Scientists had assumed the core was rotating like a merry-go-round at about the same speed as the surface.
"The most likely explanation is that this core rotation is left over from the period when the Sun formed, some 4.6 billion years ago," said Roger Ulrich, a professor at University of California, Los Angeles (UCLA) in the US.
"It is a surprise, and exciting to think we might have uncovered a relic of what the Sun was like when it first formed," said Ulrich, co-author of the study published in the journal Astronomy and Astrophysics.
The rotation might also impact sunspots, which also rotate. Sunspots can be enormous; a single sunspot can even be larger than the Earth.
The researchers studied surface acoustic waves in the Sun's atmosphere, some of which penetrate to its core, where they interact with gravity waves that have a sloshing motion similar to how water would move in a half-filled tanker truck driving on a curvy mountain road.
By carefully measuring the acoustic waves, the researchers precisely determined the time it takes an acoustic wave to travel from the surface to the centre of the Sun and back again.
That travel time turns out to be influenced slightly by the sloshing motion of the gravity waves, Ulrich said.
The researchers identified the sloshing motion and made the calculations using 16 years of observations from an instrument called GOLF (Global Oscillations at Low Frequency) on the spacecraft SoHO (Solar and Heliospheric Observatory) - a joint project of the European Space Agency and NASA.
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