From cusps to cores: a stochastic model

TL;DR

This paper introduces a stochastic theoretical model explaining how gas density fluctuations can transform dark matter haloes from cuspy to cored profiles, supported by numerical simulations confirming the analytical predictions.

Contribution

The paper presents a first-principles stochastic model linking gas fluctuations to cusp-core transformation in dark matter haloes, validated by numerical simulations.

Findings

Large-scale gas fluctuations dominate the cusp-core transformation.

The transformation efficiency depends mainly on gas fraction and fluctuation amplitude.

Numerical simulations confirm the analytical timescale for core formation.

Abstract

The cold dark matter model of structure formation faces apparent problems on galactic scales. Several threads point to excessive halo concentration, including central densities that rise too steeply with decreasing radius. Yet, random fluctuations in the gaseous component can 'heat' the centres of haloes, decreasing their densities. We present a theoretical model deriving this effect from first principles: stochastic variations in the gas density are converted into potential fluctuations that act on the dark matter; the associated force correlation function is calculated and the corresponding stochastic equation solved. Assuming a power law spectrum of fluctuations with maximal and minimal cutoff scales, we derive the velocity dispersion imparted to the halo particles and the relevant relaxation time. We further perform numerical simulations, with fluctuations realised as a Gaussian random field, which confirm the formation of a core within a timescale comparable to that derived analytically. Non-radial collective modes enhance the energy transport process that erases the cusp, though the parametrisations of the analytical model persist. In our model, the dominant contribution to the dynamical coupling driving the cusp-core transformation comes from the largest scale fluctuations. Yet, the efficiency of the transformation is independent of the value of the largest scale and depends weakly (linearly) on the power law exponent; it effectively depends on two parameters: the gas mass fraction and the normalisation of the power spectrum. This suggests that cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrised in simple terms, the physical and numerical complexities of the various implementations notwithstanding.