The dark side of solar power in Star Wars: The Force Awakens
The act of transforming the surface of a planet to become more habitable is one thing. Terraforming an entire planet to become the deadliest weapon in the Universe is quite another...
Starkiller Base is the HQ of the villainous First Order. It gets its namesake from George Lucas' original draft of Star Wars in which Luke Skywalker was named Dirk Starkiller. It also literally kills stars by absorbing nearby stellar energy to power its terrifying super-weapon, which is carved right into the icy planet itself. Believe it or not, while it may seem implausibly large, this is actually a more sensible idea than the original Death Star, which was scaffolded in space like a gargantuan ISS.
Brian Muirhead, chief engineer at NASA's JPL says the Empire may have fared much better had they made it by hollowing out an asteroid instead. After all, why cart moonloads of material through space when you can use existing material right under your feet? All the better if that ground happens to have a breathable (albeit chilly) atmosphere so you don't need to worry about life-support for all the crew.
Other details are much less plausible, however. For example, in order to charge itself, Starkiller slurps stellar fuel into the mouth of its weapon. Star matter can indeed get "sucked in" to another body like this, but it requires a much more massive body, such as a nearby black hole, to overcome the gravity of the star itself. For a puny planet like Starkiller, this poses a few problems. It's mentioned in the film that the base vents thermal energy in order to remain stable. That's a good start, but stars aren't made of weightless aether that can be sucked up like cobwebs in a vacuum.
Most of the energy released by a star is the by-product of gravity-induced nuclear fusion in its core, where lighter elements are crushed together to form heavier elements. All those atoms would need to go somewhere. Otherwise, once Starkiller absorbed the star, it would also contain all of its mass - causing everyone on the surface to be crushed under their own weight, if not cause the whole planet to collapse in on itself.
Even if the engineers managed to overcome this weighty limitation, it gets worse. The plasma pulled in from the star is depicted on screen as a sort of flame-like vapour, having absolutely no effect on the atmosphere. Not even misty overcast clouds bother to move out of the way. Seems harmless enough. But stars are, well, hot. Bring the surface of the sun to the surface of your planet and you've forced some serious climate change issues. In reality, the atmosphere would probably become superheated and combust in roiling flames, stormtrooper helmets melting into a creamy ooze à la Raiders of The Lost Ark.
But, surprise surprise, Starkiller doesn't last all that long. After destroying its (you guessed it) thermal exhaust port, the planet becomes unstable and collapses into a brand new star. But it's unlikely, even after sucking up a glut of star mass, that the star that formed from the ashes of the ruined world would have close to the amount of mass needed to spark fusion at its core, or the inward gravitational pressure to maintain a balance with the outward radiation pressure. Instead, the radiation pressure would cause it to rapidly expand to the point of bursting, spilling its stellar guts into space. Shame... a mini supernova would have made for quite the spectacle on screen - one that may have even lived up to that superb puff of spark and flame that finished of the 1977 Death Star.
Starkiller Base raises so many scientific eyebrows as to render it impossible. But then again, lightsabers wouldn't really work either, and nobody complains about that (much). Ultimately, in a galaxy far, far away, where everyone speaks English for some reason, many details don't require explanation. In the words of Master Yoda, "clear your mind of questions", sit back, and let the experience wash over you.