A Maricopa County jury heard opening statements Tuesday in the trial of celebrity vegan chef Anthony Milan Ross, who is accused of murdering his wife and two children on Christmas Day 2017 after conducting internet searches prosecutors say show planning and intent.

Ross, 53, faces three counts of first-degree murder and 20 counts of aggravated assault in the deaths of his wife, Iris, 38, and the couple’s children, Nigel, 11, and Anora, 10 months. Prosecutors told jurors that searches on Ross’s devices included terms such as “battery acid,” “sulfuric acid,” “skin-melting acid,” “guns,” “silencers” and examples of people killing their families on Christmas Day, and that those searches support a theory of premeditation.

Maricopa County prosecutor Richard Dusterhoft told the jury Ross had told people to “expect something big on Christmas” and said the defendant “thought about it before he did it. He meant to do it, and then he did it.” Prosecutors allege Ross shot Iris outside their Phoenix apartment complex on Dec. 25, 2017, then engaged in a roughly six-hour standoff with police before officers breached the residence and discovered the children’s bodies inside.

Defense attorney Carrie Gallagher told jurors the case would include grisly details and conceded the events were a “tragedy,” but urged the jury to distinguish between rumination and premeditation. Gallagher said Ross’s mental health declined in 2017, that he suffered from insomnia and that some of the internet searches took place during periods of poor or no sleep.

“You will see that much of this behavior, these searches, were done during periods when he had poor sleep or even no sleep,” Gallagher said, according to court accounts. She argued that searching for disturbing material can reflect obsessive thoughts and coping behavior rather than a plan to kill, and pointed to contemporaneous actions she said showed Ross was planning for the future — including adopting a dog, arranging social meetings after the holidays, writing a business check and proposing to a girlfriend days before the killings.

Gallagher also said Ross woke on the morning of the killings extremely depressed and messaged Iris about the pain of their separation after drinking a bottle of whiskey. Witnesses told police they saw Ross shoot Iris as she tried to flee the scene, and that he then pointed his gun at bystanders before entering the apartment, where two or three more shots were heard.

Prosecutors described Ross as a public figure who marketed a transformation tied to a vegan lifestyle and weight loss and who built a motivational image that they say was dependent on the couple’s finances. Ross, who performed under the name Milan, rose to broader visibility after losing significant weight in his 20s, producing inspirational videos and appearing alongside figures such as filmmaker James Cameron and actor Samuel L. Jackson in a feature-length documentary about veganism.

On the afternoon of Dec. 25, 2017, Ross posted a video with his 11-year-old son singing “Santa Claus Is Coming to Town,” prosecutors said; authorities say the shooting began about 90 minutes later.

If convicted of first-degree murder, Ross faces the possibility of the death penalty. Prosecutors must prove beyond a reasonable doubt that the killings were premeditated to secure first-degree murder convictions. The defense contends the evidence does not meet that standard and stresses Ross’s deteriorating mental state and insomnia as explanations for the internet searches and behavior shown to jurors.

Court proceedings are ongoing and are expected to include testimony from law enforcement, witnesses who reported the shooting, and experts who may be asked to analyze digital evidence and Ross’s mental state at the time of the deaths.