1. On the Stability of a Five-body Planetary System Embedded in the β 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. β Pictoris – a motivating observation RingRadius (AU) i (degrees) A14 ± 1-32 ± 2 B28 ± 3+25 ± 2 C52 ± 2-2 ± 2 D82 ± 2+2 ± 1 Wahhaj et al. (2003) suggest that symmetric disk warps evidence the presence of planets

4. 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 How might a 5-body system like that proposed by Wahhaj et al. behave? The basic 5-body system…

5. System Stability 1.Collides with central star 2.Orbital radius > 1000 AU 3.Orbital eccentricity > 1 A system is classified as stable if no planet meets the following criteria:

6. Implementing the simulation 1.Orbital radius 2.Orbital inclination 3.Mass 4.Orbital Phase 5.Eccentricity Planet mass and orbital phase are chosen randomly; mass is constrained to For simplicity, assume orbits begin circular Planet Parameters 1.Mass 2.Position 3.Velocity

7. Example Simulation 1 Planet # Mass (M J ) Initial phase (degrees) 12.790 22.50325 31.6245 41.98121

8. Example Simulation 2 Planet # Mass (M J ) Initial phase (degrees) 11.630 21.93164 31.51215 41.8543

9. Stability Data Total simulations: 20 457Unique 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 β Pictoris disk 6.8 percent of systems remain stable for 20 Myr (age of β 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 Time (Myr) % of systems stable 1040.92 206.80 301.17 400.22 500.07 # of planets ejected # of systems 014 12 117 211 538 36 727 467 Total simulations: 20 463Unique Simulations: 14 415

14. Analysis of Stability