On the Astrid asteroid family

Among asteroid families, the Astrid family is peculiar because of its unusual inclination distribution. Objects at $a\simeq$~2.764 au are quite dispersed in this orbital element, giving the family a "crab-like" appearance. Recent works showed that this feature is caused by the interaction of the family with the $s-s_C$ nodal secular resonance with Ceres, that spreads the inclination of asteroids near its separatrix. As a consequence, the currently observed distribution of the $v_W$ component of terminal ejection velocities obtained from inverting Gauss equation is quite leptokurtic, since this parameter mostly depends on the asteroids inclination. The peculiar orbital configuration of the Astrid family can be used to set constraints on key parameters describing the strength of the Yarkovsky force, such as the bulk and surface density and the thermal conductivity of surface material. By simulating various fictitious families with different values of these parameters, and by demanding that the current value of the kurtosis of the distribution in $v_W$ be reached over the estimated lifetime of the family, we obtained that the thermal conductivity of Astrid family members should be $\simeq$ 0.001 W/m/K, and that the surface and bulk density should be higher than 1000 kg/m$^{3}$. Monte Carlo methods simulating Yarkovsky and stochastic YORP evolution of the Astrid family show its age to be $T$ = 140$\pm$30 Myr old, in good agreement with estimates from other groups. Its terminal ejection velocity parameter is in the range $V_{EJ}= 5^{+17}_{-5}$~m/s.] Values of $V_{EJ}$ larger than 25 m/s are excluded from constraints from the current inclination distribution.

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