Skip click on the Free Travel around airport map link !
That map shows the services and boundary for Buses Train and Tube !
The Tube is free for use between T5/Central zone out to Hatton Cross (but not to alight) change at Hatton back to T4 and central zone then T5 again.
After research it is correct an Oyster card is necessary to get through the barriers.
Also Heathrow Express CentralZone/T5 and Central Zone/T4.Change Central Zone going T4/T5 or reverse.
The buses are free right round perimeter and into Central Zone, however there are few Surrey supported local buses that do not accept the free zone areas.