pith. machine review for the scientific record. sign in

arxiv: 2512.00145 · v3 · submitted 2025-11-28 · 🌌 astro-ph.GA · astro-ph.CO

Role of prompt cusps in driving the core collapse of SIDM halos

Vinh Tran , Daniel Gilman , M. Sten Delos , Xuejian Shen , Oliver Zier , Mark Vogelsberger , David Xu This is my paper

Pith reviewed 2026-05-17 03:22 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords self-interacting dark matterprompt cuspscore collapsedark matter halosN-body simulationsSIDMvelocity dispersion gradients
0
0 comments X

The pith

Prompt cusps in SIDM halos slow early core formation by a factor of two but let later collapse track standard paths after rescaling.

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

The paper uses N-body simulations to examine isolated 10 million solar mass dark matter halos that contain prompt cusps of varying strength at their centers. These cusps form from early-universe overdensities and create steeper central density profiles than ordinary NFW cusps. Stronger prompt cusps reduce inner velocity dispersion gradients, which slows the initial phase of core formation by roughly a factor of two. Once core collapse starts, the halos follow nearly the same evolutionary track in physical time when densities, radii, and velocity dispersions are rescaled to account for the extra central mass, staying within about 5 percent of the reference track for an NFW halo except near the end.

Core claim

Halos with more prominent prompt cusps show delayed core formation by a factor of approximately 2 because of smaller velocity dispersion gradients in the inner region. During most of the core-collapse phase the evolution aligns in physical time after rescaling of densities, radii, and velocity dispersions, preserving the original virial mass at higher concentration. Late-phase deviations remain at the 5 percent level relative to the NFW reference collapse track and depend on both the increased concentration and the temperature of the outer halo regions.

What carries the argument

Prompt cusps, steep central density peaks formed by direct collapse of early overdensities and embedded in SIDM halo centers.

If this is right

  • Core-collapse timing depends on the interplay between the inner prompt-cusp profile and the velocity dispersion in the outer halo.
  • The scale densities and radii after collapse still reflect the original halo virial mass but at higher concentration.
  • Deviations from the reference track grow at late times when outer-halo temperature either inhibits or enhances heat transfer.

Where Pith is reading between the lines

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

  • Accounting for prompt cusps could shift the predicted mass range where core collapse becomes observable in dwarf galaxies.
  • Full cosmological simulations that include prompt cusps may produce distinct signatures in central density profiles or rotation curves.
  • The small late-time deviations suggest that outer-halo properties can be tuned to control the final stages of collapse.

Load-bearing premise

Isolated halos with embedded prompt cusps capture the dynamics that arise in certain SIDM models with light mediators and suppressed small-scale linear power.

What would settle it

A measurement of core-collapse timescales in low-mass halos that either matches the rescaled NFW track or shows systematic deviations larger than 5 percent when central cusp mass is accounted for would test the result.

Figures

Figures reproduced from arXiv: 2512.00145 by Daniel Gilman, David Xu, Mark Vogelsberger, M. Sten Delos, Oliver Zier, Vinh Tran, Xuejian Shen.

Figure 1
Figure 1. Figure 1: FIG. 1. The density profiles (top), logarithmic density profile [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The fractional differences in the initial density profiles [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The evolution of the density (top) and velocity dis [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Evolutions of the core density [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scaled evolutions of the core density [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The self-similar density profiles of the four halos in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The scaled density profiles (top) and scaled velocity [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 1
Figure 1. Figure 1: As the halo cores evolve and thermalization [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The density (top) and velocity dispersion (bot [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison of the evolutions of the core-density [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The fractional differences of the extreme-cusp (red), [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Similar to Figure 7, but with halos in the VDCS [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

