pith. sign in

arxiv: 2606.28499 · v1 · pith:JCQWLF4Bnew · submitted 2026-06-26 · 🌌 astro-ph.HE · astro-ph.GA

Stochastic Variability of Binary Accretion

Akhil Nair , Jonathan Zrake This is my paper

Pith reviewed 2026-06-30 01:24 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GA
keywords supermassive black hole binariescircumbinary disksaccretion rate variabilitypower spectral densityAGN stochastic variabilityhydrodynamic simulationsminidisks
0
0 comments X

The pith

Unequal-mass binary black hole accretion produces a broken power-law accretion rate PSD breaking near five times the orbital frequency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the power spectral density of accretion rate time series from high-resolution 2D hydrodynamics simulations of a q=0.2 black hole binary with a surrounding circumbinary disk. It finds that the continuum PSD is flat like white noise at low frequencies and transitions to a slope of -4 above a break frequency generically about five times the binary orbital frequency. This shape arises because gas delivery from the circumbinary disk to the minidisks behaves as a damped random walk with correlation time equal to the orbital period, while the minidisks act as low-pass filters at the Kepler frequency of the outer edge of the smaller black hole's minidisk. The result requires that the secondary black hole be much smaller than its minidisk, which is achieved numerically only with a sufficiently small sink region. A reader would care because the form matches the stochastic variability observed in many active galactic nuclei and offers a potential new observational signature of supermassive black hole binaries.

Core claim

The continuum PSD is a broken power-law, transitioning from flat (white noise) to a slope of -4 at a break frequency generically ~5 times the binary orbital frequency. This form is expected when delivery of gas from the circumbinary disk to the individual minidisks is a damped random walk with correlation time equal to binary orbital period and the minidisks function as low-pass filters acting at the Kepler frequency of the outer edge of the smaller black hole's minidisk; numerical evidence supports both. The broken power-law PSD is attained in the limit where the secondary black hole is much smaller than its minidisk, realized numerically by a sufficiently small sink region.

What carries the argument

Damped random walk gas delivery from the circumbinary disk combined with minidisk low-pass filtering at the Kepler frequency of the smaller black hole's minidisk outer edge.

If this is right

  • The broken power-law PSD offers a new observational signpost for supermassive black hole binaries in AGN that complements periodic signals.
  • Larger sink regions produce excess high-frequency noise and accretion spikes that should be regarded as artificial.
  • The PSD shape resembles stochastic variability in ordinary AGN, inviting the conjecture that binarity could explain canonical AGN variability.
  • Pulsar timing array experiments may exclude the possibility that widespread binarity produces the observed AGN variability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the mechanism holds generally, measured break frequencies in AGN PSDs could be inverted to estimate binary orbital periods.
  • The result could be tested by comparing simulated PSDs against multi-band AGN light curves to search for the predicted high-frequency steepening.
  • Running the same analysis on equal-mass binaries or in 3D would show whether the break location and slope -4 are robust across parameter space.

Load-bearing premise

The secondary black hole must be much smaller than its minidisk so that numerical sink regions do not introduce artificial high-frequency accretion spikes.

What would settle it

A high-resolution simulation with vanishingly small sink radius that produces accretion rate PSD lacking the transition to slope -4 at high frequencies would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.28499 by Akhil Nair, Jonathan Zrake.

