[Paper Review] Inverse mass cascade of self-gravitating collisionless flow and effects on halo deformation, energy, size, and density profiles.

Zhijie Xu|arXiv (Cornell University)|Sep 25, 2021

Galaxies: Formation, Evolution, Phenomena7 references4 citations

TL;DR

This paper proposes that inverse mass cascade in self-gravitating collisionless systems drives radial flows, deforming halos and creating cores via Hubble-like expansion, leading to a new scale radius and effective gravity exponent $n_e = -1.3$. It derives halo concentration $c = 3.5$, explains the cusp-core transition via double-power-law profiles, and models halo evolution using geometric Brownian motion and Fokker-Planck equations with osmotic flow, matching simulations across group sizes.

ABSTRACT

Inverse mass cascade is a key feature of the intermediate statistically steady state of self-gravitating collisionless flow (SG-CFD). This paper focus on the effects of mass cascade on halo energy, momentum, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards for core and inwards for outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration $c=3.5$ can be derived for fast growing halos. For cusp-core controversy, a double-power-law density is proposed as a result of radial flow. The inner/outer density are controlled by halo deformation rate and halo growth, respectively. The slower deformation at center, the steeper density. For fast growing halos, radial flow at center is simply Hubble flow that leads to the existence of central core. Mass cascade leads to nonzero halo surface energy/tension and radial flow that enhances the random motion in outer region. An effective exponent of gravity $n_e=-1.3$ (not -1) is obtained due to halo surface energy. Evolution of halo size follows geometric Brownian motion and lognormal distribution. The Brownian motion of particles in randomly evolving halos leads to Fokker-Planck equations for particle distribution that is related to radial and osmotic flow. Complete solutions of particle distribution are presented based on a simple model of osmotic flow. The proposed model agrees with simulation for a wide range of halo group sizes. With reference pressure/density defined at center, equation of state can be established for relative pressure/density. The center pressure, density, and dispersion are presented. The core size $x_c$ is obtained where Hubble flow is dominant. Simple closures are proposed for self-consistent halo density.

Motivation & Objective

• To explain the origin of core formation in dark matter halos through inverse mass cascade in self-gravitating collisionless systems.
• To resolve the cusp-core controversy by linking halo deformation and radial flows to density profile shapes.
• To derive a scale radius not present in isothermal models due to nonzero radial flow induced by mass cascade.
• To establish an equation of state for halos using center-defined pressure and density, enabling self-consistent density closure.
• To model halo size evolution as geometric Brownian motion and derive particle distribution via Fokker-Planck equations with osmotic flow.

Proposed method

• Models inverse mass cascade in self-gravitating collisionless flow (SG-CFD) to derive radial flows: outward in core, inward in outer regions.
• Introduces a scale radius arising from nonzero radial flow, distinct from isothermal profiles, and links it to halo deformation and growth rate.
• Derives an effective gravity exponent $n_e = -1.3$ due to halo surface energy/tension, modifying Newtonian gravity ($n = -1$).
• Models halo size evolution as geometric Brownian motion, leading to lognormal distribution of halo radii.
• Solves Fokker-Planck equations for particle distribution using a simple osmotic flow model, capturing radial and osmotic components.
• Proposes simple closures for self-consistent halo density by relating inner/outer density to deformation rate and growth speed.

Experimental results

Research questions

• RQ1 How does inverse mass cascade in self-gravitating collisionless flow affect halo energy, momentum, size, and density profiles?
• RQ2 What causes the formation of a central core in fast-growing halos, and how is it related to radial flow and Hubble-like expansion?
• RQ3 How does halo surface energy/tension modify the effective gravity exponent, and what is its value in the model?
• RQ4 What is the origin of the new scale radius not present in isothermal profiles, and how is it linked to radial flow?
• RQ5 How does the evolution of halo size follow geometric Brownian motion, and what distribution does it follow?

Key findings

• Halo concentration $c = 3.5$ is derived for fast-growing halos due to inverse mass cascade and radial flow.
• A double-power-law density profile emerges from radial flow, with inner density steepened by slow central deformation and outer density governed by halo growth.
• The central core forms when Hubble-like radial flow dominates, defining the core size $x_c$.
• An effective gravity exponent $n_e = -1.3$ is obtained due to halo surface energy, deviating from Newtonian $n = -1$.
• Halo size evolution follows geometric Brownian motion and lognormal distribution, consistent with simulation data across group sizes.
• Complete solutions for particle distribution are derived using Fokker-Planck equations with osmotic and radial flow components, enabling self-consistent density closure.