsidally aligned population, the characteristic semi-major axis ratio, and the angular dispersion of eccentricity vectors, all of which plausibly vary with gamma. The same issue underlies the entire gamma-scan in Figure 3 and the '30-100 times greater' burst-enhancement factors quoted in Section 3.1.2, since these are evaluations of Eq. 12, not of simulations at those slopes. Because the forecast varies by a factor of 10 between gamma=1.75 and gamma=1, and because Section 3.1.2 cites Merritt & Milosavljevic (2005) as indicating that real major-merger cusps settle at gamma~1, the 30/yr figure in the abstract and conclusions is a load-bearing quantitative claim resting on an unvalidated assumption. I recommend either running a gamma=1 grid at the same cost as the existing runs, or explicitly reframing the gamma=1 curve as an uncalibrated scaling estimate with an uncertainty band.
  2. [Sec. 2.3, 3.2.2, 4.1.1] The GW component of the results and forecasts (Table 2, left panel of Figure 2, and the roughly 20/yr GW contribution to the 290/yr forecast) is derived from collision proxies: because the code is Newtonian, a compact object whose periastron relative to the IMBH exceeds the Schwarzschild radius is classified as a 'potential EMRI progenitor' (Section 2.3). The paper discloses this limitation honestly and repeats it in Sections 3.2.2 and 5, but the forecast still splits the observable rate into TDE and GW channels using the simulation's 1:10 ratio, and that ratio inherits an unquantified bias from the proxy. The paper's own argument (Section 2.3, citing Hochart & Portegies Zwart 2024) is that PN terms would increase the EMRI number and strain, so the direction of the bias is known but its magnitude is not; consequently the ~20/yr GW number is not a calibrated EMRI rate. Since the abstract and conclusions present 'gravitational wave mergers' as part of the headline burst, the GW branch of the forecast should be labeled as an order-of-magnitude proxy estimate, ideally calibrated against the PN-inclusive treatment cited in Section 2.3.
minor comments (6)
  1. [Sec. 3.1.1, Eq. 10] Equation 10 presents the rate as Gamma(t) proportional to A(gamma) M^0.365 v_k <m*> exp(-t/t_omega), with v_k in the numerator, but the text immediately below states that the non-spherical potential 'provides the 1/v_k dependency', and the appendix's Eq. A.44 (and the full expression A.45, where <m*> appears in the denominator) give Gamma proportional to v_k^-1. Equation 10 appears to have a misplaced superscript and should be corrected to avoid contradicting Figure 2 and the abstract's 'rates increase for lower v_k'.
  2. [Sec. 6] The energy accounting contains arithmetic errors: 5160 core-hours x 150 W = 774 kWh, not the quoted 32.250 kWh (the spurious factor 1/24 appears), and the CO2 line is internally inconsistent because 91.875 kWh x 0.27936 kg/kWh is about 25.7 kg, not 9.0 kg. The energy-consumption estimate should be recomputed.
  3. [Sec. 4.1.1 vs 4.1.2] Section 4.1.1 states that the observed NSC occupancy factor of 0.3-0.6 'can lead to a factor two to three enhancement in forecasted rates', but Section 4.1.2 states the opposite, that predicted rates 'shrink by a factor~0.3-0.6'; the latter is the correct direction and the former appears to be a wording error.
  4. [Sec. 5 vs Sec. 3.1.2, 4.2] Section 5 disclaims any extrapolation to SMBH masses ('it is difficult to motivate any extrapolation of our results to SMBH masses'), yet Figure 3 and Section 4.2 apply Eq. 12 at M = 10^6-10^7 M_sun, including the LRD rate estimates; the mass-regime caveat should be stated at the point of use in Sections 3.1.2 and 4.2.
  5. [Sec. 3.1.1] The statement that the apsidal-alignment mechanism 'can prolong the initial burst of tidal disruptions and merging events for >10^4 orbital periods' is taken from Madigan et al. (2018) and Akiba et al. (2024); the runs here cover 5-180 orbits and the fitted decay sets in at t_omega about 45-65 kyr, so the prolongation claim should be attributed explicitly to the literature at that location rather than appearing as a result of these simulations.
  6. [Sec. 3.1.1, Fig. 2] The best-fit parameters eta, alpha, beta are quoted once for fits to both panels of Figure 2, although the GW and TDE event counts differ by roughly an order of magnitude; please state whether the two channels are fitted separately and how eta is normalized per channel.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the burst result is a direct N-body finding and the forecasted rates are calibrated extrapolations, not re-statements of the inputs.

