A. Maeder - Academia.edu (original) (raw)

Papers by A. Maeder

Symposium - International Astronomical Union, 2004

We report on preliminary results of new high-resolution spectroscopic observations of the roAp st... more We report on preliminary results of new high-resolution spectroscopic observations of the roAp star HD 3980 in the Li I 6708 Å line region. Strong variations of position and intensity of this line with the rotation phase enable us to consider this star as a new member of the intriguing group of “Li-spotted” CP stars.

We present stellar evolutionary models covering the mass range from 0.4 to 1M&sun; calculated for... more We present stellar evolutionary models covering the mass range from 0.4 to 1M&sun; calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state (Hummer & Mihalas, 1988ApJ...331..794H, Mihalas et al., 1988ApJ...331..815M, Daeppen et al., 1988ApJ...332..261D). A parallel calculation using the OPAL (Rogers et al., 1996ApJ...456..902R) equation of state has been made to demonstrate the adequacy of the MHD

Symposium - International Astronomical Union, 2004

Zeeman-Doppler Imaging enables one to estimate the short term temporal evolution of surface brigh... more Zeeman-Doppler Imaging enables one to estimate the short term temporal evolution of surface brightness and magnetic structures, under the effect of differential rotation. We present here spectropolarimetric observations secured between 1998 and 2002 for two evolved active stars: the K1 subgiant of the RS CVn system HR 1099 and the single FK Com giant HD 199178. Differential rotation is detected both from brightness and magnetic images, indicating that the rotational shear, roughly solar in magnitude for the single star, is significantly weaker in the binary system. This result suggests that tidal forces, rather than stellar evolution, could be responsible for the lower rotational shear and thus the longer spot lifetime reported for binary systems.

arXiv (Cornell University), Sep 27, 2001

We briefly describe the three existing scenarios for forming massive stars and emphasize that the... more We briefly describe the three existing scenarios for forming massive stars and emphasize that the arguments often used to reject the accretion scenario for massive stars are misleading. It is usually not accounted for the fact that the turbulent pressure associated to large turbulent velocities in clouds necessarily imply relatively high accretion rates for massive stars. We show the basic difference between the formation of low and high mass stars based on the values of the free fall time and of the Kelvin-Helmoltz timescale, and define the concept of birthline for massive stars. Due to D-burning, the radius and location of the birthline in the HR diagram, as well as the lifetimes are very sensitive to the accretion ratė M accr. If a formṀ accr ∝ A (M/M ⊙) ϕ is adopted, the observations in the HR diagram and the lifetimes support a value of A ≈ 10 −5 M ⊙ • yr −1 and a value of ϕ ∼ > 1. Remarkably, such a law is consistent with the relation found by Churchwell (1998) and Henning et al. (2000) between the outflow rates and the luminosities of ultra-compact HII regions, if we assume that a fraction 0.15 to 0.3 of the global inflow is accreted. The above relation implies highṀ accr ≈ 10 −3 M ⊙ • yr −1 for the most massive stars. The physical possibility of such highṀ accr is supported by current numerical models. Finally, we give simple analytical arguments in favour of the growth ofṀ accr with the already accreted mass. We also suggest that due to Bondi-Hoyle accretion, the formation of binary stars is largely favoured among massive stars in the accretion scenario.

Symposium - International Astronomical Union, 1984

We consider stellar evolution in low mass stars (1–3 Mo) near the main sequence with the hypothes... more We consider stellar evolution in low mass stars (1–3 Mo) near the main sequence with the hypothesis that mild turbulence is present within the all star. Turbulent transport of the elements is modeled by diffusion equations where the diffusion coefficient is chosen to be D = R✶eν where ν is the kinematical viscosity and R✶e is a Reynolds number. We consider the effects of the growth of the gradient of the mean molecular weight on turbulence. The main consequences of diffusion on stellar evolution are (1) an increase of the life time near the main sequence and (2) a change of the radial distributions of chemical species (12C, 13C, 14N, 160) (figure 1). The inhibition of the turbulence, when the gradient of mean molecular weight reaches a certain critical value, allows the evolution towards the red giant branch. When stars evolve towards the giant branch, chemical species are dredged up to the surface. At this stage models with and without diffusion, predict substantially different sur...

