The sunspot.

Editor: J.S. Ricard.

Sunspot numbers, 1610-1985 : based on "The sunspot activity in the years 1610-1960" /

Mode of access: Internet.

Weather variability, sunspots, and the blooms of cyanobacteria

The roles of weather variability and sunspots in the occurrence of cyanobacteria blooms, were investigated using cyanobacteria cell data collected from the Fred Haigh Dam, Queensland, Australia. Time series generalized linear model and classification and regression (CART) model were used in the analysis. Data on notified cell numbers of cyanobacteria and weather variables over the periods 2001 and 2005 were provided by the Australian Department of Natural Resources and Water, and Australian Bureau of Meteorology, respectively. The results indicate that monthly minimum temperature (relative risk [RR]: 1.13, 95% confidence interval [CI]: 1.02-1.25) and rainfall (RR: 1.11; 95% CI: 1.03-1.20) had a positive association, but relative humidity (RR: 0.94; 95% CI: 0.91-0.98) and wind speed (RR:0.90; 95% CI: 0.82-0.98) were negatively associated with the cyanobacterial numbers, after adjustment for seasonality and auto-correlation. The CART model showed that the cyanobacteria numbers were best described by an interaction between minimum temperature, relative humidity, and sunspot numbers. When minimum temperature exceeded 18%C and relative humidity was under 66%, the number of cyanobacterial cells rose by 2.15-fold. We conclude that the weather variability and sunspot activity may affect cyanobacterial blooms in dams.

Variety matters

Countercyclical markups are a key transmission mechanism in many endogenous business cycle models. Yet, recent findings suggest that aggregate markups in the US are procyclical. The current model addresses this issue. It extends Galí's (1994) composition of aggregate demand model by endogenous entry and exit of firms and by product variety effects. Endogenous business cycles emerge with procyclical markups that are within empirically plausible ranges.

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation coefficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle either from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.

A possible explanation of the Maunder minimum from a flux transport dynamo model

We propose that the poloidal field at the end of the last sunspot cycle before the Maunder minimum fell to a very low value due to fluctuations in the Babcock-Leighton process. With this assumption, a flux transport dynamo model is able to explain various aspects of the historical records of the Maunder minimum remarkably well by suitably choosing the parameters of the model to give the correct growth time.

The dynamics of magnetically trapped fluids. I - Implications for umbral dots and penumbral grains

A study of the magnetohydrodynamic system in which a nonmagnetized fluid in a gravitational field is surrounded by a fluid carrying a vertical magnetic field is presented. It is pointed out that this study can throw some light on the fine-structural features of a sunspot. The equilibrium configuration of the field-free fluid is a tapering column ending at an apex. The regions away form the apex can be studied by the slender flux tube approximation. A scheme developed to treat the apex indicates that, just below the apex, the radius of the tapering column opens up with a 3/2 power dependence on the depth below the apex. If the internal pressure of the field-free fluid is increased, the apex rises, and a static equilibrium may not be possible beyond a limit if the magnetic pressure drops quickly above a certain height. The nature of steady-flow solutions beyond this limit is investigated. Under conditions inside a sunspot, a column of field-free gas is found to rise with a velocity of about 100 km/hr. If umbral dots and penumbral grains are interpreted as regions where the field-free gas ultimately emerges, a very natural explanation of most of their observed properties is obtained.

The influence of the Coriolis force on flux tubes rising through the solar convection zone

In order to study the effect of the Coriolis force due to solar rotation on rising magnetic flux, the authors consider a flux ring, azimuthally symmetric around the rotation axis, starting from rest at the bottom of the convection zone, and then follow the trajectory of the flux ring as it rises. If it is assumed that the flux ring remains azimuthally symmetric during its ascent, then the problem can be described essentially in terms of two parameters: the value of the initial magnetic field in the ring when it starts, and the effective drag experienced by it. For field strengths at the bottom of the convection zone of order 10,000 G or less, it is found that the Coriolis force plays a dominant role and flux rings starting from low latitudes at the bottom are deflected and emerge at latitudes significantly poleward of sunspot zones.

The evolution of loop structures in flux rings within the solar convection zone

Choudhuri and Gilman (1987) considered certain implications of the hypothesis that the magnetic flux within the Sun is generated at the bottom of the convection zone and then rises through it. Taking flux rings symmetric around the rotation axis and using reasonable values of different parameters, they found that the Coriolis force deflects these flux rings into trajectories parallel to the rotation axis so that they emerge at rather high latitudes. This paper looks into the question of whether the action of the Coriolis force is subdued when the initial configuration of the flux ring has non-axisymmetries in the form of loop structures. The results depend dramatically on whether the flux ring with the loops lies completely within the convection zone or whether the lower parts of it are embedded in the stable layers underneath the convection zone. In the first case, the Coriolis force supresses the non-axisymmetric perturbations so that the flux ring tends to remain symmetric and the trajectories are very similar to those of Choudhuri and Gilman (1987). In the second case, however, the lower parts of the flux ring may remain anchored underneath the bottom of the convection zone, but the upper parts of the loops still tend to move parallel to the rotation axis and emerge at high latitudes. Thus the problem of the magnetic flux not being able to come out at the sunspot latitudes still persists after the non-axisymmetries in the flux rings are taken into account.