Figure 1
Figure 1. Figure 1: Two-dimensional surface density snapshots at t = 3100 orbits with different s parameter values (0.05, 0.1, 0.2 and 0.3). Minidisks evolve from deep, strongly buffering structures at small s values (0.05, 0.1) to progressively shallower structures at larger s values (0.2, 0.3). The white circles indicate the sink boundaries. beyond fd ≃ 5. At q = 0.2 the expected f −2 band spans less than a decade, so the p… view at source ↗
Figure 2
Figure 2. Figure 2: Smoothed power spectral densities of M˙ for vari￾ous s values, sampled from the ∆ ln r = 0.0025 run over 100 orbits (3000–3100). azimuth and includes both inward and outward contri￾butions [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Raw accretion rate time series M˙ 1,2(t) over a 100-orbit window, for various s values. Variability diminishes as s decreases. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 M˙ 1 [hM˙ 0i] 0 1 2 3 4 dP/d ˙ M1 M˙ 1 Distribution s = 0.05 s = 0.10 s = 0.20 s = 0.30 s = 0.40 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M˙ 2 [hM˙ 0i] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 dP/d ˙ M2 0.40 0.30 0.20 0.10 0.05 s M˙ 2 Distribution [PITH_FULL_… view at source ↗
Figure 5
Figure 5. Figure 5: Probability density distributions of M˙ 1 (top) and M˙ 2 (bottom) for different s values, with M˙ in units of ⟨M˙ 0⟩. Distributions narrow systematically as s decreases. where Pdrv is the driver PSD supplied at the outer edge of the minidisk and |H| 2 is the squared transfer function of the minidisk filter. In the resolved band the supply [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Fractional rms variability amplitude of M˙ 1 and M˙ 2 as a function of s. contributes a red-noise continuum, and above the outer￾minidisk break fd the filter adds a further f −2 , giving the steep high-frequency tail. The analytic model is de￾veloped in Sec. 4. The break fd is the local Keplerian frequency at the outer edge of the secondary minidisk, fd ≈ fK,2(rout). (14) The control-surface diagnostics pl… view at source ↗
Figure 7
Figure 7. Figure 7: Fractional rms of the net mass flux through circular control surfaces centered on the secondary, as a function of rcs/a for s = 0.05. The profile peaks at rcs/a ≈ 0.10, in the circularization/sloshing region, and declines on both sides. 10−1 100 101 102 Frequency [orbit−1 ] 10−14 10−12 10−10 10−8 10−6 10−4 10−2 100 PSD( ˙M2,net flux) [h ˙M0i 2 orbits] f −2.0 rcs/a = 0.008 rcs/a = 0.183 [PITH_FULL_IMAGE:fi… view at source ↗
Figure 8
Figure 8. Figure 8: Smoothed PSDs of the net control-surface mass flux centered on M2 for s = 0.05, at two representative radii. The grey reference line is an f −2 slope. 4.1. PSD template Sec. 3.3 showed that the control-surface PSD at large rcs/a has a flat-to-f −2 morphology consistent with an Ornstein–Uhlenbeck process. As an effective descrip￾tion of the spectrum supplied to the inner minidisk in the resolved band, we mo… view at source ↗
Figure 9
Figure 9. Figure 9: Power spectral densities of M˙ at s = 0.05 for α ∈ {0.01, 0.05, 0.1, 0.2}. with asymptotic slope β = 4 at f ≫ fb. Fitting Equa￾tion (20) to the s = 0.05 PSD yields fb ≃ 5, consistent with fK,2(rout). The −4 slope predicted by this model is steeper than the f −2 expectation of damped-random-walk prescrip￾tions commonly applied to single-AGN variability (B. C. Kelly et al. 2009). The model therefore predicts… view at source ↗
read the original abstract

We measure the power spectral density (PSD) of the accretion rate time series in an unequal mass (q = 0.2) binary surrounded by a circumbinary gas disk, using very high-resolution 2D hydrodynamics simulations. Our aim is to identify new signposts of supermassive black hole (SMBH) binaries in active galactic nuclei (AGN), based on the shape of the continuum PSD, to complement well-studied line features in the PSD (periodicities). We find that the continuum PSD is a broken power-law, transitioning from flat (white noise) to a slope of -4 at a break frequency generically ~5 times the binary orbital frequency. This form is expected when (a) delivery of gas from the circumbinary disk to the individual "minidisks" is a damped random walk with correlation time equal to binary orbital period and (b) the minidisks function as low-pass filters acting at the Kepler frequency of the outer edge of the smaller black hole's minidisk; we show numerical evidence for both. The broken power-law PSD is attained in a limit where the secondary black hole is much smaller than its minidisk, realized numerically by a sufficiently small "sink" region; larger sinks lead to excess high-frequency noise seen as accretion rate spikes, and we argue these should be regarded as artificial when the black holes themselves are smaller than the sink regions. The broken power-law PSD is reminiscent of stochastic variability in ordinary AGN, inviting the conjecture that canonical AGN variability could result from widespread binarity, however pulsar timing experiments may exclude this possibility.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents results from very high-resolution 2D hydrodynamical simulations of an unequal-mass (q=0.2) supermassive black hole binary accreting from a circumbinary disk. The central claim is that the power spectral density (PSD) of the accretion-rate time series is a broken power law that is flat at low frequencies and steepens to a slope of -4 above a break frequency generically ~5 times the binary orbital frequency. This shape is interpreted as the product of (a) damped-random-walk gas delivery from the circumbinary disk with correlation time equal to the orbital period and (b) low-pass filtering by the minidisks at the Kepler frequency of the outer edge of the secondary's minidisk; numerical evidence is provided for both mechanisms. The result holds only in the limit where the secondary black hole is much smaller than its minidisk, which is realized by using a sufficiently small sink region; larger sinks produce artificial high-frequency spikes.

