In her closing argument, Elisa Long, a federal public defender representing Mr. Bowers, emphasized that he had not gotten in trouble with the law before the attack. But, she said, in the months leading up to it, he had “spent a tremendous amount of time alone on the internet absorbing all kinds of vile and extremist content.”

But Mr. Bowers is not pursuing an insanity defense, in which the defendant admits to carrying out some criminal act but argues that, due to mental incapacity, he did not fully understand that it was wrong. Insanity defenses are rare, and legislation made such defenses substantially harder to make after John W. Hinckley Jr. was found not guilty by reason of insanity in the 1981 assassination attempt on President Reagan.

“Insanity defenses, I don’t care what kind of case it is, are extremely challenging to succeed with,” said George Kendall, a lawyer who represents people on death row. It would have been particularly difficult in this case, several defense attorneys said, with a defendant who seemed explicit about his hatreds and does not show glaring signs of a debilitating psychosis.

But when it comes to deciding whether someone is deserving of execution, Mr. Kendall said, evidence of serious mental illness can give one or more jurors serious reservations — which can be enough for the defense, since death penalty verdict has to be unanimous.

In 2015, a jury rejected the insanity defense raised by James Holmes, who killed 12 people and injured scores of others in an Aurora, Colo. movie theater, and found him guilty on all charges. The jury then ruled that he had acted with aggravating cruelty and was eligible for a death sentence. But, after a month of testimony about Mr. Holmes’s struggles with mental illness, that same jury was divided on whether he should be executed. He was sentenced to life in prison without the possibility of parole.

“While jurors rejected the notion that Mr. Holmes fit the narrow legal definition of insanity,” his public defenders wrote in a 2016 article in the Denver Law Review, “the experts in the case agreed that Mr. Holmes would not have committed this horrible crime had he not been mentally ill.”

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