The orbit and size-frequency distribution of long period comets observed by Pan-STARRS1

We introduce a new technique to estimate the comet nuclear size frequency distribution (SFD) that combines a cometary activity model with a survey simulation and apply it to 150 long period comets (LPC) detected by the Pan-STARRS1 near-Earth object survey. The debiased LPC size-frequency distribution is in agreement with previous estimates for large comets with nuclear diameter greater than or similar to 1 km but we measure a significant drop in the SFD slope for small objects with diameters < 1 km and approaching only 100 m diameter. Large objects have a slope alpha(big) = 0.72 +/- 0.09(stat.) +/- 0.15(sys.) while small objects behave as alpha(small) = 0.07 +/- 0.03(stat.) +/- 0.09(sys.) where the SFD is proportional to 10(alpha HN) and H-N represents the cometary nuclear absolute magnitude. The total number of LPCs that are > 1km diameter and have perihelia q < 10 au is 0.46 +/- 0.15 x 10(9) while there are only 2.4 +/- 0.5(stat.) +/- 2(sys.) x 10(9) objects with diameters > 100m due to the shallow slope of the SFD for diameters < 1 km. We estimate that the total number of 'potentially active' objects with diameters >= 1 km in the Oort cloud, objects that would be defined as LPCs if their perihelia evolved to < 10 au, is (1.5 +/- 1) x 10(12) with a combined mass of 1.3 +/- 0.9 M-circle plus. The debiased LPC orbit distribution is broadly in agreement with expectations from contemporary dynamical models but there are discrepancies that could point towards a future ability to disentangle the relative importance of stellar perturbations and galactic tides in producing the LPC population.