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

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

Reply to comments of Dikpati et al

We present here our response to Dikpati et al.'s criticism of our recent solar dynamo model.Comment: 8 pages, 2 figure

A correction to Spruit's equation for the dynamics of thin flux tubes

It is pointed out that a term was overlooked in the derivation of the equation of motion for a thin flux tube by Spruit (1981). The correction to be applied in an inertial frame and in a rotating frame are discussed. This correction makes the formulation self-consistent, though it does not invalidate the qualitative results obtained by various investigators who have used Spruit's equation

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

Evolution of helicity in NOAA 10923 over three consecutive solar rotations

We have studied the evolution of magnetic helicity and chirality in an active region over three consecutive solar rotations. The region when it first appeared was named NOAA10923 and in subsequent rotations it was numbered NOAA 10930, 10935 and 10941. We compare the chirality of these regions at photospheric, chromospheric and coronal heights. The observations used for photospheric and chromospheric heights are taken from Solar Vector Magnetograph (SVM) and H_alpha imaging telescope of Udaipur Solar Observatory (USO), respectively. We discuss the chirality of the sunspots and associated H_alpha filaments in these regions. We find that the twistedness of superpenumbral filaments is maintained in the photospheric transverse field vectors also. We also compare the chirality at photospheric and chromospheric heights with the chirality of the associated coronal loops, as observed from the HINODE X-Ray Telescope.Comment: 8 pages, 4 figure