# A 2D Model for Coronal Bright Points:
Association with Spicules, UV bursts, Surges and EUV Coronal Jets

D. Nóbrega-Siverio Instituto de Astrofísica de Canarias, E-38205 La Laguna,
Tenerife, Spain  Universidad de La Laguna, Dept. Astrofísica, E-38206 La
Laguna, Tenerife, Spain  Rosseland Centre for Solar Physics, University of
Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway  Institute of Theoretical
Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway  F.
Moreno-Insertis  Instituto de Astrofísica de Canarias, E-38205 La Laguna,
Tenerife, Spain  Universidad de La Laguna, Dept. Astrofísica, E-38206 La
Laguna, Tenerife, Spain

(Received July 13, 2022; Revised July 28, 2022; Accepted July 30, 2022)

###### Abstract

Coronal Bright Points (CBPs) are ubiquitous structures in the solar atmosphere
composed of hot small-scale loops observed in EUV or X-Rays in the quiet Sun
and coronal holes. They are key elements to understand the heating of the
corona; nonetheless, basic questions regarding their heating mechanisms, the
chromosphere underneath, or the effects of flux emergence in these structures
remain open. We have used the Bifrost code to carry out a 2D experiment in
which a coronal-hole magnetic nullpoint configuration evolves perturbed by
realistic granulation. To compare with observations, synthetic SDO/AIA, Solar
Orbiter EUI-HRI, and IRIS images have been computed. The experiment shows the
self-consistent creation of a CBP through the action of the stochastic
granular motions alone, mediated by magnetic reconnection in the corona. The
reconnection is intermittent and oscillatory, and it leads to coronal and
transition-region temperature loops that are identifiable in our EUV/UV
observables. During the CBP lifetime, convergence and cancellation at the
surface of its underlying opposite polarities takes place. The chromosphere
below the CBP shows a number of peculiar features concerning its density and
the spicules in it. The final stage of the CBP is eruptive: magnetic flux
emergence at the granular scale disrupts the CBP topology, leading to
different ejections, such as UV bursts, surges, and EUV coronal jets. Apart
from explaining observed CBP features, our results pave the way for further
studies combining simulations and coordinated observations in different
atmospheric layers.

magnetohydrodynamics (MHD) — methods: numerical — Sun: atmosphere — Sun:
chromosphere — Sun: corona — Sun: transition region

††journal: ApJL

##  1 INTRODUCTION

Coronal Bright Points (CBPs) are a fundamental building block in the solar
atmosphere. Scattered over the whole disc, CBPs consist of sets of coronal
loops linking opposite polarity magnetic patches in regions of, typically,
from $4$ to $43$ Mm transverse size, with heights ranging from $5$ to $10$ Mm
(see the review by Madjarska, 2019). One of their most striking features is
the sustained emission, for periods of several hours up to a few days, of
large amounts of energy, which lend them their enhanced extreme-ultraviolet
(EUV) and X-ray signatures (e.g., Golub et al., 1974).

A significant fraction of the CBPs are observationally found to be formed as a
consequence of chance encounters of opposite magnetic polarities at the
surface (e.g., Harvey, 1985; Webb et al., 1993; Mou et al., 2018). First
theoretical explanations about this mechanism came in the 1990’s through
analytical models under the name of Converging Flux Models (Priest et al.,
1994; Parnell & Priest, 1995). There, the approaching motion in the
photosphere of two opposite polarities that are surmounted by a nullpoint
leads to reconnection and heating of coronal loops. Since then, this idea has
been extended and studied using magnetohydrodynamics (MHD) experiments (e.g.,
Dreher et al., 1997; Longcope, 1998; Galsgaard et al., 2000; von Rekowski et
al., 2006; Santos & Büchner, 2007; Javadi et al., 2011; Wyper et al., 2018;
Priest et al., 2018; Syntelis et al., 2019). However, the available CBP models
are idealized, i.e., they rely on ad-hoc driving mechanisms, which do not
reflect the stochastic granular motions, they lack radiation transfer to model
the lower layers of the atmosphere, and/or miss optically thin losses and/or
thermal conduction to properly capture the CBP thermodynamics.

