Asteroid age distributions determined by space weathering and collisional evolution models

Abstract: We provide evidence of consistency between the dynamical evolution of main belt asteroids and their color evolution due to space weathering. The dynamical age of an asteroid's surface \citep{bib.bot05a,bib.nes05} is the time since its last catastrophic disruption event which is a function of the object's diameter. The age of an S-complex asteroid's surface may also be determined from its color using a space weathering model \citep[e.g.][]{bib.wil10,bib.jed04,bib.wil08,bib.mar06}. We used a sample of 95 S-complex asteroids from SMASS and obtained their absolute magnitudes and $u,g,r,i,z$ filter magnitudes from SDSS. The absolute magnitudes yield a size-derived age distribution. The $u,g,r,i,z$ filter magnitudes lead to the principal component color which yields a color-derived age distribution by inverting our color-age relationship, an enhanced version of the `dual $\tau$' space weathering model of \citet{bib.wil10}. We fit the size-age distribution to the enhanced dual $\tau$ model and found characteristic weathering and gardening times of $\tau_w = 2050 \pm 80$ Myr and $\tau_g = 4400^{+700}_{-500}$ Myr respectively. The fit also suggests an initial principal component color of $-0.05 \pm 0.01$ for fresh asteroid surface with a maximum possible change of the probable color due to weathering of $\Delta PC = 1.34 \pm 0.04$. Our predicted color of fresh asteroid surface matches the color of fresh ordinary chondritic surface of $PC_1 = 0.17 \pm 0.39$.