The official version is that Trajan adopted Hadrian (his relative), but not everyone believes the official version--it's a bit like the official version of Vince Foster's death. Hadrian was very unpopular with the Senate because several leading Senators were executed early in his reign. The Senate didn't want to deify him after his death--because his adopted son Antoninus insisted on Hadrian's deification, he gained the epithet "Pius" (because he was mindful of his duties to his "father").