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.     

A heat engine based moist convection parametrization for Jupiter

We have developed a parametrization of Jovian moist convection based on a heat engine model of moist convection. In comparison to other moist convection schemes, this framework allows the computation of the total available convective energy TCAPE and the corresponding mass flux M as dynamic variables from the mean atmospheric state. The effects of this parametrization have been investigated both analytically and numerically. In agreement with previous numerical experiments and observations, the inclusion of moist convection leads to heat and water vapor transport from the water condensation level into higher altitudes. The time development of the modeled convective events was found to be strongly influenced by a rapid reduction of kinetic energy and a subsequent lowering of the cumulus tower's top in response to convective heating. We have tested the sensitivity of the scheme to different variations in the fractional cloud coverage and under the inclusion of external radiative forcing towards a stable/unstable temperature profile. While the time development of convective events differs in response to these variations, the general moist convective heating and moistening of the upper troposphere was a robust feature observed in all experiments.     

The local mixing-length theory with convective helium flux

The local mixing-length theory is extended to calculate distributions of chemical elements in the convective region. There are two different convective solutions in the convective core of the massive Main-Sequence star where convective flux of helium is positive. The condition for the convection to exist with -gradient differs from the Ledoux-Sakashita-Hayashi condition when the radiative heat loss from the convective element is taken into account.     

Temperature fluctuations in the solar photosphere

The general problem of interpreting granulation data, in particular Edmonds' r.m.s. intensity fluctuation distribution against heliocentric angle , is discussed.A method is developed for investigating a variety of models of inhomogeneous departures from radiative equilibrium using two dimensional solutions of the equation of radiative transfer, and theoretical r.m.s. intensity fluctuation distributions are computed. It is found that only a very narrow range of models yields distributions which exhibit the essential features of Edmonds' distribution (a center-of-disk value of 14 % and a maximum value of 20.5 % at a heliocentric angle of 53°). The feature of these models is a maximum in the temperature fluctuations of about 660 K r.m.s., which represents a temperature difference between hot and cold regions of 2000 K, at a depth of about 250 km below ₅₀₀₀= 0.03. Below this the temperature fluctuations decrease rapidly in the next 70 km.These results are interpreted in terms of convective and radiative transport of energy. Velocities of the order of 8 km/sec are deduced in the essentially convective regime near 320 km, decreasing through 4 km/sec near the temperature fluctuation maximum to negligible values in the radiative region above 200 km.These features are shown to be consistent with modern theoretical and laboratory studies of convection in incompressible fluids. Further, these studies indicate that a second temperature fluctuation should occur at the bottom of a convective layer. For this reason, further photospheric models are studied in which, below the region of small temperature fluctuations near 320 km, the fluctuations increase sharply. For one of these models a theoretical intensity r.m.s. distribution is obtained which closely fits not only the maximum at = 53° in Edmonds' observed distribution but also the initial decrease and smaller minimum near 24°.Of the National Bureau of Standards and the University of Colorado.     

Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona

We present a series of numerical simulations of the quiet-Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun’s atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.     

Smooth models of overshooting at the base of the solar convective zone

A set of smoothed temperature gradient profiles around overshooting layers at the solar convective zone bottom is considered. In classical local theories of convection the one point defined according to the Schwarzschild criterion is enough to describe a convective boundary. To get a sophisticated picture of the overshooting we use four points to compute the transition overshooting functions. Analyzing the transition gradient profiles we found that the overshooting convective flux may be either positive or negative. A negative overshooting flux appears in nonlocal convective theories and causes a steep temperature gradient profile. But we propose an evenly smoothed gradient which corresponds to a convective flux positive everywhere. To outline the effect of the temperature gradient on the solar oscillations the squared Brunt–Väisälä frequency N ² is calculated. In local convective theories the N ² profile shows the discontinuity of the first derivative at the convective boundary, while all smoothed profiles eliminate the break.     

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)     

Umbral boundaries,convection, and the depth of sunspots

The boundary between the umbra and penumbra of a sunspot is consistently observed to be very sharp, on the order of 500 km. Approximating the sunspot as a static region in a homogeneous medium with a radiative surface, temperature distributions resulting from a variety of convective motions exterior to the sunspot are calculated. The calculations suggest that, for the exterior convection to produce the observed boundary, the maximum depth of the region of inhibited convection below a sunspot umbra is on the order of 10³ km.     

On the appearance of magnetic flux in the solar photosphere

Ideas and models for the appearance of photospheric magnetic structure are confronted with observational data. Some findings are: The magnetic flux emerging in an active region consists of a bundle of flux tubes which were already concentrated before penetrating into the photosphere. A model of a rising bunch of flux tubes joining into a few strands at larger depths describes the coalescence of spots near the leading and following edges of the active region while more flux may surface near the center of the region. There is no observational evidence for appreciable helical twists in the flux bundles.Throughout the region's lifetime the magnetic elements move coherently, the whole magnetic structure rotates faster than the quiet photosphere. In active regions the convective flow at scales larger than the granulation is arrested by the magnetic structure. The long-lived supergranular cells around spots and in the enhanced network in turn determine the decay properties of spots and facular clusters. The modulation of the convective flow by the magnetic structure explains the slow dispersal of faculae.The hierarchy of magnetic elements (sunspots-pores-knots-facular clusters-facular points) may be explained by a set of magnetostatic flux tube models in the top of the convection zone. The underlying assumptions are that the heat flow along the magnetic field is reduced and that there is no heat exchange across the field except by radiation.A tentative model is proposed to account for the amplification, ascent and emergence of intense flux bundles. The assumptions are: (i) the field is concentrated in toroidal bundles by differential rotation, (ii) in the deep convection zone flux bundles are contained by the external turbulent pressure, and (iii) for field strengths up to the equipartition value efficient lateral heat exchange is possible. After a loop has surfaced radiative cooling and subsequent convective downflow reduce the temperature in the top of the flux tubes which then contract to field strengths well above the local equipartition value. There the heat flow is channelled along the field, which creates the conditions for the magnetostatic flux tube models without requiring a blocking of the heat flow somewhere within the tubes.The paper contains a brief review on the evolution of the magnetic field from the emergence in active regions up to the enigmatic disappearance, and a list of topics for further observational investigation.     

Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

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.     

Dynamical behavior of strong magnetic fields in the solar convection zone

Magnetic buoyancy is thought to play an important role in the dynamical behavior of the Sun's magnetic field in the convection zone. Magnetic buoyancy is commonly thought to cause inescapable rapid loss of toroidal flux from much of the convection zone, thereby suppressing effective operation of a solar dynamo. This paper re-examines the detailed character of magnetic buoyancy, especially as it is influenced by the magnetic field's effect on heat transport and temperature gradients in the convection zone. It is suggested that suppression of convective heat transport across strong magnetic flux tubes can alter the temperature within the tubes and can subdue, or even reverse, the effect of magnetic buoyancy.     

Stellar envelopes with supercritical luminosity

The analytical solutions are obtained for static envelopes at radiative equilibrium for power dependence of opacity on the temperature. The existence of an exact boundary is shown to lie between the regions of static radiative envelopes and stationary outflowing envelopes for which the asymptotic numerical solutions are foundIt is shown that convection makes the static envelope region broader and leads to the existence, for the same parameters, of outflowing and static convective envelopes — i.e., to double-valued solution. The approximate method is indicated for the definition of the boundary of the beginning of the outflow. It is pointed out that our results are, on the whole, applicable to the real cases of the dependence of opacity on the temperature and density.     

A generalized time-dependent local convection theory

The time-dependent convection theory given in [1] is generalized to include non-radial oscillations. Under some reasonable assumptions, dynamic equations are derived of the auto-correlation and cross-correlation functions of the velocity and temperature fluctuations. Steady and pulsating components are separated and solved for. Our steady component agrees with Vitense's formulae. The pulsating component contains a phase-lag, due to the inertia of the convective motion.     

Convective flux in the solar photosphere as determined from fluctuations

The fractional convective flux πF _c (x _c /πF) is computed for the effective level x _c = logτ _c = 0.125, using bi-dimensional co-spectra for relative continuum-brightness fluctuations ΔI and radial velocity fluctuations ΔV measured for the C _i 5052.16 spectral line. A more uncertain flux for x _Fe ≈ - 0.9 is obtained for the Fe _i 5049.83 line. Since the results (Figure 1) incorporate current uncertainties in RMS _ΔI , RMS _ΔV and RMS _ΔT (x), where ΔT are photospheric temperature fluctuations, they must be considered qualitative until these uncertainties are appreciably reduced. The requirement that the fractional convective flux < 1, places restrictions on these uncertainties which suggest that current RMS _ΔT (x)'s are too large. The results confirm the importance of overshoot at the top of the solar hydrogen convection zone and suggest a non-negligible fractional convective flux throughout the lower photosphere. Qualitatively, they do not agree with the predictions of the generally-used, local, mixing-length theory or those of Parsons' (1969) modified mixing-length theory. However, qualitative agreement with the predictions of the non-local, generalized mixing-length theory of Spiegel (1963) and with the non-local theory of Ulrich (1970) cannot be considered as observational confirmation of these theories.     

