Research on the Origin of Solar Activity (II) Solar Generator Theory

Astronomical Progress in the Origin of Solar Activity (): Solar Generator Theory Lin Yuanzhang (National Astronomical Observatory, Chinese Academy of Sciences, Beijing, gave a comprehensive review of the theory of solar generators trying to explain the origin of solar activity. The theory of mean field kinematics generators, including the mean field, is highlighted. The a-effect, kinematic generators and migration generators. The research overview of MHD generators and other types of generators is discussed.

1 Introduction It can be seen from the text (I) that the solar activity week models of Babcock and Leighton are empirical and semi-empirical models, respectively, rather than strict dynamic description. It is currently believed that the physical mechanism that sustains the process of periodic solar activity is the periodic phenomenon exhibited by the magnetic field induced by the motion of the solar plasma itself. The fact that a moving conductor can generate a magnetic field by induction is the principle of a self-excited motor.

The basic process is that the moving conductor cuts the magnetic field lines to generate an electric field, the electric field will generate current (Ohm's law), and the current generates a magnetic field (Ampere's law). The magnetic field will generate an electric field (Faraday's law) and Lorentz force, which will limit the conductor movement, so that The magnetic field reaches a certain balance to form a complete generator cycle. Therefore, people think that the solar magnetic cycle law may also be generated by the self-excited motor naturally formed by the sun itself. There are many conductors, insulators and wires in the artificial self-excited motor, and the delicate coupling method, the operation process is not difficult to understand. However, the sun is connected to a conductive plasma, and is always in a short-circuit state. Can it form a self-excited motor? In other words, whether there is a generator solution in the induction equation (the above equations Bv and r are respectively magnetic fields). , velocity and magnetic diffusion coefficient.) Many theoretical researchers have made difficult explorations. From the observations and the models of Babcock and Leighton, the main feature of the solar activity week is the mutual conversion between the polar magnetic field and the toroidal magnetic field. Therefore, the main idea of ​​exploration is in the existing solar velocity field (mainly poor). Under the conditions of rotation and convection, a magnetic field solution that can continuously convert between the polar magnetic field Sp and the circumferential magnetic field St is sought.

In the initial exploration process, two important constraint theorems (sometimes called the inverse generator theorem) have been proposed. One is that CowlingM found that the generator solution must be non-axisymmetric; the other is that Bullard and GellmanM found that if the velocity field is only the sun's rotation, regardless of whether the rotation is uniform, the toroidal magnetic field Bt can only be generated by the polar magnetic field. It is Sp, so that the mutual conversion between Bp and Bt cannot be completed, that is, there is no generator solution. Parker first proposed that if the concept of the mean field is used, the above constraints can be circumvented to find an axisymmetric mean field generator solution. Parker pointed out that due to the Coriolis force, the rising and falling air masses in the solar troposphere will produce rotation, and the average result of a large number of small-scale rotations is equivalent to the existence of large-scale electric fields (called effects), which can lead to the conversion of wind direction Sp. Subsequent discussions with Steenbeck et al., Steenbeck and Krause, Moffatt, and Krause and Radler gradually improved the average field generator theory.

2 The average field kinematics theoretical average field and a-effect observations show that there is a certain range of fluctuations in the surface magnetic field of the sun, so the magnetic field can be written as as the average field, which can be understood as a set of realistic magnetic fields with a large number of random changes. The average value of the body; 6 is the undulating part, the average value of which is =. At the same time, the velocity field can also be written as the average speed (蚴 can be understood as the average speed of the sun's global scale motion (especially the poor rotation), u means no The convection speed of the rule. It is usually not necessary to know the details of V, just know the statistical properties of the mean and U. In the following discussion, V will be considered given that it is not affected by B. In other words, it will be treated as a kinematic rather than a dynamic one. In fact, the solar cycle model of Babcock and Leighton is also a kinematic model.

Substituting (2) and (3) into equation (1), and separating the mean field and the undulating field, where U is the diffusion coefficient, and the average electric field 5 here is the key parameter. If E is known, can be solved by equation (4). In principle, it is necessary to first obtain a b-solution from the equation and then substitute (6) to calculate the E represented by (B). This is actually very difficult. Therefore, the so-called "first-order smooth approximation" is usually adopted, that is, the second-order micro-item is assumed. G can be neglected, so b can be obtained from (5), and five can be obtained from (6). It can be proved that when one of the following two conditions is satisfied, the first-order smooth approximation or u is u. / and T are the spatial and temporal scales of u and change respectively. Condition (8) guarantees that G is much smaller than the last term on the right end of (5), which is equivalent to the case where the magnetic Reynold number is small; and if (9) is established G is negligible compared to Bi. Unfortunately, these two conditions are not satisfied in the sun. The magnetic Reynold number of the Sun is very large, and observations show that despite this, we can still make the following instructive discussion.

