Self-Interacting Dark Matter (SIDM)

• Self-Interacting Dark Matter (SIDM) is a class of models where dark matter particles scatter with each other, leading to cored density profiles and modified halo dynamics.
• SIDM utilizes new dark-sector forces with velocity-dependent cross sections to resolve discrepancies between collisionless dark matter predictions and astrophysical observations.
• Analytical methods and simulations constrain SIDM parameters, revealing its impact on galaxy formation, core collapse, and potential gravitational wave signals.

Self-Interacting Dark Matter (SIDM) refers to a broad class of dark matter theories in which dark matter particles scatter elastically or inelastically with each other via new dark-sector interactions. Unlike collisionless cold dark matter (CDM), SIDM models aim to address small-scale discrepancies between standard CDM predictions and astrophysical observations, particularly in the inner regions of galaxies and clusters, by introducing particle physics processes that allow for significant momentum and energy transfer within halos. The cross section per unit mass, σ/m, is typically of order 0.1–10 cm²/g, and its magnitude and velocity dependence serve as a central theoretical and observational focus.

1. SIDM Microphysics and Theoretical Framework

In SIDM scenarios, new interactions between dark matter particles are mediated by light force carriers—commonly a scalar or vector boson with mass on the order of MeV–GeV—giving rise to non-gravitational Yukawa-like potentials in the non-relativistic limit. The interaction Lagrangian may take the form

$$\mathcal{L}_{\mathrm{int}} = \begin{cases} g_D\,\bar{\chi}\gamma^\mu\chi\,\phi_\mu & \text{(vector mediator)} \ g_D\,\bar{\chi}\chi\,\phi & \text{(scalar mediator)} \end{cases}$$

where $\chi$ is the dark matter particle, $g_D$ the coupling constant, and $\phi$, $\phi_\mu$ the mediator fields. The non-relativistic potential resulting from mediator exchange is

$V(r) = \pm \frac{\alpha_D}{r}\,e^{-m_{\phi}r}$

with $\alpha_D = g_D^2 / 4\pi$ and $m_{\phi}$ the mediator mass. SIDM models may feature purely elastic scattering or include inelastic transitions between internal states, with exothermic and endothermic reactions modulating the kinetic energy budget in halos (Chua et al., 2020, O'Neil et al., 2022).

For quantum-resonant cases where the $s$-wave cross section saturates the Unitarity bound, the self-scattering cross section can be expressed as

$\sigma_{\mathrm{max}} = \frac{4\pi}{k^2}$

where $k$ is the relative momentum. Near resonance, $\sigma/m \propto 1/v_\mathrm{rel}^2$, resulting in strong velocity dependence—large cross sections in dwarf galaxies and suppressed values at cluster scales (Kamada et al., 2020).

In two-component and asymmetric models, cross-species elastic scatterings drive mass segregation and enrich the phenomenology of core formation and collapse (Yang et al., 3 Apr 2025).

2. Halo Structure, Core Formation, and Gravothermal Evolution

SIDM thermalizes halo centers via particle scattering, erasing steep $\rho \propto r^{-1}$ CDM cusps and promoting constant-density cores within a characteristic radius set by the local scattering rate. This radius is where the cumulative per-particle interaction probability over the halo age reaches unity. The inner density profile is often modeled as isothermal: $$\rho_{\mathrm{SIDM}}(r) = \rho_0\,\exp\left(-\frac{\Phi(r) - \Phi(0)}{\sigma_{1\mathrm{D}}^2}\right)$$ where $\Phi$ is the gravitational potential and $\sigma_{1\mathrm{D}}$ the one-dimensional velocity dispersion (Adhikari et al., 2022, Kaplinghat et al., 2013).

Halo evolution proceeds in two regimes:

• Core Expansion: At low/moderate $\sigma/m$, heat conduction from outer (hotter) halo layers into the core causes the core to grow and the central density to fall.
• Gravothermal Core Collapse: At large $\sigma/m$ or after significant tidal stripping, the core undergoes a runaway contraction, resulting in a sharp central density spike and steeper inner profile. The characteristic timescale is

$$t_c \propto \left(\frac{\sigma_{\rm eff}}{m}\right)^{-1} c_{200}^{-7/2} M_{200}^{-1/3}$$

where $c_{200}$ is the concentration and $M_{200}$ the virial mass (Nadler et al., 2023, Ando et al., 17 Mar 2025).