Significance. If robust, the reported PSD shape supplies a new, continuum-based observational signature for SMBH binaries that complements periodic line features. The direct numerical demonstration of the damped-random-walk delivery and minidisk filtering mechanisms, obtained without fitted parameters, strengthens the physical interpretation. The resemblance to canonical AGN variability is noted, although the authors correctly flag possible tension with pulsar-timing constraints.

major comments (2)
  1. [discussion of sink regions] The central claim that the broken power-law PSD is attained only when the secondary is much smaller than its minidisk (and that larger sinks produce artificial spikes) is load-bearing for the result. The manuscript should therefore report the numerical ratio of sink radius to the outer radius of the secondary minidisk in the production runs and demonstrate convergence of the PSD shape with decreasing sink size.
  2. [results on PSD shape] The break frequency is stated to be generically ~5 times the binary orbital frequency. The manuscript should clarify whether this factor is measured directly from the simulated PSDs or derived from the combination of orbital period and outer-edge Kepler frequency, and whether it remains stable across the range of resolutions and sink sizes explored.
minor comments (2)
  1. [methods] The abstract refers to 'very high-resolution' simulations without quoting the grid resolution, cell size relative to the binary separation, or number of orbits evolved; these details belong in the methods section for reproducibility.
  2. [discussion] The statement that the result 'invites the conjecture that canonical AGN variability could result from widespread binarity' should be accompanied by a brief quantitative estimate of the implied binary fraction or a reference to existing limits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for recommending minor revision. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [discussion of sink regions] The central claim that the broken power-law PSD is attained only when the secondary is much smaller than its minidisk (and that larger sinks produce artificial spikes) is load-bearing for the result. The manuscript should therefore report the numerical ratio of sink radius to the outer radius of the secondary minidisk in the production runs and demonstrate convergence of the PSD shape with decreasing sink size.

    Authors: We agree that explicitly reporting the sink-to-minidisk radius ratio will strengthen the manuscript. Our production runs use a sink radius that is a small fraction of the secondary minidisk's outer radius, consistent with the limit discussed. We will add the specific numerical ratio to the methods section. For convergence, the manuscript already contrasts results with larger sinks showing artificial spikes, but to fully address this, we will include a statement on the stability of the PSD shape for the smallest sinks used, based on our existing simulation suite. revision: yes

  2. Referee: [results on PSD shape] The break frequency is stated to be generically ~5 times the binary orbital frequency. The manuscript should clarify whether this factor is measured directly from the simulated PSDs or derived from the combination of orbital period and outer-edge Kepler frequency, and whether it remains stable across the range of resolutions and sink sizes explored.

