We use N-body simulations to study the evolution of cuspy cold dark matter (CDM) haloes in the gravitational potential of a massive host. Tidal mass-losses reshape CDM haloes, leaving behind bound remnants whose characteristic densities are set by the mean density of the host at the pericentre of their respective orbit. The evolution to the final bound remnant state is essentially complete after ∼5 orbits for nearly circular orbits, while reaching the same remnant requires, for the same pericentre, ∼25 and ∼40 orbits for eccentric orbits with 1:5 and 1:20 pericentre-to-apocentre ratios, respectively. The density profile of tidal remnants is fully specified by the fraction of mass lost, and approaches an exponentially truncated Navarro–Frenk–White profile in the case of heavy mass-loss. Resolving tidal remnants requires excellent numerical resolution; poorly resolved subhaloes have systematically lower characteristic densities and are more easily disrupted. Even simulations with excellent spatial and time resolution fail when the final remnant is resolved with fewer than 3000 particles. We derive a simple empirical model that describes the evolution of the mass and the density profile of the tidal remnant applicable to a wide range of orbital eccentricities and pericentric distances. Applied to the Milky Way, our results suggest that 108–$10^{10}\, \mathrm{M_{\odot }}$ haloes accreted $\sim 10\, \mathrm{Gyr}$ ago on 1:10 orbits with pericentric distance $\sim 10\, \mathrm{kpc}$ should have been stripped to 0.1–1 per cent of their original mass. This implies that estimates of the survival and structure of such haloes (the possible hosts of ultra-faint Milky Way satellites) based on direct cosmological simulations may be subject to substantial revision.

中文翻译：

---

冷暗物质亚晕的渐近潮汐残余

我们使用 N 体模拟来研究在大质量宿主的引力势中尖点冷暗物质 (CDM) 晕的演化。潮汐质量损失重塑 CDM 晕圈，留下束缚的残余物，其特征密度由位于各自轨道中心的宿主平均密度决定。对于接近圆形的轨道，在大约 5 个轨道之后，向最终束缚残余状态的演化基本完成，而对于相同的中心，对于具有 1:5 和 1:20 中心的偏心轨道，达到相同的残余需要大约 25 和 40 个轨道-to-to-apocentre 比率，分别。潮汐残余物的密度分布完全由质量损失的比例指定，并且在大量质量损失的情况下接近指数截断的 Navarro-Frenk-White 分布。解决潮汐残留物需要出色的数值分辨率；分辨不佳的亚晕具有系统性较低的特征密度，并且更容易被破坏。当使用少于 3000 个粒子解决最终残余时，即使具有出色的空间和时间分辨率的模拟也会失败。我们推导出了一个简单的经验模型，该模型描述了适用于各种轨道偏心率和圆心距离的潮汐残余物的质量和密度分布。应用于银河系，我们的结果表明 108–$10^{10}\, \mathrm{M_{\odot }}$ 晕圈在 $\sim 10\, \mathrm{Gyr}$ 之前在 1:10 轨道上吸积中心距 $\sim 10\, \mathrm{kpc}$ 应该被剥离到它们原始质量的 0.1-1%。