Andres Munoz-Jaramillo

HELIOSEISMIC DATA INCLUSION IN SOLAR DYNAMO MODELS

An essential ingredient in kinematic dynamo models of the solar cycle is the internal velocity field within the simulation domain—the solar convection zone (SCZ). In the last decade or so, the field of helioseismology has revolutionized our understanding of this velocity field. In particular, the internal differential rotation of the Sun is now fairly well constrained by helioseismic observations almost throughout the SCZ. Helioseismology also gives us some information about the depth dependence of the meridional circulation in the near-surface layers of the Sun. The typical velocity inputs used in solar dynamo models, however, continue to be an analytic fit to the observed differential rotation profile and a theoretically constructed meridional circulation profile that is made to match the flow speed only at the solar surface. Here, we take the first steps toward the use of more accurate velocity fields in solar dynamo models by presenting methodologies for constructing differential rotation and meridional circulation profiles that more closely conform to the best observational constraints currently available. We also present kinematic dynamo simulations driven by direct helioseismic measurements for the rotation and four plausible profiles for the internal meridional circulation—all of which are made to match the helioseismically inferred near-surface depth dependence, but whose magnitudes are made to vary. We discuss how the results from these dynamo simulations compare with those that are driven by purely analytic fits to the velocity field. Our results and analysis indicate that the latitudinal shear in the rotation in the bulk of the SCZ plays a more important role, than either the tachocline or surface radial shear, in the induction of the toroidal field. We also find that it is the speed of the equatorward counterflow in the meridional circulation right at the base of the SCZ, and not how far into the radiative interior it penetrates, that primarily determines the dynamo cycle period. Improved helioseismic constraints are expected to be available from future space missions such as the Solar Dynamics Observatory and through analysis of more long-term continuous data sets from ground-based instruments such as the Global Oscillation Network Group. Our analysis lays the basis for the assimilation of these helioseismic data within dynamo models to make future solar cycle simulations more realistic.

A DOUBLE-RING ALGORITHM FOR MODELING SOLAR ACTIVE REGIONS: UNIFYING KINEMATIC DYNAMO MODELS AND SURFACE FLUX-TRANSPORT SIMULATIONS

The emergence of tilted bipolar active regions (ARs) and the dispersal of their flux, mediated via processes such as diffusion, differential rotation, and meridional circulation, is believed to be responsible for the reversal of the Suns polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed α-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithm for modeling the Babcock-Leighton mechanism based on AR eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations, we first show that an axisymmetric formulation—which is usually invoked in kinematic dynamo models—can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models.The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric-average of the dynamically quenched diffusivity. Here, we provide an analytic fit to the dynamically quenched diffusivity profile, which can be used in kinematic dynamo simulations. Having successfully reconciled the mixing-length theory estimated diffusivity profile with kinematic dynamo models, we argue that they remain a viable tool for understanding the solar magnetic cycle.

Small-scale and Global Dynamos and the Area and Flux Distributions of Active Regions, Sunspot Groups, and Sunspots: A Multi-database Study

In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions -- where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above)

The Minimum of Solar Cycle 23: As Deep as It Could Be?

10^{21}

POLAR NETWORK INDEX AS A MAGNETIC PROXY FOR THE SOLAR CYCLE STUDIES

Mx (

Parameter optimization for surface flux transport models.

10^{22}

How Many Active Regions Are Necessary to Predict the Solar Dipole Moment

Mx). We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended into smaller fluxes), making our results compatible with the results of Parnell et al. (2009).

The Extended Solar Cycle: Muddying the Waters of Solar/Stellar Dynamo Modeling Or Providing Crucial Observational Constraints?

In this work we introduce a new way of binning sunspot group data with the purpose of better understanding the impact of the solar cycle on sunspot properties and how this defined the characteristics of the extended minimum of cycle 23. Our approach assumes that the statistical properties of sunspots are completely determined by the strength of the underlying large-scale field and have no additional time dependencies. We use the amplitude of the cycle at any given moment (something we refer to as activity level) as a proxy for the strength of this deep-seated magnetic field. We find that the sunspot size distribution is composed of two populations: one population of groups and active regions and a second population of pores and ephemeral regions. When fits are performed at periods of different activity level, only the statistical properties of the former population, the active regions, is found to vary. Finally, we study the relative contribution of each component (small-scale versus large-scale) to solar magnetism. We find that when hemispheres are treated separately, almost every one of the past 12 solar minima reaches a point where the main contribution to magnetism comes from the small-scale component. However, due to asymmetries in cycle phase, this state is very rarely reached by both hemispheres at the same time. From this we infer that even though each hemisphere did reach the magnetic baseline, from a heliospheric point of view the minimum of cycle 23 was not as deep as it could have been.

Contextualizing Solar Cycle 24: Report on the Development of a Homogenous Database of Bipolar Active Regions Spanning Four Cycles

The Sun has a polar magnetic field which oscillates with the 11 yr sunspot cycle. This polar magnetic field is an important component of the dynamo process which operates in the solar convection zone and produces the sunspot cycle. We have direct systematic measurements of the Suns polar magnetic field only from about the mid-1970s. There are, however, indirect proxies which give us information about this field at earlier times. The Ca-K spectroheliograms taken at the Kodaikanal Solar Observatory during 1904-2007 have now been digitized with 4k x 4k CCD and have higher resolution (similar to 0.86 arcsec) than the other available historical data sets. From these Ca-K spectroheliograms, we have developed a completely new proxy (polar network index, hereafter PNI) for the Suns polar magnetic field. We calculate PNI from the digitized images using an automated algorithm and calibrate our measured PNI against the polar field as measured by the Wilcox Solar Observatory for the period 1976-1990. This calibration allows us to estimate the polar fields for the earlier period up to 1904. The dynamo calculations performed with this proxy as input data reproduce reasonably well the Suns magnetic behavior for the past century.

Area and Flux Distributions of Active Regions, Sunspot Groups, and Sunspots: A Multi-Database Study

Accurate prediction of solar activity calls for precise calibration of solar cycle models. Consequently we aim to find optimal parameters for models which describe the physical processes on the solar surface, which in turn act as proxies for what occurs in the interior and provide source terms for coronal models. We use a genetic algorithm to optimize surface flux transport models using National Solar Observatory (NSO) magnetogram data for Solar Cycle 23. This is applied to both a 1D model that inserts new magnetic flux in the form of idealized bipolar magnetic regions, and also to a 2D model that assimilates specific shapes of real active regions. The genetic algorithm searches for parameter sets (meridional flow speed and profile, supergranular diffusivity, initial magnetic field, and radial decay time) that produce the best fit between observed and simulated butterfly diagrams, weighted by a latitude-dependent error structure which reflects uncertainty in observations. Due to the easily adaptable nature of the 2D model, the optimization process is repeated for Cycles 21, 22, and 24 in order to analyse cycle-to-cycle variation of the optimal solution. We find that the ranges and optimal solutions for the various regimes are in reasonable agreement with results from the literature, both theoretical and observational. The optimal meridional flow profiles for each regime are almost entirely within observational bounds determined by magnetic feature tracking, with the 2D model being able to accommodate the mean observed profile more successfully. Differences between models appear to be important in deciding values for the diffusive and decay terms. In like fashion, differences in the behaviours of different solar cycles lead to contrasts in parameters defining the meridional flow and initial field strength.