The dynamics of Wolf numbers based on nonlinear dynamo with magnetic helicity: comparisons with observations
arXiv:1512.04363 · doi:10.1093/mnras/stw1267
Abstract
We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 years ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 % correlation over all intervals of observation (about 270 years). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependencies are in good agreement with observations.
arXiv comment9 pages, 13 figures, final revised paper for MNRAS
References in corpus (47)
- Astrophysical magnetic fields and nonlinear dynamo theory
- The case for a distributed solar dynamo shaped by near-surface shear
- Predicting solar cycle 24 with a solar dynamo model
- Detection of Equatorward Meridional Flow and Evidence of Double-Cell Meridional Circulation inside the Sun
- Magnetic Helicity Conservation and Astrophysical Dynamos
- Constraints on the magnitude of alpha in dynamo theory
- Dynamic nonlinearity in large scale dynamos with shear
- Meridional Circulation in Solar and Stellar Convection Zones
- Nonlinear theory of a "shear-current" effect and mean-field magnetic dynamos
- Global helioseismic evidence for a deeply penetrating Solar meridional flow consisting of multiple flow cells
- A History of Solar Activity over Millennia
- On Predicting the Solar Cycle using Mean-Field Models
- Magnetic Helicity Tensor for an Anisotropic Turbulence
- Solar Grand Minima and random fluctuations in dynamo parameters
- Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection
- Confirmation of bistable stellar differential rotation profiles
- New dynamo pattern revealed by solar helical magnetic fields
- Mechanism of spontaneous formation of stable magnetic structures on the Sun
- The Role of Magnetic Helicity Transport in Nonlinear Galactic Dynamos
- Nonlinear Alpha Effect in Dynamo Theory
- Magnetic Helicity Evolution During the Solar Activity Cycle: Observations and Dynamo Theory
- Detection of negative effective magnetic pressure instability in turbulence simulations
- The Radial Distribution of Magnetic Helicity in the Solar Convective Zone: Observations and Dynamo Theory
- Variations of the solar cycle profile in a solar dynamo with fluctuating dynamo governing parameters
- The negative effective magnetic pressure in stratified forced turbulence
- Nonlinear Magnetic Diffusion and Magnetic Helicity Transport in Galactic Dynamos
- Nonlinear Turbulent Magnetic Diffusion and Mean-Field Dynamo
- Large-scale magnetic flux concentrations from turbulent stresses
- Negative effective magnetic pressure in turbulent convection
- Bipolar magnetic structures driven by stratified turbulence with a coronal envelope
- Active region formation through the negative effective magnetic pressure instability
- Current helicity of active regions as a tracer of large-scale solar magnetic helicity
- Self-assembly of shallow magnetic spots through strongly stratified turbulence
- Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field
- Intense bipolar structures from stratified helical dynamos
- Correlation between Decay Rate and Amplitude of Solar Cycles as Revealed from Observations and Dynamo Theory
- Mean-field solar dynamo models with strong meridional flow at the bottom of the convection zone
- Magnetic flux concentrations from turbulent stratified convection
- The distribution of current helicity at the solar surface at the beginning of the solar cycle
- Three-dimensional stability of the solar tachocline
- Meridional circulation dynamics from 3D MHD global simulations of solar convection
- Turbulent reconnection of magnetic bipoles in stratified turbulence
- Magnetic flux concentrations from dynamo-generated fields
- Bipolar region formation in stratified two-layer turbulence
- Competition of rotation and stratification in flux concentrations
- Bipolar magnetic spots from dynamos in stratified spherical shell turbulence
- Magnetic flux concentrations in a polytropic atmosphere
Cited by in corpus (11)
- The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations
- Turbulent magnetic helicity fluxes in solar convective zone
- Nonlinear mean-field dynamo and prediction of solar activity
- Flare activity of the Sun and variations in its UV emission during cyrcle 24
- Cyclic Variations in the Solar Radiation Fluxes at the Beginning of the 21st Century
- The origin and effect of hemispheric helicity imbalance in solar dynamo
- Migrating Dynamo Waves and Consequences for Stellar Current Sheets
- Large Scale Properties of Tilt of Sunspot Groups and Joy's Law Near The Solar Equator
- Magnetic fields of low-mass main sequences stars: Nonlinear dynamo theory and mean-field numerical simulations
- Budget equations and astrophysical nonlinear mean-field dynamos
- Estimates of current helicity and tilt of solar active regions and Joy's law