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 χ^{2} 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)
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Figure 1 ― Left panel: the proper semimajor axis a_{p} vs proper inclination sin I_{p} for all asteroids in the broad surroundings of Eos family. The range of proper eccentricities is e_{p} = (0.0; 0.3). If they have colour data in the SDSS MOC4 catalogue (Parker et al. 2008), the colours correspond to indices a*, i‒z 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. |
(a_{p}, e_{p}) plots:
observed (SDSS) t = 0 1420 Myr 3980 Myr → →
(a_{p}, 1/D) plots a.k.a. 'V-shapes' ← not fitted in this method:
observed (SDSS) t = 0 1420 Myr 3980 Myr → →
χ^{2} vs time t for the nominal simulation:
χ^{2} dependence on f_{1}, f_{2} factors used to scale background below and above J7/3 resonance:
a comparison of (a_{p}, e_{p}) plots and χ^{2}(t) computed with 2× smaller box sizes:
observed (SDSS) t = 0 1420 Myr 3980 Myr → →
Miroslav Brož (miroslav.broz@email.cz), May 14th 2018