WASHINGTON — “Are you up?”

The emails arrive late, often after 1 a.m., tapped out on a secure BlackBerry from an email address known only to a few. The weary recipients know that once again, the boss has not yet gone to bed.

The late-night interruptions from President Obama might be sharply worded questions about memos he has read. Sometimes they are taunts because the recipient’s sports team just lost.

Last month it was a 12:30 a.m. email to Benjamin J. Rhodes, the deputy national security adviser, and Denis R. McDonough, the White House chief of staff, telling them he had finished reworking a speechwriter’s draft of presidential remarks for later that morning. Mr. Obama had spent three hours scrawling in longhand on a yellow legal pad an angry condemnation of Donald J. Trump’s response to the attack in Orlando, Fla., and told his aides they could pick up his rewrite at the White House usher’s office when they came in for work.

Mr. Obama calls himself a “night guy,” and as president, he has come to consider the long, solitary hours after dark as essential as his time in the Oval Office. Almost every night that he is in the White House, Mr. Obama has dinner at 6:30 with his wife and daughters and then withdraws to the Treaty Room, his private office down the hall from his bedroom on the second floor of the White House residence.