Improving Swift

1
Improving Swift

• David Kaufmann (SwRI)
• Hal Levison, PI (SwRI)
• Martin Duncan (Queens University)
• Mark Lewis (Trinity University)

2
What is Swift?

• Software package for simulating planetary system
  dynamics
• Developed by PI Levison and Co-I Duncan
• Most important integrators are
• Wisdom-Holman Mapping (WHM)
• Regularized Mixed Variable Symplectic (RMVS)
  Algorithm
• Symplectic Massive Body Algorithm (SyMBA)

3
Project Goals and Status
4
Symplectic Integrators

• Derived from a Hamiltonian, H(p,q,t)
• Divide Hamiltonian into pieces, HHAHB
• Piecewise evolution equivalent to that under a
  surrogate Hamiltonian, HHAHBHerr
• Gravitational N-body problem

5
Symplectic Tree Code

• The major bottleneck in current symplectic codes
  is the O(N2) interaction term
• Symplectic tree code requirements
• Preserve a surrogate Hamiltonian
• Scale better than O(N2)
• Prototype code combines elements of nested grids
  and traditional tree codes

6
Symplectic Tree Code
Level 0 (root)
7
Symplectic Tree Code
Level 1
8
Symplectic Tree Code
Level 2
9
Symplectic Tree Code
Level 3
10
Symplectic Tree Code
Recursive_Interaction_Check(Node n1, Node n2,
real theta) if (n1 is empty) or (n2 is empty)
then return if (n1 is a leaf) or (distance(n1,
n2) gt (size of n1)/theta) then interact n1 and
n2 else loop c1 over children of n1 loop c2
over children of n2 Recursive_Interaction_Chec
k(c1, c2, theta) End
11
Symplectic Tree Code
12
Symplectic Tree Code
13
Recent Science Using Swift

• Current theories of planet formation have
  difficulty accounting for
• the eccentricities and mutual inclinations of the
  giant planets
• the inclinations of Jupiters Trojan asteroids
• the Late Heavy Bombardment
• Can be explained by an early passage of Jupiter
  and Saturn through their 12 MMR

14
Recent Science Using Swift
15
Recent Science Using Swift
16
Recent Science Using Swift
17
Recent Science Using Swift
18
Recent Science Using Swift
19
Recent Science Using Swift

• Tsiganis K., Gomes R., Morbidelli A., and Levison
  H.F. Origin of the orbital architecture of the
  Giant Planets of the Solar System, Nature, xxx
  (2005)
• Morbidelli A., Levison H.F., Tsiganis K., and
  Gomes R. The chaotic capture of Jovian Trojan
  asteroids during the early dynamical evolution of
  the Solar System, Nature, xxx (2005)
• Gomes R., Levison H.F., Tsiganis K., and
  Morbidelli A. Origin of the Cataclysmic Late
  Heavy Bombardment of the Terrestrial Planets,
  Nature, xxx (2005)