With bodies as long as school buses, you would think that Omura's whales could never go unnoticed. Yet they are among the most mysterious of whales.

The species was only given its name, based on dead specimens, in 2003. Since then scientists have failed to find live ones.

Now the wait is over. Whale researchers have discovered a population of Omura's whales living near Madagascar. Their study, published in Royal Society Open Science, offers the first glimpse of how these elusive whales live.

Biologist Salvatore Cerchio led the study while at the Wildlife Conservation Society. He has since joined the New England Aquarium and Woods Hole Oceanographic Institution.

His team almost missed the Omura's whales. In 2011, they were surveying dolphins in the coastal waters off Madagascar when they encountered three whales: a mother-calf pair and later a lone adult. But they thought they had found Bryde's whales, another little-known whale that lives in the region.

Some teammates thought it might be a new species and began to think of new names

The next year, the team saw another four whales in fleeting encounters. They suspected that "at least one of the whales was something different."

Then in 2013, the team moved further offshore and searched deeper waters. This time they saw whales within days, racking up 13 sightings. The prize encounter was a mother-calf pair that swam close to the boat, revealing that the mother had no ridges on her head and a lower jaw with contrasting light and dark sides. That convinced the team that it was not a Bryde's whale.

"I was excited because I knew we had found Omura's whales," says Cerchio. But the whales were thousands of kilometres further west than they were thought to roam. "Some teammates thought it might be a new species and began to think of new names."

In late 2014, genetic tests confirmed that they had found the first live population of Omura's whales. By then, they had logged 44 sightings.

"Omura's whales are built for speed," says Cerchio. He describes them as "spectacular animals with long, narrow bodies". Growing up to 12m long, Omura's whales are asymmetrical: their right side is whiter and their left is darker. Light and dark patches and stripes extend from the right eye to the pectoral fin.

These patterns mean each whale is individually recognisable. But scientists also recognize beauty. The most common response to Cerchio's photos is simply "beautiful whale".

The whales surface briefly and reveal little of their bodies

Cerchio's findings tell us that Omura's whales roam more widely than previously thought. We knew they swim in the waters between the eastern Indian Ocean, Japan and Australia. Now it seems they also swim in the western Indian Ocean.

In 2003, Japanese researchers used skeletal specimens and genetic tests to establish Omura's whales as a new species. Previously they had been mistaken for unusually pale Bryde's whales or small fin whales.

That was understandable. Whale specimens are scarce and scattered in collections across the world, so it is hard to compare them, says co-discoverer Tadasu Yamada of the National Museum of Nature and Science in Tokyo, Japan.

What's more, Omura's whales never show both their heads and dorsal fins together, and never lift their tails out of water during a dive. "The whales surface briefly and reveal little of their bodies," says Cerchio.

Now we are starting to understand them.

Unlike many other whales such as humpbacks, Omura's whales almost always travel alone. Even so, "if you explore the area, you would find another one several hundred meters away," says Cerchio. The whales make low-pitched sounds, so Cerchio suspects that they socialise in loose groupings.

Human noise is a pervasive threat across the oceans

The team spotted four mothers with their calves, suggesting that the whales breed and raise young in the area around Madagascar.Nobody is sure what they eat, but Cerchio's team did see them lunge-feeding. A whale would accelerate fast, then open its mouth wide and suck in huge volumes of water, which it filter through tight, hairy plates called baleen. They may well have been eating tiny plankton, because there were no fish in sight.

For now, Cerchio says we can only speculate on how many Omura's whales are out there. But they may not be safe.

Oil exploration around Madagascar cranks out noise that could drown out the low noises made by the whales. So far Cerchio has no evidence that human-caused noise is harming the Omura's whales, but he says it is important to find out.

"Human noise is a pervasive threat across the oceans," says Cerchio. "Unfortunately, the effect is insidious and difficult to detect."