I have a civilization living on floating reefs on a pure water world (no land other than the reefs). There are creatures on the planet that extract relatively pure metals from the water to use structurally (e.g., maybe snails with aluminum or titanium shells, etc.). As a result, this civilization is moderately adept at metallurgy. They practice animal husbandry but not farming. They mostly live in small to medium sized communities but there are cities and a constant flow of trade resulting in a reasonable amount of labor specialization. They have a good understanding of mathematics and astronomy and have written language with a high level of literacy (it’s effectively a religious requirement).
now for the rocks
They live in a quaternary system. Their planet orbits a brown dwarf that in turn orbits in the habitable zone of an A-type + red dwarf binary. In a more distant and highly eccentric orbit is a white dwarf. When this white dwarf comes in towards pericenter, it brings a rain of various rocks (comets, meteors, asteroids, whatever). The three larger bodies (stars) in the inner system absorb the bulk but this planet is still pummeled by catastrophic impacts on a routine basis. Sometimes they kill lots of people; sometimes they are civilization ending; and sometimes they bring mass extinction.
and finally: the question
I need to set the orbit for my white dwarf. To do that, I need to know how frequently a civilization-ending strike can occur where I can reasonably expect civilization to rebuild before the next? Or, alternatively, if you feel there are too many variables to make a response more than a guess or opinion: what variables do I need to consider?
edit: Some issues were raised in comments that I should have addressed initially so I’ve added that information here where it’s more generally accessible that sifting through the comments.
- I’m aware of the short lifespan of an A-type star and have an in-universe explanation for how life can exist here.
- The floating reefs/islands cover 10-15% of the surface but much of that is uninhabited. Let’s say not more than 5% of the surface is inhabited (or regularly accessed).
- Although these islands float and move around, you can assume the inhabited islands are near each other when a civilization ender hits (and maybe that's why it's civilization ending instead of 'just' devastating?)
- The water is deep enough to make the bottom functionally inaccessible to most life. This would probably be a minimum of several kilometers and could go much deeper.
- Reefs can be destroyed by heavy storms (and, of course, direct impacts). If a reef is destroyed, there will be few if any survivors from that reef.