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Oscillating dynamo magnetic field in the presence of an external nondynamo field - The influence of a solar primordial field
Abstract
Dynamo magnetic fields are self-excited and, once started, can perpetrate themselves with no outside source of magnetic flux, as long as the necessary fluid motions persist. Such dynamo fields behave completely independently of the field's overall polarity. In the presence of an external field of separate origin this polarity symmetry of the dynamo states is broken; the dynamo states become asymmetric with respect to polarity. In this paper a calculation is performed of the characteristics of a spherical shell dynamo in the presence of a fossil magnetic field penetrating into the dynamo from below. The asymmetric periodic states are found as a function of the strength of underlying fossil field. Applying these results to the sun, there appears to be no evidence of any intense large-scale primordial magnetic flux, having either dipole-like or quadrupole-like symmetry about the sun's equator, penetrating into the convection zone from the sun's radiative core. Indeed, the calculations indicate, even on the basis of the presently crude observations, that any such primordial field must have an intensity smaller than a few gauss.
... Specifically, it is evident that below the SCZ bottom, in a relatively thin layer ΔR = (0.63-0.71) , called tachocline, a monotonic abrupt transition occurs from the differential rotation of the SCZ by heliolatitude to almost rigid rotation of the radiant zone. Equations (14) and (15) will be analyzed in our subsequent studies. ...
... According to the Gnevyshev-Ol' rule [2], the observed 22-year modulation (variation) in the heights of 11-year cycles in Wolf numbers can be explained by the presence in the Sun's interior of a weak relic quasi-constant poloidal field (see also [14,49]). As noted above, during the greater part of the solar cycle, the poloidal magnetic component is dominated by the dipole harmonic. ...
... Specifically, it is evident that below the SCZ bottom, in a relatively thin layer ΔR = (0.63-0.71) , called tachocline, a monotonic abrupt transition occurs from the differential rotation of the SCZ by heliolatitude to almost rigid rotation of the radiant zone. Equations (14) and (15) will be analyzed in our subsequent studies. ...
... According to the Gnevyshev-Ol' rule [2], the observed 22-year modulation (variation) in the heights of 11-year cycles in Wolf numbers can be explained by the presence in the Sun's interior of a weak relic quasi-constant poloidal field (see also [14,49]). As noted above, during the greater part of the solar cycle, the poloidal magnetic component is dominated by the dipole harmonic. ...
Within the kinematic dynamo theory, we construct a mathematical model for the evolution of the solar toroidal magnetic field, excited by the differential rotation of the convective zone in the presence of a poloidal field of a relic origin. We use a velocity profile obtained by decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculate the latitudinal profiles of the increasing-with-time toroidal field at different depths in the solar convection zone. It is found that, in the region of differential rotation, the excited toroidal field shows substantial fluctuations in magnitude with depth. Based on the simulations results, we propose an explanation for the “incorrect polarity” of magnetic bipolar sunspot groups in solar cycles.
... Although the North-South Asymmetry of solar activity has been known for a long time, the attempts to separate theoretical modeling of the northern and southern hemispheres and to estimate the difference between them appeared only 10-20 yr ago. Among the possible mechanisms responsible for differences in the activity characteristics between the northern and southern hemispheres, different authors mentioned the stochastic effect of the convection Hoyng et al. (1994), the counter effect of the generated magnetic field on matter flows, which is described by nonlinear dynamo equations (Weiss 2010), and, simply, the existence of a primary relic field (Boyer & Levy 1984;Mordvinov 2007). The latter, however, is difficult to reconcile with a strong variability of the asymmetry both in sign and in absolute value on short and long timescales. ...
Traditionally, the solar activity cycle is thought as an interplay of the main dipole component of the solar poloidal magnetic field and the toroidal magnetic field. However, the real picture as presented in the extended solar-cycle models is much more complicated. Here, we develop the concept of the extended solar cycle clarifying what zonal harmonics are responsible for the equatorward and polarward propagating features in the surface activity tracers. We arrive at a conclusion that the zonal harmonics with L = 5 play a crucial role in separating the phenomena of both types, which are associated with the odd zonal harmonics. Another objective of our analysis is the role of even zonal harmonics, which prove to be rather associated with the North-South asymmetry of the solar activity than with its 11-year solar periodicity.
... It is argued that the stochastic fraction may account for the record height of cycle 19 and may be related to a relic magnetic field in the solar convection layer (Cowling 1946. A relic dipole magnetic field in association with the Hale magnetic polarity cycle (Boyer & Levy 1984) is also invoked to explain the 22 year cyclicity in the Group Sunspot Number revealed for the last 400 yr with an amplitude of about 10% of the level indicated by present-day sunspot activity (Mursula et al. , 2002. ...
The Schwabe (~11 yr) value for the annual sunspot number is sometimes uncritically applied to other measures of solar activity, direct and indirect, including the 10.7 cm radio flux, the inflow of galactic cosmic rays, solar flare frequency, terrestrial weather, and components of space climate, with the risk of a resulting loss of information. The ruling (Babcock) hypothesis and its derivatives link the sunspot cycle to dynamo processes mediated by differential solar rotation, but despite 60 years of observation and analysis the ~11 yr periodicity remains difficult to model; the possible contribution of planetary dynamics is undergoing a revival. The various solar sequences that genuinely display an ~11 yr cycle stand to benefit from an understanding of its periodicity that goes beyond statistical kinship. The outcome could ironically prompt the demotion of sunspots from their dominant historical role in favour of other possible indicators of solar cyclicity, such as the solar wind flux and its isotopic signatures, even if they are less accessible.
... The presence of a large-scale, quasi-steady magnetic field of fossil origin in the solar interior has long been recognized as a possible explanation of the Gnevyshev-Ohl rule. Such a slowly-decaying internal fossil field being effectively steady on solar cycle timescales, its superposition with the 11-years polarity reversal of the overlying dynamo-generated field will lead to a 22-years modulation, whereby the cycle is stronger when the fossil and dynamo field have the same polarity, and weaker when these polarities are opposite (see, e.g., Boyer and Levy 1984;Boruta 1996). The magnitude of the effect is directly related to the strength of the fossil field, versus that of the dynamo-generated magnetic field. ...
This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively) simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, I begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. I move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms, followed by a discussion of recent magnetohydrodynamical simulations of solar convection generating solar-like large-scale magnetic cycles. I then turn to the origin and consequences of fluctuations in these models and simulations, including amplitude and parity modulation, chaotic behavior, and intermittency. The paper concludes with a discussion of our current state of ignorance regarding various key questions relating to the explanatory framework offered by dynamo models of the solar cycle.
... Радiальний градiєнт кутової швидкостi в глибинних шарах, охоплених первинним магнетизмом, повинен збуджувати потужне тороїдальна поле, достатнє для того, щоб викликати помiтний, поруч з ротацiйним, внесок в ефект розщеплення акустичних мод сонячних коливань. Залучення глибинного квазiоднорiдного полоїдального поля, що частково проникає в СКЗ, до моделей сонячного динамо-циклу призводить до амплiтудної асиметрiї двох напiвперiодiв змодельованого 22-рiчного магнiтного циклу [4][5][6]. ...
... In Featherstone et al. (2009) a core-fossil field system was constructed by introducing various fossil field configurations into the radiative envelope surrounding the core dynamo. The interaction between the existing dynamo and a modest fossil field possessing a net flux through the core has allowed the system to generate significantly greater (roughly tenfold) magnetic energy than kinetic energy, as might be expected from theory in other settings (Boyer & Levy 1984;Sarson et al. 1999). Such behavior is in stark contrast to simulations in the absence of a fossil field where these stars generated magnetic energies that were only 70% of the convective kinetic energy (Brun et al. 2005). ...
The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through 3-D global simulations of convective core dynamos operating within a young 10$M_{\mathrm{sun}}$ B-type star, using the anelastic spherical harmonic (ASH) code. These simulations capture the inner 65% of this star by radius, encompassing the convective nuclear-burning core (about 23% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05% to 16% of the surface breakup velocity, thereby capturing both convection barely sensing the effects of rotation to others in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent columnar velocity structures roughly aligned with the rotation axis, with magnetic fields threading through these rolls and possessing complex linkages throughout the core. The very strong fields are able to coexist with the flows without quenching them through Lorentz forces. The velocity and magnetic fields achieve such a state by being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces.
