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 suffers from needing an order of
magnitude more mass than is currently advocated by 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<2.5AU, 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~1.8AU. The
value of k is higher than the one obtained for the Long-Period Comets (LPCs),
with 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<1.8AU. We
calculate that the steady-state number of active HTCs with diameter D>2.3km and
q<1.8AU is of the order of 100.Comment: Accepted for publication in Astronomy and Astrophysic
