  The Haumea family is currently the only identified collisional family in the
Kuiper belt. We numerically simulate the long-term dynamical evolution of the
family to estimate a lower limit of the family's age and to assess how the
population of the family and its dynamical clustering are preserved over Gyr
timescales. We find that the family is not younger than 100 Myr, and its age is
at least 1 Gyr with 95% confidence. We find that for initial velocity
dispersions of 50-400 m/s, approximately 20-45% of the family members are lost
to close encounters with Neptune after 3.5 Gyr of orbital evolution. We apply
these loss rates to two proposed models for the formation of the Haumea family,
a graze-and-merge type collision between two similarly sized, differentiated
KBOs or the collisional disruption of a satellite orbiting Haumea. For the
graze-and-merge collision model, we calculate that >85% of the expected mass in
surviving family members within 150 m/s of the collision has been identified,
but that one to two times the mass of the known family members remains to be
identified at larger velocities. For the satellite-break-up model, we estimate
that the currently identified family members account for ~50% of the expected
mass of the family. Taking observational incompleteness into account, the
observed number of Haumea family members is consistent with either formation
scenario at the 1 sigma level, however both models predict more objects at
larger relative velocities (>150 m/s) than have been identified.
