Evolution of a Keplerian disk of colliding and fragmenting particles: a kinetic model with application to the Edgeworth–Kuiper belt
Evolution of a Keplerian disk of colliding and fragmenting particles: a kinetic model with application to the Edgeworth–Kuiper belt
复制标题
碰撞和破碎粒子的开普勒盘的演化：应用于埃奇沃斯-柯伊伯带的动力学模型
DOI：
10.1016/j.icarus.2004.10.003
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发表时间：
2005
期刊：
影响因子：
3.2
通讯作者：
F. Spahn
中科院分区：
文献类型：
--
作者：
A. Krivov;M. Sremčević;F. Spahn
我们提出了一个由固体粒子组成的圆盘的动力学模型，该圆盘绕初级粒子运行，并经历了非弹性碰撞。与使用2D(质量-半长轴)绑定并单独分析速度(偏心率、倾角)演化的其他碰撞模型不同，我们选择质量和轨道元素作为相空间的自变量。该空间中的分布函数包含有关粒子的质量、空间和速度组合分布的全部信息。导出了分布函数的一般动力学方程，该方程适用于任何轨道元素集和由单一核函数指定的任何碰撞结果。该模型的第一个实现利用了3D相空间(质量-半长轴-偏心)，并涉及到倾角和所有角度元素的平均值。我们假设碰撞是破坏性的，用可用的材料和大小相关的标度定律来模拟它们，并包括碰撞衰减。给出了质量-半长轴-偏心分布的闭合动力学方程，得到了圆盘材料通常的质量和空间分布的变换规则。我们方法的动态“核心”是通用的。可以将倾角作为一个附加的相空间变量添加到模型中，以包括陨石坑碰撞和聚集、动力摩擦和粘性搅拌、大扰动的重力、阻力和其他影响。作为一个具体的应用，我们研究了Edgeworth-Kuiper带(EKB)中经典粒子的碰撞演化。针对不同的初始圆盘质量、不同的径向轮廓和不同的物体撞击强度运行了该模型。我们得到的粒子大小分布、碰撞时间和质量损失的结果与以前的研究结果一致。特别是，碰撞演化在Ekb的内部被发现是最实质性的，那里超过Ekb年龄的幸存者和较早碰撞的碎片之间的间隔大小在几到几十公里之间。EKB中的尺寸分布不是单一的Dohnanyi型幂定律，它反映了强度和重力区域中临界比能的尺寸依赖关系。演化的圆盘的净质量损失率几乎是恒定的，并由较大物体的破坏所主导。最后，假设轨道偏心率的初始分布是均匀的，我们证明了一个演化的圆盘在中等偏心率的轨道上比在近圆形或更偏心的轨道上包含更多的物体。这一性质适用于任何大小的物体，并用碰撞概率来解释。这一效应应该会调整由动力学机制形成的偏心率分布，例如海王星的共振和近日点的截断。
We present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass–semimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass–semimajor axis–eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass–semimajor axis–eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic “core” of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth–Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB's age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune.