Gravitational wave mergers of accreting binary black holes in AGN discs

M. Gr\"obner; W. Ishibashi

REVIEW 2 major objections 5 minor 1 cited by

Gravitational wave mergers of accreting binary black holes in AGN discs

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper claims that the disc aspect ratio of an AGN disc determines whether an accreting binary black hole contracts toward a gravitational-wave merger (thin discs) or expands away from it (thick discs).

desk verdict Useful analytic framework whose central contraction/expansion boundary hangs on the (2,1) OLR dominance assumption—a load-bearing step the authors themselves flag, so the rates should be read as conditional. read the letter →

arxiv 2412.01925 v1 pith:WPHJBFMU submitted 2024-12-02 astro-ph.HE astro-ph.GA

W. Ishibashi , M. Gröbner This is my paper · ORCID

classification astro-ph.HEastro-ph.GA

keywords binaryblackholesAGNdiscsgravitationalwavesdisc-binaryinteractionLindbladresonancesaccretiontorquemergertimescalesrates

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

The paper tries to settle whether binary black holes embedded in the discs of active galactic nuclei shrink toward a gravitational-wave merger or drift outward. Its answer is that the disc aspect ratio, the disc height divided by radius, sets the outcome: below a critical value $h_{\rm crit}\sim0.04$–$0.16$ the binary contracts and merges, while above it the binary expands and no merger occurs. Because real AGN discs are often thin, the paper argues that a large fraction of such binaries can reach the gravitational-wave-driven regime, with merger timescales of $10^5$–$10^7$ years. It also estimates the resulting merger rate density, roughly $\mathcal{R}\sim(0.2$–$5)\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$, which would be a non-negligible part of the observed gravitational-wave event rate.

What carries the argument

The carrying object is the torque-balance equation $\dot{L}_b = T_{\rm grav}+T_{\rm acc}$, with $T_{\rm grav}$ approximated by the $(m,l)=(2,1)$ outer Lindblad resonance torque, taken as $T_{\rm grav}\approx T_{\rm OLR}=-T_{\rm visc}$ at the cavity inner edge, and $T_{\rm acc}$ parametrized from accretion onto the mini-discs around each black hole. The disc aspect ratio $h=H/r$ enters because the binary accretion rate $\dot{M}_b$ scales with the circumbinary disc aspect ratio, with thin discs suppressing accretion, so the positive accretion torque grows with $h$ while the negative viscous torque does not; the balance point defines $h_{\rm crit}$. These torques feed a coupled set of 'disc+GW'-driven evolution equations for the semi-major axis $a$ and eccentricity $e$, which are integrated from the disc-dominated regime at large separations into the gravitational-wave-driven regime at small separations.

What would settle it

A hydrodynamical simulation with a self-consistently evolving binary orbit that scans disc aspect ratios from $h=0.01$ to $h=0.2$ would settle it: the time-averaged semi-major axis derivative must change sign near $h_{\rm crit}\sim0.04$–$0.16$, remaining negative below that value.

Watch

Extended reading notes

Core claim

The paper claims that the long-running disagreement over whether accreting binaries in AGN discs contract or expand is resolved by the disc aspect ratio: below a critical value $h_{\rm crit}$ the negative viscous torque dominates over the positive accretion torque, so the binary shrinks into the gravitational-wave regime, whereas above $h_{\rm crit}$ the accreted angular momentum wins and the binary expands and never merges. It further claims that contraction is usually accompanied by eccentricity growth in the disc-driven phase, which accelerates the subsequent gravitational-wave inspiral, and that this makes accreting binaries capable of merging faster than non-accreting ones, with a non-monotonic dependence on disc thickness. Quantitatively, the paper derives merger timescales of $\tau_{\rm merger}\sim10^5$–$10^7$ years and a gravitational-wave merger rate density of roughly $0.2$–$5\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ for this channel, which it presents as a conservative estimate of a few to tens of percent of the observed rate.

