# Parallel plasma loops and the energization of the solar corona

Hardi Peter Max Planck Institute for Solar System Research, Justus-von-Liebig-
Weg 3, D-37077, Göttingen, Germany  Lakshmi Pradeep Chitta Max Planck
Institute for Solar System Research, Justus-von-Liebig-Weg 3, D-37077,
Göttingen, Germany  Feng Chen Laboratory for Atmospheric and Space Physics,
University of Colorado Boulder, Boulder, CO 80303, USA  David I. Pontin School
of Information and Physical Sciences, University of Newcastle, Callaghan, NSW
2308, Australia  School of Science and Engineering, University of Dundee,
Nethergate, Dundee, DD1 4HN, UK  Amy R. Winebarger  NASA/Marshall Space Flight
Center, Huntsville, AL 35812, USA  Leon Golub  Harvard-Smithsonian Center for
Astrophysics, 60 Garden St., Cambridge, MA 02138, USA  Sabrina L. Savage
NASA/Marshall Space Flight Center, Huntsville, AL 35812, USA  Laurel A.
Rachmeler  National Oceanic and Atmospheric Administration (NOAA), Boulder, CO
80305  Ken Kobayashi  NASA/Marshall Space Flight Center, Huntsville, AL 35812,
USA  David H. Brooks  College of Science, George Mason University, 4400
University Drive, Fairfax, VA 22030, USA  Jonathan W. Cirtain  BWX
Technologies, Inc., 800 Main St #400, Lynchburg, VA 24504  Bart De Pontieu
Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304, USA
Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029
Blindern, NO-0315, Oslo, Norway  Institute of Theoretical Astrophysics,
University of Oslo, P.O. Box 1029 Blindern, NO-0315, Oslo, Norway  David E.
McKenzie  NASA/Marshall Space Flight Center, Huntsville, AL 35812, USA
Richard J. Morton  Department of Mathematics, Physics and Electrical
Engineering, Northumbria University, Newcastle Upon Tyne, NE1 8ST, UK  Paola
Testa Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge,
MA 02138, USA  Sanjiv K. Tiwari  Bay Area Environmental Research Institute,
NASA Research Park, Moffett Field, CA 94035, USA  Lockheed Martin Solar and
Astrophysics Laboratory, Palo Alto, CA 94304, USA  Robert W. Walsh  Jeremiah
Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, UK
Harry P. Warren  Space Science Division, Naval Research Laboratory,
Washington, DC 20375, USA

###### Abstract

The outer atmosphere of the Sun is composed of plasma heated to temperatures
well in excess of the visible surface. We investigate short cool and warm
(${<}1$ MK) loops seen in the core of an active region to address the role of
field-line braiding in energising these structures. We report observations
from the High-resolution Coronal imager (Hi-C) that have been acquired in a
coordinated campaign with the Interface Region Imaging Spectrograph (IRIS). In
the core of the active region, the 172 Å band of Hi-C and the 1400 Å channel
of IRIS show plasma loops at different temperatures that run in parallel.
There is a small but detectable spatial offset of less than 1″ between the
loops seen in the two bands. Most importantly, we do not see observational
signatures that these loops might be twisted around each other. Considering
the scenario of magnetic braiding, our observations of parallel loops imply
that the stresses put into the magnetic field have to relax while the braiding
is applied: the magnetic field never reaches a highly braided state on these
length-scales comparable to the separation of the loops. This supports recent
numerical 3D models of loop braiding in which the effective dissipation is
sufficiently large that it keeps the magnetic field from getting highly
twisted within a loop.

Sun: magnetic fields — Sun: UV radiation — Sun: transition region — Sun:
corona — Magnetohydrodynamics (MHD)

Accepted for publication in The Astrophysical Journal, May 20, 2022

##  1 Introduction

The structure of the upper atmosphere above active regions on the Sun is
dominated by coronal loops at temperatures from 0.1 to 10 MK. Best seen in
extreme UV wavelengths, these loops show heated plasma that is trapped by the
magnetic field and therefore outline magnetic field lines. The energy to heat
the plasma and support it against gravity has to be supplied by the magnetic
field. Hence, knowing the structure of the magnetic field is a key to
understanding the underlying processes that create the hot coronal plasma on
the Sun, and also on other stars. Several concepts to heat the upper
atmosphere have been discussed. Heating by magneto-acoustic waves is
considered to be widespread Heyvaerts & Priest (1983); Tomczyk et al. (2007).
However, current observations do not detect sufficient wave energy flux to
power the hot parts of active regions McIntosh et al. (2011), even though wave
motions might hide from detection because of line-of-sight effects or
wavelengths and frequencies below the detection limit De Moortel & Pascoe
(2012); Karampelas et al. (2019b). An alternative is the energisation of the
corona through surface motions resulting in field line braiding Parker (1972,
1983); Cirtain et al. (2013), flux-tube tectonics Priest et al. (2002) or
injection of plasma, currents or waves Martínez-Sykora et al. (2017); De
Pontieu et al. (2017). More recently, also the role of emergence and
cancelation of magnetic flux at the footpoints of hot structures has been
investigated Chitta et al. (2017, 2018); Asgari-Targhi et al. (2019).

In a typical active region one can distinguish different types of loops Reale
(2014). Long warm loops with plasma at temperatures of around 1 MK have
lengths that are a significant fraction of the solar radius and connect to the
periphery of an active region (e.g. the long loops in Fig. 3). More compact,
hot loops, reaching temperatures of up to 5 MK, are mostly found in the core
of active regions Warren et al. (2010). The core of an active region also
hosts an abundance of shorter, cool loops reaching only a few 0.1 MK, in
particular during phases of emergence of magnetic flux, e.g. while an active
region forms. These cool loops are evident in the 1400 Å channel of the
Interface Region Imaging Spectrograph, IRIS De Pontieu et al. (2014). The
emission from the cool loops in this 55 Å wide wavelength band is clearly
dominated by photons from the Si IV doublet at 1393.76 Å and 1402.77 Å Tian et
al. (2018), showing that these loops host plasma at temperatures of the order
of only 0.1 MK. There is also some contribution by the C II doublet near 1335
Å which forms at slightly lower temperatures.

Some of these cool loops seen in the IRIS 1400 Å channel appear without any
counterparts visible at higher temperatures around 1 MK Peter et al. (2014),
some have those counterparts Li & Peter (2019). Still, most observations with
the Atmospheric Imaging Assembly, AIA Lemen et al. (2012), in the cores of
(emerging) active regions also show short loops in the 171 Å channel. Under
equilibrium conditions the 171 Å band has a peak response just below 1 MK and
is dominated by emission from Fe IX at 171.07 Å (and to a lesser extent by Fe
X at 174.53 Å). However, many of the extreme UV channels of AIA also have
contributions from lines forming at lower temperatures, e.g., the 171 Å band
has a secondary contribution around 0.3 MK Boerner et al. (2012). So the
question remains if the short loops in AIA 171 Å in active region cores are
actually originating from temperatures around 0.3 MK) or higher temperatures
(roughly 1 MK).

Essentially, this raises the question if the loops in the 171 Å band and the
1400 Å band are the same structures, or if cool and warm loops co-exist in
close vicinity. More importantly, the relation of the structures seen at 171 Å
and 1400 Å contain key information on the nature of the cool emerging loops in
the active region core. Comparing observational results to models, we will be
able to conclude how the emergence process governs the thermal evolution of
the active region core. We will find that the loops we see in Hi-C 172 Å and
in IRIS 1400 Å run in parallel, without observable signatures of braiding.
This implies that the magnetic field relaxes already while driven, which is
consistent with recent models of field-line braiding. In principle, it could
also be that the loops are aligned with emerging flux emerging too fast to
undergo braiding.

In this study we will exploit the potential of the unprecedented spatial
resolution of the High-resolution Coronal imager, Hi-C Rachmeler et al. (2019)
in the 172 Å band during its second successful flight (termed Hi-C 2.1).
Together with data from IRIS and a 3D MHD model of an emerging active region,
we can address and settle the above questions.

We will start with a brief discussion of field-line braiding (Sect. 2) before
we provide details of the observational data (Sect. 3). The key observational
result of our study, namely that the loops in Hi-C and IRIS run in parallel
with a (small) offset, will be presented in Sect. 4. We discuss the temporal
evolution and thermal structure of the compact loops in more detail in Sect. 5
before we compare the observations to one particular 3D MHD model of an
emerging loop system in Sect. 6 and conclude in Sect. 7.

##  2 Braiding of coronal structures

Braiding of magnetic field lines by motions at the solar surface will create
thin current sheets in the corona, and the dissipated magnetic energy heats
the plasma. This goes along with (bundles of) field lines being braided around
each other, as depicted by cartoons in the original papers by Parker (1972,
1983). Those cartoon representations of the magnetic field would suggest that
one should find highly braided structures when observing in the extreme UV,
which originates from highly ionized plasma outlining the magnetic field
lines.

Figure 1: Braiding of a forking flux tube. The lines depict the magnetic field
of a magnetic flux rope that is forking near the location of the arrow. Part
of the flux rope is rooted near N1, another part near N2. The background image
shows the emission near 193 Å recorded during the first flight of Hi-C. The
field-of-view is 50$\times$50 Mm2. The coloring of the field lines indicates
the strength of the currents of the non-linear force-free extrapolation. The
figure is adapted from Fig. 2c of Thalmann et al. (2014). See Sect. 2 for
details.

