Spiral patterns in planetesimal circumbinary disks

Planet formation scenarios and the observed planetary dynamics in binaries pose a number of theoretical challenges, especially in what concerns circumbinary planetary systems. We explore the dynamical stirring of a planetesimal circumbinary disk in the epoch when the gas component disappears. For this purpose, following theoretical approaches by Heppenheimer (1978) and Moriwaki and Nakagawa (2004), we develop a secular theory for the dynamics of planetesimals in circumbinary disks. If the binary is eccentric and its components have unequal masses, a spiral density wave is generated, engulfing the disk on the secular timescale, which may exceed 10^7 yr, depending on the problem parameters. The spiral pattern is transient; thus, its observed presence may betray system's young age. We explore the pattern both analytically and in numerical experiments. The derived analytical spiral is a modified lituus; it matches the numerical density wave in the gas-free case perfectly. Using the SPH scheme, we explore the effect of residual gas on the wave propagation.