I'm sketching a story about a rogue Earth (that is, Earth got flung out of the solar system) and how humanity could survive. One of the main problems is food. Hydroponic farms with grow lights are one way to generate food in a post-sun world, but these use a lot of resources.
So I was considering if it would be possible to tap a natural source for food. I found an article from PNAS about the carbon productivity from hydrothermal vents, and one in particular (Crab Spa) may reach up to 9,300 kilograms of carbon per square meter per year (9.3 kgm2yr-1).
I tried to find similar data for forests - best I could find so far is a short page from NASA measuring primary productivity from space. I see that the most productive forests have a net productivity of carbon fixation in the range of 6.5 grams of carbon per square meter per day, which is about 2.37 kgm2yr-1.
With my limited understanding of biology I am interpreting this as to mean that an hydrothermal vent can produces approximately four times more biomass per area than a patch of rain forest on the same timespan. I wonder if a post-apocalyptic society could harvest the vents for food in a sustainable form, then? Like sending a ROV to catch shrimp or something like that.
If this is possible, is there a way to measure how many people could live off a square meter of hydrothermal vent?
P.s.: this is really not the only food source people will have. There will be underground farms with grow lights, in this question I'm wondering if it would be possible to harvest from hydrothermal vents so as to reduce the pressure on those farms.