Still, Mr. Caro adds a caveat: “That doesn’t always translate into a great presidency.”

So what does it look like?

Image HE HAD IT John F. Kennedy at the Democratic National Convention in Los Angeles in 1960. Credit... The Estate of Garry Winogrand, courtesy Fraenkel Gallery, San Francisco

Charisma, as defined by the early sociologist Max Weber, was one of three “ideal types” of authority  the others were legal, as in a bureaucracy, and traditional, as in a tribe  and rested upon a kind of magical power and hero worship. That definition was, of course, unsuitable for modern times, as one of Weber’s many interpreters, Arthur M. Schlesinger Jr., wrote in “The Politics of Hope.” Its use became metaphorical, as Mr. Schlesinger wrote, “a chic synonym for heroic, or for demagogic, or even just for ‘popular.’ ”

But it was also a coolness that Norman Mailer captured in Kennedy  for whom Mr. Schlesinger became a kind of official hero-worshiper  writing about the 1960 Democratic convention in Los Angeles. Mr. Mailer described how Kennedy’s convertible, then his suntan and his teeth, emerged before a camera-filled crowd in Pershing Square, “the prince and the beggars of glamour staring at one another across a city street.”

There was, Mr. Mailer wrote: “an elusive detachment to everything he did. One did not have the feeling of a man present in the room with all his weight and all his mind. Johnson gave you all of himself, he was a political animal, he breathed like an animal, sweated like one, you knew his mind was entirely absorbed with the compendium of political fact and maneuver; Kennedy seemed at times like a young professor whose manner was adequate for the classroom but whose mind was off in some intricacy of the Ph.D. thesis he was writing.”

By any definition, the charismatic leader emerges at a time of crisis or national yearning, and perhaps a vacuum in that nation’s institutions. Mr. Schlesinger wrote in 1960 of a “new mood in politics,” with people feeling “that the mood which has dominated the nation for a decade is beginning to seem thin and irrelevant.” There was, he wrote, “a mounting dissatisfaction with the official priorities, a deepening concern with our character and objectives as a nation.”

That might well describe the climate Obama supporters feel now.

Alan Wolfe, the director of the Boisi Center for Religion and American Political Life at Boston College, says Mr. Obama is simply  understandably  making an emotional appeal to those yearnings. “Politics is about policy, but it’s also about giving people some kind of sense of participating in a common venture with their fellow citizens,” Mr. Wolfe said.

Philosophers call it “civil religion,” using the language of religion and elevation to talk about your country. A classic example is Ronald Reagan’s summoning of the “city on a hill.” That, Professor Wolfe said, was the parallel Mr. Obama was hinting at when he talked about Reagan as a transformative leader.