An Oort Cloud origin of the Halley-type comets

The origin of the Halley-type comets (HTCs) is one of the last mysteries of the dynamical evolution of the solar system. Prior investigation into their origin has focused on two source regions: the Oort Cloud and the scattered disc. From the former it has been difficult to reproduce the non-isotropic, prograde skew in the inclination distribution of the observed HTCs without invoking a multi-component Oort Cloud model and specific fading of the comets. The scattered disc origin fares better, but needs an order of magnitude more mass than is consistent with theory and observations. Here we revisit the Oort Cloud origin and include cometary fading. Our observational sample stems from the JPL catalogue. We only keep comets discovered and observed after 1950, but place no a priori restriction on the maximum perihelion distance of observational completeness. We then numerically evolve half a million comets from the Oort Cloud through the realm of the giant planets and keep track of their number of perihelion passages with perihelion distance q < 2.5 AU, below which the activity is supposed to increase considerably. We can simultaneously fit the HTC inclination and semi-major axis distribution very well with a power-law fading function of the form m^-k, where m is the number of perihelion passages with q < 2.5 AU and k is the fading index. We match both the inclination and semi-major axis distributions when k ~ 1 and the maximum imposed perihelion distance of the observed sample is q_m ~ 1.8 AU. The value of k is higher than the one obtained for the long-period comets (LPCs), for which typically k ~ 0.7. This increase in k is most likely the result of cometary surface processes. We argue the HTC sample is now most likely complete for q_m < 1.8 AU. We calculate that the steady-state number of active HTCs with diameter D > 2.3 km and q < 1.8 AU is on the order of 100.