Load-bearing premise

The load-bearing premise is that the $(2,1)$ outer Lindblad resonance dominates the disc-binary torque, so the net disc torque is just the viscous torque plus the accretion torque, with the paper's own caution that a different resonance balance or cavity density profile could change the torque direction.

Editorial extensions

If this is right

Below the critical aspect ratio, accreting BBHs in AGN discs contract and reach the gravitational-wave-driven regime, while above it they expand and never merge, so the channel's contribution is confined to thin discs.
Typical merger timescales of $10^5$–$10^7$ years are short enough to occur within an AGN disc lifetime and several orders of magnitude shorter than a purely gravitational-wave inspiral in the field.
Accretion does not always slow the inspiral: because it can pump eccentricity through the dominant outer Lindblad resonance, accreting binaries can merge faster than non-accreting ones, with the fastest mergers occurring at a moderate aspect ratio $h_{\rm tr}$ below $h_{\rm crit}$.
The implied gravitational-wave merger rate density of roughly $0.2$–$5\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ would be a non-negligible fraction of the observed binary black hole merger rate.
Even if eccentricity growth is strongly reduced, accreting binaries can still shrink and merge in thin discs, so the qualitative contraction result does not depend on the eccentricity-driving assumption.

Reading between the lines

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

If the critical-aspect-ratio picture is right, gravitational-wave events from AGN discs should preferentially come from thin-disc environments, so the host AGN population should be biased toward radiatively efficient, low-aspect-ratio discs; this is a testable demographic prediction.
The same torque-balance machinery could be applied to unequal-mass or extreme-mass-ratio binaries, where the $(2,1)$ outer Lindblad resonance dominance is less secure and $h_{\rm crit}$ would shift; scanning mass ratio in simulations would map that shift.
A discriminating observational test is the eccentricity of detected mergers: this model predicts noticeable eccentricity in the gravitational-wave band for the disc channel, so a clean measurement of eccentricity at low frequency would constrain the channel's contribution.
Because the paper finds that $h_{\rm crit}$ depends on the accretion-rate profile power law $p$, the merger-rate estimate of $0.2$–$5\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ should be read as sensitive to the outflow strength in real AGN discs.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a useful analytic framework with a clear caveat at its load-bearing joint, and the authors know it. The coupled disc+GW evolution for accreting binaries is genuinely new relative to Hayasaki (2009), who included the accretion torque but dropped the mass-variation terms in the orbital element equations. Deriving Eqs. (7)–(8) from energy and angular momentum conservation is clean, and the final rates (0.2–5 Gpc^-3 yr^-1) are forward predictions, not fits to the observed rate. The qualitative result that thin discs contract and thick discs expand matches the Tiede et al. (2020) and Heath & Nixon (2020) simulations, and the hcrit values (0.04–0.16) sit in the right ballpark. Credit where due: the model is transparent, the parameter dependence is spelled out, and the merger timescales of 10^5–10^7 yr are a concrete quantitative output.

The soft spot is exactly where the stress-test note points. Everything hinges on Tgrav ≈ TOLR = −Tvisc. The authors justify OLR dominance through the torque ratios in Eqs. (18)–(19), but those ratios assume the corotation and ILR sites sit in a depleted cavity. The paper's own Section 2.2 cautionary note admits a steep surface-density gradient can shift higher-order resonances so that ILR dominates (Chen et al. 2020), and the recent simulations finding positive gravitational torques (Muñoz et al. 2019; Duffell et al. 2020) are cited but not incorporated. If the gravitational torque is not simply −Tvisc, the hcrit boundary and the derived rates lose their quantitative grounding. This is not a fatal flaw in the sense of an internal inconsistency; it is an unverified physical assumption. The authors are upfront about it, which is more than many papers manage, but it means the central number—0.2–5 Gpc^-3 yr^-1—should be read as conditional on the resonance picture.

The 10 hcbd accretion-suppression factor from Ragusa et al. (2016) is another empirical input with a factor-of-a-few uncertainty, and the rate normalization (nAGN, NBH, fd, fb) spans the usual order-of-magnitude range, so the rate estimate is not tight. But the paper does not oversell it; they call it conservative.

