INDIANAPOLIS —  

What do you do when a political celebrity shows up for an impromptu lunch at a landmark restaurant where the cast and crew of NBC’s “Parks and Recreation” are shooting a scene? You ask him if he wants in on the action and then, on the spot, you write up a cameo role.

That’s what happened Monday when former presidential candidate Newt Gingrich unexpectedly walked into St. Elmo’s Steak House in downtown Indianapolis as actor Rob Lowe and his male co-stars were filming a scene for an upcoming episode of the popular sitcom based in fictional Pawnee, Ind.

“This is wild,” said actor Adam Scott, as Gingrich passed by on his way to makeup. It’s Scott’s character, Ben Wyatt, who’s the reason why Hollywood had taken over much of the iconic steakhouse: St. Elmo’s is the scene of Ben’s big bachelor party in Indianapolis, thrown by his steak-loving co-worker, Ron Swanson, and attended by some of the civil servants who populate Pawnee’s city hall. (Ironically, Scott’s character has recently returned from a job on Capitol Hill.)

Gingrich had stopped by the restaurant, not knowing of the film shoot, on his way to an appointment with Indiana Gov. Mitch Daniels.

“I think he’s one of the finest leaders in government today,” said Gingrich, who’s writing a book on leadership and said Daniels will be a part of it.

The Gingrich stop-by was proof to the Parks and Recreation cast and crew that Lowe — who has deep Indiana roots — knew what he was talking about when he told them that St. Elmo’s was THE place to be.

“Rob loves Indianapolis and he loves this place,” said the show’s producer Morgan Sackett, who, along with his co-workers, labor to get the Indiana details just right. That’s why Gingrich, the former Speaker of the U.S. House of Representatives, wasn’t the only politician who stopped by the restaurant during the shoot. So, too, did Brian Bosma, the Speaker of the Indiana House of Representatives and an attorney who specializes in municipal law.

A year ago, Bosma got a call from somebody who said he was with NBC and wanted Bosma to consult with the Parks and Recreational writers to give them guidance on how state and local government works in Indiana.

“I thought it was some of my pals at the Statehouse playing a joke,” Bosma said. It wasn’t. Bosma was indeed hired by NBC to offer advice for a story line involving the show’s star, Amy Poehler, who plays Leslie Knope, a Pawnee Parks Department staff member who runs for the Pawnee City Council.

“I asked for a cameo role, but they turned me down,” Bosma said. He did, though, get a chance to meet Lowe, who plays a character who was once a state auditor and now is the Pawnee city manager.

Lowe’s father grew up in Anderson and his grandparents lived in Madison County.

Lowe, who earned his star power playing a White House staff member on the TV series “The West Wing,” said he signed on for “Parks and Recreation” in part because of it’s Indiana connection. The show offers a satirical look at government bureaucracy through the eyes of some earnest Hoosier civil servants.

“My family is all from Indiana,” said Lowe, adding — with the gee-golly enthusiasm of his character Chris Traeger — that he recently discovered that his great-great-grandfather served as a Indiana volunteer in the Civil War.

“I have such affection for this state and for the way we portray its people on the show,” Lowe said. “It was one of the reasons why I so attracted to the show. As a Midwesterner, I know how Hollywood really gets our part of the country wrong. I think this show really gets it right in a lot of ways. Obviously we do it with a lot of spoof and satire, but Pawnee, Indiana, comes across as an authentic place and a place of love.”

Speaking of love: following the St. Elmo shoot, the cast and crew were off to shoot another scene at Lucas Oil Stadium. It was arranged by Lowe’s friend, Colts’ owner Jim Irsay.

They’d flown into town Sunday, just as the Colts were making a last-seconds touchdown to win its game over the Detroit Lions.

“The whole plane erupted in cheers,” said Nick Offerman, who plays Ron Swanson. “We knew we were in the right place.”