Caroline Dove holds a photo of Marine Corps Lance Cpl. Squire “Skip” Wells, her boyfriend, at her home in Savannah, Ga. Wells was among four Marines killed Thursday in an attack in Chattanooga, Tenn. (Russ Bynum/Associated Press)

IN THE hours after Thursday’s terrible killing spree at a Chattanooga military facility, a photo of one of the victims was posted on Facebook. Thomas J. Sullivan, a 40-year-old Marine, was shown proud and strong in camouflage gear as he stood grinning in front of a military vehicle. The gunnery sergeant — one of three children of Jerry and Betty Sullivan of Springfield, Mass. — had served and survived two tours of duty in Iraq and was awarded two Purple Hearts, so there was a particular cruelty to his death, along with three other U.S. Marines, at a Tennessee center where he trained reservists.

“Heartbreaking” is how President Obama described the circumstances. Navy Secretary Ray Mabus elaborated: “While we expect our Sailors and Marines to go into harm’s way, and they do so without hesitation, an attack at home, in our community, is insidious and unfathomable.” Sadly it was not the first time the nation has experienced violence at one of its domestic military facilities.

As the nation mourns the loss of Gunnery Sgt. Sullivan and the three others gunned down — Sgt. Carson A. Holmquist of Polk, Wis.; Lance Cpl. Squire “Skip” Wells of Cobb, Ga.; and Staff Sgt. David A. Wyatt of Burke, N.C. — and prays for the speedy recovery of those wounded, it is urgent that authorities determine what possessed Mohammad Youssef Abdulazeez, the alleged gunman who died during a shootout with police, to go on his murderous rampage at two military sites.

There are more questions than answers about the 24-year-old Kuwaiti-born U.S. citizen who was raised in a Chattanooga suburb by a conservative Muslim family and worked as an electrical engineer. Friends and neighbors described him as seemingly well-adjusted with a background remarkable for its normalcy; “always happy go lucky,” said one high school friend. But new details are emerging that paint a more complicated picture. Court filings show there were domestic and financial problems in the family. Recent blog postings believed to have been written by Mr. Abdulazeez show a young Muslim in search of more meaning in life and musing about jihad. The FBI is leading what authorities called “a terrorism investigation,” and among the leads being examined are Mr. Abdulazeez’s travels to the Middle East.

Did he act alone? How did he obtain the weapons used in the killings? Was the attack, as some fear, either inspired or directed by Islamic State terrorists who have stepped up calls for their followers to mount attacks against U.S. interests, including military installations?

Authorities at a news conference Friday said there is no indication of Islamic State involvement but stressed the investigation is in its early stages. They said that while the case is being investigated as a terrorist act, no conclusion will be made until all the facts are known.

Such caution is prudent. The people whose lives were taken on Thursday can never be replaced, but determining the why and how of their tragic deaths — and bringing to justice any others who might have been involved — will honor their service.