Evolution of Stars: The Photospheric Abundance Connection, 1991

Firstly, a brief account is given on the recent progresses in model assumptions, which influence ... more Firstly, a brief account is given on the recent progresses in model assumptions, which influence the evolution of surface abundances in massive stars. A concise overview of this chemical evolution is presented. We discuss in detail the surface chemistry of WN and WC stars, in particular, the effects of the initial metallicity Ζ and mass loss rates on the resulting abundances. The abundances in WN stars are not very sensitive to model assumptions and are mainly a test on nuclear cross sections. Conversely, the chemical abundances in WC stars are very much model dependent. Major differences in the composition of WC stars (and subtype distributions) are expected according to their initial metallicity. The various models proposed to explain the Ν/C enrichments in blue supergiants and the properties of the progenitor of SN 1987A are reviewed.

Problems of Calibration of Absolute Magnitudes and Temperature of Stars, 1973

A comparison of the theoretical and observed indices has been made for the UBV, u v b y and the G... more A comparison of the theoretical and observed indices has been made for the UBV, u v b y and the Geneva's UBVBi B2 Vi G systems. In the actual state of the photometric calibrations, coin cidence between theoretical and observed indices better than 0™1 are probably not significant.

Astronomy & Astrophysics, 2006

In order to investigate the possible influence of rotation on the efficiency of the first dredge-... more In order to investigate the possible influence of rotation on the efficiency of the first dredge-up we determined atmospheric parameters, masses, and abundances of carbon, nitrogen, and oxygen in a sample of evolved intermediate mass stars. We used high resolution spectra and conducted a model atmosphere analysis. The abundances were calculated through spectral synthesis and compared to the predictions of rotating and non-rotating evolutionary models. Almost all those objects in our sample where carbon and nitrogen abundances could be determined show signs of internal mixing. The stars, however, seem to be mixed to different extents. Among the mixed stars we identify five in our sample with abundances in agreement with the non-rotating models, four stars that seem to be mixed beyond that, and one star that seems to be slightly less mixed than predicted for the first dredge-up. There are also five stars that seem to be slightly more mixed than expected, but their abundances are in marginal agreement with both rotating and non-rotating models. Such differences in the extent of the mixing are not predicted by the standard models and imply the action of other mixing mechanisms than solely the convective dredge-up. We also identified for the first time an important correlation between the [N/C] ratio and the stellar mass.

Communications in Asteroseismology

Magnetic field is playing an important role at all stages of star evolution from star formation t... more Magnetic field is playing an important role at all stages of star evolution from star formation to the endpoints. The main effects are briefly reviewed. We also show that O-type stars have large convective envelopes, where convective dynamo could work. There, fields in magnetostatic balance have intensities of the order of 100 G. A few OB stars with strong polar fields (Henrichs et al. 2003a) show large N-enhancements indicating a strong internal mixing. We suggest that the meridional circulation enhanced by an internal rotation law close to uniform in these magnetic stars is responsible for the observed mixing. Thus, it is not the magnetic field itself which makes the mixing, but the strong thermal instability associated to solid body rotation. A critical question for evolution is whether a dynamo is at work in radiative zones of rotating stars. The Tayler-Spruit (TS) dynamo is the best candidate. We derive some basic relations for dynamos in radiative layers. Evolutionary models with TS dynamo show important effects: internal rotation coupling and enhanced mixing, all model outputs being affected.

The Be star phenomenon is related to fast rotation, although the cause of this fast rotation is n... more 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.

Although the theoretical study of very low metallicity (Z) and metal-free stars is not new, their... more Although the theoretical study of very low metallicity (Z) and metal-free stars is not new, their importance has recently greatly increased since two related fields have been developing rapidly. The first is cosmological simulations of the formation of the first stars and of the reionisation period. The second is the observations of extremely metal poor stars. In this paper, we present pre-supernova evolution models of massive rotating stars at very low Z (Z = 10 −8) and at Z = 0. Rotation has a strong impact on mass loss and nucleosynthesis. Models reaching break-up velocities lose up to ten percents of their initial mass. In very low Z models, rotational and convective mixing enhances significantly the surface content in carbon, nitrogen and oxygen (CNO) when the star becomes a red supergiant. This induces a strong mass loss for stars more massive than about 60 M⊙. Our models predict type Ib,c supernovae and gamma-ray bursts at very low Z. Rotational mixing also induces a large production of CNO elements, in particular of primary nitrogen. The stellar wind chemical composition is compatible with the most metal-poor star know to date, HE 1327-2326, for CNO elements. Our models reproduce the early evolution of nitrogen in the Milky Way.

