# Evidence of Significant Energy Input in the Late Phase of a Solar Flare from NuSTAR X-Ray Observations

## TL;DR

This study uses NuSTAR, SDO/AIA, and FOXSI-2 observations to analyze a solar flare's late phase, revealing ongoing energy input and a significant thermal energy increase post-flare peak, challenging standard energy estimation methods.

## Contribution

It provides new insights into the late-phase energy input in solar flares through multi-instrument observations and detailed thermal energy analysis.

## Key findings

- At least 12 post-flare loop sets formed and cooled after the flare peak.
- Total thermal energy during the late phase exceeds peak energy by an order of magnitude.
- Standard peak-time energy estimates significantly underestimate total flare energy.

## Abstract

We present observations of the occulted active region AR12222 during the third {\em NuSTAR} solar campaign on 2014 December 11, with concurrent {\em SDO/}AIA and {\em FOXSI-2} sounding rocket observations. The active region produced a medium size solar flare one day before the observations, at $\sim18$UT on 2014 December 10, with the post-flare loops still visible at the time of {\em NuSTAR} observations. The time evolution of the source emission in the {\em SDO/}AIA $335\textrm{\AA}$ channel reveals the characteristics of an extreme-ultraviolet late phase event, caused by the continuous formation of new post-flare loops that arch higher and higher in the solar corona. The spectral fitting of {\em NuSTAR} observations yields an isothermal source, with temperature $3.8-4.6$ MK, emission measure $0.3-1.8 \times 10^{46}\textrm{ cm}^{-3}$, and density estimated at $2.5-6.0 \times 10^8 \textrm{ cm}^{-3}$. The observed AIA fluxes are consistent with the derived {\em NuSTAR} temperature range, favoring temperature values in the range $4.0-4.3$ MK. By examining the post-flare loops' cooling times and energy content, we estimate that at least 12 sets of post-flare loops were formed and subsequently cooled between the onset of the flare and {\em NuSTAR} observations, with their total thermal energy content an order of magnitude larger than the energy content at flare peak time. This indicates that the standard approach of using only the flare peak time to derive the total thermal energy content of a flare can lead to a large underestimation of its value.