11:52 AM PT -- Aaron just shared a message as well, saying, "My heart is broken, we are so hurt we lost you poppa way too soon. You were never human to me, you were always my real life super hero."

11:20 AM PT -- Nick just tweeted about his dad's death, saying, "I am heartbroken to share the news that our father, Robert, passed away last night."

Nick and Aaron Carter's father has died ... TMZ has learned.

Sources connected to the family tell us Bob Carter died Tuesday night in Florida. He was 65, and right now there are very few details about the cause of death. In a tweet he later deleted, Aaron said something about his father being found unconscious.

Bob was on the family's reality show, "House of Carters" ... featuring the Backstreet Boys singer, Aaron and their 3 other siblings -- Leslie, Angel and Bobbie.

This is yet another tragedy for the Carters. You'll recall Leslie died at the age of 25 back in 2012.

#RIP