full rationale

The derivation chain is not circular. The central burst claim is a direct output of 25 N-body runs (Table 1; Fig. 2), where the kick is applied to a pre-scoured Bahcall-Wolf cusp and TDE/GW events are counted from collision detection; no fitted parameter defines the existence or timing of the burst. Equation 12 is an analytic fitting function calibrated to those simulations (eta, alpha, beta), and using a calibrated formula to extrapolate to un-simulated masses, kicks, and redshifts is standard modeling rather than a self-referential reduction: the all-sky rates in Eqs. (19)-(20) integrate Eq. 12 against independent cosmological inputs (Kritos et al. 2025 merger rates, Lousto et al. 2012 kick distribution, Furlong et al. 2015 galaxy masses, Planck cosmology), so Ndot is not equal to the fitted constant by construction. The gamma=1.0 forecast is an extrapolation of the gamma=1.75-calibrated coefficients, which the paper treats as assumption-dependent; extrapolation risk is a correctness caveat, not circularity. The 1:10 GW/TDE split from Table 2 is used for decomposition, not to generate the total rate. Self-citations (Hochart & Portegies Zwart 2024; Hochart et al. in prep.) appear only as caveats or bracketing assumptions; the central physical conclusion does not reduce to them, and the forecast is externally compared against Stone & Loeb (2012) and Komossa & Merritt (2008). No equation is equivalent to its own input by construction.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The central quantitative claims rest on a chain of domain assumptions about the post-merger stellar cusp, the HCSC shape, the apsidal-alignment mechanism, and the Newtonian collision proxy for GW events. The analytical rate equation is then calibrated to the simulations with fitted constants (eta, alpha, beta) and combined with hand-chosen inputs (occupancy, disrupted fraction, mean stellar mass) to produce the forecast. No new physical entities are introduced.

free parameters (7)
  • eta (Eq 12 normalization) = ~8.7e4
    Normalizes the analytical event rate to the simulated event counts in Figure 2; every forecasted rate scales linearly with this fitted constant.
  • alpha (Eq 12) = ~6.4e-4
    Fitted coefficient in the damping term D; sets the exponential decay timescale of the burst phase.
  • beta (Eq 12) = ~9.55
    Fitted coefficient in D; absorbs the unmeasured spread of eccentricity vectors and other unresolved dependencies.
  • GW-to-TDE ratio = 1:10 (IMBH-involving events)
    Taken from Table 2 of the simulations; used to split the forecasted event total into GW and TDE components.
  • Disrupted HCSC fraction = 0.30
    Assumed fraction of the cluster mass eventually disrupted, following O'Leary & Loeb (2012); sets the dormancy age in the forecasting model.
  • Average stellar mass in HCSC = 1 M_sun (fiducial)
    Forecast uses <m>=1 M_sun; the paper shows <m>=2 M_sun reduces rates ~4.5x, so this choice materially affects the headline rates.
  • NSC occupancy fraction = 1.0 (all galaxies host NSC)
    The 290/yr rate assumes every eligible galaxy hosts an NSC; the paper notes true occupancy ~0.3-0.6 would reduce rates. This is a hand-chosen input rather than a fit.
assumptions (8)
  • standard math Kepler's third law and orbit-averaged loss-cone theory are used to derive the event-rate integral (Eq A.11, A.19).
    Invoked in Appendix A to convert orbital parameters into event rates; standard celestial mechanics.
  • domain assumption The NSC density profile at merger is a Bahcall-Wolf cusp (gamma=1.75) with zero stars inside a_GW (Eq 5).
    Section 2.1 motivates this from Merritt et al. (2009) for the collisional, dry regime; all simulations use gamma=1.75 and the forecasting compares gamma=1.75 with gamma=1.
  • domain assumption The HCSC is mildly triaxial, giving loss-cone filling fraction scaling as 1/v_k (Eq A.7).
    Section 3 and Appendix A use Merritt (2013) non-spherical loss cone; triaxiality is checked in the simulations (Figure A.2).
  • domain assumption Apsidal alignment of eccentricity vectors sustains loss-cone refilling for more than 10^4 orbital periods (Madigan et al. 2018).
    Section 3.1.1 and 3.1.3 invoke the torque mechanism to explain prolonged bursts and to set the exponential decay timescale t_omega in Eq 12.
  • domain assumption The recoil kick exceeds the galactic escape velocity, so the galactic potential can be neglected.
    Section 3.1.1 restricts to v_k > v_esc to justify integrating an isolated cluster; this excludes the parameter range where the cluster remains bound to the galaxy.
  • domain assumption Newtonian collisions with the central BH (within ISCO or tidal radius) are proxies for GW mergers and EMRI progenitors.
    Section 2.3-2.4 state PN terms are omitted for computational cost; 'GW events' are identified by collision criteria, which the paper acknowledges is not self-consistent EMRI modelling.
  • ad hoc to paper The interaction-window factor f_win (Eq A.37-A.42) with undetermined constant k captures the finite duration of clump torques.
    Introduced in Appendix A to modulate the event rate; k and related quantities are never measured and are folded into the fitted parameters eta, alpha, beta.
  • domain assumption The fitted event-rate formula (Eq 12) extrapolates to untested gamma, M_bullet, and v_k in the cosmological forecast.
    Section 4.1.1 applies Eq 12 across a Monte Carlo draw of M_bullet and v_k from distributions, including masses up to 1e7 Msun and gamma=1, beyond the four simulated configurations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Recoiling Black Holes I. Burst of Observables." pith.science (2026). https://pith.science/paper/QVRUNPNZ

