Pith. sign in

REVIEW 2 major objections 4 minor 115 references

Ground to Dust: Collisional Cascades and the Fate of Kardashev II Megaswarms

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read Abandoned Dyson-style swarms grind themselves to dust

desk verdict A serious, clearly caveated theory paper: the collision-time argument is robust, the cascade-speed scaling is real but rests on borrowed impact physics, and the broad short-lifetime conclusion survives anyway. read the letter →

arxiv 2504.21151 v2 pith:T2RONQ4Q submitted 2025-04-29 astro-ph.EP

Brian C. Lacki This is my paper · ORCID
classification astro-ph.EP
keywords collisionalcascadesstellarmegaswarmsDysonspheresocculterswarmstechnosignaturesLidov-KozaieffectYarkovskySETI
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a stellar-scale megaswarm—a vast constellation of orbiting collectors or occulters, the usual physical form of a Dyson sphere—cannot survive passively on cosmic timescales. The collisional time is roughly one orbital period divided by the covering fraction, so a dense Dyson swarm self-destructs within about a year once its orbits randomize, and even a minimal occulter swarm lasts only about a million years at 1 AU. Ordering elements into circular, well-separated belts reduces collision speeds but does not remove the threat, because gravitational and radiative perturbations, including the Lidov-Kozai effect and the Yarkovsky effect, eventually puff the belts into overlap. Once a damaging collision occurs, a cascade accelerates: fragments become missiles, and the destruction time scales as the mean collision velocity to the $-8/3$ power. The conclusion is that most megaswarms are short-lived without active upkeep, so a detected stellar megastructure would be evidence of a maintained civilization rather than a dead one.

What carries the argument

The load-bearing object is the collisional cascade, a runaway process in which fragments from each impact become projectiles for further impacts, modelled here by a one-zone Boltzmann-like equation for the mass distribution of swarm elements with catastrophic shattering and erosive cratering terms. Its controlling parameter is $\tilde v = \langle v_{EE}\rangle/\sqrt{Q_E}$, the mean relative collision speed divided by the square root of the assumed impact strength; this sets the critical velocity for shattering, shapes the debris mass spectrum, and produces the steep $\langle v_{EE}\rangle^{-8/3}$ cascade scaling. The companion mechanism is the orbit-packing argument: a swarm shell divided into inclined belts admits only about $r_S/r_B$ non-crossing belts, and phase-space conservation implies that filling the shell forces orbital crossings at high relative speed. Together these make the naive collisional time a robust baseline and the cascade an accelerant on top of it.

What would settle it

One decisive check would be a large laboratory campaign firing hypervelocity projectiles into thin, modular, reflective panels to measure the energy per gram needed to shatter them and the fragment mass distribution; if engineered panels resist breakup far above $10^9\,\mathrm{erg\,g^{-1}}$ or fragment into far fewer large pieces than the adopted power law, the predicted $t_{\rm casc}\propto\langle v_{EE}\rangle^{-8/3}$ acceleration would not apply. Observationally, finding an old, unmaintained stellar megaswarm around an isolated low-metallicity star with no giant planets would also refute the claim that most megaswarms are short-lived.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that an abandoned stellar megaswarm is a transient technosignature, not an eonic monument. Starting from the swarm geometry, the collision rate sets $t_{\rm coll}\sim t_{\rm orb}/(2\pi F_S)$, where $t_{\rm orb}$ is the orbital period and $F_S$ the covering fraction; Liouville's theorem and a pigeonhole count of orbital belts show that no ordering of circular orbits can evade this rate while still filling the shell in all directions. Numerical solutions of a one-zone Boltzmann-like cascade equation then give $\hat t_{\rm casc}/\bar t_{\rm coll} = [1 + \tilde v^{5/3}/80]^{-1}$, so for hypervelocity collisions the cascade time falls as $\langle v_{EE}\rangle^{-8/3}$. Companion stars, planets, the swarm's own mass, stellar oblateness, passing stars, and radiation-driven Yarkovsky drift all act to raise eccentricities and disperse orbits, typically on timescales well under geological time; the final residue is micron dust that is blown out by radiation pressure or a dilute ion cloud. Hence most megaswarms are likely to be short-lived on cosmic timescales without active upkeep.

Load-bearing premise

The quick-destruction forecast depends on assuming that a swarm element shatters like a rocky asteroid or ordinary satellite—roughly a $10^9\,\mathrm{erg\,g^{-1}}$ threshold and the laboratory fragment-size distribution—and that elements are thin flat plates; if real elements are much tougher, repair themselves, or have different shapes, the cascade could take orders of magnitude longer.

Editorial extensions

If this is right

  • Stellar Dyson and occulter swarms are not permanent artifacts; searches for megastructure waste heat should expect surviving swarms to be actively maintained, not abandoned.
  • A long-lived stellar megaswarm would be strong evidence that the builders or their autonomous agents have kept it up for millions of years, not merely that a civilization once existed.
  • The most durable stellar swarms should sit in isolated, low-metallicity systems with no stellar or giant-planet companions, where general-relativistic precession or stellar oblateness suppresses Lidov-Kozai cycles, or far out where collision rates are negligible.
  • A dying swarm should produce a brief opacity pulse—the host star dimmed by processed dust, then an infrared excess that fades as grains are blown out or ionized.
  • Galactic-scale swarms embedded in the interstellar medium are the plausible long-lived survivors, because their dynamical timescale is hundreds of millions of years rather than a single orbital period.