One has to distinguish two cases of braiding of coronal structures: (1) Near-
surface flows could drive braiding within a bundle of field lines that is
rooted at each end in one single region in the photosphere, e.g. a magnetic
flux tube or sheet in the intergranular lanes. This bundle of field lines
would be co-spatial with the loop we see in coronal emission Peter & Bingert
(2012). Or in case (2) the loop we see in coronal emission could be hosted by
a larger structure with multiple footpoints at one or both ends. In this case,
large-scale shear motions of the multiple footpoints would braid the field and
thus inject energy to heat the structure.

In a paper from the first flight of Hi-C, Cirtain et al. (2013) showed the
presence of magnetic braiding according to case (2). They described an
elongated feature, resembling a loop, that was stretching above the penumbra
of a sunspot. A detailed study of the magnetic setup of this structure was
conducted by Thalmann et al. (2014) through a non-linear force-free magnetic
field extrapolation. They found that the main braiding feature of the
structure investigated by Cirtain et al. (2013) is located just where a flux-
rope forks (arrow in Fig. 1): part of the flux rope is then rooted in N1, part
in N2. Here the separation of the photospheric anchors at this end of the flux
rope is comparable to the length of the loop feature. Probably the shear
motions between locations N1 and N2 in Fig. 1 contribute to the braiding of
the structure. Relating the very same structure as observed by Cirtain et al.
(2013) to the photospheric magnetic field, Tiwari et al. (2014) found evidence
for flux cancelation. This would be consistent with the interpretation of this
structure as a flux rope and would explain why this low-lying structure is
heated to high temperatures.

Traditional models for braiding of the magnetic field in coronal loops assume
that the magnetic field is braided within the flux tube, i.e. according to
case (1). Starting with the models of Galsgaard & Nordlund (1996), there has
been an abundance of studies that essentially straighten a coronal loop and
put it into a rectangular box. In these models one can study the braiding in
detail (e.g. Rappazzo et al., 2008) and investigate the expected observational
signatures of braiding (e.g. Dahlburg et al., 2016; Pontin et al., 2017). In
these braiding models, either an internal braiding is prescribed (e.g. Wilmot-
Smith et al., 2010) or it is driven by motions within the modelled bundle of
field lines at the footpoints (e.g. Reid et al., 2018). In Fig. 2 we depict
the magnetic field in a loop braiding model during the relaxation phase. Here
some internal twisting of the field lines is visible. However, opposed to case
(2) exemplified in Fig. 1, all field lines stay within the envelope of the
single loop. The emission from a coronal loop with a braided magnetic field as
shown in Fig. 2 might not even show any signatures of braiding Pontin et al.
(2017).

Figure 2: Internal braiding of a bundle of fieldlines in a loop. The braided
magnetic field lines are shown in different colours. They are are based on a
3D MHD model similar to Pontin et al. (2017) where the magnetic field started
to relax. While the original model is for a straight loop, here we curved the
appearance to resemble a semi-circular loop. See Sect. 2 for details.

Still, one could expect that with sufficient spatial resolution one might find
braids in the internal structure of a coronal loop. Numerical 3D MHD models of
braiding have been inconclusive in that such internal braids might or might
not be present. Essentially, this depends on the setup and how quickly the
magnetic field would relax when driven from the footpoints Dahlburg et al.
(2016); Pontin et al. (2017).

Therefore, new observations will have to show if such braided magnetic fields
are observable in the extreme UV, or if the extreme UV images appear to be
combed, i.e. with structures running parallel. The main goal of this study is
to establish if the short cool and warm loops in the active region core appear
to be combed or uncombed.

Figure 3: Hi-C image showing warm loops in a solar active region. This
displays emission around 172 Å seen by Hi-C over its full field of view of
265″ $\times$ 265″ at 19:00:33 UT on May 29, 2018. The center of the image is
about 114″ east and 259″ north of disk center. The rectangle marks the core of
the active region with the abundant small loops. This 83″ $\times$ 60″ sub-
region is imaged in more detail in Fig. 4.

##  3 Observations

We investigate the core of a active region NOAA 12712 as it appeared close to
the center of the solar disk. It showed continuous emergence of new magnetic
flux for several days before our observation. The active region hosts the
typical long loops at temperatures of about 1 MK (see Fig. 3) connecting the
outer parts of the magnetic concentrations. In the core of the active region
we see numerous shorter loops that connect small patches of opposite magnetic
polarity in the region between the sunspots. A zoom into this region is
displayed in Fig. 4. Almost the same region of interest has been investigated
by Tiwari et al. (2019) who related small-scale brightenings to the
cancellation of magnetic flux in the photosphere below and its role for
heating. In our study we will focus on the thermal structure of the compact
short loops in the active region core.

Figure 4: Core of the active region. The field of view of each panel is 83″
$\times$ 60″ and corresponds to the rectangle in Fig. 3. Panels (a) and (b)
show the images in the IRIS 1400 Å channel and in Hi-C 172 Å. To highlight
fainter structures, the IRIS image is on a logarithmic scale, the Hi-C image
is scaled with a power of 0.3. The multi-color composite of these two bands is
displayed in panel (d), with green for Hi-C and red for IRIS data. For
context, in panel (c) we display a co-temporal magnetogram acquired by HMI
showing the line-of-sight component of the magnetic field in the photosphere
($\pm$200 G). The footpoints of features [1] and [2] are indicated by the
arrows. The rectangle highlights the peculiar small loop [3] that is briefly
discussed in Appendix C. The Hi-C image shown here was taken at 19:00:33 UT,
the IRIS and HMI data are those available closest in time. North is top and
west is right.

This active region was the target of the High-resolution Coronal imager (Hi-C
2.1) suborbital rocket experiment during its flight on May 29, 2018. The
details of the Hi-C experiment are described in Rachmeler et al. (2019).
During our observation, the center of the active region was located at an
heliocentric angle of $\mu{=}\cos\vartheta$ of about 0.95, i.e., close to disk
center with an angle between the line-of-sight and the local vertical of only
about 15∘. The data are freely available through the Virtual Solar Observatory
(https://www.virtualsolar.org).

Between 18:56 and 19:02 UT the Hi-C imager collected science data in a band
centered around 172 Å. The temperature response of this band is similar to 171
Å channel of the Atmospheric Imaging Assembly, AIA Lemen et al. (2012). The
bulk part of the plasma imaged by Hi-C is at temperatures just below 1 MK. The
plate scale of the Hi-C data is 0.129″ per pixel and the data have been taken
with an exposure time of 2 s and a cadence of 4.4 s. The spatial resolution in
the sharpest frames from the Hi-C flight is estimated to be 0.35″. The
resolution varied over the flight due to blurring by jitter. In our study we
concentrate on image frame # 58 taken at 19:00:33 UT which is one of the
sharpest images taken during the flight Rachmeler et al. (2019). Only when we
analyze the temporal evolution in a single loop in Sect. 5 we utilize all Hi-C
frames.

We relate the Hi-C observations to data from the Interface Region Imaging
Spectrograph, IRIS De Pontieu et al. (2014), in particular those acquired in
the 1400 Å band by the slit-jaw camera. The bright features in this band in
active regions represent plasma at just below 0.1 MK Tian et al. (2018). The
1400 Å images have been taken with an exposure time of 2 s and a cadence of 13
s. The plate scale of the IRIS slit-jaw images originally is 0.17″ per pixel,
but the data taken during the Hi-C campaign are binned by 2$\times$2 pixels.
In the end, the spatial resolution of the IRIS and Hi-C data is roughly
comparable, while it is significantly better than AIA (plate scale of 0.6″ per
pixel). While the field-of-view of the IRIS slit-jaw images is smaller than
that of Hi-C, the IRIS data fully capture the core of the active region that
we investigate here (Fig. 4a). The IRIS data are available through
http://iris.lmsal.com. The Virtual Solar Observatory also offers the IRIS data
taken during the Hi-C 2.1 flight.

The proper spatial alignment of the data from Hi-C and IRIS is important for
this study. Thus we provide details of our alignment procedure in Appendix A.
Using data from AIA we can achieve a spatial alignment between Hi-C and IRIS
better than 0.5″, corresponding to about 350 km at disk center on the Sun. The
data from AIA are available through the Joint Science Operations Center (JSOC)
at http://jsoc.stanford.edu.

For the context of the magnetic field structure we use data from the
Helioseismic and Magnetic Imager, HMI Scherrer et al. (2012). In Fig. 4c we
show the line-of-sight magnetic field in the core of the active region aligned
with the data from Hi-C and IRIS. Like AIA, the HMI data are available at
JSOC. For an overview of the temporal evolution of the active region during
the days leading up to the Hi-C observation we utilized the JHelioviewer
software Müller et al. (2017).

##  4 Parallel cool and warm loops in active region cores

The main observational goal of this study is to relate the loops in the active
region core seen in the images of Hi-C to those in IRIS. These loops are the
elongated features seen in both the Hi-C and the IRIS data (panels a, b of
Fig. 4). Comparing with the magnetic field at the solar surface (panel c),
mostly, the two footpoints of each loop feature are rooted in patches of
opposite magnetic polarities, two examples are highlighted by arrows. Of
course, in many cases the moderate spatial resolution of HMI is not sufficient
to resolve the magnetic structure at the loop footpoints Chitta et al. (2017).
Still, this comparison underlines that most of these elongated features seen
in extreme UV images are indeed plasma loops outlining the magnetic field
structure.

