Temporal and Spatial Characteristics of Hard X-Ray Sources in Flare Model with Vertical Current Sheet

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Nugget
Number:	453
1st Author:	Alexander N. SHABALIN,
2nd Author:	Evgeniia P. OVCHINNIKOVA, and Yuri E. CHARIKOV
Published:	August 7, 2023
Next Nugget:	TBD
Previous Nugget:	Spatial Distribution of Magnetic Reconnection Rate in an M6.5 Solar Flare
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Contents 1 Introduction 2 Observation 3 Modeling 4 Conclusions 5 References

Introduction

In the standard "CSHKP" flare model, the primary acceleration of charged particles occurs in the cusp and current sheet regions above the soft X-ray loops. The ejection of nearly collisionless plasma from the magnetic reconnection region is accompanied by a fast transformation of magnetic loops initially extended in the direction of the current sheet to a configuration close to that of a dipole. The magnetic loops that relax in this manner undergo longitudinal and transverse contraction, which leads to the further acceleration of electrons through betatron and Fermi first-order acceleration. We have considired such dynamic loops following Ref. [1]. Magnetic-field dynamics during the collapse result in spatial and temporal features of hard X-ray (HXR) sources in flares. This Nugget gives an overview of the validation of our "CollTr" model of this (Ref. [2]), using RHESSI HXR data and the features of HXR evolution in coronal plasma below the vertical current sheet. Such manifestations may include a decrease or constancy in the HXR source height, a negative correlation between the area of the coronal source and the HXR flux, and features in the energy spectra and time delay (TD) spectra, particularly at the initial stage of flare development.

Observation

We analyzed changes in the height of the coronal HXR source for flares SOL2013-05-13T01:50 and SOL2013-05-13T15:51 (Figure 1, middle panels). Analysis of the RHESSI data revealed the downward motion of the HXR sources and the separation of the sources of different energies by height. In the early stages of the flares, a negative correlation was found between the HXR source area in the corona and HXR flux.

Figure 2 shows the time-delay (TD) spectra obtained for the HXR of the SOL2013-05-13T15:51 event. This analysis basically uses cross-correlation in time in spectral bins, and can be carried out for any image region and time domain selected. We calculated the TD spectra for the looptop and footpoints of the flare arcade. The colored rectangles in Figure 2 mark the phases of the rise and decay of the HXR for which the TD spectra were calculated. The shaded white time interval (15:59:04--15:59:44) was excluded from the analysis because of potentially inaccurate flux values. Windows 1 and 3 correspond to the rising phases of the HXR flux. During these time intervals, the TD spectra at the footpoints exhibit an increasing trend in the spectral profiles. At the looptop, the TD spectrum exhibited a growth shape (window 1, black curve) and complex shape (window 3, black curve). During the decay phases (windows 2 and 4), the TD spectral profiles decreased at the looptop and at both footpoints.

Modeling

To model the properties of the HXR mentioned above, we numerically solved the time-dependent relativistic kinetic equation for nonthermal electrons (see Equation (1) in Ref. [2]). We assumed that the initial acceleration within the current sheet defines the injected electron parameters. In the multitude of relaxing magnetic loops, we modeled one characterized by the parameters of the ensemble-averaged loops. Consequently, we modeled magnetic loop relaxation accompanied by the injection of primary accelerated electrons in the looptop region. In the event SOL2013-05-13T15:51, at the footpoints during the rise of the HXR flux (windows 1 and 3, Figure 2), increasing TD spectra were obtained, which contradicts the electron propagation model with time-independent distributions of plasma density and magnetic field along the loop (DMTI model). At the same time, in the CollTr model, the TD spectra at the footpoints exhibited growth. This contradiction is attributed to a combination of factors: a high initial B_max/B_min during the onset of magnetic loop relaxation in the CollTr model, additional electron acceleration during propagation in the loop, and an increase in plasma density at the looptop. The modeling revealed that betatron acceleration has a dominant influence on the formation of growing TD spectra at footpoints. Because betatron acceleration is significant only during the growth phase of the HXR flux, the transition from increasing TD spectra at the footpoints to decreasing patterns in windows 2 and 4 in Figure 2 can also be explained. That is, during the increase in the HXR flux, growing TD spectra are formed at the footpoints owing to the betatron acceleration of the electrons. Subsequently, during the decay of the HXR flux, when the betatron acceleration was no longer effective and the B_max/B_min ratio was not substantial (approximately 8), the TD spectra transformed to a decreasing pattern, as anticipated by the DMTI model of electron propagation with a stationary magnetic field.

Conclusions

Numerical simulations of accelerated electron kinetics and the associated HXR emission in the CollTr model are consistent with the observed HXR data for flares SOL2013-05-13T01:50 and SOL2013-05-13T15:51. First, the separation of HXR sources of different energies by height occurs naturally during magnetic field relaxation (collapse) in a model with a vertical current sheet in the corona. Second, there was a negative correlation between the area of the HXR sources in the corona and HXR flux for both flares examined in this study. Third, there were particular characteristics of the TD spectra in the investigated flares, specifically the decreasing TD spectra in the coronal source and the increasing TD spectra in the footpoints of the SOL2013-05-13T15:51 event. We explain these characteristics using numerical simulations conducted within the CollTr model framework. In addition, our modeling of the HXR spectral index evolution suggests that soft-hard-soft and soft-hard-harder patterns may not appear due to specific processes in the accelerator or the region of suprathermal electron propagation, but rather as a consequence of the superposition of HXR fluxes from various magnetic structures, which are at different stages in terms of accelerated electron accumulation and radiation.

References

[1] "Collisionless Reconnection and High-Energy Particle Acceleration in Solar Flares"

[2] "Temporal and Spatial Characteristics of Hard X-Ray Sources in a Flare Model with a Vertical Current Sheet"