How to enforce entity existence across N-tables - postgres

Let's say we decided to split user table in two, one will have data related to authentication, another basic user description:

user_table
user_id | name
1       | Max
2       | Alex
3       | Should not be possible

auth_table
user_id | email   | password
1       | m@m.com | 123
2       | a@a.com | 321
4       | s@s.com | Should not be possible

Is it possible to enforce existence of the same user_id? Basically both tables should have exactly same number of rows and each row should have a match in both tables.