# The First Survey of Quiet Sun Features Observed in Hard X-Rays With NuSTAR

Sarah Paterson  Iain G. Hannah  Brian W. Grefenstette  Hugh S. Hudson  Säm
Krucker  Lindsay Glesener  Stephen M. White  David M. Smith  School of Physics
& Astronomy, University of Glasgow, University Avenue, Glasgow G12 8QQ, UK
Cahill Center for Astrophysics, California Institute of Technology, 1216 East
California Boulevard, Pasadena, CA 91125, USA  Space Sciences Laboratory
University of California, Berkeley, CA 94720, USA  University of Applied
Sciences and Arts Northwestern Switzerland, 5210 Windisch, Switzerland  School
of Physics & Astronomy, University of Minnesota Twin Cities, Minneapolis, MN
55455, USA  Air Force Research Laboratory, Space Vehicles Directorate,
Kirtland AFB, NM 87123, USA  Santa Cruz Institute of Particle Physics and
Department of Physics, University of California, Santa Cruz, CA 95064, USA

###### keywords:

Corona, Quiet; Heating, Coronal; Jets; Spectrum, X-Ray; X-Ray Bursts, Hard

##  1 Introduction

The study of the hard X-ray (HXR) emission from the quiet Sun could provide
insight into the source of the sustained high temperature of the solar corona,
termed the coronal heating problem. It was suggested by Parker (1988) that the
source of this heating could be a large number of small-scale energy release
events, taking place all through the solar cycle. If such events were weaker
versions of flares, they would be expected to produce a HXR signature.

One phenomenon that has been linked to coronal heating is coronal bright
points (CBPs), small-scale loop structures located in the lower corona, which
are observed in EUV and soft X-rays (SXRs) (e.g. Madjarska, 2019). These
features are observed throughout the solar cycle, including solar minimum,
when the Sun is quiet in the absence of active regions and large flares.
Bright points have been studied extensively in EUV and SXRs. In EUV, these
features typically have lifetimes of $<$ 20 hours (Alipour and Safari, 2015;
Zhang, Kundu, and White, 2001), whereas they have been found to be shorter-
lived in SXRs, with lifetimes of $\sim$ 12 hours (Harvey et al., 1993). These
features sometimes have associated transient phenomena, such as “microflares”
(Golub et al., 1974; Shimojo and Shibata, 1999), and small-scale eruptions
(Mou et al., 2018).

Previous studies have used EUV and SXR observations to investigate the
temperatures of bright points. Kariyappa et al. (2011) used SXR data from the
_Hinode_ X-ray Telescope (Hinode/XRT) (Kosugi et al., 2007) to study a number
of bright points, using filter ratios to determine that their temperatures
ranged between 1.1–3.4 MK. Another study by Doschek et al. (2010) used EUV
data from the _Hinode_ Extreme Ultra-violet Imaging Spectrometer, finding that
the bright points reached maximum temperatures between 2–3 MK. Alexander, Del
Zanna, and Maclean (2011) studied the evolution of a single bright point,
using both SXR and EUV data. This study found that throughout the 13 hours of
observation, the bright point was almost isothermal, with an average
temperature of 1.3 MK. The Hinode/XRT time profile for this bright point
showed a steady increase in intensity for the first two hours of observation,
followed by several spikes (which the authors speculated were likely due to
heating or reconnection events) until it began to decay.

Bright points can result from bipolar flux emergence. When this process
occurs, new magnetic flux emerges to create an emerging flux region (EFR),
which may subsequently evolve into a small-scale bright point, an example of
which was investigated by Kontogiannis et al. (2020). This study tracked the
evolution in Hinode/XRT of a bright point associated with an EFR, finding that
the bright point exhibited a continuous increase in emission for $\sim$ 1.5
hours before it began to fade. However, rather than a bright point, an EFR may
instead evolve into a large-scale active region if the emergence continues
(van Driel-Gesztelyi and Green, 2015).

HXR observations of bright points have been made difficult by the faintness of
this emission from these sources, and the lack of a solar dedicated instrument
able to observe them individually. Previous HXR studies of the quiet Sun
(Hannah et al., 2007, 2010) have been performed using data from the _Reuven
Ramaty High-Energy Solar Spectroscopic Imager_ (RHESSI) (Lin et al., 2002).
However, as RHESSI was designed for the observation of bright sources, such as
large flare events, only upper limits on the HXR emission from the whole solar
disk were obtained. The authors noted that using a sensitive HXR focusing
telescope would allow a more detailed study of the energy release mechanisms
occurring in quiet Sun features. A more recent paper by Buitrago-Casas et al.
(2022) also constrains the quiet Sun HXR emission in the 5–10 keV range using
data from the _Focusing Optics X-ray Solar Imager_ (FOXSI) sounding rocket.
This study found similar upper limits to Hannah et al. (2010), though using
only minutes’ worth of data, compared to the days that were required with
RHESSI.

The _Nuclear Spectroscopic Telescope ARray_ (NuSTAR) (Harrison et al., 2013)
is a HXR focusing telescope which is capable of being pointed at the Sun to
provide sensitive observations of faint solar sources (Grefenstette et al.,
2016). Since 2014, there have been a number of NuSTAR solar observing
campaigns111Summary of NuSTAR solar observations can be found at
https://ianan.github.io/nsigh˙all/. Much of the work on the NuSTAR solar
observations has focused on active region microflares (Wright et al., 2017;
Glesener et al., 2017; Hannah et al., 2019; Cooper et al., 2020; Duncan et
al., 2021; Cooper et al., 2021), with Glesener et al. (2020) reporting for the
first time on non-thermal emission detected in a microflare observed with
NuSTAR. Kuhar et al. (2017) presented work on quiet Sun flares observed by
NuSTAR outside of an active region, finding that their temperatures ranged
from 3.2–4.1 MK.

NuSTAR has two focal plane modules (FPMA and FPMB), both with a FOV of
$12^{\prime}$ $\times$ $12^{\prime}$ (Harrison et al., 2013). Each of these
focal plane modules has a 2 $\times$ 2 array of CdZnTe detectors. When
observing the Sun it has been used in two modes: dwells, where the same region
is observed over the course of one or several NuSTAR orbits (each with $\sim$
1 hour in sunlight); and full-disk mosaics, where the pointing is continually
changed over the course of an orbit to build up an image of the entire disk.

NuSTAR’s use of focusing optics means that it can directly image very faint
HXR sources on the quiet Sun, and perform spectroscopy on regions of interest.
During the recent solar minimum between cycles 24 and 25 (2018–2020), when the
solar disk was free of active regions, NuSTAR was used to observe the Sun on a
number of occasions, providing several bright points and other quiet Sun
phenomena to study. The recent solar minimum combined with NuSTAR’s
sensitivity has provided a unique opportunity to study the HXR emission from
these features and investigate their contribution to the heating of the solar
atmosphere by searching for the presence of a high temperature ($>$5MK) or
non-thermal component due to the presence of accelerated electrons.

