pith. machine review for the scientific record. sign in

arxiv: 2601.14499 · v2 · submitted 2026-01-20 · 🌌 astro-ph.HE · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Searching for Isolated Black Hole Candidates within 15 pc of the Solar System in Gaia DR3

Abdurakhmon Nosirov , Cosimo Bambi , Leda Gao , Jos de Bruijne , Jiachen Jiang , Andrea Santangelo , Fu-Guo Xie
Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:58 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords isolated black holesGaia DR3interstellar accretionastrometric candidateslocal interstellar cloudsspurious solutionsmulti-wavelength follow-up
0
0 comments X

The pith

Gaia DR3 search within 15 pc identifies five astrometric black hole candidates but dismisses them all as spurious after multi-wavelength checks.

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

The paper models the expected electromagnetic output from isolated black holes accreting from the interstellar medium and concludes that detectable signals are possible only inside Local Interstellar Clouds. It then scans Gaia DR3 for nearby sources whose astrometric solutions could indicate such objects and flags five candidates. All five sit near the Galactic plane where crowding and unmodelled binarity readily produce false astrometric signals. Follow-up infrared and radio observations show no emission consistent with accretion, reinforcing that the candidates are not black holes.

Core claim

We have searched the Gaia DR3 catalog for candidate isolated black holes accreting from the interstellar medium and identified five sources. All candidates lie close to the Galactic plane, making them likely spurious astrometric solutions, for instance caused by unmodelled background sources (crowding) and/or unmodelled binarity. Our search for infrared and radio emission from these sources further suggests that they are unlikely to be black holes accreting from the interstellar medium.

What carries the argument

Astrometric anomaly selection in Gaia DR3 combined with infrared and radio flux upper limits to test accretion models for isolated black holes.

If this is right

  • No isolated black holes within 15 pc produce observable accretion emission under current models and facilities.
  • Astrometric selection alone is insufficient for reliable identification because of crowding-induced false positives near the plane.
  • Detection of isolated black holes in the solar neighbourhood will require either improved models that lower the required accretion rate or entirely different methods such as gravitational microlensing.
  • The local population of isolated black holes may be consistent with theoretical estimates yet remain undetectable by electromagnetic means outside dense clouds.

Where Pith is reading between the lines

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

  • If the same selection and rejection criteria are applied to future Gaia releases, the absence of candidates would tighten upper limits on the local density of accreting isolated black holes.
  • Extending the search beyond 15 pc but restricting it to known interstellar clouds could test whether the cloud-volume fraction really governs detectability.
  • Cross-matching the same five sources with upcoming X-ray or radio surveys could provide an independent falsification test even without new Gaia data.

Load-bearing premise

The theoretical accretion spectra and flux thresholds used to predict detectable emission from black holes in the interstellar medium are sufficiently accurate.

What would settle it

Clear infrared or radio emission from any of the five candidates that matches the predicted accretion spectrum at the source distance would indicate they are genuine isolated black holes.

Figures

Figures reproduced from arXiv: 2601.14499 by Abdurakhmon Nosirov, Andrea Santangelo, Cosimo Bambi, Fu-Guo Xie, Jiachen Jiang, Jos de Bruijne, Leda Gao.

