Effect of the radiative background flux in convection

Numerical simulations of turbulent stratified convection are used to study models with approximately the same convective flux, but different radiative fluxes. As the radiative flux is decreased, for constant convective flux: the entropy jump at the top of the convection zone becomes steeper, the temperature fluctuations increase and the velocity fluctuations decrease in magnitude, and the distance that low entropy fluid from the surface can penetrate increases. Velocity and temperature fluctuations follow mixing length scaling laws. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

One zone modeling of irregular variability of stellar convective envelope

One zone modeling of the irregular variability of red super-giants is intended with regard to the nonlinear coupling of finite amplitude pulsation with convection. The nonlocal mixing length is employed for the evaluation of the convective flux, the turbulent pressure and the turbulent power of temperature fluctuations. The radial pulsation and the Boussinesq convection are assumed for simplicity. The one zone is defined as the layer having the entropy maximum and the minimum at the bottom and at the top, respectively. The quasi-adiabatic approximation is consistent with this definition in fixing the zone to the same mass range. The spatial derivatives are evaluated under the assumption of homologous changes with the equilibrium homologous parameters. Then, a set of 6 simultaneous first order nonlinear ordinary differential equations are obtained as the one zone representation of the irregular variability of the convective envelope.     

Inhomogeneous convection and the equatorial acceleration of the sun

The interaction of rotation and turbulent convection is assumed to give rise to an inhomogeneous, but isotropic, latitude dependent turbulent energy transport, which is described by a convective conduction coefficient _c which varies with latitude. Energy balance in the convective zone is then possible only with a slow meridian circulation in the outer convective zone of the sun. The angular momentum transported by this circulation is balanced in a steady state by turbulent viscous transport down an angular velocity gradient. A detailed model is constructed allowing for the transition from convective transport to radiative transport at the boundaries of the convective zone, by using a perturbation analysis in which the latitude variation of _c is small. The solution for a thin compressible shell gives equatorial acceleration and a hotter equator than pole, assuming that the convection is preferentially stabilised at the equator. For agreement with the sun's equatorial acceleration the model predicts an equatorial temperature excess of 70 K and a surface meridional velocity of 350 cm/sec from pole to equator.     

Transport Effects in the Evolution of the Global Solar Magnetic Field

The axisymmetric component of the large-scale solar magnetic fields has a pronounced poleward branch at higher latitudes. In order to clarify the origin of this branch we construct an axisymmetric model of the passive transport of the mean poloidal magnetic field in the convective zone, including meridional circulation, anisotropic diffusivity, turbulent pumping and density pumping. For realistic values of the transport coefficients we find that diffusivity is prevalent, and the latitudinal distribution of the field at the surface simply reflects the conditions at the bottom of the convective zone. Pumping effects concentrate the field to the bottom of the convective zone; a significant part of this pumping occurs in a shallow subsurface layer, normally not resolved in dynamo models. The phase delay of the surface poloidal field relative to the bottom poloidal field is found to be small. These results support the double dynamo wave models, may be compatible with some form of a mixed transport scenario, and exclude the passive transport theory for the origin of the polar branch.     

Overstability of acoustic modes and the solar five-minute oscillations

The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the -mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.     

Granulation and supergranulation as convective modes in the solar envelope

The stability of linear convective modes in the solar convection zone is investigated by incorporating the mechanical and thermal effects of turbulence through the eddy transport coefficients. The inclusion of turbulent thermal conductivity and viscosity, calculated in the framework of the mixing length approximation, is demonstrated to have a profound influence on the convective growth rates. The solar envelope model of Spruit (1977) is used to show that that most rapidly growing fundamental mode and the first harmonic are in reasonable accord with the observed features of granulation and supergranulation, respectively.On leave of absence from Govt. Digvijai College, Rajnandgaon 491441, India.     

Anisotropy and Dissipation of Turbulence and Their Effects on Solar Models

1 INTRODUCTIONThe maing-length theory (MLT) is the most commonly used approach to calculate convective energy transport in stars and other astrophysical situations. Based on the original idea ofPrandtl (1952) that turbulent parcels trallsfer heat in a similar way as molecules of gas do inthermal conduction, the MLT assumes that convection cells, drived by buoyancy, move thlougha ~ng length 1 and release the heat they carry when they merge with their environment. Themost widely adopted f…     

Effect of Gravity Waves on Transport Process in Stellar Radiative Region

The aim of this work is to present a transport process which is likely to have a great importance for the internal constitution of the stars. In order to set the problem, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names of `Standard Solar Model' or `Standard Stellar Models' (SSM). Next we show that an important question about SSM is that they do not explain the age dependance of lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It has been suggested a long time ago to assume the presence of a macrosocpic diffusion process in the radiative zone, below the surface convective zone of solar like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependant, contrary to the observations. Furthermore, the diffusion coefficient being large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to an impossibility of explaining the difference of helium abundance between the surface and the center of the Sun. The consequence is obviously that we need to take into account another physical process. Stars having a mass M < 1.3 M _⊙ have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of stellar radius. In the convective zone, strong stochastic motions take care, at least partially, of heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible of the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible of lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency. The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is supposed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontal uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependant of radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible of lithium burning. Due to the radial dependance of velocity amplitude, the diffusion coeficient increases when approaching the stellar center. However, very close to the center, non-linear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very center. The development of this abstract can be found in E. Schatzman (1996, J. Fluid Mech. 322, 355). This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence properties in the solar convection envelope： properties of the overshooting regions

