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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Testing Fractal Methods on Observed and Simulated Solar Magnetograms

The term "magnetic complexity" has not been sufficiently quantified. To accomplish this, we must understand the relationship between the observed magnetic field of solar active regions and fractal dimension measurements. Using data from the Marshall Space Flight Center's vector magnetograph ranging from December 1991 to July 2001, we compare the results of several methods of calculating a fractal dimension, e.g., Hurst coefficient, the Higuchi method, power spectrum, and 2-D Wavelet Packet Analysis. In addition, we apply these methods to synthetic data, beginning with representations of very simple dipole regions, ending with regions that are magnetically complex.

Adams, M.↗
NASA NTRS2014

First Use of Synoptic Vector Magnetograms for Global Nonlinear, Force-Free Coronal Magnetic Field Models

Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) − E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.

Sun: corona↗
NASA NTRS2006

Magnetic Causes of Solar Coronal Mass Ejections: Dominance of the Free Magnetic Energy Over the Magnetic Twist Alone

We examine the magnetic causes of coronal mass ejections (CMEs) by examining, along with the correlations of active-region magnetic measures with each other, the correlations of these measures with active-region CME productivity observed in time windows of a few days, either centered on or extending forward from the day of the magnetic measurement. The measures are from 36 vector magnetograms of bipolar active regions observed within -30" of disk center by the Marshal Space Flight Center (MSFC) vector magnetograph. From each magnetogram, we extract six whole-active-region measures twice, once from the original plane-of-the-sky magnetogram and again a h r deprojection of the magnetogram to disk center. Three of the measures are alternative measures of the total nonpotentiality of the active region, two are alternative measures of the overall twist in the active-region's magnetic field, and one is a measure of the magnetic size of the active region (the active region's magnetic flux content). From the deprojected magnetograms, we find evidence that (1) magnetic twist and magnetic size are separate but comparably strong causes of active-region CME Productivity, and (2) the total free magnetic energy in an active region's magnetic field is a stronger determinant of the active region's CME productivity than is the field's overall twist (or helicity) alone. From comparison of results from the non-deprojected magnetograms with corresponding results from the deprojected magnetograms, we find evidence that (for prediction of active-region CME productivity and for further studies of active-region magnetic size as a cause of CMEs), for active regions within approx.30deg of disk center, active-region total nonpotentiality and flux content can be adequately measured from line-of-sight magnetograms, such as from SOH0 MDI.

Falconer, D. A.↗
NASA NTRS2004

Measurement Scale of the SOLIS Vector Spectromagnetograph

Longitudinal magnetograms obtained with thc SOLIS Vector Spectromagnetograph (VSM) during a cross-calibration period are compared with similar data from the NASA/NSO Spectromagnetograph (SPM) at the NSO/Kitt Peak Vacuum Telescope as well as with SOHO/MDI and GONG magnetogram. The VSM began observation at the University of Arizona agricultural test site and collaborative observations were obtained with both the VSM and SPM from 2003 Aug 05 through 2003 Sep 21 where the SPM was officially retired. The VSM replaces the SPM and continues the 3O-year NSO/Kitt Peak synoptic magnetogram record. Magnetograms are compared by equating histograms and, for selected examples, by pixel-by-pixel comparison of co-registered images. The VSM was not corrected for polarization crosstalk and was operated without hast guiding. Solar activity was at best moderate during this period. Over the range of observed fields, the VSM magnetograms show greatly improved sensitivity but are otherwise virtually identical with "raw" SPM magnetogram. GONG magnetograms are also closely comparable with the SPM while MDI flux values tend to be stronger by a factor of 1.2 - 1.4. Dependence of the results on seeing will be discussed. Partial funding for this work was provided through Solar and Heliospheric Research Supporting Research and Technology grants from NASA's Office of Space Sciences.

