The Sage Bhadra narrative (the source of the temple-name etymology)
Sage Bhadra — son of the mountain-king Meru and the apsara Menaka (one source variant: 'Veru Devi' — minor variance). Initiated into the Rama mantra by Sage Narada, he performed tapasya on the Godavari bank in Dandakaranya. Sri Rama (during exile) promised liberation on return after his darshan, but did not return as Rama. Sage Bhadra continued his tapasya into the next yuga. Eventually, Vishnu appeared as Vaikuntha-Rama (with Sita and Lakshmana) and, at Sage Bhadra's request, placed his sripada on the sage's head — the sage became the hill itself. The temple-site is therefore named 'Bhadra-achalam' (Bhadra + achalam = Bhadra-hill).