Here, we present the first survey of small features in the quiet Sun observed
in HXRs with NuSTAR. We present analysis of several features from the 28
September 2018 full-disk mosaics, the first of the NuSTAR quiet Sun
observations, including the first HXR imaging spectroscopy of such features.
We include in our analysis EUV data from the _Solar Dynamics Observatory’s_
Atmospheric Imaging Assembly (SDO/AIA) (Lemen et al., 2012) and SXR data from
Hinode/XRT. An overview of this observation is presented in section 2,
including NuSTAR spectral fits for several of the observed quiet Sun features
and a calculation of NuSTAR non-thermal upper limits for a small jet. More
detailed analysis, including NuSTAR spectral fits, differential emission
measures, and non-thermal upper limits, for an EFR which later went on to
become an active region can be found in section 3. Section 4 details similar
analysis for two bright points from this observation.

##  2 Overview of Observation

Figure 1.: Full disk images for NuSTAR, SDO/AIA 211 Å and Hinode/XRT Be-thin
for the two NuSTAR orbits of observation from 28 September 2018. The SDO/AIA
and Hinode/XRT images are taken from the mid-times of each of the NuSTAR
orbits.

On 28 September 2018, NuSTAR observed the quiet Sun for two orbits
(18:25–19:25 UT and 20:01–21:01 UT), producing a full-disk mosaic for each.
The NuSTAR mosaics, formed over an orbit with $\sim$ an hour in sunlight, are
comprised of 25 pointings of duration $\sim$ 100 s which form a 5 $\times$ 5
pattern. The first pointing, P1, is in the top left corner, with the
subsequent pointings shifting to the right until P5. P6 is shifted down from
P5, with the following four pointings being increasingly shifted to the left.
This pattern continues until P25, which is in the bottom right corner of the
mosaic. The pointings overlap with each other such that a feature on the disk
can be captured up to four times within a single orbit.

For the times of these two orbits, there is also full-disk data available from
SDO/AIA and Hinode/XRT (though there is a gap in the data from Hinode/XRT
between 19:13–19:38 UT). The NuSTAR mosaics, and the SDO/AIA 211 Å and
Hinode/XRT Be-thin full-disk images from the mid-times of both NuSTAR orbits,
are shown in Figure 1. NuSTAR is a photon-counting detector, and the data list
the photons’ properties, including time of detection, energy, and position on
the detector. These NuSTAR full-disk maps are constructed by correcting each
pointing for livetime individually and aligning the NuSTAR image with SDO/AIA,
and then summing the corrected counts.

Because of the way in which the mosaic tiles overlap, the disk is sampled more
times than the limb (which is captured in only one or two pointings, compared
to four pointings on the disk). An additional correction has been applied per
detector quadrant to these mosaics to account for this by normalising by the
number of times a given region has been sampled over the whole mosaic. Note
that these NuSTAR mosaics, as well as all of the NuSTAR images shown here,
have been smoothed with a Gaussian filter.

There are several features present in the NuSTAR images, with corresponding
sources appearing also in SDO/AIA and Hinode/XRT. In the first NuSTAR orbit
but not the second (the NuSTAR images in the top and bottom rows of Figure 1,
respectively), there is a faint source that appears in the top right corner of
the mosaic, which can be seen to be a jet in SDO/AIA. There is also a set of
loops near the centre of the disk, as well as a nearby bright point which is
labelled BP3. These two features are captured by NuSTAR in both orbits, and
also observed in SDO/AIA 211 Å and Hinode/XRT. Regions of off-disk diffuse
emission are also present in NuSTAR. The source that is most striking in the
NuSTAR mosaics is the large region of emission from the east limb, which is
observed in both NuSTAR orbits. Between the NuSTAR detectors there are chip
gaps, and any photons that land on these gaps are not detected. Due to the
bright and extended nature of the bright limb emission, these detector gaps
are visible crossing through this feature in Figure 1.

One of the most interesting features from this set of mosaics is an EFR which
went on to become the NOAA active region 12723$\beta$ a few days after this
observation. This feature is captured in the mosaics from both orbits, giving
the opportunity to study its evolution. Detailed analysis of the EFR can be
found in section 3. Two of the other brightest NuSTAR sources are X-ray bright
points, labelled here as BP1 and BP2, which are analysed in section 4.

###  2.1 Jet

One of the features observed by NuSTAR is the source at the top right of the
mosaic in the first panel in Figure 1. This is present in NuSTAR in orbit 1,
but not orbit 2, suggesting that it is more short-lived than the other
features which appear in both orbits. The mosaic tiles which capture the
region that this source lies in are P4, 5, 6, and 7.

SDO/AIA images of this source confirm that it is a compact jet which begins to
brighten at around 18:27 UT, and has disappeared by 18:40 UT. SDO/AIA 211 Å
and Hinode/XRT Be-thin images from the mid-times of the relevant pointings are
plotted in Figure 2, with aligned NuSTAR contours. From the SDO/AIA images, it
can be seen that the configuration of this jet is atypical, with the jet
material being ejected perpendicularly rather than radially outwards, implying
that the overlying magnetic field is pushing it sideways. The lightcurves for
this feature are shown in Figure 3. The NuSTAR count rates for each pointing
are plotted over the lightcurves for comparison.

Around the time of P4 in Figure 3, during which NuSTAR sees the brightest
emission from the jet, there is a peak in both SDO/AIA 211 Å and Hinode/XRT
Be-thin. Another peak in SDO/AIA 211Å coincides with P5, but this feature has
decreased in brightness in both NuSTAR and Hinode/XRT. Again showing agreement
with Hinode/XRT, though not SDO/AIA 211Å, the NuSTAR brightness is at its
lowest in P6 (making the feature almost indistinguishable from the
background), before increasing in brightness in P7. This behaviour is also
apparent in the Hinode/XRT images, where the feature appears brighter during
the times of NuSTAR P4, 5, and 7 compared to P6. The jet is positioned far
enough away from any chip gaps that this change in brightness in NuSTAR is
genuine, as opposed to an effect of it moving in and out of detector gaps.

Figure 2.: SDO/AIA 211 Å (top) and Hinode/XRT Be-thin (bottom) images of the
jet from the mid-times of the four NuSTAR pointings in the first orbit which
captured it. Yellow contours represent NuSTAR FPMA + FPMB 2.2–4.0 keV, with
the contours aligned with SDO/AIA and plotted at the same levels in all panels
(5, 7, 9 $\times$ $10^{-4}$ counts s-1).

Figure 3.: SDO/AIA 211 Å and Hinode/XRT Be-thin lightcurves for the jet. The
green lines indicate the NuSTAR FPMA + FPMB livetime-corrected count rates,
and their corresponding errors, for the pointings that captured this feature.

NuSTAR is an imaging spectrometer, allowing the X-ray spectra of these quiet
Sun features to be fit to investigate their properties. The spectral fitting
of the features presented here was done using XSPEC (Arnaud, 1996), an X-ray
spectral fitting program. In order to preform spectral fitting for a given
source, a Spectral Response Matrix (SRM) for a circular region enclosing the
source is obtained from the Response Matrix and Ancillary Response Files (RMF
and ARF) which are generated using the NuSTAR Data Analysis Software. As the
features investigated here produce a low number of counts, Cash statistics
(Cash, 1979) were used for the fitting, and coronal abundances were assumed.

