A Study on the Various Modes of Parallel Heat Conduction in the Coronal Loops of Small and Large Solar Flares Using Scaling Laws

Abstract

Recent studies show that the parallel heat conduction in the plasma of coronal loops associated with solar flares is controlled by the turbulence-dominated mode, in addition to the free streaming and collision-dominated modes. Using scaling laws, we have studied the relative importance of various modes of parallel heat conduction in the coronal loops of the small (B-class) and large (X-class) solar flares. The scaling laws relate the maximum loop temperature and heating rate to the loop pressure and loop half-length for collision, turbulence, and free streaming dominated modes of the parallel heat conduction. For a set of values of loop half-length $\approx(2.0 - 3.0)\times10^{9}$ cm, loop pressure $\approx(6.0 - 20.0)$ erg cm⁻³ for the small coronal loops, and loop half-length $\approx(3.0 - 11.0)\times10^{9}$ cm, loop pressure $\approx(1.0 - 103.0)$ erg cm⁻³ for the large coronal loops at a constant value of mean free path $= 10^{7.5}$ cm, our results show that the estimated heating time is ≈ 40–125 s, which represents a fast heating rate. The estimated maximum loop temperature is found to be lower compared to the observed values for the coronal loops of the solar flares. The nature of positive and negative correlation between the scaling parameters show that the collision-dominated heat conduction is a dominant process in the loops of small flares while turbulence-dominated processes suppress the collision-dominated parallel heat conduction in the loops of large solar flares. The instabilities caused by the fast flow of evaporation from the footpoints are discussed as the source of the turbulence.