PNNL

Abstract

Using Illustris and Virgo N-body simulations, we focus on the velocity and acceleration fluctuations in collisionless dark matter involving long-range gravity. For comparison, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. Hierarchical structure formation proceeds through the merging of smaller haloes to form larger haloes, which facilitates a continuous energy cascade from small to large haloes at a constant rate $\varepsilon_u\approx -10^{-7}$m$^2$/s$^3$. Velocity fluctuations involve a critical velocity $u_c\propto (1+z)^{-3/4}$. Acceleration fluctuations involve a critical acceleration $a_c\propto (1+z)^{3/4}$. Two critical quantities are related by the rate of energy cascade $\varepsilon_{u}\approx -{a_c u_c/[2(3\pi)^2]}$, where the factor $3\pi$ is from the angle of incidence during merging. With critical velocity $u_c$ on the order of 300 km/s at $z=0$, the critical acceleration is determined to be $a_{c0}\equiv a_c(z=0) \approx 10^{-10}$m/s$^2$, suggesting $a_c$ might explain the universal acceleration $a_0\approx 10^{-10}$m/s$^2$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). The redshift evolution $a_c \propto (1+z)^{3/4}$ is proposed and in good agreement with Magneticum and EAGLE simulations. This suggests a larger $a_0$ at a higher redshift such that high-redshift galaxies of the same mass tend to rotate faster.