Figure 1
Figure 1. Figure 1: Spectrum of an isolated black hole accret￾ing from the interstellar medium as computed with the LLAGNSED model. We assume that the mass accretion rate is described by the BHL model with λ = 1 and we em￾ploy the following values for the parameters of the sys￾tem: black hole mass MBH = 10 M⊙, black hole distance D = 15 pc, black hole speed vBH = 50 km s−1 , sound speed in the interstellar medium cs = 10 km s… view at source ↗
Figure 2
Figure 2. Figure 2: Spectra of isolated black holes accreting from a hot and low-density interstellar medium at 3, 5, 10, and 15 pc from the Solar System as computed with LLAGNSED (ADAF model). We assume that the particle number density is n = 0.05 cm−3 , the mean atomic mass is µ = 0.5, the sound speed is cs = 200 km s−1 , the black hole mass is MBH = 10 M⊙, and the black hole velocity is vBH = 20 km s−1 . In the left panel,… view at source ↗
Figure 3
Figure 3. Figure 3: Spectra of isolated black holes accreting from a warm and partially ionized interstellar medium at 3, 5, 10, and 15 pc from the Solar System as computed with LLAGNSED (ADAF model). We assume that the particle number density is n = 0.3 cm−3 , the mean atomic mass is µ = 0.75, the sound speed is cs = 10 km s−1 , and the black hole mass is MBH = 10 M⊙. In the top panels, we assume the BHL accretion model with… view at source ↗
Figure 4
Figure 4. Figure 4: Spectra of isolated black holes accreting from a hot and low-density interstellar medium in the ADAF+Jet model. In the left panel, we vary the angle between the jet axis and our line of sight assuming that the mass-loss rate into jet is 10% of the black hole mass accretion rate. In the right panel, we vary the mass-loss rate into jet assuming that the angle between the jet axis and our line of sight is 35◦… view at source ↗
Figure 5
Figure 5. Figure 5: Spectra of isolated black holes accreting from a warm and partially ionized interstellar medium in the ADAF+Jet model. In the left panel, we vary the angle between the jet axis and our line of sight assuming that the mass-loss rate into jet is 10% of the black hole mass accretion rate. In the right panel, we vary the mass-loss rate into jet assuming that the angle between the jet axis and our line of sight… view at source ↗
read the original abstract

Theoretical models predict that the Galaxy hosts $10^8$-$10^9$ black holes formed from the complete gravitational collapse of heavy stars and that most of these black holes are isolated, without any companion. Within 15 pc of the Solar System ($\sim 50$ ly), there may be a few black holes. If located inside one of the Local Interstellar Clouds - which occupy 5-20% of this local volume - an isolated black hole could produce detectable electromagnetic emission via accretion from the interstellar medium, given the capabilities of current or near-future observatories. However, precise predictions remain challenging due to large uncertainties in the expected accretion spectra. Outside these clouds, the accretion rate would be too low; according to our models, the resulting electromagnetic flux is well below the detection thresholds of current and near-future observational facilities. While astrometric detection via gravitational perturbation of nearby stars is conceivable, the local stellar density is too low for this method to be realistically successful. We have searched the Gaia DR3 catalog for candidate isolated black holes accreting from the interstellar medium and identified five sources. All candidates lie close to the Galactic plane, making them likely spurious astrometric solutions, for instance caused by unmodelled background sources (crowding) and/or unmodelled binarity. Our search for infrared and radio emission from these sources further suggests that they are unlikely to be black holes accreting from the interstellar medium.

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 / 3 minor

Summary. The manuscript reports a search of the Gaia DR3 catalog for isolated stellar-mass black holes within 15 pc of the Sun that could accrete from the interstellar medium and produce detectable electromagnetic emission. Theoretical expectations are reviewed, noting that only sources inside dense Local Interstellar Clouds (5-20% volume filling factor) might yield observable fluxes, while outside these regions accretion rates are too low. The search yields five candidate sources; all lie near the Galactic plane and show no infrared or radio counterparts, leading the authors to conclude that the candidates are likely spurious astrometric solutions caused by crowding or unmodeled binarity rather than genuine accreting black holes.

Significance. If the central claim holds, the work supplies a useful local null result that constrains the nearby population of isolated black holes and tests accretion models against current observational limits. The combination of precise Gaia astrometry with multi-wavelength non-detections provides a practical template for future searches, even while acknowledging large uncertainties in predicted spectra. This strengthens the empirical basis for Galactic black-hole demographics without relying on any single untested assumption.

major comments (2)
  1. [§3] §3 (Candidate selection): Explicit quantitative thresholds for parallax significance, proper-motion anomaly, or RUWE cuts are not stated, so it is difficult to assess the expected false-positive rate near the plane or to reproduce the exact list of five sources.
  2. [§4] §4 (Accretion modeling and flux limits): Although large uncertainties in spectra are noted, the paper does not tabulate the explored parameter ranges (ISM density, relative velocity, radiative efficiency) or show that even the most optimistic models still fall below IR/radio detection thresholds for the five candidates; this step is load-bearing for the dismissal.
minor comments (3)
  1. [Abstract] Abstract: A single sentence quantifying the total number of Gaia sources examined within 15 pc would help readers gauge the rarity of the five candidates.
  2. [Figure 2] Figure 2 (sky positions): Adding 1σ error ellipses and a shaded band for the Galactic plane would clarify why proximity alone is taken as strong evidence of spurious solutions.
  3. [§2] Notation: The symbol for interstellar-medium density is used inconsistently between text and equations; a single definition in §2 would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive recommendation for minor revision. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (Candidate selection): Explicit quantitative thresholds for parallax significance, proper-motion anomaly, or RUWE cuts are not stated, so it is difficult to assess the expected false-positive rate near the plane or to reproduce the exact list of five sources.

