Changes in convective properties over the solar cycle: effect on p-mode damping rates

Measurements of both solar irradiance and p-mode oscillation frequencies indicate that the structure of the Sun changes with the solar cycle. Balmforth, Gough & Merryfield investigated the effect of symmetrical thermal disturbances on the solar structure and the resulting pulsation frequency changes. They concluded that thermal perturbations alone cannot account for the variations in both irradiance and p-mode frequencies, and that the presence of a magnetic field affecting acoustical propagation is the most likely explanation of the frequency change, in the manner suggested earlier by Gough & Thompson and by Goldreich et al. Numerical simulations of Boussinesq convection in a magnetic field have shown that at high Rayleigh number the magnetic field can modify the preferred horizontal length scale of the convective flow.
Here, we investigate the effect of changing the horizontal length scale of convective eddies on the linewidths of the acoustic resonant mode peaks observed in helioseismic power spectra. The turbulent fluxes in these model computations are obtained from a time-dependent, non-local generalization of the mixing-length formalism. The modelled variations are compared with p-mode linewidth changes revealed by the analysis of helioseismic data collected by the Birmingham Solar-Oscillations Network (BiSON); these low-degree (low- l ) observations cover the complete falling phase of solar activity cycle 22. The results are also discussed in the light of observations of solar-cycle variations of the horizontal size of granules and with results from 2D simulations by Steffen of convective granules.     

Complexes of activity of the solar cycle and very large scale convection

The magnetic field pattern associated with large scale convective motions, which are much larger than the supergranules and have been conceived as a source of maintenance of the solar differential rotation, is calculated in the framework of a slowly and differentially rotating thin spherical shell, including the effects of thermal conductivity and viscosity. The approximations of Boussinesq are used and the initial state of the magnetic field is assumed to be purely toroidal.The resulting magnetic field pattern rotates rigidly on the differentially rotating Sun with some phase delay to the convective pattern, if it is assumed that only the predominant mode with the maximum growth rate is actually realized in the solar convection zone. The obtained magnetic and convective patterns and their properties seem to explain naturally the various aspects of large scale ordering of solar activity such as the existence and behavior of complexes of activity, the rigid body rotation of proton flare active longitudes, their association with UMR's, the existence of ghost and mirror image of UMR's themselves and the fact that the rotational period derived from sunspot data is shorter than that derived spectroscopically from fluid velocity.     

Meridional energy balance of Jupiter

The meridional energy balance of Jupiter is calculated from high spatial resolution observations by the Voyager 1 infrared spectrometer and radiometer. On a hemispheric scale Jupiter radiates thermal energy to space approximately uniform with latitude while solar energy absorption varies approximately as the solar angle. This implies internal adjustment to the solar energy with a larger contribution poleward of ±45° than in the equatorial zone. The internal flux is modulated by the major visible features of the zone and belt system but, unlike the hemispheric scale where increased internal flux is correlated with decreased solar absorption, on smaller scales the inverse occurs. The energy balance is very likely to be controlled by dynamics, but the relative influence of the upper atmosphere and the interior is not yet clear. Models have been proposed that would explain the pole-to-equator variation in the thermal emission and it is suggested that the smaller scale variations may be the result of forced convective circulation.     

Thermal electrons runaway from a hot plasma during a flare in the reverse-current model and their X-ray bremsstrahlung

The behaviour of the thermal electrons escaping from a hot plasma to a cold one during a solar flare is investigated. We suppose that the direct current of fast electrons is compensated by the reverse current of the thermal electrons in ambient plasma. It is shown that the direct current strength is determined only by the regular energy losses due to Coulomb collisions. The reverse-current electric field and the distribution function of fast electrons are found in the form of an approximate analytical solution to the self-consistent kinetic problem of the dynamics of a beam of escaping thermal electrons and its associated reverse current.The reverse-current electric field in solar flares leads to a significant reduction of the convective heat flux carried by fast electrons escaping from the high-temperature plasma to the cold one. The spectrum and polarization of hard X-ray bremsstrahlung, and its spatial distribution along flare loops are calculated and can be used for diagnostics of flare plasmas and escaping electrons.Send offprint requests to B. V. Somov.     

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.     