... Second, the primordial magnetic field, which remained in the radiative interior after the Sunʼs collapse, may penetrate into the tachocline and affect Rossby waves. Both nonreversing dynamo and the primordial fields may be responsible for the observed Gnevyshev-Ohl 22 year rule (Gnevyshev & Ohl 1948), which shows that odd sunspot cycles are generally stronger than even cycles, due to the break of polarity symmetry of the dynamo state (Boyer & Levy 1984): the reversing dynamo magnetic field is aligned and antialigned with respect to the toroidal component of steady field in consecutive cycles leading to the consequence of strong and weak cycles, respectively. Similarly, the periodical variation caused by slow magnetic Rossby waves in the steady magnetic field can influence the strength of the dynamo magnetic field and consequently the cycle strength. ...
Long-term records of sunspot number and concentrations of cosmogenic
radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's
magnetic activity over hundreds and thousands of years. We identify several
clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100
years. We found that the periods of the first five spherical harmonics of the
slow magnetic Rossby mode in the presence of a steady toroidal magnetic field
of 1200-1300 G in the lower tachocline are in perfect agreement with the time
scales of observed variations. The steady toroidal magnetic field can be
generated in the lower tachocline either due to the steady dynamo magnetic
field for low magnetic diffusivity or due to the action of the latitudinal
differential rotation on the weak poloidal primordial magnetic field, which
penetrates from the radiative interior. The slow magnetic Rossby waves lead to
variations of the steady toroidal magnetic field in the lower tachocline, which
modulate the dynamo magnetic field and consequently the solar cycle strength.
This result constitutes a key point for long-term prediction of the cycle
strength. According to our model, the next deep minimum in solar activity is
expected during the first half of this century.
... Usually dynamo modelers look for mechanisms that can produce the asymmetric modulation that is observed in the solar cycle. These mechanisms include stochastic forcing from convection (Hoyng et al. 1994), nonlinear effects caused by the magnetic backreaction of the induced magnetic field on the flows (Weiss 2010) or even other more controversial explanations such as the remnant of a fossil or primordial field in the solar interior (Boyer & Levy 1984). Moreover, published modelling research addressing hemispheric asymmetries is somewhat scarce because, for simplification purposes, modelers tend to study dynamo solutions in only one hemisphere. ...
Numerical simulations that reproduce solar-like magnetic cycles can be used
to generate long-term statistics. The variations in N-S hemispheric cycle
synchronicity and amplitude produced in simulations has not been widely
compared to observations. The observed limits on asymmetry show that
hemispheric sunspot area production is no more than 20% asymmetric for cycles
12-23 and phase lags do not exceed 20% (2 yrs) of the total cycle period.
Independent studies have found a long-term trend in phase values as one
hemisphere leads the other for ~four cycles. Such persistence in phase is not
indicative of a stochastic phenomenon. We compare the findings to results from
a numerical simulation of solar convection recently produced with the EULAG-MHD
model. This simulation spans 1600 yrs and generated 40 regular, sunspot-like
cycles. While the simulated cycle length is too long and the toroidal bands
remain at too high of latitudes, some solar-like aspects of hemispheric
asymmetry are reproduced. The model reproduces the synchrony of polarity
inversions and onset of cycle as the simulated phase lags do not exceed 20% of
the cycle period. Simulated amplitude variations between the N and S
hemispheres are larger than observed in the Sun. The simulations show one
hemisphere persistently leads the other for several successive cycles, placing
an upper bound on the efficiency of transequatorial magnetic coupling
mechanisms. These include magnetic diffusion, cross-equatorial mixing within
elongated convective rolls and transequatorial meridional flow cells. One or
more of these processes may lead to magnetic flux cancellation whereby the
oppositely directed fields come in close proximity and cancel each other across
the magnetic equator late in the solar cycle. We discuss the discrepancies
between model and observations and the constraints they pose on possible
mechanisms of hemispheric coupling.
... The estimate given by equation ( Use of a more complicated expression for the fluid shear, including, for example. the nonradial component, would not alter our conclusions (Boyer and Levy, 1983). We will also take the poloidal field to be uniform and axial in the core, ...
The effect of sudden changes in the Earth's moment of inertia on the hydromagnetic state of the core is studied. Rapid changes in georotation, due to ice age transgression and regression, are described as varying boundary conditions in an axisymmetric Earth model containing both viscous and electromagnetic coupling. The deterministic equations describing the limit of rapid rotation are employed in conjunction with restricted 2-D predictive magneto-fluid equations. A kinematic description is devised for both buoyancy driven mass motions and the regeneration of the poloidal magnetic field. A pseudo-spectral method is used to solve the incompressible magneto-fluid equations. The variables are collocated in radius using Chebyshev polynomials and the pseudospectral evaluations in colatitude are done using associated Legendre polynomials. Time dependence and magnetic diffusion are controlled by a modified second order semi-implicit Runge Kutta scheme. Deterministic steady state solutions were found in full agreement with Hollerbach and Jones (1993a,b; 1995). Steady state boundary layers, arising from differential motion of the outer core boundaries, were found to induce significant departures for both alpha^2 - and alphaomega-dynamo steady state configurations. The hydromagnetic communication time of the core, determined the predictive magneto-fluid equations, is found to be consistent with the deterministic calculations. Within the context of this model, it is concluded that a causal connection is plausible between geomagnetic transients and significant changes in the Earth's moment of inertia.
... The above estimate for the strength of relic nonaxisymmetric structures is very modest. For example, Goode & Thompson (1992) claim that a relic field strength up to 30 MG (!) would not contradict the helioseismological data, although its consequences for solar dynamo theory might be more marked (Pudovkin & Benevolenskaya 1982;Boyer & Levy 1984). Here we avoid any discussion concerning the possible strength of the solar relic magnetic field, attempting to estimate to what extent a relic field present in the radiative core might penetrate into the convection zone, and subsequently be manifested at the solar surface. ...
We discuss the problem of solar active longitudes from the viewpoint of dynamo theory. We start from a recent observational analysis of the problem undertaken by Berdyugina & Usoskin (2003, A&A, 405, 1121) and Usoskin et al. (2005, A&A, 441, 347) who demonstrated from a study of sunspot data that solar active longitudes rotate differentially, with a small but significant asynchrony between northern and southern hemispheres. We suggest two concepts by which the underlying magnetic structure could lead to the observed phenomenology - the true differential rotation of a nonaxisymmetric magnetic structure and a stroboscopic effect. In the latter case, a solid body rotation of nonaxisymmetric magnetic structure is illuminated by an activity wave propagating from middle latitudes to the solar equator, and so mimics a differential rotation. We then discuss several mechanisms which could in principle lead to the excitation of active longitudes. In particular, we consider dynamo excitation of nonaxisymmetric magnetic modes, nonaxisymmetric structures as a manifestation of a relic magnetic field in the solar core, nonaxisymmetric solar hydrodynamics and nonlinear instabilities that lack axial symmetry. We conclude that these mechanisms all provide ways to explain the phenomenology, provided the stroboscopic interpretation is accepted. Of course, a quantitative explanation in the framework of any scenario requires ultimately a detailed numerical simulation. The interpretation of the available observations as a true differential rotation appears to provide a much more severe challenge for theorists. We are unable to suggest a plausible mechanism of this kind; however we can not exclude in principle such an explanation. We relate the phenomenon of solar active longitudes to the information available concerning stellar active longitudes, and also consider evidence from other tracers of solar activity.
... A plausible explanation for this striking pattern is to suppose that a steady, large-scale magnetic field of fossil origin permeates the solar radiative interior, and interferes with the cyclic, dynamogenerated magnetic field at the core-envelope interface (Boyer & Levy 1984;Bravo & Stewart 1995;Boruta 1996). When the internal fossil field is of the same (opposite) polarity as the dynamo field, the cycle amplitude is above (below) average. ...
The Gnevyshev-Ohl rule refers to a pattern of alternating higher and lower than average solar cycle amplitudes observed in the sunspot number record. In this paper, we show that such a pattern arises naturally in Babcock-Leighton models of the solar cycle as a consequence of the long time delay built into the dynamo regenerative loop. This is investigated using a simple but well-validated iterative map formulation, as well as a seasoned two-dimensional axisymmetric kinematic dynamo model. The good agreement between the results obtained via these two very different modeling approaches offers confidence that Gnevyshev-Ohl-like patterns of cycle amplitude fluctuations are a robust feature of this class of solar cycle models.
... We are led to this investigation because we noted in our previous simulations of flux-transport dynamos, which included solarlike internal rotation and solved the dynamo equations in the domain extending down to the radiative core (0:6R) below the tachocline, that a steady, mean magnetic field survives over thousands of years. Similar effects were noted by Levy & Boyer (1982), Boyer & Levy (1984), and Sonett (1983), who suggested that a steady poloidal field at or below the base of the convection zone would impart a bias to the solar cycle, and an observed asymmetry between successive activity cycles is consistent with about 0.5 G steady poloidal fields there. Mestel & Weiss (1987) suggested that dynamos with fluctuating cycles could create net interior field in the rms sense. ...
Any large-scale magnetic fields present in solar/stellar radiative interiors have so far been thought to be primordial or residuals from extinct dynamos. We show that a regular cyclic dynamo can also be the origin of strong magnetic fields in the solar radiative tachocline and interior below. By exploiting a kinematic, mean-field flux-transport dy-namo, we show that for a wide range of core-diffusivity values, from 10 9 cm 2 s À1 down to a molecular diffusivity of 10 3 cm 2 s À1 , oscillatory dynamo fields penetrate below the tachocline. Amplitudes of these fields are in the range of $1 kG to 3 ; 10 3 kG, depending on core diffusivity value, when the dynamo produces $100 kG peak toroidal fields in the overshoot tachocline. For a low enough core diffusivity (P10 7 cm 2 s À1), there is also a steady (nonreversing) dynamo in the radiative tachocline and below, which generates strong toroidal field of amplitude $1 kG to 3 ; 10 3 kG or more there. The key elements in this dynamo are the low diffusivity, the differential rotation near the bottom of the tachocline, and an assumed tachocline -effect. The Lorentz force feedback may limit oscillatory dynamo fields to $30 kG, for which the mean nonreversing toroidal fields is still $300 kG, for the lowest core diffusivity value. The presence of strong oscillatory and steady toroidal fields in the radiative tachocline implies that there cannot be a slow tachocline; the dynamics should always be fast there, dominated by MHD. These results are obtained using solar pa-rameters, but they should also apply generally to stars with convecting shells and perhaps also with convective cores.
... There are also attempts to work within the mean field approach by considering an interface dynamo (Parker 1993; Charbonneau & MacGregor 1997; Ossenddrijver & Hoyng 1997) and distributed dynamo (Markiel & Thomas 1999). Besides, note the studies of solar oscillating dynamo with allowance for the primordial field (Boyer & Levy 1984; Pudovkin & Benevolenskaya 1984 ) as well as the newest diffusion theory of solar magnetic cycle (Solov'ev & Kiritchek 2004). When generation and turbulent dissipation of magnetic flux are balanced, the cycling αΩ dynamo can be described by two induction equations (Parker 1955Parker , 1979 Krause & Rädler 1980; Vainshtein et al. 1980), ...
In order to extend the abilities of the Ω dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean-field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep-rooted fields could not become apparent at the surface as sunspots. In the near-equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo-waves propagation and for parity of excited magnetic fields. The period of the dynamo-wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo-parameters, we conclude that north-south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the Ω dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high-latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Traditionally, the solar activity cycle is thought as an interplay of the main dipole component of the solar poloidal magnetic field and the toroidal magnetic field. However, the real picture as presented in the extended solar–cycle models is much more complicated. Here, we develop the concept of the extended solar cycle clarifying what zonal harmonics are responsible for the equatorward and polarward propagating features in the surface activity tracers. We arrive at a conclusion that the zonal harmonics with l = 5 play a crucial role in separating the phenomena of both types, which are associated with the odd zonal harmonics. Another objective of our analysis is the role of even zonal harmonics, which prove to be rather associated with the North-South asymmetry of the solar activity than with its 11-year solar periodicity.
Context. Solar and heliospheric parameters occasionally depict notable differences between the northern and southern solar hemisphere. Although the hemispheric asymmetries of some heliospheric parameters vary systematically with the Hale cycle, this has not been found to be commonly valid for solar parameters. Also, no verified physical mechanism exists that can explain possible systematic hemispheric asymmetries.
Aims. We use a novel method of high heliolatitudinal vantage points to increase the fraction of one hemisphere in solar 10.7 cm radio fluxes and sunspot numbers. We aim to explore the possibility that solar radio fluxes and sunspot numbers, the two most fundamental solar parameters, depict systematic, possibly mutually similar patterns in their hemispheric activities during the last 75 yr.
Methods. We used three different sets of time intervals with increasing mean heliographic latitude and calculated corresponding hemispheric high-latitude radio fluxes and sunspot numbers. We also normalized these fluxes by yearly means in order to study the variation of fluxes in the two hemispheres over the whole 75 yr time interval.
Results. We find that cycle-maximum radio fluxes and sunspot numbers in each odd solar cycle (19, 21, 23) are larger at northern high latitudes than at southern high latitudes, while maximum fluxes and numbers in all even cycles (18, 20, 22 24) are larger at southern high latitudes than at northern high latitudes. This alternation indicates a new form of systematic, Hale-cycle-related variation in solar activity. Hemispheric differences at cycle maxima are 15% for radio flux and 23% for sunspot numbers, on average. The difference is largest during cycle 19 and smallest in cycle 24. Normalized radio fluxes depict a dominant Hale-cycle variation in both hemispheres, with an opposite phase and overall amplitude of about 5% in the north and 4% in the south. Thus, there is systematic Hale-cycle alternation in magnetic flux emergence in both hemispheres.
Conclusions. The hemispheric Hale cycle in flux emergence can be explained if there is a northward-directed relic magnetic field, which is slightly shifted northward. In that case, in odd cycles, the northern hemisphere is enhanced more than the southern hemisphere, and in even cycles, the northern hemisphere is reduced more than the southern hemisphere, establishing the observed hemispheric alternation. The temporal change of asymmetry during the seven cycles can be explained if the relic shift oscillates at the 210 yr Suess/deVries period, which also provides a physical cause to this periodicity. Gleissberg cycles are explained as off-equator excursions of the relic, each Gleissberg cycle forming one half of the full relic shift oscillation cycle. Having a relic field in the Sun also offers interesting possibilities for century-scale forecasting of solar activity.
The hypothesis is considered that the torsional wave observed on the Sun is an eigenmode oscillation excited in the presence of a weak poloidal magnetic field. We derive asymptotic linear equations for a perturbation with a large number of nodes along the radius, assuming the rotation to be slow and the characteristic perturbation period to be much longer than the rotational period. The results of a preliminary numerical study of the stability of the torsional mode indicate that the superadiabaticity of the solar convection may contribute to the excitation of this mode. In the present work the approximation of harmonic radial dependence of the perturbation has been used.
After the very suggestive results of the early days, the theory of the solar dynamo has now entered a period of re-evaluation. It is clear that our initial expectations have been too high. I shall review some of the recent attempts to formulate nonlinear and stochastic mode excitation theoretically. We now have evidence from synoptic observations that the solar dynamo features many periods. Periods both shorter and longer than the fundamental 22 yr cycle have been claimed. The phase stability of any of these periods is uncertain. The phase memory of the 22 yr period may be as short as ~ 10 cycles, but could also be much longer. Linear mean field theories permit only one marginally stable mode; they predict one period with an infinitely long phase memory. Attempts to explain multiperiodicity and finite phase memory effects fall in two categories:
(1). Nonlinear models. These feature a few nonlinearly coupled variables and may exhibit a multiperiodic or chaotic behaviour; (2). If the number of relevant variables is very high, then the dynamo behaves stochastically. It has been argued that this takes the form of stochastic excitation of many dynamo modes (overtones).