    Authors: The factor of approximately 5 is measured directly from the PSDs in our simulations. It arises from the combination of the damped random walk correlation time (equal to the orbital period) and the filtering at the Kepler frequency of the minidisk outer edge, but the specific numerical value is obtained from fitting the simulated PSDs. We will clarify this distinction in the revised text. The break frequency remains stable across the resolutions and sink sizes where the broken power-law form is attained (i.e., sufficiently small sinks), as shown in our figures; we will add an explicit statement to this effect. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central result is obtained by direct measurement of the PSD from time series produced by high-resolution 2D hydrodynamics simulations of an unequal-mass binary. The broken power-law form, break frequency, and supporting behaviors (damped random walk delivery with orbital-period correlation time; minidisk low-pass filtering at outer-edge Kepler frequency) are all extracted from the same simulation data rather than fitted to a subset and then re-predicted, or derived from self-referential equations. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work appear in the provided text. The derivation chain is therefore self-contained and independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard assumptions in astrophysical hydrodynamics simulations without introducing new free parameters or entities in the abstract. The interpretation involves domain-specific assumptions about gas dynamics in disks.

axioms (2)
  • domain assumption The hydrodynamics equations govern the gas flow in the circumbinary disk and minidisks.
    Standard assumption in astrophysical fluid simulations.
  • domain assumption The sink regions approximate the black holes' accretion.
    Common in such simulations, but the paper discusses its size effects.

pith-pipeline@v0.9.1-grok · 5817 in / 1655 out tokens · 51233 ms · 2026-06-30T01:24:54.108112+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

53 extracted references · 51 canonical work pages · 2 internal anchors

  1. [1]

    M., et al

    Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, ApJL, 951, L8, doi: 10.3847/2041-8213/acdac6

    work page doi:10.3847/2041-8213/acdac6 2023

  2. [2]

    2018, MNRAS, 476, 2501, doi: 10.1093/mnras/sty413 Ar´ evalo, P., Churazov, E., Lira, P., et al

    Bloemen, S. 2018, MNRAS, 476, 2501, doi: 10.1093/mnras/sty413 Ar´ evalo, P., Churazov, E., Lira, P., et al. 2024, A&A, 684, A133, doi: 10.1051/0004-6361/202347080

    work page doi:10.1093/mnras/sty413 2018

  3. [3]

    J., Krolik, J

    Avara, M. J., Krolik, J. H., Campanelli, M., et al. 2024, ApJ, 974, 242, doi: 10.3847/1538-4357/ad5bda

    work page doi:10.3847/1538-4357/ad5bda 2024

  4. [4]

    , keywords =

    Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307, doi: 10.1038/287307a0

    work page doi:10.1038/287307a0 1980

  5. [5]

    J., Shen, Y., Blaes, O., et al

    Burke, C. J., Shen, Y., Blaes, O., et al. 2021, Science, 373, 789, doi: 10.1126/science.abg9933

    work page doi:10.1126/science.abg9933 2021

  6. [6]

    2023, Nature Astronomy, 7, 1506, doi: 10.1038/s41550-023-02088-5

    Cai, Z.-Y., & Wang, J.-X. 2023, Nature Astronomy, 7, 1506, doi: 10.1038/s41550-023-02088-5

    work page doi:10.1038/s41550-023-02088-5 2023

  7. [7]

    A., Mingarelli, C

    Casey-Clyde, J. A., Mingarelli, C. M. F., Greene, J. E., et al. 2022, ApJ, 924, 93, doi: 10.3847/1538-4357/ac32de

    work page doi:10.3847/1538-4357/ac32de 2022

  8. [8]

    Davis, S. W. 2025, ApJ, 991, 71, doi: 10.3847/1538-4357/adf4c9

    work page doi:10.3847/1538-4357/adf4c9 2025

  9. [9]

    2016, MNRAS, 463, 2145, doi: 10.1093/mnras/stw1838

    Charisi, M., Bartos, I., Haiman, Z., et al. 2016, MNRAS, 463, 2145, doi: 10.1093/mnras/stw1838

    work page doi:10.1093/mnras/stw1838 2016

  10. [10]

    Trump, J. R. 2022, MNRAS, 510, 5929, doi: 10.1093/mnras/stab3713

    work page doi:10.1093/mnras/stab3713 2022

  11. [11]

    , keywords =

    Chen, Y.-J., Zhai, S., Liu, J.-R., et al. 2024, MNRAS, 527, 12154, doi: 10.1093/mnras/stad3981

    work page doi:10.1093/mnras/stad3981 2024

  12. [12]

