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 Vsin i and on the observed distribution Phi (u) of ratios of true rotational velocities u = V = Vc (Vc 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 Vsin i concerning the actual stellar rotation. Methods. We studied the line broadening produced by several differential rotational laws, but adopted Maunder's expression Omega (theta) = Omega(0)(1 + alpha cos(2)theta) as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the diffrential rotation parameter alpha on the measured Vsin i parameter and on the distribution Phi (u) of ratios u = V = Vc. Results. We conclude that the inferred Vsin i is smaller than implied by the actual equatorial linear rotation velocity Veq if the stars rotate with alpha < 0, but is larger if the stars have alpha > 0. For a given vertical bar alpha vertical bar the deviations of Vsin i are larger when alpha < 0. If the studied Be stars have on average alpha < 0, the number of rotators with Veq ' 0 : 9Vc is larger than expected from the observed distribution Phi(u); if these stars have on average alpha > 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 Vsin 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.