Prompt cusps (PCs) form from the direct collapse of overdensities in the early Universe, reside at the center of every dark matter halo, and have density profiles steeper than $r^{-1}$ NFW cusps. Using a suite of high-resolution N-body simulations, we study the evolution of isolated halos in self-interacting dark matter (SIDM) with massive PCs embedded at their centers, a scenario that could be realized in certain SIDM models with light mediators that predict a small-scale suppression of the linear matter power spectrum. We track the evolution of three equally concentrated $10^7\,{\rm{M}}_\odot$ halos, hosting PCs of various total masses, and quantify how the presence of a PC affects the processes of core formation and collapse. Early in the core-formation phase, halos with more prominent PCs exhibit a delayed evolution by a factor of $\sim 2$ due to smaller velocity dispersion gradients in the inner region. During most of the core-collapse phase, the halo evolution becomes closely aligned in physical time, with appropriate rescaling of densities, radii, and velocity dispersions. The scale densities and radii preserve the virial mass of the original halos, but with increased concentration. Deviations occur at the late phase of core-collapse at the level of $\sim 5\%$ relative to the reference collapse track of an NFW halo. These deviations depend non-trivially on both the increased concentration incurred by the PCs, as well as the velocity dispersion (temperature) of the outer halo regions, which can inhibit or enhance the heat transfer process. Our simulations illustrate the complex interplay between the inner and outer halo profiles in determining the onset of core collapse and motivate future studies in the full cosmological context.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript reports results from high-resolution N-body simulations of three isolated 10^7 M_⊙ SIDM halos, each initialized with an embedded prompt cusp (PC) of varying mass. It claims that more massive PCs delay the early core-formation phase by a factor of ∼2 owing to reduced inner velocity-dispersion gradients; that the subsequent core-collapse phase aligns closely with a rescaled NFW reference track (preserving virial mass but increasing concentration); and that late-phase deviations remain at the ∼5 % level, depending non-trivially on both the PC-induced concentration increase and the outer-halo velocity dispersion.

Significance. If the reported alignment and small late-time deviations hold under the stated numerical conditions, the work supplies concrete, simulation-based evidence for the interplay between inner prompt cusps and outer halo temperature in controlling SIDM core collapse. The direct tracking of three halos with controlled PC masses constitutes a clear strength, yielding falsifiable quantitative outputs that analytic models alone cannot provide.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (simulation setup): the central claim that late-phase deviations depend non-trivially on outer-halo velocity dispersion is derived from isolated runs in which outer density and dispersion profiles are held fixed after initialization. In the light-mediator SIDM models invoked in the introduction, continuous cosmological accretion would evolve those outer profiles and thereby alter the heat-conduction rate; this effect is not quantified and directly impacts the reported ∼5 % deviation size.
  2. [§4] §4 (results): no convergence tests, adopted SIDM cross-section value, or error estimation procedure for the factor-of-∼2 delay or the ∼5 % late-phase deviations are reported. Because the alignment claim rests on precise comparison of density, radius, and velocity-dispersion tracks, the absence of these diagnostics leaves the robustness of the central quantitative results unverified.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the SIDM cross-section and softening length used in each run.
  2. [Discussion] A brief comparison table to existing SIDM core-collapse tracks without PCs would help readers gauge the incremental effect of the embedded cusps.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment below and have revised the manuscript to improve clarity, documentation, and qualification of our results where appropriate.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (simulation setup): the central claim that late-phase deviations depend non-trivially on outer-halo velocity dispersion is derived from isolated runs in which outer density and dispersion profiles are held fixed after initialization. In the light-mediator SIDM models invoked in the introduction, continuous cosmological accretion would evolve those outer profiles and thereby alter the heat-conduction rate; this effect is not quantified and directly impacts the reported ∼5 % deviation size.

    Authors: We agree that the simulations are isolated with outer profiles held fixed after initialization. This setup was chosen to cleanly isolate the role of the prompt cusp while controlling for outer-halo properties. We have revised the abstract and §3 to explicitly qualify that the reported non-trivial dependence of the ∼5% late-phase deviations on outer velocity dispersion holds within the isolated-halo framework. We have also added a paragraph noting that continuous cosmological accretion in light-mediator models would evolve the outer profiles and could modify the heat-conduction rate and deviation amplitude. Our results therefore serve as a controlled baseline, and we explicitly motivate future cosmological simulations to quantify the accretion effect. revision: partial

  2. Referee: [§4] §4 (results): no convergence tests, adopted SIDM cross-section value, or error estimation procedure for the factor-of-∼2 delay or the ∼5 % late-phase deviations are reported. Because the alignment claim rests on precise comparison of density, radius, and velocity-dispersion tracks, the absence of these diagnostics leaves the robustness of the central quantitative results unverified.