    2025, MNRAS, 539, 1430, doi: 10.1093/mnras/staf585

    Clyburn, M., & Zrake, J. 2025, MNRAS, 539, 1430, doi: 10.1093/mnras/staf585

    work page doi:10.1093/mnras/staf585 2025

  13. [13]

    J., & Ryan, G

    Dittmann, A. J., & Ryan, G. 2022, MNRAS, 513, 6158, doi: 10.1093/mnras/stac935

    work page doi:10.1093/mnras/stac935 2022

  14. [14]

    Monthly Notices of the Royal Astronomical Society , archivePrefix = "arXiv", eprint =

    Done, C., Davis, S. W., Jin, C., Blaes, O., & Ward, M. 2012, MNRAS, 420, 1848, doi: 10.1111/j.1365-2966.2011.19779.x D’Orazio, D. J., & Duffell, P. C. 2021, ApJL, 914, L21, doi: 10.3847/2041-8213/ac0621 D’Orazio, D. J., Duffell, P. C., & Tiede, C. 2024, ApJ, 977, 244, doi: 10.3847/1538-4357/ad938b D’Orazio, D. J., Haiman, Z., Duffell, P., MacFadyen, A., &

    work page doi:10.1111/j.1365-2966.2011.19779.x 2012

  15. [15]

    2016, MNRAS, 459, 2379, doi: 10.1093/mnras/stw792

    Farris, B. 2016, MNRAS, 459, 2379, doi: 10.1093/mnras/stw792

    work page doi:10.1093/mnras/stw792 2016

  16. [16]

    C., D’Orazio, D., Derdzinski, A., et al

    Duffell, P. C., D’Orazio, D., Derdzinski, A., et al. 2020, The Astrophysical Journal, 901, 25, doi: 10.3847/1538-4357/abab95 15

    work page doi:10.3847/1538-4357/abab95 2020

  17. [17]

    Eggleton, P. P. 1983, ApJ, 268, 368, doi: 10.1086/160960

    work page doi:10.1086/160960 1983

  18. [18]

    D., Duffell, P., MacFadyen, A

    Farris, B. D., Duffell, P., MacFadyen, A. I., & Haiman, Z. 2014, The Astrophysical Journal, 783, 134, doi: 10.1088/0004-637X/783/2/134

    work page doi:10.1088/0004-637x/783/2/134 2014

  19. [19]

    2025, MNRAS, 543, 2093, doi: 10.1093/mnras/staf1473

    Fu, Y.-X., Li, Y.-R., Wang, J.-M., et al. 2025, MNRAS, 543, 2093, doi: 10.1093/mnras/staf1473

    work page doi:10.1093/mnras/staf1473 2025

  20. [20]

    Candidates from continued radial velocity tests

    Guo, H., Liu, X., Shen, Y., et al. 2019, MNRAS, 482, 3288, doi: 10.1093/mnras/sty2920

    work page doi:10.1093/mnras/sty2920 2019

  21. [21]

    2009, ApJ, 700, 1952, doi: 10.1088/0004-637X/700/2/1952 Ivezi´ c,ˇZ., Kahn, S

    Haiman, Z., Kocsis, B., & Menou, K. 2009, ApJ, 700, 1952, doi: 10.1088/0004-637X/700/2/1952 Ivezi´ c,ˇZ., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111, doi: 10.3847/1538-4357/ab042c

    work page doi:10.1088/0004-637x/700/2/1952 2009

  22. [22]

    C., Bechtold, J., & Siemiginowska, A

    Kelly, B. C., Bechtold, J., & Siemiginowska, A. 2009, ApJ, 698, 895, doi: 10.1088/0004-637X/698/1/895 Koz lowski, S. 2017, A&A, 597, A128, doi: 10.1051/0004-6361/201629890

    work page internal anchor Pith review doi:10.1088/0004-637x/698/1/895 2009

  23. [23]

    Lai, D., & Mu˜ noz, D. J. 2023, ARA&A, 61, 517, doi: 10.1146/annurev-astro-052622-022933

    work page doi:10.1146/annurev-astro-052622-022933 2023

  24. [24]

