The actor Gene Hackman died of natural causes days after his wife, Betsy Arakawa, succumbed to a rare respiratory virus, authorities said on Friday.

Arakawa died of hantavirus pulmonary syndrome while Hackman died of heart disease, with advanced Alzheimer’s disease contributing, said Dr Heather Jarrell, the chief medical investigator for the New Mexico office of the medical investigator. The couple’s partially mummified bodies were discovered last month at their home in New Mexico.

The 95-year-old Hackman may have lived for as long as a week after Arakawa’s death, she said. Officials speculated that he may have been unaware she was deceased.

“He was in a very poor state of health. He had significant heart disease, and I think ultimately that’s what resulted in his death,” Jarrell said.

The press conference New Mexico authorities held on Friday provided some answers in the mystery of what happened to the couple. Hackman and Arakawa were discovered last week after a maintenance worker, concerned when no one answered the door, contacted neighborhood security, who spotted their bodies through a window and called the police. One of their three dogs was also found dead.

The Santa Fe county sheriff’s office said it did not suspect foul play. But officials could not immediately determine what happened to the couple as there were no signs of trauma to their bodies and tests for carbon monoxide poisoning were negative.

At the press conference on Friday afternoon, the sheriff, Adan Mendoza, revealed that investigators had been able to piece together Arakawa’s final days and found that she had picked up her dog, who was later found dead nearby, from a veterinary appointment on 9 February and that she had responded to emails and went out shopping on 11 February. The last known activity from Arakawa was that day, the sheriff said.

Arakawa’s death was linked to hantavirus pulmonary syndrome, a rare but potentially fatal disease spread by infected rodent droppings. Exposures occur when people are near mouse droppings in homes, sheds or poorly ventilated areas.

Hackman’s pacemaker last showed activity on 17 February, nine days before maintenance and security workers showed up at the home and alerted police. Officials said it was “reasonable to conclude” that Hackman died around 18 February.

Arakawa was found with an open prescription bottle and pills scattered on the bathroom counter, while Hackman was found in the home’s entryway.

One of the couple’s three dogs also was found dead in a crate in a bathroom closet near Arakawa, while two other dogs survived. Authorities initially misidentified the breed of the dead animal.

When they were found, the bodies were decomposing with some mummification, a consequence of body type and climate in Santa Fe’s especially dry air at an elevation of nearly 7,200ft (2,200 meters).

Hackman, a Hollywood icon, won two Oscars during a storied career in films including The French Connection, Hoosiers and Superman from the 1960s until his retirement in the early 2000s.

Arakawa, born in Hawaii, studied as a concert pianist, attended the University of Southern California and met Hackman in the mid-1980s while working at a California gym.

The couple’s stucco, Pueblo-revival style home sits on a hill in a gated community at the southern tip of the Rocky Mountains. Santa Fe is known as a refuge for celebrities, artists and authors.

Hackman dedicated much of his time in retirement to painting and writing novels far from Hollywood’s social circuit. He served for several years on the board of trustees at the Georgia O’Keeffe Museum in Santa Fe, and he and his wife were investors in local businesses.