    Authors: We agree with this observation. In the revised version of the manuscript, we will explicitly state the quantitative thresholds applied in the candidate selection process, including the parallax significance cut (e.g., >5σ), criteria for proper-motion anomaly, and the RUWE threshold (RUWE < 1.4). We will also provide the exact list of the five sources with their Gaia identifiers to facilitate reproducibility and allow independent assessment of the false-positive rate. revision: yes

  2. Referee: [§4] §4 (Accretion modeling and flux limits): Although large uncertainties in spectra are noted, the paper does not tabulate the explored parameter ranges (ISM density, relative velocity, radiative efficiency) or show that even the most optimistic models still fall below IR/radio detection thresholds for the five candidates; this step is load-bearing for the dismissal.

    Authors: We acknowledge that a more detailed presentation of the accretion modeling would strengthen the paper. In the revision, we will add a table in §4 listing the explored ranges for ISM density (0.1–100 cm⁻³), relative velocity (5–200 km s⁻¹), and radiative efficiency (0.001–0.1). Additionally, we will include calculations showing that even under the most optimistic assumptions, the predicted electromagnetic fluxes for the five candidates fall below the detection thresholds in infrared and radio bands, consistent with our conclusion that they are unlikely to be accreting black holes. revision: yes

Circularity Check

0 steps flagged

No significant circularity in observational search and candidate dismissal

full rationale

The paper conducts a direct catalog search in Gaia DR3, flags five sources based on their proximity to the Galactic plane (suggesting spurious astrometry from crowding or binarity), and reports non-detections in IR/radio that rule out ISM accretion. No equations, fitted parameters, or predictions are defined in terms of the paper's own outputs; accretion models are cited with explicit large uncertainties rather than used to force a result. No self-citation chains, ansatzes, or renamings reduce the central claim to its inputs. The derivation chain rests on external Gaia data and multi-wavelength observations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard astrophysical background assumptions about black-hole formation rates and accretion physics; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Theoretical models predict 10^8-10^9 black holes in the Galaxy, most isolated
    Invoked to motivate the expected local population and the possibility of a few within 15 pc.
  • domain assumption Accretion from the interstellar medium produces detectable electromagnetic emission only inside Local Interstellar Clouds
    Used to define the search volume and to explain why sources outside clouds are undetectable.

pith-pipeline@v0.9.0 · 5589 in / 1464 out tokens · 30441 ms · 2026-05-16T11:58:04.878847+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 2 internal anchors

  1. [1]

    P., et al

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, PhRvL, 116, 221101, doi: 10.1103/PhysRevLett.116.221101 —. 2019, PhRvD, 100, 104036, doi: 10.1103/PhysRevD.100.104036

    work page doi:10.1103/physrevlett.116.221101 2016

  2. [2]

    M., & Chauhan, J

    Abdulghani, Y., Lohfink, A. M., & Chauhan, J. 2025, MNRAS, 541, 553, doi: 10.1093/mnras/staf979

    work page doi:10.1093/mnras/staf979 2025

  3. [3]

    2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806

    Demleitner, M., & Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806

    work page internal anchor Pith review doi:10.3847/1538-3881/abd806 2021

  4. [4]

    2017a, Reviews of Modern Physics, 89, 025001, doi: 10.1103/RevModPhys.89.025001 —

    Bambi, C. 2017a, Reviews of Modern Physics, 89, 025001, doi: 10.1103/RevModPhys.89.025001 —. 2017b, Black Holes: A Laboratory for Testing Strong Gravity (Springer Singapore), doi: 10.1007/978-981-10-4524-0 —. 2025a, iScience, 28, 113142, doi: 10.1016/j.isci.2025.113142 —. 2025b, arXiv e-prints, arXiv:2509.11222, doi: 10.48550/arXiv.2509.11222

    work page doi:10.1103/revmodphys.89.025001 2025

  5. [5]