For this source, and for many of the other quiet Sun features observed with
NuSTAR, the HXR emission is faint. Also, although NuSTAR has a high
sensitivity, its detector throughput is limited to 400 counts/s/FPM, and the
low energy counts dominate. The livetime for these pointings ranges from 67–92
%, though it is $\sim$ 90 % for all pointings barring those that captured the
bright region on the east limb. The issues mentioned above combined with the
short duration of the mosaic pointing times ($\sim$ 100s) result in noisy
spectra that are generally tricky to fit. This can be improved upon to some
extent by simultaneously fitting the FPMA and FPMB spectra for a given source,
introducing a multiplicative constant to the fits to account for any
systematic difference between the responses of the two telescopes. However, in
some cases this is not enough to get good fits for these faint features.
Fortunately, this can be further improved by simultaneously fitting the
features’ spectra from multiple mosaic pointings.

When performing the NuSTAR spectral fitting for this feature, the spectra from
P4, 5, and 7 were fit simultaneously. P6 was not used due to the faintness of
the NuSTAR emission. A circular region of radius $63^{\prime\prime}$, and
centred on the bright emission, was used for the spectral fitting. Though this
source is clearly evolving in SDO/AIA 211Å, the NuSTAR spectra for each of the
pointings were fit individually and it was found that there was no significant
change in the temperature or emission measure throughout. Therefore, in order
to obtain the best signal-to-noise ratio, the spectra from all three pointings
were fit simultaneously with a single thermal APEC model. While it was
previously recommended to only fit NuSTAR spectra down to 2.5 keV
(Grefenstette et al., 2016), a recent update to NuSTAR’s calibration has now
made it possible to fit down to 2.2 keV (Madsen et al., 2021). This is
particularly useful in the case of the features studied here, as their spectra
do not typically contain many counts above 2.5 keV.

Figure 4.: NuSTAR spectral fit for the jet in orbit 1, simultaneously fitting
FPMA and FPMB from P4 (18:31:24–18:33:04 UT), 5 (18:33:51–18:35:32 UT), and 7
(18:38:46–18:40:24 UT). Dotted lines indicate fitting range, and temperature
and emission measure are marked on the plot. The number in black is the
multiplicative constant introduced to account for systematic differences
between FPMA and FPMB.

The fit for the NuSTAR jet spectrum, shown in Figure 4, gives a temperature of
2.60 MK and an emission measure of 8.86 $\times$ $10^{43}$ cm-3. The
isothermal model fits the spectrum well, with no indication of a higher
temperature component or of any non-thermal emission. This temperature lies in
the range of the sensitivity of Hinode/XRT, but lies slightly above the peak
in the SDO/AIA 211Å sensitivity. This may explain the different behaviour of
SDO/AIA 211Å compared to Hinode/XRT and NuSTAR visible in Figure 3.

####  2.1.1 NuSTAR Non-thermal Upper Limits

The thermal energy of the jet was calculated using the following:

$E_{th}=3k_{B}T\sqrt{EM\mbox{ }V}\quad[\mbox{erg}]$ (1)

where $k_{B}$ is the Boltzmann constant, V is the volume of the plasma, and T
and EM are the temperature and emission measure of the plasma, respectively
(Hannah et al., 2008). Note that this equation does not take into account a
loop filling factor, which means that this is an upper limit on the thermal
energy.

From an SDO/AIA 211 Å image of the jet, it takes up an area of
$3^{\prime\prime}$ square. Assuming that the volume is $\sim A^{\frac{3}{2}}$,
this gives a volume of 1.04 $\times$ $10^{25}$ cm3. Therefore, taking the
temperature and emission measure values from the spectrum in Figure 4 (T =
2.60 MK, EM = 8.86 $\times$ $10^{43}$cm-3), the thermal energy of the jet is
3.26 $\times$ $10^{25}$ erg.

The calculated thermal energy can be used to obtain a heating requirement for
the jet, and combined with information derived from the HXR spectra to
determine whether this heating could be non-thermal in nature. The spectrum
for the jet was well fit with an isothermal model. However, following the
approach of Wright et al. (2017), the upper limits of a non-thermal source of
accelerated electrons that are still consistent with a null detection can be
determined. This was done by adding a non-thermal component to the thermal
model determined from the spectral fitting. This thick target non-thermal
model depends on three parameters: the power-law index, $\delta$, the low-
energy cutoff, $E_{c}$, and the total electron flux, $N_{N}$. The total power
in the distribution is then:

$P(>E_{c})=1.6\times 10^{-9}\frac{\delta-1}{\delta-2}N_{N}E_{c}\quad[\mbox{erg
s}^{-1}]$ (2)

For a range of $\delta$ and $E_{c}$ values, the upper limit on $N_{N}$ was
found such that it was consistent with a null detection. For each $N_{N}$
value, the thermal model and the model with the additional non-thermal
component were both folded through the NuSTAR response, and a synthetic NuSTAR
spectrum was generated for each. For each $\delta$ and $E_{c}$ combination,
$N_{N}$ was reduced until the two spectra lay within each others’ Poissonion
errors between 2 and 4 keV, and there were $<$ 4 counts above 4 keV —
consistent with a null detection to 2$\sigma$ (Gehrels, 1986). The jet
spectrum is noisy due to the short integration time and the faintness of the
source, and so this upper limit test does not result in exactly the same upper
limit being obtained every time. Therefore, for each $E_{c}$ and $\delta$
combination the upper limit on $N_{N}$ was calculated 1000 times. This
produced a distribution which was well fit with a Gaussian, of which the peak
location was taken to be the non-thermal upper limit, with the spread
indicated by the standard deviation of the distribution. This upper limit on
$N_{N}$ in turn gave a corresponding upper limit on the power on the non-
thermal distribution, as plotted in Figure 5. In addition to testing the upper
limits for several values of $\delta$, the upper limits were also found for
the case of a mono-energetic beam of electrons. In the case of the mono-
energetic beam and for $\delta$ = 9 and $E_{c}$ $<$ 4 keV the results were
more well-defined, and therefore no spread is indicated in Figure 5.

Figure 5.: Upper limits on the non-thermal heating power for a range of
$E_{c}$ and $\delta$ (= 5, 7, 9, and a mono-energetic beam) values. The shaded
regions indicate the $\pm$ 1 $\sigma$ range of the Gaussian distribution
fitted to the upper limit results. The grey shaded area indicates the heating
requirement dictated by the NuSTAR thermal emission, with the range determined
from the uncertainties on the fit temperature and emission measure.

Taking the thermal energy calculated previously for the jet, over the time
range considered here the required heating power is 6.18 $\times$ $10^{22}$
erg s-1. This heating requirement is marked on the plot with the non-thermal
upper limits in Figure 5. This demonstrates that the non-thermal emission
would have to be very steep, almost mono-energetic, between 3 and 4 keV to
power the required heating as determined from the NuSTAR thermal emission.

