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post-collision phase - Coggle Diagram
post-collision phase
tidal damping strength (assuming strong damping on c)
strong damping
comment
we didn't focus on this scenario after finding that weak damping is more plausible; so we didn't simulate the successful rate under different circumstances, i.e., massive d or not massive d, large or small perturbation on d
result classification
b, c and e go into 0th order 3BR (<10%)
b, c and e goes into 1st order resonance (>50%)
other (not in resonance)
weak damping
large perturbation on d2 in pre-collision phase(>2%)
results classification
other (~80%, need longer simulation)
b, c and e oscillate around 0th 3BR (<20%); we showed that the 3BR angle can liberate later by speeding up the simulation
comment
large perturbation is not natural in reality so we didn't focus on this and 20% is good enough
;
longer simulation is need if we want to see whether other non-successful scenario can turn into successful
; mass of d doesn't affect this scenario so much
small perturbation on d2 in pre-collision phase(1-2%)
not massive planet d (9 Earth mass)
result classification
b, c and e crosses 0th order resonance position (~50%)
other (need longer simulation)
b, c and e go into 0th order 3BR (~5%)
comment1
in this scenario simulations will not separate into 0th order and 1st order at first; instead some of simulations period ratio will oscillate to the left of 0th 3BR line, which we call "half-successful";
we therefore run long simulations to see what happened to these cases
massive planet d (18 Earth mass)
almost impossible to reform b, c and e 0th order resonance
comment2
what we actually achieved in this simulation is:
we found that it's possible to reform 0th order 3BR even with small perturbation in pre-collision phase
tiny perturbation on d2(2%)
it was not successful because d1 and d2 won't collide if perturbation is too tiny in pre-collision phase
tidal damping strength ratio
same Q are all planets
impossible to reform b, c and e resonance
strong damping on c
can reform b, c and e 0th order resonance in some scenarios
eccentricty (large e need further investigation)