    2024, Recent Progress on Gravity Tests

    Bambi, C., & C´ ardenas-Avenda˜ no, A. 2024, Recent Progress on Gravity Tests. Challenges and Future Perspectives (Springer Singapore), doi: 10.1007/978-981-97-2871-8

    work page doi:10.1007/978-981-97-2871-8 2024

  6. [6]

    Best, W. M. J., Dupuy, T. J., Liu, M. C., et al. 2025, The UltracoolSheet: Photometry, Astrometry, Spectroscopy, and Multiplicity for 4000+ Ultracool Dwarfs and Imaged Exoplanets, 2.1.0, Zenodo, doi: 10.5281/zenodo.15802304

    work page doi:10.5281/zenodo.15802304 2025

  7. [7]

    1944, MNRAS, 104, 273, doi: 10.1093/mnras/104.5.273

    Bondi, H., & Hoyle, F. 1944, MNRAS, 104, 273, doi: 10.1093/mnras/104.5.273

    work page doi:10.1093/mnras/104.5.273 1944

  8. [8]

    2019, arXiv e-prints, arXiv:1912.12699, doi: 10.48550/arXiv.1912.12699

    Braun, R., Bonaldi, A., Bourke, T., Keane, E., & Wagg, J. 2019, arXiv e-prints, arXiv:1912.12699, doi: 10.48550/arXiv.1912.12699

    work page doi:10.48550/arxiv.1912.12699 2019

  9. [9]

    Cao, Z., Nampalliwar, S., Bambi, C., Dauser, T., & Garc´ ıa, J. A. 2018, PhRvL, 120, 051101, doi: 10.1103/PhysRevLett.120.051101

    work page doi:10.1103/physrevlett.120.051101 2018

  10. [10]

    1971, PhRvL, 26, 331, doi: 10.1103/PhysRevLett.26.331

    Carter, B. 1971, PhRvL, 26, 331, doi: 10.1103/PhysRevLett.26.331

    work page doi:10.1103/physrevlett.26.331 1971

  11. [11]

    M., Skrutskie, M

    Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, 2MASS All Sky Catalog of point sources

    work page 2003

  12. [12]

    M., Wright, E

    Cutri, R. M., Wright, E. L., Conrow, T., et al. 2013, Explanatory Supplement to the AllWISE Data Release

    work page 2013

  13. [13]

    P., Maccarone, T

    Fender, R. P., Maccarone, T. J., & Heywood, I. 2013, MNRAS, 430, 1538, doi: 10.1093/mnras/sts688

    work page doi:10.1093/mnras/sts688 2013

  14. [14]

    Nakamura, K. E. 1998, ApJL, 495, L85, doi: 10.1086/311220 Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1, doi: 10.1051/0004-6361/202243940

    work page doi:10.1086/311220 1998

  15. [15]

    2025, ApJ, 978, 148, doi: 10.3847/1538-4357/ad9926 10

    Galishnikova, A., Philippov, A., Quataert, E., Chatterjee, K., & Liska, M. 2025, ApJ, 978, 148, doi: 10.3847/1538-4357/ad9926 10

    work page doi:10.3847/1538-4357/ad9926 2025

  16. [16]

    Hoyle, F., & Lyttleton, R. A. 1939, Proceedings of the Cambridge Philosophical Society, 35, 405, doi: 10.1017/S0305004100021150

    work page doi:10.1017/s0305004100021150 1939

  17. [17]

    Kaaz, N., Murguia-Berthier, A., Chatterjee, K., Liska, M. T. P., & Tchekhovskoy, A. 2023, ApJ, 950, 31, doi: 10.3847/1538-4357/acc7a1

    work page doi:10.3847/1538-4357/acc7a1 2023

  18. [18]

    Kerr, R. P. 1963, PhRvL, 11, 237, doi: 10.1103/PhysRevLett.11.237

    work page doi:10.1103/physrevlett.11.237 1963

  19. [19]

    A., Chandler, C

    Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001, doi: 10.1088/1538-3873/ab63eb

    work page doi:10.1088/1538-3873/ab63eb 2020

  20. [20]

    Lattimer, J. M. 2012, Annual Review of Nuclear and Particle Science, 62, 485, doi: 10.1146/annurev-nucl-102711-095018

    work page doi:10.1146/annurev-nucl-102711-095018 2012

  21. [21]

