Relationship of Stellar Rotation in a Spherical Rigid Body Model with Spectral Line FWHM

In this paper we calculate a sequence of convolution, which includes rotationally broadened line profiles and a instrumental profile, considering a rigidly rotational globular star with limb darkening and a Gaussian instrumental profile. This calculation suggests that the instrumental profile would not be important, if the intrinsic stellar atomic spectral line was narrow enough and RHW>2 GMW, where the RHW and GHW stand for the FWHM of rotationally broadened line and the Gaussian instrumental profile respectively .Therefore, in some cases it will become more convenient to estimate or compare stellar rotational velocities within various instruments. Along with these calculations a method of determining the limb darkening coefficient e from measuring a number of widths of rotationally broadened lines is given. Roughly, the coefficient ε obtained is 0.44-0.99 for early-type stars O9.5-B9.