Eos family halo 2

+ upto 20 % (!) of bodies can escape from the Eos-core and create a HALO
  within 1.3 Gyr ONLY via J9/4 resonance capture/release/drift,
  <- this includes bodies INITIALLY located inside the resonance
  -> the OBSERVED ratio is also approx. ~ 20 % (!) 
  => NO MIGRATION is needed to create the halo!

  (btw. this may be even used to independently constrain the AGE of the family)

  Note: I use a simple criterion to distinguish the halo and core of the family:
  everything inside a SMALL box a = 2.96-3.16 AU, e = 0.04-0.10, sin I = 0.15-0.20 is the core,
  while the bodies located in a LARGE box a = 2.96-3.16 AU, e = 0.01-0.15, sin I = 0.12-0.24  
  (and NOT contained in the small box, of course) constitute the halo.

  Note 2: There is an artefact in proper eccentricity computation beyond a = 3.08 AU,
  but it does not affect results significantly. 




t = 0 Myr, f = 0 deg
t = 1300 Myr




animace AVI




AVI




AVI




  The same figures, but with v_max = 100 m/s only, i.e. more compact family at the beginning
  (maybe, it is TOO compact, since the escape velocity from the parent body is v_esc =~ 120 m/s):




t = 0 Myr
t = 1300 Myr
















  The corresponding dependence number of bodies N(t) vs time and the halo/core ratio:




v_max = 400 m/s
v_max = 100 m/s







+ the SFD of the halo becomes steeper and that of the core shallower around D =~ 10 km
  in course of the simulation (because the delivery is via the size-dependent Yarkovsky/YORP)
  -> this naturally explains the observed difference between the SFDs
     of the Eos family and Eos-like asteroids in the surroundings (!)




simulation at t = 0 Myr, numbered asteroids only (!)
t = 1300 Myr
observed Eos-like (extracted from SDSS)









  Note: The match between the simulated and observed SFD's is NOT perfect
  - I should probably start the simulation with a steeper SFD
  or a size-dependent velocity distribution, which may produce
  more large asteroids located initially in the J9/4 resonance.

+ if the whole family would be 4 Gyr old, most (~ 90 %) of small bodies
  would be elliminated due to the Yarkovsky drift (!),
  unless they are replenished by a collisional cascade
  <- simply extrapolate the N(t) dependence

+ initial geometry of the impact seems to be important too (!)
  <- it may explain the observed asymmetry in the (a,e) plane
     on left/right side of the J9/4 resonance
  <- f =~ 135 to 180 deg is preferred, because for f =~ 0 to 45 deg
     too many bodies fall into the z_1 resonance what creates
     a prominent structure (visible even after 1.3 Gyr) which
     is NOT observed today




t = 0 Myr, f = 135 deg, v_max = 400 m/s













  This second simulation is not yet computed upto 1.3 Gyr.
  It also differs by the SIZE-DEPENDENT initial velocity field (refer to (a,H) figure).