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 ( 5 ) .
Then , from the numerical simulations of Levison and Duncan ( 26 ) , 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 ( 21 ) .
By fitting the biased model to the data , we estimate that there are \sim 75 dormant JFCs with H < 18 in the NEO region and that the slope of their cumulative SFD is -1.5 \pm 0.3 .
Our slope for the SFD of dormant JFCs is very close to that of active JFCs as determined by Weissman and Lowry ( 39 ) .
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 ^ { \prime } ) 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 ( 1 ) , suggests that scattered disk bodies reached collisional equilibrium inside the proto-planetary disk prior to their removal from the planetary region .