Based on what we see in Episode IV, Grand Moff Tarkin appears to order the destruction of Alderaan by the Death Star entirely on his own. While we know that Tarkin had extraordinary authority on the Death Star, I find it hard to believe he had so much authority that he could destroy whole planets without clearing it with the Emperor first.
Did Tarkin get permission from the Emperor to destroy Alderaan (behind the scenes)? Was Vader able to approve the destruction in the Emperor's place? Or was Tarkin allowed to order the destruction of Alderaan entirely on his own? And if Tarkin could destroy planets with the Death Star on his own authority, what (if any) restrictions did he have (for example, he presumably couldn't destroy the Imperial capital planet of Coruscant)?
Note: Answers must cite canon source(s). Legends sources are welcomed and appreciated as an optional supplement, but Legends-only answers are unacceptable.