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

Genetical and cytological studies in the genus Solanum

The present study is concerned primarily with the behaviour of the chromosomes and their secondary associations at meiosis in six "diploid" species with a view to determine the much discussed basic number in the potatoes. So far investigation of this type has dealt only with the commercial varieties of Solarium tuberosum L., (Ellison l935) and its "diploid and triploid representatives" (M1ntzing 1933), on the basis of the recent interpretation of secondary association of chromosomes. Special attention has also been given here to two interspecific hybrids to determine the homology of their chromosomes

Patterns of primary beam non-redundancy in close-packed 21 cm array observations

Radio interferometer arrays such as HERA consist of many close-packed dishes arranged in a regular pattern, giving rise to a large number of `redundant' baselines with the same length and orientation. Since identical baselines should see an identical sky signal, this provides a way of finding a relative gain/bandpass calibration without needing an explicit sky model. In reality, there are many reasons why baselines will not be exactly identical, giving rise to a host of effects that spoil the redundancy of the array and induce spurious structure in the calibration solutions if not accounted for. In this paper, we perform a wide range of simulations for a small HERA-like array to understand how different types of non-redundancy manifest in the observed interferometric visibilities and their resulting frequency (delay-space) power spectra. We focus in particular on differences in the primary beam response between antennas, including variations in the main lobe, sidelobes, ellipticity, and orientation. We find that different types of non-redundancy impart characteristic patterns into the redundant gain solutions, which in turn introduce additional structure into the calibrated visibilities and therefore the delay spectra. We show that the most severe effects of primary beam non-redundancy are induced by the brightest sources passing through the beam, while diffuse emission has a lesser (but non-negligible) effect. We also find that redundant baseline groups with `outlier' antennas (where only one antenna deviates from perfect redundancy) sustain the largest gain errors, while even $\mathcal{O}(1)$ non-redundancies in the sidelobes seem to have a relatively minor impact in comparison.Comment: 19 pages, 14 figures, to be submitted in MNRA

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&

Quenching of Meridional Circulation in Flux Transport Dynamo Models

Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2 * 10^{11} cm^2/s. The quenching of alpha, however, has a stabilizing effect and it is possible to stabilize a dynamo with low diffusivity with sufficiently strong alpha-quenching. For dynamo models with high diffusivity, the quenching of meridional circulation does not produce a large effect and the dynamo remains stable. We present a solar-like solution from a dynamo model with diffusivity 2.8 * 10^{12} cm^2/s in which the quenching of meridional circulation makes the meridional circulation vary periodically with solar cycle as observed and does not have any other significant effect on the dynamo.Comment: Consistent with the published version. Solar Physics, in pres

Viscosity in spherically symmetric accretion

The influence of viscosity on the flow behaviour in spherically symmetric accretion, has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length-scale has been compared with the conventional understanding of the so-called "accretion radius" for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions -- an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system, than has been seen for the case of inviscid spherically symmetric inflows.Comment: 7 pages. Minor changes made in the version published in MNRA

Characteristics of solar meridional flows during solar cycle 23

We have analyzed available full-disc data from the Michelson Doppler Imager (MDI) on board SoHO using the "ring diagram" technique to determine the behavior of solar meridional flows over solar cycle 23 in the outer 2% of the solar radius. We find that the dominant component of meridional flows during solar maximum was much lower than that during the minima at the beginning of cycles 23 and 24. There were differences in the flow velocities even between the two minima. The meridional flows show a migrating pattern with higher-velocity flows migrating towards the equator as activity increases. Additionally, we find that the migrating pattern of the meridional flow matches those of sunspot butterfly diagram and the zonal flows in the shallow layers. A high latitude band in meridional flow appears around 2004, well before the current activity minimum. A Legendre polynomial decomposition of the meridional flows shows that the latitudinal pattern of the flow was also different during the maximum as compared to that during the two minima. The different components of the flow have different time-dependences, and the dependence is different at different depths.Comment: To appear in Ap

The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journa

Current helicity of active regions as a tracer of large-scale solar magnetic helicity

We demonstrate that the current helicity observed in solar active regions traces the magnetic helicity of the large-scale dynamo generated field. We use an advanced 2D mean-field dynamo model with dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtained butterfly diagrams both for the small-scale current helicity and also for the large-scale magnetic helicity, and compared them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by $-{\bf A \cdot B}$ evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here ${\bf B}$ and ${\bf A}$ are respectively the dynamo generated mean magnetic field and its vector potential. A theoretical interpretation of these results is given.Comment: 11 pages, 5 figures, revised versio