    Authors: We acknowledge that the original submission did not adequately document these numerical details. In the revised manuscript we have expanded §4 with: (1) explicit convergence tests varying particle number (up to 10^7 particles) and gravitational softening, demonstrating that the core-formation delay and collapse tracks remain stable; (2) the specific SIDM cross-section value adopted in the runs; and (3) error estimation via bootstrap resampling across multiple realizations for the measured delay factor and late-time deviations. These additions confirm that the reported alignment after rescaling and the ∼5% deviations are robust under the stated numerical conditions. revision: yes

standing simulated objections not resolved
  • Quantitative assessment of how continuous cosmological accretion modifies the outer profiles, heat-conduction rate, and the precise size of the ∼5% late-phase deviations in realistic light-mediator SIDM cosmologies (this requires new cosmological simulations outside the present isolated-halo study).

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs

full rationale

The paper derives its claims exclusively from high-resolution N-body simulation outputs tracking the time evolution of density, radius, and velocity dispersion profiles in three isolated 10^7 M_⊙ SIDM halos with embedded prompt cusps. The reported factor-of-~2 delay in core formation, subsequent alignment under rescaling of densities/radii/velocity dispersions, preservation of virial mass with increased concentration, and ~5% late-time deviations from the NFW reference track are all empirical measurements extracted from the simulated trajectories. No analytic derivation, fitted functional form, or equation is introduced that reduces by construction to its own inputs; the rescaling is applied post hoc as a comparative diagnostic rather than imposed to force alignment. No load-bearing self-citations, uniqueness theorems, or ansatzes are invoked to justify the central results. The study is therefore self-contained against external benchmarks and receives a circularity score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that isolated halos with embedded PCs capture the relevant physics of certain light-mediator SIDM models; no explicit free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption Isolated halos with embedded PCs represent the scenario realized in certain SIDM models with light mediators that predict a small-scale suppression of the linear matter power spectrum.
    Invoked in the abstract to motivate the simulation setup.

pith-pipeline@v0.9.0 · 5644 in / 1235 out tokens · 47519 ms · 2026-05-17T03:22:12.784443+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.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We perform dark-matter-only N-body simulations of idealized isolated halos using the multi-physics, massively parallel simulation code Arepo... We track the evolution of three equally concentrated 10^7 M_⊙ halos, hosting PCs of various total masses, and quantify how the presence of a PC affects the processes of core formation and collapse.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    When scaled by the effective scale density ρ̄_s, scale radius r̄_s, and scale velocity dispersion σ̄_s, the time evolutions of the core density, core half-density radius, and core one-dimensional velocity dispersion evolve more similarly over time... the evolutionary trajectories of the different halos appear broadly overlapping

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

56 extracted references · 56 canonical work pages · 11 internal anchors

  1. [1]

    ¯ρs =ρ s min(ρPC c (T)) min(ρNFWc (T)) .(10)

    ¯ρs - obtained by scaling the control NFW scale density by the ratio of the minimum core density reached by the prompt-cusp halos (denotedρ PC c ) to that of the NFW control halo (denotedρ NFW c ), i.e. ¯ρs =ρ s min(ρPC c (T)) min(ρNFWc (T)) .(10)

    work page

  2. [2]

    ¯rs =r s max(rPC ρ/2(T)) max(rNFW ρ/2 (T)) .(11)

    ¯rs - determined by applying the ratios of the max- imum core half-density radii to the control NFW scale radius, i.e. ¯rs =r s max(rPC ρ/2(T)) max(rNFW ρ/2 (T)) .(11)

    work page

  3. [3]

    ¯σs =σ s ⟨˙σPC 1D,c(T= 0.25–0.5τ)⟩ ⟨˙σNFW 1D,c (T= 0.25–0.5τ)⟩ (12) where ˙σdenotes a time derivative

    ¯σs - calculated from the ratios of the rates of in- crease in the core one-dimensional velocity dis- persion over the intervalT= 10–20 Gyr (∼ 0.25–0.5τ), during which the velocity dispersion evolves approximately linearly, i.e. ¯σs =σ s ⟨˙σPC 1D,c(T= 0.25–0.5τ)⟩ ⟨˙σNFW 1D,c (T= 0.25–0.5τ)⟩ (12) where ˙σdenotes a time derivative. The values are listed in ...

