PostgreSQL update column in one table with value from another, based on key from first table

Sorry about the title, I wasn't sure how best to word this. My situation is this: I have two tables: paper_author [paper_id, author_id, author_name] authors [author_id, author_name] Right now, the author_name column in paper_author is NULL. I would like to select the author name from the authors table and insert it into the author_name column in the paper_author table. I've written the following query:

UPDATE paper_author pa 
 SET author_name = (SELECT author_name FROM authors a WHERE a.author_id = pa.author_id);

Which I think will do what I want, but this is taking a very long time to run (days). For reference, the table paper_author has ~900M rows and the table authors has ~200M rows. The author_id is the primary key in the authors table. author_id has an index in the table paper_author. The rows in paper_author are not unique on author_id (i.e. each author_id may appear multiple times associated with different papers). Is there a more efficient way to write this? Have I missed something?