Christian Baumgartner¹, Julia K. Thalmann¹, Astrid M. Veronig^1,2
1. Institute of Physics, University of Graz, A-8010 Graz, Austria
2. Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, Kanzelhöhe 19, A-9521 Kanzelhöhe, Austria

Eruptive (CME-associated) flares knowingly impact space weather on the Earth. Yet, we do suffer from moderate abilities of predicting whether a flare develops an associated CME or not (termed “confined” flares). It has been suggested that location of a flare within its host active region (AR) is of relevance concerning CME productivity apparently¹. Orientation and strength of the coronal magnetic field overlying a flare site apparently plays an even greater role. The coronal magnetic field slowly decaying with height may hinder an ejection of a CME^2,3. However, the importance of the orientation of the coronal magnetic field at successive heights above a flare site has never been studied systematically. We performed a pioneering analysis of a large number of eruptive and confined flares, with an aim at depicting the most relevant of the above-mentioned aspects regarding CME productivity.

Figure 1|Vertical component of the photospheric magnetic field for a sample AR (black/white represents negative/positive polarity). (a) Blue/red triangle represent the magnetic-flux-weighted center of negative/positive polarity. Halfway on a straight connecting line, d_PC, lies the AR center. (b) A circle of radius d_PC/2 defines the lateral and vertical extent of the underlying AR magnetic dipole field. (c) The flare distance d_FC (orange line) is measured between the flare site and the AR center. The flare site lies halfway along the linearly approximated flare-relevant PIL (blue line connecting plus signs).

We characterized the location of a flare site within its host AR based on measurements from Solar Dynamics Observatory (SDO) / Helioseismic and Magnetic Imager (HMI) magnetic field maps. We used the distance between the magnetic-flux-weighted centers of opposite magnetic polarities (d_PC; Fig. 1a) to characterize the extent of the host AR’s magnetic dipole field (Fig. 1b). We measured the flare distance (d_FC) between the flare site and the AR center (Fig. 1c). The coronal magnetic field above the flare sites was studied using three-dimensional potential magnetic field models⁴. We used a vertical plane within the magnetic field models (Fig. 2a) to derive the mean decay index as a function of height (Fig. 2b), and to determine the critical height for torus instability (h_crit=h(<n>=1.5)). We approximated the orientation of the magnetic field above a flare site by the inclination of the flare-relevant polarity inversion line (PIL), φ, at each height in the model (Fig. 2d), starting from the photospheric level (Fig. 2c).

Figure 2|(a) Decay index calculated in a vertical plane aligned with the linearly approximated flare-relevant PIL (blue line connecting plus signs). Black/white filled contours on the lower boundary resemble the negative/positive polarity vertical photospheric magnetic field. Red filled contours mark observed flare ribbons. (b) Mean decay index as function of height within the vertical plane shown in (a). (c) Sub-field (black rectangle) used to approximate the orientation of the flare-relevant PIL (orange contour) by a linear fit (black straight line). (d) Inclination of the flare-relevant PIL, φ, versus normalized height (h/d_PC). The vertical dashed line represents the apex of the host AR’s magnetic dipole field.

Based on our analysis of 44 large flares that were observed by the SDO during 2011-2015, the following can be concluded regarding the factors determining the eruptive character of solar flares⁵:

Figure 3|Change of orientation of the flare-relevant PIL, ∆φ=|φ(h)-φ(h=0)|, versus normalized height (h/d_PC) for (a) eruptive and (b) confined events. The blue vertical line indicates the apex of the host AR’s dipole field. The dashed/solid lines represent M-/X-flares. (c) Normalized flare distance (d_FC/d_PC) versus d_PC. The dashed straight line delimits the horizontal extent of the AR dipole field. Blue diamonds/red stars correspond to confined/eruptive flares. Smaller/larger symbols indicate M-/X-flares. (d) ∆φ versus h_crit.Black solid line indicates a linear fit to all data points, and “cc” denotes linear correlation coefficient.

(1) Flares that originate from the periphery of its host AR (d_FC/d_PC>0.5) are predominantly eruptive (dashed gray outline in Fig. 3c). Flares that originate from within host AR’s magnetic dipole field (d_FC/d_PC≤0.5) tend to be eruptive when hosted by a compact AR (d_PC≤60 Mm; green dash-dotted outline in Fig. 3c), and confined when launched from an extended AR (d_PC>60 Mm; yellow dotted outline in Fig. 3c).

(2) In ARs that host confined flares, the orientation of the flare-relevant PIL adjusts to the orientation of the host AR’s magnetic dipole field quickly with height (∆φ≥40° until h=d_PC/2; Fig. 3a), whereas in ARs that host eruptive flares the flare-relevant PIL can still be considerably inclined near the apex of the host AR’s magnetic dipole field (Fig. 3b).

(3) The critical height for torus instability is the more robust measure to discriminate ARs that host confined flares (mostly h_crit>40 Mm) from those that host eruptive flares (typically h_crit<40 Mm; Fig. 3d). The orientation of the flare-relevant magnetic field above a flare site appears to be a weaker constraint.

For details of this work, please refer to our recent publication:
Baumgartner, C., Thalmann, J. K., Veronig, A., M. 2018, ApJ, 853, 105

References:
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[5] Baumgartner, C., Thalmann, J. K., Veronig, A., M. 2018, ApJ, 853, 105