###  2.2 Bright Limb Emission

The brightest, and also largest, source that appears in the NuSTAR mosaics in
Figure 1 is the emission from the east limb. As seen in the SDO/AIA and
Hinode/XRT images, this NuSTAR feature is in fact comprised of emission from
two different sources: a bright loop, and surrounding diffuse emission.
Looking back to two solar rotations before this observation, this area was the
site of a SPoCA active region (Delouille et al., 2012) (though it is too faint
to be a NOAA active region), so this bright emission is likely due to the
presence of a decayed active region. From SDO/AIA images from days following
this observation, as the Sun rotates this bright region is followed by a
coronal hole.

Figure 6.: NuSTAR FPMA (top) and FPMB (bottom) images of the bright limb
emission from P11 of orbit 1 (18:48:35–18:50:16 UT) and orbit 2
(20:25:15–20:26:56 UT).

This source is captured fully by P11 and partially by P10 and 20 in both
NuSTAR orbits. Figure 6 shows the NuSTAR images of this region from P11 of
orbits 1 and 2, with FPMA and FPMB shown separately. This limb emission is
relatively bright and extended, meaning that the SNR is not as big of an issue
as it is with the other features. However, there are other factors which
complicate the fitting of its NuSTAR spectra. Firstly, in each of the
pointings this source is extended enough to be positioned over multiple NuSTAR
detector quadrants, which have varying responses. Also, as mentioned
previously, the NuSTAR emission is a combination of the bright loop and the
surrounding diffuse emission. Therefore, in order to investigate the
properties of the emission that originates only from the bright loop in
SDO/AIA and Hinode/XRT, the brightest section of the NuSTAR emission was
chosen for the fitting.

However, this bright loop is not ideally positioned in most of the pointings
that capture this area. P20 of both orbits captures the bottom half of this
region, with the edge of the FOV just missing the bright loop. In orbit 2, the
bright loop lies just off the edge of the detector in P10 and across a
detector gap in P11 in both FPMA and FPMB, resulting in these counts being
lost. This effect is demonstrated in Figure 6, where the detector gaps are
visible. These problems are also encountered in both pointings in orbit 1 for
FPMB. However, the bright loop lies within the FOV in P10 and P11 in FPMA, and
therefore this feature can be seen in the top left panel of Figure 6.
Consequently, the spectral analysis of this feature only includes these two
pointings for FPMA only.

Figure 7.: NuSTAR spectral fit for the bright loop on the east limb for NuSTAR
orbit 1, FPMA only. This fit combines P10 (18:46:07–18:47:48 UT) and 11
(18:48:35–18:50:16 UT) from this orbit.

A circular region of radius $41^{\prime\prime}$, chosen such that only the
brightest NuSTAR emission was enclosed, was used for the spectral fitting.
Figure 7 shows the NuSTAR FPMA fitted spectrum for this source, with spectra
from P10 and 11 from orbit 1 fit simultaneously. This spectrum was again fit
with an isothermal model, giving a temperature of 2.53 MK and an emission
measure of 9.62 $\times$ $10^{44}$ cm-3. Because it is only possible to do a
NuSTAR spectral fit for one point in time for this feature, and because this
temperature once again lies above the peak of SDO/AIA 211Å’s sensitivity,
comparison with SDO/AIA and Hinode/XRT is difficult here.

###  2.3 Loops and Bright Point Near Disk Centre

In both orbits, NuSTAR observes a source near the centre of the the solar
disk. Upon inspection of the SDO/AIA 211 Å and Hinode/XRT Be-thin images,
shown in Figure 8, it can be seen that the NuSTAR emission in fact originates
from two distinct sources: a perpendicular pair of loops, and a bright point
which lies nearby, labelled BP3 in Figure 1.

Figure 8.: Hinode/XRT images of the loops and bright point near disk centre
from orbits 1 and 2 (left and right, respectively). The aligned 2.2–4.0 keV
NuSTAR contours are summed over P13, 14, 17, and 18 for each orbit, and are
plotted at the same levels in both images (4, 7, 10, 15 $\times$ $10^{-4}$
counts s-1).

Figure 9.: NuSTAR fitted spectra for the loops near disk centre (top) and the
nearby bright point (bottom) simultaneously fitting FPMA and FPMB from P13,
14, 17, and 18 for both orbits (pointings lie between 18:53:29–19:07:24 UT in
orbit 1; 20:30:09 – 20:44:04 UT in orbit 2). The number in black is the
multiplicative constant introduced to account for systematic differences
between FPMA and FPMB.

Each of these features were captured in P13, 14, 17, and 18 in both of the
NuSTAR orbits. For both the loops and BP3, The NuSTAR FPMA and FPMB spectra
for these four pointings were fit simultaneously for each orbit. From the
resulting fits, shown in Figure 9, the temperature of the loops decreases from
2.51 MK in the first orbit to 2.07 MK in the second, with the emission measure
increasing from 1.03 $\times$ $10^{44}$ cm-3 to 6.39 $\times$ $10^{44}$ cm-3.
However, when the uncertainties on these values are taken into account, any
change in temperature and emission measure between the orbits is marginal for
this feature. For the bright point, the fits also suggest a decrease in
temperature, from 3.22 MK to 2.56 MK, with the emission measure increasing
from 1.33 $\times$ $10^{43}$ cm-3 to 5.10 $\times$ $10^{43}$ cm-3.

##  3 Emerging Flux Region

The EFR, which later went on to become an active region, was observed by
NuSTAR in both orbits. For this EFR, flux first begins to emerge just after
00:00 UT on 28 September. There is some cancellation between opposite
polarities, and the positive and negative polarities then spread apart. This
is the time during which this feature is observed by NuSTAR. The next day,
beginning at $\sim$ 14:00 UT on 29 September, there is more intense flux
emergence in this region, producing an active region.

In each NuSTAR orbit, the EFR was captured in four pointings, split into two
pairs of consecutive pointings: 12 and 13, and 18 and 19. Capturing this
feature four times in each orbit, for a total number of eight pointings over
the whole observation, gives the opportunity to study its temporal evolution
despite the short duration of the mosaic pointings.

Figure 10.: SDO/AIA 211Å (top two rows) Hinode/XRT Be-thin (bottom two rows)
images of the EFR from the mid-times of the eight NuSTAR pointings that
capture the feature. Yellow contours represent aligned NuSTAR FPMA + FPMB
2.2–4.0 keV, with the contours plotted at the same levels in all panels (5,
10, 15, 30 $\times$ $10^{-4}$ counts s-1). For each instrument, the top row
shows orbit 1 and the bottom shows orbit 2, with P12, 13, 18, 19 arranged from
left to right. The dashed lines indicate the regions that the lightcurves in
Figure 11 are calculated over.

Hinode/XRT Be-thin and SDO/AIA 211 Å images of the EFR are shown in Figure 10.
These images are from the mid-times of all of the mosaic pointings where
NuSTAR captured the EFR. The NuSTAR 2.2–4.0 keV contours, aligned with
SDO/AIA, are also plotted in this figure to show the HXR evolution of the
feature. These contours indicate that the feature is generally brighter in the
second orbit than the first. In the Hinode/XRT and SDO/AIA images, the EFR
appears to be comprised of three separate regions. It is clear that the
majority of the NuSTAR emission originates from the bright central region
($-250^{\prime\prime},-250^{\prime\prime}$), particularly in the second orbit
when the feature has brightened. However, there does appear to be a
contribution from the upper region ($-300^{\prime\prime},-200^{\prime\prime}$)
to the NuSTAR emission in P12 of the first orbit, as shown in the top left
panel for each instrument of Figure 10. The lower region
($-350^{\prime\prime},-350^{\prime\prime}$) does not appear to contribute
significantly to the NuSTAR emission. This is expected in P12 and 13 of each
orbit, as this region would be outside NuSTAR’s FOV. In P18 and 19, this
feature would lie close to a detector gap, which could explain the lack of
NuSTAR emission from this region.

