The Neupert Effect Revisited

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Nugget
Number: 403
1st Author: Jiong QIU
2nd Author:
Published: 8 March 2021
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Introduction

The Neupert effect (Ref. [1]) has been studied for half a century. It describes the simple observation that the time integral of the hard X-ray or microwave light curve of a solar flare well resembles its soft X-ray light curve. The flare hard X-ray and microwave emissions are produced by non-thermal electrons, whereas the flare soft X-ray emission is from plasmas heated to more than 10 million kelvin. The Neupert effect is consistent with the basic idea that flare energy be primarily carried by non-thermal electrons, which are then thermalized converting their energy to heat the coronal plasma.

In this traditional form of the Neupert effect, energy release is necessarily confined to the rise phase of the flare soft X-ray emission, often also called the ``impulsive phase" of the flare. However, decades of observations have shown that the flare soft X-ray emission often decays over a longer timescale than the cooling timescales, suggesting that energy release and flare heating may continue after the impulsive phase, when significant non-thermal emissions have often diminished. Astounding high-resolution observations have further demonstrated that flare heating takes place in a large number of loops or threads, and at any time, the total soft X-ray emission is the sum of the emissions from all these loops at their distinct evolutionary stages. The sequential heating and cooling of multiple flare loops cannot be well described by the traditional form of the Neupert effect applied to the total HXR and SXR emissions.

The Modified Neupert Effect

Our recent study (Ref. [2]) revisits the Neupert effect by taking into account the discrete nature of flare heating as well as cooling. In the modified model of the Neupert effect, spatially resolved UV lightcurves at the foot-points of flare loops, as obtained by the AIA instrument in its 1600Â passband, are each convolved with a kernel function characterizing decay of the flare loop emission, and the flare total soft X-ray emission is taken to be the sum of the contributions by all these loops. The modified model is able to reproduce the observed SXR emission from its rise to decay (Figure 1), suggesting that spatially resolved flare UV emission in the upper chromosphere can be used as a proxy for heating rates in flare loops throughout the flare evolution.

Figure 1: Light curves for six of the 16 flares studied in Ref. [2]. Black curves show the 1-8Â flux and its time derivative; pink for the UV flux in the flare regions (thin) and the synthetic SXR flux with the modified Neupert-effect model (thick), and green for the decay timescale of flare loops.

Assuming a simple scaling relation between the heating flux in a flare loop and the UV counts flux at its foot-point, we infer the heating rates in a large number of flare loops, and use them to compute the time evolution of the mean temperature and density of these loops with the zero-dimensional hydrodynamic code of Ref. [3]. The synthetic total SXR and EUV emissions by the flare corona are in good agreement with observations by GOES and AIA (Figure 2). This approach, therefore, provides an efficient way to estimate the first-order heating rates in flare loops formed and heated sequentially during the flare evolution. The experiment also suggests that, not only does the energy release continue into the gradual phase of the flare, but that flare heating in individual loops also proceeds beyond an impulsive pulse.

Figure 2: The same six flares, comparing the observed rates with model calculations incorporating both impulsive and gradual heating in each constituent loop of the event (thick and thin pink solid curves) The dashed pink curve shows the model without the gradual heating term..

Conclusion

This study is a thought experiment on the longstanding perception that energy release and flare heating takes place in numerous loops over an extended time period. The experiment shows that the flare UV emission signatures at the foot-points of flare loops well captures the heating process(es) during the flare, and motivates more comprehensive and physics-based models to unravel the mechanisms of flare heaing during the impulsive as well as the gradual phase.

References

[1] "Comparison of Solar X-Ray Line Emission with Microwave Emission during Flares"

[2] "The Neupert Effect of Flare Ultraviolet and Soft X-ray Emissions"

[3] "Highly Efficient Modeling of Dynamic Coronal Loops"

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