A Physical Bias in Cosmological Simulations

Abstract

Numerical simulation plays an important role in the study of structure formation of the universe. However, the mass resolution in current simulations is still poor. Due to technical difficulties, it is necessary to use both greatly reduced number density of particles and greatly raised unit particle mass. Consequently, the particle masses used in cosmological simulations are about $10^{70}$ times larger than the $Gev$ candidates in particle physics. This is a huge physical bias that cannot be neglected when interpreting the results of the simulations. Here we discuss how such a bias affects Cold Dark Matter (CDM) cosmological simulations. We find that the small scale properties of the CDM particle system are changed in two aspects. 1) An upper limit is imposed on the spatial resolution of the simulation results. 2) Most importantly, an unexpected short mean free path is produced, and the corresponding two body scattering cross section is close to the value expected in the Self-Interaction Dark Matter(SIDM) model. Since the mean free path of real CDM particle systems is much longer than that in the simulations, our results imply 1) that there is probably no 'cusp problem' in real CDM halos, and 2) that a much longer time is needed to form new virialized halos in real CDM particle systems than in the simulations. This last result can help us understand the 'substructure problem'. Our discussion can also explain why the massive halos in the simulations may have smaller concentration coefficients.Comment: 4 pages,no figures. Submitted to ApJ

An Excessive Core Collapse in Nbody Cosmological simulations

“…If we define the mean free path as L s ≡ vt relax , then we can follow the SIDM models (Spergel 2000,Dave 2001) defining the "scattering cross section" as σ ≡ 1/(Lρ). In the central region of a typical simulation halo, the scattering cross section is about σ sim ≃ 9 × 10 −26 cm 2 /GeV (Xiao 2004), that is approximately the value expected in SIDM models (σ sim ≃ 0.1σ SIDM ). In contrast, for the GeV CDM particles σ CDM ≃ 10 −65 σ SIDM ≃ 0.…”

Dark matter distribution function from non-extensive statistical mechanics

“…Such a bound would according to our figure 2 imply a bound on the central density profile of γ > 1, in agreement with numerical and analytical suggestions (Diemand, Moore & Stadel 2004, Reed et al 2003, Navarro et al 2004). It has indeed been suggested (Xiao, Sun & Hao 2004) that the numerical methods induce an artificial conductivity, which would then imply a central slope of −1.…”

Astrophysics in 2005

“…This year we will merely report, first, that the data may not be so unambiguous as generally advertised (Metcalf 2005 on substructure from gravitational lensing; Mashchenko et al 2005 on satellites of the Milky Way as massive and largely dark, our couple of dozen being seriously outnumbered by the 160 belonging to NGC 5044, Faltenbacher & Mathews 2005), and, second, that the models may not be so unambiguous as generally advertised, (1) because of insufficient mass resolution (remember those M , particles in even the most ex-9 1.4 # 10 tensive simulation), including an explicit statement from Xiao et al (2004) about the importance of being resolved for cusps, and (2) because of the enormous complexity in tying the mass patterns calculated to the light patterns observed (Gao et al 2004). …”

“…because of insufficient mass resolution (remember those 1.4 × 10 9 M ⊙ particles in even the most extensive simulation), including an explicit statement from Xiao et al (2004) about the importance of being resolved for cusps, and (b) because of the enormous complexity in tying the mass patterns calculated with the light patterns observed (Gao et al 2004).…”