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Stellar rotation is the rotation of a star in the same manner as the Sun and Earth rotate. It can be measured using the spectrum of the star or the timing of periodic variations. The star's rotation causes it to take a non-spherical shape through centrifugal force. The rotation can be different for different parts of the star (differential rotation), such as the Sun's higher rotation at its equator than its poles (a rotation period of 26 days at the equator, 38 days at the poles).
The spectrum of the star shows rotation by the Doppler shift of the portions of the star moving radially toward us and the portions moving away, resulting in a type of line broadening. While the angular velocity (radians-per-time-unit) is of interest, line broadening reveals radial velocity, from which the rotational velocity (the speed of points on the equator due to rotation) can be determined if the direction of the axis of rotation is known. The critical velocity (or break-up velocity or critical rotation) of a star is that above which it is unstable and would break up.
Variations in a star's brightness can be due to starspots: some variation-patterns suggest such spots that are lasting for multiple rotations, which yield very precise rotation periods.
Stars generally lose their rotation over time and the measured rotation is used as a proxy for the age of the star (gyrochronology).
When a star collapses, e.g., into a white dwarf, a neutron star, or a black hole, the conservation of angular momentum causes the rotation to increase, thus the occurrence of neutron stars observed with rotational periods on the order of a second. Accretion (e.g., from a binary companion) also affects rotation, increasing it (or in some cases, decreasing it), and is generally considered the cause of the highest rotation rates observed among neutron stars, periods of a few thousandths of a second.