To understand the physics of CBPs, realistic numerical experiments are needed
to address important open questions such as (a) the CBP energization, focusing
on whether the granulation is enough to drive and sustain the reconnection at
coronal heights to explain the CBP lifetimes; (b) the role of magnetic flux
emergence, specially at the granular scale, to know whether it can disrupt the
CBP topology and originate an eruption; and (c) the chromosphere underneath a
CBP, with the aim of unraveling the unexplored impact of CBPs on the spicular
activity and vice-versa.

In this letter, we model a CBP through the evolution of an initial fan-spine
nullpoint configuration. The choice of this configuration is because CBPs
often appear above photospheric regions with a parasitic magnetic polarity
embedded in a network predominantly of the opposite polarity, which typically
leads to a nullpoint structure in the corona (Zhang et al., 2012; Galsgaard et
al., 2017; Madjarska et al., 2021). The 2D experiment is carried out with the
Bifrost code (Gudiksen et al., 2011), which self-consistently couples the
different layers of the solar atmosphere and incorporates several physical
mechanisms not included in CBP modeling in the past. To provide a direct link
to observations, we calculate synthetic EUV images for SDO/AIA (Pesnell et
al., 2012; Lemen et al., 2012), and Solar Orbiter (SO)/EUI-HRI (Müller et al.,
2020; Rochus et al., 2020), and UV images for IRIS (De Pontieu et al., 2014).

Figure 1:  Initial condition. Top: Average stratification for the temperature
and density. Bottom: Imposed magnetic field configuration indicating some of
its major features following the terminology used in 3D nullpoints (Priest &
Titov, 1996). Red circle: region with $B<1$ G centered on the nullpoint,
$(x_{0},z_{0})=(32,8)$ Mm. Grey-dashed line: solar surface at $z=0$.

##  2 METHODS

###  2.1 Code

The experiment has been performed using Bifrost, a radiation-MHD code for
stellar atmosphere simulations (Gudiksen et al., 2011). The code includes
radiative transfer from the photosphere to the corona; the main losses in the
chromosphere by neutral hydrogen, singly-ionized calcium and magnesium;
thermal conduction along the magnetic field lines; optically thin cooling; and
an equation of state with the 16 most important atomic elements in the Sun.

###  2.2 Initial Condition

####  2.2.1 Background Stratification

The initial condition has been constructed using as background a preexisting
2D numerical simulation with statistically stationary convection in the
photosphere and below. It encompasses from the uppermost layers of the solar
interior to the corona ($-2.8$ Mm $\leq z\leq 67.0$ Mm, $z=0$ being the solar
surface). The horizontal extent is $0.0$ Mm $\leq x\leq 64.0$ Mm. The grid is
uniform with $4096\times 4096$ cells, yielding a very high spatial resolution
of $\Delta x=15.6$ km and $\Delta z=17.0$ km. The boundary conditions are the
same as for the experiment by Nóbrega-Siverio et al. (2016). The top panel of
Figure 1 shows the horizontal averages of temperature and density of the
background stratification.

####  2.2.2 Nullpoint Configuration

Over the previous snapshot, we have imposed a potential magnetic nullpoint
configuration as shown in the bottom panel of Figure 1. The potential field
was calculated from a prescribed distribution at the bottom boundary, $z=-2.8$
Mm. The nullpoint is located at $(x_{0},z_{0})=(32,8)$ Mm and the field
asymptotically becomes vertical in height with $B_{z}=-10$ G, mimicking a
coronal hole structure. The photospheric field contains a positive parasitic
polarity at the center on a negative background. At $z=0$, the total positive
flux and maximum vertical field strength are $\Phi^{+}=2.2\times 10^{10}$ G cm
and $B_{z}=41.3$ G, respectively; the parasitic polarity covers 9.7 Mm; and
the fan surface extends for 28.1 Mm. We will refer to the closed-loop domains
on either side of the inner spine as chambers.

