On the Stability of a Five-body Planetary System Embedded in the

1
On the Stability of a Five-body Planetary System
Embedded in the ß Pictoris Debris Disk

• Jared H. Crossley
• Mentor Nader Haghighipour

2
Talk Outline

• Motivating observation
• 5-body problem Stability and Implementation
• Two simulations in detail
• Statistical analysis of all simulations
• Conclusions
• Future Work

3
ß Pictoris a motivating observation
Ring Radius (AU) i (degrees)
A 14 1 -32 2
B 28 3 25 2
C 52 2 -2 2
D 82 2 2 1
Wahhaj et al. (2003) suggest that symmetric disk
warps evidence the presence of planets
4
How might a 5-body system like that proposed by
Wahhaj et al. behave?
The basic 5-body system

• Five gravitationally interacting bodies
• The initial position and velocity of each body is
  specified
• The computer then integrates the motion of these
  bodies over time

5
System Stability
A system is classified as stable if no planet
meets the following criteria

1. Collides with central star
2. Orbital radius gt 1000 AU
3. Orbital eccentricity gt 1

6
Implementing the simulation

• Planet mass and orbital phase are chosen
  randomly mass is constrained to

1. Orbital radius
2. Orbital inclination
3. Mass
4. Orbital Phase
5. Eccentricity

7
Example Simulation 1
Planet Mass (MJ) Initial phase (degrees)
1 2.79 0
2 2.50 325
3 1.62 45
4 1.98 121
8
Example Simulation 2
Planet Mass (MJ) Initial phase (degrees)
1 1.63 0
2 1.93 164
3 1.51 215
4 1.85 43
9
Stability Data
Total simulations 20 457 Unique Simulations 14
409
10
Stable system parameter analysis
11
Conclusions

• Simulations have been run for 14 000 unique
  5-body systems like that possibly embedded in the
  ß Pictoris disk
• 6.8 percent of systems remain stable for
• 20 Myr (age of ß Pictoris)
• There do exist systems that remain stable, even
  for 50 million years

12
Future work

• Extract 6 000 duplicate simulations from data set
• Further analyze parameters of all stable systems
• Run additional simulations
• use alternative integration methods
• Explore the region of measurement uncertainty

13
Stability Data
Total simulations 20 463 Unique Simulations 14
415
Time (Myr) of systems stable
10 40.92
20 6.80
30 1.17
40 0.22
50 0.07
of planets ejected of systems
0 14
1 2 117
2 11 538
3 6 727
4 67
14
Analysis of Stability