forms authentication cookie expires when browser is closed.

Is it by design that the forms authentication cookie expires when the browser window is closed?  I'm using asp.net 3.5 on Windows Server 2008.  I have an admin section of my website that is not available to users unless they sign in.  The path is www.website.com/admin
This is in my web.config file in the root website:
  <system.web>
    <authorization>
      <allow users="*" />
    </authorization>
    <authentication mode="Forms">
      <forms name="authform" loginUrl="adminlogin.aspx" requireSSL="true" timeout="900"/>
    </authentication>
  </system.web>
and in the admin section's web.config:
  <system.web>
    <authorization>
 &nb ...