Jones, Harrison P.↗
DOE OSTI2013

A MAGNETIC CALIBRATION OF PHOTOSPHERIC DOPPLER VELOCITIES

The zero point of measured photospheric Doppler shifts is uncertain for at least two reasons: instrumental variations (from, e.g., thermal drifts); and the convective blueshift, a known correlation between intensity and upflows. Accurate knowledge of the zero point is, however, useful for (1) improving estimates of the Poynting flux of magnetic energy across the photosphere, and (2) constraining processes underlying flux cancellation, the mutual apparent loss of magnetic flux in closely spaced, opposite-polarity magnetogram features. We present a method to absolutely calibrate line-of-sight (LOS) velocities in solar active regions (ARs) near disk center using three successive vector magnetograms and one Dopplergram coincident with the central magnetogram. It exploits the fact that Doppler shifts measured along polarity inversion lines (PILs) of the LOS magnetic field determine one component of the velocity perpendicular to the magnetic field, and optimizes consistency between changes in LOS flux near PILs and the transport of transverse magnetic flux by LOS velocities, assuming that ideal electric fields govern the magnetic evolution. Previous calibrations fitted the center-to-limb variation of Doppler velocities, but this approach cannot, by itself, account for residual convective shifts at the limb. We apply our method to vector magnetograms of AR 11158, observed by the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory, and find clear evidence of offsets in the Doppler zero point in the range of 50-550 m s{sup -1}. In addition, we note that a simpler calibration can be determined from an LOS magnetogram and Dopplergram pair from the median Doppler velocity among all near-disk-center PIL pixels. We briefly discuss shortcomings in our initial implementation, and suggest ways to address these. In addition, as a step in our data reduction, we discuss the use of temporal continuity in the transverse magnetic field direction to correct apparently spurious fluctuations in resolution of the 180 Degree-Sign ambiguity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

On the area expansion of magnetic flux tubes in solar active regions

We calculated the three-dimensional (3D) distribution of the area expansion factors in a potential magnetic field, extrapolated from the high-resolution Hinode/SOT magnetogram of the quiescent active region NOAA 11482. Retaining only closed loops within the computational box, we show that the distribution of area expansion factors show significant structure. Loop-like structures characterized by locally lower values of the expansion factor are embedded in a smooth background. These loop-like flux tubes have squashed cross-sections and expand with height. The distribution of the expansion factors show an overall increase with height, allowing an active region core characterized by low values of the expansion factor to be distinguished. The area expansion factors obtained from extrapolation of the Solar Optical Telescope magnetogram are compared to those obtained from an approximation of the observed magnetogram by a series of 134 submerged charges. This approximation retains the general flux distribution in the observed magnetogram, but removes the small-scale structure in both the approximated magnetogram and the 3D distribution of the area expansion factors. We argue that the structuring of the expansion factor can be a significant ingredient in producing the observed structuring of the solar corona. However, due to the potential approximation used, these results may not be applicable to loops exhibiting twist or to active regions producing significant flares.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2009

The Maximum Free Magnetic Energy Allowed in a Solar Active Region

Two whole-active-region magnetic quantities that can be measured from a line-of-sight magnetogram are (sup L) WL(sub SG), a gauge of the total free energy in an active region's magnetic field, and sup L(sub theta), a measure of the active region's total magnetic flux. From these two quantities measured from 1865 SOHO/MDI magnetograms that tracked 44 sunspot active regions across the 0.5 R(sub Sun) central disk, together with each active region's observed production of CMEs, X flares, and M flares, Falconer et al (2009, ApJ, submitted) found that (1) active regions have a maximum attainable free magnetic energy that increases with the magnetic size (sup L) (sub theta) of the active region, (2) in (Log (sup L)WL(sub SG), Log(sup L) theta) space, CME/flare-productive active regions are concentrated in a straight-line main sequence along which the free magnetic energy is near its upper limit, and (3) X and M flares are restricted to large active regions. Here, from (a) these results, (b) the observation that even the greatest X flares produce at most only subtle changes in active region magnetograms, and (c) measurements from MSFC vector magnetograms and from MDI line-of-sight magnetograms showing that practically all sunspot active regions have nearly the same area-averaged magnetic field strength: =- theta/A approximately equal to 300 G, where theta is the active region's total photospheric flux of field stronger than 100 G and A is the area of that flux, we infer that (1) the maximum allowed ratio of an active region's free magnetic energy to its potential-field energy is ~1, and (2) any one CME/flare eruption releases no more than a small fraction (less than ~10%) of the active region's free magnetic energy. This work was funded by NASA's Heliophysics Division and NSF's Division of Atmospheric Sciences.

