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Carn Dûm was the capital of Angmar.
Established on the very western end of the Mountains of Angmar, it was inhabited by the Witch-king of Angmar and his many servants: Men of Darkness, Orcs, and other fell creatures. From here he based his attacks on the three petty realms of Arnor, quickly managing to destroy Rhudaur and later Cardolan.
Arthedain fell in the Battle of Fornost in Third Age 1974, but the Witch-king was routed by Glorfindel and in 1975 Angmar itself fell under an assault, and Carn Dûm was sieged by the Dúnedain of Gondor, the survivors of Arnor, and Elves of Lindon. Carn Dûm was utterly destroyed, although some Orcs survived there until at least the War of the Dwarves and Orcs and possibly after as well, until they were wiped out by Elessar, High King of the Reunited Kingdom.[source?]
The etymology of Carn Dûm is uncertain. It could be Gaelic, in which it roughly translates as "mountain fortress"; although Tolkien uses Celtic elements for some translated Mannish names, this would have been the only instance where he uses Gaelic. It is unknown whether this is just coincidence or not.