Context. Since the occurrence of north-south asymmetry (NSA) of alternating sign may be determined by different mechanisms, the frequency and amplitude characteristics of this phenomenon should be considered separately. Aims. We propose a new approach to the description of the NSA of solar activity. Methods. The asymmetry defined as A = (N-S)/(N + S) (where N and S are, respectively, the indices of activity of the northern and southern hemispheres) is treated as a superposition of two functions: The sign of asymmetry (signature) and its absolute value (modulus). This approach is applied to the analysis of the NSA of sunspot group areas for the period 1874-2013. Results. We show that the sign of asymmetry provides information on the behavior of the asymmetry. In particular, it displays quasi-periodic variation with a period of 12 yr and quasi-biennial oscillations as the asymmetry itself. The statistics of the so-called monochrome intervals (long periods of positive or negative asymmetry) are considered and it is shown that the distribution of these intervals is described by the random distribution law. This means that the dynamo mechanisms governing the cyclic variation of solar activity must involve random processes. At the same time, the asymmetry modulus has completely different statistical properties and is probably associated with processes that determine the amplitude of the cycle. One can reliably isolate an 11-yr cycle in the behavior of the asymmetry absolute value shifted by half a period with respect to the Wolf numbers. It is shown that the asymmetry modulus has a significant prognostic value: The higher the maximum of the asymmetry modulus, the lower the following Wolf number maximum. Conclusions. A fundamental nature of this concept of NSA is discussed in the context of the general methodology of cognizing the world. It is supposed that the proposed description of the NSA will help clarify the nature of this phenomenon.
The strong magnetic fields found in the Ap and Bp stars are reviewed, with critical attention to the competing dynamo and fossil theories for their origin. A number of difficulties for the dynamo theory are identified. Whilst the fossil theory is not free of problems, they appear less severe. From the modulation of certain spectral lines, rather weaker fields are deduced to be present above the surface of Be stars. The question of whether observed spectral transients might arise from magnetic fluctuations is discussed.
The Hale solar period, τH(1) ≅ 22 yr, and its second
harmonic, τH(2) ≅ 11 yr, which characterize the
sunspot index, are imprinted in certain varved rocks of Archaean to late
Precambrian age, but the varves record climate and thus are sensitive to
solar insolation. The authors report apparent collective behaviour of
the two kinds of data. The 22-yr/11-yr amplitude spectral density ratio,
βi of the sunspot index (which is a measure of
solar-cycle asymmetry), plotted together with βis from
three ancient varve thickness sequences against the age for each
βi, results in a remarkably close fit to a decreasing
exponential with time constant τ ≅ 2 Gyr. These varves and the
sunspot index appear to link solar luminosity and the solar field,
implying that a common forcing mechanism affects luminosity and the
dynamo periods through the common decay time, τ.
Recently, using the new group sunspot number series introduced by Hoyt
and Schatten, we have shown that the weak sunspot activity during the
Maunder minimum is modulated by a 22-year periodicity. Here we
demonstrate that, after subtracting the long-term trend due to the
Gleissberg cycle and after averaging the 11-year cyclicity, the group
sunspot series depicts a 22-year cycle with an amplitude of about 10% of
the current sunspot activity level. The well known Gnevyshev-Ohl rule is
a reflection of such a persistent 22-year periodicity. We discuss the
origin of the 22-year cycle in sunspot activity in terms of a weak relic
solar magnetic field.
The accumulating observational data point clearly to a basic picture of
stellar activity dominated by magnetic fields maintained by dynamo
action, dependent on the star's rotation. A simple model for the
external magnetic field has both a wind zone and a corotating dead zone;
the predicted rotational history of the star is discussed, and some
support for the model noted from observations of a young, rapidly
rotating dwarf star. Some of the impressive achievements of current
dynamo theory are summarised.
During 42 years of observations the General Magnetic Field of the Sun as
a star demonstrates a stable picture of variability with the activity
cycle: during maximum activity GMF reaches ˜2 G, and during
minimum it reaches ˜0.2 G. The frequencies of prominent peaks in
the power spectrum of GMF significantly vary from one cycle of
activity to another one. All data folded in phase with the equatorial
synodic period ˜26.9 ° shows a specific phase curve similar to a
dipole with amplitude ˜0.2 G and the absolute ratio of positive to
negative magnetic flux ˜0.9. That is, during four decades of
observations the excess of the positive magnetic flux is concentrated on
the one side of the Sun, the excess of the negative flux is concentrated
on the opposite side, and this magnetic field does not reverse its
polarity with the 22-year Hale solar cycle. In the case, when poloidal
dipole axis coincides with rotation axis one can see a more complex
picture of variability: the power spectrum for GMF values obtained at
four minima of activity between 20 and 24 sunspot cycles demonstrates a
large difference in relative amplitude of frequencies from the power
spectrum for total GMF array and indicates the presence of the
quadrupole component. Rough empirical estimation of the upper limit
of the mean velocity of the poloidal dipole sign reverse for the
Hale cycles from 1749 to 1997 gives < V> ≈ 6.85 ± 0.05
m s-1. We suppose the presence of additional weak
large-scale magnetic field on the Sun. The axis of the field lies near
the equatorial plane. This weak large-scale magnetic field reflects
properties of the stationary global magnetic field of the solar
radiative interior on the surface of the Sun, which appears to be a
third large-scale component of the magnetic field along with known
toroidal and poloidal fields.
Based on a study of magnetic cycle variations, a new interpretation of Mounder type minima is proposed, and a new such minimum is identified at the end of the past century and beginning of this century. A singular point is shown to exist in variations of the low-frequency component, which are thought to be related to variations of the quasi-constant magnetic field of the sun. The new data are used in a discussion of criteria for the construction of prediction models and of the mechanisms of solar cycles.
The hypothesis is considered that the torsional wave observed on the Sun is an eigenmode oscillation excited in the presence of a weak poloidal magnetic field. We derive asymptotic linear equations for a perturbation with a large number of nodes along the radius, assuming the rotation to be slow and the characteristic perturbation period to be much longer than the rotational period. The results of a preliminary numerical study of the stability of the torsional mode indicate that the superadiabaticity of the solar convection may contribute to the excitation of this mode. In the present work the approximation of harmonic radial dependence of the perturbation has been used.
Fossil magnetic fields (i.e. fields that survive from one stage of stellar evolution to a significantly later epoch without being regenerated) have been invoked to explain phenomena in the Sun, magnetic CP stars, white dwarfs and neutron stars. The feasibility of such processes is discussed critically. Estimates are made that suggest that flux survival through pre-main sequence evolution is more likely to occur in stars with M>1 M_odot. Any link between CP star and white dwarf magnetism is argued to favour the fossil field origin of CP star fields.
The 22-year cycle in geomagnetic activity is characterized by high activity during the second half of even-numbered solar cycles and the first half of odd-numbered cycles. We present new evidence for this 22-year cycle using the aa magnetic index for the years 1844-1994. Over this 150-year interval, the 22-year cycle can be observed through differences between the decay phases of even- and odd-numbered cycles in (1) average values of a 27-day recurrence index; (2) the results of a X 2 "event" analysis of 27-day recurrences of both disturbed and quiet days; and (3) an apparent annual modulation of the 27-day peak in the power spectrum of the aa index. Currently, the 22-year variation is attributed to the Russell-McPherron solar wind- magnetosphere coupling mechanism working in conjunction with the Rosenberg-Coleman polarity effect. Contrary to this viewpoint, we argue that an intrinsic 22-year solar variation (other than polarity reversal), revealed in the systematic low-high alternation of even-odd sunspot maxima within the last six complete Hale cycles, is the dominant cause of the 22- year cycle in geomagnetic activity. This sunspot and related coronal mass ejection variation should lead directly to higher geomagnetic activity during the first-half of odd-numbered solar cycles. Various lines of evidence (including 1-3 above) indicate that 2Y-day recurrent wind streams are more prominent during the decline of even- numbered solar cycles, contributing to the higher geomagnetic activity observed at those times. These stronger recurrence patterns may be related to the more rapid expansion of polar coronal holes (faster movement of the coronal streamer belt to low latitudes) observed following the mama of recent even-numbered cycles. The amplitudes of the 22-year sunspot and geomagnetic activity cycles over the last 150 years are shown to be highly correlated. The 22-year pattern of geomagnetic activity appears to be a reflection of the solar dynamo coupling of poloidal magnetic fields on the decline of one solar cycle to the toroidal fields at the maximum of the following cycle. It seems likely that the 22-year variation in sunspot/solar wind activity plays a role in the observed 22-year modulation of galactic cosmic ray intensity.
