A Planetesimal Accretion Zone in a Circumbinary Disk

Abstract

We investigate the conditions for planetesimal accretion in a circumbinary disk. Until recently, it had been believed that only single solar-type stars might harbor planetary systems. On the other hand, circumbinary disks have been detected by infrared or radio observation. Planets may be formed in such disks. Binary systems give stronger gravitational perturbation against planetesimals orbiting nearer to the binary. Therefore, the relative velocities between planetesimals will be larger and when they exceed the escape velocity it is impossible for the planetesimals to accumulate into planets. We performed long-term numerical integrations of binary and planetesimal orbital motions in the framework of the coplanar elliptic restricted three-body problem and have found the upper limit of the orbital radius inside of which the relative velocity between the planetesimals exceeds the escape velocity. One of our results is that planetesimal accretion cannot occur in a zone within 13 AU from the barycenter of the binary system when the binary semimajor axis is 1 AU, the binary eccentricity 0.1, the total mass m1 + m2 = 1 M☉, and the mass ratio m2/(m1 + m2) = 0.2. In regions farther out than 13 AU, planetesimals can accrete. We also derive analytic expressions of the eccentricity of a planetesimal pumped up by the gravitational perturbation of the binary and the inner boundary radius of the planetesimal accretion zone according to the secular perturbation theory.