  We explore the hypothesis that the Eureka family of sub-km asteroids in the
L5 region of Mars could have formed in a collision. We estimate the size
distribution index from available information on family members; model the
orbital dispersion of collisional fragments; and carry out a formal calculation
of the collisional lifetime as a function of size. We find that, as initially
conjectured by Rivkin et al (2003), the collisional lifetime of objects the
size of (5261) Eureka is at least a few Gyr, significantly longer than for
similar-sized Main Belt asteroids. In contrast, the observed degree of orbital
compactness is inconsistent with all but the least energetic family-forming
collisions. Therefore, the family asteroids may be ejecta from a cratering
event sometime in the past ~1 Gyr if the orbits are gradually dispersed by
gravitational diffusion and the Yarkovsky effect (Cuk et al, 2015). The
comparable sizes of the largest family members require either negligible target
strength or a particular impact geometry under this scenario (Durda et al,
2007; Benavidez et al, 2012). Alternatively, the family may have formed by a
series of YORP-induced fission events (Pravec.et.al, 2010). The shallow size
distribution of the family is similar to that of small MBAs (Gladman et al,
2009) interpreted as due to the dominance of this mechanism for
Eureka-family-sized asteroids (Jacobson et al, 2014). However, our population
index estimate is likely a lower limit due to the small available number of
family asteroids and observational incompleteness. Future searches for fainter
family members, further observational characterisation of the known Trojans'
physical properties as well as orbital and rotational evolution modelling will
help distinguish between different formation models.
