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arxiv: 2604.02412 · v1 · submitted 2026-04-02 · 🌌 astro-ph.GA · astro-ph.SR

Recognition: 2 theorem links

· Lean Theorem

An analytical approach to binary populations in globular clusters

Christopher E. O'Connor , Kyle Kremer , Frederic A. Rasio
Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:53 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords globular clustersbinary fractionsdynamical evolutionprimordial binarieshard soft boundarystellar black holes
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The pith

Dynamical dissolution of soft primordial binaries fully explains the low main-sequence binary fractions in present-day globular clusters.

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

The paper shows that globular clusters display lower binary fractions than field stars because soft primordial binaries are disrupted by dynamical encounters over the cluster lifetime. Assuming the initial binary distribution matches that in the solar neighborhood, simple analytical estimates of the hard-soft boundary and binary ionization rates reproduce the observed fractions without requiring different star formation physics at low metallicity or high density. These estimates are checked against a full Cluster Monte Carlo N-body simulation and remain consistent. The argument further implies that the present binary fraction in any cluster encodes its birth radius, pointing to similar formation conditions for surviving Milky Way globular clusters and local young massive clusters. Stellar black holes are identified as essential because their burning sustains the dynamical heating that continues to process the binary population.

Core claim

Starting from the assumption that the initial binary distribution in GCs is the same as the binary distribution observed in the solar neighborhood, the dynamical dissolution of soft primordial binaries can fully explain the main-sequence binary fractions in present-day GCs. This is validated against a detailed N-body simulation with the Cluster Monte Carlo code. Adopting the view that the observed binary fraction in a given cluster constrains the location of the hard/soft boundary at birth, surviving Milky Way GCs had a similar distribution of birth radii to young massive clusters in the local universe. Stellar black holes play a crucial role through black hole burning in sculpting GC binary

What carries the argument

The hard/soft boundary for binary orbits, defined by the point where a binary's binding energy equals the average kinetic energy of field stars; soft binaries are ionized by encounters while hard binaries survive and harden.

If this is right

  • The observed binary fraction directly constrains the birth radius of each globular cluster through the location of the hard/soft boundary.
  • Stellar black holes are required to sustain the dynamical heating that continues to ionize soft binaries throughout the cluster lifetime.
  • Realistic initial conditions that include both a solar-neighborhood-like binary population and a full stellar black hole population are necessary for any dynamical model of globular clusters.
  • Milky Way globular clusters that survive to the present day formed with radii comparable to those of young massive clusters observed in the local universe.

Where Pith is reading between the lines

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

  • If the mechanism holds, binary fractions measured in globular clusters of different dynamical ages should follow a simple scaling with the number of relaxation times experienced since birth.
  • The same analytical framework could be applied to open clusters or nuclear star clusters to predict how their binary populations evolve under weaker tidal fields.
  • Metallicity dependence would enter only indirectly through the black-hole mass spectrum rather than through any change in the primordial binary fraction itself.

Load-bearing premise

The initial binary fraction and orbital distribution in globular clusters at formation matched the distribution observed among main-sequence stars in the solar neighborhood.

What would settle it

Direct measurement of binary fractions and period distributions in a statistically large sample of young massive clusters that would show initial soft-binary fractions significantly lower than those assumed for the solar neighborhood.

Figures

Figures reproduced from arXiv: 2604.02412 by Christopher E. O'Connor, Frederic A. Rasio, Kyle Kremer.

