The structure of the solar convective overshooting zone

Using a non-local theory of convection, we calculated the structure of the solar convection zone, paying special attention to the detailed structure of the lower overshooting zone. Our results show that an extended transition zone exists near the bottom of the convection zone, where the temperature gradient turns smoothly from adiabatic in the convection zone to radiative in solar interior. A super-radiative temperature region is found in the overshooting zone under the solar convection zone, where     ,     ,     and     . The extension of the super-radiative region (defined by     l is about 0.63  H _P (0.053 R_⊙). A careful comparison of the distribution of adiabatic sound speed and density with the local one is carried out. It is found, strikingly, that the distribution of adiabatic sound speed and density of our model is roughly consistent with the results of reversion from solar oscillation observations.     

Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

Solar dynamo models with α ‐effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α ‐effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s^–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing‐length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small‐ and large‐scale velocity fields, we obtain estimate of the ratio of the two induction effects, C _α /C _Ω ≈ 10^–3, which we keep fixed in all models. We also include a one‐cell meridional circulation pattern having a magnitude of 10–20 m s^–1 near the surface and 1–2 m s^–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α ‐effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down‐ and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B _r B _ϕ . Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α ‐effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar‐type solutions. The role of the surface shear layer is found to be important only in the case where the α ‐effect has an appreciable magnitude near the surface. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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…     

Testing turbulent convection theory in solar models – I. Structure of the solar convection zone

Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing-length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non-local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.     

A comparison of differential rotation measurements – (Invited Review)

Observers have long measured solar rotation with different techniques and obtained different results. This paper compares differential rotation measurements from four techniques: Doppler shift, Doppler feature tracking, magnetic feature tracking, and p-mode splittings. The different rotation rates measured by the first three techniques are interpreted as rotation rates of solar phenomena which depend on the properties and depth of that which is measured. This interpretation is supported by comparison with rotation measurements obtained from p-mode splittings except for Doppler features. The rotation rate of the plasma corresponds to the surface rate obtained by inversions; the rates of magnetic features correspond to the rotation rate at various depths within the convection zone. Supergranulation rotates at a rate greater than the maximum rotation rate within the convection zone, suggesting that supergranules are not simple convection cells anchored at a particular depth.     

The formation of Mg i 4571 Å in the solar atmosphere

A one-dimensional analysis of the 4571 Å line of neutral magnesium is presented. The Harvard-Smithsonian Reference Atmosphere (HSRA) and the Bilderberg Continuum Atmosphere (BCA) are used to compute the emergent line profiles at various positions on the solar disc. The resultant profiles, when compared to the observations, indicate that the HSRA electron temperature distribution is a more satisfactory representation of the solar atmosphere in the region of the temperature minimum than is the BCA. A slight modification to the HSRA is suggested which reduces the minimum temperature to 4140K and enables an even more satisfactory fit to the available data.On leave from Sacramento Peak Observatory, Air Force Cambridge Research Laboratories.     

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…     

The slender solar tachocline: a magnetic model

A model for the sharp transition from differential rotation in the solar convection zone to rigid rotation in the radiative interior is presented. Differential rotation in the radiative zone is shown to be quenched efficiently by an internal magnetic field. The poloidal field amplitude, B₀, is the input parameter for our model which determines the transition layer thickness and the toroidal field strength. It is illustrated analytically and confirmed numerically that a rather small field, B₀ = 10⁻⁴ Gauss, suffices to satisfy the helioseismological restrictions on the depth of the differential rotation penetration below the convection zone. The transition layer thickness decreases further with increasing B₀. The toroidal field amplitude B ≃ 200 Gauss is almost independent of B₀.     

Maunder convection mode on the Sun and long solar activity minima

A model of velocity field oscillations in the solar convective zone is suggested. The system of convective equations is investigated for a thin rotating spherical envelope when the rotation velocity is depended on the coordinates. It is shown that two different structures of convective cells (longitudinal, or latitudinal) can exist in the envelope depending on gradients values of the rotation velocity and Prandtl number. It is supposed that two different regimes of convection (stationary and autofluctuating) are possible in the envelope when the angular velocity gradients are determined by the convection itself. In the case of autofluctuating regime the alternation of longitudinal and latitudinal structure of convection is realized. If one assumes that on the Sun there exists an autooscillating convection regime, then the periods of the existence of latitudinal convection structure may be associated with long periods of activity minima since according to Cowling's theorem, the action of the axisymmetric magnetic field generation mechanism is impossible under conditions of axisymmetric velocity structures.     

Determining the rotation law of the solar convection zone

The condition of minimum total dissipation is used to derive stationary rotation and azimuthal magnetic field distributions in the bulk of the solar convection zone with an upper boundary at which the relative radius is r/R=0.95. General equilibrium con figurations with symmetric and antisymmetric (about the equator) angular-velocity and field components are determined. The calculated rotation law matches the observed one in general parameters, but the decrease in angular velocity at high latitudes in theory is larger than that in observations. Besides, there are additional sharp variations in the rotation and field distributions in the theoretical curves near the generation zone of solar torsional waves. The possible cause of the latter discrepancy is discussed. The change in equilibrium distributions due to the presence of an inverse molecular-weight gradient at the base of the convection zone is also studied. This gradient is known to be produced by accelerated gravitational helium settling in the convection zone.     

On Magnetic Coupling Between the Two Hemispheres in Solar Dynamo Models

By introducing an asymmetry between the two hemispheres, we study whether the solar dynamo solutions in the two hemispheres remain coupled with each other. Our calculations are based on the solar dynamo code SURYA, which incorporates the helioseismically-determined solar-rotation profile, a Babcock–Leighton α effect concentrated near the surface, and a meridional circulation. When the magnetic coupling between the hemispheres is enhanced by either increasing the diffusion or introducing an α effect distributed throughout the convection zone, we find that the solutions in the two hemispheres evolve together with a single period even when we make the meridional circulation or the α effect different in the two hemispheres. On the other hand, when the hemispheric coupling is weaker for other values of parameters, an asymmetry between the hemispheres can make solutions in the two hemispheres evolve independently with different periods.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

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.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

A map of the horizontal flows in the solar convection zone

The first map of the horizontal flows as a function of depth and heliocentric position in the solar convection zone is presented. The map is inferred from a least-squares smoothness-constrained inversion of velocities measured from ring diagrams of the solar p-mode oscillations. The data provide information in four longitude regions at a latitude just south of the solar equator. The presence of several features is suggested by the results:

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cross-correlation of solar wind parameters with sunspots (‘Long-term variations’) at 1 AU during cycles 21 and 22

Long-term variations of solar wind parameters at 1 AU are correlated with sunspots for the time interval 1973 to 1993 (solar cycles 21, 22). Using theNear-Earth Heliosphere Data OMNI the plasma density, the magnitude of the interplanetary magnetic field, the solar wind velocity and the solar wind temperature show consistent long-term variations in each cycle (21 and 22) — pointing to specifictime-lags in the coupling between sunspots (and the underlying convection zone), the solar corona and the solar wind parameters at 1 AU (ecliptic).     

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.