Moore, Ronald L.↗
NASA NTRS2009

Suppression of Active-Region CME Production by the Presence of Other Active Regions

From the SOHO mission s data base of MDI full-disk magnetograms spanning solar cycle 23, we have obtained a set of ~40,000 magnetograms of ~1,300 active regions, tracking each active region across the 30 degree central solar disk. Each active region magnetogram is cropped from the full-disk magnetogram by an automated code. The cadence is 96 minutes. From each active-region magnetogram, we have measured two whole-active-region magnetic quantities: (1) the magnetic size of the active region (the active region s total magnetic flux), and (2) a gauge of the active region s free magnetic energy (part of the free energy is released in the production of a flare and/or CME eruption). From NOAA Flare/CME catalogs, we have obtained the event (Flare/CME/SEP event) production history of each active region. Using all these data, we find that for each type of eruptive event, an active region s expected rate of event production increases as a power law of our gauge of active-region free magnetic energy. We have also found that, among active regions having nearly the same free energy, the rate of the CME production is less when there are many other active regions on the disk than when there are few or none, but there is no significant discernible suppression of the rate of flare production. This indicates that the presence of other active regions somehow tends to inhibit an active region s flare-producing magnetic explosions from becoming CMEs, contrary to the expectation from the breakout model for the production of CMEs.

Falconer, David↗
DOE OSTI2012

BIPOLAR MAGNETIC REGIONS ON THE SUN: GLOBAL ANALYSIS OF THE SOHO/MDI DATA SET

The magnetic flux that is generated by dynamo processes inside the Sun emerges in the form of bipolar magnetic regions. The properties of these directly observable signatures of the dynamo can be extracted from full-disk solar magnetograms. The most homogeneous, high-quality synoptic data set of solar magnetograms has been obtained with the Michelson Doppler Imager (MDI) instrument on the Solar and Heliospheric Observatory spacecraft during 1995-2011. We have developed an IDL program that has, when applied to the 73,838 magnetograms of the MDI data set, automatically identified 160,079 bipolar magnetic regions that span a range of scale sizes across nearly four orders of magnitude. The properties of each region have been extracted and statistically analyzed, in particular with respect to the polarity orientations of the bipolar regions, including their tilt-angle distributions and their violations of Hale's polarity law. The latitude variation of the average tilt angles (with respect to the E-W direction), which is known as Joy's law, is found to closely follow the relation 32.{sup 0}1 Multiplication-Sign sin (latitude). There is no indication of a dependence on region size that one may expect if the tilts were produced by the Coriolis force during the buoyant rise of flux loops from the tachocline region. A few percent of all regions have orientations that violate Hale's polarity law. We show explicit examples, from different phases of the solar cycle, where well-defined medium-size bipolar regions with opposite polarity orientations occur side by side in the same latitude zone in the same magnetogram. Such oppositely oriented large bipolar regions cannot be part of the same toroidal flux system, but different flux systems must coexist at any given time in the same latitude zones. These examples are incompatible with the paradigm of coherent, subsurface toroidal flux ropes as the source of sunspots, and instead show that fluctuations must play a major role at all scales for the turbulent dynamo. To confirm the profound role of fluctuations at large scales, we show explicit examples in which large bipolar regions differ from the average Joy's law orientation by an amount between 90 Degree-Sign and 100 Degree-Sign . We see no observational support for a separation of scales or a division between a global and a local dynamo, since also the smallest scales in our sample retain a non-random component that significantly contributes to the accumulated emergence of a north-south dipole moment that will lead to the replacement of the old global poloidal field with a new one that has the opposite orientation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

DECORRELATION TIMES OF PHOTOSPHERIC FIELDS AND FLOWS

We use autocorrelation to investigate evolution in flow fields inferred by applying Fourier local correlation tracking (FLCT) to a sequence of high-resolution (0.''3), high-cadence ({approx_equal} 2 minute) line-of-sight magnetograms of NOAA active region (AR) 10930 recorded by the narrowband filter imager of the Solar Optical Telescope aboard the Hinode satellite over 2006 December 12 and 13. To baseline the timescales of flow evolution, we also autocorrelated the magnetograms, at several spatial binnings, to characterize the lifetimes of active region magnetic structures versus spatial scale. Autocorrelation of flow maps can be used to optimize tracking parameters, to understand tracking algorithms' susceptibility to noise, and to estimate flow lifetimes. Tracking parameters varied include: time interval {Delta}t between magnetogram pairs tracked, spatial binning applied to the magnetograms, and windowing parameter {sigma} used in FLCT. Flow structures vary over a range of spatial and temporal scales (including unresolved scales), so tracked flows represent a local average of the flow over a particular range of space and time. We define flow lifetime to be the flow decorrelation time, {tau}. For {Delta}t > {tau}, tracking results represent the average velocity over one or more flow lifetimes. We analyze lifetimes of flow components, divergences, and curls as functions of magnetic field strength and spatial scale. We find a significant trend of increasing lifetimes of flow components, divergences, and curls with field strength, consistent with Lorentz forces partially governing flows in the active photosphere, as well as strong trends of increasing flow lifetime and decreasing magnitudes with increases in both spatial scale and {Delta}t.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

