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 $>\sim 1$~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 $\alpha_{big} = 0.72 \pm 0.09 (stat.) \pm 0.15 (sys.)$ while small objects behave as $\alpha_{small} = 0.07 \pm 0.03 (stat.) \pm 0.09 (sys.)$ where the SFD is $\propto 10^{\alpha H_N}$ and $H_N$ represents the cometary nuclear absolute magnitude. The total number of LPCs that are $>1$~km diameter and have perihelia $q<10$~au is $0.46 \pm 0.15 \times 10^9$ while there are only $2.4 \pm 0.5 (stat.) \pm 2 (sys.) \times 10^9$ objects with diameters $>100$~m due to the shallow slope of the SFD for diameters $<1$~m. We estimate that the total number of `potentially active' objects with diameters $\ge 1$~km in the Oort cloud, objects that would be defined as LPCs if their perihelia evolved to $<10$~au, is $(1.5\pm1)\times10^{12}$ with a combined mass of $1.3\pm0.9 \, M_{Earth}$. 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.