A Pretty Nice Model. Grace Telford Brett Morris

Transcription

1 A Pretty Nice Model Grace Telford Brett Morris

2 Nice Model v1.0 Outline Levison et al. 2005, Morbidelli et al. 2005, Gomes et al Issues with v1.0 and their solutions Morbidelli et al Nice Model v2.0 Levison et al Follow ups and extensions to v2.0

3 Elusive Questions in 2005 Explain the bulk orbital properties of the planets Did the planets form in the disk where they are observed today? What was the Late Heavy Bombardment that we have evidence for in the inner Solar System? Why did it happen so late? Why are the orbits of Jupiter s Trojans excited?

4 The Nice Model (2005) Jupiter Saturn Uranus Neptune Basic idea: Jupiter & Saturn crossed 1:2 Mean Motion Resonance (MMR) and caused the solar system to rearrange

5 Before MMR crossing Ice I J S Ice II Ice I After MMR crossing J S Ice II Gomes et al. 2005

6 Simulations Planets in compact configuration; P S /P J < 2 Varied ice giant semi-major axes, M disk, N disk M E planetesimal disk just outside ice giant orbits Hot and cold Dynamical evolution simulated with N-body codes 43 systems

7 Typical evolution Jupiter moves inward, other giants move out Jupiter and Saturn cross 1:2 MMR after several hundred Myr Compact system à chaotic orbits Ice giants scatter outward into disk Giants migrate rapidly until disk depleted

8 Resonance Crossing Since Uranus and Neptune may swap orbits, they are referred to as Ice I and Ice II Tsiganis et al. 2005

9 Outcomes Saturn < 3 AU from Ice I à Ice I ejected (14 runs) Of successful runs: Class A: no encounters between ice and gas giants (15 runs) Class B: encounters between Saturn and one or both ice giants (14 runs)

10 Class B runs, where Saturn has a close encounter with an ice giant, best reproduce the orbits of the outer planets Black open circles: class B Grey open circles: class A Tsiganis et al. 2005

11 Notes on Nice Model Simulations Separation between Jupiter and Saturn dependent on initial mass of planetesimal disk Eccentricities depend on hotness of disk Can only excite all orbits when Jupiter and Saturn 1:2 MMR crossed

12 v1.0 Successes Reasonable probability of reproducing current giant planet orbits 8 simulations tested survivability of satellites All satellites survive 50% of time Some disk particles trapped in orbits like those of Neptune s Trojans Companion papers: LHB, Jupiter s Trojans

13 Late Heavy Bombardment Spike in cratering rate ~700 Myr after planets formed Nice Model of rapid giant planet migration naturally accounts for: Flux of planetesimals Late timing of the event (we ll show this in v2.0)

14 Late Heavy Bombardment Both planetesimal disk and asteroid belt perturbed In-scattered material may be important for volatile delivery to the Earth The Oort Cloud forms naturally from the outwardscattered disk

15 Planetary interactions probably did not cause significant migration before solar nebula dissipated A disk that has lifetime longer than that of nebula leads to LHB ~1 Gyr after planet formation Gomes et al. 2005

16 Simulate scattered planetesimals that impact the moon Total amount of material consistent with estimates from observations This happens in all 8 simulations Ice I Ice II S J Gomes et al. 2005

17 Jupiter s Trojans Previously thought that Trojans formed with Jupiter in current locations Issue: Distribution of inclinations observed is broader than you would expect for coevolution

18 Nice model to the rescue! During migration, scattered planetesimals captured into transient Trojan orbits Once planets reach stable configuration, any bodies that happen to be in those orbits would remain there Gomes et al. 2005

19 Bottom plot: fraction of Trojans at each time that survive for 2x10 5 yrs All original Trojans before MMR crossing are emptied Morbidelli et al. 2005

20 Captured Trojans Two simulation sets, different migration speeds Find that 4x10-6 3x10-5 M E of particles trapped in Trojan region when orbits stabilize Consistent with observed mass: 1.1x10-5 M E Many simulated Nice Model Trojans were on high e orbits at some point, with 68% coming within 2 AU of Sun Observations show Trojans may be depleted of volatiles

21 Morbidelli et al Grey dots: Observed Black circles: Simulated

22 Nice Model Explains Many Observational Constraints Only model that naturally explains: Orbital properties of planets Late Heavy Bombardment Jupiter s and Neptune s Trojan asteroids BUT it isn t perfect

23 Issue #1 Original model doesn t account for interactions within the disk Likely contained ~1000 Pluto mass planetesimals computational challenge Viscous stirring would excite eccentricities, more effectively causing interactions with planets Could be harder to delay onset of LHB for ~700 Myr

24 Issue #2 Ad hoc choice of initial giant planet orbits No reliable predictions available at the time Assumed circular orbits with P Saturn /P Jupiter < 2 Initial conditions fine-tuned to produce 1:2 MMR crossing around time of LHB To be consistent, disk edge must be between AU à fine tuning

25 Morbidelli et al. (2007) studied evolution of 4 giant planets in gas disk Found that planets naturally evolve to quadruple MMR state Identified 4 configurations stable for > 1 Gyr after gas dissipated Solution Morbidelli et al. 2007