    2021, MNRAS, 500, 4025, doi: 10.1093/mnras/staa3055

    Liao, W.-T., Chen, Y.-C., Liu, X., et al. 2021, MNRAS, 500, 4025, doi: 10.1093/mnras/staa3055

    work page doi:10.1093/mnras/staa3055 2021

  25. [25]

    2026, ApJ, 997, 316, doi: 10.3847/1538-4357/ae29a7

    Lin, A., Charisi, M., & Haiman, Z. 2026, ApJ, 997, 316, doi: 10.3847/1538-4357/ae29a7

    work page doi:10.3847/1538-4357/ae29a7 2026

  26. [26]

    Lyubarskii, Y. E. 1997, MNRAS, 292, 679, doi: 10.1093/mnras/292.3.679

    work page doi:10.1093/mnras/292.3.679 1997

  27. [27]

    I., & Milosavljevi´ c, M

    MacFadyen, A. I., & Milosavljevi´ c, M. 2008, ApJ, 672, 83, doi: 10.1086/523869

    work page doi:10.1086/523869 2008

  28. [28]

    L., Ivezi´ c,ˇZ., Kochanek, C

    MacLeod, C. L., Ivezi´ c,ˇZ., Kochanek, C. S., et al. 2010, ApJ, 721, 1014, doi: 10.1088/0004-637X/721/2/1014

    work page doi:10.1088/0004-637x/721/2/1014 2010

  29. [29]

    A., & Sandage, A

    Matthews, T. A., & Sandage, A. R. 1963, ApJ, 138, 30, doi: 10.1086/147615

    work page doi:10.1086/147615 1963

  30. [30]

    Fender, R. P. 2006, Nature, 444, 730, doi: 10.1038/nature05389

    work page doi:10.1038/nature05389 2006

  31. [31]

    C., & Hernquist, L

    Mihos, J. C., & Hernquist, L. 1996, ApJ, 464, 641, doi: 10.1086/177353 Milosavljevi´ c, M., & Merritt, D. 2001, ApJ, 563, 34, doi: 10.1086/323830 Mu˜ noz, D. J., Miranda, R., & Lai, D. 2019, ApJ, 871, 84, doi: 10.3847/1538-4357/aaf867

    work page internal anchor Pith review doi:10.1086/177353 1996

  32. [32]

    2011, ApJL, 743, L12, doi: 10.1088/2041-8205/743/1/L12

    Gandhi, P. 2011, ApJL, 743, L12, doi: 10.1088/2041-8205/743/1/L12

    work page doi:10.1088/2041-8205/743/1/l12 2011

  33. [33]

    M., Assef, R

    Padovani, P., Alexander, D. M., Assef, R. J., et al. 2017, A&A Rv, 25, 2, doi: 10.1007/s00159-017-0102-9

    work page doi:10.1007/s00159-017-0102-9 2017

  34. [34]

    Peters, P. C. 1964, Physical Review, 136, 1224, doi: 10.1103/PhysRev.136.B1224

    work page doi:10.1103/physrev.136.b1224 1964

  35. [35]

    Pringle, J. E. 1981, ARA&A, 19, 137, doi: 10.1146/annurev.aa.19.090181.001033

    work page doi:10.1146/annurev.aa.19.090181.001033 1981

  36. [36]

    Salpeter, E. E. 1964, ApJ, 140, 796, doi: 10.1086/147973

    work page doi:10.1086/147973 1964

  37. [37]

    Savitzky, A., & Golay, M. J. E. 1964, Analytical Chemistry, 36, 1627, doi: 10.1021/ac60214a047

    work page doi:10.1021/ac60214a047 1964

  38. [38]

    I., & Sunyaev, R

    Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337

    1973

  39. [39]

    2010, ApJ, 725, 249, doi: 10.1088/0004-637X/725/1/249

    Shen, Y., & Loeb, A. 2010, ApJ, 725, 249, doi: 10.1088/0004-637X/725/1/249

    work page doi:10.1088/0004-637x/725/1/249 2010

  40. [40]