Outward transport of angular momentum by gas convection and the equatorial acceleration of the Sun

A new mechanism for sustaining enhanced rotational velocity of the outer layers of the solar convective envelope is considered.The gas density inside turbulent eddies decreases because of centrifugal scattering of matter. The decrease of density in eddies rotating in the same sense as the Sun on the whole is larger than that in eddies rotating in the opposite sense. As a result, the former ascend while the latter sink down, thus producing a continuous outward flux of angular momentum.A distribution of angular velocity in the radius of the solar convective envelope in the equatorial plane was obtained in the approximation of the mixing length theory of thermal convection. The results agree rather well with observations.     

Development of a Code to Analyze the Solar White-Light Images from the Kodaikanal Observatory: Detection of Sunspots,Computation of Heliographic Coordinates and Area

Sunspots are the most conspicuous aspects of the Sun. They have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter background. Sunspots cyclically appear and disappear with a 11-year periodicity and are associated with a strong magnetic field ( ～10³ G) structure. Sunspots consist of a dark umbra, surrounded by a lighter penumbra. Study of umbra–penumbra area ratio can be used to give a rough idea as to how the convective energy of the Sun is transported from the interior, as the sunspot’s thermal structure is related to this convective medium.An algorithm to extract sunspots from the white-light solar images obtained from the Kodaikanal Observatory is proposed. This algorithm computes the radius and center of the solar disk uniquely and removes the limb darkening from the image. It also separates the umbra and computes the position as well as the area of the sunspots. The estimated results are compared with the Debrecen photoheliographic results. It is shown that both area and position measurements are in quite good agreement.     

A simple model for solar isorotational contours

The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But, the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilities. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to both convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator and approximately radial contours at mid-latitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be a good agreement between isentropes and isorotational contours in sufficiently well-resolved large-scale numerical magnetohydrodynamics simulations.     

The nature of one mechanism of solar differential rotation

The mechanism of the solar differential rotation usually ascribed to an anisotropic viscosity action is shown to be caused by Coriolis forces which influence anisotropic convective elements in a stratified medium. The estimation of an anisotropy parameters as a function of the convective zone depth is given. The value of (s–1) is positive near the solar surface and negative at the convective zone base, which is in good agreement with observations and the dynamo theory.     

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.     

太阳大气锂丰度的衰减

太阳大气锂的丰度７Ｌｉ／Ｈ＝１０－１１（按原子数计）。或［７Ｌｉ］＝ｌｏｇ（７Ｌｉ／Ｈ）＋１２＝１０．它比太阳系原始星云和银河系星际介质钾的丰度要低约两个数量级．因此太阳在它形成之后，其大气锂必定经受了严重衰减．然而年轻的银河疏散星团（如昂星团和英仙ａ星团）中有效温度高于５５００ Ｋ的主序星，其锂丰度都基本是正常的，井末呈现明显的衰减．这充分说明，太阳型恒星锂的衰减主要发生在主序阶段，而非在主序前的演化阶段． 在恒星中，７Ｌｉ是通过核反应７Ｌｉ（ｐ，ａ）４Ｈｅ，而毁坏．上述反应在Ｔ≥ ２．５×１０…     

On the sun's pole-equator flux differences

We study the possibility that large flux differences between the poles and the equator at the bottom of the solar convective zone are compatible with the small differences observed at the surface. The consequences of increasing the depth of the convective zone due to overshooting are explored.A Boussinesq model is used for the convective zone and we assume that the interaction of the global convection with rotation is modelled through a convective flux coefficient whose perturbed part is proportional to the local Taylor number. The numerical integration of the equations of motion and energy shows that coexistence between large pole-equator flux differences at the bottom and small ones at the surface is possible if the solar convective zone extends to a depth of 0.4R . The angular velocity distribution inside the convective zone is in agreement with the -dynamo theories of the solar cycle.     

Magnetic field effect on the fine structure of convective motions in the solar atmosphere

Statistical properties of solar granulation in an active region on the solar surface from the photosphere to the lower chromosphere are studied. We use the values of the velocity, intensity, and magnetic field that were obtained at different heights in the solar atmosphere according to the observation data on the VTT telescope at Observatorio del Teide, Tenerife. The changes in the line??s parameters (central depth of the line, halfwidth, equivalent width, and central depth shift) and convective velocity are presented as functions of the value of the magnetic field. We propose a 16-column model of solar granulation depending on the direction of motion of convective elements and on the sign of contrast at two heights??in the continuous spectrum and in the highest layer (h = 650 km). We found that the magnetic field impedes the change in the sign and motion direction of convective elements.     