Reading between the lines

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

  • If the short-lifetime conclusion holds, an efficient search would prioritize old, metal-poor, single stars with no detected close companions; a convincing Dyson candidate there would strain the model.
  • The cascade scaling could be calibrated on Earth by hypervelocity impact tests into thin, modular panels, turning the unknown impact strength and fragment index into measured inputs rather than assumptions.
  • A corollary the paper leaves implicit: a civilization that destroys or ejects planets to protect its swarms may leave behind systems that are anomalously planet-free, which future high-contrast imaging of Dyson candidates could test.
  • The final dust pulse may be an easier technosignature to catch than the intact structure, since it is a sharp photometric event rather than a steady excess.
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.

Referee Report

2 major / 4 minor

Summary. The paper argues that abandoned (passively maintained) stellar megaswarms are collisional-cascade-limited and therefore short-lived on cosmic timescales. It derives the naive collision time for a randomized swarm as roughly an orbital period divided by the covering fraction (Eq. 4), argues that packing orbital belts cannot avoid this because the unused phase space is large, and then uses a one-zone kinetic model to show that once a cascade starts, the destruction time scales as the mean collision velocity to the -8/3 power for hypervelocity impacts (Eq. 36). The paper further inventories gravitational and radiative perturbations - Lidov-Kozai cycles from companions, stellar oblateness, general-relativistic precession, stellar flybys, and the Yarkovsky effect - that can raise collision velocities and trigger cascades. It concludes that most stellar megaswarms require active upkeep and proposes that the longest-lived passive megastructures are either far-out minimal occulter swarms, close-in swarms in stabilized niches, or galactic-scale dust swarms.

Significance. If the central result holds, the paper substantially changes the SETI search strategy for megastructures: Dyson swarms and dense occulter swarms would be transient technosignatures rather than eonic monuments, and their end states (opacity pulses, dust blowout, or ion clouds) become observational targets. The analytic estimates in Sections 2 and 4 are internally consistent and grounded in standard kinetic theory and secular dynamics, and the Liouville argument in Section 2.6 is a genuine robustness result. The paper also makes a useful, concrete census of how common destabilizing companions are. The main caveat, acknowledged by the author, is that the cascade speed is built on impact-strength and debris prescriptions calibrated to rocky asteroid and satellite impacts; the headline time scaling is not yet demonstrated to be robust across the plausible range of engineered-materials parameters.

major comments (2)
  1. [Sections 3.3-3.5, Eq. (36)] The central quantitative claim, t_casc proportional to v^(-8/3) in the hypervelocity limit, is obtained from a single-valued impact strength Q_E = 10^9 erg/g, a planar area-mass relation A_E = m_E/4, a delta-function velocity distribution, and debris laws (Eqs. 31-34) calibrated to rocky asteroid and satellite impacts. Raising Q_E to the paper's own chemical limit of 1.2e12 erg/g lengthens the hypervelocity cascade phase by roughly (1.2e12/1e9)^(5/6) ~ 300 under Eq. (36), and varying the debris-slope parameters q and xi in Eqs. (33)-(34) can shift the fitted exponent. The author explicitly flags these as simplifications in Section 3.3, but no parameter sweep or error budget is provided. Because Eq. (36) is the quantitative core of the claim that most megaswarms are short-lived, the manuscript needs a sensitivity analysis over Q_E, q, xi, and geometry before that claim can be considered established, especially for sparse outer occulter swarms where the initial collision time is long.
  2. [Sections 3.4 and 3.9] The one-zone cascade model assumes a fixed relative-velocity distribution and neglects velocity evolution and dissipation. The paper itself shows in Eq. (41) that dissipational effects can greatly alter the cascade when the collision velocity is below about 1.4 km/s for Q_E = 10^9 erg/g, which is precisely the regime expected in isolated narrow belts (Section 2.4). The fixed-velocity approximation may therefore overstate the early cascade growth rate. Since the author notes that a full treatment is warranted, the manuscript should at least include a simple test of how including a cooling or velocity-damping term changes the fitted timescale in Eq. (36), or state more explicitly which parameter regime the rapid-cascade conclusion is meant to cover.
minor comments (4)
  1. [Eq. (57), Section 4.2.2] The displayed ratio in Eq. (57) is inverted for the case a_P > a_E. From Eqs. (52) and (53), t_P;q / t_P;o = a_E/a_P for an exterior perturber, not a_P/a_E. The value cited in footnote 19 for Jupiter's effect on Earth's eccentricity (~0.01) uses the correct ratio, so the qualitative conclusion survives, but the equation must be corrected.
  2. [Section 3.4] There is a typo: 'stoppped' should be 'stopped'.
  3. [Section 3.5] There is a typo: 'characterisitc' should be 'characteristic'.
  4. [Section 3.4] The numerical method is described in prose, but no code or tabulated output is provided. For reproducibility, a supplementary repository or at least a detailed pseudocode/algorithm listing would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the derivation is self-contained and rests on external calibration.

full rationale

The paper's central chain is not circular. The initial collisional time (Eq. 4) follows from standard kinetic theory and the shell geometry, with no fitted parameter tied to the conclusion. The cascade calculation is a one-zone numerical integration of a Boltzmann-like mass distribution equation (Eq. 19), using debris and impact-strength prescriptions taken from external experimental and modeling literature (Rossi et al. 1994; Fujiwara et al. 1977; Greenberg et al. 1978), not from the paper's own conclusion. Equation 36 is presented as an approximation to the numerical solution for the cascade time, so it is an output of the simulation rather than an input. The impact strength Q_E is assumed as a material parameter (10^9 erg g^-1) and is explicitly flagged by the author as a simplification: "The simple models I present here, like the Rossi et al. (1994) model of a Kessler cascade, assume a single impact strength, but this is clearly inadequate." That is an acknowledged modeling uncertainty about external validity, not a definitional or fitted circularity. Self-citations (Lacki 2016, 2019b, 2020) supply context and prior hypotheticals, but none is load-bearing for the collisional-time or cascade derivation. No step reduces to its own input by construction, and the conclusion is not forced by a self-citation chain.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claims rest primarily on kinetic-theory collision rates, empirical impact physics, and assumptions about alien engineering choices. No new physical entity is introduced. The most consequential uncharged inputs are the single-valued impact strength Q_E and the adopted fragment mass distributions; changing them changes the cascade time directly through tilde_v. The abandonment assumption defines the scope of the conclusion.