Figure 1
Figure 1. Figure 1: Map of the primary mass–semimajor axis param￾eter space for binary systems embedded in fiducial Plummer– sphere clusters. Solid lines show the hard/soft boundary as a function of m1 in each cluster for binaries with mass ratio q = 0.5; the color of each line indicates the cluster param￾eters described in the text: blue for model A, amber for B, green for C, and red for D. Dashed lines of the correspond￾ing… view at source ↗
Figure 2
Figure 2. Figure 2: Binary fraction as a function of primary mass. The black points are the measured MF among MS stars in the solar neighborhood as compiled in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Like [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Key timescales related to soft binary evolution within GCs, as computed for fiducial models A through D. The background stars assumed to have an average mass of ¯m = 0.6M⊙ and a binary fraction of Fb = 0.3. Colored curves show the strong encounter interval as a function of η for soft binaries of various masses. The black horizontal lines indicate the cluster’s half-mass crossing time Tcross, the mass segre… view at source ↗
Figure 5
Figure 5. Figure 5: Results of a CMC simulation of a GC with a primordial binary population realized according to our fiducial IBD. Clockwise from the top left, the four panels show (i) the total number of bound stars (blue) and total bound mass (amber), normalized to their initial values; (ii) the half-mass radius (blue) and theoretical (density-weighted) core radius (amber); (iii) the number of bound BHs (blue) and binary B… view at source ↗
Figure 6
Figure 6. Figure 6: Observed binary fraction versus cluster radius for a sample of 29 well-studied Milky Way GCs (J. Ji & J. N. Bregman 2015; H. Baumgardt & M. Hilker 2018). Small points show the observed half-mass radius of each cluster, while large points and vertical error bars indicate the range of plausible virial radii implied by our analytical model. The coloration of each point corresponds to the cluster’s nominal bir… view at source ↗
read the original abstract

Globular clusters (GCs) display much lower binary fractions than found among main-sequence stars in the solar neighborhood. The physical cause of this difference is debatable: does it reflect different star formation outcomes at low metallicity and/or high density, the dynamical processing of primordial binaries over cluster lifetimes, or a combination of the two? Starting from the assumption that the initial binary distribution in GCs is the same as the binary distribution observed in the solar neighborhood, we show with straightforward analytical calculations that the dynamical dissolution of "soft" primordial binaries can fully explain the main-sequence binary fractions in present-day GCs. We validate our estimates against a detailed N-body simulation with the Cluster Monte Carlo code. Adopting the view that the observed binary fraction in a given cluster constrains the location of the hard/soft boundary at birth, we infer that surviving Milky Way GCs had a similar distribution of birth radii to young massive clusters in the local universe. Our findings underscore the crucial role of stellar black holes (through "black hole burning") in sculpting GC binary populations and reinforce the need for realistic initial conditions in theoretical modeling of GC dynamics.

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

0 major / 2 minor

Summary. The paper claims that, starting from the assumption that the initial binary distribution in globular clusters matches the solar-neighborhood field population, straightforward analytical calculations of the dynamical ionization of soft primordial binaries over a Hubble time can fully explain the observed main-sequence binary fractions (0.05–0.2) in present-day GCs. The estimates are validated against Cluster Monte Carlo N-body simulations; the observed fractions are then used to constrain the hard/soft boundary location at birth and infer that surviving Milky Way GCs had birth radii similar to local young massive clusters, with stellar black holes playing a key role via black-hole burning.

Significance. If the stated initial-condition assumption holds, the work supplies a transparent, low-parameter analytical framework that reproduces simulation results and isolates the dynamical contribution to binary depletion, reinforcing the importance of realistic initial conditions and black-hole dynamics in GC modeling. The approach offers a clear falsifiable pathway (via future constraints on primordial binary distributions at low metallicity) and complements full N-body studies without replacing them.

minor comments (2)
  1. [Abstract] Abstract: the phrasing 'can fully explain' is accurate only under the explicit premise of identical initial distributions; a parenthetical reminder of this condition would prevent misreading as an unconditional result.
  2. [Conclusions] The manuscript should add a short sensitivity discussion (perhaps in the conclusions) on how the inferred birth-radius distribution would shift if GC formation suppressed the soft-binary tail relative to the solar-neighborhood distribution, even if the central derivation remains unchanged.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and the recommendation for minor revision. The review correctly identifies the core claim that dynamical ionization of soft primordial binaries, under solar-neighborhood initial conditions, can account for the observed main-sequence binary fractions in present-day globular clusters. We will incorporate the minor changes suggested.