Figure 2:  Experiment overview. Top: Main stage illustrating a CBP at
$t=40.00$ min. Bottom: Eruptive stage showing a surge and coronal jet at
$t=85.84$ min. (a) Temperature. (b) Synthetic SDO/AIA 193 with superimposed
magnetic field lines. (c) SO/EUI-HRI 174. (d) IRIS Si IV 1393.755 Å. For the
synthesis details, check Appendix A. Olive line on Panels (b) and (c):
$T=10^{5}$ K isocontour. The associated movie comprises the whole experiment
evolution from $t=0$ to $t=85.84$ min, illustrating the development of both
stages.
(An animation of this figure is available.)

##  3 RESULTS

###  3.1 Overview of the Experiment

Figure 2 and associated movie provide an overview of the system evolution
using temperature maps and synthetic observables for coronal and transition
region (TR) temperatures (see Appendix A). In the experiment, the granulation
quickly distorts the imposed magnetic field and reconnection is triggered as a
consequence of perturbations at the nullpoint. We distinguish two well-defined
phases: main stage and eruptive stage, summarized in the following and
described in Sections 3.2 and 3.3, respectively.

The main stage (from $t=0$ to $t\approx 65$ min) covers the appearance of
post-reconnection hot loops that leads to a CBP. For instance, at $t=40$ min
(top row of Figure 2), our CBP is discernible as a set of hot coronal loops
with enhanced SDO/AIA 193 and SO/EUI-HRI 174 emission above TR temperature
loops visible in IRIS Si IV. This matches the SDO/IRIS observations by Kayshap
& Dwivedi (2017), where CBPs are inferred to be composed of hot loops
overlying cooler smaller ones. Our CBP is found in the left chamber,
indicating that there is a preferred reconnection direction, and it gets more
compact with time before vanishing, as reported in observations Mou et al.
(2018).

In the eruptive stage, the CBP comes to an end. Around $t=67$ min in the
animation, a first hot ejection results from reconnection between emerging
plasma at granular scale and the magnetic field of the right chamber,
resembling the UV burst described by Hansteen et al. (2019). More episodes of
flux emergence and reconnection take place subsequently, dramatically
destabilizing the system and producing more ejections. As an example, at
$t=85.84$ min (bottom row of Figure 2) a large and broad hot coronal jet is
seen next to a cool surge, reminiscent of previous results by Yokoyama &
Shibata (1996); Moreno-Insertis & Galsgaard (2013); Nóbrega-Siverio et al.
(2016). The synthesis clearly reflects the high spatial resolution of SO/EUI-
HRI to study coronal jets and shows that the surroundings of the surge have
significant Si IV emission, similarly to observations (e.g., Nóbrega-Siverio
et al., 2017; Guglielmino et al., 2019).

Figure 3: Magnetic reconnection and flux emergence. (a) $B$ at $t=40.00$ min
with superimposed AIA 193 response only for the values contained in the
corresponding color scale. Olive line: $T=10^{5}$ K isocontour. Purple
rectangle: region for the current sheet (CS) analysis. Yellow dots: CS region
given by $L_{B}\leq 100$ km, as defined in Appendix B. (b) CS analysis. Top:
CS center coordinates, $x_{\mathrm{CS}}$ and $z_{\mathrm{CS}}$. Bottom: CS
length, $L_{\mathrm{CS}}$, and Joule heating, $Q_{\mathrm{Joule}}$. When the
CS is elongated, positive/negative angles of reconnection are indicated with
white/green areas; otherwise, using orange. (c) Space-time map for $B_{z}$ at
$z=0.15$ Mm. (d) View of (c) with the HMI resolution. (e) AIA 193 intensity
integrated along the vertical direction. (f) Unsigned vertical magnetic flux
for the experiment and corresponding ones for SST/CRISP and HMI resolutions
measured at $z=0.15$ Mm. In the figure, colored dashed lines follow the
polarities related to the left side of the fan surface (orange), the inner
spine (blue), and the right side of the fan surface (magenta). The cyan-dotted
lines indicates the time shown in Panel (a). The associated movie shows the
evolution of the magnetic field and SDO/AIA 193 response from $t=0$ to
$t=85.84$ min.
(An animation of this figure is available.)