free parameters (6)
  • Impact strength Q_E = 10^9 erg/g (assumed; chemical upper bound approximately 1.2e12 erg/g)
    Sets velocity scale sqrt(Q_E) in tilde_v; enters cascade time Eq. 36 and damage threshold Eq. 37. Chosen by hand from Earth satellite materials, not measured for hypothetical swarm elements.
  • Debris power-law index q = 5/3 for erosional; 2 + mmax_D/m2 divided by 1 + mmax_D/m1 for catastrophic; asymptotes to 2
    Adopted notional values from Rossi et al. 1994 and Greenberg et al. 1978; directly controls how fast mass is redistributed to small fragments in Eq. 32.
  • Maximum debris mass exponent xi = Not specified numerically; from Fujiwara et al. 1977 scaling (v/v_c)^(-xi)
    Sets largest fragment in catastrophic collisions Eq. 33; affects cascade acceleration but its value is not quantified in the paper.
  • Element geometry relation A_E = m_E/4 = Planar area = m'/4 in dimensionless code
    Adopted to avoid numerical instability; the author notes actual satellite area-mass ratios deviate from planar geometry, so fragment collision cross-sections are uncertain.
  • Erosional mass fraction epsilon = 0.1
    Used in Eq. 31 and Eq. 41 for cratering mass loss; from Rossi et al. 1994; affects the erosion-dominated cascade regime and the dissipation criterion.
  • Swarm surface density Sigma_E = 100 g/cm^2 for mass estimates
    Chosen as equivalent to a meter of water in Eq. 65 for internal secular perturbation times; affects self-driven Lidov-Kozai estimates.
assumptions (7)
  • standard math Collision rate in a randomized swarm is t ~ V/(N sigma v)
    Eqs. 2-5; standard kinetic theory used throughout.
  • domain assumption Debris physics from Rossi et al. 1994 and Fujiwara et al. 1977 applies to artificial megastructure elements
    Eqs. 31-34; single impact strength and fragment size distribution assumed, explicitly noted as clearly inadequate in Section 3.3.
  • domain assumption Elements have conventional solid material strengths (Q_E = 1e9 erg/g or near the chemical bound)
    Eqs. 37, 48-49; if materials are much stronger or self-healing, cascade times scale with sqrt(Q_E), weakening the short-lifetime conclusion.
  • domain assumption Swarm is abandoned without active upkeep
    Abstract and Section 6.3; all lifetime estimates are for passive swarms, and active maintenance or self-replication invalidates the stated conclusion.
  • domain assumption One-zone homogeneous cascade model captures the relevant evolution
    Section 3; the author states it may break down near edges but gives a rough sense, and no spatial dependence is included.
  • domain assumption Base configuration of circular belts with an inclination gradient represents likely long-lived swarm designs
    Section 2.3 and Figure 3; used to derive intrabelt collision times and thermalization; if ETIs choose other architectures, timescales change.
  • domain assumption Velocity distribution is a delta function; impacts occur at a single relative speed
    Eq. 35; omits high-velocity tails that could accelerate the cascade.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ground to Dust: Collisional Cascades and the Fate of Kardashev II Megaswarms." pith.science (2026). https://pith.science/paper/T2RONQ4Q

@misc{pith2026250421151,
  author       = {Pith},
  title        = {Pith review of: Ground to Dust: Collisional Cascades and the Fate of Kardashev II Megaswarms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T2RONQ4Q}},
  note         = {Machine review of arXiv:2504.21151}
}
read the original abstract

Extraterrestrial intelligences are speculated to surround stars with structures to collect their energy or to signal distant observers. If they exist, these most likely are megaswarms, vast constellations of satellites (elements) in orbit around the hosts. Although long-lived megaswarms are extremely powerful technosignatures, they are liable to be subject to collisional cascades once guidance systems start failing. The collisional time is roughly an orbital period divided by the covering fraction of the swarm. Structuring the swarm orbits does not prolong the initial collisional time as long as there is enough randomness to ensure collisions, although it can reduce collision velocities. I further show that once the collisional cascade begins, it can develop extremely rapidly for hypervelocity collisions. Companion stars or planets in the stellar system induce perturbations through the Lidov-Kozai effect among others, which can result in orbits crossing within some millions of years. Radiative perturbations, including the Yarkovsky effect, also can destabilize swarms. Most megaswarms are thus likely to be short-lived on cosmic timescales without active upkeep. I discuss possible mitigation strategies and implications for megastructure searches.

Figures

Figures reproduced from arXiv: 2504.21151 by the authors.