The evolution of the solar magnetic field through its 22 year cycle shows a varying inclination of the magnetic equator at 2.5 Rs from about 0° during solar minimum up to 90° during solar maximum, as measured with respect to the solar equator. We show that this behaviour could be explained by the presence of a small dipolar relic field which has a high inclination with respect to the solar rotation axis and points southward. This fossil field would lead to a larger polar field during the negative polarity phase of the cycle, in accordance with observations. It may also help to explain the asymmetry observed in the solar activity of the northern and southern hemispheres, the appearance of some particularly active longitudes on the Sun, as well as other asymmetrical characteristics of the solar activity cycles.
The authors discuss the large-scale meridional circulation and
concomitant differential rotation in the radiative envelope of a
magnetic star, assuming that departures from spherical symmetry are not
too large. They consider the case of a magnetic field that has a
poloidal component and a concomitant toroidal component which is due to
rotation. Taking into account the ever-present eddy-like motions that
pervade a stellar radiative zone, the authors obtain self-consistent
solutions for the meridional flow and the mean magnetic field, which is
slowly decaying and has a poloidal part that is almost dipolar in
structure. The toroidal component of the field and the rotation law are
also discussed. Detailed numerical results are presented for a 3 M_sun;
star.
Helioseismological measurements have recently shown that the vertical
gradient in angular velocity is confined to a thin layer in the
overshoot region just below the convective zone of the Sun. A solar
dynamo operating in this configuration exhibits surface (or interface)
wave properties and is confined primarily to just below the
convective/shear boundary. A fixed primordial magnetic field bound to
the radiative core is observed to be modified at the solar surface by
the dynamo and is found to be a sensitive function of the shear layer
thickness h. If the solar dynamo operates as an alpha-o) surface dynamo,
then, based on current observations of solar cycle asymmetry and
allowing for the present uncertainty in the value for h, an upper bound
of 0.15-0.5 G for the primordial magnetic field magnitude at the bottom
of the convective zone is calculated. By comparing the age of the Sun
with the solar decay time for a magnetic field initially trapped in tile
solar core, we estimate the magnetic field in the interior of the Sun's
core to have an upper magnitude of around 30 G. Because of this low
value, solutions to the solar neutrino problem based on high magnetic
fields in the core thus become untenable.
Mean field dynamo theory has witnessed a very rapid development during the last 25 years, resulting in many models which reproduce most of the basic features of the large scale field of the Sun and the Earth. In this review the application to the Sun features prominently. After a brief discussion of the relevant observations and some basic results from laminar dynamo theory, the traditional picture of linear mean field theory is outlined, including an analysis of the properties of the plane wave solutions of the dynamo equation. The emphasis is on explaining the physical mechanisms and theoretical concepts in an elementary fashion, and not on a detailed comparison of various solar mean field models. A rigorous derivation of the dynamo equation under various conditions is also presented (isotropic/anisotropic turbulence, short/long correlation time and the two-scale approximation). Finally, I discuss some of the major problems and recent developments such as the structure of the magnetic field, nonlinear dynamos, boundary layer dynamos, internal and external forcing, and subcritical dynamo operation.
The possibility of magnetic field generation in various celestial bodies
by 'battery' effects of different kinds is analyzed. The effect is
caused by the difference in the directions of the electron pressure
gradient and the gradient of the electron number density. The
possibility that conditions suitable for the 'battery mechanisms' exist
on the earth, the sun and stars are considered. It is shown that the
observational data are not in contradiction with the hypothesis that the
effect considered plays a major or even an essential role in many cases.
The possible origin of the galactic magnetic field as a superposition of
the fields ejected from stars is discussed.
Magnetic fields of various forms, and of strengths ranging up to
5×108gauss, in the radiative core of the Sun have been
hypothesized by various authors. This paper points out that the thermal
shadows of magnetic inhomogeneities in the radiative core cause vertical
mixing of fluid, with possible consequences for the 7Li
abundance in the Sun. Magnetic fields of the order of
4×105gauss with scales of 3×104km are
sufficient to provide the partial depletion of 7Li inferred
from observation. It is found that the rms field in the outer radiative
zone cannot much exceed 4×105gauss.
We present a large set of numerical calculations describing the
rotational evolution of a solar-type star, in response to the torque
exerted on it by a magnetically coupled wind emanating from its surface.
We consider a situation where the internal redistribution of angular
momentum in the radiative part of the envelope is dominated by magnetic
stresses arising from the shearing of a preexisting, large-scale,
poloidal magnetic field.
By assuming a time-independent poloidal magnetic field, neglecting fluid
motions in meridional planes, and restricting our attention to
axisymmetric systems, we reduce the spin-down problem to solving the
(coupled) ψ-components of the momentum and induction equations.
Nevertheless, our computations remain dynamical, in that they take into
account both the generation of a toroidal magnetic field by shearing of
the preexisting poloidal field, and the back-reaction of the resulting
Lorentz force on the differential rotation. It becomes possible to draw,
for the first time, a reasonably realistic and quantitative picture of
the effects of large-scale internal magnetic fields on the main-sequence
rotational evolution of solar-type stars.
We perform spin-down calculations for a standard solar model, starting
from the ZAMS and extending all the way to the solar age. The
wind-induced surface torque is computed using the axisymmetric
formulation of Weber & Davis (1967). We consider a number of
poloidal magnetic field configurations which differ both in the degree
of magnetic coupling between the convective envelope and radiative core
and in average strength.
The rotational evolution can be divided into three more or less distinct
phases: an initial phase of toroidal field buildup in the radiative
zone, lasting from a few times 104 to a few times
106 yr; a second period in which oscillations set up in the
radiative zone during the first phase are damped; and a third period,
lasting from an age of about 107 yr onward, characterized by
a state of dynamical balance between the total stresses (magnetic +
viscous) at the core-envelope interface and the wind-induced surface
torque, leading to a quasistatic internal magnetic and rotational
evolution.
Our results also demonstrate (1) the existence of classes of large-scale
internal magnetic fields that can accommodate rapid spin-down near the
ZAMS and yield a weak internal differential rotation by the solar age,
(2) the importance of phase mixing in efficiently damping large-scale
toroidal oscillations pervading the radiative interior at early times,
(3) the near-independence of the present solar surface angular velocity
on the strength and geometry (past and present) of any internal
large-scale magnetic field pervading the radiative interior, and (4) the
greater dependence of the present solar internal differential rotation
on the overall morphology (but not on the strength) of the internal
magnetic field.
An attempt is made to place limits on the size of moderate- to
large-scale components of magnetic field in the radiative interior of
the Sun. Two approaches are employed: (1) Inferred limits on the
magnitude of the radial and transverse components of any such field at
the base of the convective envelope are used to constrain the initial
and current internal field structure via a self-consistent
time-dependent solution of the magnetohydrodynamic and thermal equations
for the solar interior. (2) The thermomagnetic circulation induced by
field inhomogeneities of somewhat smaller scale is calculated
self-consistently and, following Parker (1985), limits on 7Li
depletion at the solar surface are employed to give limits on the field
strength in the radiative interior. The results of both calculations
suggest that interior field strengths much in excess of 105G
are unlikely.
Climatic cyclicity is recorded by regular variations in the thickness of
siltstone-fine sandstone laminae interpreted as annual deposits (varves)
within the Elatina Formation, a late Precambrian (680 million years old)
periglacial lake deposit in the Flinders Ranges, South Australia.
Earlier conclusions, based on the study of limited rock outcrop, that
the climatic cycles reflect solar variability are strongly supported by
a complexity of periods revealed through study of drill cores of the 10
m thick varved sequence. The wealth of new data generated by the
drilling program, has application to solar physics and solar-planetary
science.
It is really possible that the Sun possesses a relic magnetic field of
the pre-main sequence epoch in its radiative core. Due to a stably
stratified fluid and an extremely high electrical conductivity in the
solar interior, a relic solar magnetic field can survive for a very long
time. A relic field can help us to explain many asymmetries in solar
activities, such as the north-south asymmetries of solar magnetic
activities, active longitudes and holes, low-latitude coronal holes,
Maunder minimum, etc. In addition it can affect the distribution and
evolution of solar surface magnetic field by changing the boundary
conditions of solar dynamo. This paper focuses on the introduction of
recent progress and issues in observations and theories of relic solar
magnetic field. Some unresolved problems and highlights are also
discussed.