Who is this for? People working on AGN disc channels for GW sources and anyone comparing analytic torque-balance models to hydrodynamic simulations. The paper deserves a serious referee: it is internally consistent, engages the debate honestly, and gives the community a simple model to test against simulations. My recommendation is to send it to review, with the request that the referee push for a parameter scan or a direct comparison with the positive-torque simulations in the discussion. The structure is sound; the caveat is already on the page.

Referee Report

2 major / 5 minor

Summary. The paper develops a simple analytic model for the orbital evolution of stellar-mass black hole binaries embedded in AGN discs, including mass accretion onto the binary. From energy and angular momentum conservation with a presumed (m,l)=(2,1) outer Lindblad resonance torque balanced by the viscous torque, the authors derive coupled disc-plus-GW evolution equations for the semi-major axis and eccentricity (Eqs. 33-38), integrate them, and find a critical disc aspect ratio h_crit (roughly 0.04-0.16 depending on the accretion profile) separating orbital expansion in thicker discs from contraction and merger in thinner discs. They then compute merger timescales tau ~ 10^5-10^7 yr and GW merger rates R ~ 0.2-5 Gpc^-3 yr^-1. The quantitative predictions are forward-looking, and the caveats about the torque sign and the thin-disc accretion suppression are acknowledged in Sections 2.2 and 2.4.

Significance. If the central assumption on the sign of the gravitational torque is correct, the paper provides a useful transparent framework for a contested question and a falsifiable prediction: the existence of a critical aspect ratio and a non-monotonic merger-time dependence. It improves on earlier work by including mass accretion terms consistently in both the torque balance and the orbital evolution equations, and by following the coupled disc+GW evolution through merger. The rate estimates are explicit and can be compared with LVK observations. The main limitation is that the two load-bearing ingredients, OLR dominance (so that T_grav = -T_visc) and the 10 h_cbd accretion suppression, are empirical or assumed rather than derived, and the paper's own discussion cites simulations finding a positive gravitational torque. Because the model is analytic and the equations are explicit, these assumptions could in principle be tested in a revision; the current manuscript, however, does not quantify how its central conclusions depend on them.

major comments (2)

[Section 2.2 (Eqs. 18-19) and Section 3 (Eq. 33)] The identification T_grav ≈ T_OLR = -T_visc is the load-bearing step in Eq. (33). It is introduced in Section 2.2 from the (m,l) = (2,1) outer Lindblad resonance dominance argument based on Eqs. (18)-(19), but the accompanying cautionary note states that a steep surface-density gradient can make the ILR dominate (Chen et al. 2020), and Section 7 itself cites simulations that find a positive net gravitational torque on the binary. If the gravitational torque is not equal to -T_visc, or if it is positive, then Ǉa can be positive even for thin discs, and the h_crit boundary and the rates in Sections 4-6 do not follow. The manuscript should quantify the range of T_grav/T_visc for which a critical aspect ratio still exists and state the conditions under which the central claim survives.
[Section 2.4 (Eqs. 26 and 32)] The existence and value of h_crit depend on the thin-disc accretion suppression relation Ẍ_b = 10 h_cbd Ẍ_cbd (Eq. 32, from Ragusa et al. 2016). With this relation, T_visc and the positive accretion and mass terms in Eq. (33) scale as h_cbd^2 and h_cbd^3, respectively, so the crossing at h_crit is natural. If the suppression factor were instead constant (e.g., Ẍ_b = Ẍ_cbd), both sides of Eq. (33) would scale as h_cbd^2 and the contraction/expansion boundary would not depend on the aspect ratio, so the paper's central distinction between thin and thick discs would disappear. A sensitivity study with no suppression and with modified suppression factors, together with a justification for applying the SPH-based relation to AGN discs, is required before the h_crit values in Table 1 can be considered robust.

minor comments (5)

