From cusps to cores: a stochastic model

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.

Small-scale structure of fuzzy and axion-like dark matter

“…which incorporates FDM effects only through its dependence on log Λ FDM . El-Zant et al [177] confirmed and extended these results with a method they had previously developed to model gravitational relaxation caused by baryonic turbulent density fluctuations [178]. It uses the sweeping hypothesis from turbulence theory to map spatial fluctuation power spectra to temporal ones.…”

The effect of fluctuating fuzzy axion haloes on stellar dynamics: a stochastic model

“…We start with the simplest case, in which all modes move with the same velocity. This connects the sought after derivation of the two body relaxation time to the situation studied in El-Zant et al (2016), where we assumed a spatial (one time) power law spectrum of the form |δ k (0)| 2 = Ck −n , and introduced the time dependence through a constant speed sweeping hypothesis. We do the same here, but focus on the special case of a white noise density spectrum (n = 0), appropriate of the expected spectrum of randomly scattered point masses that we take to represent the 'field stars' through which a test particle moves.…”

“…We start by considering how the basic theoretical setup introduced in El-Zant et al (2016) can be directly applied to derive the standard two body relaxation time for the case of a test star moving through an infinite system of randomly distributed 'field stars' (point particles), of average spatial mass density ρ0. As in the aforementioned work, we Fourier expand the potential Φ and density contrast δ = ρ(r)…”

“…The time dependence was then introduced through the sweeping ansatz used and tested in turbulence theory, whereby small scale fluctuations are 'swept' -that is passively advected -by large scale velocity fields, which can either represent mean bulk flows (Taylor 1938) or random large scale flows characterized by a velcity dispersion (Kraichnan 1964;Tennekes 1975). The effective assumption in El-Zant et al (2016) was that all modes are transported by the same sweeping velocity. The model is however easy to generalize to the case when each mode travels with its own velocity, drawn from a given distribution (e.g., Wilczek & Narita 2012;Wilczek et al 2014).…”

NIHAO IX: the role of gas inflows and outflows in driving the contraction and expansion of cold dark matter haloes

“…This process can increase the density of dark matter haloes by an order of magnitude. In contrast, other processes can cause the dark matter halo to expand: rapid mass-loss and/or time variability of the potential due to feedback from stars (Navarro et al 1996;Read & Gilmore 2005;Mashchenko et al 2006;Macciò et al 2012;El-Zant et al 2016) or Active Galactic Nuclei (AGN; Martizzi et al 2012Martizzi et al , 2013; mergers and stripping of smaller subhaloes that were puffed up by stellar feedback (Dekel et al 2003); and transfer of energy/angular momentum from baryons to the dark matter via dynamical friction due to minor mergers (El-Zant et al 2001;Jardel & Sellwood 2009;Johansson et al 2009;Cole et al 2011), or galactic bars (Weinberg & Katz 2002;Sellwood 2008).…”