###  4.1 Loops in Hi-C and IRIS images

Very often the loops in the core of the active region seen in Hi-C and IRIS
data do run in parallel. For a better spatial comparison between the two data
sets we plot a multi-color composite of the Hi-C 172 Å channel and the IRIS
1400 Å slit-jaw image in Fig. 4d. Here one can easily identify many green and
red features (representing Hi-C and IRIS respectively) that run parallel to
each other over a considerable part of their length. We highlight two
structures by pointing with arrows to their end or footpoints. Feature [1] is
a single loop. Feature [2] forks in the middle, so that it has two endpoints
on the eastern side and only one footpoint on the western end, indicating that
is a small bundle of loops whose footpoints diverge slightly. However, the
IRIS images (see Fig. 5) show a slightly different structure, with the common
right part of the fork being bend more southward.

Depending on the quality of the spatial alignment of the data sets, it is
possible that the loops seen in Hi-C and IRIS either run in parallel with a
small offset, or that they are at exactly the same location. These two
possibilities would imply two rather different scenarios. In the former case,
the loops we see in Hi-C and IRIS have to be different entities at different
temperatures that are separated in space. In the latter case, the Hi-C and
IRIS loops might be actually the same structure that would have to consist
either of one single temperature or be a multi-stranded multi-temperature
loop, with the strands unresolved by either instrument. If the loops appear at
the same location there is also the possibility that they are crossing the
same line of sight with some spatial offset along the line of sight. This
would apply in special situations only, because in general we cannot expect
that multiple solar structures will be aligned with the line of sight along
their entire length. A careful spatial alignment is important for our study
and we describe the alignment procedure and its test in Appendix A.

Figure 5: Spatial offset between loops seen in Hi-C and IRIS. The left and
middle panels show zooms into the Hi-C and IRIS images centered around the
features as marked in Fig. 4. The top row shows the loop feature [1] the
middle and bottom row the two parts of the double feature [2], here marked
[2a] and [2b]. In the respective right panel we display the variation of the
intensities in Hi-C and IRIS along the white lines (strips) marked in the
respective left panels, i.e. roughly perpendicular to the loop. The diamonds
show the data interpolated on the plate scale of the respective instrument,
the solid curves show interpolations at higher resolution to measure the
offsets between the two instruments. The offsets between Hi-C and IRIS are
marked with the plots. The typical error for the offsets is 0.1″. See Sect.
4.2.

###  4.2 Spatial offset between IRIS and Hi-C

To investigate the offset between the loops seen in Hi-C and IRIS we plot cuts
across the two selected loop features in Fig. 5. There we show the intensity
variation along the strip across the loop interpolated onto the plate scale of
Hi-C and IRIS. We also show intensities interpolated to a higher resolution,
which is used to determine the position of the loops and their offset. In the
case of the forking feature [2] we select two locations where it appears as a
double structure. We determine the offset between the loops through the
location of the peak of the respective cross-sectional intensity cuts (Fig.
5).

Because the profiles are quite smooth, we can determine the location of the
features and thus their offset with an accuracy that is a fraction of one
spatial resolution element (typically the error is 0.1″, see Appendix B). As
noted with Fig. 5, the offsets between the loops seen in Hi-C and IRIS are
0.53″ for feature [1] and 0.28″ and 0.46″ for the double-feature [2]. Even if
we were to change the absolute alignment between the Hi-C and the IRIS data,
we would not be able to overlay all three cross-sections simultaneously.
Investigating more examples in Appendix B confirms this finding; we find
displacements between Hi-C and IRIS ranging from 0″ to more than 0.7″ (see
Fig. 16, Table 1 and Fig. 18). Most importantly, one cannot shift (or align)
the IRIS and Hi-C data in a way that all the features would overlap. No matter
how the images are shifted with respect to each other, there would be an
offset of at least more that 0.5″ for some of features in Hi-C and IRIS. Thus
we conclude that the offset between the loops seen in IRIS and Hi-C is real.
Typically, this small displacement between the loops is smaller than or
comparable to their widths.

The loops seen in Hi-C and IRIS are not only at different locations, they are
also composed of plasma at different temperatures. While the emission seen in
the IRIS images is dominated by Si IV forming around 0.1 MK, the analysis in
Sect. 5.2 shows that the emission seen by Hi-C in these loops originates from
temperatures around 0.3 MK (and in some cases maybe up to almost 1 MK). The
temporal evolution of the loops seen in IRIS and Hi-C is mostly (but not
always) different (Sect. 5.1).

###  4.3 Spatial offsets along the loops

The multi-color image in Fig. 4 gives a first indication that the loops run in
parallel. To quantify this more, we show in Fig. 6 how the offset between a
loop seen in Hi-C and IRIS changes along the loop. Here feature [1], which is
clearly discernible in both the Hi-C and IRIS images, shows an offset that is
mostly constant over the better part of the length of the loop. Thus here the
loops in Hi-C and IRIS are parallel.

Of the eleven cases listed in Table 1 and discussed in Sect. 4.2 and Appendix
B, eight show a variation similar to feature [1], some as clear, some a little
less clear. Only three cases show a variation of the offset, with changing
signs, along the loop, meaning that they do not clearly show the offset
towards the same side (features 2a, 10, 11).

An intriguing case is the combination of features 2a, 2b and 8. Together they
seem to form a forking structure (bottom two panels of Fig. 5 and Fig. 16[8]).
One could now speculate that this is a braided structure similar to the
magnetic field lines in Fig. 1, in particular because the offsets of the left
side of the fork for [2a] and [2b] are in the opposite direction than for the
right side with feature [8] (see also Fig. 18). However, on the one hand it is
not clear if this forking structure is one single feature or the line-of-sight
composition of different loops. On the other hand, an apparent forking feature
is not necessarily braided, as can be nicely seen in the numerical models of
Chen et al. (2021) with their Figs. 4b, 4d and 5.

Figure 6: Offset between loop in Hi-C and IRIS data. This shows the offset
along feature [1] pointed to in Fig. 4 and shown in Fig. 5. The distance 0″
along the loop is at the location in Fig. 5[1] where the white slit crosses
the loop. The offset between Hi-C and IRIS is consistently to the same side.
See Sect. 4.3.

##  5 Temporal evolution and thermal structure of the loops

From Sect. 4 and Appendix B we conclude that the loops seen in Hi-C and in
IRIS are not at the same spatial location. Here we investigate the evolution
of these loops in space and time (5.1) as well as their temperatures (5.2). If
these properties are different for the loops in Hi-C and IRIS, it would be
further support that features seen in the two instruments are different.

Figure 7: Spatio-temporal evolution of the intensity in one selected loop
feature. Panels (a) and (b) show a zoom of the IRIS 1400 Å and Hi-C 172 Å
channels into feature [2a] identified in Fig. 4. Panel (c) displays the
temporal evolution in part of the respective feature integrated over the
polygons indicated in the top panels. These polygons encompass 74 and 514
pixels in the cases of IRIS and Hi-C, respectively. The light curves in Hi-C
(green) and IRIS (red) are shown in normalized to their peak value. The peak
counts are about 3600 DN for IRIS and 3.4$\times$106 DN in Hi-C. The dashed
line in panel (c) indicates the time the images in panels (a) and (b) are
recorded. A movie showing the temporal evolution is available online
(%****␣hic_loops_final.tex␣Line␣700␣****http://www2.mps.mpg.de/data/outgoing/peter/papers/2019-hic/movie-s1.mp4).
See Sect. 5.1.

###  5.1 Spatio-temporal evolution of Hi-C and IRIS loops

To analyze the evolution of the loops we follow the features as seen in Hi-C
and in IRIS in time. Because Hi-C is a sub-orbital rocket experiment, this
analysis is limited to about five minutes. Here we first concentrate on
feature [2] marked in Fig. 4. In Fig. 7 we show stills from the Hi-C and IRIS
data along with the light curves of the northern fork of this feature (the
movie attached to Fig. 7 illustrates the temporal evolution). To enhance the
signal-to-noise level of the temporal evolution and in order not to depend on
variations on small (pixel) scales, we integrate the intensity in each band
over a good part of this upper fork of the loop, marked by the polygons in
Fig. 7a,b. We do not subtract a background, because the region is quite
complex and the background subtraction would introduce artifacts. The relative
variability we see in both Hi-C (up to about 10%) and in IRIS (up to 30%) is
significant. Considering the count rates (in the spatially integrated signal;
see Fig. 7) we estimate that the uncertainties of the intensities should be
one percent or less for both Hi-C and IRIS.

The temporal variability in the Hi-C and IRIS data is different. To begin
with, the relative variations are much larger in the IRIS data. Based on
cooling time scales, one would expect a higher temporal variability for
emission lines forming at lower temperatures (towards the transition region)
as compared to those forming in hotter regions. This is because radiative and
conductive cooling times get longer with increasing temperature (e.g.,
Aschwanden, 2005, Sect. 4.3.1). Therefore the higher variability in IRIS
suggests that the IRIS loops are somewhat cooler than the loops seen in Hi-C.

In addition to differences in the overall evolution, short-term brightenings
lasting only a fraction of a minute are not related to each other in the two
bands. This is also supported by the visual impression when investigating the
movies of the IRIS and Hi-C data (see movie attached to Fig. 7). In general,
in the literature there are reports of cases where (roughly) co-spatial loops
seen in the IRIS 1400 Å band and in the AIA 171 Å band (similar to Hi-C) are
correlated in their temporal evolution. In some examples time delays between
the two bands have been observed suggesting heating of the plasma in one
single (multi-stranded) structure Li & Peter (2019). The case we show here in
this study is different. In our case, the time evolution in Hi-C and IRIS
seems to be disconnected. Together with the finding of the spatial offsets,
this suggests that the loops we see in Hi-C and IRIS are definitively
disconnected, even though they might be hosted in the same bundle of emerging
field lines.