Inclusion of baryons radically alters the equilibrium solution. In baryon-dominated (Milky Way–like) galaxies, the dark matter density profile becomes tightly coupled to the baryonic potential: $$\rho(r) = \rho_0\exp\left(\frac{\Phi_B(0)-\Phi_B(r)}{\sigma_0^2}\right)$$ where $\Phi_B$ is the baryon potential. This produces smaller, denser cores (e.g., $r_c \sim 0.3$–0.5 kpc in the Milky Way) compared to SIDM-only predictions ($r_c \sim$ a few–10 kpc), with enhanced central densities (Kaplinghat et al., 2013).

3. Astrophysical Signatures and Constraints

SIDM leads to several observationally relevant consequences:

• Galactic Rotation Curves: Core formation in dwarfs and low surface brightness galaxies naturally yields slowly rising rotation curves and low central densities. Inclusion of baryons explains the observed diversity and inner rotation curve shapes (Nadler et al., 2023, Adhikari et al., 2022).
• Galaxy Groups and Clusters: In galaxy groups, X-ray and lensing constraints favor $\sigma/m \lesssim 0.1$–1 cm²/g. For massive clusters, central densities and lensing profiles restrict $\sigma/m$ to $\lesssim 0.1$–0.4 cm²/g at velocity dispersions $v\sim 1000-2000$ km/s (K. et al., 2023, Robertson et al., 2018).
• Stellar and Disk Morphologies in Clusters: Effective SIDM drag on halos in clusters displaces stellar disks, producing observable U-shaped warps and increased disk thickness for cross sections in the range 0.5–1.0 cm²/g (Secco et al., 2017).
• Satellite and Subhalo Dynamics: SIDM enhances satellite vulnerability to tidal stripping and core collapse, leading to fewer luminous satellites, more stellar-only systems, and broader diversity in inner rotation curves (Gutcke et al., 6 Oct 2025, Zhang et al., 10 Jan 2024).
• Ultrafaint Dwarf Kinematics: Detailed Jeans modeling and Bayesian evidence analysis indicate that Milky Way ultrafaint dwarfs display a bimodal statistical preference for small and large $\sigma/m$ (core formation vs. gravothermal collapse), but in classical dwarfs, cross sections $\sigma/m \gtrsim 0.2$ cm²/g are decisively disfavored if velocity-independent (Ando et al., 17 Mar 2025).

4. Cosmological and Particle Physics Implications

Velocity-dependent SIDM models, especially with light mediators, are required to address constraints spanning dwarfs to clusters:

• Particle Model Realizations: Well-motivated models include a Dirac fermion coupled to a light scalar or vector (e.g., $U(1)_{\mu-\tau}$, leptophilic $U(1)_\ell$, or Higgs portal scenarios). Concrete constructions address relic abundance, direct detection, and indirect detection constraints (Dutta, 2023, Patel et al., 2022, Wu et al., 2022).
• Relic Abundance and Early Universe: Large self-scattering cross sections in standard radiation-dominated cosmology typically yield underabundant relic densities. Non-standard cosmological histories with early matter domination and entropy injection allow matching the observed dark matter density without tuning down the coupling strength or mediator mass (Dutta, 2023).
• Gravitational Waves and Phase Transitions: If the mediator mass arises from a first-order phase transition (FOPT) at $T\sim$ MeV, as suggested by nanohertz gravitational wave observations (NANOGrav, CPTA), the same physics that gives SIDM its mediator mass also produces potentially detectable gravitational wave backgrounds, tightly connecting astrophysical and cosmological probes (Han et al., 2023).
• Dark Stars: SIDM annihilation in early protohalos can power “dark stars,” with gravothermal collapse leading to densities high enough for annihilation heating to compete with cooling, producing objects of comparable size and luminosity to collisionless dark matter analogues (Wu et al., 2022).