PRIOR FLARING AS A COMPLEMENT TO FREE MAGNETIC ENERGY FOR FORECASTING SOLAR ERUPTIONS

From a large database of (1) 40,000 SOHO/MDI line-of-sight magnetograms covering the passage of 1300 sunspot active regions across the 30 Degree-Sign radius central disk of the Sun, (2) a proxy of each active region's free magnetic energy measured from each of the active region's central-disk-passage magnetograms, and (3) each active region's full-disk-passage history of production of major flares and fast coronal mass ejections (CMEs), we find new statistical evidence that (1) there are aspects of an active region's magnetic field other than the free energy that are strong determinants of the active region's productivity of major flares and fast CMEs in the coming few days; (2) an active region's recent productivity of major flares, in addition to reflecting the amount of free energy in the active region, also reflects these other determinants of coming productivity of major eruptions; and (3) consequently, the knowledge of whether an active region has recently had a major flare, used in combination with the active region's free-energy proxy measured from a magnetogram, can greatly alter the forecast chance that the active region will have a major eruption in the next few days after the time of the magnetogram. The active-region magnetic conditions that, in addition to the free energy, are reflected by recent major flaring are presumably the complexity and evolution of the field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

EFFECTS OF THE NON-RADIAL MAGNETIC FIELD ON MEASURING MAGNETIC HELICITY TRANSPORT ACROSS THE SOLAR PHOTOSPHERE

It is generally believed that the evolution of magnetic helicity has a close relationship with solar activity. Before the launch of the Solar Dynamics Observatory (SDO), earlier studies had mostly used Michelson Doppler Imager/SOHO line of sight (LOS) magnetograms and assumed that magnetic fields are radial when calculating the magnetic helicity injection rate from photospheric magnetograms. However, this assumption is not necessarily true. Here we use the vector magnetograms and LOS magnetograms, both taken by the Helioseismic and Magnetic Imager on SDO, to estimate the effects of the non-radial magnetic field on measuring the magnetic helicity injection rate. We find that: (1) the effect of the non-radial magnetic field on estimating tangential velocity is relatively small; (2) when estimating the magnetic helicity injection rate, the effect of the non-radial magnetic field is strong when active regions are observed near the limb and is relatively weak when active regions are close to disk center; and (3) the effect of the non-radial magnetic field becomes minor if the amount of accumulated magnetic helicity is the only concern.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Reduction, analysis, and properties of electric current systems in solar active regions

The specific attraction and, in large part, the significance of solar magnetograms lie in the fact that they give the most important data on the electric currents and the nonpotentiality of active regions. Using the vector magnetograms from the Marshall Space Flight Center (MSFC), we employ a unique technique in the area of data analysis for resolving the 180 deg ambiguity in order to calculate the spatial structure of the vertical electric current density. The 180 deg ambiguity is resolved by applying concepts from the nonlinear multivariable optimization theory. The technique is shown to be of particular importance in very nonpotential active regions. The characterization of the vertical electric current density for a set of vector magnetograms using this method then gives the spatial scale, locations, and magnitude of these current systems. The method, which employs an intermediate parametric function which covers the magnetogram and which defines the local `preferred' direction, minimizes a specific functional of the observed transverse magnetic field. The specific functional that is successful is the integral of the square of the vertical current density. We find that the vertical electric current densities have common characteristics for the extended bipolar (beta) (gamma) (delta)-regions studied. The largest current systems have j(sub z)'s which maximizes around 30 mA/sq m and have a linear decreasing distribution to a diameter of 30 Mn.

Gary, G. Allen↗