Figure 11.: Hinode/XRT Be-thin (blue) and SDO/AIA 211 Å (red) lightcurves for
the whole EFR, as well as the three separate regions within it. The green
shaded areas indicate the times of the eight NuSTAR mosaic pointings that
captured the EFR.

The Hinode/XRT Be-thin and SDO/AIA 211Å lightcurves for the EFR are plotted in
Figure 11, including lightcurves for each region separately, and also for the
EFR as a whole with all three of the regions combined. These lightcurves were
calculated over the rectangular boxes shown in the top left panel in Figure
10, chosen such that the sources remained in the boxes throughout the NuSTAR
observation period. These lightcurves confirm that the central region is the
brightest of the three in both SDO/AIA and Hinode/XRT, and the greatest
contributor to the emission from the EFR as a whole, as shown in the top row
of Figure 11. In the first orbit, both lightcurves for this region decrease
between the times of the NuSTAR pointings (18:53 UT and 19:07 UT).
Interestingly, between the two NuSTAR pointing times in the second orbit
(20:29 UT and 20:44 UT) the Hinode/XRT lightcurve decreases where the SDO/AIA
211 Å lightcurve increases. However, the change in the SDO/AIA 211 Å
lightcurve is relatively much smaller than the change in Hinode/XRT.

The Hinode/XRT lightcurve for the upper region shows a sharp peak in
brightness during P12 of the first NuSTAR orbit, before falling off. This is
consistent with the NuSTAR contours in the top left panel for each instrument
in Figure 10, where the upper region is significantly contributing to the
NuSTAR emission in P12 of orbit 1. The peak in the Hinode/XRT lightcurve
followed later by the peak in the SDO/AIA 211 Å lightcurve for this region
suggests a heating of material followed by cooling.

The lower region is outside NuSTAR’s FOV in P12 and 13, and would be
positioned near or on a detector gap in P18 and 19. However, the lightcurves
confirm that this feature is relatively very faint in Hinode/XRT in comparison
to the central region, and therefore would be unlikely to contribute
significantly to the NuSTAR emission from the EFR.

###  3.1 NuSTAR Spectral Analysis

The EFR was observed in P12, 13, 18, and 19 in each orbit. Including FPMA and
FPMB, this gives a total of 16 spectra that could be fit simultaneously or
separately. When fitting the spectra of the faint NuSTAR mosaic features, it
is important to find a balance between combining enough spectra to get a good
fit and being able to obtain information about how the feature evolves over
time. This is particularly true in the case of the EFR, a source for which the
temporal evolution is of interest. To ensure that the properties of the EFR
did not change significantly between the pointings being used, the spectra for
the two pairs of consecutive pointings, 12 and 13, and 18 and 19, were fit
simultaneously for each orbit. For this feature, the circular region used for
the fitting had a radius of $83.5^{\prime\prime}$.

Figure 12.: NuSTAR fitted spectra for the EFR, combining P12 and 13, and P18
and 19 for both orbits (pointings lie between 18:51:02–19:09:52 UT in orbit 1;
20:27:42 – 20:46:32 UT in orbit 2). The number in black is the multiplicative
constant introduced to account for systematic differences between FPMA and
FPMB.

The NuSTAR spectra for the EFR and their fits are shown in Figure 12. Each of
these spectra are well fit with a single isothermal APEC model, and show no
evidence of non-thermal emission or a higher temperature component. The
spectral fits from all four times give a reasonably constant temperature of
$\sim$ 2.5 MK, and emission measures ranging between 1.9 and 6.1 $\times$
$10^{44}$ cm-3. The fits do suggest a slight increase in temperature of the
EFR over the two orbits, from 2.54 MK to 2.63 MK. However, taking into account
the uncertainties on these temperatures, this increase is not statistically
significant. The emission measure from the spectral fits decreases from 3.42
to 1.93 $\times$ $10^{44}$ cm-3 between P12,13 and P18,19 in the first orbit
(as seen in the top row of Figure 12). It then increases up to 6.10 $\times$
$10^{44}$ cm-3 in P12,13 in the second orbit, before falling to 2.40 $\times$
$10^{44}$ cm-3 for P18,19 (as seen in the bottom row of Figure 12). This
behaviour is broadly similar to that observed in the Hinode/XRT lightcurve for
the central region in Figure 11. In both orbits, the NuSTAR fit temperature
remains approximately constant while the emission measure decreases. This is
in agreement with the decreases in the Hinode/XRT lightcurve between the
NuSTAR pointing times in both orbits, and the highest NuSTAR emission measure
corresponds to the highest peak in Hinode/XRT at 20:30 UT. This similar
behaviour is expected as Hinode/XRT and NuSTAR should be observing emission at
approximately the same temperatures.

###  3.2 Differential Emission Measures

In the EFR lightcurves in Figure 11, at around 20:30 UT (NuSTAR orbit 2, P12
and 13), there is a peak in the Hinode/XRT Be-thin lightcurve that coincides
with a minimum in the SDO/AIA 211 Å lightcurve. Later, at around 20:45 UT
(NuSTAR orbit 2, P18 and 19) there is increased SDO/AIA 211Å emission but
decreased Hinode/XRT Be-thin emission. As Hinode/XRT is sensitive to higher
temperature emission than SDO/AIA 211 Å, this suggests that there is more
higher temperature emission present at 20:30 UT than at 20:45 UT. In order to
confirm this we perform differential emission measure (DEM) analysis.

In an effort to understand the multi-thermal nature of this feature, we
reconstruct DEMs for the EFR for each orbit, combining data from NuSTAR,
Hinode/XRT, and the six SDO/AIA optically thin coronal-temperature channels.
As with the spectral fitting, we consider NuSTAR P12 and 13, and P18 and 19
for each orbit jointly by averaging both the NuSTAR data values and responses
for the two pointings. Recovering the DEM involves solving the ill-posed
inverse problem $g_{i}=K_{i,j}DEM(T)$, where $g_{i}$ [DN s-1 px-1] is the
observed flux in each channel, and $K_{i,j}$ is the temperature response for
the $i^{th}$ channel and the $j^{th}$ temperature bin. The regularized
inversion approach of Hannah and Kontar (2012) was used to reconstruct the
DEMs for the EFR, using the minimum of the EM loci curves for weighting.