Circularity Check

0 steps flagged

Derivation independent; explicit assumption plus external simulation check

full rationale

The paper states upfront the assumption that initial GC binary distributions match the solar-neighborhood field population, then applies standard hard/soft ionization criteria to compute the surviving fraction after a Hubble time. This produces the observed GC binary fractions (0.05-0.2) from an assumed starting value (~0.5) without redefining the target quantity in terms of itself. The analytical result is cross-validated against CMC N-body runs that use the same initial conditions but are an independent numerical realization. No equation reduces the final binary fraction to a fitted parameter or to a self-citation chain; the hard/soft boundary location is taken as an observable constraint rather than adjusted to force agreement. The single minor self-citation (likely to prior CMC methodology) is not load-bearing for the central analytical claim.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on one domain assumption about initial conditions and treats the hard/soft boundary location as a parameter constrained by observed binary fractions to infer birth radii.

free parameters (1)
  • hard/soft boundary location at birth
    Constrained by the observed binary fraction in each cluster to infer birth radii; not a free fit but an inference step.
axioms (1)
  • domain assumption Initial binary distribution in GCs is identical to the solar-neighborhood distribution
    Explicit starting assumption stated in the abstract that enables the analytical calculation.

pith-pipeline@v0.9.0 · 5498 in / 1196 out tokens · 38476 ms · 2026-05-13T20:53:35.850670+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Black Hole Binary Detection Landscape for the Laser Interferometer Lunar Antenna (LILA): Signal-to-Noise Calculations & Science Cases

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    LILA can detect IMBH binaries at redshifts 20-30, IMRIs, and provide months-to-years early warnings with high-SNR events for gravity tests.

Reference graph

Works this paper leans on

102 extracted references · 102 canonical work pages · cited by 1 Pith paper · 2 internal anchors

  1. [1]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, PhRvD, 93, 122003, doi: 10.1103/PhysRevD.93.122003

    work page doi:10.1103/physrevd.93.122003 2016

  2. [2]

    The Astrophysical Journal , author =

    Albrow, M. D., Gilliland, R. L., Brown, T. M., et al. 2001, ApJ, 559, 1060, doi: 10.1086/322353

    work page doi:10.1086/322353 2001

  3. [3]

    2018, MNRAS, 478, 1844, doi: 10.1093/mnras/sty1186

    Askar, A., Arca Sedda, M., & Giersz, M. 2018, MNRAS, 478, 1844, doi: 10.1093/mnras/sty1186

    work page doi:10.1093/mnras/sty1186 2018

  4. [4]

    C., Trani, A

    Atallah, D., Weatherford, N. C., Trani, A. A., & Rasio, F. A. 2024, ApJ, 970, 112, doi: 10.3847/1538-4357/ad5185

    work page doi:10.3847/1538-4357/ad5185 2024

  5. [5]

    2010, ApJ, 708, 834, doi: 10.1088/0004-637X/708/1/834

    Bartko, H., Martins, F., Trippe, S., et al. 2010, ApJ, 708, 834, doi: 10.1088/0004-637X/708/1/834

    work page doi:10.1088/0004-637x/708/1/834 2010

  6. [6]

    2025, MNRAS, 541, 2008, doi: 10.1093/mnras/staf1102

    Bashi, D., & Belokurov, V. 2025, MNRAS, 541, 2008, doi: 10.1093/mnras/staf1102

    work page doi:10.1093/mnras/staf1102 2025

  7. [7]

    A., & de Grijs, R

    Scheepmaker, R. A., & de Grijs, R. 2005, A&A, 431, 905, doi: 10.1051/0004-6361:20041078

    work page doi:10.1051/0004-6361:20041078 2005

  8. [8]

    Monthly Notices of the Royal Astronomical Society , author =

    Baumgardt, H., & Hilker, M. 2018, MNRAS, 478, 1520, doi: 10.1093/mnras/sty1057

    work page doi:10.1093/mnras/sty1057 2018

  9. [9]

