Stellar evolution with rotation and magnetic fields:I. The relative importance of rotational and magnetic effects

We compare the current effects of rotation in stellar evolution to those of the magnetic field created by the Tayler instability. In stellar regions, where magnetic field can be generated by the dynamo due to differential rotation (Spruit 2002), we find that the growth rate of the magnetic instability is much faster than for the thermal instability. Thus, meridional circulation is negligible with respect to the magnetic fields, both for the transport of angular momentum and of chemical elements. Also, the horizontal coupling by the magnetic field, which reaches values of a few $10^5$ G, is much more important than the effects of the horizontal turbulence. The field, however, is not sufficient to distort the shape of the equipotentials. We impose the condition that the energy of the magnetic field created by the Tayler--Spruit dynamo cannot be larger than the energy excess present in the differential rotation. This leads to a criterion for the existence of the magnetic field in stellar interiors. Numerical tests are made in a rotating star model of 15 M$_{\odot}$ rotating with an initial velocity of 300 km$\cdot$s$^{-1}$.Comment: Accepted for Astronomy and Astrophysics, 11 pages, 8 figure

Convective envelopes in rotating OB stars

We study the effects of rotation on the outer convective zones of massive stars. We examine the effects of rotation on the thermal gradient and on the Solberg--Hoiland term by analytical developments and by numerical models. Writing the criterion for convection in rotating envelopes, we show that the effects of rotation on the thermal gradient are much larger and of opposite sign to the effect of the Solberg-Hoiland criterion. On the whole, rotation favors convection in stellar envelopes at the equator and to a smaller extent at the poles. In a rotating 20 Msun star at 94% of the critical angular velocity, there are two convective envelopes, with the bigger one having a thickness of 13.2% of the equatorial radius. In the non-rotating model, the corresponding convective zone has a thickness of only 4.6% of the radius. The occurrence of outer convection in massive stars has many consequences.Comment: 4 pages, 3 figures, accepted by Astronomy and Astrophysic

Massive stellar models: rotational evolution, metallicity effects

The Be star phenomenon is related to fast rotation, although the cause of this fast rotation is not yet clearly established. The basic effects of fast rotation on the stellar structure are reviewed: oblateness, mixing, anisotropic winds. The processes governing the evolution of the equatorial velocity of a single star (transport mechanisms and mass loss) are presented, as well as their metallicity dependence. The theoretical results are compared to observations of B and Be stars in the Galaxy and the Magellanic Clouds.Comment: 11 pages, 7 figures, to appear in the proceedings of IAUS 272 "Active OB stars: structure, evolution, mass loss and critical limits

Stellar evolution with rotation and magnetic fields II: General equations for the transport by Tayler--Spruit dynamo

We further develop the Tayler--Spruit dynamo theory, based on the most efficient instability for generating magnetic fields in radiative layers of differentially rotating stars. We avoid the simplifying assumptions that either the $\mu$-- or the $T$--gradient dominates, but we treat the general case and we also account for the nonadiabatic effects, which favour the growth of the magnetic field. Stars with a magnetic field rotate almost as a solid body. Several of their properties (size of the core, MS lifetimes, tracks, abundances) are closer to those of models without rotation than with rotation only. In particular, the observed N/C or N/H excesses in OB stars are better explained by our previous models with rotation only than by the present models with magnetic fields that predict no nitrogen excesses. We show that there is a complex feedback loop between the magnetic instability and the thermal instability driving meridional circulation. This opens the possibility for further magnetic models, but at this stage we do not know the relative importance of the magnetic fields due to the Tayler instability in stellar interiors.Comment: 14 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Stellar evolution with rotation XI: Wolf-Rayet star populations at different metallicities

Grids of models of massive stars ($M \ge$ 20 $M_\odot$) with rotation are computed for metallicities $Z$ ranging from that of the Small Magellanic Cloud (SMC) to that of the Galactic Centre. The hydrostatic effects of rotation, the rotational mixing and the enhancements of the mass loss rates by rotation are included. The evolution of the surface rotational velocities of the most massive O--stars mainly depends on the mass loss rates and thus on the initial $Z$ value. The minimum initial mass for a star for entering the Wolf--Rayet (WR) phase is lowered by rotation. For all metallicities, rotating stars enter the WR phase at an earlier stage of evolution and the WR lifetimes are increased, mainly as a result of the increased duration of the eWNL phase. Models of WR stars predict in general rather low rotation velocities ($< 50$ km s$^{-1}$) with a few possible exceptions, particularly at metallicities lower than solar where WR star models have in general faster rotation and more chance to reach the break--up limit.The properties of the WR populations as predicted by the rotating models are in general in much better agreement with the observations in nearby galaxies. The observed variation with metallicity of the fractions of type Ib/Ic supernovae with respect to type II supernovae as found by Prantzos & Boissier (\cite{Pr03}) is very well reproduced by the rotating models, while non--rotating models predict much too low ratios.Comment: 20 pages, 16 figure, Astronomy and Astrophysics, in pres

Stellar evolution with rotation VII: Low metallicity models and the blue to red supergiant ratio in the SMC

We calculate a grid of models with and without the effects of axial rotation for massive stars in the range of 9 to 60 M$_{\odot}$ and metallicity $Z$ = 0.004 appropriate for the SMC. Remarkably, the ratios $\Omega/\Omega_{\mathrm{crit}}$ of the angular velocity to the break-up angular velocity grow strongly during the evolution of high mass stars, contrary to the situation at $Z$ = 0.020. The reason is that at low $Z$, mass loss is smaller and the removal of angular momentum during evolution much weaker, also there is an efficient outward transport of angular momentum by meridional circulation. Thus, a much larger fraction of the stars at lower $Z$ reach break-up velocities and rotation may thus be a dominant effect at low $Z$. The models with rotation well account for the long standing problem of the large numbers of red supergiants observed in low $Z$ galaxies, while current models with mass loss were predicting no red supergiants. We discuss in detail the physical effects of rotation which favour a redwards evolution in the HR diagram. The models also predict large N enrichments during the evolution of high mass stars. The predicted relative N-enrichments are larger at $Z$ lower than solar and this is in very good agreement with the observations for A-type supergiants in the SMC.Comment: 18 pages, 16 figures, in press in Astronomy and Astrophysic