The observed rotation curves of galaxies present one of the most compelling pieces of evidence for dark matter's existence. While Newtonian dynamics predict that rotational velocities should decrease with distance from the galactic center (following a Keplerian decline), observations consistently show flat or even rising rotation curves at large radii. This discrepancy suggests either:
Traditional N-body simulations model dark matter as collisionless particles governed solely by gravity. However, an alternative approach treats the dark matter halo as a continuous fluid medium with specific rheological properties. This paradigm shift allows us to apply established fluid dynamical principles while introducing novel non-Newtonian behaviors.
Non-Newtonian fluids exhibit viscosity that changes with applied stress or shear rate, unlike Newtonian fluids with constant viscosity. Several characteristics make non-Newtonian models appealing for dark matter:
The generalized Navier-Stokes equations for a non-Newtonian fluid can be written as:
ρ(∂v/∂t + (v·∇)v) = -∇p + ∇·τ + ρg
where the deviatoric stress tensor τ incorporates the non-Newtonian behavior through a constitutive relation. For dark matter applications, we often consider:
The Ostwald-de Waele power-law model describes many non-Newtonian fluids:
τ = m|γ̇|n-1γ̇
where n < 1 indicates shear-thinning behavior particularly relevant for dark matter halos.
The Oldroyd-B model introduces elastic effects through:
τ + λ1(∂τ/∂t + v·∇τ - (∇v)T·τ - τ·(∇v)) = η0(γ̇ + λ2(∂γ̇/∂t + v·∇γ̇ - (∇v)T·γ̇ - γ̇·(∇v)))
Modern galactic simulations incorporating fluid dark matter require specialized numerical approaches:
Smoothed Particle Hydrodynamics (SPH) can be adapted for non-Newtonian fluids by:
Eulerian methods benefit from:
| Feature | Collisionless N-body | Non-Newtonian Fluid |
|---|---|---|
| Rotation Curves | Requires fine-tuned halo profiles | Naturally produces flat curves through shear effects |
| Cusp/Core Problem | Tends to produce cuspy profiles | Can generate cores via rheological properties |
| Substructure Survival | Overpredicts satellite survival | Damping effects reduce substructure counts |
The fluid approach raises fundamental questions:
Implementation hurdles include:
Weak lensing measurements constrain the total mass distribution and can distinguish between fluid and particle dark matter predictions, particularly in halo outskirts where rheological effects become significant.
The morphology of stellar streams around galaxies provides sensitive probes of the underlying gravitational potential and potential dissipative effects in the dark matter component.