J. Todd Hoeksema

Evolution of Magnetic Field and Energy in a Major Eruptive Active Region Based on SDO/HMI Observation

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ∼2.6 × 10 32 erg, about 50% of which is stored below 6 Mm. It decreases by ∼0.3 × 10 32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field “implosion”, and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more “compact” after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.

Prediction of the interplanetary magnetic field strength

A new model of the coronal and interplanetary magnetic field can predict both the interplanetary magnetic field strength and its polarity from measurements of the photospheric magnetic field. The model includes the effects of the large-scale horizontal electric currents flowing in the inner corona, of the warped heliospheric current sheet in the upper corona, and of volume currents flowing in the region where the solar wind plasma totally controls the magnetic field. The model matches the MHD solution for a simple dipole test case better than earlier source surface and current sheet models. The strength and polarity of the radial interplanetary magnetic field component predicted for quiet time samples in each year from 1977 to 1986 agree with observations made near the Earths orbit better than the hybrid MHD-source surface model (Wang and Sheeley, 1988). The results raise the question of whether coronal holes are the only solar source of the interplanetary magnetic field in the solar wind. If some interplanetary flux originates outside coronal holes, the model can match the observed field using the accepted 1.8 saturation correction factor for λ5250 A magnetograph observations. Requiring open flux to come exclusively from coronal holes requires an additional factor of two.

Large-scale solar and heliospheric magnetic fields

Abstract The magnetic structure of the extended solar corona varies with the changing photospheric field during the solar cycle. A simple potential model of the corona using solar surface observations from 1976 to the present shows how the large-scale coronal field evolves over more than a solar activity cycle. These predictions match well with large stable structures inferred from measurements of coronal electron density and the interplanetary magnetic field (IMF), though dynamic changes are poorly modeled. The Suns polar field was about 25% stronger at solar minimum in 1986 than in 1976; the heliospheric current sheet was also flatter. In Cycle 21 the coronal and photospheric large-scale long-lived field patterns rotated every 26.9 days in the northern hemisphere; the southern field rotated every 28 days. Similar periods have been present in the IMF and in the occurrence of solar flares during the last several solar cycles. Improved understanding will require more comprehensive physical models, more accurate and continuous photospheric field observations, and more complete coronal data at all heights and latitudes with which to compare and test the models. Important observations with improved accuracy and better spatial and temporal resolution will be provided by instruments on future space missions.

Extending the sun's magnetic field through the three-dimensional heliosphere

Abstract The Suns magnetic field determines the configuration of the three-dimensional heliospheric field. Measurements, inferences, and computations of the magnetic field in the corona near the Sun, extended out to 1 or 2 AU, correspond fairly well with the measurements of the interplanetary magnetic field structure. Transient and activity related events are superposed on a slowly evolving background field configuration composed primarily of dipole and quadrupole components that vary in absolute and relative intensity and in orientation during the solar cycle. The heliospheric current sheet (HCS) separates regions of the heliosphere having different interplanetary magnetic field polarity, either toward or away from the Sun. During most of the solar cycle the HCS has a fairly simple configuration: it is roughly symmetric about the solar equator, but has 2 or 4 warps of varying latitudinal extent. Near solar minimum the HCS reaches less than 20° from the equator, but during most of the cycle it extends much nearer the poles. At solar maximum the polar fields weaken and reverse; then the HCS extends all the way to the poles. During this period there may be multiple current sheets. During the declining phase of the cycle the HCS is simpler and sometimes looks like a tilted dipole. Field structures of the northern and southern hemispheres rotate at different rates in Cycle 21 and perhaps in several earlier cycles as well. Extrapolating the structure farther into the heliosphere is problematic. Small variations and perturbations of the solar wind near the Sun are amplified with increasing distance and the simple structure breaks down. Even the stability of the large-scale structure from one rotation to the next is greatly diminished at large distances.

