There have been 77 TNOs discovered to be librating in the distant
transneptunian resonances (beyond the 2:1 resonance, at semimajor axes greater
than 47.7~AU) in four well-characterized surveys: the Outer Solar System
Origins Survey (OSSOS) and three similar prior surveys. Here we use the OSSOS
Survey Simulator to measure their intrinsic orbital distributions using an
empirical parameterized model. Because many of the resonances had only one or
very few detections, j:k resonant objects were grouped by k in order to
have a better basis for comparison between models and reality. We also use the
Survey Simulator to constrain their absolute populations, finding that they are
much larger than predicted by any published Neptune migration model to date; we
also find population ratios that are inconsistent with published models,
presenting a challenge for future Kuiper Belt emplacement models. The estimated
population ratios between these resonances are largely consistent with
scattering-sticking predictions, though further discoveries of resonant TNOs
with high-precision orbits will be needed to determine whether
scattering-sticking can explain the entire distant resonant population or not.Comment: Accepted for publication in Planetary Sciences Journal (PSJ