Oxford University don Dr Devinder Sivia, held on suspicion of the murder of professor Stephen Rawling has been released on police bail.
After Dr Sivia left Abingdon police station today, police said the death may be "a matter for a coroner's inquest rather than a criminal court".
Detectives arrested Dr Devinder Sivia on suspicion of murdering "well-respected and liked" Professor Steven Rawling, an official fellow and tutor at St Peter's College, Oxford on 11 January.
Rawling, with whom Sivia had co-authored a book, was found dead at Sivia’s suburban bungalow in Southmoor, Oxfordshire on Wednesday night.
A university source confirmed that Dr Sivia, 49, of St John's College, was in custody and is still being questioned. Thames Valley Police said they are not seeking anyone else in connection with their inquiry.
Officers were called at 11.22pm on Wednesday to reports of an incident at the property in which a man had been injured. Paramedics attended but Prof Rawlings, 50, was declared dead at the scene.
A post-mortem examination carried out yesterday on the married Oxford University professor was unable to establish a cause of death. Authorities said further tests will be conducted.
The don lived with his wife Linda, who had recently celebrated her 50th birthday.
Police are refusing to speculate on the circumstances surrounding his death and said they were "keeping an open mind".
Detective Superintendent Rob Mason, from Thames Valley Police's Major Crime Unit, said: "We are liaising closely with Oxford University and it is apparent that he was well-respected and liked within the college and colleagues and students have been devastated by the news."
He added: "It does appear that no one else was present at the address and we are not currently looking for anyone else in connection with this incident."
The force was unable to confirm if the two men had been out socially together in the hours before the professor's death. They were said to be friends for at least 15 years and published a book together in 1999 - Foundations Of Science Mathematics.
Tributes were yesterday paid to the academic, whose relatives have been informed of his death.
The vice-chancellor of Oxford University, Professor Andrew Hamilton, said in a statement: "The entire university community has been profoundly saddened and shocked by the tragic and untimely death of Professor Steve Rawlings.
"Our thoughts are with his family and friends."
Former BBC Radio 4 controller Mark Damazer, now master at St Peter's College, said Prof Rawlings was a "much liked and admired tutor".
He said: "Steve was elected to his fellowship in 1994, having initially been employed by the college for two years as lecturer in mathematics.
"He undertook his undergraduate and doctoral studies at the University of Cambridge, and remained there to do post-doctoral work prior to moving to Oxford.
"Steve held his St Peter's fellowship in conjunction with a University Lecturership in Astrophysics, later becoming professor.
"He was head of the sub-department of astrophysics of the University of Oxford from 2006 to 2010.
"He was one of the lead scientists in the international Square Kilometre Array (SKA) project and also played a prominent role in the redevelopment of the Goonhilly Satellite Earth Station in Cornwall as a radio astronomy facility.
"He was a much liked and admired tutor and colleague within the college and will be greatly missed. We extend our deepest sympathy to his wife Linda."