@misc{pith2026260809662,
  author       = {Pith},
  title        = {Pith review of: Recoiling Black Holes I. Burst of Observables},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QVRUNPNZ}},
  note         = {Machine review of arXiv:2608.09662}
}
abstract

We aim to investigate the tidal disruption and gravitational wave events shortly after a massive black hole binary merges in the galactic centre and whose remnant black hole is ejected from the galaxy. Using computational methods, black holes of mass $M_{\bullet}=10^{5}$ M$_\odot$ and $4\times10^{5}$ M$_\odot$ embedded in a nuclear star cluster are kicked at velocities of $v_k=300$ and $600$ km s$^{-1}$. Systems are integrated for $0.1$ Myr using a $4$th-order Hermite scheme. The kick instantaneously repopulates the loss cone, producing a strong burst of tidal disruption events and gravitational wave mergers. The anisotropy in the apsidal orientation of bound stars prolongs this burst phase. Rates increase for lower $v_k$, larger $M_{\bullet}$ and for steeper nuclear star cluster density profiles at moment of merger. Assuming binary black holes scour a Bahcall-Wolf density profile during coalescence, ejected remnants with mass between $10^{5}\leq M_{\bullet}$ [M$_\odot] \leq 4\times10^{5}$ generate observable offset events at a forecasted rate of $\dot{N}\lesssim290$ yr$^{-1}$ up to redshift $z=3$. If, at the moment of merger, the milliparsec scales of the nuclear star cluster are described by a shallow density profile ($\gamma=1$), this decreases to $\dot{N}\lesssim30$ yr$^{-1}$. The strong dependence on the initial density profile and recoil kick makes observables powerful probes of the nuclear star cluster post-massive black hole binary coalescence, and provides test for numerical relativity.

Figures

Figures reproduced from arXiv: 2608.09662 by the authors.

Figure 1
Figure 1. Left: Particle argument of periapsis, ω, pre-kick (red contour) and post-kick (black bars). Right: Normalised distribution of the eccentricity￾vector, ˆe, orientation relative to the kick direction, pre-kick (red) and post-kick (black). Data considers M• = 4 × 105 M⊙ and vk = 600 km s−1 . 0.00 0.02 0.04 0.06 0.08 0.10 t [Myr] 5 10 15 20 25 N G W 0.00 0.02 0.04 0.06 0.08 0.10 t [Myr] 20 40 60 80 100 120 NTD E 10 5 M … view at source ↗
Figure 2
Figure 2. Collision events with the central IMBH in time. Left corresponds to GW events while right, TDEs. Solid coloured lines represent the median events when vk = 300 km s−1 , while dotted lines vk = 600 km s−1 . Shaded regions in 75% and 25% interquartile range. Gray lines represent the best-fit (Equation 12). of merger, the surrounding region is characterised with density slope γ ≲ 1.2 − 1.4, then recoiling IMBH will app… view at source ↗
Figure 3
Figure 3. Thick lines use Equation 12 assuming vkick = vesc. Dashed lines assume vkick = 5vesc. In both cases we assume vesc ≈ 2σ. Note that this means vkick will change depending on the BH mass. Black solid and dashed line fix M• = 106 M⊙ and vk = 103 km s−1 . This is to mimic a model of KM08. The solid line uses Equation 12, while the dashed one equation 4 of KM08 where r• = 3pc. The blue shaded region represents rates in g… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Frequency vs. strain for GW events occuring in all runs with M• = 4 × 105 M⊙. Events are assumed to be sourced at redshift z = 1 and adopt the cosmological parameters observed by Planck Collabora￾tion et al. (2020). Orbital parameters are the osculating elements cal￾cu…
Figure 5
Figure 5. Figure 5: Cumulative merger rates up to z < 3 for recoiling BHs ejected from their host galaxy. Solid lines denote the total number of observ￾ables, while dashed lines the number of GW events following our cho￾sen IMF and without primordial mass segregation. (2015). These galact…
Figure 3
Figure 3. Figure 3: Since rates are sensitive to γ, future observations of HCSC can reveal aspects of the inner parsec regions shortly be￾fore SMBHB or IMBHB coalescence. Considering only HCSC hosting a BH with mass between 105 ≤ M• [M⊙] ≤ 4×105 , we expect at most N˙ ≲ 290 yr−1 events up…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

135 extracted references · 52 canonical work pages

  1. [1]

    D., Abraham, S., et al

    Abbott, R., Abbott, T. D., Abraham, S., et al. 2020, Phys. Rev. Lett., 125, 101102

    2020

  2. [2]