###  3.2 Main Stage

####  3.2.1 Magnetic Reconnection and Association with CBP Features

To illustrate the crucial role of coronal reconnection for the CBP during the
main stage, Panel (a) of Figure 3 contains the magnetic field strength with
the SDO/AIA 193 response superimposed. Soon after starting the experiment (see
animation), a current sheet (CS) is formed (yellow dots in the panel).
Focusing on the region delimited by the purple rectangle, we distinguish three
clear patterns: (a) the reconnection site slowly drifts to the left; (b) the
reconnection and associated heating behaves in a bursty way; and (c) the
reconnection is oscillatory.

The reconnection-site’s displacement is shown in the top frame of Panel (b).
The horizontal position of the CS center, $x_{\mathrm{CS}}$ (black), moves 7.4
Mm to the left in 65 minutes, while its vertical position, $z_{\mathrm{CS}}$
(blue), first moves from 8.0 Mm up to 9.2 Mm, to descend later to 7.6 Mm.
These results are akin to observations, where CBP nullpoints are inferred to
rise, descend, or show both types of behavior in addition to important
horizontal displacement (Galsgaard et al., 2017).

The bursty behavior is depicted in the bottom frame of Panel (b). The CS
length, $L_{\mathrm{CS}}$, abruptly changes over times of minutes, reaching a
maximum of $3.3$ Mm. These fluctuations are well correlated with the Joule
heating released in the reconnection site, $Q_{\mathrm{Joule}}$: the Pearson
correlation coefficient between both curves is 0.93. Note that when the
diffusion region does not have an elongated CS (orange background in the
panel), the Joule heating is minimal. This intermittent heating seems to be
consistent with observed CBP emission variations over timescales of minutes
(see, e.g, Habbal & Withbroe, 1981; Ugarte-Urra et al., 2004; Kumar et al.,
2011; Ning & Guo, 2014; Chandrashekhar & Sarkar, 2015; Gao et al., 2022).

The elongated CS also changes its angle, $\theta_{\mathrm{CS}}$ (defined
anticlockwise with respect to the x-axis), several times, from, approximately,
$45$ to $-45$ degrees, indicating oscillatory reconnection. Panel (b) shows a
white/green background for the intervals when $\theta_{\mathrm{CS}}$ is
positive/negative. Most of the time, the angle is positive: the reconnection
inflows come from the right chamber and the upper-left part of the external
field, while the outflows are located in the left chamber and upper-right part
of the external field. This explains why the left chamber is the one showing
the CBP, as hot post-reconnection loops are being deposited predominantly in
this region. The predominance seems to be associated with the concentration
near the inner spine of the structure, indicated with a blue-dashed line in
Panel (a), which mainly moves to the left (see animation). Oscillatory
reconnection is also found in CBP observations (Zhang et al., 2014).

####  3.2.2 The Photospheric Magnetic Field

Figure 3 contains space-time magnetograms near the photosphere ($z=0.15$ Mm)
with the actual resolution of the simulation (Panel (c)) and reducing it to
the level of the SDO/HMI instrument (Panel (d), see Appendix A). To emphasize
the CBP evolution, Panel (e) contains a space-time diagram showing the
synthesized intensity of SDO/AIA 193 integrated along the vertical line-of-
sight. Panels (a), (c) and (d) show that the magnetic field around the
photospheric basis is quickly concentrated by the granular motions, leading to
strong magnetic patches at the solar surface. In the figure, we have
highlighted with colored dashed lines the concentrations that have collected
the field lines near the fan surface on each side (orange and magenta) and
near the inner spine (blue). The magnetic field concentrations are buffeted
and dragged by the granular motions while being substantially deformed in the
convection zone. In fact, the one related to the inner spine gets bent several
times underneath the surface and develops horizontal magnetized structures
(see animation of Panel (a) from $t\approx 20$ to $30$ min at $z\approx-1$ Mm
and $x$ between 30 and 32 Mm). Simultaneously with the convergence at the
photosphere of the two strong opposite concentrations (orange and blue lines),
the post-reconnection loops in the corona start to brighten up in the EUV
bands (see the superimposed SDO/AIA 193 response in Panel (a) and the space-
time diagram of Panel (e)) marking the appearance of our CBP at around $t=30$
min. From observations, convergence is frequently involved in CBP formation
(see, e.g., Mou et al., 2016, 2018, and references therein). The convergence
continues, and the CBP goes through a quiet phase until around $t=65$ min,
when the eruptive phase starts, triggered by flux emergence, as explained in
the next section.