    2025, ApJ, 990, 88, doi: 10.3847/1538-4357/adec66

    Vieira, K. 2025, ApJ, 990, 88, doi: 10.3847/1538-4357/adec66

    work page doi:10.3847/1538-4357/adec66 2025

  22. [22]

    Maccarone, T. J. 2005, MNRAS, 360, L30, doi: 10.1111/j.1745-3933.2005.00039.x

    work page doi:10.1111/j.1745-3933.2005.00039.x 2005

  23. [23]

    1998, ApJL, 494, L181, doi: 10.1086/311194

    Maoz, E. 1998, ApJL, 494, L181, doi: 10.1086/311194

    work page doi:10.1086/311194 1998

  24. [24]

    1985, MNRAS, 217, 77, doi: 10.1093/mnras/217.1.77

    McDowell, J. 1985, MNRAS, 217, 77, doi: 10.1093/mnras/217.1.77

    work page doi:10.1093/mnras/217.1.77 1985

  25. [25]

    2024, A&A, 682, A34, doi: 10.1051/0004-6361/202347165

    Merloni, A., Lamer, G., Liu, T., et al. 2024, A&A, 682, A34, doi: 10.1051/0004-6361/202347165

    work page internal anchor Pith review doi:10.1051/0004-6361/202347165 2024

  26. [26]

    1975, A&A, 44, 59

    Meszaros, P. 1975, A&A, 44, 59

    work page 1975

  27. [27]

    Murchikova, L., & Sahu, K. C. 2025, ApJL, 988, L12, doi: 10.3847/2041-8213/ade7f8

    work page doi:10.3847/2041-8213/ade7f8 2025

  28. [28]

    1994, ApJL, 428, L13, doi: 10.1086/187381 —

    Narayan, R., & Yi, I. 1994, ApJL, 428, L13, doi: 10.1086/187381 —. 1995a, ApJ, 444, 231, doi: 10.1086/175599 —. 1995b, ApJ, 452, 710, doi: 10.1086/176343

    work page doi:10.1086/187381 1994

  29. [29]

    2020, A&A, 638, A94, doi: 10.1051/0004-6361/201936557

    Olejak, A., Belczynski, K., Bulik, T., & Sobolewska, M. 2020, A&A, 638, A94, doi: 10.1051/0004-6361/201936557

    work page doi:10.1051/0004-6361/201936557 2020

  30. [30]

    2013, ApJ, 767, 163, doi: 10.1088/0004-637X/767/2/163

    Park, K., & Ricotti, M. 2013, ApJ, 767, 163, doi: 10.1088/0004-637X/767/2/163

    work page doi:10.1088/0004-637x/767/2/163 2013

  31. [31]

    W., Palumbo, D

    Pesce, D. W., Palumbo, D. C. M., Narayan, R., et al. 2021, ApJ, 923, 260, doi: 10.3847/1538-4357/ac2eb5

    work page doi:10.3847/1538-4357/ac2eb5 2021

  32. [32]

    2020, PhRvL, 125, 141104, doi: 10.1103/PhysRevLett.125.141104

    Psaltis, D., Medeiros, L., Christian, P., et al. 2020, PhRvL, 125, 141104, doi: 10.1103/PhysRevLett.125.141104

    work page doi:10.1103/physrevlett.125.141104 2020

  33. [33]

    Redfield, S., & Linsky, J. L. 2008, ApJ, 673, 283, doi: 10.1086/524002

    work page doi:10.1086/524002 2008

  34. [34]

    E., & Ruffini, R

    Rhoades, C. E., & Ruffini, R. 1974, PhRvL, 32, 324, doi: 10.1103/PhysRevLett.32.324

    work page doi:10.1103/physrevlett.32.324 1974

  35. [35]

    Robinson, D. C. 1975, PhRvL, 34, 905, doi: 10.1103/PhysRevLett.34.905

    work page doi:10.1103/physrevlett.34.905 1975

  36. [36]

    2021, MNRAS, 505, 4036, doi: 10.1093/mnras/stab1533

    Scarcella, F., Gaggero, D., Connors, R., et al. 2021, MNRAS, 505, 4036, doi: 10.1093/mnras/stab1533

    work page doi:10.1093/mnras/stab1533 2021

  37. [37]

