A two-dimensional perspective of the rotational evolution of rapidly rotating intermediate-mass stars Implications for the formation of single Be stars

Abstract

Context. Recently, the first successful attempt at computing stellar structure and evolution models in two dimensions was presented with models that include centrifugal deformation and self-consistently compute the velocity field. Aims. The aim of the present study is to explore the rotational evolution of two-dimensional models of stars rotating at a significant fraction of their critical angular velocity. From the predictions of these models, we aim to improve our understanding of the formation of single Be stars. Methods. Using the ESTER code, which solves the stellar structure of a rotating star in two dimensions with time evolution, we computed evolution tracks of stars of between 4 and 10 M for initial rotation rates ranging between 60 and 90% of the critical rotation rate. Furthermore, we compute models for both a Galactic metallicity and an SMC metallicity. Results. A minimum initial rotation rate at the start of the main sequence is needed to spin up the star to critical rotation within its main sequence lifetime. This threshold depends on the stellar mass, and increases with increasing mass. The models do not predict any stars above 8 M to reach (near-)critical rotation during the main sequence. Furthermore, we find the minimum threshold of initial angular velocity is lower for SMC metallicity than for Galactic metallicity, which is in agreement with the increased fraction of observed Be stars in lower metallicity environments. The strong difference in the rotational evolution between different masses is not predicted by any one-dimensional stellar evolution models. Conclusions. Our self-consistent two-dimensional stellar evolution models provide further insight into the rotational evolution of intermediate-mass stars, and our predictions are consistent with observations of velocity distributions and the fraction of Be stars amongst B-type stars. We find that stars with a mass above 8 M do not increase their fraction of critical rotation during the main sequence. As a fraction of stars above 8 M have been observed to display the Be phenomenon, other processes or formation channels must be at play, or, alternatively, critical rotation is not required for the Be phenomenon above this mass.