[Section 2.2 and Section 2.4] The symbol p is used both for the surface-density power-law index in Eq. (17) and for the radial accretion-rate index in Eq. (25); these are different quantities and the notation should be changed to avoid confusion.
[Section 5] The merger time is defined as "the point where the numerical solution approaches the abscissa axis"; please specify a quantitative stopping criterion (e.g., a = 6GM/c^2 or a separation of a few Schwarzschild radii), because the quoted timescales depend on the cutoff.
[Pages 7 and 11] There are typographical issues: "T able 1" appears before Table 1, and "L VK" appears in Sections 7 and 8; these should read "LIGO/Virgo/KAGRA" or "LVK".
[Figure 1] The caption of Fig. 1 does not define h_cbd, h_crit, or h_tr; please add definitions directly in the caption, since these quantities are central to the figure.
[Section 7] The discussion of reduced eccentricity growth mentions a factor-of-ten reduction but gives no corresponding merger-rate estimate; a brief rate estimate for that case would complete the parameter scan.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the contraction/expansion boundary and merger-rate estimates are derived from the model's torque balance and external simulation inputs, not from the conclusions.

full rationale

The central result is the sign change of da/dt in Eq. (33). The authors explicitly set T_grav ≈ T_OLR = −T_visc in Section 2.3, combine this with the accretion torque T_acc from Eqs. (22)–(24), and integrate the coupled disc+GW equations (37)–(38). The critical aspect ratio h_crit is a derived crossing point of these torque terms, not a parameter fitted to the outcome. The accretion-rate scalings, including the thin-disc suppression factor from Ragusa et al. (2016) and the relative accretion fraction from Duffell et al. (2020), are external empirical inputs with stated provenance; the paper does not adjust them to force contraction in thin discs. The GW merger rate, Eq. (41), is a forward estimate using independently stated AGN/BH abundance parameters and is compared with, not fitted to, LIGO/Virgo rates. The self-citations to Ishibashi & Gröbner (2020) and Gröbner et al. (2020) supply parameter conventions and a non-accreting comparison case; they are not used as an authority to forbid alternative torque signs. The paper's own cautionary note in Section 2.2—that a steep surface-density gradient could make the ILR dominate—undermines the assumed sign of T_grav, but that is a modeling assumption and robustness limitation, not a circular reduction of the result to its inputs. No step in the derivation chain is equivalent by construction to the claimed prediction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a small number of physical assumptions about disc-binary torques and on several hand-picked parameters. The main free parameter is the accretion torque normalization, controlled by mini-disc aspect ratios, viscosities, and the suppression factor from Ragusa et al. (2016). The critical aspect ratio is a derived quantity, not a fitted constant, but its value is sensitive to these inputs.

free parameters (5)

Mini-disc aspect ratios h1, h2 = 0.1 (fiducial)
Enter Eq. 24 for T_acc via c_s,i^2 = h_i^2 G M_i / r_i. The accretion torque, and hence the location of h_crit, scales with h_1^2 and h_2^2. Chosen by hand, not derived, and no variation is explored.
Mini-disc viscosity parameters alpha1, alpha2 = 0.1 (fiducial)
Enter Eq. 24 as linear factors multiplying h_i^2. Chosen equal to the CBD alpha with no dedicated motivation for mini-disc viscosity.
Accretion profile power-law index p = 1/2 fiducial (0 and 1 also considered)
Sets how the inflow rate decays inward (Eq. 25). Table 1 shows h_crit varies from 0.04 to 0.16 across p, so the central quantitative result is sensitive to this choice.
Thin-disc accretion suppression factor (10 h_cbd) = 10 h_cbd for h_cbd <= 0.1
Adopted from Ragusa et al. (2016) simulations (Sec. 2.4). Controls M_dot_b and therefore T_acc; this empirical fit is a major input to the contraction/expansion threshold.
Merger-rate normalization nAGN, NBH, fd, fb = 5e4 Gpc^-3, 1e4, 0.01, 0.1 (fiducial)
Used in Eq. 41 for the rate estimate. These astrophysical parameters are taken from prior work without uncertainty propagation; the quoted rate range 0.2-5 Gpc^-3 yr^-1 depends linearly on them.

