Structure and Evolution of Giant Cells in Global Models of Solar Convection

The global scales of solar convection are studied through three-dimensional simulations of compressible convection carried out in spherical shells of rotating fluid which extend from the base of the convection zone to within 15 Mm of the photosphere. Such modelling at the highest spatial resolution to date allows study of distinctly turbulent convection, revealing that coherent downflow structures associated with giant cells continue to play a significant role in maintaining the strong differential rotation that is achieved. These giant cells at lower latitudes exhibit prograde propagation relative to the mean zonal flow, or differential rotation, that they establish, and retrograde propagation of more isotropic structures with vortical character at mid and high latitudes. The interstices of the downflow networks often possess strong and compact cyclonic flows. The evolving giant-cell downflow systems can be partly masked by the intense smaller scales of convection driven closer to the surface, yet they are likely to be detectable with the helioseismic probing that is now becoming available. Indeed, the meandering streams and varying cellular subsurface flows revealed by helioseismology must be sampling contributions from the giant cells, yet it is difficult to separate out these signals from those attributed to the faster horizontal flows of supergranulation. To aid in such detection, we use our simulations to describe how the properties of giant cells may be expected to vary with depth, how their patterns evolve in time, and analyze the statistical features of correlations within these complex flow fields.Comment: 22 pages, 16 figures (color figures are low res), uses emulateapj.cls Latex class file, Results shown during a Press release at the AAS meeting in June 2007. Submitted to Ap

Solar Multi-Scale Convection and Rotation Gradients Studied in Shallow Spherical Shells

The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and mid-latitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients, and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller-scale convective overturning motions comparable in size to solar supergranulation (20--40 Mm). We find that convection within these simulations spans a large range of horizontal scales, and that the radial angular velocity gradient in these models is typically negative, especially in low- and mid-latitude regions. Analyses of the angular momentum transport indicates that such gradients are maintained by Reynolds stresses associated with the convection, transporting angular momentum inward to balance the outward transport achieved by viscous diffusion and large-scale flows in the meridional plane. We suggest that similar mechanisms associated with smaller-scale convection in the sun may contribute to the maintenance of the observed radial shear layer located immediately below the solar photosphere.Comment: 45 pages, 17 figures, ApJ in press. A preprint of paper with hi-res figures can be found at http://www-lcd.colorado.edu/~derosa/modelling/modelling.htm

Inferring Maps of the Sun's Far-side Unsigned Magnetic Flux from Far-side Helioseismic Images using Machine Learning Techniques

Accurate modeling of the Sun's coronal magnetic field and solar wind structures require inputs of the solar global magnetic field, including both the near and far sides, but the Sun's far-side magnetic field cannot be directly observed. However, the Sun's far-side active regions are routinely monitored by helioseismic imaging methods, which only require continuous near-side observations. It is therefore both feasible and useful to estimate the far-side magnetic-flux maps using the far-side helioseismic images despite their relatively low spatial resolution and large uncertainties. In this work, we train two machine-learning models to achieve this goal. The first machine-learning training pairs simultaneous SDO/HMI-observed magnetic-flux maps and SDO/AIA-observed EUV 304$\r{A}$ images, and the resulting model can convert 304$\r{A}$ images into magnetic-flux maps. This model is then applied on the STEREO/EUVI-observed far-side 304$\r{A}$ images, available for about 4.3 years, for the far-side magnetic-flux maps. These EUV-converted magnetic-flux maps are then paired with simultaneous far-side helioseismic images for a second machine-learning training, and the resulting model can convert far-side helioseismic images into magnetic-flux maps. These helioseismically derived far-side magnetic-flux maps, despite their limitations in spatial resolution and accuracy, can be routinely available on a daily basis, providing useful magnetic information on the Sun's far side using only the near-side observations.Comment: Accepted by Ap

Implications of Different Solar Photospheric Flux-Transport Models for Global Coronal and Heliospheric Modeling

The concept of surface-flux transport (SFT) is commonly used in evolving models of the large-scale solar surface magnetic field. These photospheric models are used to determine the large-scale structure of the overlying coronal magnetic field, as well as to make predictions about the fields and flows that structure the solar wind. We compare predictions from two SFT models for the solar wind, open magnetic field footpoints, and the presence of coronal magnetic null points throughout various phases of a solar activity cycle, focusing on the months of April in even-numbered years between 2012 and 2020, inclusive. We find that there is a solar cycle dependence to each of the metrics considered, but there is not a single phase of the cycle in which all the metrics indicate good agreement between the models. The metrics also reveal large, transient differences between the models when a new active region is rotating into the assimilation window. The evolution of the surface flux is governed by a combination of large scale flows and comparatively small scale motions associated with convection. Because the latter flows evolve rapidly, there are intervals during which their impact on the surface flux can only be characterized in a statistical sense, thus their impact is modeled by introducing a random evolution that reproduces the typical surface flux evolution. We find that the differences between the predicted properties are dominated by differences in the model assumptions and implementation, rather than selection of a particular realization of the random evolution.Comment: Accepted for publication in The Astrophysical Journa

