Spiral structure when setting up pericentre glow: possible giant planets at hundreds of AU in the HD 141569 disk

This paper discusses the impact of introducing a planet on an eccentric orbit into a dynamically cold planetesimal disk. That planet's secular perturbations cause the orbits of the planetesimals to evolve in such a way that at any one time planetesimals at the same distance from the star have common pericentres and eccentricities. This causes the surface density distribution of an extended planetesimal disk to exhibit two spirals, one exterior the other interior to the planet's orbit. These two spirals unwind in different directions and their structure is described by just two parameters: the time since the planet was introduced relative to the characteristic secular timescale, t(sec(3: 2)) = 0.651 root a(pl)(3)/ M-star(M-star/M-pl); and the planet's eccentricity, e(pl). At late times the spirals become tightly wound and the offset centre of symmetry of the pericentre glow approximation is recovered. Comparison with spiral structure seen in the HD 141569 disk shows that its spiral at 325 AU is similar to the structure that would be caused by introducing a planet into the disk 5 Myr ago with a mass in the range 0.2- 2 M-Jup orbiting at 235 - 250 AU with an eccentricity of 0.05 - 0.2; likewise a Saturn mass planet at 150 AU would cause structure like that seen at 200 AU. More definitive statements about any planets orbiting HD 141569 from this model could be made once the effect of the binary companion on the disk is known ( e. g., from knowledge of its orbit), and once the disk's structure has been better characterised down to 100 AU, including the location of the star within the disk. The relatively young age of this system (similar to 5 Myr) means that if giant planets really do exist at hundreds of AU from HD 141569, this provides a unique opportunity to set constraints on the mechanism by which those planets came to be at such large distances, especially since the structure of the disk out of which those planets would have formed can be imaged.