###  3.3 Eruptive Stage

####  3.3.1 Magnetic Flux Emergence at the Surface

The strong and complex subphotospheric magnetic structures developing around
the inner spine mentioned in the previous section become buoyant and rise.
They reach the surface to the right of the inner spine from $t=42$ min
onwards, leading to anomalous granulation and increasing the unsigned vertical
magnetic flux. The enhanced magnetic pressure in the anomalous granules
further pushes the strong positive patch to the left, accelerating the
convergence of the two main opposite polarities of the CBP. Panel (f) shows
the total unsigned flux in the horizontal domain of Figure 3, i.e.,

$\Phi=\int_{x_{0}=14.0\,\mathrm{Mm}}^{x_{f}=47.5\,\mathrm{Mm}}{\left|B_{z}(z=0)\right|dx},$
(1)

with the integral calculated with the $B_{z}$ distributions in the experiment
(black curve) and in the reduced-resolution counterparts for SST/CRISP (green)
and SDO/HMI (red). The unsigned flux grows roughly by a factor two from $t=42$
min to $t=70.67$ min, when it reaches its maximum. Interestingly, in contrast
to a high-resolution instrument like SST/CRISP, the reduced resolution of
SDO/HMI would miss a significant fraction of the flux. From this time onwards,
the unsigned magnetic flux at the surface decreases while the two main
polarities continue converging. This could be interpreted as magnetic
cancellation, a fact that is frequently observed at the end of CBPs (e.g., Mou
et al., 2016, 2018).

Figure 4: Chromospheric analysis. Left: Space-time maps for
$z^{max}_{10^{4}\hskip 0.3pt\mathrm{K}}(x)$. Right: Corresponding density
$\rho(x,z^{max}_{10^{4}\hskip 0.3pt\mathrm{K}})$. Dashed lines: CBP’s main
polarities (see also Figure 3). Red-solid lines: fan surface at $z=1.5$ Mm in
the main stage.

####  3.3.2 Eruptive ejections

In the atmosphere, the emerging field quickly expands, interacting with the
preexisting magnetic structure of the right chamber and leading to eruptive
behavior with different ejections. The first one occurs at $t=67$ min, between
$x=24$ and 30 Mm, and it resembles a UV burst because of its enhanced TR
emission (see animation of Figure 2). The evolution of the system becomes
quite complex at this stage. The current sheet of the UV burst interacts with
the CBP current sheet, disrupting its magnetic configuration and causing the
end of our CBP (see the horizontal dark band at $t=71$ min in Panel (d) of
Figure 3). Another ejection with EUV signatures occurs right after, around
$t=74$ min, developing an Eiffel tower shape, followed by the ejection of the
broad EUV jet (reaching up to 13 MK) and surge that are shown in the bottom
row of Figure 2.

###  3.4 The Chromosphere and Spicular Activity

To analyze the chromosphere below the CBP, Figure 4 illustrates space-time
maps for $z^{max}_{10^{4}\hskip 0.3pt\mathrm{K}}(x)$, defined as the maximum
height at which $T=10^{4}$ K for each $x$, and the corresponding density
$\rho(x,z^{max}_{10^{4}\hskip 0.3pt\mathrm{K}})$ at that point. A major
distinction is apparent between the regions inside and outside the fan
surface. To clearly separate them, red-solid lines have been drawn at the
horizontal position where the fan surface cuts the plane $z=1.5$ Mm. Those
outside have an interesting flake or scale-like appearance. Each scale is
flanked by a quasi-parabolic trajectory signaling the rise and fall of
individual spicules: an example is indicated around $x=5$ Mm and $t\approx$ 44
min.