    Rocha-Pinto, H. J. 2017, MNRAS, 471, 2812, doi: 10.1093/mnras/stx1763

    work page doi:10.1093/mnras/stx1763 2017

  10. [10]

    G., & Heggie, D

    Breen, P. G., & Heggie, D. C. 2013, MNRAS, 432, 2779, doi: 10.1093/mnras/stt628

    work page doi:10.1093/mnras/stt628 2013

  11. [11]

    2020 , note =

    Breivik, K., Coughlin, S., Zevin, M., et al. 2020, ApJ, 898, 71, doi: 10.3847/1538-4357/ab9d85

    work page doi:10.3847/1538-4357/ab9d85 2020

  12. [12]

    Galactic

    Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392

    work page internal anchor Pith review doi:10.1086/376392 2003

  13. [13]

    M., & Rasio, F

    Chatterjee, S., Umbreit, S., Fregeau, J. M., & Rasio, F. A. 2013, MNRAS, 429, 2881, doi: 10.1093/mnras/sts464

    work page doi:10.1093/mnras/sts464 2013

  14. [14]

    C., Geller, A

    Childs, A. C., Geller, A. M., von Hippel, T., Motherway, E., & Zwicker, C. 2024, ApJ, 962, 41, doi: 10.3847/1538-4357/ad18c0

    work page doi:10.3847/1538-4357/ad18c0 2024

  15. [15]

    J., et al

    Chomiuk, L., Strader, J., Maccarone, T. J., et al. 2013, ApJ, 777, 69, doi: 10.1088/0004-637X/777/1/69

    work page doi:10.1088/0004-637x/777/1/69 2013

  16. [16]

    S., Do, T., Ghez, A., et al

    Chu, D. S., Do, T., Ghez, A., et al. 2023, ApJ, 948, 94, doi: 10.3847/1538-4357/acc93e

    work page doi:10.3847/1538-4357/acc93e 2023

  17. [17]

    Ritchie, B. W. 2023, MNRAS, 521, 4473, doi: 10.1093/mnras/stad449

    work page doi:10.1093/mnras/stad449 2023

  18. [18]

    S., Ritchie, B

    Clark, J. S., Ritchie, B. W., & Negueruela, I. 2020, A&A, 635, A187, doi: 10.1051/0004-6361/201935903

    work page doi:10.1051/0004-6361/201935903 2020

  19. [19]

    I., Girard, T

    Dinescu, D. I., Girard, T. M., & van Altena, W. F. 1999, AJ, 117, 1792, doi: 10.1086/300807

    work page doi:10.1086/300807 1999

  20. [20]

    1991, A&A, 248, 485

    Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485

    work page 1991

  21. [21]

    2019, MNRAS, 482, L139, doi: 10.1093/mnrasl/sly206

    El-Badry, K., & Rix, H.-W. 2019, MNRAS, 482, L139, doi: 10.1093/mnrasl/sly206

    work page doi:10.1093/mnrasl/sly206 2019

  22. [22]

    C., Pringle, J

    Fabian, A. C., Pringle, J. E., & Rees, M. J. 1975, MNRAS, 172, 15, doi: 10.1093/mnras/172.1.15P

    work page doi:10.1093/mnras/172.1.15p 1975

  23. [23]

    M., Ivanova, N., & Rasio, F

    Fregeau, J. M., Ivanova, N., & Rasio, F. A. 2009, ApJ, 707, 1533, doi: 10.1088/0004-637X/707/2/1533

    work page doi:10.1088/0004-637x/707/2/1533 2009

  24. [24]

    M., & Rasio, F

    Fregeau, J. M., & Rasio, F. A. 2007, ApJ, 658, 1047, doi: 10.1086/511809

    work page doi:10.1086/511809 2007

  25. [25]

    2021, ApJ, 922, 110, doi: 10.3847/1538-4357/ac2610

    Kalogera, V. 2021, ApJ, 922, 110, doi: 10.3847/1538-4357/ac2610

    work page doi:10.3847/1538-4357/ac2610 2021

  26. [26]