In some cases there are also similarities between the light curves between
IRIS and Hi-C. In feature [2a] in Fig. 7 the intensity in both instruments
increases during the last minute. However, during the first 4 minutes, they
differ significantly. Firstly, as mentioned above, the short brightenings in
IRIS (at 18:58 and just after 18:59) have no counterparts in Hi-C. Secondly,
when discarding these short peaks, during the first 3.5 minutes the IRIS curve
would increase by more than 50% (in normalized intensity from 0.5 to 0.75)
before it drops again (to 0.3 at 19:00:30). During this time the variability
in Hi-C is only 10% at a rather constant level. Looking at the movie attached
to Fig. 7 it is also clear that the spatio-temporal evolution of the two loops
in Hi-C and IRIS is quite different. Blobs appear in both the IRIS and Hi-C
loops, but at different locations along the loop and at different times.
Therefore, this provides support to the idea that the temporal evolution seen
in this feature [2a] is quite different in Hi-C and IRIS, despite some
similarities.

This case of feature [2a] is representative: mostly, the loops show a
different evolution in Hi-C and IRIS, in both time and space. In Fig. 8 we
show the temporal evolution for more examples, now with a broader coverage in
temperature by using data from AIA. Because the variation in Hi-C is very
similar to the 171 Å channel of AIA (and to keep the figure more clean) we do
not add Hi-C in Fig. 8. In general, the loops in the active region core
brighten over time scales on the order of a fraction of a minute to a few
minutes. Following the evolution in AIA for longer than the duration of the
Hi-C flight, the loops seem to be present at the same location for longer
times. This could be either because the same structure brightens up again, or
that a different strand appears. The loops we study here are probably related
to inter-moss loops Winebarger et al. (2013): at least one feature shows a
very similar evolution in the AIA channels as the inter-moss loops (cf. Fig. 8
feature [5]), the other cases are less clear. Furthermore, those inter-moss
loops have comparable length and lifetime as the loops studied here.

Based on the comparison of the spatio-temporal evolution of the loops seen in
Hi-C and IRIS we conclude that they are sometimes but not always identical.
Still, the question remains if they might have the same or different
temperatures which we address in the following Sect. 5.2.

Figure 8: Temporal evolution of selected loops. Each panel shows the light
curves for one loop example for four AIA channels and the IRIS 1400 Å images.
The number of each feature is given in the top right corner of each panel. The
temperature contributions (or kernels) of these AIA channels and the Si IV
line are displayed in Fig. 9. The labels in the panels refer to the features
shown in Figs. 5 and 16. In order not to overcrowd the panels, we do not show
the light curves in the Hi-C 172 Å band which are almost exactly the same as
for the AIA 171 Å channel. All light curves are normalized by mapping the
respective minimum and maximum values to the range of [0,1]. See Sect. 5.1 and
Appendix D.3.

###  5.2 Temperature of the loops seen in Hi-C and IRIS

Here we investigate the temperatures the loops in the active region core seen
by Hi-C. The availability of AIA data with a broader temperature coverage can
provide some information on the temperature of the plasma from where the
emission captured by Hi-C originates. In particular we want to investigate if
indeed the source region of Hi-C is at a higher temperature than the plasma
seen with IRIS, i.e. that IRIS shows cool loops and Hi-C warm loops.

####  5.2.1 Temperatures seen in extreme-UV channels

The emission recorded by the IRIS slit-jaw images in the 1400 Å channel is
dominated by the Si IV doublet at 1394 Å
and 1403 Å, at least in the bright active-region features we investigate here
(cf. De Pontieu et al., 2014; Tian et al., 2018). Under ionisation-equilibrium
conditions Si IV originates from plasma just below 0.1 MK, as illustrated by
its contribution function shown in Fig. 9 (red line).

Figure 9: Contribution functions for Hi-C, AIA and Si IV. The response
functions for the (selected) AIA channels are calculated using the routines
available in SolarSoft (http://www.lmsal.com/solarsoft/). The corresponding
curve for Hi-C is from the Hi-C instrument paper Rachmeler et al. (2019). The
contribution function for the Si IV line is calculated using Chianti Dere et
al. (2019) and is scaled to fit on this plot. For each of the curves the
temperature $T_{\rm{p}}$ of the peak of the contribution function is listed
with the legend as $\log_{10}\,T_{\rm{p}}$ [K]. The dotted line indicates a
temperature of 0.26 MK. See Sect. 5.2.1 and Appendix D.2.

For the 172 Å channel of Hi-C the situation is a bit more complex. Besides the
main peak just below 1 MK, the Hi-C contribution function shows also a
significant bump at lower temperatures at about 0.3 MK (as indicated by the
dashed line in Fig. 9). So, depending on the density and temperature
distribution along the line of sight, the emission seen in Hi-C could
originate from plasma at temperatures somewhere between 0.3 MK and 1 MK. The
situation is similar for many of the extreme UV channels of AIA, where the
channels at 171 Å, 193 Å, and 211 Å show even a side peak at about 0.3 MK (see
Fig. 9).

Comparing the temporal variability in the different EUV channels, Winebarger
et al. (2013) agued that one can distinguish whether a particular brightening
is originating from about 0.3 MK or just below 1 MK. We apply their arguments
to the small loop structures investigated here and describe this in Appendix
D. In the end, it does not really matter if the source region of Hi-C is
mostly at around 0.3 MK as would be argued following Winebarger et al. (2013),
or closer to 0.8 MK as one would judge from the the peak of the contribution
function alone (cf. Fig. 9). The main conclusion is that in some cases the
source region of Hi-C is hotter than the plasma IRIS sees, so that IRIS shows
cool loops while Hi-C shows warm loops.

####  5.2.2 Dichotomy of temperatures in loops seen by Hi-C and IRIS

The above result indicates that in some cases there is some observational
dichotomy for the presence of plasma around 0.1 MK (seen in IRIS 1400 Å) and
at higher temperatures (seen in Hi-C 172 and the AIA channels). There will be
also plasma at temperatures in-between, as seen in the 3D MHD model (Sect. 6),
but plasma at those temperatures is not contributing (significantly) to the
observables that we have available for analysis here, i.e. the images in the
IRIS 1400 Å and the Hi-C 172 Å bands.

###  5.3 Summary of spatial, temporal and thermal structure

Combining the results on the spatial offsets of the loops seen in Hi-C and
IRIS (Appendix B) with those on their spatio-temporal evolution (Sect. 5.1)
and temperature (Sect. 5.2) we conclude that at least some of the loops seen
in Hi-C and IRIS are different entities. They appear at slightly different
location, with an offset being smaller than their width, have different
evolutions, and are at different temperatures.

This suggests that the loops seen in Hi-C and IRIS are neighboring strands at
(slightly) different temperature in a bundle of magnetic field lines. The
field lines in this bundle cannot be twisted significantly on observable
scales because the loops in Hi-C and IRIS are essentially parallel. Some of
the loops in Hi-C and IRIS loops overlap partly, i.e. their distance is
smaller than their width, which is indicative of a gradual change of
temperature perpendicular to the magnetic field, so that the source region of
the lines contributing to the different instrument bands are overlapping in
space. This implies that there should be no (significant) twist of the
magnetic field even within each loop. These conjectures are supported by the
model presented in the next section.

Figure 10: View of the 3D MHD model from straight above. The layout is similar
to the observations in Fig. 4. Panels (a) and (b) show the emission
originating from Si IV, similar to the IRIS 1400 Å image, and from Hi-C. Both
the Si IV and Hi-C intensity have been integrated vertically through the
computational domain. Panel (c) shows the vertical component of the magnetic
field in the photosphere of the simulation. The multi-color composite of the
cool and warm emission is displayed in panel (d). Here the red channel
represents Si IV, the green channel Hi-C. The field of view covers only about
one quarter of the horizontal extent of the 3D MHD model. The red and green
dashed lines show the projection of magnetic field lines passing through the
center of the loops seen in Si IV and Hi-C (traced in the 3D data cube). The
vertical yellow lines shows the location of the cuts in intensity shown in
Fig. 11 and of the vertical cuts in Fig. 12. The arrows in panels (a) and (b)
point to the respective loop in Si IV and Hi-C highlighted also by arrows in
Figs. 11 and 12. See Sect. 6.2.

##  6 3D MHD model of loops in an emerging active region

To improve the interpretation of our observations we use a three-dimensional
magneto-hydrodynamic (3D MHD) coronal model of an emerging active region. In
that model a new active region forms in response to the large-scale emergence
of magnetic flux resulting in two sunspots and a complex evolving magnetic
field between and around the spots. During the flux emergence process the
plasma along the rising magnetic field lines is heated and forms a system of
coronal loops Chen et al. (2014). The loops are energized by surface motions:
the footpoints of magnetic field lines are dragged by magneto-convective
flows, often toward the sunspots Chen et al. (2015). This is similar to the
flux-tube tectonics scenario Priest et al. (2002). This model is thought
mainly to illustrate a possible magnetic configuration of how the loops at
different temperatures relate to each other spatially. As such, the model
output should be considered as a guide for the interpretation, while the
specific spatial or temporal variation might not necessarily fit exactly the
observations.