26 Nice Model v2.0 (2011) New initial orbital configurations informed by gas disk models (Morbidelli et al. 2007) Planets become locked in quadruple MMR Inner ice giant has a larger eccentricity than other giants: e Ice I ~0.05 vs. e others ~0.01 This drives the energy exchange between planetesimal disk and planets Eliminates fine-tuning problems with planetesimal disk inner edge Discover new energy exchange mechanism for triggering instability Morbidelli et al. 2007

27 Simulations 50 M E planetesimal disk with ~1500 particles Surface density goes as 1/r Vary disk inner edge r in à does it affect LHB timing? N-body integration with SyMBA Include viscous stirring - gravitational interactions between disk particles

28 Nice v2.0 Simulation shows slow transfer of energy between the planetesimal disk and giant planets what s the cause? Levison et al. 2011

29 de dt What s driving? planets Levison et al Saturates N p ~ 500 Set N p = 1000, planets crossing MMRs with planetesimal disk would cause jumps. No jumps seen à MMRs not responsible for energy exchange between planets and disk

30 de dt What s driving? MMRs are not responsible so what else is changing? Eccentricity of Ice I increases whether or not Ice II is in the simulation planets

31 de dt What s driving? planets Previously though that close encounters between Ice II and the disk would dominate energy exchange Levison et al. 2011

32 de dt What s driving? planets Previously though that close encounters between Ice II and the disk would dominate energy exchange Thus, in order for Ice I to play a decisive role, the dynamical mechanism responsible for the coupling must be a strong function of the eccentricity. Given the results thus far, we can infer that the observed energy exchange is related to secular interactions between the planets and the disk. Levison et al. 2011

33 Secular interactions between disk and high-e inner ice giant de dt proportional to M Ice I *M disk planets de dt What s driving? planets Ice I would migrate inward but MMRs halt a, increase e instead For some systems e is damped by giant planets If e increases faster than damping, secular interactions grow and e continues to increase Ice I e grows large enough to throw 25% of multiresonant systems unstable in <1 Gyr

34 Secular interactions between disk and high-e inner ice giant de dt proportional to M Ice I *M disk planets de dt What s driving? planets Ice I would migrate inward but MMRs halt a, increase e instead For some systems e is damped by giant planets If e increases faster than damping, secular interactions grow and e continues to increase Ice I e grows large enough to throw 25% of multiresonant systems unstable in <1 Gyr

35 Surprise! Dynamical lifetime NOT monotonic with r in 75% of systems never leave multi-resonant state Unstable system median lifetime ~730 Myr LHB timing is a natural consequence Levison et al. 2011

36 Can Nice II explain SS Architecture? Gas disk sets initial orbits (generic!) Eccentricity of Ice I mediates energy exchange with disk (generic!) 25% of disks go unstable Instability time commensurate with LHB (generic!) Not strongly dependent on r in (generic!)

37 </Nice II standard canon> <Follow Ups And Extensions>

38 Other Initial Configurations Ejected 5 th outer planet? Could get ejected during scattering Microlensing Observations in Astrophysics, Sumi et al We report the discovery of a population of unbound or distant Jupiter-mass objects, which are almost twice as common as mainsequence stars Planet mass objects: t E < 2 days Sumi et al. 2013

39 Five Planet Simulations N-body simulations 4 and 5 planet configurations Initially multi-resonant orbits New ice giant mass between 1/3 3M Uranus Nesvorny 2011

40 Results: 5 Planets = Maybe 5 planet configurations better reproduce SS 4 planet initial configurations ~10% end up with 4 planets 3% of runs produce systems matching current SS 5 planet initial configurations 37% end up with 4 planets 23% match observational constraints Nesvorny 2011 Triangle: real planet Dots: sim. planets

41 What about the terrestrial planets? Can inner planets survive such a violent instability? How would dynamics of inner planets be changed? Brasser et al. (2013) attempt to constrain primordial terrestrial planet orbits using Nice model

42 Results Nice-like simulations significantly alter the angular momentum deficit (AMD) of terrestrial planets When you hear AMD, think difference from coplanarity and from e = 0 To reproduce observed AMD, need to have little migration in Jupiter/Saturn after MMR crossing More probable when starting with 5 giant planets

43 Primordial Terrestrial Planet Orbits To reproduce terrestrial orbits with probability ~ 20%, primordial AMD < 70% current value (orbits start more circular, lower inclinations) Inner 3 planets were excited more than Mars by giant planet migration Currently AMD roughly equally split Original inner three orbits were circular and coplanar Mars current orbit original orbit Terrestrial orbits best reproduced with 5 outer planets

44 Do Planets Really Cross MMRs? Kepler Architectures - Lissauer et al Some planets have been found near MMRs Lissauer et al. 2011

45 If you look at the period ratios of planets in Kepler multi-planet systems, there are small piles of planets near first-order MMRs strongest peaks near 1:2 MMR and 2:3 MMR in Kepler data, 1:2 MMR strong in RV data Lissauer et al. 2011

46 Kepler Architectures Most multiple planet candidates are neither in nor very near mean-motion orbital resonances. Nonetheless, such resonances and near resonances are clearly more numerous than would be the case if period ratios were random. Lissauer et al. 2011

47 Final Summary: Did the Nice Model Happen? Model nicely explains many observational constraints of our SS Major limiting probability may be that systems become unstable within 1 Gyr in only ~25% of simulations The probability to exactly reproduce our SS is pretty low but not impossible