After the very suggestive results of the early days, the theory of the solar dynamo has now entered a period of re-evaluation. It is clear that our initial expectations have been too high. I shall review some of the recent attempts to formulate nonlinear and stochastic mode excitation theoretically. We now have evidence from synoptic observations that the solar dynamo features many periods. Periods both shorter and longer than the fundamental 22 yr cycle have been claimed. The phase stability of any of these periods is uncertain. The phase memory of the 22 yr period may be as short as ~ 10 cycles, but could also be much longer. Linear mean field theories permit only one marginally stable mode; they predict one period with an infinitely long phase memory. Attempts to explain multiperiodicity and finite phase memory effects fall in two categories:
(1).
Nonlinear models. These feature a few nonlinearly coupled variables and may exhibit a multiperiodic or chaotic behaviour;
(2).
If the number of relevant variables is very high, then the dynamo behaves stochastically. It has been argued that this takes the form of stochastic excitation of many dynamo modes (overtones).
As the solar magnetic field evolves through its activity cycle the polar
field strength changes in both magnitude and sign, and the heliomagnetic
equator at 2.5RS shows a varying inclination from about
0° during solar minimum up to 90° during solar maximum, as
measured with respect to the solar equator. This behavior of the
heliomagnetic equator is mainly due to the behavior of the dipole
component of the field, which is the dominant component at this height.
We show that this behavior could be explained by the presence of a small
dipolar relic field pointing southward but tilted with respect to the
solar rotation axis. This fossil field would lead to a larger polar
field during the negative polarity phase of the cycle, in accordance
with observations. It may also help to explain the asymmetry observed in
the solar activity of the northern and southern hemispheres, the
appearance of some particularly active longitudes on the Sun, as well as
other asymmetrical characteristics of the solar activity cycles. The
possibility of random variations in the dynamo-generated dipole field is
also discussed.
This paper examines the effects of dynamical and resistive instabilities
on magnetic redistribution of angular momentum within a star. It is
tentatively concluded that if significant differential rotation survives
in a stably stratified radiative zone over a stellar evolution time,
then the poloidal field, Bp, cannot exceed an upper limit of
order 3×10-2G and is probably less than
10-3G. In the radiative core of the Sun Bp is
estimated to be at least of order 5×10-2G and probably
100 G or more. Values greater than 0.1 G cannot easily be reconciled
with the rotational shear inferred from frequency splitting of solar
oscillations.
As stars of low or moderate mass contract towards the main sequence,
there may be a time when a convectively unstable region is threaded by a
large scale relic field, trapped from the interstellar medium during the
star formation process. If the convection zone supports a dynamo, then
the interaction of such a relic field with the dynamo is of interest.
Thus mean field dynamo models are studied in the presence of an imposed
background field. For most of the investigation, an alpha-quenching
nonlinearity is assumed. It is then shown that, when differential
rotation is present, the total field energy is less than that of the
relic field alone, lying between this value and that of the dynamo with
no imposed field, except when the imposed field strength is small.
However, if the field strength is limited at finite amplitude by a
magnetic buoyancy mechanism, the situation is somewhat less clear cut,
and modest enhancement of the total field energy above the level of the
pure relic field (itself modified by the buoyancy) may then be possible
for some parameter values.
In this contribution we study the question of the relationships between regularities and chaos in the dynamo mechanism producing sunspot activity. Following the idea of the threshold-like mechanism of sunspot production, we considered a simple phenomenological model consisiting of regular and random-driven components. The model describes pretty well the main features of the sunspot activity for both normal activity times (11-year, 22-year cycles, variations of cycle length and amplitude) and for the Maunder minimum (seemingly sporadic sunspot occurrence).
We model solar activity cycle as a forced and damped harmonic oscillator consisting of two parts, sinusoidal and transient. The amplitudes, frequencies, phases and decay factors of such a harmonic oscillator are determined by fitting the equation of the sinusoidal and transient parts to the sunspot data for the years 1755–1996 (cycles 1–22) with the results: (i) there is a long-term decreasing trend in the phase, while the amplitude and the frequency (or period of ∼11 yr) of the sinusoidal part remain constant for all the solar cycles; (ii) the amplitude of the transient part is phase locked with the phase of the sinusoidal part; (iii) for all the cycles, the period and decay factor (that is much less than 1) of the transient part remain approximately constant; (iv) except in cycles 6 and 15, the phases of the transient part are approximately constant with a magnitude of ∼π/2 radians and; (v) for cycles 6 and 15, the simultaneous change in magnitude of phase difference (∼2π radians) between the transient and sinusoidal parts and of very low sunspot activity may be due to the Maunder minimum type of oscillations. The constancy of the amplitudes and the frequencies of the sinusoidal part and a very small decay factor from the transient part suggests that the solar activity cycle mainly consists of a persistent oscillatory part that might be compatible with long-period (∼22 yr) Alfven oscillations.
The sunspot number series forms the longest directly observed index of solar activity and allows one to trace its variations on the time scale of about 400years since 1610. This time interval covers a wide range from seemingly vanishing sunspots during the Maunder minimum in 1645–1700 to the very high activity during the last 50years. Although the sunspot number series has been studied for more than a century, new interesting features have been found even recently. This paper gives a review of the recent achievements and findings in long-term evolution of solar activity cycles such as determinism and chaos in sunspot cyclicity, cycles during the Maunder minimum, a general behaviour of sunspot activity during a great minimum, the phase catastrophe and the lost cycle in the beginning of the Dalton minimum in 1790s and persistent 22-year cyclicity in sunspot activity. These findings shed new light on the underlying physical processes responsible for sunspot activity and allow a better understanding of such empirical rules as the Gnevyshev–Ohl rule and the Waldmeier relations.
Magnetic fields are studied to understand the nature of activity on stars with convective envelopes. Results of high-accuracy
General Magnetic Field (GMF) measurements of different luminosity stars on the right hand side of the Cepheid instability
strip of the H-R diagram are reviewed: the presence of a weak general magnetic field for 21 stars with vigorous convection
is detected (F9-M3 spectral types and I-V luminosity classes). A substantial (up to some dozens) GMF value was detected on
two supergiant stars, three bright giants, twelve giant stars, one subgiant, and three solar-like dwarfs. Furthermore, the
variation of global nonaxisymmetric magnetic fields as a function of the stellar rotation is determined for two solar-like
stars other than the Sun: the magnetic field of the young solar-like star ξ Boo A shows periodic variations from -10 G to
+30 G, and the magnetic field of the old solar-like star 61 Cyg A varies from -10 G up to +4 G. Currently, the nature of this
field is unknown. The nonaxisymmetric GMF as a phenomenon is absent in the Babcock’ and Leighton’ phenomenological magneto-kinematic
model of the solar cycle. In terms of standard α-Ω dynamo theory, GMF is absent also. There are only two main components of
large-scale magnetic fields on the Sun: the toroidal magnetic field and the axisymmetric poloidal field. The coincidence of
theoretical conclusions of different authors as well as results of their numerical simulations and new data on the observed
magnetic field for solar-like stars (i.e., the presence of a nonaxisymmetric large-scale field) leads to a working hypothesis
that GMF reflects properties of a stationary global magnetic field of the Sun’s (or convective star’s) radiative interior
onto its surface. There appears to be a third nonaxisymmetric, large-scale component of the magnetic field (Origin Magnetic
Field) - the initial magnetic field for dynamo mechanisms; a global magnetic field of radiative interior penetrates into surface
of the Sun, and the observed GMF is a time-dependent superposition of all large-scale components: axisymmetric poloidal, nonaxisymmetric
toroidal and nonaxisymmetric origin fields.
A general mathematical theory of magnetic field generation by inductive fluid motion (the dynamo theory) is developed with reference to the generation of the magnetic fields of the earth and sun. Attention is given to the more fundamental aspects of the problem with a treatment of those basic results of magnetohydrodynamics which are the foundation of the theory. An effort is made to find a common framework for the diverse dynamo theories which have evolved in recent years. The key concept in the theory developed here is that of the lack of reflectional symmetry of a fluid flow, the simplest measure of which is helicity. The invariance and topological interpretation of helicity are examined and its influence in turbulent flows with and without magnetic fields is discussed. Consideration is given to laminar dynamo theory, Braginskii's theory (1964) for weakly asymmetric systems, the structure and solution of the dynamo equations, and dynamically consistent dynamos. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints
The angular rotation velocities of stable, recurrent sunspots were investigated using data from the Greenwich Photoheliographic Results 1940 until 1968. We found constant rotation velocities during the passages on the solar disk with errors of about 4 m s–1. During their lifetime these spots show a decreasing braking of their rotation velocities from 0.8 to 0.3 m s–1 per day. A plausible interpretation is found by assuming the spots to be coupled to a slowly rising subsurface flux tube and a rotation velocity which increases with depth.