5. Numerical Methods, Simulation Approaches, and Analytical Tools

SIDM phenomenology is explored across a spectrum of computational strategies:

• N-body and Hydrodynamical Simulations: Modern codes (e.g., GADGET, Arepo, GIZMO, and full-physics platforms like LYRA) implement Monte Carlo approaches for rare (large-angle) scattering and effective drag-force algorithms for frequent, small-angle scattering regimes. The latter methods accurately capture the cumulative impact of forward-peaked cross sections as expected from light mediator exchange (Fischer et al., 2020, Ragagnin et al., 1 Apr 2024).
• Semi-analytic and Subhalo Frameworks: Tools such as SASHIMI-SIDM and conducting fluid models efficiently link gravothermal evolution, core collapse, and subhalo structure to observable stellar kinematics and rotation curves (Ando et al., 17 Mar 2025).
• Partial-Wave and Hulthén Potential Analysis: Transfer cross sections are computed numerically via partial-wave expansions or analytically for s-wave Hulthén potentials, with careful treatment of resonances and Sommerfeld enhancements that critically shape velocity dependence (Patel et al., 2022, Kamada et al., 2020).
• Profile Fitting and Empirical Relations: Observationally derived density profiles (e.g., Einasto, core+NFW hybrids) are fit to gravitational lensing, X-ray, and stellar kinematic data to extract and constrain $\sigma/m$ using empirical or simulation-based scaling relations (K. et al., 2023).

6. Extensions, Degeneracies, and Future Directions

• Model Extensions: SIDM with composite or multi-component sectors, inelastic channels, or dissipative interactions exhibits phenomena such as mass segregation, enhanced core collapse, and non-trivial subhalo survival patterns, offering diagnostic power on the microphysical content of the dark sector (Yang et al., 3 Apr 2025, O'Neil et al., 2022).
• Degeneracy with Baryonic Effects: Supernova feedback, bursty star formation, and baryonic contraction can also modify central densities. Disentangling baryonic and SIDM contributions requires multiwavelength, resolved kinematic/structural studies, and high-resolution hydrodynamical modeling (Robertson et al., 2018, Gutcke et al., 6 Oct 2025, Adhikari et al., 2022).
• Observational Prospects: Next-generation surveys (LSST, Euclid, Roman, JWST, TMT/ELT) and advances in strong lensing, HI mapping, and stellar stream analyses will robustly test SIDM-predicted signatures such as central cores/cusps, disk warps, subhalo abundances, and gravitational wave backgrounds. Simulations with improved baryon–SIDM coupling and code–code comparisons are critical for future progress (Ragagnin et al., 1 Apr 2024, Adhikari et al., 2022, Nadler et al., 2023, Han et al., 2023).
• Direct and Indirect Detection: Portal couplings to the Standard Model (kinetic or Higgs mixing) provide laboratory probes, but are typically bounded by direct-detection data and cosmological constraints on mediator lifetime and energy injection (Dutta, 2023, Patel et al., 2022).

7. Key Equations and Parameter Regimes

Physical Quantity	Formula	Context/Notes
Yukawa Potential	$V(r) = \pm (\alpha_D/r)\,e^{-m_\phi r}$	Non-relativistic DM-DM interaction
Transfer Cross Section	$$\sigma_T = \int\!\!\! d\Omega\, (d\sigma/d\Omega)\,(1-\cos\theta)$$	Momentum transfer relevance
Core Radius (with baryons)	$$r_c \approx r_0 \frac{\sqrt{1+\frac{2}{3}\ln2\cdot a_0/a_1^2}-1}{1 + a_0/(3a_1) - \sqrt{1+\frac{2}{3}\ln2\cdot a_0/a_1^2}}$$	(Kaplinghat et al., 2013); $a_0$, $a_1$ depend on baryonic potential
Shear Viscosity (kin. theory)	$$\eta = (1.18\,m\,\langle v\rangle^2) / (3\langle \sigma v\rangle)$$	Viscous SIDM, cosmic acceleration (Atreya et al., 2017)
SIDM Density Profile (isothermal)	$$\rho(r) = \rho_0\,\exp\left(-\frac{\Phi(r)-\Phi(0)}{\sigma_{1\mathrm{D}}^2}\right)$$	Core formation, analytic solutions

Summary

SIDM, as a paradigm, modifies dark matter phenomenology on subgalactic to cluster scales by enabling heat and momentum transport through particle scattering, in turn generating cored profiles, isotropized orbits, and distinctive morphological features in galaxies and clusters. The velocity and angular dependence of the cross section, the possibility of inelastic and multi-component interactions, and the rich dynamical interplay with baryons and environment all conspire to produce a vast, observationally accessible spectrum of cosmic structures. Observational, numerical, and theoretical studies together constrain the allowed SIDM parameter space, shape particle physics model-building, and offer a resolution to multiple open problems at the intersection of galaxy formation, cosmology, and fundamental physics.