Figure 1
Figure 1. Sketch of the assumed shell geometry of a megaswarm. The shell contains belts, one example of which is depicted in blue. Within each belt, elements orbit, possibly slightly displaced from the belt center by random velocity deviations (black dashed line). Note that the belts do not fill the entire swarm shell, much of which may be empty. tween elements is AEE. 3 For a swarm with NE S elements, the collisional time is… view at source ↗
Figure 2
Figure 2. A sketch of a series of coplanar belts heating up with randomized velocities. In panel (a), the belt is a single orbit on which elements are placed in an orderly fashion. Very small random velocities (meters per second or less) cause small deviations in the elements’ orbits, though so small that the belt is still “sharp”, narrower than the elements themselves (b). The random velocities cause the phases to desynchron… view at source ↗
Figure 3
Figure 3. Sketch of the “base configuration” posited as a likely geometry for megaswarms, as viewed edge-on. The swarm includes circular belts (one example in blue) covering the full range of incli￾nations, but the semimajor axis gradually increases (or decreases) as it grows. and helping to prevent collisions. Still, elements could acquire slight velocity offsets that desynchronize them and ultimately enable collisions, perh… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Computed time for destruction of original swarm according to the dimensionless cascade equations. Different line styles indicate different measures for the survival of the swarm: number of elements in the original mass bin (solid), number of elements (dashed) and mass …
Figure 5
Figure 5. Figure 5: Mass distribution of the cascade according to the dimensionless cascade equations, as it evolves in cascades with different characteristic velocities. The distribution evolves from its initial shape (black), with all elements the same mass. After the first time step, t…
Figure 6
Figure 6. Figure 6: Effective rate of destruction that an element of the original mass (m′ E = 1, mE = ¯mE) would experience. At first the destruction is dominated by catastrophic shattering resulting from the original swarm members and the largest fragments (orange). As the collisional c…
Figure 34
Figure 34. Figure 34: ). Ultimately, it might settle down into a cir [PITH_FULL_IMAGE:figures/full_fig_p019_34.png]
Figure 7
Figure 7. Figure 7: Characteristic perturbation times within the Solar System for an object orbiting at different semimajor axes. Shad￾ing indicates mechanisms that can pump eccentricity, in addition to precession. The quadrupole perturbation times from Venus (gray), Jupiter (pink), Satur…
Figure 8
Figure 8. Figure 8: Illustrative figures for perturbing bodies orbiting stars, and their quadrupole and octupole effects. On left, a plot of semimajor axes and mass ratios for these companions. Black dots are stellar companions from Tokovinin (2014); blue dots are exoplanets listed in exo…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

115 extracted references · 21 canonical work pages

  1. [1]

    Benedict, G. F. 2021, AJ, 162, 14, doi: 10.3847/1538-3881/abfaff

    doi:10.3847/1538-3881/abfaff 2021

  2. [2]

    2024, A&A, 683, A118, doi: 10.1051/0004-6361/202348899

    Andama, G., Mah, J., & Bitsch, B. 2024, A&A, 683, A118, doi: 10.1051/0004-6361/202348899

    doi:10.1051/0004-6361/202348899 2024

  3. [3]

    Antognini, J. M. O. 2015, MNRAS, 452, 3610, doi: 10.1093/mnras/stv1552

    doi:10.1093/mnras/stv1552 2015

  4. [4]

    Arnold, L. F. A. 2005, ApJ, 627, 534, doi: 10.1086/430437

    doi:10.1086/430437 2005

  5. [5]

    P., M´ erand, A., Coud´ e du Foresto, V., et al

    Aufdenberg, J. P., M´ erand, A., Coud´ e du Foresto, V., et al. 2006, ApJ, 645, 664, doi: 10.1086/504149

    doi:10.1086/504149 2006

  6. [6]

    D., & Anz-Meador, P

    Badhwar, G. D., & Anz-Meador, P. D. 1989, Earth Moon and Planets, 45, 29, doi: 10.1007/BF00054659

    work page doi:10.1007/bf00054659 1989

  7. [7]

    Balbi, A., & ´Cirkovi´ c, M. M. 2021, AJ, 161, 222, doi: 10.3847/1538-3881/abec48

    doi:10.3847/1538-3881/abec48 2021

  8. [8]

    Barnes, S. A. 2007, ApJ, 669, 1167, doi: 10.1086/519295 Beaug´ e, C., Nesvorn´ y, D., & Dones, L. 2006, AJ, 131, 2299, doi: 10.1086/500048

    doi:10.1086/519295 2007

Show all 115 references
  1. [9]

    1987, Galactic dynamics (Princeton: Princeton University Press) Megastructures and Collisional Cascades 35

    Binney, J., & Tremaine, S. 1987, Galactic dynamics (Princeton: Princeton University Press) Megastructures and Collisional Cascades 35

    1987

  2. [10]

    Snellen, I. A. G. 2017, AJ, 153, 138, doi: 10.3847/1538-3881/aa5c87

    2017 doi

  3. [11]

    C., & Byers, M

    Boley, A. C., & Byers, M. 2021, Scientific Reports, 11, 10642, doi: 10.1038/s41598-021-89909-7

    2021 doi

  4. [12]

    P., & Nesvorn´ y, D

    Bottke, William F., J., Vokrouhlick´ y, D., Rubincam, D. P., & Nesvorn´ y, D. 2006, Annual Review of Earth and Planetary Sciences, 34, 157, doi: 10.1146/annurev.earth.34.031405.125154

    2006

  5. [13]

    F., Durda, D

    Bottke, W. F., Durda, D. D., Nesvorn´ y, D., et al. 2005, Icarus, 175, 111, doi: 10.1016/j.icarus.2004.10.026

    2005 doi

  6. [14]

    2010, AJ, 139, 994, doi: 10.1088/0004-6256/139/3/994

    Morbidelli, A. 2010, AJ, 139, 994, doi: 10.1088/0004-6256/139/3/994

    2010 doi

  7. [15]

    Bradbury, R. J. 2000, Matrioshka Brains. http://citeseerx. ist.psu.edu/viewdoc/download?doi=10.1.1.692.6584

    2000

  8. [16]

    J., Cirkovic, M

    Bradbury, R. J., Cirkovic, M. M., & Dvorsky, G. 2011, Journal of the British Interplanetary Society, 64, 156

    2011

  9. [17]

    A., Lamy, P

    Burns, J. A., Lamy, P. L., & Soter, S. 1979, Icarus, 40, 1, doi: 10.1016/0019-1035(79)90050-2

    1979 doi

  10. [18]

