closely spaced period-luminosity relations, corresponding to the first, second and third overtones of radial pulsation models for stars of certain masses and luminosities, but that dipole and quadrupole non-radial pulsations are also present leading to the semi-regular nature of the variations. The fundamental mode does not appear, and the underlying cause of the excitation is not known. Stochastic convection has been suggested as a cause, similar to solar-like oscillations. Two additional types of variation have been discovered in RGB stars: long secondary periods, which are associated with other variations but can show larger amplitudes with periods of hundreds or thousands of days; and ellipsoidal variations. The cause of the long secondary periods is unknown, but it has been proposed that they are due to interactions with low-mass companions in close orbits. The ellipsoidal variations are also thought to be created in binary systems, in this case contact binaries where distorted stars cause strictly periodic variations as they orbit. References Bibliography External links Post-main sequence evolution through helium burning Long period variables – period luminosity relations and classification in the Gaia Mission Hertzsprung–Russell classifications Red giants