Steven M. Tobias

An Active Sun Throughout the Maunder Minimum

Measurements of 10Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Suns overall activity was drastically reduced and sunspots virtually disappeared. Thus the dates of maxima and minima can now be reliably estimated. Similar behaviour is shown by a nonlinear dynamo model, which predicts that, after a grand minimum, the Suns toroidal field may switch from being antisymmetric to being symmetric about the equator. The presence of cyclic activity during the Maunder Minimum limits estimates of the solar contribution to climatic change.

Transport and Storage of Magnetic Field by Overshooting Turbulent Compressible Convection

We present the results of a series of numerical experiments that investigate the transport of magnetic —elds by turbulent penetrative compressible convection. We —nd that magnetic —ux is preferentially transported downward out of a turbulent convecting region and stored in a stably strati—ed region below. This pumping mechanism is believed to be a crucial component for the operation of a large-scale solar interface dynamo since it may be responsible for the transport of —ux from the solar convection zone to the stable overshoot region. The high-resolution three-dimensional simulations show that efficient pumping occurs as a result of the action of strong coherent down—owing plumes. The properties of the transport are evaluated as a function of magnetic —eld strength, rotation rate, supercriticality, stiUness of the interface, and con—guration. The turbulent pumping of magnetic —ux is remarkably robust and more efficient than its laminar counterpart. The turbulent convection naturally ampli—es magnetic energy from any existing mean —eld. The transport of —ux from the convection zone removes the source for this local ampli—cation there, and thus the peak magnetic energy also comes to reside in the stable region. This is important for an eUective interface dynamo.

For how long will the current grand maximum of solar activity persist

[1] Understanding the Sun’s magnetic activity is important because of its impact on the Earth’s environment. The sunspot record since 1610 shows irregular 11-year cycles of activity; they are modulated on longer timescales and were interrupted by the Maunder minimum in the 17th century. Future behavior cannot easily be predicted – even in the short-term. Recent activity has been abnormally high for at least 8 cycles: is this grand maximum likely to terminate soon or even to be followed by another (Maunder-like) grand minimum? To answer these questions we use, as a measure of the Sun’s open magnetic field, a composite record of the solar modulation function F, reconstructed principally from the proxy record of cosmogenic 10 Be abundances in the GRIP icecore from Greenland. This F record extends back for almost 10,000 years, showing many grand maxima and grand minima (defined as intervals when F is within the top or bottom 20% of a Gaussian distribution). We carry out a statistical analysis of this record and calculate the life expectancy of the current grand maximum. We find that it is only expected to last for a further 15–36 years, with the more reliable methods yielding shorter expectancies, and we therefore predict a decline in solar activity within the next two or three cycles. We are not able, however, to predict the level of the ensuing minimum. Citation: Abreu, J. A., J. Beer, F. Steinhilber, S. M. Tobias, and N. O. Weiss (2008), For how long will the current grand maximum of solar activity persist?, Geophys. Res. Lett., 35, L20109, doi:10.1029/2008GL035442.

Pumping of Magnetic Fields by Turbulent Penetrative Convection

A plausible scenario for solar dynamo action is that the large-scale organized toroidal magnetic field is generated by the action of strong radial shear at the base of the solar convection zone, whereas the weaker poloidal field is regenerated by cyclonic convection throughout the convection zone. We show, using high-resolution three-dimensional numerical simulations, that the required transport of magnetic field from the convection zone to the overshoot region can be achieved on a convective rather than diffusive timescale by a pumping mechanism in turbulent penetrative compressible convection. A layer of magnetic field initially placed in the convection zone is swept down by strong sinking plumes, locally amplified, and deposited in the stable region at the base of the convection zone, despite the opposing action of magnetic buoyancy. The rate of transport is insensitive to the strength of the initial imposed field.

Convective and absolute instabilities of fluid flows in finite geometry

Abstract Dynamics of linear and nonlinear waves in driven dissipative systems in finite domains are considered. In many cases (for example, due to rotation) the waves travel preferentially in one direction. Such waves cannot be reflected from boundaries. As a consequence in the convectively unstable regime the waves ultimately decay; only when the threshold for absolute instability is exceeded can the waves be maintained against dissipation at the boundary. Secondary absolute instabilities are associated with the break-up of a wave train into adjacent wave trains with different frequencies, wave numbers and amplitudes, separated by a front. The process of frequency selection is discussed in detail, and the selected frequency is shown to determine the wave number and amplitude of the wave trains. The results are described using the complex Ginzburg-Landau equation and illustrated using a mean-field dynamo model of magnetic field generation in the Sun.

THE ORIGIN OF PENUMBRAL STRUCTURE IN SUNSPOTS: DOWNWARD PUMPING OF MAGNETIC FLUX

This paper offers the first coherent picture of the interactions between convection and magnetic fields that lead to the formation of the complicated filamentary structure of a sunspot penumbra. Recent observations have revealed the intricate interlocking-comb structure of the penumbral magnetic field. Some field lines, with associated Evershed outflows, plunge below the solar surface near the edge of the spot. We claim that these field lines are pumped downward by small-scale granular convection outside the sunspot. This mechanism is demonstrated in numerical experiments. Magnetic pumping is a key new ingredient that links several theoretical ideas about penumbral structure and dynamics; it explains not only the abrupt appearance of a penumbra as a pore increases in size but also the behavior of moving magnetic features outside a spot. Subject headings: MHD — Sun: magnetic fields — Sun: photosphere — sunspots On-line material: color figures

Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae

The structure of a sunspot is determined by the local interaction between magnetic fields and convection near the Suns surface. The dark central umbra is surrounded by a filamentary penumbra, whose complicated fine structure has only recently been revealed by high-resolution observations. The penumbral magnetic field has an intricate and unexpected interlocking-comb structure and some field lines, with associated outflows of gas, dive back down below the solar surface at the outer edge of the spot. These field lines might be expected to float quickly back to the surface because of magnetic buoyancy, but they remain submerged. Here we show that the field lines are kept submerged outside the spot by turbulent, compressible convection, which is dominated by strong, coherent, descending plumes. Moreover, this downward pumping of magnetic flux explains the origin of the interlocking-comb structure of the penumbral magnetic field, and the behaviour of other magnetic features near the sunspot.

On Predicting the Solar Cycle Using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyze the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model—this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target time series that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilized in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes it impossible to predict the solar cycle using the output from such models.

β-Plane Magnetohydrodynamic Turbulence in the Solar Tachocline

This Letter discusses the role of a weak toroidal magnetic field in modifying the turbulent transport properties of stably stratified rotating turbulence in the tachocline. A local two-dimensional β-plane model is investigated numerically. In the absence of magnetic fields, nonlinear interactions of Rossby waves lead to the formation of strong mean zonal flows. However, the addition of even a very weak toroidal field suppresses the generation of mean flows. We argue that this has serious implications for angular momentum transport in the lower tachocline.

The solar dynamo

In this article I review the fundamentals of solar–dynamo theory. I describe both historical and contemporary observations of the solar magnetic field before outlining why it is believed that the solar field is maintained by a hydromagnetic dynamo. Having explained the basic dynamo process and applications of the theory to the Sun, I shall conclude by speculating on future directions for the theory.