    K., Do, T., Ghez, A

    Gautam, A. K., Do, T., Ghez, A. M., et al. 2024, ApJ, 964, 164, doi: 10.3847/1538-4357/ad26e6

    work page doi:10.3847/1538-4357/ad26e6 2024

  27. [27]

    M., de Grijs, R., Li, C., & Hurley, J

    Geller, A. M., de Grijs, R., Li, C., & Hurley, J. R. 2013, ApJ, 779, 30, doi: 10.1088/0004-637X/779/1/30

    work page doi:10.1088/0004-637x/779/1/30 2013

  28. [28]

    2025, arXiv e-prints, arXiv:2510.06942, doi: 10.48550/arXiv.2510.06942 Gonz´ alez Prieto, E., Kremer, K., Chatterjee, S., et al

    Giersz, M., Askar, A., Hypki, A., et al. 2025, arXiv e-prints, arXiv:2510.06942, doi: 10.48550/arXiv.2510.06942 Gonz´ alez Prieto, E., Kremer, K., Chatterjee, S., et al. 2021, ApJL, 908, L29, doi: 10.3847/2041-8213/abdf5b 16O’Connor, Kremer & Rasio Gonz´ alez Prieto, E., Kremer, K., Fragione, G., et al. 2022, ApJ, 940, 131, doi: 10.3847/1538-4357/ac9b0f G...

    work page doi:10.48550/arxiv.2510.06942 2025

  29. [29]

    Kremer, K., & Rasio, F. A. 2024, ApJ, 969, 29, doi: 10.3847/1538-4357/ad43d6

    work page doi:10.3847/1538-4357/ad43d6 2024

  30. [30]

    1984, ApJ, 280, 298, doi: 10.1086/161996 Grudi´ c, M

    Goodman, J. 1984, ApJ, 280, 298, doi: 10.1086/161996 Grudi´ c, M. Y., Guszejnov, D., Hopkins, P. F., Offner, S. S. R., & Faucher-Gigu` ere, C.-A. 2021, MNRAS, 506, 2199, doi: 10.1093/mnras/stab1347

    work page doi:10.1086/161996 1984

  31. [31]

    Guszejnov, D., Markey, C., Offner, S. S. R., et al. 2022, MNRAS, 515, 167, doi: 10.1093/mnras/stac1737

    work page doi:10.1093/mnras/stac1737 2022

  32. [32]

    N., Offner, S

    Guszejnov, D., Raju, A. N., Offner, S. S. R., et al. 2023, MNRAS, 518, 4693, doi: 10.1093/mnras/stac3268

    work page doi:10.1093/mnras/stac3268 2023

  33. [33]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  34. [34]

    2003, The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics

    Heggie, D., & Hut, P. 2003, The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics

    work page 2003

  35. [35]

    Heggie, D. C. 1975, MNRAS, 173, 729, doi: 10.1093/mnras/173.3.729 H´ enon, M. 1971a, Ap&SS, 13, 284, doi: 10.1007/BF00649159 H´ enon, M. 1971b, Ap&SS, 14, 151, doi: 10.1007/BF00649201

    work page doi:10.1093/mnras/173.3.729 1975

  36. [36]

    2020, MNRAS, 498, 3,

    Hong, J., Vesperini, E., Askar, A., et al. 2018, MNRAS, 480, 5645, doi: 10.1093/mnras/sty2211

    work page doi:10.1093/mnras/sty2211 2018

  37. [37]

    2017, MNRAS, 464, 2511, doi: 10.1093/mnras/stw2595

    Hong, J., Vesperini, E., Belloni, D., & Giersz, M. 2017, MNRAS, 464, 2511, doi: 10.1093/mnras/stw2595

    work page doi:10.1093/mnras/stw2595 2017

  38. [38]

