Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct highresolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation.Collision outcomes are described in terms of the impact conditions and the catastrophic disruption criteria, Q * RD -the specific energy required to disperse half the total colliding mass. All planet formation and collisional evolution studies have assumed that catastrophic disruption follows pure energy scaling; however, we find that catastrophic disruption follows nearly pure momentum scaling. As a result, Q * RD is strongly dependent on the impact velocity and projectile-to-target mass ratio in addition to the total mass and impact angle. To account for the impact angle, we derive the interacting mass fraction of the projectile; the outcome of a collision is dependent on the kinetic energy of the interacting mass rather than the kinetic energy of the total mass. We also introduce a new material parameter, c * , that defines the catastrophic disruption criteria between equal-mass bodies in units of the specific gravitational binding energy. For a diverse range of planetesimal compositions and internal structures, c * has a value of 5 ± 2; whereas for strengthless planets, we find c * = 1.9 ± 0.3. We refer to the catastrophic disruption criteria for equal-mass bodies as the principal disruption curve, which is used as the reference value in the calculation of Q * RD for any collision scenario. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution.

The resistance of planetesimals to collisional erosion changes dramatically during planet formation. The transition between accretion and erosion from a collision is defined by the relationship between the mass of the largest remnant (M lr) and the normalized specific impact energy (Q/Q * D), where Q * D are the size-dependent catastrophic disruption criteria (the Q required to disperse half the target mass). Here, we calculate Q * D for gravitationally bound aggregates subject to low-velocity collisions (1-300 m s −1) and compare the results to previous work at high velocities. We find that Q * D varies by orders of magnitude depending on the impact velocity and material properties. We define new variables to describe catastrophic disruption that remove ambiguities (over material density and projectile-totarget mass ratio) that are inherent in the traditional variables (Q and target radius): R C1 is the spherical radius of the combined projectile and target masses (M tot) at a density of 1 g cm −3 , Q R is 0.5μV 2 i /M tot (μ is the reduced mass and V i is the impact velocity), and Q * RD is the Q R required to disperse half the combined mass. We derive a universal law for the largest remnant, M lr /M tot = −0.5(Q R /Q * RD − 1) + 0.5, and velocity-dependent catastrophic disruption criteria for strong and weak planetesimals for use in numerical studies of planet formation. Weak aggregate bodies are easily disrupted due to efficient momentum coupling during low-velocity collisions. Collisional growth of planetesimals requires a dynamically cold environment; alternatively, a noncollisional mechanism is required to form planetesimals large enough to be resistant to collisional disruption (several tens of kilometers).

ABSTRACT25-50 per cent of all white dwarfs (WDs) host observable and dynamically active remnant planetary systems based on the presence of close-in circumstellar dust and gas and photospheric metal pollution. Currently accepted theoretical explanations for the origin of this matter include asteroids that survive the star's giant branch evolution at au-scale distances and are subsequently perturbed on to WD-grazing orbits following stellar mass-loss. In this work, we investigate the tidal disruption of these highly eccentric (e > 0.98) asteroids as they approach and tidally disrupt around the WD. We analytically compute the disruption time-scale and compare the result with fully self-consistent numerical simulations of rubble piles by using the N-body code PKDGRAV. We find that this time-scale is highly dependent on the orbit's pericentre and largely independent of its semimajor axis. We establish that spherical asteroids readily break up and form highly eccentric collisionless rings, which do not accrete on to the WD without additional forces such as radiation or sublimation. This finding highlights the critical importance of such forces in the physics of WD planetary systems.

The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High‐energy, high‐angular‐momentum giant impacts can create a post‐impact structure that exceeds the corotation limit, which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super‐corotation‐limit body, traditional definitions of mantle, atmosphere, and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic, and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with bulk silicate Earth vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon‐forming synestia. Giant impacts that produce potential Moon‐forming synestias were common at the end of terrestrial planet formation.

The outcome of collisions between small icy bodies, such as Kuiper belt objects, is poorly understood and yet a critical component of the evolution of the trans-Neptunian region. The expected physical properties of outer solar system materials (high porosity, mixed ice-rock composition, and low material strength) pose significant computational challenges. We present results from catastrophic small body collisions using a new hybrid hydrocode to N -body code computational technique. This method allows detailed modeling of shock propagation and material modification as well as gravitational reaccumulation. Here, we consider a wide range of material strengths to span the possible range of Kuiper belt objects. We find that the shear strength of the target is important in determining the collision outcome for 2 to 50-km radius bodies, which are traditionally thought to be in a pure gravity regime. The catastrophic disruption and dispersal criteria, Q * D , can vary by up to a factor of three between strong crystalline and weak aggregate materials. The material within the largest reaccumulated remnants experiences a wide range of shock pressures. The dispersal and reaccumulation process results in the material on the surfaces of the largest remnants having experienced a wider range of shock pressures compared to material in the interior. Hence, depending on the initial structure and composition, the surface materials on large, reaccumulated bodies in the outer solar system may exhibit complex spectral and albedo variations. Finally, we present revised catastrophic disruption criteria for a range of impact velocities and material strengths for outer solar system bodies.