Mars Growth Stunted by an Early Orbital Instability between the Giant Planets M.S. Clement University of Oklahoma Advisor: Professor N.A. Kaib Collaborators: S.N. Raymond, K.J. Walsh 19 September 2017
My Past Life
Studying Planetary Dynamics with N- Body Integrators Two Bodies: Can be solved exactly. Many Bodies: Approximations: Circularly Restricted 3 Body. Computer Integration: Midpoint Method. Euler Method. Leapfrog Method
Complications Integration Time: Solar System formed from millions of small bodies colliding over Myr- Gyr timescales. Close Encounters: Approximations such as circularly restrictive 3-body break down during close encounters. Collisional Fragmentation: What happens when things collide. Energy and Momentum conservation: How much error is acceptable? Relativity: ~2 degrees/century precession in Mercury s orbit. Images: nasa.gov
Solutions Hamiltonian Splitting: Symplectic Integration scheme. Split Hamiltonian into a purely Keplerian and an Interaction component. Switch integration schemes for close encounters. Perturbative methods to handle relativity. Map parameter space for collisions: Perfectly accretionary. Erosive. Hit and Run. Hit and re-accrete. Figure: Chambers, 1999
The Evolution of the Outer Solar System AFTER dissipation of gas and dust in the primordial disk. Saturn, Uranus and Neptune interact with the primordial Kuiper Belt. Scatter Objects inward. Fernandez and Ip (1984). Jupiter interacts with these scattered objects: Ejects them from the Solar System. Over time, Jupiter s Orbit moves in and Saturn s moves out. Cross a 2:1 (3:2) MMR and destabilizes the entire system. Figure: Gomes et al (2005)
Levison et al, 2008
Small Mars Problem Images: nasa.gov Mars analogues are rare in embryo accretion models, Mercurys are almost non-existent. (Chambers and Wetherill 1998; Chambers, 2001; O Brien et al, 2006; Raymond et al, 2009) Possible Solutions: Extra Eccentric Jupiter and Saturn (Raymond et al, 2009) 0.7-1.0 AU annulus (Hansen, 2009) Grand Tack Model (Walsh et al, 2011) Local Depletion (Izidoro et al, 2015)
Mars Formed
Mars Formed
Control
Planets Formed
Summary/Future Work An early instability significantly REDUCES the MASS of MARS ANALOGUES. When the instability occurs ~1-10 Myr after gas disk dispersal: Mars is left behind as a stranded embryo. Significant amount of material from > 2 AU is scattered towards the forming Earth. BLUE WATERS: Include Collisional Fragmentation. Could Mercury be formed by a high velocity impact with Venus? Thoroughly investigate consequences for the Asteroid Belt.
Questions
Motivation for an Early Instability Timing of instability dependent on initial disk properties (Gomes et al, 2005). Difficult for terrestrial planets to survive a late instability (Brasser et al, 2009, Kaib & Chambers, 2016). Projectile size distribution for a late instability different than observed (Morbidelli et al, 2017). Self Interacting Disks unlikely to last 400 Myr (Quarles & Kaib, in prep). New lunar data from LRO and better dating of samples. (Zeller et al, 2017) Fassett and Minton (2012)
How would an early instability affect the forming Terrestrial Planets? Integrate a resonant configuration of Giant Planets right up to the instability: 3:2 3:2 3:2 3:2 Evolve the terrestrial planets, take snapshots of the system at 104,105,106 and 107 yrs: 3:2 Imbed the forming terrestrial planets in the instability and integrate for 200 Myr:
Simulation Parameters Mercury6 Hybrid Integrator, 6.0 day time-step (Chambers, 1999). Inner Disk: 100 embryos/1000 planetesimals/ r -3/2 surface density profile: Outer Disk: 1000 bodies/ r -1 surface density profile (Nesvorny & Morbidelli, 2012):
Results 70.9% of all Mars analogues formed small. 38.9% of systems form no Mars (82% no or small). Most successful when instability is delayed 10 Myr in to terrestrial planetary formation: 20% correct architecture of inner planets. 25% form Mars in less than 15 Myr. 95% form Earth in greater than 50 Myr. 39% leave behind an Asteroid Belt with no Embryos. 83% sufficiently deliver volatiles to Earth.
Planets Formed
Earliest Instabilities and Collisional Fragmentation The earliest instabilities we look at often look nothing like the solar system: No Mars. Only one planet. All planets too small. System s with the most violent instabilities are most likely to finish with a few small, or no terrestrial planets. Collisional Fragmentation can play a large role in embryo accretion and must be accounted for (Chambers, 2013). Collisional velocities in our runs are LOW for Earth and Mars analogues and HIGH for Venus analogues.