When the surface angular velocity is above about 70% of the critical angular velocity, many inter... more When the surface angular velocity is above about 70% of the critical angular velocity, many interesting features appear which may be tested by interferometric observations, like significant deformation of stars, variation of the effective temperature with the latitude. Also polar winds become important and equatorial disks may appear. Near the critical limit, convection is also favored in the outer layers. In the present paper, we emphasize the need for a proper estimate of the critical velocity since this is the ratio of the actual velocity of the star to that critical velocity which determines the amplitude of the above effects. We recall the existence of two critical velocities. The first one, also called the classical critical velocity is the one to consider when the star has an Eddington factor inferior to 0.639, while the second one is the one to be considered when the Eddington factor is above 0.639. The features of the star at these two critical limits may be very different.

Astronomy & Astrophysics, 2004

Detailed models of α Cen A and B based on new seismological data for α Cen B by Carrier & Bourban... more Detailed models of α Cen A and B based on new seismological data for α Cen B by Carrier & Bourban (2003) have been computed using the Geneva evolution code including atomic diffusion. Taking into account the numerous observational constraints now available for the α Cen system, we find a stellar model which is in good agreement with the astrometric, photometric, spectroscopic and asteroseismic data. The global parameters of the α Cen system are now firmly constrained to an age of t = 6.52± 0.30 Gyr, an initial helium mass fraction Y i = 0.275± 0.010 and an initial metallicity (Z/X) i = 0.0434± 0.0020. Thanks to these numerous observational constraints, we confirm that the mixing-length parameter α of the B component is larger than the one of the A component, as already suggested by many authors (Noels et al. 1991; Fernandes & Neuforge 1995; Guenther & Demarque 2000): α B is about 8% larger than α A (α A = 1.83 ± 0.10 and α B = 1.97 ± 0.10). Moreover, we show that asteroseismic measurements enable to determine the radii of both stars with a very high precision (errors smaller than 0.3%). The radii deduced from seismological data are compatible with the new interferometric results of Kervella et al. (2003) even if they are slightly larger than the interferometric radii (differences smaller than 1%).

Astronomy and Astrophysics, 2004

We describe and discuss the properties of three numerical methods for solving the diffusion equat... more We describe and discuss the properties of three numerical methods for solving the diffusion equation for the transport of the chemical species and of the angular momentum in stellar interiors. We study through numerical experiments both their accuracy and their ability to provide physical solutions. On the basis of new tests and analyses applied to the stellar astrophysical context, we show that the most robust method to follow the secular evolution is the implicit finite differences method. The importance of correctly estimating the diffusion coefficient between mesh points is emphasized and a procedure for estimating the average diffusion coefficient between a convective and a radiative zone is described.

Astronomy & Astrophysics, 2001

We calculate a grid of models with and without the effects of axial rotation for massive stars in... more 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 and metallicity Z = 0.004 appropriate for the SMC. Remarkably, the ratios Ω/Ωcrit 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.

Astronomy and Astrophysics, 2009

Context. The recent observations of solar-like oscillations in many red giant stars with the CoRo... more Context. The recent observations of solar-like oscillations in many red giant stars with the CoRoT satellite stimulated the theoretical study of the effects of various physical processes on the modelling of these stars. Aims. The influence of rotation on the properties of red giants is studied in the context of the asteroseismic modelling of these stars. Methods. The effects of rotation on the global and asteroseismic properties of red giant stars with a mass larger than the mass limit for degenerate He burning are investigated by comparing rotating models computed with a comprehensive treatment of shellular rotation to non-rotating ones. Results. While red giants exhibit low surface rotational velocities, we find that the rotational history of the star has a large impact on its properties during the red giant phase. In particular, for stars massive enough to ignite He burning in non-degenerate conditions, rotational mixing induces a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a higher luminosity in the HR diagram. This of course results in a change of the seismic properties of red giants at the same evolutionary state. As a consequence the inclusion of rotation significantly changes the fundamental parameters of a red giant star as determined by performing an asteroseismic calibration. In particular rotation decreases the derived stellar mass and increases the age. Depending on the rotation law assumed in the convective envelope and on the initial velocity of the star, non-negligible values of rotational splitting can be reached, which may complicate the observation and identification of non-radial oscillation modes for red giants exhibiting moderate surface rotational velocities. By comparing the effects of rotation and overshooting, we find that the main-sequence widening and the increase of the H-burning lifetime induced by rotation (V ini = 150 km s −1) are well reproduced by non-rotating models with an overshooting parameter of 0.1, while the increase of luminosity during the post-main sequence evolution is better reproduced by non-rotating models with overshooting parameters twice as large. This illustrates the fact that rotation not only increases the size of the convective core but also changes the chemical composition of the radiative zone.

