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

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 X: Wolf-Rayet star populations at solar metallicity

We examine the properties of Wolf--Rayet (WR) stars predicted by models of rotating stars taking account of the new mass loss rates for O--type stars and WR stars (Vink et al. \cite{Vink00}, \cite{Vink01}; Nugis & Lamers \cite{NuLa00}) and of the wind anisotropies induced by rotation. We find that the rotation velocities $v$ of WR stars are modest, i.e. about 50 km s$^{-1}$, not very dependant on the initial $v$ and masses. For the most massive stars, the evolution of $v$ is very strongly influenced by the values of the mass loss rates; below $\sim$12 M$_\odot$ the evolution of rotation during the MS phase and later phases is dominated by the internal coupling. Massive stars with extreme rotation may skip the LBV phase. Models having a typical $v$ for the O--type stars have WR lifetimes on the average two times longer than for non--rotating models. The increase of the WR lifetimes is mainly due to that of the H--rich eWNL phase. Rotation allows a transition WN/WC phase to be present for initial masses lower than 60 M$_\odot$. The durations of the other WR subphases are less affected by rotation. The mass threshold for forming WR stars is lowered from 37 to 22 M$_\odot$ for typical rotation. The comparisons of the predicted number ratios WR/O, WN/WC and of the number of transition WN/WC stars show very good agreement with models with rotation, while this is not the case for models with the present--day mass loss rates and no rotation. As to the chemical abundances in WR stars, rotation brings only very small changes for WN stars, since they have equilibrium CNO values. However, WC stars with rotation have on average lower C/He and O/He ratios. The luminosity distribution of WC stars is also influenced by rotation.Comment: 17 pages, 20 figures, accepted for publication in A&

Physics of rotation in stellar models

In these lecture notes, we present the equations presently used in stellar interior models in order to compute the effects of axial rotation. We discuss the hypotheses made. We suggest that the effects of rotation might play a key role at low metallicity.Comment: 32 pages, 7 figures, lectures, CNRS school, will be published by Springe

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

Can very massive stars avoid Pair-instability Supernovae?

Very massive primordial stars ($140 M_{\odot} < M < 260 M_{\odot}$) are supposed to end their lives as pair-instability supernovae. Such an event can be traced by a typical chemical signature in low metallicity stars, but at the present time, this signature is lacking in the extremely metal-poor stars we are able to observe. Does it mean that those very massive objects did not form, contrarily to the primordial star formation scenarios? Could they avoid this tragical fate? We explore the effects of rotation, anisotropic mass loss and magnetic fields on the core size of a very massive Population III model, in order to check if its mass is sufficiently modified to prevent the pair instability. We obtain that a Population III model of $150 M_{\odot}$ with $\upsilon/\upsilon_{\rm crit}=0.56$ computed with the inclusion of wind anisotropy and Tayler-Spruit dynamo avoids the pair instability explosion.Comment: to be published in the conference proceedings of First Stars III, Santa Fe, 200

Research Note: Rotation and the wind momentum-luminosity relation for extragalactic distances

The effects of axial stellar rotation on the wind-momentum relation (WLR) for determining the extragalactic distances are investigated. Despite the fact that the mass loss rates grow quite a lot with rotation, remarkably the effects on the WLR are found to be very small on the average. As an example, for an average orientation angle between the rotation axis and the line of sight, the luminosity would be overestimated by 5.9 % for a star rotating at 90% of its break-up rotational velocity. Different orientation angles between the rotation axis and the line of sight produce some limited scatter.Comment: 4 pages, 1 figure, in press in A&