    work page

  4. [4]

    However, be- cause the PCs initially incur a lower temperature gradient, halos with more prominent PCs form cores more slowly

    DM self-interactions rapidly thermalize the halos, erasing the signatures of the PCs in both the den- sity and velocity dispersion profiles. However, be- cause the PCs initially incur a lower temperature gradient, halos with more prominent PCs form cores more slowly

    work page

  5. [5]

    These values deviate at a level of∼10% among halos with PCs and the NFW reference

    We find that halos with embedded PCs follow a nearly self-similar evolution once they are rescaled to characteristic densities, radii, and velocity dis- persions. These values deviate at a level of∼10% among halos with PCs and the NFW reference

    work page

  6. [6]

    In general, the most significant impact of the PC is the delay introduced in core formation

    During the late core-collapse phase, interplay be- tween increasing central density and the elevated velocity dispersion in the outer halo exert compet- ing influences on the collapse time. In general, the most significant impact of the PC is the delay introduced in core formation. Although brief, during the first∼0.04 Gyr (approximately 1% of the collaps...

    work page

  7. [7]

    D. N. Spergel and P. J. Steinhardt, Observational Evi- dence for Self-Interacting Cold Dark Matter, Phys. Rev. Lett.84, 3760 (2000), arXiv:astro-ph/9909386 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  8. [8]

    Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe

    S. Balberg, S. L. Shapiro, and S. Inagaki, Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe, ApJ568, 475 (2002), arXiv:astro-ph/0110561 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  9. [9]

    Gravothermal collapse of isolated self-interacting dark matter haloes: N-body simulation versus the fluid model

    J. Koda and P. R. Shapiro, Gravothermal collapse of iso- lated self-interacting dark matter haloes: N-body simu- lation versus the fluid model, MNRAS415, 1125 (2011), arXiv:1101.3097 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  10. [11]

    M. S. Delos, M. Bruff, and A. L. Erickcek, Predicting the density profiles of the first halos, Phys. Rev. D100, 023523 (2019), arXiv:1905.05766 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  11. [12]

    M. S. Delos and S. D. M. White, Inner cusps of the first dark matter haloes: formation and survival in a cosmological context, MNRAS518, 3509 (2023), arXiv:2207.05082 [astro-ph.CO]

    work page arXiv 2023

  12. [13]

    M. S. Delos and S. D. M. White, Prompt cusps and the dark matter annihilation signal, J. Cosmol. Astropart. Phys.2023, 008 (2023), arXiv:2209.11237 [astro-ph.CO]

    work page arXiv 2023

  13. [14]

    Ondaro-Mallea, R

    L. Ondaro-Mallea, R. E. Angulo, J. St¨ ucker, O. Hahn, and S. D. M. White, Phase-space simulations of prompt cusps: simulating the formation of the first haloes with- out artificial fragmentation, MNRAS527, 10802 (2024), arXiv:2309.05707 [astro-ph.GA]

    work page arXiv 2024

  14. [15]

    Nishikawa, K

    H. Nishikawa, K. K. Boddy, and M. Kaplinghat, Accel- erated core collapse in tidally stripped self-interacting dark matter halos, Phys. Rev. D101, 063009 (2020), arXiv:1901.00499 [astro-ph.GA]

    work page arXiv 2020

  15. [16]

    C. A. Correa, Constraining velocity-dependent self- interacting dark matter with the Milky Way’s dwarf spheroidal galaxies, MNRAS503, 920 (2021), arXiv:2007.02958 [astro-ph.GA]

    work page arXiv 2021

  16. [17]

    E. O. Nadler, D. Yang, and H.-B. Yu, A Self- interacting Dark Matter Solution to the Extreme Diver- sity of Low-mass Halo Properties, ApJ958, L39 (2023), arXiv:2306.01830 [astro-ph.GA]

    work page arXiv 2023

  17. [18]

    Dutra, P

    I. Dutra, P. Natarajan, and D. Gilman, Self-interacting Dark Matter, Core Collapse, and the Galaxy–Galaxy Strong-lensing Discrepancy, ApJ978, 38 (2025), arXiv:2406.17024 [astro-ph.CO]

    work page arXiv 2025

  18. [19]

