I use Owin to authorize through Google oAuth. Here is how my cookies are configured:
// Enable the application to use a cookie to store information for the s
"SignOut(DefaultAuthenticationTypes.ExternalCookie)" is to "cleanup, the external cookie" as per Hao Kung's answer https://stackoverflow.com/a/20575643/2710179
There is a nice implementation in the Microsoft.aspnet.identity.samples project which you can download from nuget. In this implementation they use:-
var userIdentity = await manager.CreateIdentityAsync(this, DefaultAuthenticationTypes.ApplicationCookie);
"ExternalCookie" is the "Default value used for the ExternalSignInAuthenticationType configured" I believe this means it is used as temporary cookie use to verify the user against an external sight