Radiative accelerations, accumulation of iron and thermohaline convection inside stars

The radiative acceleration on iron inside stars may lead to an accumulation of this element in stellar internal layers. As discussed by several authors, this iron accumulation has many important consequences. It may lead to an extra convective zone, and in some cases it may help triggering stellar pulsations. However, the computations which have been done up to now ignore an important effect: the double-diffusive, or “thermohaline” convection induced by the inverse μ gradient. Detailed computations of all these processes have been introduced in the TGEC stellar evolution code. We show how thermohaline convection modifies the profiles of iron inside stars, with important consequences     

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M _⊙ and an angular momentum of 3.25 × 10⁵² g cm² s^?1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s^?1.     

Present problems of the solar interior

The standard model of solar evolution is reviewed and a number of problems highlighted. A fundamental question is whether there is any mixing of matter in the central regions, since such mixing could radically alter the model of the present Sun and modify our understanding of the evolution of other stars. Standard models of solar evolution become unstable to ³He driven global oscillations at an age of 3 × 10⁸ years and this may drive some mixing, even if this is not the case the finite amptitude limit of these oscillations is likely to produce modifications in the standard model. Convective overshooting at the bottom of the outer convective zone leads to an increased depth of this zone and small changes in the interior. It is pointed out that the young Sun had a ¹²C driven convective core whose extent and duration depends on the extent of overshooting. Such a core is likely to produce a magnetic field which will affect the internal dynamics. The internal rotation of the Sun remains an enigma and absence of knowledge of any internal magnetic field makes it difficult to study the problem. Rotationally driven instabilities are ineffective in the central chemically inhomogenous regions but may contribute to the inward diffusion of lithium from the convective zone. These and other problems are considered, but few solutions are proposed.     

The influences of convective overshooting and semiconvection on the chemical evolution of massive stars

In massive stars,convection in the interior is different from that of intermediate and small mass stars. In the main-sequence phase of small mass stars,there is a convective core and a radiative envelope,between which are the radiative intermediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting,the semiconvection is more pronounced. In these two processes,we introduce one diffusive parameter D,which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.     

On a physical mechanism for extra mixing in globular cluster red giants

For the first time we propose a real physical mechanism for 'extra mixing' in red giants that can quantitatively interpret all the known star-to-star abundance variations in globular clusters. This is Zahn's mechanism. It considers extra mixing in a radiative zone of a rotating star as a result of the joint operation of meridional circulation and turbulent diffusion. It is shown that the only free parameter, the angular velocity at the base of the convective envelope, can be so adjusted as to fit the observed abundance correlations without leading to a conflict with available data on rotation velocities of blue horizontal branch stars in the same cluster. There are two critical assumptions in our model, that the top of the radiative zone is not in synchronous rotation with the stellar surface but rotates significantly faster and that the criterion for shear instability takes a particular form. These will eventually be tested by three-dimensional hydrodynamical simulations.     

Seismic study of stellar convective regions: the base of the convective envelope in low-mass stars

The possibility of observing solar-type oscillations on other stars is of great relevance to investigating the uncertain aspects of the internal structure of stars. One of these aspects is the convective overshoot that takes place at the borders of the envelopes of stars of mass similar to, or lower than, the Sun. It affects the temperature stratification, mixing, rotation and magnetic-field generation. Asteroseismology can provide an observational test for the studies of the structure of such overshoot regions.
The seismic study of the transition in the Sun, located at the base of the convection zone, has been successful in determining the characteristics of this layer in the Sun. In this work we consider the extension of the analysis to other solar-type stars (of mass between 0.85 and 1.2 M_⊙) in order to establish a method for determining the characteristics of their convective envelopes. In particular, we hope to be able to establish seismologically that a star does indeed possess a convective envelope, to measure the size of the convective region and also to constrain the properties of an overshoot layer at the bottom of the envelope. The limitations in terms of observational uncertainties and stellar characteristics, and the detectability of an overshoot layer, are discussed.     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity η_T of the convection zone to the (microscopic or turbulent) diffusivity η_in of the radiative interior is η_T/η_in ≥ 10⁵. Confinement in younger stars requires larger η_T/η_in. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Acceleration and Transport of Energetic Charged Particles in Space