Astronomy and Astrophysics, 2010

Context. Observations of solar-like oscillations obtained either from the ground or from space st... more Context. Observations of solar-like oscillations obtained either from the ground or from space stimulated the study of the effects of various physical processes on the modelling of solar-type stars. Aims. The influence of rotational mixing on the evolution and asteroseismic properties of solar-type stars is studied. Methods. Global and asteroseismic properties of models of solar-type stars computed with and without a comprehensive treatment of shellular rotation are compared. The effects of internal magnetic fields are also discussed in the framework of the Tayler-Spruit dynamo. Results. Rotational mixing changes the global properties of a solar-type star with a significant increase of the effective temperature resulting in a shift of the evolutionary track to the blue part of the HR diagram. These differences observed in the HR diagram are related to changes of the chemical composition, because rotational mixing counteracts the effects of atomic diffusion leading to larger helium surface abundances for rotating models than for non-rotating ones. Higher values of the large frequency separation are then found for rotating models than for non-rotating ones at the same evolutionary stage, because the increase of the effective temperature leads to a smaller radius and hence to an increase of the stellar mean density. In addition to changing the global properties of solartype stars, rotational mixing also has a considerable impact on the structure and chemical composition of the central stellar layers by bringing fresh hydrogen fuel to the central stellar core, thereby enhancing the main-sequence lifetime. The increase of the central hydrogen abundance together with the change of the chemical profiles in the central layers result in a significant increase of the values of the small frequency separations and of the ratio of the small to large separations for models including shellular rotation. This increase is clearly seen for models with the same age sharing the same initial parameters except for the inclusion of rotation as well as for models with the same global stellar parameters and in particular the same location in the HR diagram. By computing rotating models of solar-type stars including the effects of a dynamo that possibly occurs in the radiative zone, we find that the efficiency of rotational mixing is strongly reduced when the effects of magnetic fields are taken into account, in contrast to what happens in massive stars.

Symposium - International Astronomical Union, 2004

We report on preliminary results of new high-resolution spectroscopic observations of the roAp st... more We report on preliminary results of new high-resolution spectroscopic observations of the roAp star HD 3980 in the Li I 6708 Å line region. Strong variations of position and intensity of this line with the rotation phase enable us to consider this star as a new member of the intriguing group of “Li-spotted” CP stars.

We present stellar evolutionary models covering the mass range from 0.4 to 1M&sun; calculated for... more We present stellar evolutionary models covering the mass range from 0.4 to 1M&sun; calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state (Hummer & Mihalas, 1988ApJ...331..794H, Mihalas et al., 1988ApJ...331..815M, Daeppen et al., 1988ApJ...332..261D). A parallel calculation using the OPAL (Rogers et al., 1996ApJ...456..902R) equation of state has been made to demonstrate the adequacy of the MHD

Symposium - International Astronomical Union, 2004

Zeeman-Doppler Imaging enables one to estimate the short term temporal evolution of surface brigh... more Zeeman-Doppler Imaging enables one to estimate the short term temporal evolution of surface brightness and magnetic structures, under the effect of differential rotation. We present here spectropolarimetric observations secured between 1998 and 2002 for two evolved active stars: the K1 subgiant of the RS CVn system HR 1099 and the single FK Com giant HD 199178. Differential rotation is detected both from brightness and magnetic images, indicating that the rotational shear, roughly solar in magnitude for the single star, is significantly weaker in the binary system. This result suggests that tidal forces, rather than stellar evolution, could be responsible for the lower rotational shear and thus the longer spot lifetime reported for binary systems.

