The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard q=3.5 power-law index of the Dohnanyi (1969) differential size spectrum to an index as large as q=4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88<q<3.14 of Pan & Sari (2005) can steepen to values as large as q=3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.
We describe an extensive suite of numerical calculations for the collisional evolution of irregular satellite swarms around 1--300 M-earth planets orbiting at 120 AU in the Fomalhaut system. For 10--100 M-earth planets, swarms with initial masses of roughly 1% of the planet mass have cross-sectional areas comparable to the observed cross-sectional area of Fomalhaut b. Among 30--300 M-earth planets, our calculations yield optically thick swarms of satellites for ages of 1-10 Myr. Observations with HST and ground-based AO instruments can constrain the frequency of these systems around stars in t…
We consider whether equilibrium size distributions from collisional cascades match the frequency of impactors derived from New Horizons crater counts on Charon (Singer et al 2019). Using an analytic model and a suite of numerical simulations, we demonstrate that collisional cascades generate wavy size distributions; the morphology of the waves depends on the binding energy of solids $Q_d^\star$ and the collision velocity $v_c$. For an adopted minimum size of solids, $r_{min}$ = 1 micron, and collision velocity $v_c$ = 1-3 km/sec, the waves are rather insensitive to the gravitational component …
We derive a new analytical model for the evolution of a collisional cascade in a thin annulus around a single central star. In this model, $r_{max}~$ the size of the largest object declines with time (t); $r_{max} \propto t^{-γ}$, with $γ$ = 0.1-0.2. Compared to standard models where $r_{max}~$ is constant in time, this evolution results in a more rapid decline of $M_d$, the total mass of solids in the annulus and $L_d$, the luminosity of small particles in the annulus: $M_d \propto t^{-(γ+ 1)}~$ and $L_d \propto t^{-(γ/2 + 1)}~~$. We demonstrate that the analytical model provides an excellent…
We consider the long-term collisional and dynamical evolution of solid material orbiting in a narrow annulus near the Roche limit of a white dwarf. With orbital velocities of 300 km/sec, systems of solids with initial eccentricity $e \gtrsim 10^{-3}$ generate a collisional cascade where objects with radii $r \lesssim$ 100--300 km are ground to dust. This process converts 1-100 km asteroids into 1 $μ$m particles in $10^2 - 10^6$ yr. Throughout this evolution, the swarm maintains an initially large vertical scale height $H$. Adding solids at a rate $\dot{M}$ enables the system to find an equilib…
We analyze two new sets of coagulation calculations for solid particles orbiting within the terrestrial zone of a solar-type star. In models of collisional cascades, numerical simulations demonstrate that the total mass, the mass in 1 mm and smaller particles, and the dust luminosity decline with time more rapidly than predicted by analytic models, $\propto t^{-n}$ with $n \approx$ 1.1-1.2 instead of 1. Size distributions derived from the numerical calculations follow analytic predictions at radii less than 0.1 km but are shallower than predicted at larger sizes. In simulations of planet forma…
A radially broad collisional cascade in the debris disk of $γ$ Ophiuchi observed by JWST
California Institute of Technology（加州理工学院）；University of Cambridge（剑桥大学）；Space Science Institute（空间科学研究所）；University of Arizona（亚利桑那大学）；Center for Astrophysics, Harvard & Smithsonian（哈佛-史密森尼天体物理中心）；Instituto de Astrofísica de Canarias（加那利天体物理学研究所）；Universidad de la Laguna（拉帕鲁纳大学）；Academia Sinica（中央研究院）；University of Exeter（埃克塞特大学）
We consider the long-term evolution of gaseous disks fed by the vaporization of small particles produced in a collisional cascade inside the Roche limit of a 0.6 Msun white dwarf. Adding solids with radius \r0\ at a constant rate $\dot{M}_0$ into a narrow annulus leads to two distinct types of evolution. When $\dot{M}_0 > \dot{M}_{0,crit}$ = $3 \times 10^4 ~ (r_0 / {\rm 1~km})^{3.92}$~g s$^{-1}$, the cascade generates a fairly steady accretion disk where the mass transfer rate of gas onto the white dwarf is roughly $\dot{M}_0$ and the mass in gas is $M_g \approx 2.3 \times 10^{22} ~ (\dot{M}_0…