A Method for Data-Driven Simulations of Evolving Solar Active Regions

We present a method for performing data-driven simulations of solar active region formation and evolution. The approach is based on magnetofriction, which evolves the induction equation assuming the plasma velocity is proportional to the Lorentz force. The simulations of active region coronal field are driven by temporal sequences of photospheric magnetograms from the Helioseismic Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). Under certain conditions, the data-driven simulations produce flux ropes that are ejected from the modeled active region due to loss of equilibrium. Following the ejection of flux ropes, we find an enhancement of the photospheric horizontal field near the polarity inversion line. We also present a method for the synthesis of mock coronal images based on a proxy emissivity calculated from the current density distribution in the model. This method yields mock coronal images that are somewhat reminiscent of images of active regions taken by instruments such as SDO's Atmospheric Imaging Assembly (AIA) at extreme ultraviolet wavelengths.Comment: Accepted to ApJ; comments/questions related to this article are welcome via e-mail, even after publicatio

Global MHD Simulations of the Time-Dependent Corona

We describe, test, and apply a technique to incorporate full-sun, surface flux evolution into an MHD model of the global solar corona. Requiring only maps of the evolving surface flux, our method is similar to that of Lionello et al. (2013), but we introduce two ways to correct the electric field at the lower boundary to mitigate spurious currents. We verify the accuracy of our procedures by comparing to a reference simulation, driven with known flows and electric fields. We then present a thermodynamic MHD calculation lasting one solar rotation driven by maps from the magnetic flux evolution model of Schrijver & DeRosa (2003). The dynamic, time-dependent nature of the model corona is illustrated by examining the evolution of the open flux boundaries and forward modeled EUV emission, which evolve in response to surface flows and the emergence and cancellation flux. Although our main goal is to present the method, we briefly investigate the relevance of this evolution to properties of the slow solar wind, examining the mapping of dipped field lines to the topological signatures of the "S-Web" and comparing charge state ratios computed in the time-dependently driven run to a steady state equivalent. Interestingly, we find that driving on its own does not significantly improve the charge states ratios, at least in this modest resolution run that injects minimal helicity. Still, many aspects of the time-dependently driven model cannot be captured with traditional steady-state methods, and such a technique may be particularly relevant for the next generation of solar wind and CME models

Large-Scale Spatial Cross-Calibration of Hinode/SOT-SP and SDO/HMI

We investigate the cross-calibration of the Hinode/SOT-SP and SDO/HMI instrument meta-data, specifically the correspondence of the scaling and pointing information. Accurate calibration of these datasets gives the correspondence needed by inter-instrument studies and learning-based magnetogram systems, and is required for physically-meaningful photospheric magnetic field vectors. We approach the problem by robustly fitting geometric models on correspondences between images from each instrument's pipeline. This technique is common in computer vision, but several critical details are required when using scanning slit spectrograph data like Hinode/SOT-SP. We apply this technique to data spanning a decade of the Hinode mission. Our results suggest corrections to the published Level 2 Hinode/SOT-SP data. First, an analysis on approximately 2,700 scans suggests that the reported pixel size in Hinode/SOT-SP Level 2 data is incorrect by around 1%. Second, analysis of over 12,000 scans show that the pointing information is often incorrect by dozens of arcseconds with a strong bias. Regression of these corrections indicates that thermal effects have caused secular and cyclic drift in Hinode/SOT-SP pointing data over its mission. We offer two solutions. First, direct co-alignment with SDO/HMI data via our procedure can improve alignments for many Hinode/SOT-SP scans. Second, since the pointing errors are predictable, simple post-hoc corrections can substantially improve the pointing. We conclude by illustrating the impact of this updated calibration on derived physical data products needed for research and interpretation. Among other things, our results suggest that the pointing errors induce a hemispheric bias in estimates of radial current density.Comment: Under revisions at ApJ

First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted Force-Free Fields

The three-dimensional (3D) coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 Apr 30, May 9, May 19, Dec 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of $\mu=19^\circ-46^\circ$ for a potential field model, which is reduced to $\mu=14^\circ-19^\circ$ for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors ($\mu_{SE} \approx 8^\circ-12^\circ$). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components $(B_x, B_y, B_z)$, as well as a non-potential field forward-fitting code that determines the full length of twisted loops ($L \approx 50-300$ Mm), the number of twist turns (median $N_{twist}=0.06$), the nonlinear force-free $\alpha$-parameter (median $\alpha \approx 4 \times 10^{-11}$ cm$^{-1}$), and the current density (median $j_z \approx 1500$ Mx cm$^{-2}$ s$^{-1}$). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found be be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter $\alpha$), represents the first code that enables fast forward-fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.Comment: The Astrophysical Journal (in press), 37 pages, 14 Figure