We simulate the passage through the Sun-Jupiter system of interstellar objects ( ISOs ) similar to 1I/ ‘ Oumuamua or 2I/Borisov .
Capture of such objects is rare and overwhelmingly from low incoming speeds onto orbits akin to those of known long-period comets .
This suggests that some of these comets could be of extra-solar origin , in particular inactive ones .
Assuming ISOs follow the local stellar velocity distribution , we infer a volume capture rate of 0.051 \mathrm { au } ^ { 3 } \mathrm { yr } ^ { -1 } .
Current estimates for orbital lifetimes and space densities then imply steady-state captured populations of \sim 10 ^ { 2 } comets and \sim 10 ^ { 5 } ‘ Oumuamua-like rocks .