    2015, MNRAS, 449, 629, doi: 10.1093/mnras/stv306

    Hong, J., Vesperini, E., Sollima, A., et al. 2015, MNRAS, 449, 629, doi: 10.1093/mnras/stv306

    work page doi:10.1093/mnras/stv306 2015

  39. [39]

    W., Lu, J

    Hosek, Jr., M. W., Lu, J. R., Anderson, J., et al. 2019, ApJ, 870, 44, doi: 10.3847/1538-4357/aaef90

    work page doi:10.3847/1538-4357/aaef90 2019

  40. [40]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  41. [41]

    R., Aarseth, S

    Hurley, J. R., Aarseth, S. J., & Shara, M. M. 2007, ApJ, 665, 707, doi: 10.1086/517879

    work page doi:10.1086/517879 2007

  42. [42]

    Hut, P., McMillan, S., & Romani, R. W. 1992a, ApJ, 389, 527, doi: 10.1086/171229

    work page doi:10.1086/171229

  43. [43]

    1992b, PASP, 104, 981, doi: 10.1086/133085

    Hut, P., McMillan, S., Goodman, J., et al. 1992b, PASP, 104, 981, doi: 10.1086/133085

    work page doi:10.1086/133085

  44. [44]

    C., Zakamska, N

    Hwang, H.-C., Ting, Y.-S., Schlaufman, K. C., Zakamska, N. L., & Wyse, R. F. G. 2021, MNRAS, 501, 4329, doi: 10.1093/mnras/staa3854

    work page doi:10.1093/mnras/staa3854 2021

  45. [45]

    2025, A&A, 693, A41, doi: 10.1051/0004-6361/202348653

    Hypki, A., Vesperini, E., Giersz, M., et al. 2025, A&A, 693, A41, doi: 10.1051/0004-6361/202348653

    work page doi:10.1051/0004-6361/202348653 2025

  46. [46]

    A., Brink, T

    Irwin, J. A., Brink, T. G., Bregman, J. N., & Roberts, T. P. 2010, ApJL, 712, L1, doi: 10.1088/2041-8205/712/1/L1

    work page doi:10.1088/2041-8205/712/1/l1 2010

  47. [47]

    T., Drinkwater , M

    Ivanova, N., Belczynski, K., Fregeau, J. M., & Rasio, F. A. 2005, MNRAS, 358, 572, doi: 10.1111/j.1365-2966.2005.08804.x

    work page doi:10.1111/j.1365-2966.2005.08804.x 2005

  48. [48]

    Fregeau, J. M. 2008, MNRAS, 386, 553, doi: 10.1111/j.1365-2966.2008.13064.x Jeˇ r´ abkov´ a, T., Kroupa, P., Dabringhausen, J., Hilker, M., & Bekki, K. 2017, A&A, 608, A53, doi: 10.1051/0004-6361/201731240

    work page doi:10.1111/j.1365-2966.2008.13064.x 2008

  49. [49]

    Ji, J., & Bregman, J. N. 2015, ApJ, 807, 32, doi: 10.1088/0004-637X/807/1/32

    work page doi:10.1088/0004-637x/807/1/32 2015

  50. [50]

    J., Rasio, F

    Joshi, K. J., Rasio, F. A., & Portegies Zwart, S. 2000, ApJ, 540, 969, doi: 10.1086/309350

    work page doi:10.1086/309350 2000

  51. [51]

    Kamlah, A. W. H., Leveque, A., Spurzem, R., et al. 2022, MNRAS, 511, 4060, doi: 10.1093/mnras/stab3748

    work page doi:10.1093/mnras/stab3748 2022

  52. [52]

    The Astronomical Journal , author =

    King, I. 1962, AJ, 67, 471, doi: 10.1086/108756 Kıro˘ glu, F., Kremer, K., & Rasio, F. A. 2025, ApJL, 994, L37, doi: 10.3847/2041-8213/ae1eeb

    work page doi:10.1086/108756 1962

  53. [53]