Locating the seat of the solar dynamo

The hypothesis that the solar dynamo operates in a thin layer at the bottom of the convection zone is addressed. Recent work on the question whether the magnetic flux can be made to emerge at sunspot latitudes is reviewed. It is concluded that this hypothesis can fit the observational facts only if there is turbulence with a length scale of a few hundred kilometers in and around the dynamo region.

Importance of meridional circulation i flux transport dynamo: the possibility of a maunder-like grand minimum

Meridional circulation is an important ingredient in flux transport dynamo models. We have studied its importance on the period, the amplitude of the solar cycle, and also in producing Maunder-like grand minima in these models. First, we model the periods of the last 23 sunspot cycles by varying the meridional circulation speed. If the dynamo is in a diffusion-dominated regime, then we find that most of the cycle amplitudes also get modeled up to some extent when we model the periods. Next, we propose that at the beginning of the Maunder minimum the amplitude of meridional circulation dropped to a low value and then after a few years it increased again. Several independent studies also favor this assumption. With this assumption, a diffusion-dominated dynamo is able to reproduce many important features of the Maunder minimum remarkably well. If the dynamo is in a diffusion-dominated regime, then a slower meridional circulation means that the poloidal field gets more time to diffuse during its transport through the convection zone, making the dynamo weaker. This consequence helps to model both the cycle amplitudes and the Maunder-like minima. We, however, fail to reproduce these results if the dynamo is in an advection-dominated regime.

Locating the seat of the solar dynamo

The hypothesis that the solar dynamo operates in a thin layer at the bottom of the convection zone is addressed. Recent work on the question whether the magnetic flux can be made to emerge at sunspot latitudes is reviewed. It is concluded that this hypothesis can fit the observational facts only if there is turbulence with a length scale of a few hundred kilometers in and around the dynamo region.

Effect of Turbulence on Emerging Magnetic Flux Tubes in the Convection Zone

Working under the hypothesis that magnetic flux in the sun is generated at the bottom of the convection zone, Choudhuri and Gilman (1987; Astrophys. J. 316, 788) found that a magnetic flux tube symmetric around the rotation axis, when released at the bottom of the convection zone, gets deflected by the Coriolis force and tends to move parallel to the rotation axis as it rises in the convection zone. As a result, all the flux emerges at rather high latitudes and the flux observed at the typical sunspot latitudes remains unexplained. Choudhuri (1989; Solar Physics, in press) finds that non-axisymmetric perturbations too cannot subdue the Coriolis force. In this paper, we no longer treat the convection zone to be passive as in the previous papers, but we consider the role of turbulence in the convection zone in inhibiting the Coriolis force. The interaction of the flux tubes with the turbulence is treated in a phenomenological way as follows: (1) Large scale turbulence on the scale of giant cells can physically drag the tubes outwards, thus pulling the flux towards lower latitudes by dominating over the Coriolis force. (2) Small scale turbulence of the size of the tubes can exchange angular momentum with the tube, thus suppressing the growth of the Coriolis force and making the tubes emerge at lower latitudes. Numerical simulations show that the giant cells can drag the tubes and make them emerge at lower latitufes only if the velocities within the giant cells are unrealistically large of if the radii of the flux tubes are as small as 10 km. However, small scale turbulence can successfully suppress the growth of the Coriolis force if the tubes have radii smaller than about 300 km which may not be unreasonable. Such flux tubes can then emerge at low latitudes where sunspots are seen.

Can equipartition fields produce the tilts of bipolar magnetic regions?

The effect of turbulence on the nonaxisymmetric flux rings of equipartition field strength in bipolar magnetic regions is studied on the basis of the small-scale momentum exchange mechanism and the giant cell drag combined with the Kelvin-Helmholtz drag mechanism. It is shown that the giant cell drag and small-scale momentum exchange mechanism can make equipartition flux loops emerge at low latitudes, in addition to making them exhibit the observed tilts. However, the sizes of the flux tubes have to be restricted to a couple of hundred kilometers. An ad hoc constraint on the footpoints of the flux loops is introduced by not letting them move in the phi direction, and it is found that equipartition fields of any size can be made to emerge at sunspot latitudes with the observed tilts by suitably adjusting the footpoint separations.

The Waldmeier effect and the flux transport solar dynamo

We confirm that the evidence for the Waldmeier effect WE1 (the anticorrelation between rise times of sunspot cycles and their strengths) and the related effect WE2 (the correlation between rise rates of cycles and their strengths) is found in different kinds of sunspot data. We explore whether these effects can be explained theoretically on the basis of the flux transport dynamo models of sunspot cycles. Two sources of irregularities of sunspot cycles are included in our model: fluctuations in the poloidal field generation process and fluctuations in the meridional circulation. We find WE2 to be a robust result which is produced in different kinds of theoretical models for different sources of irregularities. The Waldmeier effect WE1, on the other hand, arises from fluctuations in the meridional circulation and is found only in the theoretical models with reasonably high turbulent diffusivity which ensures that the diffusion time is not more than a few years.