###  6.1 Basics of 3D MHD model

The 3D MHD model solves the mass, momentum, and energy balance along with the
induction equation Bingert & Peter (2011), and uses a super-time-stepping
scheme to improve the computational speed. The energy dissipated through Ohmic
and viscous dissipation is redistributed through field-aligned heat conduction
and is lost through optically thin radiative losses.

For our study we re-analyze a high-resolution version of the aforementioned 3D
MHD model Chen & Peter (2015). This covers the emerging active region with a
computational domain spanning over about 147 Mm $\times$ 74 Mm horizontally.
The grid spacing (in the horizontal directions) is about 145 km, which
corresponds to about 0.2″ at disk center for Earth-based observations. This is
of the order of the spatial resolution of the observations we use here (cf.
Sect. 3).

Using the temperature and density provided by the MHD model, we synthesize
optically thin emission lines in the 3D data cube assuming ionization balance
and electron collisional excitation Peter et al. (2004, 2006). To calculate
the extreme UV images we integrate the synthesized intensity along the
vertical direction. This corresponds to an observation of an active region
from straight above, i.e., near disk center (as is the case for the active
region we observe). In this model part of our study we use the emission line
of Si IV which is dominating the IRIS 1400 Å channel when observing bright
transition region structures in an active region, as it is the case here. To
synthesise the emission as seen in the Hi-C 172 Å band we employ the Hi-C
temperature response function as published in the instrument paper Rachmeler
et al. (2019). Because we do not perform a one-to-one quantitative comparison
between observations and numerical model, we do not apply a point-spread-
function or other instrumental effects to the synthesized data.

###  6.2 Cool and warm loops in 3D MHD model

The 3D MHD model produces an active region with numerous loops over a range of
temperatures in its core, i.e. between the sunspots. We show the core of that
simulated active region in Fig. 10 as it would appear when observed from
straight above. With 73 Mm $\times$ 59 Mm this represents about one quarter of
the horizontal extent of the computational domain. These simulation data are
shown in the same format as the observations in Fig. 4. The loops in Si IV
(similar to IRIS 1400 Å) and Hi-C are displayed in panels (a) and (b) of Fig.
10. A composite image of these two in panel (d) shows how they relate to each
other.

The loops in the core of the active region in this simulation are longer than
those in the observations. The modeled loops have lengths of some 30 Mm to 40
Mm, while in the loops seen in the Hi-C observations have lengths of up to
15″, corresponding to about 10 Mm. Still, model and observations are
comparable in that in both cases magnetic field is emerging giving rise to the
formation of these loops. In the model the scale of the flux emergence is
larger, but we can expect the processes to be similar if the flux emergence
occurred on a smaller scale, comparable with the observations. Shorter loops
(at lower heights and thus higher densities) would require substantially more
heating to balance the radiative losses (that increase with density squared).
MHD models for different setups produced loops with lengths of 20″ reaching
temperatures of well in excess of 1 MK Bourdin et al. (2013). Thus it should
be possible that emerging loops with 15″ length as observed here might reach
temperatures in the MK range. Therefore we consider the difference between 3D
model and observations to be quantitative but not qualitative.

Figure 11: Cut through cool and warm loops in the 3D MHD model. This shows the
intensity variation in Si IV and Hi-C along the yellow line in Fig. 10. The
offset between the loops in Si IV and Hi-C near $y{\approx}42$ Mm is about 400
km. These loops are highlighted by arrows and are the same as pointed to in
Figs. 10 and 12. See Sect. 6.2.

As in the observations, the Si IV and Hi-C loops run in parallel. One
particular example for parallel cool and warm loops is the structure at around
$y{\approx}42$ Mm marked by arrows in Fig. 10. The cut across these loops
shown in Fig. 11 highlights that the 3D MHD model shows a spatial offset
between loops in Si IV and Hi-C, just like in the observations. In this
example the loop separation of about 400 km roughly corresponds to about 0.5″.
In general, the separation of the loops at different temperature will depend
on the viewing angle (cf. Fig. 12c), and the good quantitative match found
here is largely by chance.

In contrast to the observations, in the 3D MHD model we can investigate what
causes this offset. For this we first look at a 3D view of the simulation box
in Fig. 12c. Clearly, the loops in Si IV and Hi-C show a significant spatial
offset, in both the horizontal and the vertical directions. Checking the
vertical cut through the the midplane of the loop in Fig. 12a reveals that the
loops in Si IV and Hi-C are offset in the vertical direction by about 2 Mm.
More importantly, they are also at different temperatures. As expected, the Si
IV loop appears at about 0.1 MK and the Hi-C loop at just below 1 MK. So in
the 3D MHD model we have a clear distinction between a cool (order 0.1 MK)
loop and a warm (order 1 MK) loop.

Figure 12: Structure of the loops in the 3D MHD model. A vertical cut through
the midplane of the loop(s) is shown in panels (a) and (b) for the temperature
and the density. The vertical cut is located at the yellow line in Fig. 10 The
white line indicates the isocontour of a temperature of $10^{4}$ K. The red
and green lines show isocontours of the emission in Si IV and Hi-C.
Essentially they show the location where the cool and warm loops cross the
midplane. Panel (c) shows a 3D visualization of the cool and warm loops seen
in Si IV and Hi-C together with a temperature isosurface at $10^{4}$ K. The
arrows point at the same cool and warm loops as in Figs. 10 and 11. See Sect.
6.2.

There is a significant difference between the warm and the cool loop, though.
The warm loop is a structure in a high-temperature and high-density region
that is a distinct feature in the upper atmosphere (cf. Fig. 12a,b). The
density at the location of the warm loop synthesised for Hi-C is higher than
in the regions directly below, which can be seen clearly in particular for the
Hi-C loop at $y{=}35$ Mm and $z{=}10$ Mm in Fig. 12b. This is what one might
call a proper coronal loop. In contrast, the cool transition region loop sits
just above the chromosphere which is itself elevated by the emerging magnetic
flux. In both the vertical cuts (Fig. 12a,b) and in the 3D view (Fig. 12c) the
$T{=}10^{4}$ K isocontour, indicating the top of the chromosphere, is clearly
elevated under the coronal loop which is because the emerging and rising field
lines push up the chromosphere. In some sense the cool transition region loop
could be considered as grazing the top of the chromosphere.

In this 3D MHD model the magnetic field expands into the upper atmosphere, and
as it expands, the plasma trapped on the field lines gets heated Chen et al.
(2015). The cool and the warm loops represent two (transient) stages of the
evolution of an emerging bundle of magnetic field lines. Still, at each given
time the cool and the warm loops are aligned with the magnetic field, i.e.,
there is a field line that runs (roughly) along the center of the respective
plasma loops. Most importantly, this shows that (at least in this model), the
warm and cool loops are different structures originating from different
spatial locations. To some extent, this distinction between cool and warm
loops is an artifact of our limited observational capabilities. If we had
imaging instruments with a fine temperature coverage between 0.1 MK and 1 MK,
essentially we would see a continuum of loops with increasing temperature
side-by-side. Using synthesized emission for a sequence of ions from Si IV
through C IV, O IV, O V, O VI, Ne VIII, and Mg X we indeed find such an
overlapping continuous distribution of loops.

The cool and warm loops are part of the same emerging bundle of field lines,
but they form in different places of this bundle, clearly separated spatially.
In the model this difference originates from the distribution of upward-
directed Poynting flux at the surface. Like in the flux-tube tectonics or the
braiding scenario, the magneto-convection moves around patches of magnetic
flux. During the emergence process this can temporarily create small regions
that have an enhanced upward Poynting flux at a fixed location, like a hot
spot Chen et al. (2014, 2015). This structure in the Poynting flux at the
solar surface then results in the loops being heated while expanding into the
upper atmosphere, so that at each given time the low-lying field lines would
host cooler plasma while those field lines already emerged to larger heights
carry hotter plasma. Hence we see the cool loops just above the chromosphere
and the warm loops at larger heights. Because of the complex magnetic
structure, the loops are free to move in all three directions as they expand,
resulting in vertical and horizontal offsets. If the emerging bundle of field
lines would be strongly twisted and braided, then the field lines hosting the
cool and warm loops, respectively, would be wound around each other. Not
seeing that the cool and warm loops are wound around each other implies that
the magnetic field relaxes faster than the field is stressed. This prevents
braiding on length scales that are comparable to the width of the bundle of
emerging field lines, viz. the spatial separation of the cool and warm loops.

In conclusion, the 3D MHD model of an emerging active region shows similar
loop features as we find in the observations. The magnetic structure that is
modeled here is of case (1) as defined in Sect. 2, i.e. a bundle of field
lines that is rooted at each end in one single region. Plasma at different
temperatures is seen in loops that run in parallel with a small offset. In the
model the (large) dissipation leads to a relaxation that is faster than the
braiding. Consequently the emerging bundle of field lines does not show
signatures of a highly braided state of the magnetic field. Instead, the loops
loaded with plasma at (slightly) different temperatures run in parallel.