    2001, PASP, 113, 1449, doi: 10.1086/324269

    Calzetti, D. 2001, PASP, 113, 1449, doi: 10.1086/324269

    2001 doi

  11. [19]

    Carrigan, R. A. 2012, Acta Astronautica, 78, 121, doi: 10.1016/j.actaastro.2011.12.002

    2012 doi

  12. [20]

    2015, NewA, 34, 245, doi: 10.1016/j.newast.2014.07.011

    Werthimer, D. 2015, NewA, 34, 245, doi: 10.1016/j.newast.2014.07.011

    2015 doi

  13. [21]

    R., Ostro, S

    Chesley, S. R., Ostro, S. J., Vokrouhlick´ y, D., et al. 2003, Science, 302, 1739, doi: 10.1126/science.1091452

    2003 doi

  14. [22]

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

    Chu, D. S., Do, T., Hees, A., et al. 2018, ApJ, 854, 12, doi: 10.3847/1538-4357/aaa3eb

    2018 doi

  15. [23]

    Criswell, D. R. 1985, in Interstellar migration and the human experience, ed. B. R. Finney & E. M. Jones, 50

    1985

  16. [24]

    R., Ryan, E

    Davis, D. R., Ryan, E. V., & Farinella, P. 1994, Planet. Space Sci., 42, 599, doi: 10.1016/0032-0633(94)90035-3

    1994 doi

  17. [25]

    Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium (Princeton: Princeton University Press)

    2011

  18. [26]

    Dyson, F. J. 1960, Science, 131, 1667, doi: 10.1126/science.131.3414.1667

    1960

  19. [27]

    B., Kozinsky, B., & Rasio, F

    Ford, E. B., Kozinsky, B., & Rasio, F. A. 2000, ApJ, 535, 385, doi: 10.1086/308815

    2000 doi

  20. [28]

    R., et al

    Fujiwara, A., Cerroni, P., Davis, D. R., et al. 1989, in Asteroids II, ed. R. P. Binzel, T. Gehrels, & M. S. Matthews, 240–265

    1989

  21. [29]

    1977, Icarus, 31, 277, doi: 10.1016/0019-1035(77)90038-0

    Fujiwara, A., Kamimoto, G., & Tsukamoto, A. 1977, Icarus, 31, 277, doi: 10.1016/0019-1035(77)90038-0

    1977 doi

  22. [30]

    T., & Johnson, J

    Ghezzi, L., Montet, B. T., & Johnson, J. A. 2018, ApJ, 860, 109, doi: 10.3847/1538-4357/aac37c

    2018 doi

  23. [31]

    L., & Ptuskin, V

    Ginzburg, V. L., & Ptuskin, V. S. 1976, Reviews of Modern Physics, 48, 161, doi: 10.1103/RevModPhys.48.161 GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2020, A&A, 636, L5, doi: 10.1051/0004-6361/202037813

    1976 doi

  24. [32]

    Chapman, C. R. 1978, Icarus, 35, 1, doi: 10.1016/0019-1035(78)90057-X

    1978 doi

  25. [33]

    R., & Williams, A

    Hainaut, O. R., & Williams, A. P. 2020, A&A, 636, A121, doi: 10.1051/0004-6361/202037501

    2020 doi

  26. [34]

    C., & Rasio, F

    Heggie, D. C., & Rasio, F. A. 1996, MNRAS, 282, 1064, doi: 10.1093/mnras/282.3.1064

    1996 doi

  27. [35]

    Heller, R., & Pudritz, R. E. 2016, Astrobiology, 16, 259, doi: 10.1089/ast.2015.1358

    2016

  28. [36]

    1997, Nature, 386, 254, doi: 10.1038/386254a0

    Holman, M., Touma, J., & Tremaine, S. 1997, Nature, 386, 254, doi: 10.1038/386254a0

    1997 doi

  29. [37]

    Y.-Y., Goto, T., Hashimoto, T., et al

    Hsiao, T. Y.-Y., Goto, T., Hashimoto, T., et al. 2021, MNRAS, 506, 1723, doi: 10.1093/mnras/stab1832

    2021 doi

  30. [38]

    M., Duchˆ ene, G., & Matthews, B

    Hughes, A. M., Duchˆ ene, G., & Matthews, B. C. 2018, ARA&A, 56, 541, doi: 10.1146/annurev-astro-081817-052035

    2018 doi

  31. [39]

    2022, ApJ, 924, 78, doi: 10.3847/1538-4357/ac3421

    Huston, M., & Wright, J. 2022, ApJ, 924, 78, doi: 10.3847/1538-4357/ac3421

    2022 doi

  32. [40]

    2011, Journal of the British Interplanetary Society, 64, 59

    Inoue, M., & Yokoo, H. 2011, Journal of the British Interplanetary Society, 64, 59

    2011

  33. [41]

    2003, Celestial Mechanics and Dynamical Astronomy, 86, 277, doi: 10.1023/A:1024223200686 —

    Iorio, L. 2003, Celestial Mechanics and Dynamical Astronomy, 86, 277, doi: 10.1023/A:1024223200686 —. 2008, Ap&SS, 318, 51, doi: 10.1007/s10509-008-9889-1 —. 2011, PhRvD, 84, 124001, doi: 10.1103/PhysRevD.84.124001 —. 2019, MNRAS, 484, 4811, doi: 10.1093/mnras/stz304 —. 2024, ...

