  We estimate the total number and the slope of the size frequency distribution
(SFD) of dormant Jupiter Family Comets (JFCs) by fitting a one-parameter model
to the known population. We first select 61 Near Earth Objects (NEOs) that are
likely to be dormant JFCs because their orbits are dynamically coupled to
Jupiter (Bottke et al, 2002). Then, from the numerical simulations of Levison &
Duncan (1997), we construct an orbit distribution model for JFCs in the NEO
orbital element space. We assume an orbit independent SFD for all JFCs, the
slope of which is our unique free parameter. Finally, we compute observational
biases for dormant JFCs using a calibrated NEO survey simulator (Jedicke et al.
2003). By fitting the biased model to the data, we estimate that there are ~75
dormant JFCs with H<18 in the NEO region and that the slope of their cumulative
SFD is -1.5 +/- 0.3. Our slope for the SFD of dormant JFCs is very close to
that of active JFCs as determined by Weissman and Lowry (2003). Thus, we argue
that when JFCs fade they are likely to become dormant rather than to disrupt
and that the fate of faded comets is size independent. Our results imply that
the size distribution of the JFC progenitors - the scattered disk
trans-Neptunian population - either (i) has a similar and shallow SFD or (i')
is slightly steeper and physical processes acting on the comets in a
size-dependent manner creates the shallower active comet SFD. Our measured
slope, typical of collisionally evolved populations with a size dependent
impact strength (Benz and Asphaug 1999), suggests that scattered disk bodies
reached collisional equilibrium inside the proto-planetary disk prior to their
removal from the planetary region.
