Roles for specific event registration
There's an extension for a very similar scenario: Member Only Event.  If your authenticated members have memberships this will do the trick.  There are similar options here: Is it possible to restrict event registration to members?  Ultimately, if none of these meet your needs a small extension might be in order.

One other option is to use Webform CiviCRM integration to make either your authenticated events (or more likely, the single unauthenticated event) a webform, which you can then restrict access to separately from your other event signup pages.