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 \gtrsim 1 \mathrm { km } but we measure a significant drop in the SFD slope for small objects with diameters < 1 \mathrm { km } and approaching only 100 \mathrm { 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 \mathrm { km } diameter and have perihelia q < 10 \mathrm { 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 \mathrm { m } due to the shallow slope of the SFD for diameters < 1 \mathrm { km } .
We estimate that the total number of ‘ potentially active ’ objects with diameters \geq 1 \mathrm { km } in the Oort cloud , objects that would be defined as LPCs if their perihelia evolved to < 10 \mathrm { au } , is ( 1.5 \pm 1 ) \times 10 ^ { 12 } with a combined mass of 1.3 \pm 0.9 \mathrm { M } _ { \oplus } .
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 .