Based on the results of our simulations we have tried to estimate the ages of the Adeona and Gefion families. We have used two different methods: the first is based on the values of the dispersion  in e and i of the real members of the two families integrated under the effect of close encounters with large asteroids (Nesvorny'et al. 2001), while for the second we tried to match the current observed values of standard deviation in a, e, and i with the results of our Yarkovsky simulations.   Both method are subjects to large uncertainties, so our estimate have to be taken with caution. For the first method we considered only members of the families larger than 20 km, so as to exclude mobility due to Yarkovsky, and computed their dispersion in e and i. There were only 10 members of Adeona and 9 of Gefion with diameter larger than 20 Km, so we are conscious that our results could be affected by errors due to statistics of small numbers. We assumed that: The standard deviation in e, i is proportional to Ct0.5, with C a constant to be determined (i.e. we assumed that chaotic diffusion in mean motion resonances can be modeled with a random walk (Murray and Holman 1997). That the initial orbital diffusion in e and i were delta-functions: this unrealistic assumption can be useful to set an upper limit on the family age. We then calculate the standard deviation in e, i  for each time step of the averaged elements: given that at the beginning of the simulation we had sigma0=CT0.5, where T is the family age, and at time t sigmat=C(t+T)0.5, it follows that: T(t)=sigma02 t/(sigmat2-sigma02)

We computed T(t) for each time step of the averaged elements (10⁵ years) and then averaged over the length of the integration (we eliminate the first 100 Myr of data in order to have values of sigma_t significantly different from sigma₀). Our estimates of the families ages, with an error corresponding to the 3-sigmavalues of T(t), are given in the table. We found an age of ~300 Myr for Adeona and of ~400 Myr for Gefion. We then used the results of the Yarkovsky simulations and tried to match the current values of sigma_a, sigma_e, sigma_i with the dispersion we computed from the simulation with the synthetic family's members. Any estimate obtained with this method it is going to be uncertain due to the inherent arbitrariness of the choice of initial conditions. In particolar, since Yarkovsky effect is acting mainly on the semimajor axis, due to the conservative value of velocity at infinity with which our synthetic families were generated we were not able to reproduce the distribution in e and  i. Nevertheless, we can try to use the estimate the family age from sigma_a(t). On the figure we report the time evolution of sigma_a for Adeona and Gefion.   Straight lines represent the current values of sigma_a for members of the families as from Nesvorny program with a cutoff of 80 and 90 m/s, and diameters between 2 and 4 km (we used this set of diameters because we need to consider the same range of diameters for simulated and observed objects, and these objects were both well sampled in the simulated and observed population, David Nesvorny's suggestion). Results are in the table. The age of Adeona is in a range between 250 Myr and 580 Myr, while for Gefion our estimates are between 340 and 744 (or more for v=90 m/s) Myr. The combined results of the two methods suggest an age of  ~510 Myr for Adeona and ~590 My for Gefion. Not surprisingly, considered their relatively clustered distribution in proper elements and the isotropy of their current ejection velocity field, these are two relatively young families. We believe that the fact we can actually detect small families like those is due to their age: the Yarkovsky effect did not have enough time to disperse their members' distances beyond the Quasi-Random-Level of Zappala' et al. (1995).
 
 

Integrator	SWIFT-SKEEL	SWIFT-SKEEL	SWIFT-RMVSY	SWIFT-RMVSY
			v=80 m/s	v=90 m/s
	Te [Myr]	Ti [Myr]	Ta [Myr]	Ta [Myr]
Adeona	250+/-170	750+/-450	453	580
Gefion	340+/-390	490+/-360	744	/

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