arXiv (Cornell University), Sep 27, 2001

We briefly describe the three existing scenarios for forming massive stars and emphasize that the... more We briefly describe the three existing scenarios for forming massive stars and emphasize that the arguments often used to reject the accretion scenario for massive stars are misleading. It is usually not accounted for the fact that the turbulent pressure associated to large turbulent velocities in clouds necessarily imply relatively high accretion rates for massive stars. We show the basic difference between the formation of low and high mass stars based on the values of the free fall time and of the Kelvin-Helmoltz timescale, and define the concept of birthline for massive stars. Due to D-burning, the radius and location of the birthline in the HR diagram, as well as the lifetimes are very sensitive to the accretion ratė M accr. If a formṀ accr ∝ A (M/M ⊙) ϕ is adopted, the observations in the HR diagram and the lifetimes support a value of A ≈ 10 −5 M ⊙ • yr −1 and a value of ϕ ∼ > 1. Remarkably, such a law is consistent with the relation found by Churchwell (1998) and Henning et al. (2000) between the outflow rates and the luminosities of ultra-compact HII regions, if we assume that a fraction 0.15 to 0.3 of the global inflow is accreted. The above relation implies highṀ accr ≈ 10 −3 M ⊙ • yr −1 for the most massive stars. The physical possibility of such highṀ accr is supported by current numerical models. Finally, we give simple analytical arguments in favour of the growth ofṀ accr with the already accreted mass. We also suggest that due to Bondi-Hoyle accretion, the formation of binary stars is largely favoured among massive stars in the accretion scenario.

Symposium - International Astronomical Union, 1984

We consider stellar evolution in low mass stars (1–3 Mo) near the main sequence with the hypothes... more We consider stellar evolution in low mass stars (1–3 Mo) near the main sequence with the hypothesis that mild turbulence is present within the all star. Turbulent transport of the elements is modeled by diffusion equations where the diffusion coefficient is chosen to be D = R✶eν where ν is the kinematical viscosity and R✶e is a Reynolds number. We consider the effects of the growth of the gradient of the mean molecular weight on turbulence. The main consequences of diffusion on stellar evolution are (1) an increase of the life time near the main sequence and (2) a change of the radial distributions of chemical species (12C, 13C, 14N, 160) (figure 1). The inhibition of the turbulence, when the gradient of mean molecular weight reaches a certain critical value, allows the evolution towards the red giant branch. When stars evolve towards the giant branch, chemical species are dredged up to the surface. At this stage models with and without diffusion, predict substantially different sur...

Evolution of Stars: The Photospheric Abundance Connection, 1991

Firstly, a brief account is given on the recent progresses in model assumptions, which influence ... more Firstly, a brief account is given on the recent progresses in model assumptions, which influence the evolution of surface abundances in massive stars. A concise overview of this chemical evolution is presented. We discuss in detail the surface chemistry of WN and WC stars, in particular, the effects of the initial metallicity Ζ and mass loss rates on the resulting abundances. The abundances in WN stars are not very sensitive to model assumptions and are mainly a test on nuclear cross sections. Conversely, the chemical abundances in WC stars are very much model dependent. Major differences in the composition of WC stars (and subtype distributions) are expected according to their initial metallicity. The various models proposed to explain the Ν/C enrichments in blue supergiants and the properties of the progenitor of SN 1987A are reviewed.

Problems of Calibration of Absolute Magnitudes and Temperature of Stars, 1973

A comparison of the theoretical and observed indices has been made for the UBV, u v b y and the G... more A comparison of the theoretical and observed indices has been made for the UBV, u v b y and the Geneva's UBVBi B2 Vi G systems. In the actual state of the photometric calibrations, coin cidence between theoretical and observed indices better than 0™1 are probably not significant.

Astronomy & Astrophysics, 2006

In order to investigate the possible influence of rotation on the efficiency of the first dredge-... more In order to investigate the possible influence of rotation on the efficiency of the first dredge-up we determined atmospheric parameters, masses, and abundances of carbon, nitrogen, and oxygen in a sample of evolved intermediate mass stars. We used high resolution spectra and conducted a model atmosphere analysis. The abundances were calculated through spectral synthesis and compared to the predictions of rotating and non-rotating evolutionary models. Almost all those objects in our sample where carbon and nitrogen abundances could be determined show signs of internal mixing. The stars, however, seem to be mixed to different extents. Among the mixed stars we identify five in our sample with abundances in agreement with the non-rotating models, four stars that seem to be mixed beyond that, and one star that seems to be slightly less mixed than predicted for the first dredge-up. There are also five stars that seem to be slightly more mixed than expected, but their abundances are in marginal agreement with both rotating and non-rotating models. Such differences in the extent of the mixing are not predicted by the standard models and imply the action of other mixing mechanisms than solely the convective dredge-up. We also identified for the first time an important correlation between the [N/C] ratio and the stellar mass.