    & Madigan, A.-M

    Akiba, T. & Madigan, A.-M. 2021, ApJ, 921, L12

    2021

  3. [3]

    & Madigan, A.-M

    Akiba, T. & Madigan, A.-M. 2023, ApJ, 958, 137

    2023

  4. [4]

    2024, ApJ, 966, L4

    Akiba, T., McIntyre, S., & Madigan, A.-M. 2024, ApJ, 966, L4

    2024

  5. [5]

    B., Casey, C

    Akins, H. B., Casey, C. M., Lambrides, E., et al. 2025, ApJ, 991, 37

    2025

  6. [6]

    2017, arXiv e-prints, arXiv:1702.00786

    Amaro-Seoane, P., Audley, H., Babak, S., et al. 2017, arXiv e-prints, arXiv:1702.00786

    arXiv 2017

  7. [7]

    T., Bogdán, Á., Kovács, O

    Ananna, T. T., Bogdán, Á., Kovács, O. E., Natarajan, P., & Hickox, R. C. 2024, ApJ, 969, L18

    2024

  8. [8]

    Baggen, J. F. W., van Dokkum, P., Brammer, G., et al. 2024, ApJ, 977, L13

    2024

Show all 135 references
  1. [9]

    Baggen, J. F. W., van Dokkum, P., Labbé, I., & Brammer, G. 2025, arXiv e-prints, arXiv:2512.03239

    2025 arXiv

  2. [10]

    Bahcall, J. N. & Wolf, R. A. 1976, ApJ, 209, 214

    1976

  3. [11]

    G., Boggs, W

    Baker, J. G., Boggs, W. D., Centrella, J., et al. 2008, ApJ, 682, L29

    2008

  4. [12]

    F., Dickey, C., Geha, M., & Reines, A

    Baldassare, V . F., Dickey, C., Geha, M., & Reines, A. E. 2020, ApJ, 898, L3

    2020

  5. [13]

    F., Reines, A

    Baldassare, V . F., Reines, A. E., Gallo, E., & Greene, J. E. 2015, The Astrophys- ical Journal, 809, L14

    2015

  6. [14]

    S., Comerford, J

    Barrows, R. S., Comerford, J. M., Negus, J., & Muller-Sanchez, F. 2025, Re- coiling Black Hole Candidates from Spatially Offset Broad Emission Lines in MaNGA

    2025

  7. [15]

    E., Treister, E., Schawinski, K., et al

    Bauer, F. E., Treister, E., Schawinski, K., et al. 2017, MNRAS, 467, 4841

    2017

  8. [16]

    C., Blandford, R

    Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307

    1980

  9. [17]

    C., V olonteri, M., & Rees, M

    Begelman, M. C., V olonteri, M., & Rees, M. J. 2006, MNRAS, 370, 289

    2006

  10. [18]

    Bekenstein, J. D. 1973, ApJ, 183, 657

    1973

  11. [19]

    2025, ApJ, 984, L55

    Bellovary, J. 2025, ApJ, 984, L55

    2025

  12. [20]

    2006, ApJ, 642, L21

    Berczik, P., Merritt, D., Spurzem, R., & Bischof, H.-P. 2006, ApJ, 642, L21

    2006

  13. [21]

    Boekholt, T. C. N., Moerman, A., & Portegies Zwart, S. F. 2021, Phys. Rev. D, 104, 083020 Bogdán, Á., Goulding, A. D., Natarajan, P., et al. 2024, Nature Astronomy, 8, 126 Bogdanovi´c, T., Reynolds, C. S., & Miller, M. C. 2007, ApJ, 661, L147

    2021

  14. [22]

    2004, ApJ, 613, L37

    Boylan-Kolchin, M., Ma, C.-P., & Quataert, E. 2004, ApJ, 613, L37

    2004

  15. [23]

    L., et al

    Buikema, A., Cahillane, C., Mansell, G. L., et al. 2020, Phys. Rev. D, 102, 062003

    2020

  16. [24]

    O., Zlochower, Y ., & Merritt, D

    Campanelli, M., Lousto, C. O., Zlochower, Y ., & Merritt, D. 2007, Phys. Rev. Lett., 98, 231102

    2007

  17. [25]

    2008, Modern Physics Letters A, 23, 99

    Capozziello, S., de Laurentis, M., de Paolis, F., Ingrosso, G., & Nucita, A. 2008, Modern Physics Letters A, 23, 99

    2008

  18. [26]

    C., Li, R., & Zhuang, M.-Y

    Chen, C.-H., Ho, L. C., Li, R., & Zhuang, M.-Y . 2025, ApJ, 983, 60

    2025

  19. [27]

    & Shen, R.-F

    Chen, J.-H. & Shen, R.-F. 2018, ApJ, 867, 20

    2018

  20. [28]

    G., Kotok, E

    Diener, P., Kosovichev, A. G., Kotok, E. V ., Novikov, I. D., & Pethick, C. J. 1995, MNRAS, 275, 498 2 https://www.nowtricity.com/country/netherlands/ Article number, page 10 of 15 E. Hochart and S. Portegies Zwart: Recoiling Black Holes I. D’Orazio, D. J. & Samsing, J. 2018, ...

