Critical study of the distribution of rotational velocities of Be stars - II: Differential rotation and some hidden effects interfering with the interpretation of the V sin i parameter

Aims. We assume that stars may undergo surface differential rotation to study its impact on the interpretation of V sin i and on the observed distribution Φ ( u ) of ratios of true rotational velocities u = V / V c ( V c is the equatorial critical velocity). We discuss some phenomena affecting the formation of spectral lines and their broadening, which can obliterate the information carried by V sin i concerning the actual stellar rotation. Methods. We studied the line broadening produced by several differential rotational laws, but adopted Maunder’s expression Ω( θ ) = Ω 0 (1 + α cos 2 θ ) as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameter α on the measured V sin i parameter and on the distribution Φ ( u ) of ratios u = V / V c . Results. We conclude that the inferred V sin i is smaller than implied by the actual equatorial linear rotation velocity V eq if the stars rotate with α α > 0. For a given | α | the deviations of V sin i are larger when α α V eq ≃ 0.9 V c is larger than expected from the observed distribution Φ ( u ); if these stars have on average α > 0, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried by V sin i and, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.