As mentioned at the onset of this Sect. 6, this model is mainly thought to be
an illustration of one possibility of how to have loops at different
temperatures running in parallel with some offset (depending on the viewing
angle). Certainly it should not be considered as unique. For example, the
magnetic setup of the emerging low-lying loops might not be typical for long
stable loops that have been claimed to be heated by braiding. Also, if the
emergence would be fast enough, braiding might not have sufficient time to
create braided structures that could be visible in the observations.
Furthermore, the small-scale loops found in the center of the active region in
the Hi-C and IRIS observations discussed in this study might have a different
magnetic configuration. The observed emerging loops might be energised by
large-angle reconnection events that are triggered by the interaction between
the emerging magnetic flux and the pre-existing coronal magnetic field (e.g.
Ortiz et al., 2016). Despite of all these shortcomings, the model illustrates
one way of creating parallel loops in IRIS and Hi-C observations.

##  7 Discussion and conclusions

The key observational result of our study is that in most cases distinct loops
(at different temperatures) are offset from each other and roughly parallel.
Being part of the same bundle of (emerging) field lines, these show no sign of
braiding or twisting. The spatial separation (perpendicular to line of sight)
of the distinct loops is less than their width (cf. Fig. 5). Therefore the
lack of twisting between the loops as seen in EUV emission implies that there
is also no (noticeable) braiding of the field lines within each loop. Still,
field-line braiding might be the source to energise the corona, but we simply
do not see the observational signatures of this in the EUV imaging
observations.

If the energisation of the corona is due to braiding of magnetic field lines,
the observation of these parallel loops and the absence of braiding signatures
has a significant implication: the magnetic field has to relax already while
driven by horizontal motions at surface, and the field will not reach a highly
braided state Schrijver (2007). This is consistent with current 3D models for
the braiding of field lines: the coronal emission from a loop model driven by
footpoint shuffling does not shows signatures of braiding Dahlburg et al.
(2016). When self-consistently driven from the footpoints, the magnetic field
relaxes before reaching a highly braided state Reid et al. (2018). In 3D MHD
models of the corona Hansteen et al. (2010); Bingert & Peter (2011); Rempel
(2017); Warnecke & Peter (2019) computational constraints restrict the
resolution so that the effective dissipation is rather large. This translates
to (magnetic) Reynolds numbers in the models that are orders of magnitude
smaller than expected for the solar coronal plasma Peter (2015). While often
considered as a shortcoming of the models, our results might hint that the
(comparably) large dissipation in the upper solar atmosphere might be more
realistic than generally thought, e.g. because turbulence increases the
effective dissipation Biskamp (1984, 1996). Even under the presence of
magnetic turbulence, the guide field is still rather smooth in the direction
along the loop because the relaxation is as fast as (or even faster than) the
driving Reid et al. (2018). In the (upper) chromosphere ambipolar diffusion is
very strong and plays a key role (e.g. Martínez-Sykora et al., 2017). Hence
there the magnetic Reynolds number can be represented by the numerical models.

Our observations of parallel loops in Hi-C and IRIS put a new constraint on
models for field-line braiding. Despite the braiding and twisting of the
magnetic field, the loops observable in EUV should not show twisted
structures. This condition is fulfilled by some models of footpoint shuffling
and is also satisfied by models with a sufficient level of magnetic
resistivity, as outlined above. Our observations would not be consistent with
a cartoon picture of highly braided magnetic field in which bundles of
magnetic field lines or flux tubes are wound around each other on length-
scales that are large compared with the diameter of each bundle. While still
being braided, the field relaxes while driven and would not reach the highly
braided state as often depicted in cartoons.

Only if a highly braided state is prescribed as the initial condition in a 3D
model, braided structures might be visible Pontin et al. (2017). Such a
signature of braiding has been seen in coronal emission during the first
flight of Hi-C (Cirtain et al., 2013, their Fig. 2). This structure at the
edge of a sunspot was part of a low-lying twisted magnetic flux rope Thalmann
et al. (2014). At the location where the braiding feature is seen, the flux
rope forks (see Sect. 2). The braiding of this flux rope might be induced by
shearing of the magnetic field Aulanier et al. (2010). Traditional models of
braided coronal loops assume that the braiding is internal to the loop,
without forking of the magnetic field into multiple anchors at one or both
footpoints (see Sect. 2). The feature seen by Cirtain et al. (2013) is a
braided structure of case (2) with disparate footpoints (as defined in Sect.
2), and not a good prototype of a single coronal loop bundle of case (1) that
we investigate here.

A number of promising processes to energize the solar corona also do not show
signatures of braiding. Models that account for the key properties of the
chromosphere produce spicules in which thin threads of material are injected
into the upper atmosphere Martínez-Sykora et al. (2017). These spicules can be
associated with heating of coronal plasma De Pontieu et al. (2017). Wave
heating might produce strands of coronal emission within a loop that do not
appear to be braided Karampelas et al. (2019a).

In conclusion, our combination of high-resolution data from Hi-C and IRIS with
a 3D MHD model provides an understanding of the cool and warm loops in the
cores of active regions. Because the magnetic field emerges while it gets
heated from the footpoints, the cool loops are found just grazing above the
chromosphere, while the warmer loops are found higher up at the top of the
emerging bundle of magnetic field lines. This causes a spatial offset in the
vertical and (in general) also in the horizontal direction between loops
showing plasma at (slightly) different temperatures. While they are part of
the same larger emerging structure, the cool and warm loops seen in EUV
emission in the cores of active regions are still spatially distinct and show
little evidence of twist. These loops can be heated by stressing the magnetic
field in the photosphere, e.g. through field-line braiding, but the relaxation
of the magnetic field is efficient enough so that no (clear) signatures of
this braiding will be observable.

We acknowledge the constructive comments and patience of an anonymous referee
that helped to improve the manuscript. L.P.C. received funding from the
European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie grant agreement No. 707837. F.C. acknowledges the
George Ellery Hale Postdoctoral Fellowship offered by the University of
Colorado. P.T. acknowledges support by contracts 8100002705 and SP02H1701R
from Lockheed-Martin to SAO. S.K.T. gratefully acknowledges support by NASA
contracts NNG09FA40C (IRIS), and NNM07AA01C (Hinode). We acknowledge the High-
resolution Coronal Imager (Hi-C 2.1) instrument team for making the second re-
flight data available under NASA proposal 17-HTIDS17_2-003. MSFC/NASA led the
mission with partners including the Smithsonian Astrophysical Observatory, the
University of Central Lancashire, and Lockheed Martin Solar and Astrophysics
Laboratory. Hi-C 2.1 was launched out of the White Sands Missile Range on 2018
May 29. IRIS is a NASA small explorer mission developed and operated by LMSAL
with mission operations executed at NASA Ames Research center and major
contributions to downlink communications funded by ESA and the Norwegian Space
Centre. SDO data are courtesy of NASA/SDO and the AIA and HMI science teams.
Figure 12c is generated using the VAPOR tool (www.vapor.ucar.edu). This
research has made use of NASA’s Astrophysics Data System. H.P. and F.C.
acknowledge PRACE for awarding us the access to SuperMUC based in Germany at
the Leibniz Supercomputing Centre (LRZ).

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##  Appendix A Spatial alignment of Hi-C and IRIS data

The images of the Hi-C 172 Å band and the IRIS 1400 Å slit-jaw images cannot
be spatially aligned directly. In active regions and assuming equilibrium
conditions, these two channels would show plasma predominantly at temperatures
just below 1 MK and at about 0.1 MK. Hence their appearance will be quite
different in most places. Still, using the full-disk data from AIA, we can
perform the spatial alignment indirectly.

For this indirect spatial alignment we use the 171 Å and 1600 Å channels of
AIA. The choice of the 171 Å channel is obvious, because it is dominated by
the same line of Fe IX and has a similar (but more narrow) temperature
response function as the Hi-C 172 Å band Rachmeler et al. (2019). The AIA 1600
Å band is dominated by the Ly-continuum of Si I and the C IV doublet at 1548 Å
and 1550 Å. The IRIS 1400 Å band is mainly composed by the same Si I Ly-
continuum and the doublet of Si IV at 1393.76 Å and 1404.77 Å (with some
contribution also from the C II doublet near 1335 Å). Because C IV and Si IV
form at similar temperatures, the AIA 1600 Å and IRIS 1400 Å bands show, for
the most part, similar features. Consequently, these two bands have been used
frequently for spatial alignment, and our study is no exception.

The alignment between Hi-C 172 Å and AIA 171 Å is straight forward. The same
is the case for IRIS 1400 Å and AIA 1600 Å. Both can be achieved easily with
standard cross-correlation techniques. Here we use the publicly available
procedure rotalign.pro (by R. Molowny, available at
http://www.staff.science.uu.nl/~rutte101/rridl/dotlib/rotalign.pro). This
calculates both the lateral and rotational offsets which are then applied to
the data. The residual offset for the Hi-C vs. AIA 171 Å and IRIS vs. AIA 1600
Å is very small, smaller than 0.1″. So the problem of indirectly aligning Hi-C
with IRIS relies on the alignment of the AIA data in the 171 Å and the 1600 Å
bands. The remainder of this section will be devoted to this.

The AIA data cover the full solar disk, which is why one can use the position
of the limb for a reliable alignment. We select the AIA 171 Å and 1600 Å
images closest in time to the Hi-C frame we concentrate our analysis on (frame
# 58 at 19:00:33 UT). These data headers contain information on the alignment
of the AIA data provided by the instrument team. We then use procedures from
the Maps package available in SolarSoft (http://www.lmsal.com/solarsoft/) to
co-register the 171 Å and 1600 Å images. These co-registered images are
displayed in Fig. 13.