    1995

  21. [29]

    2010, MNRAS, 402, 682

    Dotti, M., V olonteri, M., Perego, A., et al. 2010, MNRAS, 402, 682

    2010

  22. [30]

    G., et al

    Ebisuzaki, T., Makino, J., Tsuru, T. G., et al. 2001, ApJ, 562, L19

    2001

  23. [31]

    & Ford, H

    Ferrarese, L. & Ford, H. 2005, Space Sci. Rev., 116, 523

    2005

  24. [32]

    2006, ApJ, 649, 91

    Freitag, M., Amaro-Seoane, P., & Kalogera, V . 2006, ApJ, 649, 91

    2006

  25. [33]

    G., Theuns, T., et al

    Furlong, M., Bower, R. G., Theuns, T., et al. 2015, MNRAS, 450, 4486

    2015

  26. [34]

    J., Labbé, I., Zitrin, A., et al

    Furtak, L. J., Labbé, I., Zitrin, A., et al. 2024, Nature, 628, 57

    2024

  27. [35]

    J., Zitrin, A., Plat, A., et al

    Furtak, L. J., Zitrin, A., Plat, A., et al. 2023, ApJ, 952, 142 García-Bellido, J. & Nesseris, S. 2018, Physics of the Dark Universe, 21, 61

    2023

  28. [36]

    2003, ApJ, 594, 812

    Genzel, R., Schödel, R., Ott, T., et al. 2003, ApJ, 594, 812

    2003

  29. [37]

    2026, MNRAS, 545, staf1979

    Geris, S., Maiolino, R., Isobe, Y ., et al. 2026, MNRAS, 545, staf1979

    2026

  30. [38]

    2021, ARA&A, 59, 21 Gondán, L

    Gezari, S. 2021, ARA&A, 59, 21 Gondán, L. & Kocsis, B. 2021, MNRAS, 506, 1665

    2021

  31. [39]

    Greene, J. E. & Ho, L. C. 2006, ApJ, 641, L21

    2006

  32. [40]

    E., Labbe, I., Goulding, A

    Greene, J. E., Labbe, I., Goulding, A. D., et al. 2024, ApJ, 964, 39

    2024

  33. [41]

    M., Bortolas, E., et al

    Gualandris, A., Khan, F. M., Bortolas, E., et al. 2022, Monthly Notices of the Royal Astronomical Society, 511, 4753

    2022

  34. [42]

    & Merritt, D

    Gualandris, A. & Merritt, D. 2008, ApJ, 678, 780

    2008

  35. [43]

    I., Dehnen, W., & Bortolas, E

    Gualandris, A., Read, J. I., Dehnen, W., & Bortolas, E. 2017, MNRAS, 464, 2301

    2017

  36. [44]

    A., Pacucci, F., & Kocevski, D

    Guia, C. A., Pacucci, F., & Kocevski, D. D. 2024, Research Notes of the Ameri- can Astronomical Society, 8, 207

    2024

  37. [45]

    2023, ApJ, 959, 39 Häring, N

    Harikane, Y ., Zhang, Y ., Nakajima, K., et al. 2023, ApJ, 959, 39 Häring, N. & Rix, H.-W. 2004, ApJ, 604, L89

    2023

  38. [46]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357

    2020

  39. [47]

    & Portegies Zwart, S

    Hochart, E. & Portegies Zwart, S. 2024, A&A, 685, A123

    2024

  40. [48]

    Hogg, D. W. 1999, arXiv e-prints, astro

    1999

  41. [49]

    2008, ApJ, 686, 829

    Holley-Bockelmann, K., Gültekin, K., Shoemaker, D., & Yunes, N. 2008, ApJ, 686, 829

    2008

  42. [50]

    & Sigurdsson, S

    Holley-Bockelmann, K. & Sigurdsson, S. 2006, arXiv e-prints, astro

    2006

  43. [51]

    & Alexander, T

    Hopman, C. & Alexander, T. 2006, ApJ, 645, 1152

    2006

  44. [52]

    Howell, D. A. 2011, Nature Communications, 2, 350

    2011

  45. [53]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90 Ivezi´c, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111

    2007

  46. [54]

    Jeans, J. H. 1919, MNRAS, 79, 408

    1919

  47. [55]

    G., Torres, M

    Jonker, P. G., Torres, M. A. P., Fabian, A. C., et al. 2010, MNRAS, 407, 645 Juodžbalis, I., Marconcini, C., D’Eugenio, F., et al. 2026, Nature, 653, 1017

    2010

  48. [56]

    & Dong, S

    Katz, B. & Dong, S. 2012, arXiv e-prints, arXiv:1211.4584

    2012 arXiv

  49. [57]

