Abstract
The understanding of the rotational evolution of early-type stars is deeply related to that of anisotropic mass and angular momentum loss. In this paper, we aim to clarify the rotational evolution of rapidly rotating early-type stars along the main sequence (MS). We have used the 2D ESTER code to compute and evolve isolated rapidly rotating early-type stellar models along the MS, with and without anisotropic mass loss. We show that stars with Z = 0.02 and masses between 5 and 7 M⊙ reach criticality during the main sequence provided their initial angular velocity is larger than 50% of the Keplerian one. More massive stars are subject to radiation-driven winds and to an associated loss of mass and angular momentum. We find that this angular momentum extraction from the outer layers can prevent massive stars from reaching critical rotation and greatly reduce the degree of criticality at the end of the MS. Our model includes the so-called bi-stability jump of the Ṁ − Teff relation of 1D-models. This discontinuity now shows up in the latitude variations of the mass-flux surface density, endowing rotating massive stars with either a single-wind regime (no discontinuity) or a two-wind regime (a discontinuity). In the two-wind regime, mass loss and angular momentum loss are strongly increased at low latitudes inducing a faster slow-down of the rotation. However, predicting the rotational fate of a massive star is difficult, mainly because of the non-linearity of the phenomena involved and their strong dependence on uncertain prescriptions. Moreover, the very existence of the bi-stability jump in mass-loss rate remains to be substantiated by observations.
Highlights
The evolution of the rotation rate of stars is one of the open challenges of current stellar physics
We note that Eq (15) has been obtained assuming that the global mass-loss rate in the non-rotating regime M = 4πR2mis equivalent to the one of Vink et al (2001). k has been calibrated with ESTER models at zero age main sequence (ZAMS), it slightly varies with the evolutionary stage along the main sequence (MS) due to the evolution of geff
Rotational evolution of intermediate-mass stars with masses inbetween 5 and 7 M. The evolution of such stars along the MS is relatively simple because at first order it can be modelled with constant angular momentum, that is, without considering any mass loss
Summary
The evolution of the rotation rate of stars is one of the open challenges of current stellar physics. They can be used to investigate the rotational evolution of early-type stars along the main sequence, using a simple method that we implement here to compute the change in the hydrogen mass fraction in the convective core of the model, and which provides an acceptable description of the main sequence evolution With these state-ofthe-art 2D models we have access to the latitude variations of surface quantities that matter for mass loss, namely effective gravity and effective temperature, as the star evolves. In the SWR, we find a maximum mass-flux at the poles, while in the TWR both mass and angular momentum losses are strongly enhanced in equatorial regions This 2D mass loss prescription opens the door to the present study of the main-sequence evolution of rotation in rapidly rotating early-type stars.
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