Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisions are allowed, N-body numerical simulations develop cored density profiles, in perfect agreement with the theoretical expectation. We compare theory and two types of numerical simulations: (1) when DM particles are self-interacting (SIDM) with enough cross-section, then the effective two-body relaxation time-scale becomes shorter than the Hubble time resulting in cored DM haloes. The haloes thus obtained, with masses from dwarf galaxies to galaxy clusters, collapse to a single shape after normalization, and this shape agrees with the polytropic density profile theoretically expected. (2) The inner radii in canonical N-body numerical simulations are always discarded because the use of finite-mass DM particles artificially increases the two-body collision rate. We show that the discarded radii develop cores which are larger than the employed numerical softening and have polytropic shape independently of halo mass. Our work suggests that the presence of cores in simulated (or observed) density profiles can used as evidence for systems in thermodynamic equilibrium.

中文翻译：

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暗物质晕的数值模拟在达到热力学平衡时产生多向中心核

自引力天体通常在密度分布（核心）中显示出一个中央高原，其物理起源受到激烈争论。理论上，核心预计存在于最大熵的 N 体系​​统中，但是，它们不存在于冷暗物质 (CDM) 的规范 N 体数值模拟中。我们的工作表明，尽管理论和数值模拟之间存在明显的矛盾，但它们是完全一致的。简而言之，核心是热力学平衡系统的特征，但在 CDM 模拟中有意抑制热化碰撞。当允许碰撞时，N 体数值模拟会产生核心密度分布，与理论预期完全一致。我们比较了理论和两种类型的数值模拟：(1) 当 DM 粒子具有足够横截面的自相互作用 (SIDM) 粒子时，有效二体弛豫时间尺度变得比哈勃时间短，从而导致核心 DM 晕。由此获得的晕圈，质量从矮星系到星系团，在归一化后坍缩成单一形状，这种形状与理论上预期的多向密度分布一致。(2) 规范N体数值模拟中的内半径总是被丢弃，因为有限质量DM粒子的使用人为地增加了二体碰撞率。我们表明，丢弃的半径发展出比所采用的数值软化更大的核心，并且具有独立于晕质量的多方形状。