http://arxiv.org/abs/2109.09985
The inverse mass cascade is proposed for statistically steady state of self-gravitating collisionless flow (SG-CFD). The continuous mass transfer from small to large mass scales (inverse cascade) is formulated. Direct effect on mass functions is discussed. Mass cascade is local, two-way, and asymmetric in mass space. Halos inherit/pass their mass from/to halos of similar size. Two distinct ranges are identified: a propagation range with a scale-independent rate of mass transfer and a deposition range with cascaded mass consumed to grow halos. Dimensional analysis leads to a power-law mass function in propagation range with a geometry exponent (${\lambda}$). A fundamental merging frequency $f_0{\sim}m_p^{\lambda-1}a^{-1}$ is identified, where $a$ is the scale factor. The particle mass $m_p$ can be determined if frequency is known. The rate of mass transfer ${\epsilon}_m{\sim}a^{-1}$ is independent of halo mass (key feature of propagation range). Typical halos grow as $m_h{\sim}a^{3/2}$ and the waiting time (halo lifespan) scales as ${\sim}m_h^{-\lambda}$. Chain reaction of mass cascade provides non-equilibrium system (SG-CFD) a mechanism to continuously release energy and maximize entropy. A continuous injection of mass (“free radicals”) at the smallest scale is required to sustain the everlasting inverse mass cascade such that the total halo mass $M_h$ increases as $a^{1/2}$. These “radicals” might be directly generated at the smallest Planck scale or by a direct cascade from large to small scales. The entire mass cascade can be formulated by random walk in mass space, where halos migrate with an exponential distribution of waiting time. This results in a heterogeneous diffusion model, where mass function can be fully derived without relying on specific collapse models. A double-$\lambda$ mass function is proposed with different $\lambda$ for two ranges and compared to simulations.
Z. Xu
Wed, 22 Sep 21
41/57
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