Blackbox :: Observations versus N-body simulations (of Eos)

BLACKBOX is a simple tool which can be used to rigorously compare observations of asteroid families to the respective N-body simulations. First, we select observed asteroids according to their colours (or albedos). Second, we account for a background population. Third, we match the synthetic size-frequency distribution to the observed one. Finally, we compute a suitable χ2 metric, and determine both lower and upper limits for the age.

  eos2.pdf              ... (revised) manuscript
  blackbox.py           ... Python script to compare observations to the N-body simulation
  Ktypes.tar.gz         ... observational data
  background.tar.gz     ... dtto
  eos-5_blackbox.tar.gz ... synthetic data (Swift N-body simulation)

versus  

Figure 1 ― Left panel: the proper semimajor axis ap vs proper inclination sin Ip for all asteroids in the broad surroundings of Eos family. The range of proper eccentricities is ep = (0.0; 0.3). If they have colour data in the SDSS MOC4 catalogue (Parker et al. 2008), the colours correspond to indices a*, iz which are closely related to taxonomy, namely blue is close to C-complex taxonomy, red to S-complex, and magenta to K-type. The whole sample contains 18 471 asteroids. There are other prominent families visible: Hygeia (C-type, bottom-right), Veritas (C, next to Eos), Tirela (S, upper right), Telramund (S, below Eos); a close inspection would show 32 families in total! Right panel: the same plot for a typical outcome of N-body simulations, assuming a disruption of a parent body, ejection of fragments with some velocity field, and their long-term dynamical evolution due to gravitational perturbations, resonances, chaotic diffusion, the Yarkovsky effect, the YORP effect, etc. The two panels are not directly comparable.

Supporting material

(ap, ep) plots:

observed (SDSS) t = 0 1420 Myr 3980 Myr

(ap, 1/D) plots a.k.a. 'V-shapes' ← not fitted in this method:

observed (SDSS) t = 0 1420 Myr 3980 Myr

χ2 vs time t for the nominal simulation:

χ2 dependence on f1, f2 factors used to scale background below and above J7/3 resonance:

a comparison of (ap, ep) plots and χ2(t) computed with 2× smaller box sizes:

observed (SDSS) t = 0 1420 Myr 3980 Myr


Miroslav Brož (miroslav.broz@email.cz), May 14th 2018