The end states of long-period comets and the origin of Halley-type comets

We analyse a sample of 73 old long-period comets (LPCs) (orbital periods 200 < P < 1000 yr) with perihelion distances q < 2.5 au, discovered in the period 1850-2014. We cloned the observed comets and also added fictitious LPCs with perihelia in the Jupiter's zone. We consider both a purely dynamical evolution and a physico-dynamical one with different physical lifetimes. We can fit the computed energy distribution of comets with q < 1.3 au to the observed one only within the energy range 0.01 < x < 0.04 au(-1) (or periods 125 < P < 1000 yr), where the 'energy' is taken as the inverse of the semimajor axis a, namely x = 1/a. The best results are obtained for physical lifetimes of about 200-300 revolutions (for a comet with a standard q = 1 au). We find that neither a purely dynamical evolution, nor a physico-dynamical one can reproduce the long tail of larger binding energies (x greater than or similar to 0.04 au-1) that correspond to most Halley-type comets (HTCs) and Jupiter-family comets. We conclude that most HTCs are not the end states of the evolution of LPCs, but come from a different source, a flattened one that we identify with the Centaurs that are scattered to the inner planetary region from the trans-Neptunian belt. These results also show that the boundary between LPCs and HTCs should be located at an energy x similar to 0.04 au(-1) (P similar to 125 yr), rather than the conventional classical boundary at P = 200 yr.