The fluxes for SDO/AIA and Hinode/XRT were obtained from an image from each
channel averaged over the relevant NuSTAR pointing time, using only the
central region of the EFR (as in Figure 10). A systematic error of 20$\%$ was
assigned to the SDO/AIA, Hinode/XRT, and NuSTAR fluxes in order to account for
uncertainties in their temperature responses. The photon shot noise was
calculated for all three instruments. In the case of SDO/AIA and Hinode/XRT,
this uncertainty was found to be negligible compared to the systematic
uncertainty as this flux was calculated as an average over all of the pixels
that capture the EFR. However, in the case of NuSTAR, the shot noise was not
negligible, and therefore was added in quadrature with the 20$\%$ systematic
error. For the DEM calculation, the NuSTAR data was split into two energy
bands: 2.2–2.6 keV and 2.6–3.6 keV. The SDO/AIA and Hinode/XRT temperature
responses were calculated using the standard Solarsoft routines from the
instrument teams: aia_get_response.pro for SDO/AIA and make_xrt_temp_resp.pro
for Hinode/XRT. The NuSTAR response was calculated in
Python222https://github.com/ianan/nustar˙sac/blob/master/python/ns˙tresp.py
using the spectral responses used in section 3.1.

DEM analysis combining data from NuSTAR, SDO/AIA and Hinode/XRT has been done
before by Wright et al. (2017). In this study, it was found that multiplying
the Hinode/XRT responses by a factor of 2 before calculating the DEMs produced
a solution with smaller residuals. This choice was made following the
suggestion of previous authors who also found discrepancies when using
Hinode/XRT data (Schmelz et al., 2015; Testa et al., 2011; Cheung et al.,
2015). In the case of the EFR, the DEMs were calculated using the Hinode/XRT
responses both with and without an added multiplicative factor of 2.
Introducing this factor was similarly found to improve the DEM results here,
and so was used for all of the DEMs shown.

Figure 13.: DEMs for the EFR for NuSTAR orbit 1 (left) and orbit 2 (right),
combining P12 and 13 (red) and P18 and 19 (purple). These DEMs are
reconstructed using data from NuSTAR, Hinode/XRT and SDO/AIA.

A comparison between the DEMs calculated for P12 and 13, and P18 and 19 is
shown for each orbit in Figure 13. In orbit 1, between these two times, the
emission in both the Hinode/XRT Be-thin and SDO/AIA 211 Å lightcurves in
Figure 11 decreases, though the change in brightness is smaller than the
20$\%$ systematic error used in the DEM calculation in both cases. This is
reflected in the two DEMs for these times, as the DEM for P12 and 13 is higher
than the one for P18 and 19 for log(T) higher than $\sim$ 6.2, though they are
not significantly different when taking into account the error bars.

In the case of orbit 2, the Hinode/XRT lightcurve shows a peak at around the
time of NuSTAR P12 and 13, before decreasing for NuSTAR P18 and 19. Between
these two times, the decrease in Hinode/XRT emission and corresponding
increase in SDO/AIA 211 Å emission suggests that there is hotter material
present at the earlier time. The change in Hinode/XRT is higher than the
20$\%$ systematic errors, whereas the change in 211 Å is again very small.
From the calculated DEMs, there is more emission above log(T) $\sim$ 6.3 at
the earlier time, in agreement with the fall-off in the Hinode/XRT lightcurve.
The DEM for P18 and 19 is higher than that for P12 and 13 for log(T) between
$\sim$ 6.1 and 6.3, though there is no difference between the DEMs at these
temperatures outwith the error bars. Material at these temperatures could be
responsible for the peak in the SDO/AIA 211Å at the later time.

Figure 14.: An exmaple of a DEM reconstructed using data from SDO/AIA only
(blue), from SDO/AIA and Hinode/XRT (green), and from SDO/AIA, Hinode/XRT and
NuSTAR (red). The NuSTAR EM loci curves are also plotted in grey.

Adding X-ray data to a DEM calculation using SDO/AIA is useful in constraining
the higher temperature emission. Figure 14 shows a comparison between one of
the EFR DEMs (from orbit 2 P12 and 13) reconstructed using data from SDO/AIA
only, from SDO/AIA and Hinode/XRT, and from SDO/AIA, Hinode/XRT, and NuSTAR.
In addition to the three DEMs plotted here, a DEM was also reconstructed using
data from SDO/AIA and NuSTAR only. It was found that the solution was
consistent within the error bars with the DEM including all three instruments.
In this figure, the NuSTAR EM loci curves are marked on. The point of
intersection between the loci curves for the two energy bands corresponds to
the T and EM values from the NuSTAR spectral fit.

All three of the DEMs in Figure 14 peak at log(T) $\sim$ 6.15, and are in good
agreement below log(T) $\sim$ 6.4. This figure demonstrates that the addition
of Hinode/XRT to the calculation helps to constrain the DEM at temperatures
higher than this, and adding NuSTAR strengthens this constraint. From
including the X-ray data rather than relying on SDO/AIA alone, it is clear
that there is virtually no emission above 4 MK here. Previous studies looking
at non-flaring active regions and using different DEM approaches to those used
in this paper also found that erroneous higher temperature DEM components
could appear if HXR data was not included (Schmelz et al., 2009; Reale,
McTiernan, and Testa, 2009).

A previous study of an EFR in the quiet Sun by Kontogiannis et al. (2020) also
included DEM analysis, using data from Hinode/EIS. The results from this study
agree with the results found here, with both finding a DEM peak of comparable
magnitude at a similar temperature (log(T) $\sim$ 6.1). Using only data from
Hinode/EIS, this study obtained solutions that were not well-defined for
log(T) $>$ 6.3. Including the X-ray data here provides a constraint at higher
temperatures to produce a more well-defined solution in this range.

###  3.3 NuSTAR Non-thermal Upper Limits

Using the approach detailed in section 2.1.1, the upper limits on any non-
thermal emission present in the EFR were calculated and compared to the
required heating power obtained from the thermal energy of the plasma. This
calculation was done for the peak time in the Hinode/XRT lightcurve,
corresponding to NuSTAR orbit 2 P12 and 13. The central region of the EFR is
$\sim$ $35^{\prime\prime}$ square and therefore, following the same approach
as for the jet, has a volume of 1.65 $\times$ $10^{28}$ cm3. Using equation 1
and the fit values from the spectrum in Figure 12, its thermal energy is 3.37
$\times$ $10^{27}$ erg, with a heating power of 1.37 $\times$ $10^{25}$ erg
s-1 over the observation time.

It was found that none of the upper limits on the non-thermal power were
consistent with the required heating power. The area used here may have been
an over-estimate, and making this value smaller would in turn lower the
heating requirement. However, even reducing the area by 50% results in a
required heating power that is reduced by less than a factor of 2, and this
power is an order of magnitude larger than the upper limits on the non-thermal
heating power. Therefore, it can be concluded that, in the case of the EFR,
any non-thermal component that is present is not responsible for the observed
heating.

##  4 Bright Points

Two bright points, labelled BP1 and BP2 in Figure 1, were observed with
NuSTAR, and also with Hinode/XRT and SDO/AIA. Figure 15 shows Hinode/XRT and
SDO/AIA 211 Å images, with aligned NuSTAR contours, of the bright points from
the time of P17 of the second NuSTAR orbit. In both 211 Å and Hinode/XRT, BP2
is a more compact feature than BP1, but it is brighter in NuSTAR at this time.