To check the (automated) co-registration of the AIA images, we calculate the
position of the limb in the 171 Å and 1600 Å bands. For this, we define ten
segments at the limb spread over the whole limb but avoiding an active region
at the west limb (see Fig. 13). For each segment we determine the intensity
variation in the radial direction across the limb averaged in the azimuthal
direction (along the limb). These cuts are presented in Fig. 14 for both the
171 Å and 1600 Å bands. As expected, the solar limb in the coronal images of
AIA 171 Å is further out than in images of AIA 1600 Å that mostly show the
temperature minimum region at the base of the chromosphere. Here we define the
limb position as the (local) maximum just before the intensity drops above the
limb and mark these positions by dots in Fig. 14.

If the AIA 171 Å and 1600 Å images are aligned well, then the distance between
the limb positions in the two channels should be the same for all the limb
segments we choose in Figs. 13 and 14. These differences between the AIA 171 Å
and 1600 Å limb positions are shown in Fig. 15 for these ten segments. We can
discard segments 2, 3 and 8 because these are at locations of (polar) coronal
holes as revealed by their darker appearance in the AIA 171 Å image in Fig.
13. The intensity as a function of height in a coronal hole is different due
to different plasma properties; we discard them to remove this uncertainty.
The other segments all show offsets around a mean value of 7.88″ and a
standard deviation of 0.39″. From this we can conclude that the co-
registration of the AIA 171 Å and 1600 Å images is good and within about 0.4″.
Together with the good alignment of Hi-C vs. AIA 171 Å and IRIS vs. AIA 1600 Å
we estimate that the final alignment between Hi-C and IRIS should be better
than 0.5″, i.e. slightly better than the AIA pixel size of 0.6″.

To further confirm our (automated) co-registration of the AIA 171 Å and 1600 Å
images, we align these two images using a recent beta version of the
aia$\\_$prep routine (at the time of writing the first draft not yet available
publicly, G. Slater, private communication). This beta version co-registers
the images by taking into account the limb positions determined from a three-
hour running average. This procedure essentially removes any jitter and
thermal drifts in the pointing information that could affect the co-
registration. With this independent check, we find that all the aforementioned
segments (excluding 2, 3 and 8) show offsets around a mean value of 8″ and a
standard deviation of 0.29″. This slightly differs (by about 0.1″) from the
standard AIA procedures and is well within the errors we estimated for the
alignment of the AIA 171 Å and 1600 Å images.

Figure 13: Full-Sun images acquired by AIA in its 1600 Å and 171 channels. The
solid/dotted lines show the limb through a circle with the solar radius as
recorded in the header of the AIA 171 Å image. The segments numbered 1 to 10
mark the regions to verify the limb alignment between the two channels.
Segments 2, 3, and 8 are at locations where (polar) coronal holes are
presents. The coronal holes are revealed by lower intensities in the 171 Å
image. The target region of the Hi-C campaign is the bright active region
north-east (top-left) of disk center. See Appendix A.

Figure 14: Limb positions in the AIA full-disk data. We show the intensity as
a function of radial distance across the limb averaged in the azimuthal
direction (i.e. along the limb) for the ten limb segments marked in Fig. 13.
The red lines are for the 1600 Å channel, the green lines for the 171 Å band.
The dots mark the respective limb positions defined as the local maximum
before the intensity drops above the limb. The radial distance is measured
from disk center. See Appendix A.

Figure 15: Offset of the limb position between the AIA 171 Å and 1600 Å
images. The numbered diamonds show the difference of the limb position between
the two bands as derived from the respective intensity variations in Fig. 14
in the segments marked in Fig. 13. The grey band indicates the standard
deviation around the mean value (discarding segments 2, 3, and 8 are within
the polar coronal holes). See Appendix A.

##  Appendix B Examples of parallel loops in Hi-C and IRIS

In the main text we discuss the offsets between loops seen in Hi-C and IRIS of
two features marked [1] and [2] in Fig. 4. Here we will investigate further
examples of such cool and warm loops running parallel to each other in the
core of the active region. We show the zooms of Hi-C image cut-outs and the
variation of the intensity across the respective loop feature as seen in Hi-C
and IRIS in Fig. 16. Each of these further examples is displayed in the same
format as the plots for features [1] and [2] in Fig. 5. Some of these examples
overlap with examples used in a study on the role of magnetic flux cancelation
for fine-scale explosive energy release Tiwari et al. (2019), based on the
same Hi-C data data set.

We determine the offsets between the loops in Hi-C and IRIS by calculating the
position of the respective feature along the cross-sectional cuts (roughly)
perpendicular to the loop. We define the location of a loop as the position of
the peak intensity along the cut as following from a cubic interpolation. Of
course, this is only one possible choice. We preferred this over the
calculation of the centroid of the cut or a Gaussian fit, because the profiles
are asymmetric and have different background levels on both sides of the loop.
We define the spatial offset as the difference in location of the loops in
Hi-C and IRIS data, and these offsets are noted with the plots in Fig. 16 and
listed in Table 1. Feature [6] in Fig. 16 illustrates the accuracy we can
expect for the determination of the offsets. While having an offset of just
below 0.1″, this offset is clearly visible, even though this is significantly
smaller than the spatial resolution of both Hi-C and IRIS (i.e. about 0.3″ to
0.5″). This is because a centroid (or the peak) of a profile can be determined
with sub-pixel or sub-resolution-element accuracy as long as the profile is
smooth and not noisy. This visual error estimation is confirmed by a Monte-
Carlo-type analysis. From 300 normal random realizations of photon noise added
to both the Hi-C and IRIS maps, we repeated the determination of the offsets
between the Hi-C and IRIS loops. This provides a more rigorous error estimate
and results also in a typical uncertainty of 0.1″.

One of the thinnest loops we noticed in the active region core is feature [4]
in Fig. 16. In Hi-C the full width at half maximum is about 0.5″. So clearly
the spatial resolution of Hi-C is at least as good as 0.5″.

The offsets between the loops seen in Hi-C and IRIS range from essentially
zero, i.e. no offset, to more than 0.7″ (Table 1). The largest relative offset
between two features is found between [5] and [8] and is more than 1.4″.
Still, it could be speculated if there is an alignment between Hi-C and IRIS
so that most the offsets get close to zero. To illustrate the offsets
graphically, we show these in Fig. 18 on a plane with the offsets separately
in the $x$ and $y$ directions, ${\Delta}x$ and ${\Delta}y$. Because of the
large-scale orientation of the magnetic field in the active region core, the
core loops are (an average) generally oriented in a direction from North-East
to South-West (see Fig. 4b), as indicated by the dashed line in Fig. 18.
Because we determine the offsets perpendicular to the loops, the data points
in Fig. 18 are mostly found roughly along a line perpendicular to the average
loop direction. Of course, some features show only small offsets, but others
have significant offsets, and towards different sides of the respective loop.
So, we can safely conclude that the loops in Hi-C and IRIS cannot all be
brought to overlap by applying a shift of the IRIS and Hi-C images with
respect to each other. Instead, in general the loops seen in Hi-C and IRIS
have to be at different locations and essentially run in parallel with small
but clearly resolvable offsets.

Here we make the implicit assumption that the images in both Hi-C and IRIS are
perfectly flat. In principle, also optical deformations could lead to variable
offsets across the field-of-view of both instruments. Some structures are very
close to each other and still show a significant differential offset. For
example, features [2a] and [2b] are less than 2″ apart and show a differential
offset of 0.2″, i.e. two pixels of Hi-C. Based on still images alone we cannot
finally rule out that optic deformations of Hi-C and/or IRIS would cause our
offsets. However, the temporal evolution shows that the features seen in Hi-C
and IRIS are at different temperatures (cf. Sect. 5), which gives us
reassurance that the offsets we see are a real effect on the Sun.

Figure 16: Examples [4] – [7] of loops with spatial offsets between Hi-C and
IRIS. The panels have the same format as used for the features in Fig. 5. For
each feature the left panels shows a zoom into the Hi-C and IRIS images with
the white line marking the cut. The respective right panel shows the
intensities in Hi-C (green) and IRIS (red) across the loop along the cut. The
diamonds show the data interpolated on the plate scale of the respective
instrument, the solid curves show interpolations at higher resolution to
measure the offsets between the two instruments. The offsets are indicated
with the plots and are listed in Table 1. The typical error for the offsets is
0.1″. The distance along the slit is counted positive towards the northern
(large values of Y) tip of the cut. See Appendix B.

Figure 17: Further examples for offsets. Same as Fig. 16, but for cases [8–11]
in Table 1. See Appendix B.

Table 1: Offsets between loops seen in Hi-C and IRIS.

feature† | [1] | [2a] | [2b] | [4] | [5] | [6] | [7] | [8] | [9] | [10] | [11]
---|---|---|---|---|---|---|---|---|---|---|---
$|$offset$|$‡ | 0.53″ | 0.46″ | 0.28″ | 0.11″ | 0.61″ | 0.09″ | 0.40″ | 0.73″ | 0.72″ | 0.05″ | 0.03″

† Features [1] and [2a,b] are shown in Fig. 5, the other features are
displayed in Fig. 16.
‡ The offsets listed here are the absolute values. See Fig. 18 for the offsets
in the $x$ and $y$ directions. Their typical error is 0.1″.

Figure 18: Offsets between loops in Hi-C and IRIS. Each diamond represents one
feature labeled in the same scheme as in Fig. 5, Fig. 16 and Table 1. The
dashed line shows the average direction of the loops (cf. Fig. 4b) reflecting
the overall orientation of the magnetic features. The circle has a diameter of
0.5″ that is a slightly larger than the resolution of either Hi-C or IRIS. See
Appendix B.

