"turns" can take quite a long time late-game, especially if you've got NPR's on. Especially if you're trying to do the 30-day increment. Even if you don't have NPR's, once you start getting lots of civilian ships it can really start to slow down.
There's not much you can do about turns taking a long time, short of getting a tool which will let you alter the processor priority of a program. If you get one of those, you can crank Aurora's priority up which will make it run quicker at the expensive of your other programs. And it can really slow other programs down, for example iTunes will hang sometimes while Aurora's especially busy.
You can totally alt-tab, just don't expect your other programs to run quickly either. Unless you turn down Aurora's priority.