Ah … I think I get it now … even if dark matter is uniformly distributed throughout the universe … we only care about the dark matter within the orbit of these outlying stars … using shell theory … and the uniformity is because condensing matter requires the energy outlet of electromagnetic radiation … something dark matter cannot do …
Asympotically fat, I think I’ve mentioned before that I love your user name. (For anyone who doesn’t know, it’s a pun on asymptotically flat).
(Hmm… perhaps he or she is surrounded by a large spherical shell of dark matter, such that from great distances his or her mass appears much greater than it actually is.;))
But, I just noticed you’re missing a t in “asymptotically”. Is that deliberate?
Still a ways off. It’s not the total amount of dark matter within a shell that matters, it’s the extra amount of dark matter that … matters.
At the galactic scale, there’s a lot of extra. At the star system level, there isn’t. Tiny objects like the Sun are too puny to accumulate enough extra dark matter to be worth caring about even if you are a fan of lots of decimal places.