James and Lachlan Murdoch, along with lawyers and their father Rupert, who has been phoning in from vacation, have had daily discussions about the crisis at Fox News.

The "crisis" is the sexual harassment allegations against Fox News boss Roger Ailes. 

Although the Murdoch brothers have made a number of changes at 21st Century Fox after their dad handed over the reigns, one place they have not touched is Fox News.

The NY Times writes that the brothers have left it alone for two reasons. First, Fox News, which continues to dominate in the ratings, contributes roughly 20 percent of the conglomerate’s annual earnings, and any changes, even seemingly minor ones, could endanger that profit. Second, Roger Ailes, who has run Fox News for 20 years, has little interest in corporate oversight. He has sparred with Lachlan Murdoch in the past — and won.

But the Murdoch siblings now have little choice. Gretchen Carlson, the former Fox News host, filed a sexual harassment lawsuit against Mr. Ailes on July 6. Her charges have resulted in a public-relations nightmare for Fox News, and 21st Century Fox now faces questions about succession planning at the linchpin operation. In short, analysts say, it has become the Murdoch brothers’ biggest leadership challenge since taking over.

Moving with notable speed, the Murdochs hired the law firm Paul, Weiss, Rifkind, Wharton & Garrison to run an internal investigation. A leader of the firm’s inquiry is Michele Hirshman, a former deputy New York attorney general known for helping Eliot Spitzer fend off criminal charges in the federal prostitution case that led to his resignation as governor. Ms. Hirshman’s team, which includes multiple Paul, Weiss partners and associates, has started to interview employees and review emails.

Mr. Ailes, 76, a towering figure in media and Republican politics, has denied any wrongdoing, and 21st Century Fox has expressed its “full confidence” in him.

There are also things to consider beyond the specifics of Ms. Carlson’s lawsuit. What happens if the investigation turns up nothing to support her claims but finds a hostile workplace nonetheless?

Upending Fox News with a seismic leadership change, particularly as the presidential election season intensifies, is a scenario the brothers are not eager to confront. Despite their personal feelings toward Mr. Ailes, which run cool, and despite their eagerness to modernize 21st Century Fox, the company needs Mr. Ailes, analysts say.

In addition to the more than $1 billion in profit it delivers annually, Fox News gives 21st Century Fox a weapon in talks with cable and satellite operators: Carry all of our networks, and at favorable terms, or we will withhold the enormously popular Fox News. Without the omnipotent Mr. Ailes in charge, Fox News could quickly lose its focus and become less of a juggernaut. Moreover, Mr. Ailes has no clear replacement.

More from the Times.