You can use your browser to examine the content of your cookies. For example my stack over flow cookie looks like:
F650CE82F53D2C39C8C06B5F26EB34E20FEAC3585035E2A6E9FA30B8ECF5051F4D9C8....
The value is an encrypted goo of a username and potentially the user roles.
The cookie is good as long as you want it to be. It isn't tied to the session.
In your sample code you created a persistent cookie, so it lives for the life of the cookie, even if you close your browser. Now if the cookie is memory based, it lasts until you close your browser, even if the expiration time would let it live longer.
Here are the default values:
<forms loginUrl="Login.aspx"
protection="All"
timeout="30"
name=".ASPXAUTH"
path="/"
requireSSL="false"
slidingExpiration="true"
defaultUrl="default.aspx"
cookieless="UseDeviceProfile"
enableCrossAppRedirects="false" />