The Long-Term Evolution of J2/1, J3/2 and J4/3 Resonant Asteroids During Planetary Migration and Beyond

Main results:

  1. The J3/2 and J4/3 populations are destabilized during the 1:2 MMR crossing (both `static' simulations and simulations of migration due to the planetesimal disc confirm this).
  2. Thule might represent a signle remaining planetary embryo (there are no small asteroids in J4/3 except 2001 QG207).
  3. J2/1 and J3/2 ??? populations can be created by the resonance sweeping following AFTER the 1:2 MMR
  4. J2/1 is further destabilised by G.I. vs J2/1 libration resonance, but not all asteroids escape, the J3/2 are stable anyway
  5. The Schubart group in the J3/2 has steeper SFD than the surrounding J3/2 population; there are no apparent groupings in the J2/1, although they would disperse slowly ??? in the resonant elements space.

Questions:

  1. What is the second group in the (a,i) plot of the J3/2?
  2. How many configurations and planetesimal discs shall we try?
  3. How to properly include collisions and YORP to N-body simulations?

    (Adjust collisional rates for the outer MB, use randomly assigned YORP evolution of Gaussian spheres.)

  4. Why there is no sign of a recent impact in the J2/1?
  5. How to model J2/1 vs G.I. period?

    (Lighter hot disc?)


Table of Contents:

  1. Current resonant populations, shifted Saturn and no migration
  2. Current populations (and current Jupiter) with migration due to a planetesimal disc
  3. Cold primordial MBAs and resonance sweeping across 1:2 MMR
  4. Evolution of a Karin-like cluster inside the J2/1 and J3/2
  5. Size-frequency distributions of resonant populations
  6. Yarkovsky assisted escape on a 4 Gyr timescale
  7. What 2DO?
  8. Abstract for the DPS 2006:

Download an Mplayer binary (Linux, i386) to play all the MPEG-4/DivX animations (or see http://www.mplayerhq.hu).

Current resonant populations, shifted Saturn and NO MIGRATION

J2/1

r21-js_lftime.eps

r21-js_loglftime.eps

J3/2

r32-js_lftime.eps

r32-js_loglftime.eps

J4/3

r43-js_lftime.eps

r43-js_loglftime.eps

Trojans

(for comparison)

trojans-js_lftime.eps

trojans-js_loglftime.eps


Current populations (and current Jupiter) with MIGRATION due to a planetesimal disc

J2/1

Jupiter was started at 5.202 AU,

50 ME cold planetesimal disc

j21_pdisc_50ME_cold_I00j_aet.avi

   

j21_pdisc_50ME_cold_I00j_ait.avi

   

j21_pdisc_50ME_cold_I00j_xyt.avi

   

j21_pdisc_50ME_cold_I00j_xzt.avi

   

2DO: 30 ME cold planetesimal disc

2DO: 30 ME hot planetesimal disc

J3/2

j32_pdisc_50ME_cold_I00j_aet.avi

   

j32_pdisc_50ME_cold_I00j_ait.avi

   

2DO: 30 ME cold planetesimal disc

2DO: 30 ME hot planetesimal disc

J4/3

2DO: integrate hundreds of Thule and 2001 QG207 clones

2DO: 30 ME cold planetesimal disc

2DO: 30 ME hot planetesimal disc


Cold primordial MBAs and resonance sweeping across 1:2 MMR

Jupiter was started at 5.45 AU,

50 ME cold planetesimal disc

J2/1

j21_pdisc_50ME_cold_I00_at.eps

j21_pdisc_50ME_cold_I00_at_JS.eps

j21_pdisc_50ME_cold_I00_aet.avi

   

j21_pdisc_50ME_cold_I00_ait.avi

   

j21_pdisc_50ME_cold_I00_xyt.avi

   

j21_pdisc_50ME_cold_I00_xzt.avi

   

J4/3

j43_pdisc_50ME_cold_I00_at.eps

j43_pdisc_50ME_cold_I00_at_JS.eps

j43_pdisc_50ME_cold_I00_aet.avi

   

j43_pdisc_50ME_cold_I00_ait.avi

   

j43_pdisc_50ME_cold_I00_xyt.avi

   

j43_pdisc_50ME_cold_I00_xzt.avi

   

2DO:

J3/2

2DO: different configurations of planets, planetesimal disc masses, ...


Evolution of a Karin-like cluster inside the J2/1 and J3/2

r21_arer_karin.eps

r21_arir_karin.eps

2DO: r21-impye run

2DO: a longer run with collisions and YORP included


Size-frequency distributions of resonant populations

J2/1

r21_arer_sizes.eps

r21_arir_sizes.eps

r21_librating_absmag_distribution_bw.eps

Both stable and unstable in the J2/1 are included here.

r21.dat.sloan_spectra_ZGu.eps

J3/2 with Schubart cluster

r32_arer_sizes_schubart.eps

r32_arir_sizes_schubart.eps

r32_schubart_absmag_distribution_bw.eps

schubart_vN.eps

schubart.astorb.sloan_spectra_hildas.eps


Yarkovsky assisted escape on a 4 Gyr timescale

J2/1

2DO: already calculated, have to include collisions and YORP for the smalles bodies...

J3/2

2DO: is still running...


What 2DO?

variable number of integrations notes
inicond of planets >3 sets aJ = 5.45 AU
Mdisc 2-3 sets 30, 35, 40 M_E
hot/cold disc >2 sets e, sin i = 10-3 or 0.05
number of PLs >2 sets 3500, 5000, 7500
number of TPs 1 or more
sigma(r) 1 trial r-1.5 or even steeper falloff
integration accuracy 1 trial
SyMBA vs Mercury 1 trial
self gravity 1 trial
beginning and the end of the disc 1 trial


Abstract for the DPS 2006:

The observed asteroids residing on long-lived orbits inside low-order mean motion resonances provide a unique opportunity to study early stages of the Solar System evolution. E.g., the stability of resonant orbits might be violated when planets migrate due to interactions with a massive disc of remaining planetesimals.

We provide a complete update of resonant populations based on recent orbital catalogues. There are approximately 150 long-lived objects in the J2/1 resonance, ~1000 in the J3/2 and only a few objects in J4/3. We classify them according to their dynamical lifetimes, as inferred from N-body simulations spanning ~4 Gyr, and we present available physical properties and size-frequency distributions for the respective sub-groups.

We compute long-term orbital evolution of resonant bodies driven by slow chaotic diffusion, the Yarkovsky effect and collisions. We also test the stability of the resonant orbits under the influence of various mutual resonances between Jupiter and Saturn (1:2, 3:7, 4:9, 2:5), which were possibly encountered during the planetary migration period.


Miroslav Broz (mira@sirrah.troja.mff.cuni.cz), Aug 4th 2006