    H. Xiao, X. Shen, P. F. Hopkins, and K. M. Zurek, SMBH seeds from dissipative dark matter, J. Cosmol. Astropart. Phys.2021, 039 (2021), arXiv:2103.13407 [astro-ph.CO]

    work page arXiv 2021

  19. [20]

    T. Shen, X. Shen, H. Xiao, M. Vogelsberger, and F. Jiang, Massive Black Holes Seeded by Dark Matter – Impli- cations for Little Red Dots and Gravitational Wave Signatures, arXiv e-prints , arXiv:2504.00075 (2025), arXiv:2504.00075 [astro-ph.GA]

    work page arXiv 2025

  20. [21]

    Jiang, Z

    F. Jiang, Z. Jia, H. Zheng, L. C. Ho, K. Inayoshi, X. Shen, M. Vogelsberger, and W.-X. Feng, Formation of the Little Red Dots from the Core-collapse of Self-interacting Dark Matter Halos, arXiv e-prints , arXiv:2503.23710 (2025), arXiv:2503.23710 [astro-ph.GA]

    work page arXiv 2025

  21. [22]

    Grant Roberts, L

    M. Grant Roberts, L. Braff, A. Garg, S. Profumo, T. Jel- tema, and J. O’Donnell, Early formation of supermassive black holes from the collapse of strongly self-interacting dark matter, J. Cosmol. Astropart. Phys.2025, 060 (2025), arXiv:2410.17480 [astro-ph.GA]

    work page arXiv 2025

  22. [23]

    M. S. Delos, Massive prompt cusps: a new signa- ture of warm dark matter, MNRAS522, L78 (2023), arXiv:2302.03040 [astro-ph.CO]

    work page arXiv 2023

  23. [24]

    M. S. Delos, The cusp-halo relation, arXiv e-prints , arXiv:2506.03240 (2025), arXiv:2506.03240 [astro- ph.CO]

    work page arXiv 2025

  24. [25]

    Z. C. Zeng, A. H. G. Peter, X. Du, A. Benson, J. Li, C. Mace, and S. Yang, Diversity and universality: Evo- 11 lution of dwarf galaxies with self-interacting dark mat- ter, Phys. Rev. D112, 063008 (2025), arXiv:2412.14621 [astro-ph.GA]

    work page arXiv 2025

  25. [26]

    Banik, J

    N. Banik, J. Bovy, G. Bertone, D. Erkal, and T. J. L. de Boer, Novel constraints on the particle nature of dark matter from stellar streams, J. Cosmol. Astropart. Phys. 2021, 043 (2021), arXiv:1911.02663 [astro-ph.GA]

    work page arXiv 2021

  26. [27]

    Nibauer, A

    J. Nibauer, A. Bonaca, A. M. Price-Whelan, D. N. Spergel, and J. E. Greene, Measurement of Dark Mat- ter Substructure from the Kinematics of the GD-1 Stel- lar Stream, arXiv e-prints , arXiv:2510.02247 (2025), arXiv:2510.02247 [astro-ph.GA]

    work page arXiv 2025

  27. [28]

    Gilman, J

    D. Gilman, J. Bovy, T. Treu, A. Nierenberg, S. Birrer, A. Benson, and O. Sameie, Strong lensing signatures of self-interacting dark matter in low-mass haloes, MNRAS 507, 2432 (2021), arXiv:2105.05259 [astro-ph.CO]

    work page arXiv 2021

  28. [29]

    Gilman, Y.-M

    D. Gilman, Y.-M. Zhong, and J. Bovy, Constrain- ing resonant dark matter self-interactions with strong gravitational lenses, Phys. Rev. D107, 103008 (2023), arXiv:2207.13111 [astro-ph.CO]

    work page arXiv 2023

  29. [30]

    W. J. R. Enzi, C. M. Krawczyk, D. J. Ballard, and T. E. Collett, The overconcentrated dark halo in the strong lens SDSS J0946 + 1006 is a subhalo: evidence for self-interacting dark matter?, MNRAS540, 247 (2025), arXiv:2411.08565 [astro-ph.CO]

    work page arXiv 2025

  30. [31]

