STATISTICS OF FLARING LOOPS OBSERVED BY THE NOBEYAMA RADIOHELIOGRAPH. III. ASYMMETRY OF TWO FOOTPOINT EMISSIONS

Two footpoint (FP) emissions are compared in a total of 24 events with loop-like structures imaged by the Nobeyama Radioheliograph (NoRH), which are divided into two groups: when the optically thin radio spectrum in the looptop is harder than those in the two FPs (group 1) and when it is softer than those in at least one FP (group 2). There are always correlative variations of the brightness temperatures and polarization degrees, the spectral indices, the column densities of nonthermal electrons, and magnetic field strengths in the two FPs. The maximum differences of these parameters in the two FPs may reach one or two orders of magnitude (except the polarization degree). The logarithm of the ratio of the magnetic field strengths in the two FPs is always anti-correlated with the logarithms of the ratios of the brightness temperatures in the two FPs, but correlated with the differences of the spectral indices in the two FPs. Only two anti-correlations exist in group 1, between the difference of the absolute polarization degrees in the two FPs and the logarithm of the ratio of the brightness temperatures in the two FPs and between the difference of the spectral indices in the two FPs and the logarithm of the ratio of the column densities of nonthermal electrons in the two FPs. Only two positive correlations appear in group 1, between the difference of the absolute polarization degrees in the two FPs and the relative ratio of magnetic field strengths in the two FPs and between the logarithm of the ratio of the column densities of nonthermal electrons in the two FPs and the logarithm of the ratio of the brightness temperatures in the two FPs. These four statistics in group 2 are just opposite to those in group 1, which may be directly explained by gyrosynchrotron theory. Moreover, the asymmetry of the two FP emissions in group 2 is more evident than that in group 1, which may be explained by two kinds of flare models, respectively, in the two groups of events, i.e., the energy release above a single loop (group 1) and in the coalescence of two flaring loops (group 2). The asymmetry of the two FP emissions cannot simply be explained by the mirroring effect, but it may strongly depend on the asymmetry of the initial pitch angles of nonthermal electrons in the two FPs. The normal or abnormal events are defined as whether a stronger emission corresponds to a stronger or weaker polarization in the two FPs, with a comparable proportion of the normal and abnormal events in the two groups.