BP1 is observed with NuSTAR in P14, 15, 16, and 17 of both orbits. BP2 is
close to BP1, and lies in a region that is captured by NuSTAR also in P14, 15,
16, and 17. However, this feature is extremely faint in the first orbit,
making it unusable for spectroscopy. Though it is present in all pointings in
orbit 2, BP2 is located over the edge of the detector in P14 and 15, and is
therefore only well observed in P16 and 17.

Figure 15.: SDO/AIA 211 Å (left) and Hinode/XRT Be-thin (right) images of the
two bright points from 20:41 UT, coinciding with NuSTAR orbit 2 P17. Yellow
contours represent NuSTAR 2.2–4.0 keV (contour levels are 5, 10, 20 $\times$
$10^{-4}$ counts s-1), aligned with SDO/AIA. The dashed boxes indicate regions
used for obtaining the lightcurves in Figure 16.

The SDO/AIA 211Å and Hinode/XRT Be-thin lightcurves for the two bright points
are shown in Figure 16. These lightcurves were calculated over the boxes
enclosing the bright points shown in Figure 15. In the case of BP1, the
lightcurves indicate an increase in brightness in both channels, peaking just
before the NuSTAR pointings in the first orbit, and then they continue to
increase in brightness until the pointings in the second orbit. The two
lightcurves for BP2 also show increasing brightness throughout both orbits of
NuSTAR observation. This behaviour explains why BP2 is not observed by NuSTAR
in the first orbit; it is not yet producing sufficiently bright emission to be
detected by NuSTAR.

Figure 16.: SDO/AIA 211 Å (red) and Hinode/XRT (blue) Be-thin lightcurves for
BP1 (left) and BP2 (right). The green shaded areas indicate the times of the
NuSTAR pointings suitable for spectroscopy.

###  4.1 NuSTAR Spectral Analysis

In order to investigate the properties of both of these features, the NuSTAR
spectra of the bright points were fitted. As was the case with the EFR, the
spectra from individual pointings for these features are noisy and poorly fit
due to their faintness and the short integration time. Therefore, spectra from
multiple pointings were fit simultaneously (also combining FPMA and FPMB) to
improve the SNR. In the case of both bright points, the spectra were fit using
an isothermal APEC model, once again fitting down to 2.2 keV. The circular
regions used for the fitting had radii of $68^{\prime\prime}$ and
$47^{\prime\prime}$ for BP1 and BP2 respectively.

Figure 17.: NuSTAR spectral fits for BP1 for NuSTAR orbits 1 and 2. NuSTAR
FPMA and FPMB spectra from P14, 15, 16, and 17 are fit simultaneously for both
orbits (pointings lie between 18:55:56–19:04:56 UT in orbit 1; 20:32:36 –
20:41:36 UT in orbit 2). The number in black is the multiplicative constant
introduced to account for systematic differences between FPMA and FPMB.

For BP1, a NuSTAR spectrum was fit for each orbit, combining data from P14,
15, 16, and 17 for both. The resulting fits, shown in Figure 17, indicate that
this feature has a temperature of $\sim$ 2.5 MK, with the emission measure
increasing from 1.14 to 4.07 $\times$ $10^{44}$ cm-3 between the two orbits.
This increase in emission measure is in agreement with the increase in
brightness shown in the Hinode/XRT and SDO/AIA lightcurves in Figure 16.
Considering both the fits and the lightcurves, NuSTAR sees an increase in EM
by a factor of $\sim$ 4, while the feature brightens by a factor of $\sim$ 1.2
in SDO/AIA 211 Å and $\sim$ 2 in Hinode/XRT Be-thin. This could be due to both
of these channels, 211Å in particular, being also sensitive to cooler material
than NuSTAR, meaning that if this brightening is occurring at higher
temperatures, it is less significant to the overall emission in these
channels.

Figure 18.: NuSTAR spectral fit for BP2 for NuSTAR orbit 2. This fit combines
P16 (20:37:31–20:39:12 UT) and 17 (20:39:58–20:41:36 UT), FPMA and FPMB, from
this orbit. The number in black is the multiplicative constant introduced to
account for systematic differences between FPMA and FPMB.

For BP2, which was only well observed in P16 and 17 in the second NuSTAR
orbit, a spectrum containing these two pointings was fit, with the resulting
plot shown in Figure 18. The fit values for the temperature and emission
measure of this spectrum are 3.22 MK and 5.98 $\times$ $10^{43}$ cm-3,
respectively. These fit parameters indicate that the NuSTAR emission from BP2
originates from a hotter temperature than for BP1. The spectra for both bright
points are well fit with the isothermal model and, similarly to the previous
examples, do not show any evidence of either a higher temperature or non-
thermal component.

###  4.2 Differential Emission Measures

Following the approach of section 3.2, differential emission measures were
reconstructed for both BP1 and BP2 in order to further investigate the
temperature difference between the two bright points that is apparent in their
NuSTAR spectral fits. BP1 was observed in both NuSTAR orbits, and a combined
DEM was obtained for this feature for each. As was the case with the spectra
shown in Figure 17, these DEMs were reconstructed by combining data from P14,
15, 16, and 17 of each orbit. The DEM for BP2 was calculated using combined
data from P16 and 17 from the second orbit only. Several of the Hinode/XRT Be-
thin pixels which covered BP2 were saturated at the times of these pointings,
so only SDO/AIA and NuSTAR data were included in the DEM calculation for this
feature (though including Hinode/XRT was found to not change the shown
solution significantly).

All three of the resulting DEMs are plotted in Figure 19. The brightening in
BP1 between the two orbits seen in Figure 16 is reflected in the DEMs for this
feature. The DEM for orbit 2 is higher than for orbit 1 for log(T) $\geq$ 6.2,
which is consistent with the observed brightening.

Compared to the 2.5 MK NuSTAR fit temperature for BP1, a temperature of 3.2 MK
was found when fitting the NuSTAR spectrum for BP2. The DEM for BP2 is higher
than the ones for BP1 for log(T) $>$ 6.2, and it extends to higher
temperatures. This suggests that there is more high temperature emission
present in this bright point, which explains the higher fit temperature found
for BP2 in the NuSTAR spectroscopy.

Figure 19.: DEMs for the two bright points. The DEMs for BP1 in orbits 1
(light blue) and 2 (dark blue) were reconstructed using data from SDO/AIA,
Hinode/XRT, and NuSTAR. The DEM for BP2 in orbit 2 (red) was reconstructed
using data from only SDO/AIA and NuSTAR (due to saturation in Hinode/XRT Be-
thin).

The DEMs for both of the bright points have a peak at log(T) $\sim$ 6.15, a
result which has also been found in previous DEM analyses of coronal bright
points (Brosius et al., 2008; Doschek et al., 2010). Similarly to the case of
the EFR, the DEMs of both bright points confirm that there are no higher
temperature components, with no significant emission present above 4 MK. Once
again, these DEMs benefit from using the X-ray data from NuSTAR and Hinode/XRT
to constrain the higher temperature emission.

