Modeling Magnetic-Polarity Distributions of Active Regions from their Helioseismic Signatures
Modelling Magnetic-Polarity Distributions of Active Regions from their Helioseismic Signatures
by
A.-C. Donea (Monash University), alina.donea@monash.edu
and
C. Lindsey (NorthWest Research Associates), lindsey@nwra.com
The algorithm can be applied to:
- - Simple Bipolar Magnetic Configurations
- - Complex Magnetic Configurations
Also presented at the Annual (2018 in this case) Space Weather Workshop, organized by the National Oceanic and Atmospheric Administration's (NOAA's) Space Weather Prediction Center (SWPC) here in Boulder. The website for he 2018 meeting is
https://www.swpc.noaa.gov/content/annual-meeting
You can download the paper (July 19th, 2018, submitted to the Mathematical Journal "Inverse Problems"_ :
ms.pdf
There are major potentialities of seismic monitoring of the Sun that have yet to be fully developed. Space-weather forecasting based on observations of the Sun’s near hemisphere, for example, enjoy detailed maps showing the polarities of magnetic configurations that pervade the active regions that impact space weather. While highly sensitive to photospheric magnetic fields, helioseismic signatures are invariant under reversal of the sign of the magnetic flux density, hence unable to determine, on their own, the signs of the local magnetic polarities attached to the flux. Helioseismic signatures are therefore missing much desired information on an aspect of solar activity that is crucial to major aspects of space weather and its forecasting.
Hale Polarity Law as a Resource for Magnetic-Polarity Information:
Arge et al. (2013) introduced the use of the Hale Polarity Law as a complement, first to STEREO EUV observations of the Sun from the far side of the solar system, and then to helioseismic maps of the far hemisphere for application in their Air Force Data As- similative Photospheric Flux Transport (ADAPT) algorithm for global modeling of the Sun’s coronal magnetic field. Observations of the Sun’s near hemisphere show the Hale Law to be highly reliable for large active regions, those of real concern to space-weather forecasting. This can be useful not only for assigning a flare potentiality to active re- gions born in the Sun’s far hemisphere, but also for realistically modeling the global coronal magnetic field over the entirety of the Sun’s surface. The latter utility helps us to anticipate the formation of coronal holes, which are a source of high-speed streams once they rotate into the near hemisphere.
Figure 1. Composite map of the Sun on 2014-11-05.0 posted by the SDOs Joint Science Oper- ations center (JSOC) at Stanford (see http://jsoc.stanford.edu/data/farside). The amber region the seismic signatures of active regions designated “FS-103” and “FS-101” in the Sun’s far hemisphere. The blue-gray region shows the concurrent line-of-sight magnetogram of the near hemisphere.
Figure 2. SDO/HMI visible intensity (top left) and magnetic (top right) and /AIA inten- sity maps of the near hemisphere in 1,700 ̊A(bottom left) and HeI 304 ̊A (bottom right) on
2014-11-17, when both FS-101 and FS-103 had rotated into direct view from Earth. The total HeI 304 ̊A attributed to FS-101 and FS-103 was ∼70% of the total.
Figure 3. Seismic map of NOAA AR11416 in the Sun’s near hemisphere (Frame d) is shown
on 2011-02-12 concurrently and cospatially with a visible-continuum-intensity map (Frame a), a line-of-sight magnetic map (Frame b), and a HeII 304 ̊A intensity map (Frame c).
Figure 4. Diagram expressing a somewhat simplified representation of the helioseismic signa- ture of a recently emerged active region suspected to include magnetic polarities of opposing sign. Closed contours identifed with capital letters respresent what can be plausibly inter- preted as distinct components of the photospheric magnetic-flux distribution. The helioseis- mic signatures—while they are sensitive in a straight-forward way to the absolute value of the magnetic flux density—are insensitive to the sign thereof. Given such a signature, the basic pole-pairing problem asks for the most prospective magnetic connectivity between the individ- ual components, here identified by “A”, “B”, “C”, and “D”, consistent with (1) the seismic signatures and (2) the Hale Polarity Law. In this simplified representation, the nominal Hale Polarity Law is represented by an expectation displacement, ζ0, separating regions magneti- cally connected to each other.
