Origin of the hemispheric asymmetry of solar activity

The frequency spectrum of the hemispheric asymmetry of solar activity shows enhanced power for the period ranges around 8.5 years and between 30 and 50 years. This can be understood as the sum and beat periods of the superposition of two dynamo modes: a dipolar mode with a (magnetic) period of about 22 years and aquadrupolar mode with a period between 13 and 15 years. An updated Babcock-Leighton-type dynamo model with weak driving as indicated by stellar observations shows an excited dipole mode and a damped quadrupole mode in the correct range of periods. Random excitation of the quadrupole by stochastic fluctuations of the source term for the poloidal field leads to a time evolution of activity and asymmetry that is consistent with the observational results.Comment: Astronomy & Astrophysics, accepte

Are the strengths of solar cycles determined by converging flows towards the activity belts?

It is proposed that the observed near-surface inflows towards the active regions and sunspot zones provide a nonlinear feedback mechanism that limits the amplitude of a Babcock-Leighton-type solar dynamo and determines the variation of the cycle strength. This hypothesis is tested with surface flux transport simulations including converging latitudinal flows that depend on the surface distribution of magnetic flux. The inflows modulate the build-up of polar fields (represented by the axial dipole) by reducing the tilt angles of bipolar magnetic regions and by affecting the cross-equator transport of leading-polarity magnetic flux. With flux input derived from the observed record of sunspot groups, the simulations cover the period between 1874 and 1980 (corresponding to solar cycles 11 to 20). The inclusion of the inflows leads to a strong correlation of the simulated axial dipole strength during activity minimum with the observed amplitude of the subsequent cycle. This in agreement with empirical correlations and in line with what is expected from a Babcock-Leighton-type dynamo. The results provide evidence that the latitudinal inflows are a key ingredient in determining the amplitude of solar cycles.Comment: accepted in A&

Penumbral structure and outflows in simulated sunspots

Sunspots are concentrations of magnetic field on the visible solar surface that strongly affect the convective energy transport in their interior and surroundings. The filamentary outer regions (penumbrae) of sunspots show systematic radial outward flows along channels of nearly horizontal magnetic field. These flows were discovered 100 years ago and are present in all fully developed sunspots. Using a comprehensive numerical simulation of a sunspot pair, we show that penumbral structures with such outflows form when the average magnetic field inclination to the vertical exceeds about 45 degrees. The systematic outflows are a component of the convective flows that provide the upward energy transport and result from anisotropy introduced by the presence of the inclined magnetic field.Comment: 19 pages, 8 figures, main Science article + supporting online material combined into one fil

Surface flux transport modeling for solar cycles 15--21: effects of cycle-dependent tilt angles of sunspot groups

We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycle-to-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux, and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.Comment: Accepted for publication by Ap

The Complexity of the List Partition Problem for Graphs

The k-partition problem is as follows: Given a graph G and a positive integer k, partition the vertices of G into at most k parts A1, A2, . . . , Ak, where it may be specified that Ai induces a stable set, a clique, or an arbitrary subgraph, and pairs Ai, Aj (i≠j) be completely nonadjacent, completely adjacent, or arbitrarily adjacent. The list k-partition problem generalizes the k-partition problem by specifying for each vertex x, a list L(x) of parts in which it is allowed to be placed. Many well-known graph problems can be formulated as list k-partition problems: e.g., 3-colorability, clique cutset, stable cutset, homogeneous set, skew partition, and 2-clique cutset. We classify, with the exception of two polynomially equivalent problems, each list 4-partition problem as either solvable in polynomial time or NP-complete. In doing so, we provide polynomial-time algorithms for many problems whose polynomial-time solvability was open, including the list 2-clique cutset problem. This also allows us to classify each list generalized 2-clique cutset problem and list generalized skew partition problem as solvable in polynomial time or NP-complete

Mesogranular structure in a hydrodynamical simulation

We analyse mesogranular flow patterns in a three-dimensional hydrodynamical simulation of solar surface convection in order to determine its characteristics. We calculate divergence maps from horizontal velocities obtained with the Local Correlation Tracking (LCT) method. Mesogranules are identified as patches of positive velocity divergence. We track the mesogranules to obtain their size and lifetime distributions. We vary the analysis parameters to verify if the pattern has characteristic scales. The characteristics of the resulting flow patterns depend on the averaging time and length used in the analysis. We conclude that the mesogranular patterns do not exhibit intrinsic length and time scales

Observing and modeling the poloidal and toroidal fields of the solar dynamo

Context. The solar dynamo consists of a process that converts poloidal field to toroidal field followed by a process which creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We use synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories to construct the poloidal field as a function of time and latitude, and Wilcox Solar Observatory and SOHO/MDI full disk images to infer the longitudinally averaged surface azimuthal field. We show that the latter is consistent with an estimate of that due to flux emergence and therefore closely related to the subsurface toroidal field. Results. We present maps of the poloidal and toroidal magnetic field of the global solar dynamo. The longitude-averaged azimuthal field observed at the surface results from flux emergence. At high latitudes this component follows the radial component of the polar fields with a short time lag (1-3 years). The lag increases at lower latitudes. The observed evolution of the poloidal and toroidal magnetic fields is described by the (updated) Babcock-Leighton dynamo model.Comment: A&

The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolomogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large scale radiative hydrodynamic simulations. We reach two primary conclusions: 1. The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. 2. Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large scale modes in the deep layers are artificially reduced. Since the large scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small scale convective correlations are maintained through the bulk of the solar convection zone.Comment: 36 pages, 6 figure

Limits to solar cycle predictability: Cross-equatorial flux plumes

Within the Babcock-Leighton framework for the solar dynamo, the strength of a cycle is expected to depend on the strength of the dipole moment or net hemispheric flux during the preceding minimum, which depends on how much flux was present in each hemisphere at the start of the previous cycle and how much net magnetic flux was transported across the equator during the cycle. Some of this transport is associated with the random walk of magnetic flux tubes subject to granular and supergranular buffeting, some of it is due to the advection caused by systematic cross-equatorial flows such as those associated with the inflows into active regions, and some crosses the equator during the emergence process. We aim to determine how much of the cross-equatorial transport is due to small-scale disorganized motions (treated as diffusion) compared with other processes such as emergence flux across the equator. We measure the cross-equatorial flux transport using Kitt Peak synoptic magnetograms, estimating both the total and diffusive fluxes. Occasionally a large sunspot group, with a large tilt angle emerges crossing the equator, with flux from the two polarities in opposite hemispheres. The largest of these events carry a substantial amount of flux across the equator (compared to the magnetic flux near the poles). We call such events cross-equatorial flux plumes. There are very few such large events during a cycle, which introduces an uncertainty into the determination of the amount of magnetic flux transported across the equator in any particular cycle. As the amount of flux which crosses the equator determines the amount of net flux in each hemisphere, it follows that the cross-equatorial plumes introduce an uncertainty in the prediction of the net flux in each hemisphere. This leads to an uncertainty in predictions of the strength of the following cycle.Comment: A&A, accepte