Fedora
From Tardis Wiki, the free Doctor Who reference
A Fedora is a felt hat most commonly worn by men. It can come in many different shapes and sizes and it may be called different things.
Such a hat was part of the Fourth Doctor's outfit. He occasionally used it to cover his face to nap. (DW: Robot, The Androids of Tara) However, during the middle of his life, he preferred to go without it unless the weather called for a hat.
