Predicting solar cycle 24 with a solar dynamo model

Whether the upcoming cycle 24 of solar activity will be strong or not is being hotly debated. The solar cycle is produced by a complex dynamo mechanism. We model the last few solar cycles by `feeding' observational data of the Sun's polar magnetic field into our solar dynamo model. Our results fit the observed sunspot numbers of cycles 21-23 extremely well and predict that cycle~24 will be about 35% weaker than cycle~23.Comment: 10 pages 1 table 3 figure

The origin of grand minima in the sunspot cycle

One of the most striking aspects of the 11-year sunspot cycle is that there have been times in the past when some cycles went missing, a most well-known example of this being the Maunder minimum during 1645-1715. Analyses of cosmogenic isotopes (C14 and Be10) indicated that there were about 27 grand minima in the last 11,000 yr, implying that about 2.7% of the solar cycles had conditions appropriate for forcing the Sun into grand minima. We address the question how grand minima are produced and specifically calculate the frequency of occurrence of grand minima from a theoretical dynamo model. We assume that fluctuations in the poloidal field generation mechanism and the meridional circulation produce irregularities of sunspot cycles. Taking these fluctuations to be Gaussian and estimating the values of important parameters from the data of last 28 solar cycles, we show from our flux transport dynamo model that about 1-4% of the sunspot cycles may have conditions suitable for inducing grand minima.Comment: Accepted for publication in Physical Review Letter

Towards A Mean-Field Formulation Of The Babcock-Leighton Type Solar Dynamo. I. Alpha Coefficient Versus Durney's Double Ring Approach

We develop a model of the solar dynamo in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes like the production of poloidal field from the decay of active regions, and, on the other hand, we attempt to develop a mean field theory that can be studied in quantitative detail. One of the main challenges in developing such models is to treat the buoyant rise of toroidal field and the production of poloidal field from it near the surface. We build up a dynamo model with two contrasting methods of treating buoyancy. In one method, we incorporate the generation of the poloidal field near the solar surface by Durney's procedure of double ring eruption. In the second method, the poloidal field generation is treated by a positive alpha-effect concentrated near the solar surface, coupled with an algorithm for handling buoyancy. The two methods are found to give qualitatively similar results.Comment: 32 pages, 27 figures, uses aastex.cls and epsfig.st

Study of implosion in an attractive Bose-Einstein condensate

By solving the Gross-Pitaevskii equation analytically and numerically, we reexamine the implosion phenomena that occur beyond the critical value of the number of atoms of an attractive Bose-Einstein condensate (BEC) with cigar-shape trapping geometry. We theoretically calculate the critical number of atoms in the condensate by using Ritz's variational optimization technique and investigate the stability and collapse dynamics of the attractive BEC by numerically solving the time dependent Gross-Pitavskii equation

Fluctuations in the Alpha-Effect and Grand Solar Minima

Parameters of a special kind of \alpha-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates evidence the presence of the Babcock-Leighton \alpha-effect on the Sun. Fluctuations of the \alpha-effect are also estimated. The fluctuation amplitude appreciably exceeds the mean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numerical model for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene.Comment: To appear in Astronomy Reports, 20 pages, 9 figure

Solar activity forecast with a dynamo model

Although systematic measurements of the solar polar magnetic field exist only from mid 1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. This suggests that the Babcock Leighton mechanism of poloidal field generation from decaying sunspots involves randomness, whereas the other aspects of the dynamo process must be reasonably ordered and deterministic. Only if the magnetic diffusivity within the convection zone is assumed to be high, we can explain the correlation between the polar field at a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. To model actual solar cycles with a dynamo model having such high diffusivity, we have to feed the observational data of the poloidal field at the minimum into the theoretical model. We develop a method of doing this in a systematic way. Our model predicts that cycle 24 will be a very weak cycle. Hemispheric asymmetry of solar activity is also calculated with our model and compared with observational data.Comment: 17 pages, 18 figures, submitted to MNRA

Transport of toroidal magnetic field by the meridional flow at the base of the solar convection zone

In this paper we discuss the transport of toroidal magnetic field by a weak meridional flow at the base of the convection zone. We utilize the differential rotation and meridional flow model developed by Rempel and incorporate feedback of a purely toroidal magnetic field in two ways: directly through the Lorentz force (magnetic tension) and indirectly through quenching of the turbulent viscosity, which affects the parametrized turbulent angular momentum transport in the model. In the case of direct Lorentz force feedback we find that a meridional flow with an amplitude of around 2 m/s can transport a magnetic field with a strength of 20 to 30 kG. Quenching of turbulent viscosity leads to deflection of the meridional flow from the magnetized region and a significant reduction of the transport velocity if the magnetic field is above equipartition strength.Comment: 8 pages, 6 figure

Extreme Value Theory and the Solar Cycle

We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. The recent advances in the methodology of the theory of extreme values is applied to the maximal extremes of the time series of sunspots. We focus on the extreme events that exceed a carefully chosen threshold and a generalized Pareto distribution is fitted to the tail of the empirical cumulative distribution. A maximum likelihood method is used to estimate the parameters of the generalized Pareto distribution and confidence levels are also given to the parameters. Due to the lack of an automatic procedure for selecting the threshold, we analyze the sensitivity of the fitted generalized Pareto distribution to the exact value of the threshold. According to the available data, that only spans the previous ~250 years, the cumulative distribution of the time series is bounded, yielding an upper limit of 324 for the sunspot number. We also estimate that the return value for each solar cycle is ~188, while the return value for a century increases to ~228. Finally, the results also indicate that the most probable return time for a large event like the maximum at solar cycle 19 happens once every ~700 years and that the probability of finding such a large event with a frequency smaller than ~50 years is very small. In spite of the essentially extrapolative character of these results, their statistical significance is very large.Comment: 6 pages, 4 figures, accepted for publication in A&

The effect of a meridional flow on Parker's interface dynamo

Parker's interface dynamo is generalized to the case when a homogeneous flow is present in the high-diffusivity (upper) layer in the lateral direction (i.e. perpendicular to the shear flow in the lower layer). This is probably a realistic first representation of the situation near the bottom of the solar convective zone, as the strongly subadiabatic stratification of the tachocline (lower layer in the interface dynamo) imposes a strong upper limit on the speed of any meridional flow there. Analytic solutions to the eigenvalue problem are presented for the cases of vanishing diffusivity contrast and infinite diffusivity contrast, respectively. Unlike the trivial case of a homogeneous system, the ability of the meridional flow to reverse the propagation of the dynamo wave is strongly reduced in the interface dynamo. In particular, in the limit of high diffusivity contrast relevant to the solar case it is found that a meridional flow of realistic amplitude cannot reverse the direction of propagation of the dynamo wave. The implications of this result for the solar dynamo problem are discussed.Comment: 5 pages, 3 figures; MNRAS, in pres