This paper addresses resonantly forced spiral density waves in a dense planetary ring which is close to the threshold for viscous overstability. We solve numerically the hydrodynamical equations for a dense, axisymmetric thin disk in the vicinity of an inner Lindblad resonance with a perturbing satellite. The spiral shape of a density wave is taken into account through a suitable approximation of the advective terms arising from the fluid orbital motion. This paper is a first attempt to model the co-existence of resonantly forced density waves and short-scale axisymmetric overstable wavetrains in Saturn's rings by conducting large-scale hydrodynamical integrations. These integrations reveal that the two wave types undergo complex interactions, not taken into account in existing models for the damping of density waves. In particular it is found that, depending on the relative magnitude of both wave types, the presence of viscous overstability can lead to a damping of an unstable density wave and vice versa. The damping of viscous overstability by a density wave is investigated further by employing a simplified model of an axisymmetric ring perturbed by a nearby Lindblad resonance. A linear hydrodynamic stability analysis as well as local N-body simulations of this model system are performed and support the results of our large-scale hydrodynamical integrations.
A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings
在本文中，我们解决的稳定性共振强迫密度波在稠密的行星环。Goldreich & Tremaine（1978）已经提出，密度波可能是不稳定的，取决于环的粘性和表面质量密度之间的关系。在Schmidt et al.（2016）最近的论文中，我们指出，当在环动力学的流体描述中满足粘性超稳定性标准时，强迫螺旋密度波也变得不稳定。在这种情况下，线性理论无法描述阻尼，但基本方程的非线性保证了有限的振幅，并最终保证了波的阻尼。我们应用多尺度形式主义推导出一个弱非线性阻尼关系的流体动力学模型。该关系描述了具有密度相关输运系数的垂直积分流体圆盘中螺旋密度波的共振激励和非线性粘性阻尼。该模型一致地预测密度波是（线性）不稳定的粘性超稳定的条件得到满足的环形区域。足够远离Lindblad共振，表面质量密度扰动预计饱和到一个恒定的值，由于非线性粘性阻尼。模型的波阻尼长度依赖于某些输入参数，如参数空间中到粘性超稳定性阈值的距离和基态表面质量密度。
Constraints on the initial mass, age and lifetime of Saturn's rings from viscous evolutions that include pollution and transport due to micrometeoroid bombardment
Accretion of Saturn's mid-sized moons during the viscous spreading of young massive rings: solving the paradox of silicate-poor rings versus silicate-rich moons
In this work, we model the radial density profile of the outer A ring of Saturn observed with Cassini cameras (Tiscareno & Harris 2018): An axisymmetric diffusion model has been developed, accounting for the outward viscous flow of the ring material, and the counteracting inward drift caused by resonances of the planet's large outer moons. It has been generally accepted that the 7:6 resonance of Janus alone confines the outer A ring which, however, was disproved by Tajeddine et al. (2017). We show that the step-like density profile of the outer A ring is predominantly defined by the discrete f…
行星环的粘性扩散被认为是由卫星扭矩抵消，通过单独的共振或通过重叠的共振。对于土星的A环，人们普遍认为只有卫星Janus可以通过其7：6 Lindblad共振阻止环的扩散。我们讨论了这种常见的误解，并表明，在现实中，A环是由卫星潘，阿特拉斯，普罗米修斯，潘多拉，Janus，Epimetheus和Mimas，其累积扭矩从各种谐振逐渐减少的角动量通量通过密度和弯曲波传输向外环的贡献。我们进一步认为，这种角动量通量的减少是通过“通量反转”发生的。此外，我们使用卫星的共振扭矩的大小来估计整个A环的有效粘度分布，表明它随着半径从~50 cm 2 s-1减小到小于~10 cm 2 s-1。的角动量通量和有效粘度的逐渐减少的估计是大致一致的结果，通过平衡的牧羊扭矩从潘和Daphnis与粘性扭矩的恩克和基勒间隙的边缘，以及边缘的A环。另一方面，Mimas 2：1 Lindblad共振单独似乎能够限制B环的边缘，与A环的情况相反，我们表明B环上的有效粘度相对恒定在~24-30 cm 2 s-1。
Incomplete cooling down of Saturn's A ring at solar equinox: Implication for seasonal thermal inertia and internal structure of ring particles
在2009年8月的太阳分点，卡西尼号上的复合红外光谱仪（CIRS）显示了有史以来观测到的最低土星环温度。详细的辐射转移模型表明，只要只考虑土星的通量，土星A环观测到的春分温度就比模型预测的要高得多。这表明A环在春分点没有完全冷却下来。我们开发了一个简单的季节性环温度模型，并首先假设环颗粒的内部密度和热惯性是均匀的深度。颗粒大小估计为1-2 μ m。A环中部的季节热惯量为30-50 JmPDMATHABMM K $^{-1}$ s $^{-1/2}$，而A环内外区的季节热惯量为10 JmPDMATHABMM K $^{-1}$ s $^{-1/2}$或与昼夜热惯量一样低。一个附加的内部结构模型，其中一个粒子有一个高密度的核心周围的蓬松的风化层地幔，表明核心半径相对于粒子半径约为0.9的中间A环和更小的内部和外部区域的A环。这意味着环粒子内部密度的径向变化存在于整个A环。一些机制可能是将致密颗粒限制在中间A环中以防止粘性扩散。或者，（中间的）A环可能是最近（$<$ 10 $^{8}$ yr）由于一颗冰冷的卫星的破坏而形成的，因此致密的颗粒还没有扩散到A环上，颗粒的风化层地幔还没有变厚。我们的模型结果还表明，核心的成分主要是水冰，而不是岩石。
The University of Tokyo（东京大学）；National Astronomical Observatory of Japan（日本国立天文台）；University of Tokyo（东京大学）；Université Côte d’Azur（蔚蓝海岸大学）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；CNRS（法国国家科学研究中心）；Centre national d’études spatiales (CNES)（法国国家空间研究中心）；Charles University（查理大学）；University of Michigan（密歇根大学）；Johns Hopkins University Applied Physics Lab（约翰斯·霍普金斯大学应用物理实验室）
Saturn's rings age I.: Reconsideration of the exposure age
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（法国蔚蓝海岸大学、蔚蓝海岸天文台、法国国家科学研究中心、拉格朗日实验室）；MAUCA — Master track in Astrophysics, Université Côte d’Azur & Observatoire de la Côte d’Azur（天体物理学硕士课程，法国蔚蓝海岸大学与蔚蓝海岸天文台）
Saturn's rings are composed of icy grains, most in the mm to m size ranges, undergoing several collisions per orbit. Their collective behaviour generates a remarkable array of structure over many orders of magnitude, much of it not well understood. On the other hand, the collisional properties and parameters of individual ring particles are poorly constrained; usually N-body simulations and kinetic theory employ hard-sphere models with a coefficient of restitution $ε$ that is constant or a decreasing function of impact speed. Due to plastic deformation of surface regolith, however, it is likel…
One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. (1982, 1989) show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly pe…
