Planet Formation in Binaries

Planets have been observed both around stars with a nearby companion, and in circumbinary orbits around tight binary stars. Theories of planet formation must be able to account for the presence of planets in such systems. A commonly held viewpoint is that rocky planets, and also the cores of giant planets, form from small building blocks called planetesimals. These planetesimals collide with one another in a gaseous disk, and stick together to form larger bodies.

In binary systems, the gravitational perturbations from the companion star excite eccentricity in the orbits of these planetesimals. This results in high-velocity collisions which lead to destruction, rather than growth. This effect is mediated by the role of gas drag, which tends to apsidally align planetesimals of similar sizes, thus reducing their collision velocities. The plot on the right shows the collision velocity as a function of collision size at a particular location in a model disk around the primary star in the γ-Cephei system. Planetesimals of dissimilar sizes have large collision velocities. Planetesimals of the same size follow apsidally aligned orbits, and therefore collide at low velocity. Regions of parameter space leading to erosion and destruction of planetesimals are outlined in the dotted and solid contours. These are calculated using the model for solid planetesimals in Stewart & Leinhardt (2009).

Collision velocities between planetesimals as a function of their size. Regions in the space of collision partner sizes corresponding to destruction are outlined in solid contours, and those corresponding to erosion are outlined in dashed contours.

The size of the initial planetesimals is not known. Using the collision outcomes we calculated, we ran a coagulation simulation to determine whether planet sized bodies can form. Because larger planetesimals are more resistant to fragmentation, if one starts with sufficiently large planetesimals, further growth will not be hindered by fragmentation. By varying the starting size of the planetesimals, we determined the critical size such that large bodies form. The figure below shows this size as a function of disk parameters. In each panel, one parameter is varied. The others are held at their fiducial values which are circled in red.