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 - Zorec, Juan (2017)
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 Φ(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 Ω(0) = Ω0(1 + α cos2 0) 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 a on the measured Vsin i parameter and on the distribution Φ(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 α < 0, but is larger if the stars have a α > 0. For a given |α| the deviations of Vsin i are larger when α < 0. If the studied Be stars have on average α < 0, the number of rotators with Veq 0.9Vc 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 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.