Not an astronomer, but let's try going by Wikipedia: Neptune has apparent magnitude of about 8. If you displaced it to twice as far, it'd become 16 times as dim

Not an astronomer, but let's try going by Wikipedia: Neptune has apparent magnitude of about 8. If you displaced it to twice as far, it'd become 16 times as dim (twice the distance, squared). The scale of apparent magnitude is a factor of 2.512 per step, so that'd be a change of about 3, to magnitude 11. The biggest ground-based telescopes can go up to around 24-26, if you dedicate significant observing time. So (26-8)/3=6 doublings: they could detect Neptune at 64 times as far out as it is, if they knew where to look. That's ~1900 AU. But of course Neptune is bigger and likely more reflective than the target. I guess you could expect a brightness about one more magnitude lower. A quick skim of https://arxiv.org/abs/1601.05438 https://arxiv.org/abs/1601.05438 (the paper proposing the new planet) is difficult for me, but one concrete number they mention as a possibility is 700 AU. So, apparently, that'd be within reach of a ground-based telescope but it'd have to be a darned big state-of-the-art one.