    M., Berczik, P., Sobolenko, M., et al

    Khan, F. M., Berczik, P., Sobolenko, M., et al. 2026, A&A, 706, A354

    2026

  50. [58]

    Khan, F. M. & Holley-Bockelmann, K. 2021, MNRAS, 508, 1174

    2021

  51. [59]

    M., Holley-Bockelmann, K., Berczik, P., & Just, A

    Khan, F. M., Holley-Bockelmann, K., Berczik, P., & Just, A. 2013, ApJ, 773, 100

    2013

  52. [60]

    M., Javed, F., Holley-Bockelmann, K., et al

    Khan, F. M., Javed, F., Holley-Bockelmann, K., et al. 2024, ApJ, 976, 22

    2024

  53. [61]

    2024, A&A, 691, A52

    Killi, M., Watson, D., Brammer, G., et al. 2024, A&A, 691, A52

    2024

  54. [62]

    E., & Márka, S

    Kocsis, B., Gáspár, M. E., & Márka, S. 2006, ApJ, 648, 411

    2006

  55. [63]

    I., Greene, J

    Kokorev, V ., Caputi, K. I., Greene, J. E., et al. 2024, ApJ, 968, 38

    2024

  56. [64]

    & Merritt, D

    Komossa, S. & Merritt, D. 2008, ApJ, 689, L89

    2008

  57. [65]

    B., Cornell, M

    Kormendy, J., Fisher, D. B., Cornell, M. E., & Bender, R. 2009, ApJS, 182, 216

    2009

  58. [66]

    & Richstone, D

    Kormendy, J. & Richstone, D. 1995, ARA&A, 33, 581

    1995

  59. [67]

    Kovacs, Jr., S. J. & Thorne, K. S. 1978, ApJ, 224, 62

    1978

  60. [68]

    L., Amaro-Seoane, P., et al

    Kremer, K., Rodriguez, C. L., Amaro-Seoane, P., et al. 2019, Phys. Rev. D, 99, 063003

    2019

  61. [69]

    S., Silk, J., et al

    Kritos, K., Beckmann, R. S., Silk, J., et al. 2025, ApJ, 991, 58

    2025

  62. [70]

    E., Bezanson, R., et al

    Labbe, I., Greene, J. E., Bezanson, R., et al. 2025, ApJ, 978, 92

    2025

  63. [71]

    G., Rauer, J

    Lena, D., Jonker, P. G., Rauer, J. P., Hernandez, S., & Kostrzewa-Rutkowska, Z. 2020, MNRAS, 495, 1771

    2020

  64. [72]

    D., Shen, Y ., et al

    Li, J., Silverman, J. D., Shen, Y ., et al. 2025, ApJ, 981, 19

    2025

  65. [73]

    K., Berczik, P., Chen, X., & Spurzem, R

    Li, S., Liu, F. K., Berczik, P., Chen, X., & Spurzem, R. 2012, ApJ, 748, 65

    2012

  66. [74]

    R., Webb, N

    Lin, D., Carrasco, E. R., Webb, N. A., et al. 2016, ApJ, 821, 25

    2016

  67. [75]

    O., Zlochower, Y ., Dotti, M., & V olonteri, M

    Lousto, C. O., Zlochower, Y ., Dotti, M., & V olonteri, M. 2012, Phys. Rev. D, 85, 084015

    2012

  68. [76]

    2018, ApJ, 853, 141

    Madigan, A.-M., Halle, A., Moody, M., et al. 2018, ApJ, 853, 141

    2018

  69. [77]

    2005, Nature, 437, 381

    Magain, P., Letawe, G., Courbin, F., et al. 2005, Nature, 437, 381

    2005

  70. [78]

    2024, A&A, 691, A145

    Maiolino, R., Scholtz, J., Curtis-Lake, E., et al. 2024, A&A, 691, A145

    2024

  71. [79]

    2026, MNRAS, 548, staf2109

    Maiolino, R., Übler, H., D’Eugenio, F., et al. 2026, MNRAS, 548, staf2109

    2026

  72. [80]

    2012, ApJ, 749, 168

    Mapelli, M., Hayfield, T., Mayer, L., & Wadsley, J. 2012, ApJ, 749, 168

    2012

  73. [81]

    J., et al

    Mastrobuono-Battisti, A., Amaro Seoane, P., Fullana i Alfonso, M. J., et al. 2025, A&A, 693, A22

    2025

  74. [82]

    2023, MNRAS, 521, 6089

    Mastrobuono-Battisti, A., Ogiya, G., Hahn, O., & Schultheis, M. 2023, MNRAS, 521, 6089

    2023

  75. [83]

    P., Brammer, G., et al

    Matthee, J., Naidu, R. P., Brammer, G., et al. 2024, ApJ, 963, 129

    2024

  76. [84]

