Are we Mindful in Jhana?

When a person enters into Jhana (particularly 2nd onward): 1. What is he mindful of? 2. What kind of meta awareness or introspective awareness(Sampajānakārī) is there? Note: it says that the 2nd onward is without vitaka and vicara. So my doubt is, if there is no object of attention, then what is one mindful of? And what is one peripherally aware (Sampājano) about? Tripitaka, and even no person, is referring to "co-existence of mindfulness and Jhana". Am I missing something very obvious?