Thermal and nonthermal hard X-ray source sizes in solar flares obtained from RHESSI observations

II. Scaling relations and temporal evolution

Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: awarmuth@aip.de

Received: 5 April 2012
Accepted: 5 February 2013

Abstract

Context. A thorough understanding of solar flares requires determining the physical parameters of both the hot thermal plasma and the accelerated nonthermal electrons. This can be provided by hard X-ray (HXR) observations. In addition to HXR spectroscopy, imaging is needed to measure the geometric HXR source sizes. These parameters may vary as a function of flare size, importance, and time.

Aims. We determine the scaling relations of the geometric source parameters of both thermal and nonthermal HXR sources with respect to length scale and flare importance, and we characterize their temporal evolution. This is required for further studies involving parameters such as thermal energies, plasma densities, and current densities.

Methods. In a previous paper, we obtained time series of the geometric HXR source sizes (thermal and nonthermal) for 24 flares from GOES class C3.4 to X17.2 using the RHESSI instrument. Here, we investigate how themal volumes, nonthermal footpoint areas, and footpoint separations depend on the flare length scale and GOES importance. In addition,we study the time evolution of these geometric parameters.

Results. The increase in the thermal source volume with length scale is slightly below a Euclidian scaling, but not too far from it. The thermal source volume is correlated with GOES class, which contrasts with what was found for RHESSI microflares. The nonthermal footpoint areas, on the other hand, are not well-correlated with either length scale or GOES class. With regard to temporal evolution, the RHESSI thermal source volumes tend to show a more complex behavior than the simple growth-decline pattern typical of flares observed in EUV. In most events, the thermal volume shows a rapid initial rise to a peak in the early impulsive phase. This peak is correlated with the initial downward motion of the coronal source, and is consistent with the notion of initially contracting magnetic field lines.

Conclusions. The behavior of the geometric parameters of thermal and nonthermal HXR sources is generally consistent with the standard model of eruptive solar flares: a quasi-Euclidian scaling of volume with length scale, an initially decreasing thermal volume due to field line shrinking, followed by an increase in both volume and footpoint separation with time as the arcade of reconnected flare loops grows. However, the thermal volume is not the dominant factor in determining thermal energy, as well as thermal SXR and HXR flux. Electron density and/or temperature seem to be more important parameters in this respect.