Figure 5. A convenient scheme for assessing relative prospectivities of a magnetic connection between different components of a helioseismic signature consistent with the Hale Polarity Law is attempted by superposing the helioseismic signature shown in Figure 4 with a version of the same (top frame) that is displaced by the nominal Hale displacement vector, ζ0, but is other- wise unwarped. Positive matches for this ζ0 are represented by vertical arrows, i.e., accurate superpositions of lobe B and D in the displaced overlay onto A and C, respectively, in the un- derlying original. It can happen that an alternative choice of ζ0 will prescribe a similarly posi- tive superposition. In this figure, such an alternative is shown by tilted green arrows, matching C to A and D to B.
More Complex Magnetic Configurations
Figure6.
The relationship between helioseimic signatures and the magnetic configurations
that give rise to them is illustrated by application of basic analytical tools to observations of NOAA AR11416 as it crosses central solar meridian on 2012-02-12, and again in the following solar rotation. Panel a shows the region in the visible continuum on 2012-02-12. Panel b shows the concurrent, cospatial helioseismic signature, H. Panel c shows Pn, derived from equation (16). Panel d shows a control reconstruction of the helioseimic signature derived by applying
J to Pn^2 + Ps^2. Panel e shows the magnetic flux density derived by subtracting Ps from Pn, as prescribed by equation (8). Panel f shows a cospatial line-of-sight magnetogram of the re- gion for comparison. Panel g shows the magnetic flux density projected a full solar rotation subsequent that shown in panel e by applying the evolution operators, Un and Un to Pn and Pn, respectively for the 27-day synodic solar-rotation period. Panel h shows a cospatial line-of- sight HMI magnetogram at that moment.
<>hr>More Complex Magnetic Configurations
The application of distortionless Hale mapping may work quite well for magnetic regions significtantly more complex than AR11416. An example is AR11158 circa 2011-02-13, consisting of two bipoles with very similar separations. Figure 7 shows results of the analysis described in Figure 6 applied to AR11158.
In this case, the leading (westward) pole of the lagging (eastern) bipole was pressed against the following (eastward) pole of the leading (western) bipole, the composite forming the continguous central lobe of the helioseismic signature (Fig 7b). The result of distortionless Hale mapping is artificially weak magnetic flux densities in the middle lobe with Pn and Ps both individually strong but largely canceling each other. The algorithm does not have the leaverge to resolve the degee to which the northern and southern components are separated in the central lobe. However, it does recognize the existence of both northern and southern magnetic flux in the general region of the center lobe of the seismic signatures.
Figure 7. The magnetic extrapolation illustrated in Figure 6 for the simple bipole configuration of NOAA AR11416 is applied here to more magnetically complex NOAA AR11158 (2011-02- 13), a region consisting of two bipoles in which the helioseismic signature of leading pole of
the eastern bipole coincides with the following pole of the more western bipole. See caption of Figure 6 for details.
Summary:
At least for a significant class of newly-emerged active regions the Hale Polarity Law of- fers the possibility of judging magnetic flux distributions from helioseismic maps with a credible account for the signs of the polarities of the different components. This idea, first proposed by Nick Arge, Carl Henney and their colleagues, appears to have useful extensions to more complex magnetic configurations consisting of multiple magnetic bipoles. We have experimented successfully with an algorithm that addresses this prob- lem for simple magnetic configurations. If this can be extended to still more complex ac- tive regions, and to helioseismic signature of active regions in the Sun’s far hemisphere, it can considerably extend the range of space-weather forecasting benefits of far-side seis- mic monitoring of the Sun.