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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2026-06-11 23:58 |
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Conference: Bucharest University Faculty of Physics 2026 Meeting
Section: Theoretical and Computational Physics, Applied Mathematics
Title:
SHELL-CROSSING ONSET IN DISSIPATIVE DARK MATTER: A FOKKER-PLANCK N-BODY STUDY
Authors:
Gabriel-Paul FILIPCIUC (1),(2),(3)
*
Affiliation:
1) Faculty of Physics of the University of Bucharest
2) Centre International de Formation et de Recherche Avancées en Physique
3) Institute of Space Science - INFLPR Subsidiary
E-mail
gabriel-paul.filipciuc@s.unibuc.ro
Keywords:
shell-crossing, self-interacting dark matter, structure formation, particle mesh
Abstract:
Shell-crossing represents a phenomenon in cosmology in which cold dark matter trajectories
intersect, leading to caustic formation and diverging density fields. At this point the system transitions
from a single-stream fluid regime to one with multi-valued velocity fields, rendering cold fluid
descriptions invalid and posing a central challenge to analytic and numerical treatments of cosmic
structure formation [1, 2].
We begin by implementing a classical ΛCDM N-body simulation framework using the Particle
Mesh (PM) method [2], validated against the analytical Zeldovich pancake test, a single sinusoidal
displacement yielding an exact shell-crossing prediction of a_sc = 0.080, recovered by the simulation to
within 6% consistent with finite grid resolution at 643. Shell-crossing onset is identified through one
geometric diagnostic: phase-space folding. We then consider an alternative framework that could prove
useful in tackling the shell-crossing phenomenon, namely the self-interacting dark matter (SIDM)
formalism. Within this approach, we implement a SIDM N-body simulation, using a Langevin stochastic differential equation scheme (Euler–Maruyama combined with KDK leapfrog) together with Fokker-
Planck dynamics [1], parametrized by a friction coefficient α following the Chandrasekhar dynamical friction formulation [3] and a diffusion coefficient β. We derive analytical perturbative limits α_pert ≈ 1.8
and β_phys ≈ 4.5×10−3 for the tested range α ∈ [0, 50] and β ∈ [0, 2*10-3]. At α=50 collapse transitions
qualitatively from a sharp caustic to a broad trapped slab. For diffusion, the phase-space detector saturates
at β~10−3 where noise-to-signal reaches ~47%, defining the observational resolution limit of the
geometric detector at 643 resolution. Our results show that friction delays the onset of shell-crossing by
dissipating infall momentum, while diffusion decouples the geometric and dynamical shell-crossing
signals. These findings suggest that self-interacting dark matter (SIDM) can alter structure formation
timescales and provide a mechanism to mitigate the effects of shell-crossing, potentially contributing to
the resolution of small-scale tensions by delaying or suppressing the formation of overdense structures.
References:
[1] Ma & Bertschinger (2004) — "A Cosmological Kinetic Theory for the Evolution of Cold Dark Matter Halos with Substructure: Quasi-Linear Theory", The Astrophysical Journal, 612, 28–49.
[2] F. Leclercq (2015) — "Bayesian large-scale structure inference and cosmic web analysis", PhD Thesis, Université Pierre et Marie Curie.
[3] S. Chandrasekhar, January, (1943), “Stochastic Problems in Physics and Astronomy”
Acknowledgement:
The author would like to acknowledge the guidance and support of their PhD coordinator, Prof.Dr. Virgil Baran.
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