If it is limited to understanding the qualitative results, then except for ignoring G, the <> item of (5) is omitted. At the same time, taking into account the high conductivity of the solar plasma, and then skipping the diffusion term of (5), the solution of b can be obtained immediately as a time integral, but there is no need to write the starting field u(-oo) Because it is definitely not related to u(1), so it does not contribute to the calculation *. If u is a weak isotropic turbulent flow field, it can be proved that * can be written as tml and (11) is substituted into (4), and the average field induction equation is obtained by comparing (14) with (1). Found two changes. One is that the diffusion coefficient is increased by a /3, the size of which is in the solar troposphere, 吼 "= 108l9m2S*. Another more important change> that is, an a is added to the equation. It is this one that guarantees that the average field is not restricted by the two inverse generator theorems above. This key term added to the mean field induction equation (14) is usually referred to as the a effect. As can be seen from equation (12), a actually represents the felinity of the turbulent convection field u. The value of a in the solar troposphere is difficult to estimate. However, it can be seen from equation (12) that a 0 requires that the flow field must have a spiral. Kraust has proved that M, the density stratification in the solar troposphere combined with the Coriolis force, can cause the flow field to have a spiral. In the northern hemisphere of the sun, the rising and expanding air mass in the troposphere will obtain a left-handed spiral due to the Coriolis force, and the sinking air mass will also obtain a left-handed spiral. Thus, the left hemisphere's left-handedness is dominant, so the snail is negative. This has been confirmed by observations. It is known from (12) that "the symbol is opposite to the sway, so the sun north hemisphere a is a positive value. Krause et al.'s calculations show that p is the average angular velocity of the sun, with positive and negative signs corresponding to the northern and southern hemispheres, respectively. In the solar troposphere, the range of spatial scales of variation Z is large, so the size of a is from a few cm to 100 m per second. The average field induction equation (14) is the basis of most solar generator theory researchers, and also It has been adopted by scholars who have studied the theory of earth magnetic field generators and stellar magnetic field generators, and has even been applied to the study of other celestial bodies such as accretion disks and galaxies. But it contains many assumptions, the most serious of which is the first-order smooth approximation. The conditions (8) and (9) required for this approximation can only reach critical satisfaction at most in the sun.

The kinematic afi generator can be seen from the above, the effect of the a effect is to ensure the existence of the average field, and the a effect combined with the solar rotation velocity field D can constitute an aD generator. If you still use kinematics, it is a kinematic generator. It is assumed that in the spherical coordinate system (rAp), a given form of a(r) and the angular velocity distribution of the sun are simultaneously taken as an opposition to the solar equator according to equation (17), that is, the angular velocity of rotation is taken as symmetrical to the equator. That is, if there is no other motion except for the rotation, the average field is decomposed into a polar field and a ring field, that is, therein. The vector potential of A(r, 0, i) of Sp(22) is determined by the axis symmetry. Then the inductive equation of the mean field is also decomposed into the polar and hoop components. For the simplest case of = constant, they are the key role in which the a effect can be seen by equations (24) and (25). When a =0, ​​(24) degenerates into a diffusion equation, the polar field immediately decays exponentially, and 4 disappears. At this time (25) also becomes a diffusion equation, and B also decays after exponential decay. It is also clear from (26) that the toroidal field is the original polar field generated by the poor rotation and the a effect. However, for the sun, the latter contributes less than the former, so the items contained in (25) are often omitted, provided that the sum is the radius of the sun. Although the size of a is not clear, (27) may be established. Thus, the principle of kinematics a/generator can be summarized as follows: 5tk2 must be negative by the a effect, so the positive signs in (36) and (37) can be eliminated. Another solution, the critical stability solution (38) corresponding to Im(W)=0., indicates that the product 炻 must exceed a certain value, that is, the number of generators must exceed a critical value for the generator to operate.

For the critical solution, the real part of the vibration frequency is a negative value. So the mean field (34) is the wave that propagates along the a: axis forward. If fc<0 is assumed at first, as long as a% < 0, the result is the same. Conversely, if a) > 0, the wave will propagate along the negative: c-axis direction. By properly placing the coordinate system, it can be shown that the generator waves will generally migrate along the equiangular velocity plane. At the same time, there are magnetic flux loss problems in generators working in the troposphere. Therefore, some researchers have proposed an overshoot layer generator (overshootlayerdynamo) working in the overburden layer at the bottom of the troposphere. The overburden layer at the bottom of the troposphere is a thin layer below the lower troposphere defined by the Schwarzchild criterion. This layer does not satisfy Schwarzchild's convection criterion (|f|ad< |J, however the air mass motion in the upper troposphere still impacts this layer. Therefore there is still convective air mass motion in the overburden layer. After the overburden layer, The air mass will completely disintegrate, so the thickness of the overburden layer is about a mixed long distance. For the sun, it is estimated that the leoookmWi. Although the overburden layer is more stable than the troposphere, there is still air mass movement, so there is an effect, and the afi generator can work. Many researchers have explored overburden generators. The interface here refers to the interface between the solar troposphere and the internal non-convective zone, and therefore also the bottom of the troposphere. However, unlike the overshoot layer generator working in the overburden layer, There are actually two working source areas of the interface generator, which are located above and below the interface. The working source area below the interface is mainly a large-scale shearing motion, which is to complete the conversion of the polar field into a toroidal field; The a-effect of the polar field producing the polar field is completed at the interface. Then Macgregor and Charbonneau et al. 134, 351 made specific calculations for the interface generator model. They are in the mean field.

In addition, studies have shown that MHD generators also have chaotic behavior. Weiss et al. have studied one of the simplest generator models. They found that when the number of generators is large and the diffusion is small, the periodic solution of the generator becomes unstable. It was first replaced by a variety of cycles, and eventually became a mixed solution. At this time, in addition to the normal cycle of the solar activity week, it also contains a period of low activity, much like the century minimum period of the solar long-term change law. 37,38. In addition to the current mainstream generator model There may also be generator models that rely on other effects to explain the magnetic field of the celestial body. For example, its working principle does not require convective motion to rely solely on plasma turbulent wave effects and celestial body rotation of a plasma turbulent generator (pfi generator) 391. However, the a/2 generator has been able to basically explain the main characteristics of the solar activity week. Under the premise, it is still difficult to determine whether the generator effect will play a role in the generation and evolution of the large-scale magnetic field of the sun, even if it is secondary.