First results on the origin of universal correlation between flare temperature and emission measure for solar and stellar flares

Abstract

We investigate the correlation between flare temperature T and emission measure EM = n2V found by Feldman (1995) by extending the temperature and emission measure range to include solar microflares and protostellar flares. We found that the correlation is well represented by the power-law relation, EM ∝ Ta with power-law index a ⋍ 8.3 ± 1.0, where n is the electron density and V is the volume. We then present a theory to explain the observed power-law relation between T and EM on the basis of a magnetic reconnection model with heat conduction and chromospheric evaporation, assuming that the gas pressure of a flare loop is comparable to the magnetic pressure. This theory predicts the relation cm−3, which explains well the observed correlation in the range of 6 × 106 K < T < 108 K and 1044 < EM < 1055 cm−3 from solar microflares to protostellar flares observed by ASCA. Here, B is the magnetic field strength, n0 is the pre-flare proton (electron) number density.