Universal scaling laws and density slopes for dark matter haloes

Area of Science:

• Cosmology
• Astrophysics
• Particle Physics

Background:

• Current dark matter models face small-scale challenges.
• A cascade phenomenon, similar to hydrodynamic turbulence, is proposed for dark matter.

Purpose of the Study:

• To propose a cascade theory for dark matter.
• To provide insights into dark matter's behavior on various scales.
• To derive universal laws for dark matter halo properties.

Main Methods:

• Developed a cascade theory for dark matter energy transfer.
• Utilized N-body simulations to confirm energy cascade predictions.
• Analyzed galaxy rotation curves to verify halo density laws.

Main Results:

• Confirmed a two-thirds law for kinetic energy cascade on scale r.
• Established a four-thirds law for mean halo density, consistent with galaxy rotation curves.
• Derived critical halo scales based on velocity dispersion and dark matter properties (collisionless vs. self-interacting).

Conclusions:

• The cascade theory offers a new framework for understanding dark matter.
• The theory predicts universal properties of dark matter halos, including density profiles.
• A modified Einasto profile is proposed to better describe halo density based on radial flow and mass accretion.