We apply the turbulent convection model (TCM) to investigate properties of tur-bulence in the solar convective envelope, especially in overshooting regions. The results show TCM gives negative turbulent heat flux uγ′T′in overshooting regions, which is sim-ilar to other nonlocal turbulent convection theories. The turbulent temperature fluctuation T′T′shows peaks in overshooting regions. Most important, we find that the downward overshooting region below the base of the solar convection zone is a thin cellular layer filled with roll-shaped convective cells. The overshooting length for the temperature gradi-ent is much shorter than that for element mixing because turbulent heat flux of downward and upward moving convective cells counteract each other in this cellular overshooting region. Comparing the models' sound speed with observations, we find that raking the convective overshooting into account helps to improve the sound speed profile of our nonlocal solar models. Comparing the p-mode oscillation frequencies with observations,we validated that increasing the diffusion parameters and decreasing the dissipation pa-rameters of TCM make the p-mode oscillation frequencies of the solar model be in betteragreement with observations.     

The space spectrum of convective instability

Growth rates are obtained for convective disturbances propagating in an atmosphere with a linear variation of entropy. The dispersion equation for small-scale disturbances in the parabolic entropy diagram case is considered by means of the WKB-approximation. It is shown for that case that the small-scale disturbances are reflected inside the convective zone and so cannot be observed at the Sun's surface. If the atmosphere is polytropic, it is shown that the small-scale disturbances can easily reach the sun's surface.     

Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

The effect of turbulent mixing on the g‐mode spectrum of MS stars

Understanding transport processes inside stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μ near the energy generating core, having an effect on the evolutionary tracks similar to that of overshooting. This mixing leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behavior of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We describe the effects of convective overshooting and turbulent mixing on the frequencies of gravity modes in B‐type main sequence stars. In particular, the cases of p‐g mixed modes in β Cep stars and high‐order modes in SPBs are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radial mixing in the outer Milky Way disc caused by an orbiting satellite

The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.     

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.     

Some properties of the kinetic energy flux and dissipation in turbulent stellar convection zones

We investigate simulated turbulent flow within thermally driven stellar convection zones. Different driving sources are studied, including cooling at the top of the convectively unstable region, as occurs in surface convection zones; and heating at the base by nuclear burning. The transport of enthalpy and kinetic energy, and the distribution of turbulent kinetic energy dissipation are studied. We emphasize the importance of global constraints on shaping the quasi-steady flow characteristics, and present an analysis of turbulent convection which is posed as a boundary value problem that can be easily incorporated into standard stellar evolution codes for deep, efficient convection. Direct comparison is made between the theoretical analysis and the simulated flow and very good agreement is found. Some common assumptions traditionally used to treat quasi-steady turbulent flow in stellar models are briefly discussed. The importance and proper treatment of convective boundaries are indicated.     

Self-excitation of motions in near-convection zones and the generation of solar magnetic field

In view of the recently discovered time variations in rotation velocity within the solar differentially rotating tachocline (Howe et al. 2000), we study conditions for the equilibrium and excitation of motions in nonrigidly rotating magnetized layers of the radiative zones located near the boundaries of the convection zone. The emphasis is on the possible relationship between quasi-periodic tachocline pulsations and the generation of a nonaxisymmetric magnetic field in the convection zone. This field generation is studied under the assumption that it results from a reduction in the expenditure of energy on convective heat transport. The (antisymmetric about the equator) field is shown to increase in strength if there are both a radial gradient in angular velocity and steady-state axisymmetric meridional circulation of matter. The sense of circulation is assumed to change (causing the sign of the generated field to change) after the maximum permissible field strength is reached. This is apparently attributable to the excitation of the corresponding turbulent viscosity of the medium. It is also important that the cyclic field variations under discussion are accompanied by variations in solar-type dipole magnetic field.     

Excitation of solar-like oscillations: From PMS to MS stellar models

The amplitude of solar-like oscillations results from a balance between excitation and damping. As in the sun, the excitation is attributed to turbulent motions that stochastically excite thep modes in the uppermost part of the convective zone. We present here a model for the excitation mechanism. Comparisons between modeled amplitudes and helio and stellar seismic constraints are presented and the discrepancies discussed. Finally the possibility and the interest of detecting such stochastically excited modes in pre-main sequence stars are also discussed.     

Differential rotation and meridional circulation in global models of solar convection

In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)