Communications in Asteroseismology

Magnetic field is playing an important role at all stages of star evolution from star formation t... more Magnetic field is playing an important role at all stages of star evolution from star formation to the endpoints. The main effects are briefly reviewed. We also show that O-type stars have large convective envelopes, where convective dynamo could work. There, fields in magnetostatic balance have intensities of the order of 100 G. A few OB stars with strong polar fields (Henrichs et al. 2003a) show large N-enhancements indicating a strong internal mixing. We suggest that the meridional circulation enhanced by an internal rotation law close to uniform in these magnetic stars is responsible for the observed mixing. Thus, it is not the magnetic field itself which makes the mixing, but the strong thermal instability associated to solid body rotation. A critical question for evolution is whether a dynamo is at work in radiative zones of rotating stars. The Tayler-Spruit (TS) dynamo is the best candidate. We derive some basic relations for dynamos in radiative layers. Evolutionary models with TS dynamo show important effects: internal rotation coupling and enhanced mixing, all model outputs being affected.

The Be star phenomenon is related to fast rotation, although the cause of this fast rotation is n... more 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.

Although the theoretical study of very low metallicity (Z) and metal-free stars is not new, their... more Although the theoretical study of very low metallicity (Z) and metal-free stars is not new, their importance has recently greatly increased since two related fields have been developing rapidly. The first is cosmological simulations of the formation of the first stars and of the reionisation period. The second is the observations of extremely metal poor stars. In this paper, we present pre-supernova evolution models of massive rotating stars at very low Z (Z = 10 −8) and at Z = 0. Rotation has a strong impact on mass loss and nucleosynthesis. Models reaching break-up velocities lose up to ten percents of their initial mass. In very low Z models, rotational and convective mixing enhances significantly the surface content in carbon, nitrogen and oxygen (CNO) when the star becomes a red supergiant. This induces a strong mass loss for stars more massive than about 60 M⊙. Our models predict type Ib,c supernovae and gamma-ray bursts at very low Z. Rotational mixing also induces a large production of CNO elements, in particular of primary nitrogen. The stellar wind chemical composition is compatible with the most metal-poor star know to date, HE 1327-2326, for CNO elements. Our models reproduce the early evolution of nitrogen in the Milky Way.

When the surface angular velocity is above about 70% of the critical angular velocity, many inter... more When the surface angular velocity is above about 70% of the critical angular velocity, many interesting features appear which may be tested by interferometric observations, like significant deformation of stars, variation of the effective temperature with the latitude. Also polar winds become important and equatorial disks may appear. Near the critical limit, convection is also favored in the outer layers. In the present paper, we emphasize the need for a proper estimate of the critical velocity since this is the ratio of the actual velocity of the star to that critical velocity which determines the amplitude of the above effects. We recall the existence of two critical velocities. The first one, also called the classical critical velocity is the one to consider when the star has an Eddington factor inferior to 0.639, while the second one is the one to be considered when the Eddington factor is above 0.639. The features of the star at these two critical limits may be very different.

Astronomy & Astrophysics, 2004

Detailed models of α Cen A and B based on new seismological data for α Cen B by Carrier & Bourban... more Detailed models of α Cen A and B based on new seismological data for α Cen B by Carrier & Bourban (2003) have been computed using the Geneva evolution code including atomic diffusion. Taking into account the numerous observational constraints now available for the α Cen system, we find a stellar model which is in good agreement with the astrometric, photometric, spectroscopic and asteroseismic data. The global parameters of the α Cen system are now firmly constrained to an age of t = 6.52± 0.30 Gyr, an initial helium mass fraction Y i = 0.275± 0.010 and an initial metallicity (Z/X) i = 0.0434± 0.0020. Thanks to these numerous observational constraints, we confirm that the mixing-length parameter α of the B component is larger than the one of the A component, as already suggested by many authors (Noels et al. 1991; Fernandes & Neuforge 1995; Guenther & Demarque 2000): α B is about 8% larger than α A (α A = 1.83 ± 0.10 and α B = 1.97 ± 0.10). Moreover, we show that asteroseismic measurements enable to determine the radii of both stars with a very high precision (errors smaller than 0.3%). The radii deduced from seismological data are compatible with the new interferometric results of Kervella et al. (2003) even if they are slightly larger than the interferometric radii (differences smaller than 1%).

