Now that the Ashley Madison hack has outed as many as 15,000 federal employees and active duty military, government agencies say they’re combing through the e-mail addresses of possible adulterers to see if their extramarital activity on work time amounts to anything punishable.

The rules of the game for morality in federal offices may be straightforward for pornography (watching it can definitely get you fired) — but the kind of skeleton in the closet that showed up in the trove of 36 million users exposed on the cheating Web site presents officials with a murkier problem, experts say.

The rules vary on the kind of personal use of work computers that’s allowed on government time. Mostly, they’re more restrictive than a private company’s. It’s okay to make a doctor’s appointment, call the babysitter, tell your spouse you’ll be home late. It’s okay to check on your investments during the stock market’s current nosedive. These are technically called “private use” exceptions to authorized uses of government property.

Things you can’t do from your government e-mail address: Endorse a product or service, sell a product for profit, advertise or do anything else that “interferes with the agency’s mission or brings discredit to the agency.” Pornography, by being sexually explicit, falls into this category.

“In that case, it’s not like you’re spending a long time with your elderly aunt because she’s having health problems,” said John Palguta, a former federal manager who is now a vice president at the nonprofit Partnership for Public Service. With pornography, “we have this interest in contemporary American standards,” he said.

But the employees who browsed the goods on Ashley Madison or used the Internet connections in their federal offices to pay membership fees may or may not have been doing anything sexually explicit. They could have spent hours every week on the site, or visited once. They may be actually having an affair, or they may not.

“Is the agency making moral judgments about whether or not it’s okay to be arranging an affair?” asked Joseph Kaplan, a federal employment attorney with Passman & Kaplan in Washington, who says it could be wrong to automatically fire someone or haul them in on misconduct charges just because they got to the site through their government e-mail address.

“Where do they draw the line between what’s acceptable and what’s not?” Kaplan asked.

What's ripple effects of the Ashley Madison hack. (Jorge Ribas/The Washington Post)

Let’s say an employee is having an affair and e-mailing his or her lover from work, but the infidelity did not start on Ashley Madison. Why does that person fall under the radar of a supervisor, while the employee with the hacked e-mail address does not?  A federal employee could be in an open relationship. Or going through a divorce and testing the waters. That’s still doing something other than work at work. But it suddenly seems more innocuous than the most  salacious affairs we can imagine, federal personnel experts said.

The Associated Press combed through the data dump and found hundreds of civilian employees who logged onto Ashley Madison from government Internet addresses. Other estimates have listed 15,000 accounts using addresses belonging to domains used by the government or the military.

Those who used military addresses to access the site could face disciplinary action, since adultery can be a crime under the Uniform Code of Military Justice.

But it could be hard to prove that an Ashley Madison membership translates to an affair, said a Defense Department official who requested anonymity because the agency is looking through the data leak for accounts affiliated with DOD e-mail addresses.

Government officials and employment attorneys agreed that the likelihood of getting hit with a misconduct charge could depend on how much time the employee has spent on the site and how sexually explicit the e-mails are.

“You could in that case have an agency say, ‘This is conduct unbecoming a federal employee because you’re having sex talk, exchanging e-mails that say, ‘These are my sexual interests,” Kaplan said.

At DOD, any disciplinary action “would be a determination by department officials based on a review of all credible evidence,” agency spokesman Joseph Sowers said.

Sowers cautioned that some of the e-mail addresses in the hacked Ashley Madison user data “may not even be accurate.” Barack Obama’s e-mail domain was a fraud, for example. “We’re not going to rush to judgment,” Sowers said.

The Department of Homeland Security and General Services Administration also said they’re reviewing allegations that employees may have misused government property.

DHS, in a statement. called potential violations “both a personnel and security matter.” The agency considers “viewing, downloading, storing, transmitting or copying materials that are sexually explicit or sexually oriented, related to gambling, illegal weapons, terrorist activities, or any other prohibited activities” an “inappropriate personal use” of government office equipment.

The question is, does going on a Web site qualify as inappropriate use just because the government doesn’t approve of the content?