Prediction of Sunspot Cycles by Data Assimilation Method

Despite the known general properties of the solar cycles, a reliable forecast of the 11-year sunspot number variations is still a problem. The difficulties are caused by the apparent chaotic behavior of the sunspot numbers from cycle to cycle and by the influence of various turbulent dynamo processes, which are far from understanding. For predicting the solar cycle properties we make an initial attempt to use the Ensemble Kalman Filter (EnKF), a data assimilation method, which takes into account uncertainties of a dynamo model and measurements, and allows to estimate future observational data. We present the results of forecasting of the solar cycles obtained by the EnKF method in application to a low-mode nonlinear dynamical system modeling the solar $\alpha\Omega$-dynamo process with variable magnetic helicity. Calculations of the predictions for the previous sunspot cycles show a reasonable agreement with the actual data. This forecast model predicts that the next sunspot cycle will be significantly weaker (by $\sim 30$) than the previous cycle, continuing the trend of low solar activity.Comment: 10 pages, 3 figure

Mechanism of spontaneous formation of stable magnetic structures on the Sun

One of the puzzling features of solar magnetism is formation of long-living compact magnetic structures; such as sunspots and pores, in the highly turbulent upper layer of the solar convective zone. We use realistic radiative 3D MHD simulations to investigate the interaction between magnetic field and turbulent convection. In the simulations, a weak vertical uniform magnetic field is imposed in a region of fully developed granular convection; and the total magnetic flux through the top and bottom boundaries is kept constant. The simulation results reveal a process of spontaneous formation of stable magnetic structures, which may be a key to understanding of the magnetic self-organization on the Sun and formation of pores and sunspots. This process consists of two basic steps: 1) formation of small-scale filamentary magnetic structures associated with concentrations of vorticity and whirlpool-type motions, and 2) merging of these structures due to the vortex attraction, caused by converging downdrafts around magnetic concentration below the surface. In the resulting large-scale structure maintained by the converging plasma motions, the magnetic field strength reaches ~1.5 kG at the surface and ~6 kG in the interior; and the surface structure resembles solar pores. The magnetic structure remains stable for the whole simulation run of several hours with no sign of decay.Comment: 13 pages, 4 figures, submitted to the Astrophysical Journa

Radiative hydrodynamic simulations of turbulent convection and pulsations of Kepler target stars

The problem of interaction of stellar pulsations with turbulence and radiation in stellar convective envelopes is central to our understanding of excitation mechanisms, oscillation amplitudes and frequency shifts. Realistic ("ab initio") numerical simulations provide unique insights into the complex physics of pulsation-turbulence-radiation interactions, as well as into the energy transport and dynamics of convection zones, beyond the standard evolutionary theory. 3D radiative hydrodynamics simulations have been performed for several Kepler target stars, from M-to A-class along the main sequence, using a new 'StellarBox' code, which takes into account all essential physics and includes subgrid scale turbulence modeling. The results reveal dramatic changes in the convection and pulsation properties among stars of different mass. For relatively massive stars with thin convective envelopes, the simulations allow us to investigate the dynamics the whole envelope convection zone including the overshoot region, and also look at the excitation of internal gravity waves. Physical properties of the turbulent convection and pulsations, and the oscillation spectrum for two of these targets are presented and discussed in this paper. In one of these stars, with mass 1.47 M⊙, we simulate the whole convective zone and investigate the overshoot region at the boundary with the radiative zone. Copyright © International Astronomical Union 2014

Mechanisms of formation ofsolar pores and sunspots

Spontaneous formation of self-organized magnetic structures, such as sunspots and pores, is one of intriguing and oldest problems, which represents a complicated interaction of convection and magnetic fields on different scales. Observations of sunspots and pores formation reveal a fast process of accumulation of emerging magnetic field into stable long-living magnetic structures. However, the physical mechanisms of the flux accumulation into the compact magnetic structures with high field strength and their stability are not clear. Development of observational capabilities, theory, and realistic-type MHD numerical simulations open a new level of our understanding of the turbulent processes of the magnetic field accumulation. I discuss the recent progress in observations and radiative MHD simulations that provide important clues for possible mechanisms of formation and stability of sunspots and pores, and their links to the dynamo process. © International Astronomical Union 2013

Non-zero phase-shifts of acoustic waves in the lower solar atmosphere measured from realistic simulations and their role in local helioseismology

Previous studies analyzing the evanescent nature of acoustic waves in the lower solar atmosphere, up to 300\,km above the photosphere, have shown an unexpected phase shift of an order of 1\,s between different heights. Those studies investigated the spectral line \ion{Fe}{1} 6173.3\,\AA, commonly used for helioseismic measurements. Such phase-shifts can contribute to a misinterpretation of the measured travel times in local helioseismology, complicating inferences of, e.g., the deep meridional flow. In this study, we carry out phase-shift computations using a simulated, fully radiative, and convective atmosphere from which the \ion{Fe}{1} 6173.3\,\AA\ line is synthesized. The resulting phase-shifts as functions of frequency across multiple heights show non-zero values in evanescent waves, similar to what was found in observational data. Comparing the Doppler-velocities estimated from the synthesized absorption line with the true velocities directly obtained from the simulated plasma motions, we find substantial differences in phase-shifts between the two. This leads us to hypothesize that the non-adiabaticity of the solar atmosphere yields extra phase-shift contributions to Doppler velocities. Finally, computing phase-differences for different viewing angles reveals a systematic center-to-limb variation, similar to what is present in observations. Overall, this study helps to improve our understanding of the physical cause of the helioseismic center-to-limb effect

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this paper, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical field regions of similar strength. This is consistent with the behavior of fast MHD waves.Comment: 9 pages, 6 figures, Solar Physics (in press