    2012, in Astronomical Society of the Pacific Conference Series, V ol

    McMillan, S., Portegies Zwart, S., van Elteren, A., & Whitehead, A. 2012, in Astronomical Society of the Pacific Conference Series, V ol. 453, Advances in Computational Astrophysics: Methods, Tools, and Outcome, ed. R. Capuzzo-

    2012

  77. [85]

    Limongi, & A

    Dolcetta, M. Limongi, & A. Tornambè, 129 Mérida, R. M., Gaspar, G., Sawicki, M., et al. 2025, A&A, 698, A317

    2025

  78. [86]

    2006, ApJ, 648, 976

    Merritt, D. 2006, ApJ, 648, 976

    2006

  79. [87]

    2013, Classical and Quantum Gravity, 30, 244005

    Merritt, D. 2013, Classical and Quantum Gravity, 30, 244005

    2013

  80. [88]

    2007, ApJ, 671, 53

    Merritt, D., Mikkola, S., & Szell, A. 2007, ApJ, 671, 53

    2007

  81. [89]

    & Milosavljevi´c, M

    Merritt, D. & Milosavljevi´c, M. 2005, Living Reviews in Relativity, 8, 8

    2005

  82. [90]

    & Poon, M

    Merritt, D. & Poon, M. Y . 2004, ApJ, 606, 788

    2004

  83. [91]

    D., & Komossa, S

    Merritt, D., Schnittman, J. D., & Komossa, S. 2009, ApJ, 699, 1690

    2009

  84. [92]

    2006, MNRAS, 367, 1746

    Merritt, D., Storchi-Bergmann, T., Robinson, A., et al. 2006, MNRAS, 367, 1746

    2006

  85. [93]

    2017, International Journal of Modern Physics D, 26, 1730021

    Mezcua, M. 2017, International Journal of Modern Physics D, 26, 1730021

    2017

  86. [94]

    2024, ApJ, 966, L30 Milosavljevi´c, M

    Mezcua, M., Pacucci, F., Suh, H., Siudek, M., & Natarajan, P. 2024, ApJ, 966, L30 Milosavljevi´c, M. & Merritt, D. 2001, ApJ, 563, 34

    2024

  87. [95]

    R., Portegies Zwart, S

    Nelemans, G., Yungelson, L. R., Portegies Zwart, S. F., & Verbunt, F. 2001, A&A, 365, 491

    2001

  88. [96]

    2024, gwastro/pycbc: v2.3.3 release of Py- CBC O’Leary, R

    Nitz, A., Harry, I., Brown, D., et al. 2024, gwastro/pycbc: v2.3.3 release of Py- CBC O’Leary, R. M., Kocsis, B., & Loeb, A. 2009, MNRAS, 395, 2127 O’Leary, R. M. & Loeb, A. 2012, MNRAS, 421, 2737 Ordenes-Briceño, Y ., Eigenthaler, P., Taylor, M. A., et al. 2018, ApJ, 859, 52

    2024

  89. [97]

    2025, MNRAS, 537, 956

    Partmann, C., Naab, T., Lahén, N., et al. 2025, MNRAS, 537, 956

    2025

  90. [98]

    I., van Elteren, A., de Vries, N., et al

    Pelupessy, F. I., van Elteren, A., de Vries, N., et al. 2013, A&A, 557, A84

    2013

  91. [99]

    1962, Physical Review, 128, 2471

    Peres, A. 1962, Physical Review, 128, 2471

    1962

  92. [100]

    2025, Universe, 11, 294

    Perger, K., Fogasy, J., & Frey, S. 2025, Universe, 11, 294

    2025

  93. [101]

    Peters, P. C. 1970, Phys. Rev. D, 1, 1559

    1970

  94. [102]

    Peters, P. C. & Mathews, J. 1963, Physical Review, 131, 435 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2020, A&A, 641, A6

    1963

  95. [103]

    Poon, M. Y . & Merritt, D. 2001, ApJ, 549, 192 Portegies Zwart, S. & McMillan, S. 2018, Astrophysical Recipes; The art of AMUSE (IOP Publishing) Portegies Zwart, S., McMillan, S., Harfst, S., et al. 2009, New A, 14, 369 Portegies Zwart, S. F. & McMillan, S. L. W. 2002, ApJ, 57...

    2001

  96. [104]

    & Amaro-Seoane, P

    Preto, M. & Amaro-Seoane, P. 2010, ApJ, 708, L42

    2010

  97. [105]

    Rantala, A., Rawlings, A., Naab, T., Thomas, J., & Johansson, P. H. 2024, Monthly Notices of the Royal Astronomical Society, 535, 1202–1227

    2024

  98. [106]

    Rauch, K. P. & Ingalls, B. 1998, MNRAS, 299, 1231

    1998

  99. [107]

    Rauch, K. P. & Tremaine, S. 1996, New A, 1, 149

    1996

  100. [108]

    H., Naab, T., et al

    Rawlings, A., Johansson, P. H., Naab, T., et al. 2025, ApJ, 991, 83

    2025

  101. [109]

