Perhaps Tim Sullivan, the city’s chief of staff of intergovernmental affairs, was cooperating with federal authorities. Maybe he was not. Perhaps he had been thinking about it.

Such are the theories circulating in the wake of Wednesday’s second indictment in the federal investigation into City Hall employees’ relationship with local labor unions.

Some legal analysts speculate that investigators had a breakthrough since the first indictment was handed out May 19.

“I suspect that news of the first indictment broke some logjam, and developed some evidence and developed it quickly,’’ said Paul V. Kelly, a former US prosecutor who is now a Boston-based defense attorney with Jackson Lewis. “Thirty days is a short period of time, but I’m betting something significant developed in the meantime.’’

He added, “These cases don’t get wrapped up in one slug like that; they tend to evolve, as one domino leads into another.’’

Sullivan, 36, of Dorchester, was named in an indictment Wednesday that had earlier charged his colleague Kenneth Brissette, the city’s director of tourism, sports, and entertainment, with “union-related extortion.’’ They now both face charges of conspiracy and extortion for allegedly withholding city permits from a popular Boston music festival, Boston Calling, until it hired union stagehands. If convicted, they face a maximum of 20 years in prison.

After a brief court hearing Wednesday, Sullivan’s lawyer, William Cintolo, denied to reporters that his client was involved in wrongdoing. He said prosecutors were trying to criminalize his legitimate work on behalf of constituents.

Martin Weinberg, a Boston attorney, said he believed the arrest of Sullivan could signal the end of the federal investigation, as least as it relates to Boston Calling. He noted a US Supreme Court decision Monday that set a new standard in defining public corruption cases, protecting public employees who perform legitimate work.

“It’s clear that the federal judiciary is requiring that federal prosecutors reduce their charges to the heart and core of a statute . . . particularly when they’re charging state and local officials,’’ he said.

“You can hypothesize that they have new evidence, or hypothesize they weren’t ready at the time of the initial indictment,’’ he said. “But I think you’re dealing with a closed compartment. I don’t think this is an open-ended vehicle for further charges on this subject.’’

Other legal analysts say it is too early to say what effect the arrest of Sullivan might have on the ongoing investigation into City Hall. But several said prosecutors have shown they will bring a new indictment if they develop new evidence.

“It might mean this is all they have, but is it over? It probably means this is all they have right now,’’ said Max Stern, an attorney with the Boston firm Todd & Weld. “But in any case, it doesn’t mean they won’t do more if they get more.’’

The Globe has previously reported that federal authorities have embarked on a widespread investigation into unions allegedly pressuring local developers and event organizers, and that the investigation has examined Mayor Martin J. Walsh’s actions as a labor leader before he took office in 2014.

His administration has also come under scrutiny for actions beyond the Boston Calling investigation: Brissette was named in the case of five Teamsters members accused of attempting to extort jobs from a television show production crew that was looking to film in Boston. That case is pending.

Some legal analysts said the arrest of Sullivan four weeks after the arrest of Brissette could signify that the investigation has intensified — or that the arrest could be an attempt to send a message to City Hall, to see whether more witnesses are willing to talk.

“It’s what’s called tickling the wire; they just sort of watch to see what it does,’’ said Robert Sheketoff, a Boston attorney.

If investigators are targeting Walsh, he said, “you work your way up the ladder, by convicting the underlings and getting them to flip.’’

Walsh told reporters during a press briefing Wednesday that he assumed that the name withheld in last month’s indictment would surface — he maintained he did not know who it was — but he hopes Wednesday’s indictment will close the case.

“I think that I read the indictment today, and it didn’t seem like there was anything else that was going to come in the indictment,’’ he said.

Andrew Ryan of the Globe Staff contributed to this report. Milton Valencia can be reached at milton.valencia@globe.com. Follow him on Twitter @MiltonValencia.