Excitation of Radial P-Modes in the Sun and Stars

P-mode oscillations in the Sun and stars are excited stochastically by Reynolds stress and entropy fluctuations produced by convection in their outer envelopes. The excitation rate of radial oscillations of stars near the main sequence from K to F and a subgiant K IV star have been calculated from numerical simulations of their surface convection zones. P-mode excitation increases with increasing effective temperature (until envelope convection ceases in the F stars) and also increases with decreasing gravity. The frequency of the maximum excitation decreases with decreasing surface gravity.     

Large-scale circulations and energy transport in contact binaries

A hydrodynamic model for the energy transport between the components of a contact binary is presented. Energy is transported by a large-scale, steady circulation carrying high entropy matter from the primary to secondary component. The circulation is driven by the baroclinic structure of the common envelope, which is a direct consequence of the non-uniform heating at the inner critical Roche lobes due to unequal emergent energy fluxes of the components. The mass stream flowing around the secondary is bound to the equatorial region by the Coriolis force and its width is determined primarily by the flow velocity. Its bottom is separated from the underlying secondary's convection zone by a radiative transition layer acting as an insulator. For a typically observed degree of contact the heat capacity of the stream matter is much larger than radiative losses during its flow around the secondary. As a result, its effective temperature and entropy decrease very little before it returns to the primary. The existence of the stream changes insignificantly specific entropies of both convective envelopes and sizes of the components. Substantial oversize of the secondaries, required by the Roche geometry, cannot be explained in this way. The situation can, however, be explained by assuming that the primary is a main-sequence star whereas the secondary is in an advanced evolutionary stage with hydrogen depleted in its core. Such a configuration is reached past mass transfer with mass ratio reversal. Good agreement with observations is demonstrated by model calculations applied to actual W UMa-type binaries. In particular, a presence of the equatorial bulge moving with a relative velocity of  10–30 km s^−!  around both components of AW UMa is accounted for.     

The role of turbulent convection in the primitive solar nebula: I. Theory

The theoretical framework for modeling the primordial solar nebula is presented in which convection is assumed to be the sole source of turbulence that causes the nebula to evolve. We use a new model of convective turbulence that takes into account the important effects of radiative dissipation, rotation, and anisotropy of convective motions. This model is based on a closure for the nonlinear interactions that employs the growth rates of hydrodynamic instabilities, a procedure that allows one to compute turbulence coefficients for instabilities other than convection. The vertical structure equations in the thin-disk approximation are developed for this new model, and a detailed comparison and critique of previous convective models of the solar nebula are presented. Numerical results are presented in a subsequent paper.     

CO2 clouds, CAPE and convection on Mars: Observations and general circulation modeling

The thermal emission spectrometer (TES) and the radio science (RS) experiment flying on board the Mars Global Surveyor (MGS) spacecraft have made observations of atmospheric temperatures below the saturation temperature of carbon dioxide (CO₂). This supersaturated air provides a source of convective available potential energy (CAPE), which, when realized may result in vigorous convective mixing. To this point, most Mars atmospheric models have assumed vertical mixing only when the dry adiabatic lapse rate is exceeded. Mixing associated with the formation of CO₂ clouds could have a profound effect on the vertical structure of the polar night, altering the distribution of temperature, aerosols, and gasses.Presented in this work are estimates of the total planetary inventory of CAPE and the potential convective energy flux (PCEF) derived from RS and TES temperature profiles. A new Mars Global Circulation Model (MGCM) CO₂ cloud model is developed to better understand the distribution of observed CAPE and its potential effect on Martian polar dynamics and heat exchange, as well as effects on the climate as a whole. The new CO₂ cloud model takes into account the necessary cloud microphysics that allow for supersaturation to occur and includes a parameterization for CO₂ cloud convection. It is found that when CO₂ cloud convective mixing is included, model results are in much better agreement with the observations of the total integrated CAPE as well as total column non-condensable gas concentrations presented by Sprague et al. [2005a, GRS measurements of Ar in Mars’ atmosphere, American Astronomical Society, DPS meeting #37, #24.08, and 2005b, Distribution and Abundance of Mars’ Atmospheric Argon, 36th Annual Lunar and Planetary Science Conference, #2085] When the radiative effects of water ice clouds are included the agreement is further improved.