During the main stage, mainly from $t=30$ to $t=65$ min, the strong field in
the CBP’s opposite polarities (dashed tracks) lowers the height of the
chromospheric level below $2$ Mm. As these polarities converge, the
chromosphere underneath the CBP (i.e., in the left chamber) gradually moves
down, from $4$ Mm to 1 Mm, while the density roughly increases by an order of
magnitude there. This region also shows some spicules, predominantly
originated near the fan surface, with associated propagating disturbances that
cross the magnetic field loops of this region (see example of both phenomena
indicated within the left chamber).

The most striking characteristic of the right chamber is the enormous
rarefaction during the main stage resulting from the predominant reconnection
direction that extracts plasma from here (a fact also found in idealized 3D
nullpoint simulations without flux emergence by Moreno-Insertis and Galsgaard,
in preparation). In fact, the density can be so low as a few $10^{-17}$ g
cm-3: these are coronal densities with cold temperatures. There are also
spicular incursions in this chamber mainly coming from regions around the fan
surface (see example around $x=39$ Mm and $t=$ 32 min), but without associated
propagating disturbances. In the eruptive stage, the leftmost part of the
domain with $z^{max}_{10^{4}\hskip 0.3pt\mathrm{K}}(x)>8$ Mm corresponds to
the ejection of the surge. Trajectories of multiple dense plasmoids expelled
from the reconnection site are also visible with a fibril-like pattern.

##  4 DISCUSSION

In this letter we have shown that a wide class of CBPs may be obtained through
magnetic reconnection in the corona driven by stochastic granular motions. Our
numerical experiment has significant differences to previous CBP models: in
contrast to, e.g., Priest et al. (1994, 2018) or Syntelis et al. (2019);
Syntelis & Priest (2020), the magnetic field topology consists in a nullpoint
created by a parasitic polarity within a coronal hole environment; more
importantly, the reconnection and creation of the CBP is self-consistently
triggered by the convection that naturally occurs in the realistic framework
provided by the Bifrost code. The latter feature also sets it apart from the
idealized CBP coronal hole model of Wyper et al. (2018), in a which high-
velocity horizontal driving at the photosphere is imposed to provide the
energy released in the CBP.

Our experiment shows striking similarities to observed CBP features in spite
of the simplified 2D configuration. For instance, the CBP is composed of loops
at different temperatures, with hotter loops overlying cooler smaller ones,
and enhanced EUV/UV emission akin to observations (Kayshap & Dwivedi, 2017).
The projected length of these loops is around 8-10 Mm, which fits in the lower
range of CBP sizes (Madjarska, 2019). We can also reproduce other
distinguishable observational features such as the motion of the nullpoint
(Galsgaard et al., 2017), the convergence of the CBP footpoints (Madjarska,
2019, and references therein), the brightness variations over periods of
minutes (Habbal & Withbroe, 1981; Ugarte-Urra et al., 2004; Kumar et al.,
2011; Ning & Guo, 2014; Chandrashekhar & Sarkar, 2015; Gao et al., 2022), as
well as the oscillatory behavior (Zhang et al., 2014).

Magnetic flux emergence is crucial for the formation of roughly half of the
CBPs (Mou et al., 2018) and it can enhance the activity of already existing
CBPs (Madjarska et al., 2021). In our model, flux emergence plays a role for
the final eruptive stage of the CBP: only a few granules were affected by the
emergence, but the consequences for the CBP and the subsequent phenomena are
enormous. Observations with high-resolution magnetograms (e.g. by SST/CRISP)
are needed to explore this relationship and to discern whether hot/cool
ejections in the late stage of CBPs (e.g., Hong et al., 2014; Mou et al.,
2018; Galsgaard et al., 2019; Madjarska et al., 2022) may also follow,
directly or indirectly, from small-scale flux emergence episodes.