Astronomy and Astrophysics, 2004

We describe and discuss the properties of three numerical methods for solving the diffusion equat... more We describe and discuss the properties of three numerical methods for solving the diffusion equation for the transport of the chemical species and of the angular momentum in stellar interiors. We study through numerical experiments both their accuracy and their ability to provide physical solutions. On the basis of new tests and analyses applied to the stellar astrophysical context, we show that the most robust method to follow the secular evolution is the implicit finite differences method. The importance of correctly estimating the diffusion coefficient between mesh points is emphasized and a procedure for estimating the average diffusion coefficient between a convective and a radiative zone is described.

Astronomy & Astrophysics, 2001

We calculate a grid of models with and without the effects of axial rotation for massive stars in... more 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 and metallicity Z = 0.004 appropriate for the SMC. Remarkably, the ratios Ω/Ωcrit 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.

Astronomy and Astrophysics, 2009

Context. The recent observations of solar-like oscillations in many red giant stars with the CoRo... more Context. The recent observations of solar-like oscillations in many red giant stars with the CoRoT satellite stimulated the theoretical study of the effects of various physical processes on the modelling of these stars. Aims. The influence of rotation on the properties of red giants is studied in the context of the asteroseismic modelling of these stars. Methods. The effects of rotation on the global and asteroseismic properties of red giant stars with a mass larger than the mass limit for degenerate He burning are investigated by comparing rotating models computed with a comprehensive treatment of shellular rotation to non-rotating ones. Results. While red giants exhibit low surface rotational velocities, we find that the rotational history of the star has a large impact on its properties during the red giant phase. In particular, for stars massive enough to ignite He burning in non-degenerate conditions, rotational mixing induces a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a higher luminosity in the HR diagram. This of course results in a change of the seismic properties of red giants at the same evolutionary state. As a consequence the inclusion of rotation significantly changes the fundamental parameters of a red giant star as determined by performing an asteroseismic calibration. In particular rotation decreases the derived stellar mass and increases the age. Depending on the rotation law assumed in the convective envelope and on the initial velocity of the star, non-negligible values of rotational splitting can be reached, which may complicate the observation and identification of non-radial oscillation modes for red giants exhibiting moderate surface rotational velocities. By comparing the effects of rotation and overshooting, we find that the main-sequence widening and the increase of the H-burning lifetime induced by rotation (V ini = 150 km s −1) are well reproduced by non-rotating models with an overshooting parameter of 0.1, while the increase of luminosity during the post-main sequence evolution is better reproduced by non-rotating models with overshooting parameters twice as large. This illustrates the fact that rotation not only increases the size of the convective core but also changes the chemical composition of the radiative zone.

Astronomy and Astrophysics, 2010

Context. Observations of solar-like oscillations obtained either from the ground or from space st... more Context. Observations of solar-like oscillations obtained either from the ground or from space stimulated the study of the effects of various physical processes on the modelling of solar-type stars. Aims. The influence of rotational mixing on the evolution and asteroseismic properties of solar-type stars is studied. Methods. Global and asteroseismic properties of models of solar-type stars computed with and without a comprehensive treatment of shellular rotation are compared. The effects of internal magnetic fields are also discussed in the framework of the Tayler-Spruit dynamo. Results. Rotational mixing changes the global properties of a solar-type star with a significant increase of the effective temperature resulting in a shift of the evolutionary track to the blue part of the HR diagram. These differences observed in the HR diagram are related to changes of the chemical composition, because rotational mixing counteracts the effects of atomic diffusion leading to larger helium surface abundances for rotating models than for non-rotating ones. Higher values of the large frequency separation are then found for rotating models than for non-rotating ones at the same evolutionary stage, because the increase of the effective temperature leads to a smaller radius and hence to an increase of the stellar mean density. In addition to changing the global properties of solartype stars, rotational mixing also has a considerable impact on the structure and chemical composition of the central stellar layers by bringing fresh hydrogen fuel to the central stellar core, thereby enhancing the main-sequence lifetime. The increase of the central hydrogen abundance together with the change of the chemical profiles in the central layers result in a significant increase of the values of the small frequency separations and of the ratio of the small to large separations for models including shellular rotation. This increase is clearly seen for models with the same age sharing the same initial parameters except for the inclusion of rotation as well as for models with the same global stellar parameters and in particular the same location in the HR diagram. By computing rotating models of solar-type stars including the effects of a dynamo that possibly occurs in the radiative zone, we find that the efficiency of rotational mixing is strongly reduced when the effects of magnetic fields are taken into account, in contrast to what happens in massive stars.