assumptions (6)

domain assumption The disc is geometrically thin (h << 1) and follows Keplerian rotation around the SMBH.
Section 2 opening; used for all resonance locations and torque expressions.
domain assumption Disc-binary interaction is adiabatic with small non-axisymmetric perturbations, so E_dot_b = Omega_p L_dot_b.
Section 2.1 around Eq. 6; basis of the orbital evolution equations 7-8.
ad hoc to paper The (m,l)=(2,1) outer Lindblad resonance dominates the torque, so T_grav is approximately T_OLR.
Section 2.2, justified by torque ratios (Eqs. 18-19), but the paper's own cautionary note admits higher-order resonances or density gradients could change the balance.
domain assumption The gravitational torque is balanced by the viscous torque at the inner edge: T_grav = -T_visc.
Section 2.3; standard gap-edge equilibrium, used to set L_dot_b = -T_visc + T_acc.
ad hoc to paper Mass accretion onto the binary adds positive angular momentum via mini-discs, T_acc > 0.
Eqs. 22-24 parametrize T_acc as positive definite. If the accreted gas carries lower specific angular momentum than the binary, the torque could be negative, which would change the expansion/contraction picture.
standard math Peters (1964) GW evolution equations apply in the GW regime.
Eqs. 35-36, standard.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Gravitational wave mergers of accreting binary black holes in AGN discs." pith.science (2026). https://pith.science/paper/WPHJBFMU

@misc{pith2026241201925,
  author       = {Pith},
  title        = {Pith review of: Gravitational wave mergers of accreting binary black holes in AGN discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WPHJBFMU}},
  note         = {Machine review of arXiv:2412.01925}
}

abstract

Binary black hole (BBH) evolution in the discs of active galactic nuclei (AGN) is a promising channel for gravitational wave (GW)-driven mergers. It is however unclear whether binaries interacting with the surrounding disc undergo orbital contraction or expansion. We develop a simple analytic model of accreting BBHs in AGN discs to follow the orbital evolution from the disc-dominated regime at large separations into the GW-driven regime at small separations (the coupled `disc+GW'-driven evolution). We obtain that accreting binaries expand in thick discs with aspect ratio greater than a critical value ($> h_\mathrm{crit}$); whereas accreting binaries contract and eventually merge in thin discs ($< h_\mathrm{crit}$). Interestingly, accreting BBHs can experience faster mergers compared to non-accreting counterparts, with a non-monotonic dependence on the disc aspect ratio. The orbital contraction is usually coupled with eccentricity growth in the disc-dominated regime, which lead to accelerated inspirals in the GW-driven regime. We quantify the resulting BBH merger timescales in AGN discs ($\tau_\mathrm{merger} \sim 10^5 - 10^7$ yr) and estimate the associated GW merger rates ($\mathcal{R} \sim (0.2 - 5) \, \text{Gpc}^{-3} \text{yr}^{-1}$). Overall, accreting binaries may efficiently contract and merge in thin discs, hence this particular BBH-in-AGN channel may provide a non-negligible contribution to the observed GW merger event rate.

Figures

Figures reproduced from arXiv: 2412.01925 by the authors.

**Figure 2.** Orbital eccentricity as a function of semi-major axis for different values of the disc aspect ratio hcbd. The eccentricity increases in the disc-driven regime (at large separations) and decreases in the GW-driven regime (at small separations). 105 106 107 Time [Years] 10-4 10-2 100 102 104 Semi-Major Axis [AU] 0 0.05 0.1 0.13 0.14 0.15 0.16 0.17 hcbd [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Temporal evolution of the semi-major axis. Analogous to [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** shows the merger time (τmerger) of accreting binaries as a function of the initial semi-major axis a0, for different values of the disc aspect ratio. We see that the BBH merger times mostly span the range τmerger ∼ (105 − 107 ) years, depending on the initial separation, with a typical value of ∼ 106 yr for a0 = 1 AU. Such ∼Myr timescales are comparable to typical AGN disc lifetimes. We recall that the corresponding… view at source ↗