    2026, in Encyclopedia of Astrophysics, Volume 3, Vol

    Kremer, K. 2026, in Encyclopedia of Astrophysics, Volume 3, Vol. 3, 458–472, doi: 10.1016/B978-0-443-21439-4.00103-6

    work page doi:10.1016/b978-0-443-21439-4.00103-6 2026

  54. [54]

    L., & Rasio, F

    Kremer, K., Chatterjee, S., Rodriguez, C. L., & Rasio, F. A. 2018, ApJ, 852, 29, doi: 10.3847/1538-4357/aa99df

    work page doi:10.3847/1538-4357/aa99df 2018

  55. [55]

    Rasio, F. A. 2019, ApJ, 871, 38, doi: 10.3847/1538-4357/aaf646

    work page doi:10.3847/1538-4357/aaf646 2019

  56. [56]

    L., & Li, D

    Kremer, K., Piro, A. L., & Li, D. 2021, ApJL, 917, L11, doi: 10.3847/2041-8213/ac13a0

    work page doi:10.3847/2041-8213/ac13a0 2021

  57. [57]

    C., Hopkins, P

    Kremer, K., Weatherford, N. C., Hopkins, P. F., Rui, N. Z., & Ye, C. S. 2025, ApJL, 993, L34, doi: 10.3847/2041-8213/ae1233

    work page doi:10.3847/2041-8213/ae1233 2025

  58. [58]

    S., Rui, N

    Kremer, K., Ye, C. S., Rui, N. Z., et al. 2020, ApJS, 247, 48, doi: 10.3847/1538-4365/ab7919

    work page doi:10.3847/1538-4365/ab7919 2020

  59. [59]

    1995, MNRAS, 277, 1507, doi: 10.1093/mnras/277.4.1507

    Kroupa, P. 1995, MNRAS, 277, 1507, doi: 10.1093/mnras/277.4.1507

    work page doi:10.1093/mnras/277.4.1507 1995

  60. [60]

    S., White, S

    Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    work page doi:10.1046/j.1365-8711.2001.04022.x 2001

  61. [61]

    R., McKee, C

    Krumholz, M. R., McKee, C. F., & Bland-Hawthorn, J. 2019, ARA&A, 57, 227, doi: 10.1146/annurev-astro-091918-104430

    work page doi:10.1146/annurev-astro-091918-104430 2019

  62. [62]

    Leigh, N. W. C., Giersz, M., Marks, M., et al. 2015, MNRAS, 446, 226, doi: 10.1093/mnras/stu2110

    work page doi:10.1093/mnras/stu2110 2015

  63. [63]

    Leigh, N. W. C., Giersz, M., Webb, J. J., et al. 2013, MNRAS, 436, 3399, doi: 10.1093/mnras/stt1825

    work page doi:10.1093/mnras/stt1825 2013

  64. [64]

    2025, ApJL, 982, L43, doi: 10.3847/2041-8213/adbe60

    Liu, R., Shao, Z., & Li, L. 2025, ApJL, 982, L43, doi: 10.3847/2041-8213/adbe60

    work page doi:10.3847/2041-8213/adbe60 2025

  65. [65]

    R., Do, T., Ghez, A

    Lu, J. R., Do, T., Ghez, A. M., et al. 2013, ApJ, 764, 155, doi: 10.1088/0004-637X/764/2/155

    work page doi:10.1088/0004-637x/764/2/155 2013

  66. [66]

    J., Kundu, A., Zepf, S

    Maccarone, T. J., Kundu, A., Zepf, S. E., & Rhode, K. L. 2007, Nature, 445, 183, doi: 10.1038/nature05434

    work page doi:10.1038/nature05434 2007

  67. [67]

    D., Wilkinson, M

    Mackey, A. D., Wilkinson, M. I., Davies, M. B., & Gilmore, G. F. 2007, MNRAS, 379, L40, doi: 10.1111/j.1745-3933.2007.00330.x Binaries in globular clusters17

    work page doi:10.1111/j.1745-3933.2007.00330.x 2007

  68. [68]

