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

¹ Sorbonne Universités, UPMC Université Paris 06 et CNRS UMR 7095, Institut d’Astrophysique de Paris, 75014 Paris, France
² CNRS UMR 7095, Institut d’Astrophysique de Paris, 98bis Bd Arago, 75014 Paris, France
e-mail: zorec@iap.fr
³ Royal Observatory of Belgium, 3 Av. Circulaire, 1180 Bruxelles, Belgium
⁴ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS UMR 7293, Lagrange, 28 Avenue Valrose, 06108 Nice Cedex 2, France
⁵ GEPI, Observatoire de Paris, PSL Research University, CNRS UMR 8111, Université Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92190 Meudon, France
⁶ Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque S/N, 1900 La Plata, Argentina
⁷ Instituto de Astrofísica La Plata, CONICET, 1900 La Plata, Argentina
⁸ Geneva Observatory, University of Geneva, Maillettes 51, 1290 Sauverny, Switzerland
⁹ European Organization for Astronomical Research in the Southern Hemisphere, 3107 Alonso de Cordova, Vitacura, Santiago de Chile, Chile

Received: 21 April 2016
Accepted: 9 February 2017

Abstract

Aims. We assume that stars may undergo surface differential rotation to study its impact on the interpretation of Vsini 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 Vsini concerning the actual stellar rotation.

Methods. We studied the line broadening produced by several differential rotational laws, but adopted Maunder’s expression Ω(θ) = Ω₀(1 + αcos²θ) 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 Vsini parameter and on the distribution Φ(u) of ratios u = V/V_c.

Results. We conclude that the inferred Vsini is smaller than implied by the actual equatorial linear rotation velocity V_eq if the stars rotate with α < 0, but is larger if the stars have α > 0. For a given | α | the deviations of Vsini are larger when α < 0. If the studied Be stars have on average α < 0, the number of rotators with V_eq ≃ 0.9V_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 Vsini 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.