    D. M. Powell, J. P. McKean, S. Vegetti, C. Sp- ingola, S. D. M. White, and C. D. Fassnacht, A million-solar-mass object detected at a cosmological dis- tance using gravitational imaging, Nature Astronomy 10.1038/s41550-025-02651-2 (2025), arXiv:2510.07382 [astro-ph.CO]

    work page doi:10.1038/s41550-025-02651-2 2025

  31. [32]

    ETHOS - An Effective Theory of Structure Formation: Dark matter physics as a possible explanation of the small-scale CDM problems

    M. Vogelsberger, J. Zavala, F.-Y. Cyr-Racine, C. Pfrom- mer, T. Bringmann, and K. Sigurdson, ETHOS - an effective theory of structure formation: dark matter physics as a possible explanation of the small-scale CDM problems, MNRAS460, 1399 (2016), arXiv:1512.05349 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  32. [33]

    E. O. Nadler, R. An, D. Yang, H.-B. Yu, A. Ben- son, and V. Gluscevic, COZMIC. III. Cosmological Zoom-in Simulations of SIDM with Suppressed Initial Conditions, arXiv e-prints , arXiv:2412.13065 (2024), arXiv:2412.13065 [astro-ph.CO]

    work page arXiv 2024

  33. [34]

    V. Tran, D. Gilman, M. Vogelsberger, X. Shen, S. O’Neil, and X. Zhang, Gravothermal catastrophe in resonant self-interacting dark matter models, Phys. Rev. D110, 043048 (2024), arXiv:2405.02388 [astro-ph.GA]

    work page arXiv 2024

  34. [35]

    V. Tran, X. Shen, D. Gilman, M. Vogelsberger, S. O’Neil, D. Xiong, J. Hu, and Z. Wu, Core collapse in res- onant self-interacting dark matter across two decades in halo mass, Phys. Rev. D112, 083003 (2025), arXiv:2504.02928 [astro-ph.GA]

    work page arXiv 2025

  35. [36]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, A Uni- versal Density Profile from Hierarchical Clustering, ApJ 490, 493 (1997), arXiv:astro-ph/9611107 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  36. [37]

    Yang and H.-B

    D. Yang and H.-B. Yu, Gravothermal evolution of dark matter halos with differential elastic scattering, Journal of Cosmology and Astroparticle Physics2022(09), 077

    work page

  37. [38]

    S. Yang, X. Du, Z. C. Zeng, A. Benson, F. Jiang, E. O. Nadler, and A. H. G. Peter, Gravothermal So- lutions of SIDM Halos: Mapping from Constant to Velocity-dependent Cross Section, ApJ946, 47 (2023), arXiv:2205.02957 [astro-ph.CO]

    work page arXiv 2023

  38. [39]

    Essig, S

    R. Essig, S. D. McDermott, H.-B. Yu, and Y.-M. Zhong, Constraining Dissipative Dark Matter Self-Interactions, Phys. Rev. Lett.123, 121102 (2019), arXiv:1809.01144 [hep-ph]

    work page arXiv 2019

  39. [40]

    D. Yang, E. O. Nadler, H.-B. Yu, and Y.-M. Zhong, A parametric model for self-interacting dark matter halos, J. Cosmol. Astropart. Phys.2024, 032 (2024), arXiv:2305.16176 [astro-ph.CO]

    work page arXiv 2024

  40. [41]

    V. Tran, X. Shen, M. Vogelsberger, D. Gilman, S. O’Neil, and J. Gao, A Novel Density Profile for Isothermal Cores of Dark Matter Halos, arXiv e-prints , arXiv:2411.11945 (2024), arXiv:2411.11945 [astro-ph.CO]

    work page arXiv 2024

  41. [42]

    E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh

    V. Springel, E pur si muove: Galilean-invariant cosmolog- ical hydrodynamical simulations on a moving mesh, MN- RAS401, 791 (2010), arXiv:0901.4107 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  42. [43]

    Weinberger, V

    R. Weinberger, V. Springel, and R. Pakmor, The AREPO Public Code Release, ApJS248, 32 (2020), arXiv:1909.04667 [astro-ph.IM]

    work page arXiv 2020

  43. [44]

    C. Mace, Z. Carton Zeng, A. H. G. Peter, X. Du, S. Yang, A. Benson, and M. Vogelsberger, Convergence Tests of Self-Interacting Dark Matter Simulations, arXiv e-prints , arXiv:2402.01604 (2024), arXiv:2402.01604 [astro-ph.GA]

    work page arXiv 2024

  44. [45]

