Problem set 4Ge/Ay 133Due 03 November 20111Gaps and migration(a) Large planets open gaps in disks and then become tied to the evolution of the disk. Thus,if the disk is evolving on the viscous timescale, the planet will also migrate on the viscoustimescale. Based on the viscous disk evolution timescale discussed in class, write an approximateexpression for the speed of the migration for a giant planet which has formed a gap.(b) Assume that every planetary system forms planets at 5 AU and then these planets migrateinwards on the viscous timescale. Then, at some random time, the gas in the disk instantlydisappears (halting migration). If this happens in a huge set of planetary systems, what dis-tribution of semi-major axes might you expect to observe in planetary systems? (You can tryyour own simulation, or else create a sketch of what you think it will look like.)(c) Compare this predicted distribution to that of extrasolar planets. Be sure to consider the(severe) biases in the discoveries of extrasolar planets. You can make your own up-to-date plot
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