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A Detailed Comparison of Simulations of Neptune s Migration to Observations of the Kuiper Belt Joseph M Hahn Renu Malhotra Saint Mary s University Institute for Computational Astrophysics University of Arizona 1 Examine the consequences of conventional planet migration use Mercury integrator Chambers 1999 to evolve 4 giant planets 104 massless particles over Solar Age external torques drive smooth planet migration aNep 9 AU over 107 yr timescale resonances sweep outwards capture KBOs in eccentric orbits 2 Simulated Observed Endstates Neptune s advancing res s traps particles black dots at resonances Note observed Main Belt KBOs red dots have e 0 1 sim adopts initial e0 0 1 allows trapping at exotic res s 13 7 9 4 5 2 3 1 7 2 Chiang et al 2003 could account for KBOs 5 2 3 The Scattered Disk perhaps not so scattered sim shows that trapping 9 4 7 3 5 2 3 1 promotes particles into Scattered Disk 30 q 40 AU suggests the real Scattered Disk might also contains trapped particles inspect particles in gray box 90 of survivors are res trapped particles only 10 of survivors were scattered by Neptune this suggests that the so called Scattered Disk might be composed mostly of resonantly trapped particles that never came close to Neptune 4 Use Monte Carlo methods to infer the abundance of KBOs replicate each Nbody survivor 104 times assign radii R according to bright end mag 24 of KBO size distribution from Bernstein et al 2004 cumulative size distribution N R R Q Q 4 4 or Q 5 0 88 Note plot of relative KBO abundances are insensitive telescopic selection effects 2 1 MB ratios the observed 2 1 is depleted by factor 20 relative to model Ditto for 3 2 5 same MC method yields relative abundance of other KBO sub populations eg SD Centaurs Neptune Trojans etc fitting the model s luminosity function to observed yields total KBO population N 1 7 105 KBOs having radii R 50 km mass M 0 08 M assuming albedo 0 04 or M 0 02 M if albedo 0 1 KBO Census according to Nbody MC model Population N R

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