HOT SPINE LOOPS AND THE NATURE OF A LATE-PHASE SOLAR FLARE

The fan-spine magnetic topology is believed to be responsible for many curious emission signatures in solar explosive events. A spine field line links topologically distinct flux domains, but direct observation of such structure has been rare. Here we report a unique event observed by the Solar Dynamic Observatory (SDO) where a set of hot coronal loops (over 10 MK) that developed during the rising phase of a flare connected to a quasi-circular ribbon at one end and a remote brightening at the other. Magnetic field extrapolation suggests these loops are partly tracers of the evolving spine field line. The sequential brightening of the ribbon, the apparent shuffling loop motion, and the increasing volume occupied by the hot loops suggest that continuous slipping- and null-point-type reconnections were at work, energizing the loop plasma and transferring magnetic flux within and across the dome-shaped, fan quasi-separatrix layer (QSL). We argue that the initial reconnection is of the “breakout” type, which then transitioned to a more violent flare reconnection nearing the flare peak with an eruption from the fan dome. Significant magnetic field changes are expected and indeed ensued, which include a change of the horizontal photospheric field, a shift of the QSL footprint, and reduction in shear of the coronal loops. This event also features an extreme-ultraviolet (EUV) late phase, i.e. a secondary emission peak observed in warm EUV lines (about 2‐7 MK) as much as 1‐2 hours after the soft X-ray peak. We show that this peak comes from the large post-reconnection loops beside and above the compact fan dome, a direct product of eruption in such topological settings. Cooling of these “late-phase arcades” naturally explains the sequential delay of the late-phase peaks in increasingly cooler EUV lines. The long cooling time of the large arcades contributes to the long delay; additional heating may also be required. Our result demonstrates the critical nature of cross-scale magnetic coupling ‐ minor topological change in a sub-system may lead to explosions on a much larger scale. Subject headings: Sun: activity — Sun: corona — Sun: flares — Sun: surface magnetism — Sun: magnetic topology

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.

DATA-DRIVEN MAGNETOHYDRODYNAMIC MODEL FOR ACTIVE REGION EVOLUTION

We present a self-consistent, three-dimensional, magnetohydrodynamics model together with time-dependent boundary conditions based on the projected method of characteristics at the source surface (photosphere) to accommodate the observations. The new physics included in this model are differential rotation, meridional flow, effective diffusion, and cyclonic turbulence effects in which the complex magnetic field structure can be generated through the nonlinear interaction between the plasma and magnetic field. This solution, again, is accomplished by including the time-dependent boundary conditions derived from the method of characteristics. This procedure is able to accommodate observations via self-consistent and appropriate data inputs to the boundary. Thus, subphotospheric (i.e., convective zone) effects, through observations, are able to be coupled with the corona. To illustrate this new model, we have employed an observed active regions (NOAA AR 8100) magnetic field measurements from SOHO MDI magnetograms to demonstrate the models capability. Thus, the evolution of three-dimensional magnetic field, velocity field, and energy transport are shown, thereby enabling us to study the physical mechanisms of AR evolution.

ON POLAR MAGNETIC FIELD REVERSAL AND SURFACE FLUX TRANSPORT DURING SOLAR CYCLE 24

As each solar cycle progresses, remnant magnetic flux from active regions (ARs) migrates poleward to cancel the old-cycle polar field. We describe this polarity reversal process during Cycle 24 using four years (2010.33--2014.33) of line-of-sight magnetic field measurements from the Helioseismic and Magnetic Imager. The total flux associated with ARs reached maximum in the north in 2011, more than two years earlier than the south; the maximum is significantly weaker than Cycle 23. The process of polar field reversal is relatively slow, north-south asymmetric, and episodic. We estimate that the global axial dipole changed sign in October 2013; the northern and southern polar fields (mean above 60

Stratospheric volcanic aerosols and changes in air-earth current density at solar wind magnetic sector boundaries as conditions for the Wilcox tropospheric vorticity effect

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An atlas of photospheric magnetic field observations and computed coronal magnetic fields: 1976-1985

latitude) reversed in November 2012 and March 2014, respectively, about 16 months apart. Notably, the poleward surges of flux in each hemisphere alternated in polarity, giving rise to multiple reversals in the north. We show that the surges of the trailing sunspot polarity tend to correspond to normal mean AR tilt, higher total AR flux, or slower mid-latitude near-surface meridional flow, while exceptions occur during low magnetic activity. In particular, the AR flux and the mid-latitude poleward flow speed exhibit a clear anti-correlation. We discuss how these features can be explained in a surface flux transport process that includes a field-dependent converging flow toward the ARs, a characteristic that may contribute to solar cycle variability.