    H., Lubow, S

    Shi, J.-M., Krolik, J. H., Lubow, S. H., & Hawley, J. F. 2012, ApJ, 749, 118, doi: 10.1088/0004-637X/749/2/118

    work page doi:10.1088/0004-637x/749/2/118 2012

  41. [41]

    C., & Frank, J

    Shlosman, I., Begelman, M. C., & Frank, J. 1990, Nature, 345, 679, doi: 10.1038/345679a0

    work page doi:10.1038/345679a0 1990

  42. [42]

    J., & Hernquist, L

    Siwek, M., Weinberger, R., Mu˜ noz, D. J., & Hernquist, L. 2023, MNRAS, 518, 5059, doi: 10.1093/mnras/stac3263

    work page doi:10.1093/mnras/stac3263 2023

  43. [43]

    L., Mushotzky, R

    Smith, K. L., Mushotzky, R. F., Boyd, P. T., et al. 2018, ApJ, 857, 141, doi: 10.3847/1538-4357/aab88d

    work page doi:10.3847/1538-4357/aab88d 2018

  44. [44]

    2025, ApJ, 986, 158, doi: 10.3847/1538-4357/add408

    Tiwari, V., Chan, C.-H., Bogdanovi´ c, T., et al. 2025, ApJ, 986, 158, doi: 10.3847/1538-4357/add408

    work page doi:10.3847/1538-4357/add408 2025

  45. [45]

    Ulrich, M.-H., Maraschi, L., & Urry, C. M. 1997, ARA&A, 35, 445, doi: 10.1146/annurev.astro.35.1.445

    work page doi:10.1146/annurev.astro.35.1.445 1997

  46. [46]

    Monthly Notices of the Royal Astronomical Society , eprint =

    Vaughan, S., Edelson, R., Warwick, R. S., & Uttley, P. 2003, MNRAS, 345, 1271, doi: 10.1046/j.1365-2966.2003.07042.x

    work page doi:10.1046/j.1365-2966.2003.07042.x 2003

  47. [47]

    G., et al

    Vaughan, S., Uttley, P., Markowitz, A. G., et al. 2016, MNRAS, 461, 3145, doi: 10.1093/mnras/stw1412

    work page doi:10.1093/mnras/stw1412 2016

  48. [48]

    2022, PhRvD, 106, 103010, doi: 10.1103/PhysRevD.106.103010

    Haiman, Z. 2022, PhRvD, 106, 103010, doi: 10.1103/PhysRevD.106.103010

    work page doi:10.1103/physrevd.106.103010 2022

  49. [49]

    2024, ApJ, 962, 76, doi: 10.3847/1538-4357/ad1a17

    Haiman, Z. 2024, ApJ, 962, 76, doi: 10.3847/1538-4357/ad1a17

    work page doi:10.3847/1538-4357/ad1a17 2024

  50. [50]

    A., Charisi, M., Taylor, S

    Witt, C. A., Charisi, M., Taylor, S. R., & Burke-Spolaor, S. 2022, ApJ, 936, 89, doi: 10.3847/1538-4357/ac8356

    work page doi:10.3847/1538-4357/ac8356 2022

  51. [51]

    2025, A&A, 698, A105, doi: 10.1051/0004-6361/202452469

    Yuk, H., & Dai, X. 2025, A&A, 698, A105, doi: 10.1051/0004-6361/202452469

    work page doi:10.1051/0004-6361/202452469 2025

  52. [52]

    2024, Sailfish: GPU-accelerated grid-based astrophysics gas dynamics code,, Astrophysics Source Code Library, record ascl:2408.004 http://ascl.net/2408.004

    Zrake, J., & MacFadyen, A. 2024, Sailfish: GPU-accelerated grid-based astrophysics gas dynamics code,, Astrophysics Source Code Library, record ascl:2408.004 http://ascl.net/2408.004

    2024

  53. [53]

    2021, ApJL, 909, L13, doi: 10.3847/2041-8213/abdd1c

    Zrake, J., Tiede, C., MacFadyen, A., & Haiman, Z. 2021, ApJL, 909, L13, doi: 10.3847/2041-8213/abdd1c

    work page doi:10.3847/2041-8213/abdd1c 2021