Reputation: Narwhals are mythical creatures – unicorns of the sea. They are "toothed whales" so obviously have teeth in their mouths. They spear their food, and are as aggressive and dangerous as they look.

Reality: Narwhals are not mythical. They do not have teeth in their mouths, but their characteristic tusk is actually an overgrown tooth. They do not catch food by spearing it. They are shy and skittish.

Narwhals are iconic creatures of the Arctic. They have intrigued explorers and scientists for hundreds of years.

The narwhal's tusk was once passed off for exorbitant sums as unicorn horn

But they spend long Arctic winters in dark, pack-ice covered waters, and live in vast remote seas that are difficult to get to. That makes them difficult to study, so perhaps it is not surprising that misconceptions abound.

"A lot of people really don't believe they are still alive," says Martin Nweeia of Harvard University in Cambridge, Massachusetts, US. Adults are apparently more prone to this misperception. "Oddly enough, kids are little more savvy these days about narwhals."

Nweeia, a dentist, became obsessed with narwhal teeth over a decade ago and has since made it his mission to figure out what the tusk does.

The narwhal's tusk was once passed off for exorbitant sums as unicorn horn. It is a mainly male feature, but occasionally female narwhals have one. There are also a few "double tuskers": males that have two tusks rather than one, for unknown reasons.

A lot of people think this whale has teeth in its mouth, and it has none

Perhaps the most pervasive myth about the tusk is that narwhals use it to spear food. Anyone who believes this needs to think through the practicalities, says Kristin Westdal of The Pew Charitable Trusts' Oceans North Canada.

Narwhal tusks can grow to lengths of 2-3m, and they eat relatively small prey like halibut, shrimp and squid. Spearing these animals would be really difficult, and even if a narwhal managed it, it would not have any other appendages long enough to retrieve the fish from its tusk.

Many people also have the idea that narwhals chew their food. This is understandable, given that they belong to a group of animals known as "toothed whales", but it's not true.

"A lot of people think this whale has teeth in its mouth, and it has none," says Nweeia. The only tooth they have is the tusk.

This tooth is almost like a piece of skin in the sense that it has all these sensory nerve endings

All sorts of suggestions have been made about the function of the narwhal tusk. Perhaps it is an acoustic probe for detecting sound, or a temperature regulator, or a breathing organ. Maybe it is an aggressive weapon for narwhal-narwhal battles, or for fending off predators. It could also be an icebreaker, a digging tool, or a way to show off to females.

To solve this puzzle, Nweeia has assembled a team that includes marine and developmental biologists, comparative zoologists, dentists, and orthopedic surgeons.

In a 2014 study that is perhaps the most detailed and high-tech analysis of the tusk ever attempted, they concluded that it is a highly sensitive organ.

"This tooth is almost like a piece of skin in the sense that it has all these sensory nerve endings," says Nweeia. That is not seen in other mammalian teeth except when they are diseased.

In all the encounters I've had with them, they are beautiful… and quite graceful

The narwhal tusk is "essentially built inside out," says Nweeia. Unlike our own teeth, it is soft on the outside, and gradually gets hard and dense on the inside.

Nweeia's team showed that the tusk can sense changes in the salinity of the water, suggesting that it is a giant, antennae-like sensor.

That is a little tricky to explain. "The tusk is most common in males and is only infrequently found in females," says Westdal. That suggests that it isn't "anything special required for survival", but is something to do with courtship and mating.

They are not mutually exclusive explanations, says Nweeia. Tusks could be multifunctional: a good tusk could be a useful sensor, and as a result females might decide "that guy's got a great tusk, I'm going with him."

Cartoons sometimes suggest that narwhals are fierce creatures, perhaps dueling with their tusks.

But that is not what Westdal has seen. "In all the encounters I've had with them, they are beautiful… and quite graceful," she says.

Conservationists are already trying to protect critical areas like Lancaster Sound

Narwhals are also shy and skittish. That is not particularly surprising, as humans have hunted them for centuries. Today, the Inuit hunt them under carefully-managed quotas, a practice that "is important culturally and from a dietary perspective," says Westdal.

The hunting is not a threat to the species, but noise might be. As the Arctic sea ice retreats due to global warming, ever more shipping is passing through the Arctic, and that means it is getting noisier.

That could be a problem for narwhals. Being whales, they communicate using sound: specifically, buzzy clicks, squeaks like a creaking door and strange whistles. They also use sonar to navigate. It is possible that all the extra noise will force them out of important habitats.

Alternatively, they might shrug it off. "We don't know the answers to this at all," says Westdal. Preferring not to wait, conservationists are already trying to protect critical areas like Lancaster Sound, which most of the world's narwhals pass through every year.

Lesley Evans Ogden is on Twitter @ljevanso