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

Abstract

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 $\Phi (u)$ of ratios of true rotational velocities $u=V/V_\rm c$ ($V_\rm c$ 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. We studied the line broadening produced by several differential rotational laws, but adopted Maunder's expression $\Omega (\theta )={\Omega }_o(1+\alpha {\cos }^2\theta )$ as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameter $\alpha$ on the measured $V\sin i$ parameter and on the distribution $\Phi (u)$ of ratios $u=V/V_\rm c$. We conclude that the inferred $V\sin i$ is smaller than implied by the actual equatorial linear rotation velocity $V_\rm eq$ if the stars rotate with $\alpha <0$, but is larger if the stars have $\alpha >0$. For a given $|\alpha |$ the deviations of $V\sin i$ are larger when $\alpha <0$. If the studied Be stars have on average $\alpha <0$, the number of rotators with $V_\rm eq\simeq0.9V_\rm c$ 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 $V\sin i$ 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.

arXiv commentTo appear in A&A

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• Fourier analysis of He 4471/Mg 4481 line profiles for separating rotational velocity and axial inclination in rapidly-rotating B-type stars