The chromosphere underneath the CBP in the model shows a number of remarkable
features. Spicules are mainly originated from the fan surface (accompanied
with propagating disturbances), which could perturb the CBP brightness (see,
e.g., Madjarska et al., 2021 and Bose et al. in preparation). The chromosphere
related to the CBP footpoints is reached at low heights, while there is a
chamber that gets greatly rarefied because of the reconnection, reaching
coronal densities with chromospheric temperatures. These results can be
potentially interesting to unravel the chromospheric counterpart of CBPs and
nullpoint configurations in general and need to be explored using coordinated
observations as well.

This research has been supported by the European Research Council through the
Synergy Grant number 810218 (“The Whole Sun”, ERC-2018-SyG) and by the Spanish
Ministry of Science, Innovation and Universities through project
PGC2018-095832-B-I00. The authors acknowledge the computer resources at the
MareNostrum supercomputing installation and the technical support provided by
the Barcelona Supercomputing Center (BSC, RES-AECT-2021-1-0023), as well as
the support by the International Space Science Institute (ISSI, Berne) to the
team Unraveling surges: a joint perspective from numerical models,
observations, and machine learning. The authors thank Dr. Frédéric Auchère for
his help to compute the synthetic observables for SO/EUI-HRI and Luc Rouppe
van der Voort for illuminating conversations related to SST/CRISP. The authors
are also grateful to Drs. Klaus Galsgaard and Maria Madjarska as well as to
the two referees for their interesting comments and advice. DNS acknowledges
support by the Research Council of Norway through its Centres of Excellence
scheme, project number 262622, and through grants of computing time from the
Programme for Supercomputing.

##  Appendix A SYNTHETIC OBSERVABLES

For the coronal and TR emissivity images, we assume statistical equilibrium
and coronal abundances (Feldman, 1992). Thus, the emissivity can be computed
as

$\epsilon=n_{H}\ n_{e}\
G(T,n_{e})\quad[\mathrm{erg}\,\mathrm{cm}^{-3}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}],$
(A1)

where $n_{e}$ is the electron number density, $n_{H}$ is the hydrogen number
density, and $G(T,n_{e})$ is the contribution function.

For the coronal 193 channel of the Atmospheric Imaging Assembly (AIA; Lemen et
al., 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell et al., 2012),
we generate a lookup table for $G(T,n_{e})$ with aia_get_response.pro from
SSWIDL with the flags /temp and /dn varying the electron number density from
$10^{6}$ to $10^{13}$ cm-3. Once we compute the emissivity, we degrade it to
the SDO/AIA spatial resolution, which is 1$\farcs$5 (Lemen et al., 2012). To
obtain the intensity map shown in Panel (e) of Figure 3, we integrate the
emissivity along the vertical line-of-sight assuming no absorption from cool
and dense features like the surge. In addition, we degrade the space-time map
to the SDO/AIA cadence, which is 12 s.

For the coronal 174 channel of the Extreme Ultraviolet Imager of the High
Resolution Imager (EUI-HRI; Rochus et al., 2020) on Solar Orbiter (SO; Müller
et al., 2020), we use the contribution function privately provided by Dr.
Frédéric Auchère, member of the Solar Orbiter team, since, at the moment of
writing this letter, the team is implementing the function in SSWIDL. The
results are afterwards degraded to the EUI-HRI resolution, which corresponds
to $100$ km pixel-size for perihelion observations (Rochus et al., 2020).