Figures from the paper (2 more)

**Figure 6.** Figure 6: Merger time versus initial semi-major axis for different binary mass Mb (with fiducial parameters and hcbd = 0.01). 10-2 10-1 100 Initial Semi-Major Axis a0 [AU] 105 106 107 Time to Merger [years] 0.1 0.2 0.3 0.5 1 q [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Merger time versus initial semi-major axis for different mass ratio q (with fiducial parameters and hcbd = 0.01). nary mass and larger mass ratio at small initial separations (a0 ∼ 0.01 AU). The two opposite trends may be interpreted in terms of the different analytic…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Observable signature of magnetic tidal coupling in hierarchical triple systems
gr-qc 2025-10 conditional novelty 6.0 of 10

Magnetic tidal fields from a supermassive black hole trigger new orbital resonances in a companion compact binary, boosting eccentricity and altering its gravitational-wave signal.

Reference graph

Works this paper leans on

61 extracted references · 50 canonical work pages · cited by 1 Pith paper

[1]

write newline

" write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...
[2]

@esa (Ref

\@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded aguplus natbib The aguplus class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later rem...
[3]

@stdbsttrue NAT@ctr \@lbibitem[ NAT@ctr ] \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 [ @natanchorstart #2\@extra@b@citeb \@biblabel @num @natanchorend] @ifcmd#1(@)(@)\@nil #2 @lbibitem\@undefined @lbibitem\@lbibitem \@lbibitem[#1]#2 @lb...
[4]

@open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifundefined NAT@sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifundefined bib@heading @heading NAT@ctr thebibliography [1] @ \@biblabel NAT@ctr \@bibsetup #1 NAT@ctr 0 @openbib .11em \@plus.33em \@minus.07em 4000 4000 `\.=1000 \@...

work page
[5]

J., Natarajan P., 2005, , 634, 921

Armitage P. J., Natarajan P., 2005, , 634, 921

work page 2005
[6]

J., Lubow S

Artymowicz P., Clarke C. J., Lubow S. H., Pringle J. E., 1991, , 370, L35

work page 1991
[7]

H., 1994, The Astrophysical Journal, 421, 651

Artymowicz P., Lubow S. H., 1994, The Astrophysical Journal, 421, 651

work page 1994
[8]

H., 1996, , 467, L77

Artymowicz P., Lubow S. H., 1996, , 467, L77

1996

Show all 61 references

[9]

Bartos I., Kocsis B., Haiman Z., M \'a rka S., 2017, , 835, 165

2017
[10]

Belczynski K., Doctor Z., Zevin M., Olejak A., Banerje S., Chattopadhyay D., 2022, , 935, 126

2022
[11]

Chen Y.-X., Zhang X., Li Y.-P., Li H., Lin D. N. C., 2020, , 900, 44

2020
[12]

Choksi N., Chiang E., Fung J., Zhu Z., 2023, , 525, 2806

2023
[13]

DeLaurentiis S., Epstein-Martin M., Haiman Z., 2023, , 523, 1126

2023
[14]

C., D'Orazio D., Derdzinski A., Haiman Z., MacFadyen A., Rosen A

Duffell P. C., D'Orazio D., Derdzinski A., Haiman Z., MacFadyen A., Rosen A. L., Zrake J., 2020, , 901, 25

2020
[15]

D., Duffell P., MacFadyen A

Farris B. D., Duffell P., MacFadyen A. I., Haiman Z., 2014, , 783, 134

2014
[16]

Ford K. E. S., Bartos I., McKernan B., Haiman Z., Corsi A., Keivani A., Marka S., Perna R., Graham M., Ross N. P., Stern D., Bellovary J., Berti E., O'Dowd M., Lyra W., MacLow M.-M., Marka Z., 2019, , 51, 247

