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

TL;DR

This study examines how differential rotation and spectral line broadening phenomena affect the interpretation of rotational velocities in Be stars, highlighting the need for advanced modeling to accurately determine their rotation rates.

Contribution

It introduces a model considering differential rotation laws and analyzes their impact on observed rotational velocity parameters in Be stars, emphasizing the importance of two-dimensional radiation transfer calculations.

Findings

Inferred V sin i is smaller for negative alpha and larger for positive alpha.

Deviations in V sin i are more significant when alpha<0.

Differential rotation influences the observed distribution of stellar rotation velocities.

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.