Letting it fall off on it's own could be dissasterous. You should really consider trimming it. You don't want a nasty fungal infection to occur. Trust me it's happened to me, and the infection was so deep it killed my marble catfish. Almost the exact same injury as your's. I hope it does work out, but if you look at it, the spine is not broken off it is ripped out of socket. That wound goes straight down on top of his spinal column. How large is the TSN? Might be time to consider an indoor pond. 8x2x2 is a little small unless your tsn is really small. I have a 350 gal cattle trough that's 6' dia and 2' deep. Nothing to injure the fish in a pond. Just a suggestion. Hope it turns out ok though. There's a chance it will, but you will definitely need to medicate, and use an antibiotic(can't stress that enough) WHen I say trim I don't mean the whole fin just a verticle cut to get rid of the spine which is definitely a loss, and trust me it will never grow back because the whole thing is gone. They can grow back if just part of it is broken off, and it might heal if only pulled out part of the way, but this is pulled out all the way. I expect that he will never have at least the first ray, maybe the second. The bottom of them are closely tied together. Share pics daily of his progress if you can.