2019
[17]

Ford K. E. S., McKernan B., 2022, , 517, 5827

2022
[18]

Goldreich P., Sari R., 2003, , 585, 1024

2003
[19]

Goldreich P., Tremaine S., 1979, , 233, 857

1979
[20]

Goldreich P., Tremaine S., 1980, , 241, 425

1980
[21]

Gr \"o bner M., Ishibashi W., Tiwari S., Haney M., Jetzer P., 2020, , 638, A119

2020
[22]

Hayasaki K., 2009, , 61, 65

2009
[23]

M., Nixon C

Heath R. M., Nixon C. J., 2020, , 641, A64

2020
[24]

J., Gonzalez J.-F., Ubeira-Gabellini M

Hirsh K., Price D. J., Gonzalez J.-F., Ubeira-Gabellini M. G., Ragusa E., 2020, , 498, 2936

2020
[25]

Hu H., Inayoshi K., Haiman Z., Quataert E., Kuiper R., 2022, , 934, 132

2022
[26]

Ishibashi W., Gr \"o bner M., 2020, , 639, A108

2020
[27]

Li Y.-P., Chen Y.-X., Lin D. N. C., 2023, , 526, 5346

2023
[28]

M., Li H., Li S., Li J., 2022, , 928, L19

Li Y.-P., Dempsey A. M., Li H., Li S., Li J., 2022, , 928, L19

2022
[29]

H., Artymowicz P., 2000, in Mannings V., Boss A

Lubow S. H., Artymowicz P., 2000, in Mannings V., Boss A. P., Russell S. S., eds, Protostars and Planets IV Interactions of Young Binaries with Disks . p. 731

2000
[30]

J., 1972, , 157, 1

Lynden-Bell D., Kalnajs A. J., 1972, , 157, 1

1972
[31]

I., Milosavljevi \'c M., 2008, , 672, 83

MacFadyen A. I., Milosavljevi \'c M., 2008, , 672, 83

2008
[32]

McKernan B., Ford K. E. S., Bellovary J., Leigh N. W. C., Haiman Z., Kocsis B., Lyra W., Mac Low M. M., Metzger B., O'Dowd M., Endlich S., Rosen D. J., 2018, , 866, 66

2018
[33]

McKernan B., Ford K. E. S., Lyra W., Perets H. B., 2012, , 425, 460

2012
[34]

Moody M. S. L., Shi J.-M., Stone J. M., 2019, , 875, 66

2019
[35]

E., Duffell P

M \"o sta P., Taam R. E., Duffell P. C., 2019, , 875, L21

2019
[36]

J., Miranda R., Lai D., 2019, , 871, 84

Mu \ n oz D. J., Miranda R., Lai D., 2019, , 871, 84

2019
[37]

I., Lubow S

Ogilvie G. I., Lubow S. H., 2003, , 587, 398

2003
[38]

Perna R., Lazzati D., Farr W., 2019, , 875, 49

2019
[39]

C., 1964, Physical Review, 136, 1224

Peters P. C., 1964, Physical Review, 136, 1224

1964
[40]

E., 1991, , 248, 754

Pringle J. E., 1991, , 248, 754

1991
[41]

Quataert E., Gruzinov A., 2000, , 539, 809

2000
[42]

J., 2016, , 460, 1243

Ragusa E., Lodato G., Price D. J., 2016, , 460, 1243

2016
[43]

H., Miller M

Roedig C., Krolik J. H., Miller M. C., 2014, , 785, 115

2014
[44]

D., Thrane E., 2022, , 940, 171

Romero-Shaw I., Lasky P. D., Thrane E., 2022, , 940, 171

2022
[45]

M., Chiang E

Rosenthal M. M., Chiang E. I., Ginzburg S., Murray-Clay R. A., 2020, , 498, 2054

2020
[46]

Rowan C., Boekholt T., Kocsis B., Haiman Z., 2023, , 524, 2770

2023
[47]

