During the formation of terrestrial planets, large rocky bodies orbiting around a star occasionally get close enough to interact with one another. If two bodies collide head on or obliquely, the result is that the two bodies merge to form a larger one, perhaps leaving behind a disk of debris from which a moon can form. This is the standard picture for how Earth got its moon and a possible explanation for Pluto's moon, Charon.
If the two bodies collide in a grazing manner but at high velocity, then the two bodies "hit and run" bouncing off each other initially and separating, failing to form a bound pair. The research presented searched for a middle ground -- a scenario in which the interaction results in two large bodies that do not merge but still remain locked in orbit.
To test for this possibility, a simulation technique called Smoothed Particle Hydrodynamics (SPH) was utilized. Smoothed Particle Hydrodynamics represents a body as a collection of tens of thousands of particles.
Using SPH, collisions between two rocky Earth-sized bodies were simulated, with impact velocity and impact parameter (a measure of how head-on a collision is) being varied and the output observed. In the cases where the bodies underwent substantial collision, the scientists replicated previous results in which a binary system did not arise but a moon might form. However, by including interactions where the bodies are close enough to undergo a large tidal distortion, initial conditions were found that led to a terrestrial binary planetary system.
Despite the specialized computer hardware used to speed up the calculations, each simulation still took up to a week to run. Using SPH during these stretches was unnecessary and time consuming. To combat this, a novel method was introduced to the SPH code which dynamically switched between modeling methods, cutting simulation time down to as little as a day.
With the simulation time long but manageable, the input space was mapped out. Some pairs of impact parameter and impact velocity led to accretion, some led to escape, and some even led to binary systems. Point by point the boundaries between these outcomes began to appear, eventually creating a map of the input space which would give rise to a binary system.
Binary asteroids are well established, and systems that have merged to become dumbbells or other shapes have also been detected. Binary stars are also very common. However, binary (or double) planets involving large bodies have only figured in science fiction until now.