Analysis

Magnetic Reconnection in Solar Flares: the Importance of Spines and SeparatorsAngela Des Jardins1, Richard Canfield1, Dana Longcope1, Emily McLinden2, Crystal Fordyce3 and Scott Waitukaitis4

1Montana State University, Bozeman, MT; 2Loyola University Chicago, Chicago, IL; 3Clemson University, Clemson, SC; 4University of Arizona, Tucson, AZ

Discussion

BA C

Flare, Track

Footpoint Angle

Spine Angle

Difference

A, 1 4.13 4.95 0.82

A, 2 3.31 2.96 0.35

A, 3 0.69 0.29 0.40

B, 1 3.34 3.36 0.02

B, 2 2.67 2.00 0.67

B, 3 0.70 0.68 0.02

B, 4 2.20 2.04 0.16

C, 1 1.65 1.23 0.42

C, 2 0.64 0.41 0.23

C, 3 3.51 3.69 0.18

C, 4 2.55 2.55 0.00

C, 5 1.09 1.49 0.40

Introduction

Observations

In order to improve the understanding of both flare initiation and evolution, we take advantage of powerful new topological methods and the high spatial resolution of RHESSI to examine where magnetic reconnection takes place in flare-producing solar active regions. Using a MDI line of sight magnetogram as the photospheric boundary condition, we extrapolate the magnetic field into the corona via the Minimum Current Corona Model. The extrapolation gives the location of topological features such as poles, nulls, separatricies, separators, and spine lines. For four flares well observed by RHESSI and MDI,

we examine the locations of flare HXR emission in the context of these topological features. Two noteworthy relationships are found. First, when footpoints move, they move along spine lines. Second, when separators significantly change over the course of a flare, only those associated with the flare footpoints do so. In this poster, we present observations supporting the relationship between spine lines and footpoint tracks, discuss possible interpretations of the reported results and demonstrate the importance of separator analysis in the study of flares.

Separator analysis for the M5 flare on 4 November 2004. The flare began at 22:30, peaked at 23:02 and ended at 23:29 UT. Shown on the left are the isolated separators whose ends connect the observed HXR footpoints. On the right, all of the separators for the active region are plotted.The average length of the isolated separators increased by 32% from 22:00 to 23:02 UT, while the average length of all of the separators increased by only 2%. A similar pattern was present for the height: the isolated separators increased by 43% while the average of all separators increased by only 0.5%. These first results indicate that the involved separators contain important information about flare processes. Further analysis is currently being done on the evolution of separator properties prior to and during flares.

Separators

Flare Date Location Peak Time (UT)

GOES Class

Active Region

FP Motion (UT)

A 29 Oct 2003 (100, -350) 20:48 X10 10486 20:41-20:57

B 7 Nov 2004 (330, 170) 16:06 X2 10696 16:21-16:30

C 15 Jan 2005 (150, 310) 22:50 X2 10720 22:34-22:58

A

C

GOES and RHESSI lightcurves for flares A, B and C. Dashed lines in the left panels indicate the time range for the right panels. Solid lines give the time range over which the footpoints were observed to move. Dotted lines indicate the time of the images shown above.

Properties of three eruptive flares who’s footpoint motions we analyzed. Each of these flares was well observed by RHESSI and occurred within 30 degrees of disk center. ‘FP motion’ gives the time range over which the HXR footpoints were observed to move.

MDI magnetograms and footpoint motions. Each + symbol, following the color coded UT timing, marks the centroid location of a source at 50-300, 25-300 and 25-300 keV for flares A, B and C respectively.

We have established the association between footpoint tracks and spine lines. Now, we address two questions:- The standard 2.5D flare model fails to predict the direction and speed of footpoint motions. What type of 3D model can make the correct predictions?- Why do the HXR footpoints move along spine lines? Consider two cases with the quadrupolar configuration shown to the right. The red, orange and violet lines are field lines which lie on the separatrix surfaces. The green lines are spine lines and the solid black line is the separator. As before, the dashed lines in the lower figure mark the intersection of the separatrix surfaces with the photosphere. In the two cases described below, we assume that reconnection occurs at current sheets which are located on the separator. This produces fast-precipitating electrons which stream along the separator field line until they encounter the chromosphere, resulting in HXR footpoint sources. Hence, footpoint sources are located at the chromospheric ends of separators.

Poles, nulls, spine lines and footpoint tracks for flare A. Spine lines marked with non-violet colors were identified and quantitatively analyzed with footpoint tracks of like color.

In order to quantify the association between footpoint tracks and spine lines, we completed a statistical analysis of the two feature’s average angles. Due to the nature of the uncertainties in spine lines, the angle at which the footpoints moved relative to the spines is more important than the distance of the footpoints from the spines.

Same as left panel, but for flare B. Notice the similarity in the spine line and footpoint angles in tracks 2, 3 and 4.

Same as far left panel, but for flare C. In this flare, there are two sets of conjugate footpoints - a pair to the west and a pair to the east (red and green).

BDemonstration of footpoint conjugacy for flares A, B and C. Flare B: 25-300 keV HXR footpoint lightcurves (1N - black, 1P - grey).

Top: Topological footprint for flare A. Poles (positive: P, +; negative: N, x) are an idealization of well defined features like sunspots and pores. The set of all field lines origination at a positive pole and ending at a negative pole fill a volume of space called a domian. A separatrix is a boundary surface dividing domains (dashed lines: intersection of separatrix surfaces with the photosphere). Null points (triangles) are the locations where the magnetic field vanishes. Spine lines (solid lines) lie in the photosphere and form part of a domain’s boundary. Spines extend from a pole through a null to another pole of the same polarity. The separator field line, which starts and terminates at null points, is the intersection of separatrix surfaces. A separator is the generalization to three dimensions of a 2D X-point and is theorized to be the main location for reconnection. As a visual example of source connectivity, notice that pole P01 (pointed out by the arrow) is connected to many negative poles including N22, N14, N08 and N13, which lie to the east of P01.

Bottom: Example field lines connecting pole P01 to the negative poles associated with the footpoints of flare A (centroids shown with colored + symbols).

Histogram of the differences (solid line). A random distribution of 12 angles would have the histogram shown with the dotted line. We can reject the null hypothesis that our observed distribution is random with 97% confidence.

Average footpoint and spine angles as well as their differences (in radians).

- Case 1: impulsive flares. If the underlying domian P2/N2 has too much flux, reconnection can reduce the overall energy of the configuration. In this process, a pair of field lines from domians P2/N2 and P1/N1 reconnect to form a new pair in domains P1/N2 and P2/N1. As a result, the nulls at the ends of the separator (and hence the footpoints) move toward P2 and N2 along the spine lines. The separator shortens in length and decreases in height and the distance between the footpoints shortens.

- Case 2: eruptive flares. If the underlying domian P2/N2 has too little flux, reconnection will act to transfer flux into it. Here, a pair of field lines from domians P1/N2 and P2/N1 reconnect to form a new pair in P1/N1 and P2/N2. As a result, the nulls at the ends of the separator move toward P1 and N1 along the spine lines. The separator increases in length and height and the distance between the footpoints increases.

This model can explain footpoint motion parallel to the magnetic inversion line, as is commonly observed. The standard flare model only predicts motion perpendicular to the inversion line. In this model, footpoints move along the spine lines because reconnection moves the nulls between two like poles. The model can also account for the high footpoint speeds (observed up to 100 km/s) as reconnection proceeds from one separator to another.