A former soldier shot and killed his wife and their two young children Sunday afternoon, set his stately home on fire then turned his gun on himself, authorities said.

The children, ages 5 and 4, were found dead Sunday in their beds on the second floor of the brick home in a southeast Louisville neighborhood, Jefferson County Deputy Coroner Eddie Robinson said. Their mother's body was found in the basement, he said.

Louisville Metro Police Lt. Todd Kessinger said the children and mother were shot and killed before the house was set ablaze.

Police offered no immediate motive for the slayings, saying the investigation was ongoing.

Kessinger said he was not aware of any history of domestic violence involving the family.

The woman's husband, Brad L. Hettinger, a 33-year-old former Army helicopter pilot and father of the two children, died of an apparent self-inflicted gunshot wound to the head, Robinson said.

Hettinger's wife, 32-year-old Billie Jo Hettinger, died of gunshot wounds to the chest and head, the deputy coroner said. Her identification was tentative, pending review of dental records, Robinson said.

The children — 5-year-old Collin Hettinger and 4-year-old Courtney Hettinger — each died of a single gunshot wound to the head, he said.

The mother and children also were burned from the fire, he said.

The older child would have celebrated a birthday later in the week.

Flowers leaned against the front door of the family's home Monday in an affluent neighborhood of well-manicured lawns and large brick homes. Second-story windows on the front and side of the home were broken, but there were no other visible signs of the tragedy that struck down the family.

Neighbors and friends planned a Monday evening prayer vigil.

"Something like this just rocks you," said Eddie Smith, a neighbor who was walking his dog Monday afternoon. "You wonder how something like this could happen in your neighborhood."

Brad Hettinger's body was found in the first-floor living room near the front door, Robinson said.

The bodies were found after firefighters responded to the fire Sunday afternoon, and investigators quickly determined the fire was arson.

Jeffersontown Fire Chief Sean Dreisbach said there were multiple fires set on different floors of the home, according to media reports.

The Hettingers were parishioners of St. Michael Catholic Parish, and the children were pupils at the parish school. The Archdiocese of Louisville issued a statement Monday expressing its sympathies and asking for prayers for the family.

"Archdiocesan counselors are working with the school counselor to assist teachers and students, and parents have been encouraged to talk with their children about this situation," the archdiocese said in its statement.

Smith, the neighbor, said his wife last saw Billie Jo Hettinger midday Sunday. The women waved at each other, and his wife didn't notice anything out of the ordinary, he said. The Hettingers were friendly and generous donors to his children's school fundraisers, Smith said.

According to his LinkedIn social media site, Brad Hettinger spent about a dozen years in the Army as a helicopter pilot.

Smith said that Hettinger had mentioned his military past, but said the two usually chatted about current events.

"You just wonder, what you could have done differently," he said. "What you could have done to help, what you could have done to prevent things."