Title: Evidence of Significant Energy Input in the Late Phase of a Solar Flare from NuSTAR X-Ray Observations,
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.