Varför bor Vader på Mustafar?

Eftersom Palpatine gjorde honom

Från Rogue One Ultimate Visual Guide :

Vader's personal abode is an obsidian tower on an inhospitable world. It is by the Emperor's design that Vader lives in such an unforgiving environment.

Eftersom det har speciell betydelse

Enligt en intervju med Lucasfilm VP Doug Chiang:

Doug Chiang: [Laughs] Vader’s castle was really fun. When I knew that we were going to possibly go back to Vader’s castle, I loved that idea of, “Okay, lets establish Vader’s home.” The initial idea was, “Why would Vader live here?” In our minds, we started to come up with a little bit of a backstory. That perhaps this place had special meaning for him, and that this is where he comes to meditate and to heal himself. We started with the idea that maybe it should be built around his bacta tank chamber, and he comes back here to rejuvenate himself and also to meditate. So from there, the structure itself grew out from the bacta tank, and there were certain ideas that we tried. We were trying to go for a very iconic shape, and we always love tall towers. Ralph McQuarrie actually drew quite a few small thumbnail sketches [of Vader’s castle] that were very intriguing. They were kind of angular versions of a tower, and I saw the potential of where he was going, and I just exaggerated that quite a bit.

One of the things we landed on early was this idea of a tuning fork — a twin tower kind of look. And it was really interesting, because then that started to give Gareth a lot of ideas like, “Well, maybe the structure is built this way because it is like a tuning fork. It’s tuning the dark side in terms of the energy.”

Vader är igen en Sith. Att påminna sig om sitt lidande är en väg till styrka. Dessutom är det möjligt att Mustafar är en särskilt bra plats för att "ställa in den mörka sidan."