http://arxiv.org/abs/2110.03126
The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless flow (SG-CFD). How the inverse mass cascade maximizes system entropy and develops limiting velocity/energy distributions are fundamental questions to answer. We present a statistical theory concerning the maximum entropy distributions of particle velocity, speed, and energy for self-gravitating systems involving a power-law long-range interaction with an arbitrary exponent $n$. For system with long-range interaction ($-2<n<0$), a broad spectrum of halos and halo groups are necessary to form from inverse mass cascade to maximize the system entropy. While particle velocity in each halo group is still Gaussian, the velocity distribution of entire system can be non-Gaussian. With the virial equilibrium for local mechanical equilibrium of halo groups, the maximum entropy principle is applied for statistical equilibrium of global system to derive the limiting distributions. Halo mass function is not required in this formulation, but it is a direct result of entropy maximization. The predicted velocity distribution involves a shape parameter $\alpha$ that is dependent on the exponent $n$. The velocity distribution approaches Laplacian with $\alpha\rightarrow0$ and Gaussian with $\alpha\rightarrow\infty$. For intermediate $\alpha$, the maximum entropy distribution naturally exhibits a Gaussian core at small velocity and exponential wings at large velocity. The total energy of collisionless particles at a given speed follows a parabolic scaling for small speed ($\epsilon \propto v^2$) and a linear scaling ($\epsilon \propto v$) for large speed. Results are compared against a N-body simulation with good agreement.
Z. Xu
Fri, 8 Oct 21
29/70
Comments: 7 Figures, 2 Tables
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