    2008, , 385, 1053, 10.1111/j.1365-2966.2008.12909.x

    Mackey, A. D., Wilkinson, M. I., Davies, M. B., & Gilmore, G. F. 2008, MNRAS, 386, 65, doi: 10.1111/j.1365-2966.2008.13052.x

    work page doi:10.1111/j.1365-2966.2008.13052.x 2008

  69. [69]

    Martinez, M. A. S., Fragione, G., Kremer, K., et al. 2020, ApJ, 903, 67, doi: 10.3847/1538-4357/abba25

    work page doi:10.3847/1538-4357/abba25 2020

  70. [70]

    Matzner, C. D. 2024, ApJL, 975, L17, doi: 10.3847/2041-8213/ad85d4

    work page doi:10.3847/2041-8213/ad85d4 2024

  71. [71]

    McMillan, S. L. W., McDermott, P. N., & Taam, R. E. 1987, ApJ, 318, 261, doi: 10.1086/165365

    work page doi:10.1086/165365 1987

  72. [72]

    P., Piotto, G., Bedin, L

    Milone, A. P., Piotto, G., Bedin, L. R., et al. 2012, A&A, 540, A16, doi: 10.1051/0004-6361/201016384

    work page doi:10.1051/0004-6361/201016384 2012

  73. [73]

    2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    Moe, M., & Di Stefano, R. 2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    work page Pith review doi:10.3847/1538-4365/aa6fb6 2017

  74. [74]

    M., & Badenes, C

    Moe, M., Kratter, K. M., & Badenes, C. 2019, ApJ, 875, 61, doi: 10.3847/1538-4357/ab0d88

    work page doi:10.3847/1538-4357/ab0d88 2019

  75. [75]

    A., & Umbreit, S

    Morscher, M., Pattabiraman, B., Rodriguez, C., Rasio, F. A., & Umbreit, S. 2015, ApJ, 800, 9, doi: 10.1088/0004-637X/800/1/9

    work page doi:10.1088/0004-637x/800/1/9 2015

  76. [76]

    M., & Rasio, F

    Morscher, M., Umbreit, S., Farr, W. M., & Rasio, F. A. 2013, ApJL, 763, L15, doi: 10.1088/2041-8205/763/1/L15 M¨ uller-Horn, J., G¨ ottgens, F., Dreizler, S., et al. 2025, A&A, 693, A161, doi: 10.1051/0004-6361/202450709

    work page doi:10.1088/2041-8205/763/1/l15 2013

  77. [77]

    Offner, S. S. R., Moe, M., Kratter, K. M., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka, Y. Aikawa, T. Muto, K. Tomida, & M. Tamura, 275, doi: 10.48550/arXiv.2203.10066

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2203.10066 2023

  78. [78]

    2025, ApJL, 994, L54, doi: 10.3847/2041-8213/ae1447

    Sedda, M. 2025, ApJL, 994, L54, doi: 10.3847/2041-8213/ae1447

    work page doi:10.3847/2041-8213/ae1447 2025

  79. [79]

    2013, ApJS, 204, 15, doi: 10.1088/0067-0049/204/2/15

    Pattabiraman, B., Umbreit, S., Liao, W.-k., et al. 2013, ApJS, 204, 15, doi: 10.1088/0067-0049/204/2/15

    work page doi:10.1088/0067-0049/204/2/15 2013

  80. [80]

    2026, arXiv e-prints, arXiv:2603.06790, doi: 10.48550/arXiv.2603.06790 Portegies Zwart, S

    Phillips, A., Conroy, C., Nibauer, J., et al. 2026, arXiv e-prints, arXiv:2603.06790, doi: 10.48550/arXiv.2603.06790 Portegies Zwart, S. F., McMillan, S. L. W., & Gieles, M. 2010, ARA&A, 48, 431, doi: 10.1146/annurev-astro-081309-130834

    work page doi:10.48550/arxiv.2603.06790 2026

Showing first 80 references.