Sustained magneto-shear instabilities in the solar tachocline

We present nonlinear three-dimensional simulations of the stably-stratified portion of the solar tachocline in which the rotational shear is maintained by mechanical forcing. When a broad toroidal field profile is specified as an initial condition, a clam-shell instability ensues which is similar to the freely-evolving cases studied previously. After the initial nonlinear saturation, the residual mean fields are apparently too weak to sustain the instability indefinitely. However, when a mean poloidal field is imposed in addition to the rotational shear, a statistically-steady state is achieved in which the clam-shell instability is operating continually. This state is characterized by a quasi-periodic exchange of energy between the mean toroidal field and the instability mode with a longitudinal wavenumber m=1. This quasi-periodic behavior has a timescale of several years and may have implications for tachocline dynamics and field emergence patterns throughout the solar activity cycle.Comment: 5 pages, 3 figures (eps format). Fig. 3 also in jpg format. Submitted to Astrophysical Journal Letter

Predicting cycle 24 using various dynamo-based tools

Various dynamo-based techniques have been used to predict the mean solar cycle features, namely the amplitude and the timings of onset and peak. All methods use information from previous cycles, including particularly polar fields, drift-speed of the sunspot zone to the equator, and remnant magnetic flux from the decay of active regions. Polar fields predict a low cycle 24, while spot zone migration and remnant flux both lead to predictions of a high cycle 24. These methods both predict delayed onset for cycle 24. We will describe how each of these methods relates to dynamo processes. We will present the latest results from our flux-transport dynamo, including some sensitivity tests and how our model relates to polar fields and spot zone drift methods

Meridional flow and differential rotation by gravity darkening in fast rotating solar-type stars

An explanation is presented for the rather strong total surface differential rotation of the observed very young solar-type stars like AB Dor and PZ Tel. Due to its rapid rotation a nonuniform energy flux leaves the stellar core so that the outer convection zone is nonuniformly heated from below. Due to this `gravity darkening' of the equator a meridional flow is created flowing equatorwards at the surface and thus accelerating the equatorial rotation. The effect linearly grows with the normalized pole-equator difference, \epsilon, of the heat-flux at the bottom of the convection zone. A rotation rate of about 9 h leads to \epsilon=0.1 for a solar-type star. In this case the resulting equator-pole differences of the angular velocity at the stellar surface, \delta\Omega, varies from unobservable 0.005/day to the (desired) value of 0.03 day$^{-1}$ when the dimensionless diffusivity factors $c_\nu$ and c_\chi vary between 1 and 0.1 (standard value c_\nu \simeq c_\chi \simeq 0.3, see Table 1.) In all cases the related temperature differences between pole and equator at the surface are unobservably small. The (clockwise) meridional circulation which we obtain flows opposite to the (counterclockwise) circulation appearing as a byproduct in the \Lambda-theory of the nonuniform rotation in outer convection zones. The consequences of this situation for those dynamo theories of stellar activity are discussed which work with the meridional circulation as the dominant magnetic-advection effect in latitude to produce the solar-like form of the butterfly diagram. Key words: Hydrodynamics, Star: rotation, Stars: pre-main sequence, Stellar activityComment: 4 pages, 3 figures, Astronomy and Astrophysics (subm.

The Waldmeier Effect in Sunspot Cycles

We discuss two aspects of the Waldmeier Effect, namely (1) the rise times of sunspot cycles are anti-correlated to their strengths (WE1) and (2) the rates of rise of the cycles are correlated to their strengths (WE2). From analysis of four different data sets we conclude that both WE1 and WE2 exist in all the data sets. We study these effects theoretically by introducing suitable stochastic fluctuations in our regular solar dynamo model.Comment: Magnetic Coupling between the Interior and Atmosphere of the Sun; Astrophysics and Space Science Proceeding

Solar Magnetic Field Reversals and the Role of Dynamo Families

The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case.Comment: Accepted to ApJ; comments/corrections to this article are welcome via e-mail, even after publicatio

A BABCOCK-LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of butterfly wing to an anti-solar type. A butterfly diagram constructed from middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow-speed is strong enough, of similar order of magnitude as the surface flow-speed.Comment: 40 pages, 19 figures, accepted in Ap

The Origin of Solar Activity in the Tachocline

Solar active regions, produced by the emergence of tubes of strong magnetic field in the photosphere, are restricted to within 35 degrees of the solar equator. The nature of the dynamo processes that create and renew these fields, and are therefore responsible for solar magnetic phenomena, are not well understood. We analyze the magneto-rotational stability of the solar tachocline for general field geometry. This thin region of strong radial and latitudinal differential rotation, between the radiative and convective zones, is unstable at latitudes above 37 degrees, yet is stable closer to the equator. We propose that small-scale magneto-rotational turbulence prevents coherent magnetic dynamo action in the tachocline except in the vicinity of the equator, thus explaining the latitudinal restriction of active regions. Tying the magnetic dynamo to the tachocline elucidates the physical conditions and processes relevant to solar magnetism.Comment: 10 pages, 1 figure, accepted for publication in ApJ

Numerical Calculation of Convection with Reduced Speed of Sound Technique

Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential equation. Frequent global communication is negative factor for the parallel computing with a large number of CPUs. Aims. The main purpose of this paper is to test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. The reduction of speed of sound allows for larger time steps in spite of low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic and thus does not require frequent global communication. Methods. Two and three dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (due to reduction of speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the reduced speed of sound) remains less than 0.7.Comment: 16 pages, 10 figures, accepted to A&

Solar Polar Fields During Cycles 21 --- 23: Correlation with Meridional Flows

We have examined polar magnetic fields for the last three solar cycles, {$\it{viz.}$}, cycles 21, 22 and 23 using NSO Kitt Peak synoptic magnetograms. In addition, we have used SoHO/MDI magnetograms to derive the polar fields during cycle 23. Both Kitt Peak and MDI data at high latitudes (78${^{\circ}}$--90${^{\circ}}$) in both solar hemispheres show a significant drop in the absolute value of polar fields from the late declining phase of the solar cycle 22 to the maximum of the solar cycle 23. We find that long term changes in the absolute value of the polar field, in cycle 23, is well correlated with changes in meridional flow speeds that have been reported recently. We discuss the implication of this in influencing the extremely prolonged minimum experienced at the start of the current cycle 24 and in forecasting the behaviour of future solar cycles.Comment: 4 Figures 11 pages; Revised version under review in Solar Physic