J., Haiman Z., Kocsis B., Leigh N

Samsing J., Bartos I., D'Orazio D. J., Haiman Z., Kocsis B., Leigh N. W. C., Liu B., Pessah M. E., Tagawa H., 2022, , 603, 237

2022
[48]

Secunda A., Hernandez B., Goodman J., Leigh N. W. C., McKernan B., Ford K. E. S., Adorno J. I., 2021, , 908, L27

2021
[49]

I., Sunyaev R

Shakura N. I., Sunyaev R. A., 1973, , 500, 33

1973
[50]

H., Lubow S

Shi J.-M., Krolik J. H., Lubow S. H., Hawley J. F., 2012, , 749, 118

2012
[51]

C., Metzger B

Stone N. C., Metzger B. D., Haiman Z., 2017, , 464, 946

2017
[52]

Tagawa H., Haiman Z., Kocsis B., 2020, , 898, 25

2020
[53]

S., Haiman Z., Perna R., Tanaka H., Bartos I., 2022, , 927, 41

Tagawa H., Kimura S. S., Haiman Z., Perna R., Tanaka H., Bartos I., 2022, , 927, 41

2022
[54]

Tang Y., MacFadyen A., Haiman Z., 2017, , 469, 4258

2017
[55]

D., Acernese et al

The LIGO Scientific Collaboration the Virgo Collaboration the KAGRA Collaboration Abbott R., Abbott T. D., Acernese et al. 2021, arXiv e-prints, p. arXiv:2111.03634

2021 arXiv
[56]

D., et al

The LIGO Scientific Collaboration the Virgo Collaboration the KAGRA Collaboration Abbott R., Abbott T. D., et al. 2021, arXiv e-prints, p. arXiv:2111.03606

2021 arXiv
[57]

Tiede C., Zrake J., MacFadyen A., Haiman Z., 2020, , 900, 43

2020
[58]

Wang H.-Y., Bai X.-N., Lai D., Lin D. N. C., 2023, , 526, 3570

2023
[59]

arXiv:2309.11561

Whitehead H., Rowan C., Boekholt T., Kocsis B., 2023, arXiv e-prints, p. arXiv:2309.11561

2023 arXiv
[60]

Yuan F., Narayan R., 2014, , 52, 529

2014
[61]

S., Berry C

Zevin M., Bavera S. S., Berry C. P. L., Kalogera V., Fragos T., Marchant P., Rodriguez C. L., Antonini F., Holz D. E., Pankow C., 2021, , 910, 152

2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

write newline

" write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

[2] [2]

@esa (Ref

\@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded aguplus natbib The aguplus class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later rem...

[3] [3]

@stdbsttrue NAT@ctr \@lbibitem[ NAT@ctr ] \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 [ @natanchorstart #2\@extra@b@citeb \@biblabel @num @natanchorend] @ifcmd#1(@)(@)\@nil #2 @lbibitem\@undefined @lbibitem\@lbibitem \@lbibitem[#1]#2 @lb...

[4] [4]

@open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifundefined NAT@sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifundefined bib@heading @heading NAT@ctr thebibliography [1] @ \@biblabel NAT@ctr \@bibsetup #1 NAT@ctr 0 @openbib .11em \@plus.33em \@minus.07em 4000 4000 `\.=1000 \@...

work page

[5] [5]

J., Natarajan P., 2005, , 634, 921

Armitage P. J., Natarajan P., 2005, , 634, 921

work page 2005

[6] [6]

J., Lubow S

Artymowicz P., Clarke C. J., Lubow S. H., Pringle J. E., 1991, , 370, L35

work page 1991

[7] [7]

H., 1994, The Astrophysical Journal, 421, 651

Artymowicz P., Lubow S. H., 1994, The Astrophysical Journal, 421, 651

work page 1994

[8] [8]

H., 1996, , 467, L77

Artymowicz P., Lubow S. H., 1996, , 467, L77

1996