    2003 doi

  34. [42]

    S., Shakht, N

    Izmailov, I. S., Shakht, N. A., Polyakov, E. V., Gorshanov, D. L., & Pogodin, M. A. 2021, Astrophysics, 64, 160, doi: 10.1007/s10511-021-09677-0

    2021 doi

  35. [43]

    A., Aller, K

    Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905, doi: 10.1086/655775

    2010 doi

  36. [44]

    L., & Li, H

    Johnson, J. L., & Li, H. 2012, ApJ, 751, 81, doi: 10.1088/0004-637X/751/2/81

    2012 doi

  37. [45]

    Kardashev, N. S. 1964, Soviet Ast., 8, 217

    1964

  38. [46]

    Kardashev, N. S. 1985, in The Search for Extraterrestrial Life: Recent Developments, ed. M. D. Papagiannis, Vol. 112, 497–504

    1985

  39. [47]

    2011, PhRvL, 107, 181101, doi: 10.1103/PhysRevLett.107.181101

    Katz, B., Dong, S., & Malhotra, R. 2011, PhRvL, 107, 181101, doi: 10.1103/PhysRevLett.107.181101

    2011 doi

  40. [48]

    Kawaler, S. D. 1987, PASP, 99, 1322, doi: 10.1086/132120

    1987 doi

  41. [49]

    2008, A&A, 488, 667, doi: 10.1051/0004-6361:200810080

    Kervella, P., M´ erand, A., Pichon, B., et al. 2008, A&A, 488, 667, doi: 10.1051/0004-6361:200810080

    2008 doi

  42. [50]

    Kessler, D. J. 1981, Icarus, 48, 39, doi: 10.1016/0019-1035(81)90151-2 36 Lacki

    1981 doi

  43. [51]

    J., & Cour-Palais, B

    Kessler, D. J., & Cour-Palais, B. G. 1978, J. Geophys. Res., 83, 2637, doi: 10.1029/JA083iA06p02637

    1978 doi

  44. [52]

    2019, Research Notes of the American Astronomical Society, 3, 91, doi: 10.3847/2515-5172/ab2fdb

    Kipping, D. 2019, Research Notes of the American Astronomical Society, 3, 91, doi: 10.3847/2515-5172/ab2fdb

    2019 doi

  45. [53]

    2020, International Journal of Astrobiology, 19, 430, doi: 10.1017/S1473550420000208

    Kipping, D., Frank, A., & Scharf, C. 2020, International Journal of Astrobiology, 19, 430, doi: 10.1017/S1473550420000208

    2020 doi

  46. [54]

    1962, AJ, 67, 591, doi: 10.1086/108790

    Kozai, Y. 1962, AJ, 67, 591, doi: 10.1086/108790

    1962 doi

  47. [55]

    Kraft, R. P. 1967, ApJ, 150, 551, doi: 10.1086/149359

    1967 doi

  48. [56]

    Lacki, B. C. 2016, arXiv e-prints, arXiv:1604.07844. https://arxiv.org/abs/1604.07844 —. 2019a, PASP, 131, 084401, doi: 10.1088/1538-3873/ab1304 —. 2019b, PASP, 131, 024102, doi: 10.1088/1538-3873/aaf3df —. 2020, ApJ, 905, 18, doi: 10.3847/1538-4357/abc1e3 —. 2024, ApJ, 966, 1...

    2016 arXiv

  49. [57]

    2004, A&A, 428, 261, doi: 10.1051/0004-6361:20041335 Le May, S., Gehly, S., Carter, B

    Laskar, J., Robutel, P., Joutel, F., et al. 2004, A&A, 428, 261, doi: 10.1051/0004-6361:20041335 Le May, S., Gehly, S., Carter, B. A., & Flegel, S. 2018, Acta Astronautica, 151, 445, doi: 10.1016/j.actaastro.2018.06.036

    2004 doi

  50. [58]

    1991, Reviews of Geophysics, 29, 505, doi: 10.1029/91RG01895

    Lean, J. 1991, Reviews of Geophysics, 29, 505, doi: 10.1029/91RG01895

    1991 doi

  51. [59]

    G., Swinerd, G

    Lewis, H. G., Swinerd, G. G., Newland, R. J., & Saunders, A. 2009, Advances in Space Research, 44, 568, doi: 10.1016/j.asr.2009.05.018

    2009 doi

  52. [60]

    Lidov, M. L. 1962, Planet. Space Sci., 9, 719, doi: 10.1016/0032-0633(62)90129-0

    1962 doi

  53. [61]

    H., Fenner, Y., & Gibson, B

    Lineweaver, C. H., Fenner, Y., & Gibson, B. K. 2004, Science, 303, 59, doi: 10.1126/science.1092322

    2004 doi

  54. [62]

    C., Hall, D

    Liou, J. C., Hall, D. T., Krisko, P. H., & Opiela, J. N. 2004, Advances in Space Research, 34, 981, doi: 10.1016/j.asr.2003.02.027

    2004 doi

  55. [63]

    2011, ApJ, 742, 94, doi: 10.1088/0004-637X/742/2/94

    Lithwick, Y., & Naoz, S. 2011, ApJ, 742, 94, doi: 10.1088/0004-637X/742/2/94

    2011 doi

  56. [64]

    2023, Research Notes of the American Astronomical Society, 7, 43, doi: 10.3847/2515-5172/acc10d

    Loeb, A. 2023, Research Notes of the American Astronomical Society, 7, 43, doi: 10.3847/2515-5172/acc10d

    2023 doi

  57. [65]

    Lovell, A. C. B., Blackwell, M. R., D. E., & Wilson, R. 1962, QJRAS, 3, 100

    1962

  58. [66]

    I., & Sivaraman, K

    Makarov, V. I., & Sivaraman, K. R. 1989, SoPh, 123, 367, doi: 10.1007/BF00149112

    1989 doi

  59. [67]

    McDowell, J. C. 2020, ApJL, 892, L36, doi: 10.3847/2041-8213/ab8016

    2020 doi

  60. [68]

    1995, International Journal of Impact Engineering, 17, 547

    McKnight, D., Maher, R., & Nagl, L. 1995, International Journal of Impact Engineering, 17, 547