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…     

Multiscale Magnetic Underdense Regions on the Solar Surface: Granular and Mesogranular Scales

The Sun is a non-equilibrium, dissipative system subject to an energy flow that originates in its core. Convective overshooting motions create temperature and velocity structures that show a temporal and spatial multiscale evolution. As a result, photospheric structures are generally considered to be a direct manifestation of convective plasma motions. The plasma flows in the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns, which are observed as a variety of multiscale magnetic patterns. High-resolution magnetograms of the quiet solar surface revealed the presence of multiscale magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered to be a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales, from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales, we used a voids-detection method. The computed distribution of void length scales shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at mesogranular scales. The absence of preferred scales of organization in the 2?–?10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale.     

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.     

Thermal evolution of the early Moon

The early thermal evolution of Moon has been numerically simulated to understand the magnitude of the impact-induced heating and the initially stored thermal energy of the accreting moonlets. The main objective of the present study was to understand the nature of processes leading to core–mantle differentiation and the production and cooling of the initial convective magma ocean. The accretion of Moon was commenced over a time scale of 100 yr after the giant impact event around 30–100 million years in the early solar system. We studied the dependence of the planetary processes on the impact scenarios, the initial average temperature of the accreting moonlets, and the size of the protomoon that accreted rapidly beyond the Roche limit within the initial 1 yr after the giant impact. The simulations indicate that the accreting moonlets should have a minimum initial averaged temperature around 1600 K. The impacts would provide additional thermal energy. The initial thermal state of the moonlets depends upon the environment prevailing within the Roche limit that experienced episodes of extensive vaporization and recondensation of silicates. The initial convective magma ocean of depth more than 1000 km is produced in the majority of simulations along with the global core–mantle differentiation in case the melt percolation of the molten metal through porous flow from bulk silicates was not the major mode of core–mantle differentiation. The possibility of shallow magma oceans cannot be ruled out in the presence of the porous flow. Our simulations indicate the core–mantle differentiation within the initial 10² to 10³ yr of the Moon accretion. The majority of the convective magma ocean cooled down for crystallization within the initial 10³ to 10⁴ yr.     

A graphical method for estimating overshoot in convective stellar atmospheres

A graphical method for estimating convective overshoot in stellar atmospheres is proposed. Applying the method to the solar atmosphere, we find that a convective element which starts at a depth of about 1000 km below the top of convection zone can penetrate to a height about 300 km above it.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Lithium depletion in the solar atmosphere

Using a complete non-local convection theory, we carried out the theoretical calculations of ⁷Li depletion of the solar convective envelope models with different convective parameters c₁ and c₂, and got a model of the solar convection zone consistent with the observed ⁷Li abundance and the depth of the solar convection zone determined by helioseismic techniques. The overshooting distance of effective non-local convective mixing of ⁷Li is very extensive, which is about 1.07H_P or 0.09R. However, the super-radiative temperature zone is much narrower, and it is only 0.20H_P or 0.016R.     

Solar Activity and Deep Convection Modeling

We suggest from synoptic charts of radial magnetic field and intensities of spectral lines (Fe?i, He?ii, and Fe?ix/x) over Carrington rotations 1942??C?2050 that deep convective layers control the pattern of large-scale solar activity. A new result is a Kolmogorov-type energy spectrum of the longitudinal variations of solar activity. This spectrum for nonphotospheric scales of convection (harmonic number m<100) is a new ??fingerprint?? of turbulence in the deep layers of the solar convection zone (CZ). The manifestation of one source of convective turbulence in the deep CZ is revealed as the excess in the power spectrum over the Kolmogorov spectrum. This source may be identified with giant convection cells at the CZ bottom. The convective cascade of the turbulence starts at the vortex size corresponding to the trans-CZ convective cells with the turnover time which the mixing length theory (MLT) predicts. This connection between the MLT formalism and real features in the Sun could account for the success of the MLT in stellar modeling.