###  4.3 NuSTAR Non-thermal Upper Limits

Again following the approach from section 2.1.1, the non-thermal upper limits
were calculated for BP1 and BP2, both for orbit 2 when they were at their
brightest in NuSTAR. For BP1, which is $35^{\prime\prime}$ square and
therefore has an associated volume of 1.65 $\times$ $10^{28}$ cm3, the thermal
energy was found to be 2.71 $\times$ $10^{27}$ erg, giving a heating power of
5.02 $\times$ $10^{24}$ erg s-1. The largest non-thermal upper limits for BP1
were about an order of magnitude smaller than the heating requirement. If
there was some filling factor $<$ 1 and the area used here was an
overestimate, then the heating requirement could be reduced. However, BP1
would still be at the very limit of being a possible non-thermally heated
source.

BP2, which was $15^{\prime\prime}$ square with a volume of 1.30 $\times$
$10^{27}$ cm3, has a thermal energy of 3.71 $\times$ $10^{26}$ erg, meaning
the heating power is 1.52 $\times$ $10^{24}$ erg s-1. The upper limits on the
non-thermal heating power are only slightly lower than this value for a very
steep, almost mono-energetic, spectrum with a low energy cutoff of $\sim$ 3
keV. Again, the heating requirement could be shifted down by using a filling
factor $<$ 1 and reducing the area. Therefore, it is possible that this
feature could have been heated non-thermally, but this result is marginal.

##  5 Discussion and Conclusions

In this paper, we have presented the first survey of quiet Sun features in
HXRs observed during solar minimum. NuSTAR’s full-disk solar mosaic mode
allowed for a range of different types of features to be observed. In these
two mosaics, NuSTAR observed steady features, such as bright points and an
EFR, but also captured a transient jet. This is the first observation of these
types of features using a HXR focusing telescope. The mosaics also reveal
large-scale sources (the diffuse sources in Figure 1), diagnostically
important for investigating the heating of the diffuse corona.

From fitting the NuSTAR spectra of these features, we find their temperatures
lie in the range 2.0–3.2 MK, but we find no evidence of a higher temperature
or non-thermal component present in their X-ray spectra. We have used EUV and
SXR data from SDO/AIA and Hinode/XRT in addition to NuSTAR to investigate the
temperature evolution of the quiet Sun features, including successfully
reconstructing DEMs which combine data from all three of these instruments.
The DEM solutions for these quiet Sun features show no evidence of emission
above 4 MK, a result achieved by using X-ray data in the DEM calculation to
constrain the solution at high temperatures.

The temperatures found from the NuSTAR spectral fits for all of the features
investigated here lie in a narrow temperature range between 2.0–3.2 MK. This
is consistent with the findings from previous studies that used EUV and SXR
data, which have found that bright point temperatures are generally $<$ 3 MK
(Doschek et al., 2010; Alexander, Del Zanna, and Maclean, 2011; Kariyappa et
al., 2011). In the work presented in this paper we have also found two
slightly hotter bright points (BP2 and BP3), with the NuSTAR spectral fit
giving 3.2 MK. However, these studies have found that some bright points have
temperatures $<$ 2 MK when investigated using EUV and/or SXR data. Although
NuSTAR is more sensitive to higher temperature emission, there is so little of
it in these features that the spectra are dominated by these cooler sources,
appearing effectively isothermal, capturing the 2–3 MK peak of the DEM.

Difficulties arise in this analysis when working with with SDO/AIA data
because none of the SDO/AIA channels have a peak in sensitivity in the 2–3MK
range. As a result, the SDO/AIA 211 Å lightcurves for these features sometimes
do not show behaviour consistent with Hinode/XRT or with NuSTAR. Previous
analysis of microflares observed with NuSTAR (for example, Cooper et al.
(2020, 2021)) has made use of the SDO/AIA Fe XVIII proxy channel (Del Zanna,
2013). Unfortunately, the temperatures of these quiet Sun features are too low
for this to be useful. However, Hinode/XRT has sensitivity in a similar
temperature range to NuSTAR, and makes a useful comparison.

As all of the NuSTAR spectra were adequately fitted with an isothermal model,
only non-thermal upper limits were found for some of the features. In most
cases, it was found that the possible non-thermal component was not sufficient
to produce the required heating. The feature that was the best candidate for
non-thermal heating was the jet. However, even this would require a very steep
(effectively mono-energetic) non-thermal distribution with a low energy cutoff
between 3–4 keV.

From the spectral, DEM, and non-thermal upper limit analysis performed here,
it can be concluded that if there are any higher temperature or non-thermal
sources in the features from this observation, they would have to be very
weak. However, the NuSTAR full-disk solar mosaics, while useful in allowing
the observation of multiple sources present within an orbit, have limitations
when investigating the properties and evolution of these quiet Sun features.
For these faint features, the short 100 s pointings combined with NuSTAR’s
limited throughput (which is dominated by lower energy X-rays) makes it
unlikely that higher temperature or non-thermal components that are present
would be detectable unless they were relatively stong.

The work presented in this paper used the first NuSTAR quiet Sun campaign from
the recent solar minimum. Additional data sets were taken throughout the solar
minimum (2018–2020) in both the full-disk mosaic mode as well as longer
dwells, in which pointing was not changed. In these dwells, any bright points
would be observed for several hours over multiple orbits. These longer
observing campaigns could provide a better opportunity to detect more
energetic HXR emission from the quiet Sun, and also increase the chances of
capturing more atypical harder sources. Having observations of quiet Sun
features over a longer period of time will also mean that a more rigorous
investigation of their temporal evolution in HXRs will be possible.

The NuSTAR quiet Sun dwell data will be used to further the work presented
here, and will be the subject of future papers. However, shorter time-scale
variability in the HXR emission from quiet Sun features such as these may
remain difficult to detect until there is a dedicated solar X-ray instrument
with higher sensitivity and throughput.

##### Acknowledgements

This paper made use of data from the NuSTAR mission, a project led by the
California Institute of Technology, managed by the Jet Propulsion Laboratory,
funded by the National Aeronautics and Space Administration. We thank the
NuSTAR Operations, Software and Calibration teams for support with the
execution and analysis of these observations. This research made use of the
NuSTAR Data Analysis Software (NUSTARDAS) jointly developed by the ASI Science
Data Center (ASDC, Italy), and the California Institute of Technology (USA).
Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as
domestic partner and NASA and UKSA as international partners. It is operated
by these agencies in co-operation with ESA and NSC (Norway). AIA on the Solar
Dynamics Observatory is part of NASA’s Living with a Star program. This
research has made use of SunPy, an open-source and free community-developed
solar data analysis package written in Python (SunPy Community et al., 2015)
This research made use of Astropy, a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2018, 2013)

## Funding

SP acknowledges support from the UK’s Science and Technology Facilities
Council (STFC) doctoral training grant (ST/T506102/1). IGH acknowledges
support from a Royal Society University Fellowship (URF/R/180010) and STFC
grant (ST/T000422/1).

## Data Availability

All the data used in this paper are publicly available. In particular, NuSTAR
via the NuSTAR Master Catalog with the OBSIDs 90410101001 - 90410125001 and
90410201001 - 90410225001.

## Declarations

## Conflict of interest

The authors declare that they have no conflicts of interest.

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