Critical study of the distribution of rotational velocities of Be stars

I. Deconvolution methods, effects due to gravity darkening, macroturbulence, and binarity^⋆

¹ Sorbonne Universités, UPMC Université Paris 6 et CNRS UMR 7095, Institut d’Astrophysique de Paris 75014 Paris France
e-mail: zorec@iap.fr
² CNRS UMR 7095, Institut d’Astrophysique de Paris, 98bis bd Arago, 75014 Paris, France
³ Royal Observatory of Belgium, 3 avenue 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, chemin des Maillettes 51, 1290 Sauverny, Switzerland
⁹ European Organization for Astronomical Research in the Southern Hemisphere, Alonso de Cordova 3107, Vitacura, Santiago de Chile, Chile

Received: 21 April 2016
Accepted: 8 June 2016

Abstract

Context. Among intermediate-mass and massive stars, Be stars are the fastest rotators in the main sequence (MS) and, as such, these stars are a cornerstone to validate models of structure and evolution of rotating stars. Several phenomena, however, induce under- or overestimations either of their apparent Vsini, or true velocity V.

Aims. In the present contribution we aim at obtaining distributions of true rotational velocities corrected for systematic effects induced by the rapid rotation itself, macroturbulent velocities, and binarity.

Methods. We study a set of 233 Be stars by assuming they have inclination angles distributed at random. We critically discuss the methods of Cranmer and Lucy-Richardson, which enable us to transform a distribution of projected velocities into another distribution of true rotational velocities, where the gravitational darkening effect on the Vsini parameter is considered in different ways. We conclude that iterative algorithm by Lucy-Richardson responds at best to the purposes of the present work, but it requires a thorough determination of the stellar fundamental parameters.

Results. We conclude that once the mode of ratios of the true velocities of Be stars attains the value V/V_c ≃ 0.77 in the main-sequence (MS) evolutionary phase, it remains unchanged up to the end of the MS lifespan. The statistical corrections found on the distribution of ratios V/V_c for overestimations of Vsini, due to macroturbulent motions and binarity, produce a shift of this distribution toward lower values of V/V_c when Be stars in all MS evolutionary stages are considered together. The mode of the final distribution obtained is at V/V_c ≃ 0.65. This distribution has a nearly symmetric distribution and shows that the Be phenomenon is characterized by a wide range of true velocity ratios 0.3 ≲ V/V_c ≲ 0.95. It thus suggests that the probability that Be stars are critical rotators is extremely low.

Conclusions. The corrections attempted in the present work represent an initial step to infer indications about the nature of the Be-star surface rotation that will be studied in the second paper of this series.