Spherical kinematic dynamo models with axisymmetric magnetic fields are examined, which arise from the mean field electrodynamics of Steenbeck and Krause, and also from the nearly axisymmetric limit of Braginskii. Four main cases are considered: (i) there is no mean flow, but the dynamo is maintained by microscale motions which create a mean electromotive force, [Note: See the image of page 663 for this formatted text] E, proportional to the mean magnetic field, B (the alpha effect); (ii) in addition to an alpha effect which creates poloidal mean field from toroidal, a mean toroidal shearing flow (angular velocity omega ) is present which creates toroidal mean field from poloidal more efficiently than by the alpha effect; (iii) in addition to the processes operative in (ii), a mean meridional circulation, m, is present; (iv) [Note: See the image of page 663 for this formatted text] E is produced by a second order inductive process first isolated by Radler. When these processes are sufficiently strong, they can maintain magnetic fields. The resulting situations are known as (i) alpha 2 dynamos, (ii) alpha omega dynamos, (iii) alpha omega dynamos with meridional circulations, and (iv) Radler dynamos. Models of each type are considered below, but cases (ii) and (iii) give rise to particularly interesting results. If |m| is sufficiently small, or zero [case (ii)], the most easily excited dynamo is oscillatory and is of dipole type if alpha omega ' 0 in the northern hemisphere, the direction of wave motion is reversed, and also the quadrupolar solution is more readily excited than the dipolar. If |m| is sufficiently large, and of the right magnitude and sense (which is model dependent), it is found that the dynamo which regenerates most easily is steady. It is of dipolar form if alpha omega ' > 0 but quadrupolar if alpha omega ' < 0. These models appear to be relevant to the Earth, where meridional circulations might be provided by, for example, Ekman pumping. Evidence for a remarkable symmetry property is adduced. If m and alpha omega ' are reversed everywhere in the state in which the dipole (say) is most readily excited, it is found that the state in which a quadrupole is most easily regenerated is recovered, almost precisely. Moreover, the critical magnetic Reynolds number for each is closely similar. As a corollary, the critical Reynolds numbers for dipolar and quadrupolar solutions of opposite alpha omega ' are nearly identical for the alpha omega dynamo (m = 0).
The main object of the paper is to discuss the possibility of a body of homogeneous fluid acting as a self-exciting dynamo. The discussion is for the most part confined to the solution of Maxwell's equations for a sphere of electrically conducting fluid in which there are specified velocities. Solutions are obtained by expanding the velocity and the fields in spherical harmonics to give a set of simultaneous linear differential equations which are solved by numerical methods. Solutions exist when harmonics up to degree four are included. The convergence of the solutions when more harmonics are included is discussed, but convergence has not been proved. The simultaneous solution of Maxwell's equations and the hydrodynamic equations has not been attempted, but a velocity system has been chosen that seems reasonable from a dynamical point of view. A parameter in the velocity system has been adjusted to satisfy the conservation of angular momentum in a rough way. Orders of magnitude are derived for a number of quantities connected with the dynamo theory of terrestrial magnetism. It is concluded that the dynamo theory does provide a self-consistent account of the origin of the earth's magnetic field and raises no insuperable difficulties in other directions.
The sun's internal angular velocity is estimated from observations of rotational splitting of low-order, low-degree global oscillations detected as fluctuations in the limb-darkening function. The inferred rapid rotation implies a unitless gravitational quadrupole moment, Jâ, of (5.5 +- 1.3) x 10â»â¶. When this result is combined with two published planetary radar results values of 0.987 +- 0.006 and 0.991 +- 0.006 are obtained for (1/3)(2+2..gamma..-..beta..), a quantity equal to one in the general theory of relativity. .ID LRK206 .PG 1798 1798
The first two paragraphs of this paper were omitted from the January 1976 issue due to an oversight by the AGU Office.
We report the discovery of a large anomaly in the isotopic composition of Mg in a Ca‐Al rich chondrule from the Allende meteorite. This anomaly is manifest independently of instrumental fractionation and is due to an enrichment of about 1.3 percent in ²⁶ Mg while the abundances of ²⁵ Mg and ²⁴ Mg are terrestrial in value. There is a strong correlation in this chondrule between the ²⁶ Mg excess and the Al/Mg ratio so that the most plausible cause of the anomaly is the in situ decay of now extinct ²⁶ Al (τ ½ = 0.72 × 10 ⁶ yr). Mineral phases extracted from a Ca‐Al‐rich aggregate have distinct Al/Mg but show identical, small Mg anomalies which are apparent after correction for fractionation (δ ²⁶ Mg = 0.3%). These data indicate that this aggregate was isotopically homogenized in a high Al/Mg environment after the decay of ²⁶ Al had occurred or that some of the Mg anomalies are due to effects other than in situ decay of ²⁶ Al.
A summary is presented of the evidence, observational and theoretical,
that points to the importance of magnetic fields in star formation and,
in fact, in all large-scale interstellar gas dynamics. Recent
theoretical advances are discussed, taking into account the formation
and equilibria of diffuse interstellar clouds, nonhomologous contraction
and equilibria of self-gravitating clouds, magnetic braking, and the
loss of magnetic flux as a single mechanism for the formation of all
binary stars. Attention is also given to the relevance of new results on
the magnetic field to star formation.
The book discussed is intended to give a systematic introduction to
mean-field magnetohydrodynamics and the dynamo theory which is based on
it, and to provide a survey of the results achieved. Basic ideas of
mean-field electrodynamics are considered along with the elementary
treatment of a simple example, general methods for a calculation of the
turbulent electromotive force, two-scale turbulence, homogeneous
turbulence, mean-field electrodynamics for homogeneous turbulence in the
case of vanishing mean flow, the turbulent electromotive force in the
case of rotational mean motion, and the back-reaction of the magnetic
field on the motions. Attention is also given to the dynamo problem of
magnetohydrodynamics, fundamentals of the theory of the turbulent
dynamo, toroidal and poloidal vector fields, a simple model of an
alpha-effect dynamo, spherical models of turbulent dynamos as suggested
by cosmical bodies, and applications to cosmical object.
Dynamo waves, as solutions of the dynamo equations governing the solar
cycle, propagate along isorotation surfaces inside the sun. This
theorem, universal in most of the dynamo models of the solar cycle, is
proven analytically, and the nature of the propagation is analyzed. The
effects of meridional circulation and the diffusion process on the
propagation nature of the dynamo waves are estimated. The importance of
this theorem is stressed for understanding the solar cycle and for
inferring the rotational law of the interior of the sun.
Remanent magnetization of carbonaceous chondrite meteorites apparently
reflects the presence of a strong magnetic field during the formation of
the solar system. This remanence implies that primitive carbonaceous
chondrites have experienced a magnetic field having an intensity of the
order of one gauss. The major possible models for the origin of this
field are discussed. Magnetic fields of planetary-scale parent objects
or the compressed interstellar field seem to offer the least likely
explanations. An extended solar field and a nebular dynamo magnetic
field offer possible explanations. These are discussed, and the need for
additional work is pointed out.
Eddington's assessment (1) of the rate of circulation in meridian planes in the Sun, produced by its rotation, is reviewed, using a first-order perturbation theory. The resulting velocity is found to be of the order of 10–10 cm./sec., as compared with Eddington's figure of |$2\,\times\,{10}^{-4}\,\text{cm./sec}.,$| a reduction of importance when considering the amount of mixing of material in the Sun during its lifetime.
The theory is applied to stars in general, and the equatorial rotation velocity necessary to provide a significant rate of stirring in a star is found in terms of its magnitude and effective temperature. These rotation rates are found to lie within the range actually observed for early-type stars, but are in excess of those for the later types.
In view of the widely held opinion that giants are stars with non-uniform composition, the distribution of rotation rates among the stars thus assumes an added interest. The rotation rate can similarly govern the possibility of local exhaustion of hydrogen in the core, with its consequent effects on evolution.
