The Neupert Effect of Flare Ultraviolet and Soft X-ray Emissions

Abstract:

We model the Neupert effect that relates flare heating energy with the observed soft X-ray (SXR) emission. The common form of the Neupert effect refers to the correlation between the time-integrated hard X-ray (HXR) or microwave light curve and the SXR light curve. In this study, instead, we use as the proxy for heating energy the ultraviolet (UV) emission at the foot-points of flare loops, and modify the model of the Neupert effect by taking into account the discrete nature of flare heating as well as cooling. In the modified model, spatially resolved UV light curves, which are indicative of energy release in individual flare loops, are each convolved with a kernel function characterizing decay of the flare loop emission. Contributions by all flare loops are summed to compare with the observed total SXR emission. The model has successfully reproduced the observed SXR emission from its rise to decay, supporting the hypothesis that flare UV emission in the transition region are indicators of energy release in flare loops. We subsequently model the flare evolution using a zero-dimensional hydrodynamic code (EBTEL, Klimchuk et al. 2008) and heating rates of flare loops inferred from the UV light curves at the foot points of the loops -- the UV Footpoint Calorimeter (UFC) method, to produce synthetic SXR light curves in comparison with observations. The combination of these two methods helps improve estimates of flare energetics. In the majority of the 16 flares modeled, we confirm the previous finding that a two-phase heating model, that the heating rate of a flare loop consists of an impulsive component followed by a gradual component, is required to reproduce the observed decay timescales of flare SXR light curves (Zhu et al. 2018; Kerr et al. 2020). The amount of heating energy in the gradual component varies from flare to flare, and, on average, makes at least one third of the total heating energy. The establishment of the UV Neupert effect will provide a simple approach to estimate heating rates in flare loops continuously formed by magnetic reconnection throughout the flare evolution, and it invokes further investigation on what mechanisms produce the impulsive and gradual heating in flare loops.