##  Appendix C A peculiar short loop

While not being the main topic of the study, we want to use this opportunity
to highlight a peculiar short loop labeled as feature [3] in Fig. 4. The main
goal of this short discussion is to report a novel feature that might or might
not be found regularly on the Sun. This feature has been discussed also in the
study on flux emergence and explosive energy release based on the very same
Hi-C data set Tiwari et al. (2019), but not in the following sense of temporal
evolution and heating.

In the small rectangle in Fig. 4b, a short loop feature in the Hi-C image is
visible with with a length of less than 5 Mm. This small feature even seems to
show some sub-structure. Also in the first flight of Hi-C, such short
miniature loops were seen in coronal emission Peter et al. (2013) — those were
even shorter than our example here. In contrast to the examples from the first
Hi-C flight, we can clearly identify the loop footpoints at opposite magnetic
polarities (Fig. 4c).

Most interestingly, this loop seems to be surrounded by emission from cooler
plasma as seen in the IRIS 1400 Å slit-jaw images, as it is evident from the
multi-color composite image in Fig. 4d. There it appears as if the warm loop
in Hi-C has a cool halo in IRIS. Actually, at the place of the short loop in
Hi-C, there is a hole in the emission of IRIS 1400 Å (Fig. 4a). This indicates
that the core of a cooler structure has been heated to higher temperature,
with the plasma in the outer part being not (or less) heated. However, the
short time interval covered through the suborbital rocket flight prevents a
more detailed analysis of the temporal evolution.

##  Appendix D Temperatures of the plasma seen by Hi-C, AIA, and IRIS

In Sect. 5.2.1 we discuss the possible temperature(s) in the source regions of
the emission recorded by Hi-C, AIA and IRIS. The main conclusion is that Hi-C
sees plasma at higher temperatures than IRIS does. Here we follow a procedure
outlined by Winebarger et al. (2013) to check if the source region of Hi-C (or
AIA) is closer to 0.3 MK or 0.8 MK by investigating the temporal variation of
the intensity in the various channels.

###  D.1 DEM and EM-loci methods

Usually, one would employ an inversion and obtain the differential emission
measure (DEM) to get a measure at which temperature(s) the bulk part of the
plasma is radiating (e.g. Cheung et al., 2015). However, when using AIA data,
these inversions are not reliable for temperatures below about
${\log}T\,[{\rm{K}}]{\approx}5.7$, because of the limited temperature
sensitivity in the AIA channels for those low temperatures. Furthermore, one
has to treat these inversions with care if applied to small dynamic
structures, and the features we investigate here change on time scales of one
minute (e.g. Figs. 7 and 8). This is fast, because it is comparable to or
smaller than the radiative cooling time. The latter can be defined as the time
scale to radiate the internal energy. Using the radiative loss function from
Chianti Dere et al. (2019), for a density of a low-lying loop of $10^{10}$
cm-3 and temperatures from 0.3 MK to 1 MK this ranges from 20 s to 60 s.
Performing a sparse DEM analysis Cheung et al. (2015) we typically find peaks
of the DEM around $\log{T\,[{\rm{K}}]}{\approx}5.8$ and $6.2$ in the cool and
warm loops in the active region core. However, we get similar results if we
check a neighboring quiet region or a moss area. So we cannot find a reliable
temperature estimate through the DEM inversion.

An alternative to the DEM analysis is the emission-measure (EM) loci method.
Under isothermal conditions, the EM curves from different channels of AIA
would intersect at one temperature that characterizes the plasma emission.
This technique has been applied, e.g., to inter-moss loops that show
simultaneous brightening in extreme-UV channels and provided evidence that
those loops are at temperatures significantly below 1 MK, at ${\approx}$0.3 MK
Winebarger et al. (2013). However, for our data set this technique suffers
from the same problems as the DEM inversion. Furthermore, when we apply this
technique to the model results (see Sect. 6) it also returns temperatures
around 0.3 MK, while in the model we find the true temperature distribution in
the loop to be at significantly higher values, closer to 1 MK.

###  D.2 Temporal evolution and implications for loop temperature

Acknowledging the limitations of the DEM and EM-loci techniques, we restrict
our analysis to a direct look at the light curves from the loops and relate
this to the temperature contributions of the respective channels. In Fig. 9 we
show the contributions (sometimes refereed to as temperature kernels) for the
AIA channels at 131 Å, 171 Å, 193 Å, and 211 Å. The main peaks of their
contributions range from 0.6 MK to 2 MK. However, except for the 131 Å
channel, the other three have a clear secondary peak at about 0.3 MK
(highlighted in Fig. 9), originating from transition region lines such as O V.

Following the temporal evolution of the loops, i.e. their light curves, one
might be able to distinguish at least if the contribution in the AIA channels
would be around 0.3 MK or at significantly higher temperatures. If the light
curves of the AIA channels are evolving in the same way, there are two
possible interpretations for the observed loop: (1) The loop is multi-thermal,
i.e. it consists of a mixture of (non-resolved) strands at different
temperatures that are heated simultaneously, or (2) the loop has a temperature
well below 1 MK, probably around 0.3 MK, as argued for the inter-moss loops
(Winebarger et al., 2013, their Sect. 2.2).

The fast evolution seen in the light curves raises the question of the
validity of ionisation equilibrium that is used to calculate the contribution
functions in Fig. 9. Considering their length, the loops we investigate here
most probably will be low-lying compact objects in the active region core. If
they indeed do not reach too high temperatures and assuming a constant
pressure, they will be at comparably high density. This would shorten
ionisation and recombination times. In their numerical model, Peter et al.
(2006) investigated the ionisation and recombination times for O V, that will
be a major contributor to the side peaks around 0.3 MK of AIA bands (cf. Fig.
9). For O V they find these time scales to be only 30 s to 40 s on average
(Fig. 4 of Peter et al., 2006). Consequently, the assumption of ionisation
equilibrium might be reasonable here.

###  D.3 Temporal evolution of loops in different bands

We now turn to the application of the temporal evolution of the features in
different wavelength bands to get an estimate of their temperature. The light
curves for selected loops for the AIA channels is displayed in Fig. 8. We also
add the light curves for the loops as seen in the IRIS 1400 Å channel, so that
the panels in Fig. 8 are extended versions of Fig. 7. Here we do show a
normalization for each of the light curves that maps the minimum and maximum
values during the time considered to the range $[0,1]$. This will highlight
small changes above a (slowly varying) background. We do not show the Hi-C 172
Å light curves, because as expected they are almost exactly the same as for
the AIA 171 Å band.

In principle we could perform this analysis for all the loop samples discussed
in Appendix B, because the data sets from AIA and Hi-C are properly aligned.
However, the spatial resolution of AIA is not sufficient to pick up the other
loops properly and would most probably only show the variability of the
background. Consequently we refrain from analysing these other cases.

Of the cases we show, feature [5] is closest in temporal evolution when
compared to inter-moss loops Winebarger et al. (2013). Here all the AIA
channels evolve very similarly with a transient brightening lasting for about
2 minutes (see Fig. 8 [5]). From this we would conclude that the loop seen in
171 Å (and in the other AIA channels) is at a temperature of around 0.3 MK.
Still, the temporal variation in the IRIS 1400 Å channel (dominated by Si IV)
is significantly different in that it increases much slower than the AIA
channels. Comparing the contribution function of Si IV in Fig. 9, it is clear
that most probably the emission we see in IRIS is originating from plasma that
is cooler (${\approx}0.1$ MK) than the emission from the 171 Å channel (and
hence Hi-C 172 Å), the latter originating from 0.3 MK or above.

The other examples show a less clear picture. Feature [2a] shows a two-peaked
structure in the AIA channels, with one peak around 18:57 and another around
19:00 UT (see Fig. 8 [2a]). However, during the first peak the brightening is
strongest in 211 Å, while during the second one 131 Å and 171 Å show the
strongest intensity increase. Thus we might consider in this case the AIA
emission to originate not from 0.3 MK, but from a different (higher)
temperature, probably above 1 MK during the first and 0.6 to 1 MK during the
second peak. As mentioned already with Fig. 7, here the peaks in the 1400 Å
channel of IRIS (i.e. Si IV, $<$0.1 MK) are not coinciding in time with the
peaks in the AIA channels, so also in this case the structures seen in IRIS
and Hi-C 172 Å will be at different temperatures and thus they will be
different loops.

Only in one case, in feature [4], we see a very similar variation between the
IRIS 1400 Å light curve and the AIA channels (see Fig. 8 [4]). So in this case
the emission in IRIS and Hi-C might actually originate from the same short
loop at a low temperature between 0.1 MK and 0.2 MK. Checking the offsets
between the IRIS and Hi-C loops in Table 1, reveals that this is one of the
three cases with offsets around 0.1″ or below. This is within the limits of
the alignment procedure (about 0.1″; see Appendix B). So it might be that in
this case the Hi-C and IRIS loops are indeed co-spatial and at the same
temperature. Feature [7] is similar to Feature [4] in that there the AIA light
curves are similar to each other (though to a lesser extent). Also the IRIS
1400 Å variation (see Fig. 8 [7]) is related: while a first peak around 18:58
UT is similar between IRIS and AIA, the second peak just before 19:00 is
broader in IRIS. So the similarity between IRIS and AIA is less clear than in
feature [4], but still present.