    Rees, M. J. 1988, Nature, 333, 523

    1988

  102. [110]

    Rees, M. J. 1998, in Black Holes and Relativistic Stars, ed. R. M. Wald, 79

    1998

  103. [111]

    E., Greene, J

    Reines, A. E., Greene, J. E., & Geha, M. 2013, ApJ, 775, 116

    2013

  104. [112]

    G., Fliri, J., & Valls-Gabaud, D

    Riess, A. G., Fliri, J., & Valls-Gabaud, D. 2012, ApJ, 745, 156

    2012

  105. [113]

    H., et al

    Rinaldi, P., Bonaventura, N., Rieke, G. H., et al. 2025, ApJ, 992, 71

    2025

  106. [114]

    J., & Liu, C

    Robson, T., Cornish, N. J., & Liu, C. 2019, Classical and Quantum Gravity, 36, 105011

    2019

  107. [115]

    Salpeter, E. E. 1955, ApJ, 121, 161

    1955

  108. [116]

    J., et al

    Samsing, J., Bartos, I., D’Orazio, D. J., et al. 2022, Nature, 603, 237

    2022

  109. [117]

    & D’Orazio, D

    Samsing, J. & D’Orazio, D. J. 2018, MNRAS, 481, 5445

    2018

  110. [118]

    & D’Orazio, D

    Samsing, J. & D’Orazio, D. J. 2019, Phys. Rev. D, 99, 063006

    2019

  111. [119]

    & Ilan, T

    Samsing, J. & Ilan, T. 2018, Monthly Notices of the Royal Astronomical Society, 476, 1548 Sánchez-Janssen, R., Côté, P., Ferrarese, L., et al. 2019, ApJ, 878, 18 Schödel, R., Nogueras-Lara, F., Gallego-Cano, E., et al. 2020, A&A, 641, A102

    2018

  112. [120]

    E., & Greene, J

    Schutte, Z., Reines, A. E., & Greene, J. E. 2019, The Astrophysical Journal, 887, 245

    2019

  113. [121]

    Z., Farahat, E

    Selim, H. Z., Farahat, E. A., Mohareb, A. S. O., Toto, S. M., & Hassan, K. T. S. 2024, Egyptian Journal of Botany, 64, 258

    2024

  114. [122]

    & Loeb, A

    Stone, N. & Loeb, A. 2011, MNRAS, 412, 75

    2011

  115. [123]

    & Loeb, A

    Stone, N. & Loeb, A. 2012, MNRAS, 422, 1933

    2012

  116. [124]

    C., Küpper, A

    Stone, N. C., Küpper, A. H. W., & Ostriker, J. P. 2017, MNRAS, 467, 4180

    2017

  117. [125]

    2021, ApJ, 907, L20

    Tagawa, H., Kocsis, B., Haiman, Z., et al. 2021, ApJ, 907, L20

    2021

  118. [126]

    L., Fan, X., Wang, F., & Yang, J

    Tee, W. L., Fan, X., Wang, F., & Yang, J. 2025, ApJ, 983, L26

    2025

  119. [127]

    1977, ApJ, 216, 610 van Dokkum, P., Pasha, I., Buzzo, M

    Turner, M. 1977, ApJ, 216, 610 van Dokkum, P., Pasha, I., Buzzo, M. L., et al. 2023, ApJ, 946, L50 van Velzen, S. & Farrar, G. R. 2014, ApJ, 792, 53

    1977

  120. [128]

    2019, MNRAS, 482, 1525

    Vasiliev, E. 2019, MNRAS, 482, 1525

    2019

  121. [129]

    2015, ApJ, 810, 49

    Vasiliev, E., Antonini, F., & Merritt, D. 2015, ApJ, 810, 49

    2015

  122. [130]

    & Merritt, D

    Wang, J. & Merritt, D. 2004, ApJ, 600, 149

    2004

  123. [131]

    White, S. D. M. & Rees, M. J. 1978, MNRAS, 183, 341

    1978

  124. [132]

    2007, ApJ, 665, L59

    Willems, B., Kalogera, V ., Vecchio, A., et al. 2007, ApJ, 665, L59

    2007

  125. [133]

    2026, arXiv e-prints, arXiv:2601.06015

    Yanagisawa, H., Ouchi, M., Golubchik, M., et al. 2026, arXiv e-prints, arXiv:2601.06015

    2026

  126. [134]

    Zhang, Z., Jiang, L., Liu, W., & Ho, L. C. 2025, ApJ, 985, 119

    2025

  127. [135]

    & Lousto, C

    Zlochower, Y . & Lousto, C. O. 2015, Phys. Rev. D, 92, 024022 Article number, page 11 of 15 A&A proofs:manuscript no. aanda Appendix A: Deriving the Event Rate The simulations here are integrated fort=0.1 Myr. This is much shorter than RR timescales oft RR≈10 3 Myr (c.f Equati...

    2011

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.