Projected rotational velocity

Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface.

The rotation of a star produces an equatorial bulge due to centrifugal force. As stars are not solid bodies, they can also undergo differential rotation. Thus the equator of the star can rotate at a different angular velocity than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a stellar magnetic field.

The magnetic field of a star interacts with the stellar wind. As the wind moves away from the star its rate of angular velocity slows. The magnetic field of the star interacts with the wind, which applies a drag to the stellar rotation. As a result, angular momentum is transferred from the star to the wind, and over time this gradually slows the star's rate of rotation.

Unless a star is being observed from the direction of its pole, sections of the surface have some amount of movement toward or away from the observer. The component of movement that is in the direction of the observer is called the radial velocity. For the portion of the surface with a radial velocity component toward the observer, the radiation is shifted to a higher frequency because of Doppler shift. Likewise the region that has a component moving away from the observer is shifted to a lower frequency. When the absorption lines of a star are observed, this shift at each end of the spectrum causes the line to broaden. However, this broadening must be carefully separated from other effects that can increase the line width.

The component of the radial velocity observed through line broadening depends on the inclination of the star's pole to the line of sight. The derived value is given as ${\displaystyle v_{e}\cdot \sin i}$, where v_e is the rotational velocity at the equator and i is the inclination. However, i is not always known, so the result gives a minimum value for the star's rotational velocity. That is, if i is not a right angle, then the actual velocity is greater than ${\displaystyle v_{e}\cdot \sin i}$. This is sometimes referred to as the projected rotational velocity.

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