Lionel Simenya was hit by a stolen Peugeot 207 and left to die on Fords Road, next to Saughton Park, in the early hours of last Thursday.
Detectives launched a murder investigation and major manhunt after the thieves abandoned the car and fled over a footbridge by the Water of Leith. Detective Inspector Stuart Alexander said: “I’ve sat across from people who’ve done this before in an interview room and I can tell you they can’t live with themselves after a period of time and that pressure will intensify.”
Police are now trying to piece together exactly what happened in the moments leading up to Mr Simenya, 36, originally from Burundi, being found dying in the street.
They know the Peugeot 207 was stolen from a garage on Fords Road shortly before it ploughed into Mr Simenya.
Detectives refused to confirm reports Mr Simenya was sleeping in his Fiat Fiorino found on the same road.
Officers know Mr Simenya had been working as a chef earlier in the evening on Gorgie Road before visiting a gym.
But they refused to speculate on how he came to be in the street at 3:50am when he was hit.
One theory is that he may have heard the thieves stealing the car and tried to intervene to prevent their getaway.
Detectives have been trawling CCTV footage, including from the garage, and confirmed there were more than one person in the Peugeot at the time.
Mr Alexander said: “Anybody who has any information, no matter how insignificant you think that is, please come forward. Let us know anything that might assist me bring the perpetrators and persons that were in that Peugeot 207 last week to justice for the sake of Lionel’s family.”
Mr Simenya’s family moved to Belgium from their East African homeland in 1994 before he moved on to Edinburgh in 2011, working across Scotland.
Younger brother Nicolas, 35, flew into Edinburgh from Belgium for a press conference yesterday to appeal for help.
He also went to see his brother’s body at the morgue on Wednesday.
Nicolas fought back tears as he made a direct plea to the killers of his “hardworking and wonderful” older brother.
He described Mr Simenya’s death as “cruel” on his family and said such an “atrocious” end was unbefitting of a “peaceful” life.