Recent advances in constructing stellar evolution models of hydrogen-deficient post-asymptotic giant branch (AGB) stars are presented. Hydrogen-deficiency can originate from mixing and subsequent convective burning of protons in the deeper layers during a thermal pulse on the post-AGB (VLTP). Dredge-up alone may also be responsible for hydrogen-deficiency of post-AGB stars. Models of the last thermal pulse on the AGB with very small envelope masses have shown efficient third dredge-up. The hydrogen content of the envelope is diluted sufficiently to produce H-deficient post-AGB stars (AFTP). Moreover, dredge-up alone may also cause H-deficiency during the Born-again phase (LTP). During the second AGB phase a convective envelope develops. A previously unknown lithium enrichment at the surface of Born-again stellar models may be used to distinguish between objects with different post-AGB evolution. The observed abundance ratios of C, O and He can be reproduced by all scenarios if an AGB starting model with inclusion of overshoot is used for the post-AGB model sequence. An appendix is devoted to the numerical methods for models of proton capture nucleosynthesis in the He-flash convection zone during a thermal pulse.     

Do not forget gravity waves

The physics of the Sun involves all possible physical processes and year after year forgotten processes are taken into account. A brief and partial history of recent dealing with gravity waves is presented here.There are random motions in the solar convective zone. They generate, at the boundary of the convective zone, gravity waves which propagate in the radiative zone. Random gravity waves generate three physical processes: (1) diffusion induced by the stochastic properties of random gravity waves; (2) transport of angular momentum; (3) influence of nonlinear properties on the rate of thermonuclear energy production. Taking into account processes (1) and (3) can possibly lead to the solution of the solar neutrino problem.Dedicated to Cornelis de Jager     

Rotational evolution of the Sun

The evolutionary behaviour of rotating solar models with different initial angular-momentum distributions has been investigated through the pre-Main-Sequence and Main-Sequence phases. The angular momentum was removed from the convective evelope of the solar models according to the Kawaler's model of magnetic stellar wind (Kawaler, 1988). The models show that (i) the surface rotational velocities of the solar mass stars are independent of initial angular momentum for ages greater than 10⁸ years and (ii) it is not possible to explain the neutrino problem and the sufficient depletion of lithium in the Sun.     

Starspots

Starspots are created by local magnetic fields on the surfaces of stars, just as sunspots. Their fields are strong enough to suppress the overturning convective motion and thus block or redirect the flow of energy from the stellar interior outwards to the surface and consequently appear as locally cool and therefore dark regions against an otherwise bright photosphere (Biermann in Astronomische Nachrichten 264:361, 1938; Z Astrophysik 25:135, 1948). As such, starspots are observable tracers of the yet unknown internal dynamo activity and allow a glimpse into the complex internal stellar magnetic field structure. Starspots also enable the precise measurement of stellar rotation which is among the key ingredients for the expected internal magnetic topology. But whether starspots are just blown-up sunspot analogs, we do not know yet. This article is an attempt to review our current knowledge of starspots. A comparison of a white-light image of the Sun (G2V, 5 Gyr) with a Doppler image of a young solar-like star (EK Draconis; G1.5V, age 100 Myr, rotation 10 × Ω _Sun) and with a mean-field dynamo simulation suggests that starspots can be of significantly different appearance and cannot be explained with a scaling of the solar model, even for a star of same mass and effective temperature. Starspots, their surface location and migration pattern, and their link with the stellar dynamo and its internal energy transport, may have far reaching impact also for our understanding of low-mass stellar evolution and formation. Emphasis is given in this review to their importance as activity tracers in particular in the light of more and more precise exoplanet detections around solar-like, and therefore likely spotted, host stars.     

Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors

Small levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial‐to‐horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non‐diffusive transport known as the Λ‐effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test‐scalar method. As a consequence of the non‐diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (≲100 Myr) between radiative core and convective envelope in young solar‐type stars is much shorter compared to the time‐scale of Lithium depletion (∼1 Gyr) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diurnal thermal tides in a non-synchronized hot Jupiter

We perform a linear analysis to investigate the dynamical response of a non-synchronized hot Jupiter to stellar irradiation. In this work, we consider the diurnal Fourier harmonic of the stellar irradiation acting at the top of a radiative layer of a hot Jupiter with no clouds and winds. In the absence of the Coriolis force, the diurnal thermal forcing can excite internal waves propagating into the planet's interior when the thermal forcing period is longer than the sound crossing time of the planet's surface. When the Coriolis effect is taken into consideration, the latitude-dependent stellar heating can excite weak internal waves (g modes) and/or strong baroclinic Rossby waves (buoyant r modes) depending on the asynchrony of the planet. When the planet spins faster than its orbital motion (i.e. retrograde thermal forcing), these waves carry negative angular momentum and are damped by radiative loss as they propagate downwards from the upper layer of the radiative zone. As a result, angular momentum is transferred from the lower layer of the radiative zone to the upper layer and generates a vertical shear. We estimate the resulting internal torques for different rotation periods based on the parameters of HD 209458b.     

