The spectral lines of a rapidly rotating star are broadened by the Doppler effect, because one half of the disc is coming towards the observer, while the other half is moving away from him. The centre of the disc is travelling across the line of sight, so light from there suffers neither blue nor red shift, and figure 2.20 illustrates this point. Imagine the star’s disc divided into strips, and that each strip contributes a spectral line of intensity proportional to its area, and shifted from its rest wavelength by AX=Xv/c (where v is the strip’s velocity along the line of sight of the observer); v is zero at the centre of the disc, and has its maximum value at the edges.

Rapid rotation makes it very difficult to measure the intensity of the spectral lines, as they are often so blurred as to be indistinguishable from the continuum. However, the shapes of stellar line profiles have revealed how rapidly stars rotate. Unfortunately, what is actually measured for an individual star is not the true rotational velocity at the star’s equator, v, but v sin i where i is the angle between the star’s rotation axis and the observer’s line of sight. One consequence of this effect is that stars seen ‘pole on’ have unbroadened lines. We have every reason to suppose that the directions of stellar rotation axes are distributed randomly in space, so it is possible to apply statistics to find the average rotation velocities of various groups of stars. The results show that there is a general dependence of rotation velocity on spectral type: the hot¬test stars rotate most rapidly; 0 and B stars typically have rotational velocities of 200 to 250 km s;1 G stars have values much lower, generally around 20kms”1. The extended clouds of gas surrounding shell stars are probably the result of extremely rapid rotation, up to 500 km s-1.

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