    1995

  61. [69]

    2014, ApJS, 211, 24, doi: 10.1088/0067-0049/211/2/24

    McQuillan, A., Mazeh, T., & Aigrain, S. 2014, ApJS, 211, 24, doi: 10.1088/0067-0049/211/2/24

    2014 doi

  62. [70]

    2021, MNRAS, 506, 2671, doi: 10.1093/mnras/stab1827

    Mecheri, R., & Meftah, M. 2021, MNRAS, 506, 2671, doi: 10.1093/mnras/stab1827

    2021 doi

  63. [71]

    T., & Simon, J

    Montet, B. T., & Simon, J. D. 2016, ApJL, 830, L39, doi: 10.3847/2041-8205/830/2/L39

    2016 doi

  64. [72]

    E., J., & MacLellan, D

    Morrow, W. E., J., & MacLellan, D. C. 1961, AJ, 66, 107, doi: 10.1086/108384

    1961 doi

  65. [73]

    2016, ARA&A, 54, 441, doi: 10.1146/annurev-astro-081915-023315

    Naoz, S. 2016, ARA&A, 54, 441, doi: 10.1146/annurev-astro-081915-023315

    2016 doi

  66. [74]

    2013a, MNRAS, 431, 2155, doi: 10.1093/mnras/stt302

    Teyssandier, J. 2013a, MNRAS, 431, 2155, doi: 10.1093/mnras/stt302

    doi

  67. [75]

    2013b, ApJ, 773, 187, doi: 10.1088/0004-637X/773/2/187 Nesvorn´ y, D., Alvarellos, J

    Naoz, S., Kocsis, B., Loeb, A., & Yunes, N. 2013b, ApJ, 773, 187, doi: 10.1088/0004-637X/773/2/187 Nesvorn´ y, D., Alvarellos, J. L. A., Dones, L., & Levison, H. F. 2003, AJ, 126, 398, doi: 10.1086/375461 Nesvorn´ y, D., Beaug´ e, C., & Dones, L. 2004, AJ, 127, 1768, doi: 10.1...

    2003 doi

  68. [76]

    L., De Rosa, R

    Nielsen, E. L., De Rosa, R. J., Macintosh, B., et al. 2019, AJ, 158, 13, doi: 10.3847/1538-3881/ab16e9

    2019 doi

  69. [77]

    2022, International Journal of Impact Engineering, 168, 104313

    Francesconi, A. 2022, International Journal of Impact Engineering, 168, 104313

    2022

  70. [78]

    2016, International Journal of Astrobiology, 15, 127, doi: 10.1017/S1473550415000257

    Osmanov, Z. 2016, International Journal of Astrobiology, 15, 127, doi: 10.1017/S1473550415000257

    2016 doi

  71. [79]

    Pitjeva, E. V. 2005, Astronomy Letters, 31, 340, doi: 10.1134/1.1922533

    2005 doi

  72. [80]

    A., Henry, T

    Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1, doi: 10.1088/0067-0049/190/1/1

    2010 doi

  73. [81]

    2013, Journal of Astrophysics and Astronomy, 34, 341, doi: 10.1007/s12036-013-9186-4

    Renzetti, G. 2013, Journal of Astrophysics and Astronomy, 34, 341, doi: 10.1007/s12036-013-9186-4

    2013 doi

  74. [82]

    2004, Nature, 431, 47, doi: 10.1038/nature02884

    Rose, C., & Wright, G. 2004, Nature, 431, 47, doi: 10.1038/nature02884

    2004 doi

  75. [83]

    2005, Serbian Astronomical Journal, 170, 1, doi: 10.2298/SAJ0570001R

    Rossi, A. 2005, Serbian Astronomical Journal, 170, 1, doi: 10.2298/SAJ0570001R

    2005 doi

  76. [84]

    Rossi, A., Cordelli, A., Farinella, P., & Anselmo, L. 1994, J. Geophys. Res., 99, 23195, doi: 10.1029/94JE02320

    1994 doi

  77. [85]

    J., & Crawford-Taylor, K

    Sallmen, S., Korpela, E. J., & Crawford-Taylor, K. 2019, AJ, 158, 258, doi: 10.3847/1538-3881/ab5300

    2019 doi

  78. [86]

    1963, Science, 141, 797, doi: 10.1126/science.141.3583.797

    Sandage, A., & Kowal, C. 1963, Science, 141, 797, doi: 10.1126/science.141.3583.797

    1963 doi

  79. [87]

    2021, Acta Astronautica, 178, 265, doi: 10.1016/j.actaastro.2020.09.014

    Schimmerohn, M., Matura, P., Watson, E., et al. 2021, Acta Astronautica, 178, 265, doi: 10.1016/j.actaastro.2020.09.014

    2021 doi

  80. [88]

    2011, A&A, 532, A79, doi: 10.1051/0004-6361/201116713

    Zolotukhin, I. 2011, A&A, 532, A79, doi: 10.1051/0004-6361/201116713

    2011 doi

  81. [89]

    T., & Kipping, D

    Scoggins, M. T., & Kipping, D. 2023, MNRAS, 523, 3251, doi: 10.1093/mnras/stad1617 Megastructures and Collisional Cascades 37 Semiz, ˙I., & O˘ gur, S. 2015, arXiv e-prints, arXiv:1503.04376, doi: 10.48550/arXiv.1503.04376

    2023 doi arXiv

  82. [90]

    Shapiro, I. I. 1966, Science, 154, 1445, doi: 10.1126/science.154.3755.1445

    1966

  83. [91]

    Sheikh, S. Z. 2020, International Journal of Astrobiology, 19, 237, doi: 10.1017/S1473550419000284

    2020 doi

  84. [92]