FUSE Observations of EC14026 Stars

We present a FUSE abundance analysis of EC14026 stars. We compare the abundances of heavy elements in the atmospheres of EC14026 stars to non-pulsating stars with similar atmospheric parameters, and investigate whether weak stellar winds could explain the coexistence of variable and non-variable sdB stars in the log g – T_eff diagram. We also present preliminary results on time-dependent diffusion calculations of iron in presence of radiative levitation and mass loss, and show how weak stellar winds can affect the diffusive equilibrium between gravitational settling and radiative support.     

Mass loss from solar-type stars

Winds are directly detected from solar-type stars only when they are very young. At ages 10⁶ yr, these stars have mass loss rates 10⁶ times the mass flux of the present solar wind. Although these young T Tauri stars exhibit ultraviolet transition-region and X-ray coronal emission, the large particle densities of the massive winds lead to efficient radiative cooling, and wind temperatures are only 10⁴ K. In these circumstances thermal acceleration is unlikely to play an important role in driving the mass loss. Turbulent energy fluxes may be responsible for the observed mass loss, particularly if substantial magnetic fields are present.The presence of stellar mass loss is indirectly shown by the spindown of low-mass stars as they age. It appears that many solar-mass stars spin up as they contract toward the Main-Sequence, reaching a maximum equatorial velocity of 50 to 100 km s^–1. These stars spin down rapidly upon reaching the Main Sequence. Spindown may be enhanced by a decoupling or lag between convective envelope and radiative core. Because this spindown occurs fairly early in a solar-type star's history, the internal structure of old stars like the Sun may not depend upon initial conditions.     

First stars. I. Evolution without mass loss

The first generation of stars was formed from primordial gas. Numerical simulations suggest that the first stars were predominantly very massive, with typical masses M≥100M _⊙. These stars were responsible for the reionization of the universe, the initial enrichment of the intergalactic medium with heavy elements, and other cosmological consequences. In this work, we study the structure of Zero Age Main-Sequence stars for a wide mass and metallicity range and the evolution of 100, 150, 200, 250 and 300M _⊙ galactic and pregalactic Pop III very massive stars without mass loss, with metallicity Z=10⁻⁶ and 10⁻⁹, respectively. Using a stellar evolution code, a system of 10 equations together with boundary conditions are solved simultaneously. For the change of chemical composition, which determines the evolution of a star, a diffusion treatment for convection and semiconvection is used. A set of 30 nuclear reactions are solved simultaneously with the stellar structure and evolution equations. Several results on the main sequence, and during the hydrogen and helium burning phases, are described. Low-metallicity massive stars are hotter and more compact and luminous than their metal-enriched counterparts. Due to their high temperatures, pregalactic stars activate sooner the triple alpha reaction self-producing their own heavy elements. Both galactic and pregalactic stars are radiation pressure dominated and evolve below the Eddington luminosity limit with short lifetimes. The physical characteristics of the first stars have significant influence in predictions of the ionizing photon yields from the first luminous objects; also they develop large convective cores with important helium core masses which are important for explosion calculations.     

Wolf-Rayet stars

This paper reviews the current status of knowledge regarding the basic physical and chemical properties of Wolf-Rayet stars; their overall mass loss and stellar wind characteristics and current ideas about their evolutionary status. WR stars are believed to be the evolved descendents of massive O-type stars, in which extensive mass loss reveals successive stages of nuclear processed material: WN stars the products of interior CNO-cycle hydrogen burning, and WC and WO stars the products of interior helium burning. Recent stellar evolution models, particularly those incorporating internal mixing, predict results which are in good accord with the different chemical compositions observationally inferred for WN, WC and WO stars. WR stars exhibit the highest levels of mass loss amongst earlytype stars: mass loss rates, typically, lie in the range [1–10]×10⁻⁵ M _⊙yr⁻¹. Radiation pressure-driven winds incorporating multi-scattering in high ionisation-stratified winds may cause these levels, but additional mechanisms may also be needed.     

Equatorially trapped Rossby waves in radiative stars

Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This article aims to study the theoretical dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near-surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained. The solutions were found to be confined around the equator, leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes.