We extend the analysis of Penev et al. (2007) to calculate effective viscosities for the surface convective zones of three main sequence stars of 0.775Msun, 0.85Msun and the present day Sun. In addition we also pay careful attention to all normalization factors and assumptions in order to derive actual numerical prescriptions for the effective viscosity as a function of the period and direction of the external shear. Our results are applicable for periods that are too long to correspond to eddies that fall within the inertial subrange of Kolmogorov scaling, but no larger than the convective turnover time, when the assumptions of the calculation break down. We find linear scaling of effective viscosity with period and magnitudes at least three times larger than the Zahn (1966, 1989) prescription.
A one-dimensional turbulent convection model in the form of a time-dependent diffusion equation for the turbulent energy is incorporated into our numerical pulsation code. The effect of turbulent convection on the structural rearrangement of the static equilibrium star is taken into account, and the linear eigenvalues (periods and growth-rates) for the complete turbulent convective nonadiabatic pulsations of the equilibrium models are calculated. The linearized code allows us to perform efficiently a systematic survey of the stability of Cepheid models for a wide range of astrophysical paramet…
Under nonlocal convection theory, convection extends without limit therefore no apparent boundary can be defined clearly as in the local theory. From the requirement of a similar structure for both local and non-local models having the same depth of convection zone, and taking into account the driving mechanism of turbulent convection, we argue that a proper definition of the boundary of a convective zone should be the place where the convective energy flux (i.e. the correlation of turbulent velocity and temperature) changes its sign. Therefore, it is convectively unstable region when the flux…
The mass of the outer convective zone in FGK main sequence stars decreases dramatically with stellar mass. Therefore, any contamination of a star's atmosphere by accreted planetary material should affect hotter stars much more than cool stars. If recent suggestions that high metal abundances in stars with planets are caused by planetesimal accretion are correct, then metallicity enhancements in earlier-type stars with planets should be very pronounced. No such trend is seen, however.
Predicted rates for solar neutrino experiments that are obtained with a modified stellar evolution code originally developed to study the advanced stages of stellar evolution are shown to be in agreement with other recently-calculated precise solar models to about 2% (0.2 SNU for the chlorine experiment). Different scenarios for pre-main sequence evolution are explored and are found to change the predicted rates for solar neutrino experiments by less than or of order 1%. The influence of the depth of the solar convective zone on the predicted solar neutrino fluxes is established by direct calc…
A new mean-field theory of turbulent convection is developed. This theory predicts the convective wind instability in a shear-free turbulent convection which causes formation of large-scale semi-organized fluid motions in the form of cells or rolls. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection which results in generation of convective shear waves with a nonzero …
We evaluate the logarithmic derivative of the depth of the solar convective zone with respect to the logarithm of the radiative opacity. We use this expression to show that the radiative opacity near the base of the solar convective zone (CZ) must be known to an accuracy of +- 1% in order to calculate the CZ depth to the accuracy of the helioseismological measurement, R(CZ) = (0.713 +- 0.001)R(Sun). The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by about 21% in the Bahcall-Pinsonneault (2004) solar model if one wants to invoke opacity errors i…
Recent solar photospheric abundance analyses have led to a significant reduction of the metal abundances compared to the previous determinations. The solar models computed with standard opacities and diffusion processes using these new abundances give poor agreement with helioseismic inversions for the sound-speed profile, the surface helium abundance, and the convective zone depth. We attempt to obtain a good agreement between helioseismic inversions and solar models which present the "old" mixture in the interior and new chemical composition in the convective zone. To reach this result, we a…
The value of the effective convective viscosity, in the framework of the mixing length theory (MLT), is 2 orders of magnitude too small compared to that required by the observational data. Moreover, the reduction of the effective viscosity due to the fast time-variation of the tidal shear in short period binaries, increases the discrepancy to about three orders of magnitude. In this work, we examine the possibility that the apparent inefficiency of turbulent convection is merely a shortcoming of MLT approach. We employ a model for stellar turbulent convection (Canuto, Goldman & Mazzitelli 1996…
We review the numerical modelling of the nonlinear pulsations of classical variable stars with hydrocodes that include the effects of turbulent convection. Despite their simplicity these turbulent convective recipes appear to remove many of the difficulties that radiative codes faced. In particular, the numerical modelling of double mode pulsations has become possible.
Turbulent motions in the interior of a star play an important role in its evolution, since they transport chemical species, thermal energy and angular momentum. Our overall goal is to construct a practical turbulent closure model for convective transport that can be used in a multi-dimensional stellar evolution calculation including the effects of rotation, shear and magnetic fields. Here, we focus on the first step of this task: capturing the well-known transition from radiative heat transport to turbulent convection with and without rotation, as well as the asymptotic relationship between tu…
Previous work on the angular momentum balance and meridional circulation of the solar convective zone (SCZ) generally consists either of semi-analytic approaches in which a simple turbulence model is adopted, or full direct numerical simulation (DNS) of the hydrodynamics or magnetohydrodynamics (MHD). In both instances the inclusion of magnetic fields has been troublesome. Also, both approaches have had difficulty reproducing the known angular velocity profile of the SCZ; this is the Taylor Number Puzzle. I discuss preliminary work in which I incorporate magnetic fields into a viscoelastic tur…
The influence of extended convective mixing (overshoot) on asymptotic giant branch stellar evolution is investigated in detail. The extended mixing is treated time-dependently, and the efficiency declines exponentially with the geometric distance from the convective boundary. It has been considered at all convective boundaries, including the He-flash convection zone in the intershell region which forms during the thermal pulses. Both the structural and the chemical evolution are affected by the inclusion of overshoot. The main results include a very efficient third dredge-up which leads to the…
In this paper we describe our convective hydrocodes for radial stellar pulsation. We adopt the Kuhfuss (1986) model of convection, reformulated for the use in stellar pulsation hydrocodes. Physical as well as numerical assumptions of the code are described in detail. Described tests show, that our models are numerically robust and reproduce basic observational constraints. We discuss the effects of different treatment of some quantities in other pulsation hydrocodes. Our most important finding concerns the treatment of the turbulent source function in convectively stable regions. In our code w…
The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of a…
We investigate dynamical interactions between turbulent convection and g-mode pulsations in ZZ Ceti variables (DAVs). Since our understanding of turbulence is rudimentary, we are compelled to settle for order of magnitude results. A key feature of these interactions is that convective response times are much shorter than pulsation periods. Thus the dynamical interactions enforce near uniform horizontal velocity inside the convection zone. They also give rise to a narrow shear layer in the region of convective overshoot at the top of the radiative interior. Turbulent damping inside the convecti…
We present the results of a detailed set of one-zone models that account for the coupling between pulsation and convection following the original prescriptions of Stellingwerf (1986). Motivated by the arbitrary nature of the input parameters adopted in this theoretical framework, we computed several sequences of models that cover a substantial fraction of the parameter space and a longer integration time. We also included a turbulent pressure term and found that this physical mechanism plays a crucial role in the pulsation characteristics of the models by removing the sharp discontinuities alo…
A self-consistent solution for a thin accretion disk with turbulent convection is presented. The disk viscosity and the convective flux are derived from a physical model for turbulence, and expressed in terms of the local physical conditions of the disk which, in turn, are controlled by the former two. In the gas pressure region, two distinct solutions are obtained. In one, the convective flux is much larger than the radiative flux and the blackbody region extends over the entire gas pressure region and could also extend down to the inner boundary of the disk. In this solution the temperature …
A-type stars have a complex internal structure with the possibility of multiple convection zones. If not sufficiently separated, such zones will interact through the convectively stable regions that lie between them. It is therefore of interest to ask whether the typical conditions that exist within such stars are such that these convections zones can ever be considered as disjoint. In this paper we present results from numerical simulations that help in understanding how increasing the distance between the convectively unstable regions are likely to interact through the stable region that sep…
We have adapted the anelastic spectral code of Barranco & Marcus (2006) to simulate a turbulent convective layer with the intention of studying the effectiveness of turbulent eddies in dissipating external shear (e.g. tides). We derive the anelastic equations, show the time integration scheme we use to evolve these equations and present the tests we ran to confirm that our code does what we expect. Further we apply a perturbative approach to find an approximate scaling of the effective eddy viscosity with frequency, and find that it is in general agreement with an estimate obtained by applying…
The understanding of transport processes inside the stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μnear 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 mode…
Protostellar accretion discs have cool, dense midplanes where externally originating ionisation sources such as X-rays or cosmic rays are unable to penetrate. This suggests that for a wide range of radii, MHD turbulence can only be sustained in the surface layers where the ionisation fraction is sufficiently high. A dead zone is expected to exist near the midplane, such that active accretion only occurs near the upper and lower disc surfaces. Recent work, however, suggests that under suitable conditions the dead zone may be enlivened by turbulent transport of ions from the surface layers into …
We give a status report of convective Cepheid and RR Lyrae model pulsations. Some striking successes can be reported, despite the use of a rather simple treatment of turbulent convection with a 1D time-dependent diffusion equation for the turbulent energy. It is now possible to obtain stable double-mode (beat) pulsations in both Cepheid and RR Lyrae models with astrophysical parameters, i.e. periods and amplitude ratios, that are in agreement with observations. The turbulent convective models, however, have difficulties giving global agreement with the observations. In particular, the Magellan…
We present the results of a very large aspect ratio (42.6) numerical simulation of fully compressible turbulent convection in a polytropic atmosphere, and focus on the properties of large-scale flows. Mesoscale patterns dominate the turbulent energy spectrum. We show that these structures, which had already been observed in Boussinesq simulations by Cattaneo et al. (2001), have a genuine convective origin and do not result directly from collective interactions of the smaller scales of the flow, even though their growth is strongly affected by nonlinear transfers. If this result is relevant to …
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 angu…
We present 3-d numerical magneto-hydrodynamic simulations of a buoyant, twisted magnetic flux rope embedded in a stratified, solar-like model convection zone. The flux rope is given an initial twist such that it neither kinks nor fragments during its ascent. Moreover, its magnetic energy content with respect to convection is chosen so that the flux rope retains its basic geometry while being deflected from a purely vertical ascent by convective flows. The simulations show that magnetic flux is advected away from the core of the flux rope as it interacts with the convection. The results thus su…
The development of 2D and 3D simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We investigate the impact of this changed structure on the dissipation properties of the convection zone, parametrized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh 1997, applied to a numerical model of solar convection (Robinson et al. 2003) to calculate an effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of…
Migration of protoplanets in their gaseous host disks may be largely responsible for the observed orbital distribution of extrasolar planets. Recent simulations have shown that the magnetorotational turbulence thought to drive accretion in protoplanetary disks can affect migration by turning it into an orbital random walk. However, these simulations neglected the disk's ionization structure. Low ionization fraction near the midplane of the disk can decouple the magnetic field from the gas, forming a dead zone with reduced or no turbulence. Here, to understand the effect of dead zones on protop…
We propose a simple interpretation of the rotation period data for solar- and late-type stars. The open cluster and Mt. Wilson star observations suggest that rotating stars lie primarily on two sequences, initially called I and C. Some stars lie in the intervening gap. These sequences, and the fractional numbers of stars on each sequence evolve systematically with cluster age, enabling us to construct crude rotational isochrones allowing `stellar gyrochronology', a procedure, upon improvement, likely to yield ages for individual field stars. The age and color dependences of the sequences allow…
Differences between observed and theoretical eigenfrequencies of the Sun have characteristics which identify them as arising predominantly from properties of the oscillations in the vicinity of the solar surface: in the super-adiabatic, convective boundary layer and above. These frequency differences may therefore provide useful information about the structure of these regions, precisely where the theory of solar structure is most uncertain. In the present work we use numerical simulations of the outer part of the Sun to quantify the influence of turbulent convection on solar oscillation frequ…
In previous work, we have shown that recent updated standard solar models cannot reproduce the radial profile of the sound speed at the base of the convective zone (CZ) and fail to predict the Li7 depletion. In parallel, helioseismology has shown that the transition from differential rotation in the CZ to almost uniform rotation in the radiative solar interior occurs in a shallow layer called the tachocline. This layer is presumably the seat of large scale circulation and of turbulent motions. Here, we introduce a macroscopic transport term in the structure equations, which is based on a hydro…
Precise Li abundances are determined for 54 giant stars mostly evolving across the Hertzsprung gap. We combine these data with rotational velocity and with information related to the deepening of the convective zone of the stars to analyse their link to Li dilution in the referred spectral region. A sudden decline in Li abundance paralleling the one already established in rotation is quite clear. Following similar results for other stellar luminosity classes and spectral regions, there is no linear relation between Li abundance and rotation, in spite of the fact that most of the fast rotators …
We have performed the first three-dimensional non-linear simulation of the turbulent convective envelope of a rotating 0.8 Msun RGB star using the ASH code. Adopting a global typical rotation rate of a tenth of the solar rate, we have analyzed the dynamical properties of the convection and the transport of angular momentum within the inner 50% in radius of the convective envelope. The convective patterns consist of a small number of large cell, associated with fast flows (about 3000 m/s) and large temperature fluctuations (about 300 K) in order to carry outward the large luminosity (L* = 400 L…
We present results from new, detailed computations of lithium production by hot bottom burning (HBB) in asymptotic giant branch (AGB) stars of intermediate mass. The dependance of lithium production on stellar mass, metallicity, mass loss rate, convection and overshooting are discussed. In particular, nuclear burning, turbulent mixing and convective overshooting (if any) are self-consistently coupled by a diffusive algorythm, and the Full Spectrum of Turbulence (FST) model of convection is adopted, with test comparisons to Mixing Length Theory (MLT) stellar models.
We present a selfconsistent model for stellar turbulent convection which is similar in spirit to the CM model (Canuto \& Mazzitelli 1991) since it accounts for the full spectrum of the turbulent eddies rather than only one eddy, as done in the mixing length theory (MLT). The model differs from the CM model in the treatment of the rate of energy input $n_s(k)$ from the source that generates the turbulence. In the present model, $n_s(k)$ is controlled by both the {\it source} and {\it the turbulence} it ultimately generates, thus ensuring a selfconsistent modeling of the turbulence. This improve…