    Subhaloes in Self-Interacting Galactic Dark Matter Haloes

    M. Vogelsberger, J. Zavala, and A. Loeb, Subhaloes in self-interacting galactic dark matter haloes, MNRAS 423, 3740 (2012), arXiv:1201.5892 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  45. [46]

    Tidal tails in CDM cosmologies

    V. Springel and S. D. M. White, Tidal tails in cold dark matter cosmologies, MNRAS307, 162 (1999), arXiv:astro-ph/9807320 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  46. [47]

    Generating Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation

    S. Kazantzidis, J. Magorrian, and B. Moore, Generat- ing Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation, ApJ601, 37 (2004), arXiv:astro-ph/0309517 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  47. [48]

    Lynden-Bell, R

    D. Lynden-Bell, R. Wood, and A. Royal, The Gravo- Thermal Catastrophe in Isothermal Spheres and the On- set of Red-Giant Structure for Stellar Systems, Monthly Notices of the Royal Astronomical Society138, 495 (1968)

    work page 1968

  48. [49]

    Binney and S

    J. Binney and S. Tremaine,Galactic dynamics(1987)

    work page 1987

  49. [50]

    Anatomy of Eddington-like inversion methods in the context of dark matter searches

    T. Lacroix, M. Stref, and J. Lavalle, Anatomy of Eddington-like inversion methods in the context of dark matter searches, J. Cosmol. Astropart. Phys.2018, 040 (2018), arXiv:1805.02403 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  50. [51]

    S. J. Aarseth and F. Hoyle, Dynamical evolu- tion of clusters of galaxies, i, Monthly Notices of the Royal Astronomical Society126, 223 (1963), https://academic.oup.com/mnras/article- pdf/126/3/223/8074955/mnras126-0223.pdf

    work page 1963

  51. [52]

    Springel, N

    V. Springel, N. Yoshida, and S. D. M. White, GADGET: a code for collisionless and gasdynamical cosmological simulations, New Astronomy6, 79 (2001), arXiv:astro- ph/0003162 [astro-ph]

    work page arXiv 2001

  52. [53]

    J. J. Monaghan and J. C. Lattanzio, A refined parti- cle method for astrophysical problems, A&A149, 135 (1985)

    work page 1985

  53. [54]

    Z. C. Zeng, A. H. G. Peter, X. Du, A. Benson, S. Kim, F. Jiang, F.-Y. Cyr-Racine, and M. Vogelsberger, Core- collapse, evaporation, and tidal effects: the life story of a self-interacting dark matter subhalo, MNRAS513, 4845 (2022), arXiv:2110.00259 [astro-ph.CO]. 12 Appendix A: Initial conditions sampling

    work page arXiv 2022

  54. [55]

    We assume that the system is bounded and isotropic, thusfonly de- pends onξ, andf(<0) = 0

    Eddington’s distribution function In order to achieve dynamical equilibrium in the ini- tial conditions (ICs) with respect to the CDM model, we utilize Eddington’s inversion formula [43] ρ(r) = Z √ 2ψ(r) 0 4πv2dv f(ξ).(A1) Here,ξ=ψ(r)−v 2/2 is the binding energy per unit of mass,ψis the negative gravitational potential, and f(ξ) is a phase-space distribut...

    work page

  55. [56]

    ICs in the context of softened gravity Typically, the Eddington distributions are constructed with the Newtonian gravitational potential. However, under the softened gravity schemes employed in simula- tions, even without DM self-interaction, halos sampled using such distributions would become unstable, leading to the formation of small cores roughly the ...

    work page

  56. [57]

    extended

    +A( 1 2)−A(u 1), u 1 ≤ 1 2 ≤u 2 B(u2)−B(u 1), u 1 ≥ 1 2 0, u 1 ≥u 2 (A8) Here, the final case occurs whenris outside of the kernel width, i.e.,|r−R| ≥h. The two auxiliary equations A(u) andB(u) are defined as A(u) = 1 2 u2 − 3 2 u4 + 6 5 u5,(A9) B(u) =u 2 −2u 3 + 3 2 u4 − 2 5 u5.(A10) In simulations that employ such a spline softening ap- proach, such as ...

    work page