We investigated fundamental processes of collisional sticking and fragmentation of dust aggregates by carrying out N-body simulations of submicron-sized icy dust monomers. We examined the condition for collisional growth of two colliding dust aggregates in a wide range of the mass ratio, 1-64. We found that the mass transfer from a larger dust aggregate to a smaller one is a dominant process in collisions with a mass ratio of 2-30 and impact velocity of \approx 30-170 m s^-1. As a result, the critical velocity, v_fra, for fragmentation of the largest body is considerably reduced for such unequ…
Debris disks are scaled-up analogs of the Kuiper Belt in which dust is generated by collisions between planetesimals. In the "collisional cascade" model of debris disks, dust lost to radiation pressure and winds is constantly replenished by grinding collisions between planetesimals. The model assumes that collisions are destructive and involve large velocities; this assumption has not been tested beyond our Solar System. We present 0"25 ($\approx$2.4 au) resolution observations of the $λ$ = 450 $μ$m dust continuum emission from the debris disk around the nearby M dwarf AU Microscopii with the …
Understanding the collisional outcomes of dust aggregates and dependence on material properties of the constituting particles is of great importance toward understanding planet formation. Recent numerical simulations have revealed that interparticle tangential friction plays a crucial role in energy dissipation during collisions between porous dust aggregates; however, the importance of friction on the collisional growth of dust aggregates remains poorly understood. Here we demonstrate the effects of interparticle tangential friction on the collisional growth of dust aggregates. We performed n…
Accretion in Protoplanetary Disks by Collisional Fusion
太阳系的形成被认为是围绕原恒星的多阶段过程。惠普尔首先注意到，微行星的成长受到气体阻力的强烈影响;在米尺度上，这样的天体会迅速螺旋进入中央恒星，而更小或更大的粒子则不会。因此，成功的行星吸积需要快速的小行星增长到公里级。一种普遍接受的观点是，对于高于某一阈值碰撞速度的碰撞速度$V_c$，${V_{th}} \sim$ 0.1-10 cm s $^{-1}$，颗粒团聚是不可能的;弹性回弹克服了表面吸引力和分子间力。然而，如果假设所有的碰撞都是完美的粘附，那么这个瓶颈可以通过快速的星子生长来克服。虽然以前的工作已经明确地处理了碰撞压力的影响和粒子断裂或渗透的可能性，物质的相行为的基本作用-相图，无定形物和多晶型物-被忽略了。在这里，它表明，新的方面的表面相变提供了一个物理基础，有效地坚持通过碰撞熔化或双晶/多晶化和融合，以延长初级吸积的碰撞速度范围为$ΔV_c \sim$ 1-100 m s $^{-1}$，这约束湍流RMS速度和巨石大小和小晶粒之间的速度差$\sim$ 1-50 m s $^{-1}$。因此，当吸入的米大小的物体在这种高速碰撞融合状态下与较小的粒子碰撞时，它们迅速增长到千米级，因此在光蒸发风清除源物质盘之前的$^5$ $\sim$ 10年内进入稳定的开普勒轨道。
More than a half of asteroids in the main belt have irregular shapes with the ratios of the minor to major axis lengths less than 0.6. One of the mechanisms to create such shapes is collisions between asteroids. The relationship between shapes of collisional outcomes and impact conditions such as impact velocities may provide information on the collisional environments and its evolutionary stages when those asteroids are created. In this study, we perform numerical simulations of collisional destruction of asteroids with radii 50 km and subsequent gravitational reaccumulation using Smoothed Pa…
By performing $N$-body simulations, we investigated fundamental processes of collisions between dust aggregates composed of submicron-sized icy dust monomers. We examined the mass distribution of fragments in the collisional outcomes in a wide range of the mass ratio and the collision velocity between colliding dust aggregates. We derived analytic expressions of the mass distribution of large remnants and small fragments by numerical fitting to the simulation results. Our analytic formulae for masses of the large remnants can reproduce the contribution of mass transfer from a large target to a…
Context. Following the first discovery of a planet orbiting a giant star in 2002, we started the CORALIE radial-velocity search for companions around evolved stars (CASCADES). We present the observations of three stars conducted at the 1.2 m Leonard Euler Swiss telescope at La Silla Observatory, Chile, using the CORALIE spectrograph. Aims. We aim to detect planetary companions to intermediate-mass G- and K- type evolved stars and perform a statistical analysis of this population. We searched for new planetary systems around the stars HD22532 (TIC 200851704), HD64121 (TIC 264770836), and HD6912…
Millimetre continuum observations of debris discs can provide insights into the physical and dynamical properties of the unseen planetesimals that these discs host. The material properties and collisional models of planetesimals leave their signature on the grain size distribution, which can be traced through the millimetre spectral index. We present 8.8 mm observations of the debris discs HD 48370, CPD 72 2713, HD 131488, and HD 32297 using the Australian Telescope Compact Array (ATCA) as part of the PLanetesimals Around TYpicalPre-main seqUence Stars (PLATYPUS) survey. We detect all four tar…
