In the wake of the US Supreme Court's landmark ruling to overturn the Defence of Marriage Act, New Yorker magazine has decided to answer the question.

That ruling grants same-sex couples the "equal liberty" guaranteed by the US constitution's Fifth Amendment.

In response, the magazine has put Bert and Ernie — the iconic residents (and roomates) of the long-running children's TV series Sesame Street — on the cover of next week's issue.

The cover image — titled Moment of Joy — depicts them sitting on a couch, Bert's arm wrapped around Ernie and Ernie's head nestled against Bert's shoulder.

They are seen watching the Supreme Court decision on a black and white TV.

The release of the cover image has provoked fierce debate in the US, about whether the image explicitly states they are a couple, or even whether Sesame Workshop — who own the characters — will sue the magazine.

The question of whether Bert and Ernie "are" or "are not" has persisted for years, fuelled largely by the fact that they share a bedroom, though it should be noted they sleep in separate, single beds.

Back in 2007, Sesame Workshop addresses the issue, saying: "[Bert and Ernie] are not gay, they are not straight, they are puppets. They do not exist below the waist."

The issue was revisited again in 2011 when Sesame Workshop issued a longer statement, stating they were "best friends".

"[Bert and Ernie] were created to teach preschoolers that people can be good friends with those who are very different from themselves," the statement said. "Even though they are identified as male characters and possess many human traits and characteristics (as most Sesame Street Muppets do), they remain puppets, and do not have a sexual orientation."

The characters were created more than four decades ago by Jim Henson, who created the Sesame Street and Muppet Show programs.

Bert is taller, and crankier. Ernie is shorter and more playful. Their different personalities — and Bert's disapproval of Ernie's behaviour — is the basis for most of their interaction. In that sense, they are written like a Muppet version of The Odd Couple.

Ernie, notably, is frequently seen in the bath playing with a rubber duck. It should also be noted that a portrait of the pair hangs on one of the walls of the room they share.

Back in 2011, The New York Daily News felt the issue significant enough to address in an editorial. They were not amused.

"Why stop there? Why not march Yogi Bear and Boo Boo down the aisle, too?" the editorial said. "The only hands Henson ever intended to go up Ernie's horizontally striped shirt, or Bert's vertically striped one, were human puppeteers'."

The urban myth website Snopes has traced references to the issue back to 1980, when a book, The Real Thing, claimed the two co-habiting puppets were in fact a couple.

"Bert and Ernie conduct themselves in the same loving, discreet way that millions of gay men, women and hand puppets to," the book's author, Kurt Andersen, wrote. "They do their jobs well and live a splendidly settled life together in an impeccably decorated cabinet."

The New Yorker cover image was not created for the magazine.

The artist, Jack Hunter, first submitted it to a Tumblr photo blog in May, 2012. In that version, the television image was of US president Barack Obama.

In a brief statement accompanying the cover image posted on the magazine's website, Hunter said: "It's amazing to witness how attitudes on gay rights have evolved in my lifetime. This is great for our kids, a moment we can all celebrate."

New Yorker is not commenting except to say "the cover speaks for itself."

Sesame Workshop has not commented.