Expansion of the Soft X-ray Source and “Magnetic Detonation” in Solar Flares

The detection of radio emission from solar flares at frequencies below ∼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 νp. 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) ∼ dL(t)/dt, which are compared
with the estimates of the sound speed and the Alfve´ n speed. By “magnetic detonation” wemean the process
of the propagation of magnetic reconnectionwith 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-Alfve´ n speeds were reached if the density of the SXR
source was lower than 2.1 × 109 and 7.4 × 108 cm−3 (νp < 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 × 1010 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.