For the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al., 2014)
TR Si IV 1393.755 Å line, we create a lookup table employing ch_synthetic.pro
from SSWIDL with the flag /goft varying the electron number density from
$10^{6}$ to $10^{13}$ cm-3. The output of this routine is multiplied by the
silicon abundance relative to hydrogen to obtain the contribution function. To
transform CGS units to the IRIS count number, the emissivity is multiplied by
$(A\,p\,w\,\lambda)/(k\,r^{2}\,h\,c)$, where $A=2.2$ cm2 pix-1 is the
effective area for wavelengths between $1389$ and $1407$ Å, $p=0\farcs 167$ is
the spatial pixel size, $w=0\farcs 33$ is the slit width, $\lambda=1393.755$ Å
is the wavelength of interest, $k=4$ is the number of photons per DN in the
case of FUV spectra, $r=3600\cdot 180/\pi$ is the conversion of arcsec to
radians, $h$ is the Planck constant, and $c$ is the speed of light. Finally,
we degrade the results to the IRIS spatial resolution of 0$\farcs$33 (see De
Pontieu et al., 2014). Note that we have used statistical equilibrium as an
assumption; however, nonequilibrium ionization effects are relevant for TR
lines such as Si IV 1393.755 Å. In fact, in dynamic phenomena like surges,
statistical equilibrium underestimates the real population of Si IV ions, so
the actual emissivity could be larger than the one shown in Figure 2 (see
Nóbrega-Siverio et al., 2018, and references therein for details).

Regarding the SDO/HMI magnetogram of Panel (d) of Figure 3, we simply reduce
the spatial/time resolution of the Panel (c) to the instrumental HMI values:
1″$\approx$ 726 km at 6173Å and $45$ s of time cadence (Scherrer et al.,
2012). The same approach is used for SST/CRISP (Scharmer et al., 2008), which
has 0$\farcs$13 $\approx$ 94 km at 6301Å and $6$ s cadence, to obtain the
unsigned vertical magnetic flux shown in Panel (f) of the figure. The chosen
height to illustrate the magnetograms, $z=0.15$ Mm, is an approximation of the
formation height of the Fe I lines in which HMI and CRISP observe.

##  Appendix B CURRENT SHEET ANALYSIS

To analyze the current sheet (CS) behavior, we focus on the inverse
characteristic length of the magnetic field

$L_{B}^{-1}=\frac{\left|\nabla\times\hbox{{{B}}}\right|}{\left|\hbox{{{B}}}\right|}.$
(B1)

This quantity allows us to know where the abrupt changes of $B$ occur. The
analysis is limited to the region within $22\leq x\leq 40$ Mm and $5.5\leq
z\leq 12$ Mm (purple rectangle in Panel (a) of Figure 3), and for $0\leq t\leq
65$ min to avoid having secondary current sheets related to the flux emergence
episode described in Section 3.3. In this region, we take all the grid points
with $L_{B}^{-1}\geq 0.01$ km-1, so $L_{B}\leq 100$ km (yellow dots in Panel
(a) of Figure 3), performing a linear fit to their spatial distribution. The
goodness of the fit (the $r^{2}$ parameter) tells us whether there is a
collapsed/elongated CS or not. We have selected $r^{2}\geq 0.8$ as a criterion
for a collapsed/elongated CS. Thus, we obtain the horizontal and vertical
center position of the CS ($x_{\mathrm{CS}}$ and $z_{\mathrm{CS}}$,
respectively); its length ($L_{\mathrm{CS}}$); and its angle
($\theta_{\mathrm{CS}}$), defined in the anticlockwise direction with respect
to the $x$ axis, which is helpful to detect oscillatory reconnection. For
example, at $t=17.67$ min, the linear fit is $z=-0.988\,x+38.8$ Mm, with
$L_{\mathrm{CS}}=1.08$ Mm, $r^{2}=0.946$, and $\theta_{\mathrm{CS}}=-44.6$
degrees, meaning that there is a collapsed CS whose inflows from the
reconnection come from the left chamber and the upper-right part of the
external field. In contrast, at $t=40.00$ min, the time shown in Figure 3, the
linear fit is $z=0.927\,x-17.4$ Mm, with $L_{\mathrm{CS}}=1.94$ Mm,
$r^{2}=0.964$, and $\theta_{\mathrm{CS}}=42.8$ degrees, indicating that there
is also an elongated CS but with reconnection inflows occurring now from the
right chamber and the upper-left part of the external field. At $t=23.33$ min,
instead, the $r^{2}$ parameter is 0.383, so there is not a collapsed/elongated
CS.

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