The telescope, spectrograph, and magnetograph at the 150-ft Tower
Telescope at Mount Wilson are described, and a chronology of changes in
the instrumentation is given. The average magnetic field strengths over
the last seven years are discussed. The changes in polarity at the poles
of the sun are described. The characteristics of these polarity
reversals at both poles are similar. A reversal is not seen in the
sunspot latitudes but is observed to start in the 40-50 deg zone and
proceed slowly poleward, reaching the pole within 12 to 18 months. At
the time of the polarity reversal at the pole, field strengths over a
large portion of the disk show similar behavior. Rapid changes of solar
magnetic fields over large portions of the solar disk are discussed. Two
possible models are suggested to explain the frequent 'monopole'
appearance of the solar fields.
Cycles conspicuous in late Precambrian (~680 Myr) glacial varves in Australia reveal strong climatic periods of about 11, 22, 145 and 290 yr and a weaker period near 90 yr. The 11-, 22- and 90-yr cycles equate with sunspot periods, and the longer cycles with solar and climatic periods as indicated by tree-ring studies. The varve cycles provide clear evidence of 11- and 22-yr climatic periods in the geological record and may carry important implications for solar physics and planetary science.
Spectral line shift data obtained from full-disk magnetograms recorded at Mt. Wilson are analyzed for differential rotation. The method of analysis is discussed and the results from the data for 1966 through 1968 are presented. The average equatorial velocity over this period is found to be 1.93 km/sec or 13.76 deg/day (sidereal). This corresponds to a sidereal period of 26.16 days. The average results are = 2.78 10-6 - 3.51 10-7 sin2
B - 4.43 10-7 sin4
B rad/sec, whereB is the solar latitude. This indicates a smaller decrease of angular velocity with latitude than found by earlier investigators. Variations from day to day are caused by large-scale short-lived velocity fields on the solar surface. There also appear to be secular variations.
The concept of the solar general magnetic field is extended from that of the polar fields to the concept of any axisymmetric fields of the whole Sun. The poloidal and toroidal general magnetic fields are defined and diagrams of their evolutionary patterns are drawn using the Mount Wilson magnetic synoptic chart data of Carrington rotation numbers from 1417 to 1620 covering approximately half of cycle 19 and cycle 20. After averaging over many rotations long-term regularities appear in the patterns. The diagrams of the patterns are compared with the Butterfly Diagram of sunspots of the same period. The diagram of the poloidal field shows that the Sun behaves like a magnetic quadrupole, each hemisphere having two branches of opposite polarities with mirror images on the other hemisphere. This was predicted by a solar cycle model driven by the dynamo action of the global convection by Yoshimura and could serve as a verification of the model. The diagram of the toriodal field is similar to the Butterfly Diagram of sunspots. The slight differences which do exist between the two diagrams seems to show that the fields responsible for the two may originate from different zones of the Sun. Common or different characteristics of the three diagrams are examined in terms of dynamical structure of the convection zone referring to the theoretical model of the solar cycle driven by the dynamo action of the global convection.
The equatorial photospheric rotation rate has been observed on 14 days in 1978–1980. The resulting rotation rate, = 14.140.04/day, is 2% slower than the rate as observed for long-lived sunspots.
We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.
A model of the convection zone is presented which matches an empirical model atmosphere (HSRA) and an interior model. A mixing length formalism containing four adjustable parameters is used. Thermodynamical considerations provide limits on two of these parameters. The average temperature-pressure relation depends on two or three combinations of the four parameters. Observational information on the structure of the outermost layers of the convection zone, and the value of the solar radius limit the range of possible parameter combinations. It is shown that in spite of the remaining freedom of choice of the parameters, the mean temperature-pressure relation is fixed well by these data.The reality of a small density inversion in the HSRA model is investigated. The discrepancy between the present model and a solar model by Mullan (1971) is discussed briefly.
It is suggested that the explosion of a Type II supernova triggered the collapse of a nearby interstellar cloud and led to the formation of the solar system. Estimates of the abundances resulting from nuclear processing of the supernova ejecta are presented. It appears promising that nucleosynthesis in this single supernova event can account for most isotopic anomalies and traces of extinct radioactivities in solar system material.
Thesis (Ph. D. - Physics)--University of Arizona, 1982. Includes bibliographical references (leaves 125-129). Microfiche. s
Astrophysical objects magnetic field generation, examining behavior at large dynamo numbers
Earth and sun magnetic field production models as function of dynamo states, discussing solar field effects on terrestrial space environment
Carbonaceous chondrites have apparently been magnetized in their early history in magnetic fields with intensities of 0.1 to 10 G, but the origin of the magnetizing field has remained obscured. It is suggested that the magnetic field recorded in the remanence of carbonaceous chondrites may have been produced by a self-excited hydromagnetic dynamo in the gaseous preplanetary nebula from which the solar system is thought to have formed. Recently computed models for the evolution of the preplanetary nebula, consisting of turbulent and differentially rotating gaseous disks with characteristic radial scales of several AU, are used to demonstrate the feasibility of this hypothesis. The maximum field intensity that might be realized by the dynamo production process is estimated to be as high as 1 to 10 G, taking into account two dynamical mechanisms that limit the strength of the field (the Coriolis force and ambipolar diffusion).
The spectrum of the sunspot index can be qualitatively accounted for by a very simple time series model which the Hale 22 year cycle dominates; the series is amplitude modulated at the 90 year Gleissberg period with an index of 25%. The square of the modulated Hale cycle reproduces all of the spectral lines of the Zurich sunspot index spectrum, provided that a small offset is included in the Hale carrier. Without this, evidence of the 22 year periodicity disappears. The squaring explains the dominance of the 11 year cycle which is an artifact of the modulation as is the 45 year line. The offset suggests a small relict magnetic field in the sun's core. Lastly Gilliland (1981) finds a radial eigenmode in the sun with period of 76 + or - 8 years suggestive of a physical basis for the Gleissberg modulation.
Photoelectric observations of solar p-modes obtained with improved wavenumber and frequency resolution are presented. The observations are compared with model calculations of the p-modes, and the degree of spatial and temporal coherence of the observed wave pattern is investigated. It is found that the p-mode oscillations pervade the visible surface of the sun with a high degree of coherence in space and time, so that the whole complex pattern of standing waves with its nodes and antinodes can be regarded as a fixed pattern corotating with the solar surface layers. The p-modes are introduced as a tracer of solar rotational flow velocities. The equatorial differential rotation is estimated as a function of effective depth on the basis of the theoretical contribution functions for the p-modes recently derived by Ulrich et al. (1978). The results strongly indicate that the angular speed of rotation is not uniform even in the relatively shallow layer extending about 20,000 km below the photosphere.
Hydromagnetic dynamo generation of oscillating magnetic fields in the presence of an external, ambient magnetic field introduces a marked polarity asymmetry between the two halves of the magnetic cycle. The principle of oscillating dynamo interaction with external fields is developed, and a tentative application to the sun is described. In the sun a dipole moment associated with the stable fluid beneath the convection zone would produce an asymmetrical solar cycle.
The (14)C production rate in the upper atmosphere changes with time because the galactic cosmic-ray flux responsible for (14)C production is modulated by the changes in solar wind magnetic properties. The resulting changes in the atmospheric (14)C level are recorded in tree rings and are used to calculate past (14)C production rates from a carbon reservoir model that describes terrestrial carbon exchange between the atmosphere, ocean, and biosphere. These past (14)C production rate changes are compared with (14)C production rates determined from 20th-century neutron flux measurements, and a theory relating (14)C production and solar variability, as given by geomagnetic Aa indices and sunspot numbers, is developed. This theory takes into account long-term solar changes that were previously neglected. The 860-year (14)C record indicates three episodes when sunspots apparently were absent: A.D. 1654 to 1714 (Maunder minimum), 1416 to 1534 (Spörer minimum), and 1282 to 1342 (Wolf minimum). A less precisely defined minimum occurred near A.D. 1040. The part of this record after A.D. 1645 correlates well with the basic features of the historical record of sunspot numbers. The magnitude of the calculated (14)C production rates points to a further increase in cosmic-ray flux when sunspots are absent. This flux was greatest during the Spörer minimum. A record of approximate sunspot numbers and Aa indices for the current millennium is also presented.