    F., Meisner, A

    Schlafly, E. F., Meisner, A. M., & Green, G. M. 2019, ApJS, 240, 30, doi: 10.3847/1538-4365/aafbea

    work page doi:10.3847/1538-4365/aafbea 2019

  38. [38]

    2021, Research Notes of the American Astronomical Society, 5, 40, doi: 10.3847/2515-5172/abea23

    Scholz, R.-D. 2021, Research Notes of the American Astronomical Society, 5, 40, doi: 10.3847/2515-5172/abea23

    work page doi:10.3847/2515-5172/abea23 2021

  39. [39]

    W., Hardcastle, M

    Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2022, A&A, 659, A1, doi: 10.1051/0004-6361/202142484

    work page doi:10.1051/0004-6361/202142484 2022

  40. [40]

    Shvartsman, V. F. 1971, Soviet Ast., 15, 377

    work page 1971

  41. [41]

    X., Woosley S

    Timmes, F. X., Woosley, S. E., & Weaver, T. A. 1996, ApJ, 457, 834, doi: 10.1086/176778

    work page doi:10.1086/176778 1996

  42. [42]

    B., et al

    Tripathi, A., Nampalliwar, S., Abdikamalov, A. B., et al. 2019a, ApJ, 875, 56, doi: 10.3847/1538-4357/ab0e7e

    work page doi:10.3847/1538-4357/ab0e7e

  43. [43]

    B., et al

    Tripathi, A., Zhang, Y., Abdikamalov, A. B., et al. 2021, ApJ, 913, 79, doi: 10.3847/1538-4357/abf6cd

    work page doi:10.3847/1538-4357/abf6cd 2021

  44. [44]

    2019b, ApJ, 874, 135, doi: 10.3847/1538-4357/ab0a00

    Tripathi, A., Yan, J., Yang, Y., et al. 2019b, ApJ, 874, 135, doi: 10.3847/1538-4357/ab0a00

    work page doi:10.3847/1538-4357/ab0a00

  45. [45]

    2018, MNRAS, 477, 791, doi: 10.1093/mnras/sty699

    Tsuna, D., Kawanaka, N., & Totani, T. 2018, MNRAS, 477, 791, doi: 10.1093/mnras/sty699

    work page doi:10.1093/mnras/sty699 2018

  46. [46]

    2023, Classical and Quantum Gravity, 40, 165007, doi: 10.1088/1361-6382/acd97b

    Vagnozzi, S., Roy, R., Tsai, Y.-D., et al. 2023, Classical and Quantum Gravity, 40, 165007, doi: 10.1088/1361-6382/acd97b

    work page doi:10.1088/1361-6382/acd97b 2023

  47. [47]

    J., Schneider, A

    Vrba, F. J., Schneider, A. C., Munn, J. A., et al. 2026, arXiv e-prints, arXiv:2601.09671, doi: 10.48550/arXiv.2601.09671

    work page doi:10.48550/arxiv.2601.09671 2026

  48. [48]

    2014, MNRAS, 442, L110, doi: 10.1093/mnrasl/slu068

    Xie, F.-G., Yang, Q.-X., & Ma, R. 2014, MNRAS, 442, L110, doi: 10.1093/mnrasl/slu068

    work page doi:10.1093/mnrasl/slu068 2014

  49. [49]

    A., Ma, R., & Yang, Q.-X

    Xie, F.-G., Zdziarski, A. A., Ma, R., & Yang, Q.-X. 2016, MNRAS, 463, 2287, doi: 10.1093/mnras/stw2132

    work page doi:10.1093/mnras/stw2132 2016

  50. [50]

    Yagi, K., & Stein, L. C. 2016, Classical and Quantum Gravity, 33, 054001, doi: 10.1088/0264-9381/33/5/054001

    work page doi:10.1088/0264-9381/33/5/054001 2016

  51. [51]

    2016, Research in Astronomy and Astrophysics, 16, 62, doi: 10.1088/1674-4527/16/4/062

    Yang, Q.-X. 2016, Research in Astronomy and Astrophysics, 16, 62, doi: 10.1088/1674-4527/16/4/062

    work page doi:10.1088/1674-4527/16/4/062 2016

  52. [52]

    2005, ApJ, 620, 905, doi: 10.1086/427206

    Yuan, F., Cui, W., & Narayan, R. 2005, ApJ, 620, 905, doi: 10.1086/427206

    work page doi:10.1086/427206 2005