How frequently can I pound my civilization with rocks and expect it to rebuild between?

Question

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.

Answer 1

I have to point out that the scenario is problematic when it comes to actually knocking down this civilisation without just killing everyone, and in fact almost everything, on the planet.

Given that the water on this world is very deep, the OP has stated several km or deeper, and the civilisation floats, and the population is quite thinly spread across the world; a civilisation ending strike is either going to be a shower of impacts directly hitting an improbable number of islands simultaneously or a huge single impact that sends a blast wave around the world and kills almost everything on, and in, the ocean.

It is really hard to dial in the damage to a point of viable population survival with major damage under these conditions. A near miss, within 10-50km, of a smaller impactor, i.e. less than 2 km across, would be enough to smash an island under the impact wave, but just a little further away and the island will ride the dissipating swell and hardly notice (change distance for the same result with a bigger rock). It's like ships at sea riding over the wave of a tsunami, in deep water they barely notice but when that same wave reaches shallow water the breaking wave is lethal, except on this world there is no shallow water to make a breaking wave.

The atmospheric shockwave of a bolide passing over an island might be the better mechanism for devastating it's infrastructure without totally destroying the island itself. In fact the most dangerous impactors may be sulfur loaded carbonaceous skimmers that cloud the upper atmosphere and disrupt the ecology with nuclear autumn and bounce off back into space.

The only scenario I can think of that would constitute both ending civilisation and be survived by enough people to rebuild would be if all the inhabited islands happened to be close together when a sufficiently sized bolide splashed down in the middle of the group destroying much of the population and scattering the survivors. That is the scenario I'm going to pursue.

The OP has stated that the primary methods for holding onto information are written parchment and oral teaching. An oral tradition will be more robust than such written records in the event of an island being overtopped but the population largely surviving but less so in the event of an ecological upset as the elders are the most versed and, along with the very young, the first to die when times get lean. In my scenario both methods will be preserved on the islands that survive but with the population both devastated and scattered they will have more information than they can use. Population density is required for diversion and specialisation of labour. If these people have a religion that lets them retain their knowledge base then the infrastructure/material culture recovery will be limited by resource availability and reproduction rate, so the question of how often you can hit them is really a question of how fast they can breed back. There will be space and resources available for them to settle on other islands as the population grows.

Answer 2

To quote Jeff Goldblum in Jurassic Park, "Life Finds A Way".

The floating coral islands are just the latest evolutionary adaptation to surviving on an impact riddled water world. Life of course tried bottom dwellers and fish first, but water is too good a conductor of heat so creatures who lived completely surrounded by that water were boiled to death by even relatively distant meteor strikes. Random selection eventually discovered that by floating on the surface, a life form could reduce its exposure to the boiling water by whatever percentage it could elevate above the surface. These floating creatures also benefited from their extreme mobility as surface waves quickly carried them away from every new impact. Those which grew a buoyant center surrounded by a rocky shell survived better then the lighter weight, lighter shielded versions.

Over an evolutionary time scale, living floating islands became a thing, despite the regular bombardment.

Later life tried fish again and this time the fish found hiding spots in the underside of the floating islands, fortified caves where they could hide from the heat. Eventually some of those fish climbed up onto the top side beginning an epoch of surface life on this surface-less world. These surface dwelling creatures forged a life cycle, catching fish from the surrounding waters, consuming them and then dumping the resulting waste into holes in the surface for the island to consume. Islands which hosted surface life therefore had a better food supply than their barren cousins. Life helping life, soon all of the floating islands had surface life.

Where ever the sentient lifeforms came from, they arrived during this experimental epoch and learned from the indigenous life that they should hide in the caves when the firestorms came.

Thus their culture evolved to allow for periodic mass destruction. They kept their sacred scrolls and tool forges in the deepest most well-protected surface caves and stored plenty of food so they could wait out the bad times.

They found a way, not to thrive and rise into a mighty civilization, but rather to spread out across the planet's floating living islands, so that some of their kind would survive even the worst that their cruel god could throw at them.

With that mindset and cultural mandate, it didn't really matter how often the sky fell. They were ready for it.