    2018, ApJ, 855, 110, doi: 10.3847/1538-4357/aaae66

    Socas-Navarro, H. 2018, ApJ, 855, 110, doi: 10.3847/1538-4357/aaae66

    2018 doi

  85. [93]

    Solanki, S. K. 2003, A&A Rv, 11, 153, doi: 10.1007/s00159-003-0018-4

    2003 doi

  86. [94]

    S., Raymond, S

    Spiegel, D. S., Raymond, S. N., Dressing, C. D., Scharf, C. A., & Mitchell, J. L. 2010, ApJ, 721, 1308, doi: 10.1088/0004-637X/721/2/1308

    2010 doi

  87. [95]

    C., & Lin, D

    Spurzem, R., Giersz, M., Heggie, D. C., & Lin, D. N. C. 2009, ApJ, 697, 458, doi: 10.1088/0004-637X/697/1/458

    2009 doi

  88. [96]

    Statler, T. S. 2009, Icarus, 202, 502, doi: 10.1016/j.icarus.2009.03.003

    2009 doi

  89. [97]

    A., & Durda, D

    Stern, S. A., & Durda, D. D. 2000, Icarus, 143, 360, doi: 10.1006/icar.1999.6263 Su´ arez Mascare˜ no, A., Faria, J. P., Figueira, P., et al. 2020, A&A, 639, A77, doi: 10.1051/0004-6361/202037745

    2000

  90. [98]

    K., et al

    Suazo, M., Zackrisson, E., Mahto, P. K., et al. 2024, MNRAS, 531, 695, doi: 10.1093/mnras/stae1186

    2024 doi

  91. [99]

    2022, MNRAS, 512, 2988, doi: 10.1093/mnras/stac280

    Huston, M. 2022, MNRAS, 512, 2988, doi: 10.1093/mnras/stac280

    2022 doi

  92. [100]

    Talent, D. L. 1992, Journal of Spacecraft and Rockets, 29, 508, doi: 10.2514/3.25493

    1992 doi

  93. [101]

    2014, AJ, 147, 86, doi: 10.1088/0004-6256/147/4/86

    Tokovinin, A. 2014, AJ, 147, 86, doi: 10.1088/0004-6256/147/4/86

    2014 doi

  94. [102]

    2015, ApJ, 807, 26, doi: 10.1088/0004-637X/807/1/26 van Belle, G

    Torres, G., Claret, A., Pavlovski, K., & Dotter, A. 2015, ApJ, 807, 26, doi: 10.1088/0004-637X/807/1/26 van Belle, G. T. 2012, A&A Rv, 20, 51, doi: 10.1007/s00159-012-0051-2 van Belle, G. T., Ciardi, D. R., Thompson, R. R., Akeson, R. L., & Lada, E. A. 2001, ApJ, 559, 1155, do...

    2015

  95. [103]

    Wang, L., & Stark, J. P. W. 1999, Journal of Spacecraft and Rockets, 36, 114, doi: 10.2514/2.3423

    1999 doi

  96. [104]

    A., & Heller, R

    Wells, R., Poppenhaeger, K., Watson, C. A., & Heller, R. 2018, MNRAS, 473, 345, doi: 10.1093/mnras/stx2077

    2018 doi

  97. [105]

    G., Henry, T

    Winters, J. G., Henry, T. J., Jao, W.-C., et al. 2019, AJ, 157, 216, doi: 10.3847/1538-3881/ab05dc

    2019 doi

  98. [106]

    Wright, J. T. 2020, Serbian Astronomical Journal, 200, 1, doi: 10.2298/SAJ2000001W —. 2023, ApJ, 956, 34, doi: 10.3847/1538-4357/acf44f

    2020 doi

  99. [107]

    T., Cartier, K

    Wright, J. T., Cartier, K. M. S., Zhao, M., Jontof-Hutter, D., & Ford, E. B. 2016, ApJ, 816, 17, doi: 10.3847/0004-637X/816/1/17

    2016 doi

  100. [108]

    T., Mullan, B., Sigurdsson, S., & Povich, M

    Wright, J. T., Mullan, B., Sigurdsson, S., & Povich, M. S. 2014, ApJ, 792, 26, doi: 10.1088/0004-637X/792/1/26

    2014 doi

  101. [109]

    Wyatt, M. C. 2008, ARA&A, 46, 339, doi: 10.1146/annurev.astro.45.051806.110525

    2008 arXiv

  102. [110]

    C., & Dent, W

    Wyatt, M. C., & Dent, W. R. F. 2002, MNRAS, 334, 589, doi: 10.1046/j.1365-8711.2002.05533.x

    2002

  103. [111]

    C., Dermott, S

    Wyatt, M. C., Dermott, S. F., Telesco, C. M., et al. 1999, ApJ, 527, 918, doi: 10.1086/308093

    1999 doi

  104. [112]

    M., Scott, N., Serra, P., et al

    Young, L. M., Scott, N., Serra, P., et al. 2014, MNRAS, 444, 3408, doi: 10.1093/mnras/stt2474

    2014 doi

  105. [113]

    2016, ApJ, 833, 214, doi: 10.3847/1538-4357/833/2/214

    Zackrisson, E., Calissendorff, P., Gonz´ alez, J., et al. 2016, ApJ, 833, 214, doi: 10.3847/1538-4357/833/2/214

    2016 doi

  106. [114]

    J., Wehrhahn, A., & Reiter, J

    Zackrisson, E., Korn, A. J., Wehrhahn, A., & Reiter, J. 2018, ApJ, 862, 21, doi: 10.3847/1538-4357/aac386

    2018 doi

  107. [115]

    P., Ranc, C., & Morel, P

    Zahn, J. P., Ranc, C., & Morel, P. 2010, A&A, 517, A7, doi: 10.1051/0004-6361/200913817

    2010 doi

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.