Expansion of the Soft X-ray Source and ‘‘Magnetic Detonation’’ in Solar Flares

Abstract

The detection of radio emission from solar flares at frequencies below ${\sim}2$ GHz allows the upper limits for the characteristic size of the soft X-ray (SXR) source $L(t)$ to be estimated under the assumption that the density $n(t)$ is determined by the plasma frequency $\nu_{p}$. If the SXR source with a higher density is inside the radio source, then the size of the SXR source will be $L(t)<(EM(t)/2n(t)^{2})^{1/3}$, where $EM(t)$ is the emission measure. For three flares (C7.2 on December 22, 2009, M2.9 on July 6, 2012, and X1.1 on July 6, 2012) we calculate the expansion speeds of the SXR source $V(t)\sim dL(t)/dt$, which are compared with the estimates of the sound speed and the Alfvén speed. By ‘‘magnetic detonation’’ we mean the process of the propagation of magnetic reconnection with a supersonic speed in eruptive flares. Magnetic detonation and the succeeding coronal mass ejection (CME) were realized in the December 22, 2009 C7.2 and July 6, 2012 X1.1 flares, in which supersonic and super-Alfvén speeds were reached if the density of the SXR source was lower than $2.1\times 10^{9}$ and $7.4\times 10^{8}$ cm${}^{-3}$ ($\nu_{p}<410$ and ${<}245$ MHz), respectively. There were no magnetic detonation and CME in the July 6, 2012 M2.9 flare, whose radio emission frequencies were only above 1415 MHz ($n>2.5\times 10^{10}$ cm${}^{-3}$). For magnetic detonation in the July 6, 2012 X1.1 flare we have estimated the magnetic field strength, the reconnection electric field strength, the plasma flow, and the CME mass.