Rotating ellipsoidal variables are a class of variable star

Variable star

A star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth...

. They are close binary

Binary star

A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

 systems whose components are ellipsoidal. They are not eclipsing, but fluctuations in apparent magnitude

Apparent magnitude

The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...

 occur due to changes in the amount of light emitting area visible to the observer. Typical brightness fluctuations do not exceed 0.1 magnitudes.

The brightest rotating ellipsoidal variable is Spica

Spica

Spica is the brightest star in the constellation Virgo, and the 15th brightest star in the nighttime sky. It is 260 light years distant from Earth...

(α Virginis).