The Telegraph writes:

Australian photographer Jason Edwards, who took the images off Tonga, was stunned by the "brief but tender" copulation.

While humpback "heat runs" - in which 15m-long, 40-tonne males fight to win a female's attention - have been well documented, and often wrongly described as mating, this is the first time the actual act of copulation has been photographed, the National Geographic Channel said.

"It was amazing. There were four or five males vying for her attention and while the larger ones were busy jostling each other, the smallest one swam away with the female," Mr Edwards said yesterday.

"Their coupling lasted less than 30 seconds, which might explain why it's never been captured on film before."

I had to look HEAT RUN up on YouTube:

I thought they were hugging until I saw the animated GIF rendition: