11institutetext:  Department of Mathematics, Physics and Electrical
Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK
22institutetext: Université Paris-Saclay, CNRS, Institut d’Astrophysique
Spatiale, 91405, Orsay, France 33institutetext: Max Planck Institute for Solar
System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
44institutetext: Solar-Terrestrial Centre of Excellence – SIDC, Royal
Observatory of Belgium, Ringlaan -3- Av. Circulaire, 1180 Brussels, Belgium
55institutetext: Physikalisch-Meteorologisches Observatorium Davos, World
Radiation Center, 7260, Davos Dorf, Switzerland 66institutetext: ETH Zürich,
Institute for Particle Physics and Astrophysics , Wolfgang-Pauli-Strasse 27,
8093 Zürich 77institutetext: European Space Agency, ESTEC, Keplerlaan 1, PO
Box 299, NL-2200 AG Noordwijk, The Netherlands 88institutetext: UCL-Mullard
Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK
99institutetext: Southwest Research Institute, 1050 Walnut Street, Suite 300,
Boulder, CO 80302, USA 1010institutetext: Skobeltsyn Institute of Nuclear
Physics, Moscow State University, 119992 Moscow, Russia 1111institutetext:
Sorbonne Université, Observatoire de Paris - PSL, École Polytechnique,
Institut Polytechnique de Paris, CNRS, Laboratoire de physique des plasmas
(LPP), 4 place Jussieu, F-75005 Paris, France 1212institutetext: Rosseland
Centre for Solar Physics, University of Oslo, P.O. Box 1029, Blindern, NO-0315
Oslo, Norway 1313institutetext: Laboratoire Charles Fabry, Institut d’Optique
Graduate School, Université Paris-Saclay, 91127 Palaiseau Cedex, France
1414institutetext: Centre Spatial de Liège, Université de Liège, Av. du Pré-
Aily B29, 4031 Angleur, Belgium 1515institutetext: AESTER INCOGNITO, 75008
Paris, France 1616institutetext: LATMOS, CNRS - UVSQ - Sorbonne Université,
78280, Guyancourt, France 1717institutetext: Centre for mathematical Plasma
Astrophysics, KU Leuven, 3001 Leuven, Belgium 1818institutetext: Institute of
Physics, University of Maria Curie-Skłodowska, Pl. M. Curie-Skłodowskiej 5,
20-031 Lublin, Poland 1919institutetext: Astrophysics Research Centre, School
of Mathematics and Physics, Queen’s University Belfast, University Road,
Belfast, BT7 1NN, Northern Ireland, UK

# EUV fine structure and variability associated with coronal rain revealed by
Solar Orbiter/EUI HRIEUVand SPICE

P. Antolin, Corresponding author: Patrick Antolin EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE
<EMAIL_ADDRESS>A. Dolliou EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE F. Auchère EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE L. P. Chitta EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE S. Parenti EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE D. Berghmans EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE R. Aznar Cuadrado EUV fine
structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICE K. Barczynski EUV
fine structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE S. Gissot EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE L. Harra EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE Z. Huang EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE M. Janvier EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE E. Kraaikamp EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE D. M. Long EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE S. Mandal EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE H. Peter EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE L. Rodriguez EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE U. Schühle EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE P. J. Smith EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE S. K. Solanki EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE K. Stegen EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE L. Teriaca EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE C. Verbeeck EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE M. J. West EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE A. N. Zhukov EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE T. Appourchaux EUV fine
structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICE G. Aulanier EUV
fine structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE E. Buchlin EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE F. Delmotte EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE J. M. Gilles EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE M. Haberreiter EUV fine
structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICE J.-P. Halain EUV
fine structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE K. Heerlein EUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE J.-F. Hochedez EUV fine
structure and variability associated with coronal rain revealed by Solar
Orbiter/EUI HRIEUVand SPICEEUV fine structure and variability associated with
coronal rain revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure
and variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE M. Gyo EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE S. Poedts EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICEEUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE P. Rochus EUV fine structure and
variability associated with coronal rain revealed by Solar Orbiter/EUI
HRIEUVand SPICEEUV fine structure and variability associated with coronal rain
revealed by Solar Orbiter/EUI HRIEUVand SPICE

(Received ; accepted )

###### Abstract

Context. Coronal rain is the most dramatic cooling phenomenon of the solar
corona. Recent observations in the visible and UV spectrum have shown that
coronal rain is a pervasive phenomenon in active regions. Its strong link with
coronal heating through the Thermal Non-Equilibrium (TNE) - Thermal
Instability (TI) scenario, makes it an essential diagnostic tool for the
heating properties. Another puzzling feature of the solar corona, besides the
heating, is its filamentary structure and variability, particularly in the
EUV.

Aims. We aim to identify observable features of the TNE-TI scenario underlying
coronal rain at small and large spatial scales, to understand the role it
plays in the solar corona.

Methods. We use EUV datasets at unprecedented spatial resolution of $\approx
240\leavevmode\nobreak\ $km from the High Resolution Imager (HRI) in the EUV
(HRIEUV) of the Extreme Ultraviolet Imager (EUI) and SPICE on board Solar
Orbiter from the spring 2022 perihelion.

Results. EUV absorption features produced by coronal rain are detected at
scales as small as 260 km. As the rain falls, heating and compression is
produced immediately downstream, leading to a small EUV brightening
accompanying the fall and producing a ‘fireball’ phenomenon in the solar
corona. Just prior to impact, a flash-like EUV brightening downstream of the
rain, lasting a few minutes is observed for the fastest events. For the first
time, we detect the atmospheric response to the rain’s impact on the
chromosphere and consists of upward propagating rebound shocks and flows
partly reheating the loop. The observed widths of the rain clumps are $500\pm
200\leavevmode\nobreak\ $km. They exhibit a broad velocity distribution of
$10-150\leavevmode\nobreak\ $km s-1, peaking below 50 km s-1. Coronal strands
of similar widths are observed along the same loops co-spatial with cool
filamentary structure seen with SPICE, which we interpret as the Condensation
Corona Transition Region. Matching with the expected cooling, prior to the
rain appearance sequential loop brightenings are detected in gradually cooler
lines from corona to chromospheric temperatures. Despite the large rain
showers, most cannot be detected in AIA 171 in quadrature, indicating that
line-of-sight effects play a major role in coronal rain visibility. Still, AIA
304 and SPICE observations reveal that only a small fraction of the rain can
be captured by HRIEUV.

Conclusions. Coronal rain generates EUV structure and variability over a wide
range of scales, from coronal loop to the smallest resolvable scales. This
establishes the major role that TNE-TI plays in the observed EUV morphology
and variability of the corona.

###### Key Words.:

Sun: transition region – Sun: corona – Sun: activity – Sun: filaments,
prominences – Magnetohydrodynamics – Instabilities

##  1 Introduction

The solar corona is mysteriously heated to millions of degrees by yet unclear
mechanisms of magnetic energy conversion and transport in plasmas. Coronal
loops, the building blocks of the inner solar corona, constitute the prime
target for the coronal heating investigation, due to their visibility above
the diffuse background. Many of their properties remain a puzzle, such as
their lifetimes (EUV variation), and morphologies (in particular their sub-
structure) (Reale, 2010; Klimchuk, 2015; Viall et al., 2021). For instance, a
long-standing puzzle of the corona is the observed filamentary / strand-like
structure of loops (as opposed to being diffused) and their high variability,
particularly in the upper transition region (TR) spectral lines (Kjeldseth-Moe
& Brekke, 1998; Ugarte-Urra et al., 2009; Hinode Review Team et al., 2019).
The filamentary structure is linked with the loop sub-structure, with the
concept of coronal strands introduced and usually assumed to be part of a
larger entity (or coronal loop ‘bundle’). This multi-stranded vs. monolithic
structure has been a long-standing debate in the solar community. Its
importance stems from its strong link with the fundamental scales in which the
heating operates in the solar atmosphere, either directly associated with the
scales at granular level, where most of the energy originates (Martínez-Sykora
et al., 2018), or indirectly, e.g. by modifying how MHD waves propagate and
dissipate in inhomogeneous plasmas (Van Doorsselaere et al., 2014, 2020).

Prior to the Solar Orbiter launch (Müller et al., 2020), Hi-C (1st and 2nd
flights Kobayashi et al., 2014; Rachmeler et al., 2019), provided the highest
spatial resolution observations in the EUV, namely in the Fe xii 193 Å line
forming at $\approx 1.5\times 10^{6}$ K (1st flight) and in the Fe ix 172 Å
line forming at $\approx 10^{5.9}$ K (2nd flight). These observations indicate
coronal strand widths on the order of a few hundred km (Peter et al., 2013;
Brooks et al., 2013; Aschwanden & Peter, 2017; Williams et al., 2020). On the
other hand, such sub-structure does not appear to be present for all coronal
loops and across different temperature regimes, as the above reports show.
Sub-structure, such as coronal strands, may appear during the evolution of the
loops, particularly their cooling, and thus may be linked to specific aspects
of how the cooling happens.

Coronal rain is the most dramatic display of cooling in the solar corona. It
corresponds to cool ($10^{3}-10^{5}$ K) and dense ($10^{10}-10^{13}$ cm -3)
plasma clumps appearing over a timescale of minutes in chromospheric and TR
spectral lines in the solar corona, that preferentially fall towards the solar
surface along coronal loops (Kawaguchi, 1970; Leroy, 1972; Habbal et al.,
1985; Foukal, 1978; Wiik et al., 1996; Schrijver, 2001; De Groof et al., 2004,
2005). Coronal rain is closely related to prominences (Vial & Engvold, 2015),
but high-resolution observations over the last decade with Hinode (Kosugi et
al., 2007; Antolin & Shibata, 2010; Hinode Review Team et al., 2019), the
Swedish 1-m Solar Telescope (SST; Scharmer et al., 2003; Antolin & Rouppe van
der Voort, 2012), the Goode Solar Telescope (GST; Goode et al., 2003; Ahn et
al., 2014; Jing et al., 2016), the Solar Dynamics Observatory (SDO; Pesnell et
al., 2012; Vashalomidze et al., 2015) and the Interface Region Imaging
Spectrograph (IRIS; De Pontieu et al., 2014; Antolin et al., 2015; Schad,
2017; De Pontieu et al., 2021) have shown that coronal rain presents unique
features in terms of its morphology and kinematics. At the smallest scales,
coronal rain appears to be composed of clumps, which seem to also constitute
the coolest and densest part. The widths (in the direction transverse to the
flow) can be as low as 120 km (Jing et al., 2016) but generally are a few
hundred km in H$\alpha$ (Antolin & Rouppe van der Voort, 2012) to $\approx
500-600\leavevmode\nobreak\ $km in TR lines (Antolin et al., 2015), with
little variation other than that expected by spatial resolution. On the other
hand, they can extend greatly longitudinally (along the flow), with lengths
about an order of magnitude or more. Recently, Sahin et al. (2023) studied
large-scale coronal rain over an active region (AR) with IRIS in chromospheric
and TR lines, finding little variation in its morphological and dynamical
properties over several hours and across the AR. The observed coronal rain
strands appear to have very similar widths to the coronal strands observed by
Hi-C, described above, which may either directly reflect a fundamental heating
scale (Jing et al., 2016; Antolin & Froment, 2022) or be associated with the
cooling, as explained below.

One of the most interesting aspects of coronal rain is that the clumps occur
in tandem across a relatively large cross-section across the magnetic field
(of a few Mm in width). This synchronicity and shared trajectory of clumps has
led to the concept of rain shower, i.e. a larger-structure composed of coronal
rain clumps (Antolin & Rouppe van der Voort, 2012). Şahin & Antolin (2022)
have shown that rain showers match well with cooling coronal loops observed in
EUV, thereby helping to identify these in the large superposition (leading to
line-of-sight confusion) of the optically thin solar corona (what Malanushenko
et al., 2022, refer to as ‘coronal veil’).

There are currently 3 different kinds of coronal rain. The most commonly
observed kind is known as ‘quiescent’, and occurs preferentially in AR coronal
loops. This kind does not require any specific magnetic topology (other than a
loop-forming bi-polar structure). The second kind is linked to solar flares
and is known as ‘flare-driven’ coronal rain. It corresponds to the cool
chromospheric loops (sometimes known as H$\alpha$ loops) appearing at the end
of the gradual phase. The last kind is known as prominence-coronal rain
hybrids, and involves a complex magnetic field with null-point topology at the
top of loop arcades. A review of each can be found in Antolin & Froment
(2022). This work concerns the first kind, that is, the quiescent coronal rain
of ARs. This kind is the most actively studied probably because of its strong
link with coronal heating.

Numerical work since the 90s have shown that complex magnetic topologies such
as magnetic dips are not necessary for the generation of cool and dense,
prominence-like structures in loops (Antiochos & Klimchuk, 1991; Antiochos et
al., 1999; Karpen et al., 2001). Although we do not know what exactly the
agents of coronal heating are (e.g. MHD waves or stress-induced magnetic
reconnection), the generated spatial and temporal distribution of the magnetic
energy along loops has unique consequences on the evolution of coronal loops,
specifically on how they cool down. When the heating is strongly stratified
(also known as ‘footpoint concentrated’), even if constant over time, the loop
is often unable to reach thermal equilibrium and enters a state of thermal
non-equilibrium (TNE). Its thermodynamic evolution undergoes cycles of heating
and cooling, generally referred as TNE cycles, also known as evaporation-
condensation cycles (Kuin & Martens, 1982; Mok et al., 1990; Reale et al.,
1996; Müller et al., 2003; Mendoza-Briceño et al., 2005; Susino et al., 2010;
Luna et al., 2012). This is true as long as the repetition frequency of the
stratified heating events is faster than the radiative cooling time of the
loop (Johnston et al., 2019). Klimchuk & Luna (2019) have quantified some of
the requirements needed for TNE, and found that a volumetric heating ratio
between apex and footpoint below 0.3 and a heating asymmetry between both
footpoints under 3 ensures TNE.

(a)  (b)

Figure 1: Full FOV of HRIEUV for the 2022 March 30 (left) and April 1 (right)
datasets analysed in this work. The inner white rectangles show sub-FOVs shown
in later figures. The solid red curves denote the trajectories of some of the
observed coronal rain clumps.

In a nutshell, with a strongly stratified heating, the loop apex relies on
thermal conduction for its heating. However, this spatial distribution leads
to an essentially flat temperature profile along the loop length, or even a
temperature dip at the apex, thus making conduction inefficient. Furthermore,
the footpoint heating is very efficient at injecting material upwards (through
chromospheric ablation / evaporation), making the loop overdense relative to
the RTV scaling law (Rosner et al., 1978). The apex ends up having a thermal
imbalance, which results in a runaway or catastrophic cooling due to the
higher efficiency for plasmas at radiating their energy away at lower
temperatures (in the TR - corona temperature range). While the heating can be
very rapid (with the loop essentially empty) and therefore very hard to
observe, the cooling progresses over a timescale of tens of minutes to hours,
depending on the loop conditions. These long cooling times can lead to very
long loop lifetimes (Lionello et al., 2016). The loop eventually evacuates and
the cycle restarts if the heating conditions do not change, hence leading to
cycles of heating and cooling. During the initial stages of the cooling, and
when the cooling time is long enough relative to the cadence of the
observations, the loop is expected to sequentially appear in cooler coronal
passbands with specific non-zero timelags (Kamio et al., 2011; Viall &
Klimchuk, 2012; Viall et al., 2021). The cyclic pattern can lead to highly
periodic EUV intensity pulsations on the order of hours, recently detected
with EIT (Auchère et al., 2014) and the Atmospheric Imaging Assembly (AIA;
Lemen et al., 2012; Froment et al., 2015), indicating a heating function that
is stable over days (and up to a week). At the end of the cooling part of the
TNE cycle accelerated cooling is observed and coronal rain appears, which can
therefore also occur periodically (Auchère et al., 2018; Froment et al.,
2020). This acceleration in the cooling rate and also the spatial and temporal
character of coronal rain have been interpreted as a product of thermal
instability (TI), but a debate exists in the community (Klimchuk, 2019;
Antolin, 2020). The essential role that TI may play in the observed coronal
rain phenomena (and probably the long-period intensity pulsations as well),
has led to the cycles being known as TNE-TI cycles (Antolin & Froment, 2022).

Thermal instability is a fundamental MHD process (Parker, 1953; Field, 1965;
Waters & Proga, 2019; Claes, N. & Keppens, R., 2019). Besides coronal rain, it
has been invoked to explain phenomena from the short laboratory scales
(Lipschultz, 1987; Stacey, 1996), to very large intracluster medium scales
(White & Rees, 1978; Cavagnolo et al., 2008; Sharma, 2013). In the context of
the solar corona, thermal instability is less straightforward to apply because
the corona is very dynamic and is out of hydrostatic equilibrium (Aschwanden
et al., 2001). Nonetheless, various analytic studies have argued that given
the long timescales of TNE cycles, TI theory still holds, given the local and
short timescale characteristics of its occurrence (Claes & Keppens, 2021).
Antolin & Rouppe van der Voort (2012) and Antolin et al. (2015) have argued
that TI may act as a synchronising mechanism for catastrophic cooling to occur
simultaneously across a loop in TNE, thereby providing an explanation for rain
showers (see also Froment et al., 2020; Antolin, 2020). Şahin & Antolin (2022)
have used this link to unlock a way to estimate the TNE volume over an AR. By
calculating the number of rain showers and their properties, they have
estimated that at least 50% of the AR is subject to TNE.

Figure 2: Co-aligned HRIEUV (left) and SPICE (right) full FOV for March 30
(top) and April 1 (bottom). The SPICE images correspond to a 96- and 160-step
rasters for March 30 and April 1, respectively, and show the total intensity
over the Ne VIII line. The corresponding HRIEUV images are synthetic rasters
that match the time and space distribution of data acquisition with SPICE. A
spatial binning has been applied to HRIEUV to match the platescale of SPICE.
The red rectangles correspond to regions of interest (ROI) in each FOV with
overlaid rain paths in red identified with HRIEUV. The ROI on March 30 is
shown in Figure 5. The ROIs on April 1 to the West and East are shown in
Figures 13 and 17, respectively. See text for further details.

2.5-D radiative MHD simulations by Antolin et al. (2022) have shown that the
TI-driven catastrophic cooling leads to the formation of cool and dense cores
at the head of the rain emitting in chromospheric lines, surrounded by thin
but strongly emitting shells in TR lines that elongate in the wake of the
rain, in what is known as the Condensation Corona Transition Region (CCTR).
These structures are seen clearly in the Si IV 1402 line observed by IRIS
(forming at $\approx 10^{4.8}\leavevmode\nobreak\ $K), and the Fe xii 171 line
observed by AIA 171 (forming at $\approx 10^{5.8}$ K), and could therefore
explain the filamentary/stranded morphology and dynamic nature of the corona
seen in these lines (Ugarte-Urra et al., 2009), as well as the common widths
between coronal rain strands and coronal EUV sub-structure. High-resolution
observations in the EUV are needed to confirm this hypothesis. Furthermore,
Antolin et al. (2022) have shown that TI produces a local enhancement of the
magnetic field strength, due to the gas pressure loss during TI and frozen-in
conditions. Due to the compression ahead of the rain (downstream) as it falls,
a strong UV and EUV enhancement is obtained over the last few Mm prior to
impact with the chromosphere. Furthermore, a strong rebound shock and upward
flow is obtained from the impact, propagating at different speeds
(corresponding to the tube speed and flow). These features have remained
elusive in observations until now.

Solar Orbiter was launched in early 2020 on a highly elliptical orbit around
the Sun. By now, it has concluded two science close perihelia in its nominal
mission phase, where the distance to the Sun was less than 0.32 au. In this
work we analyse data from one of the two High Resolution Imagers (HRI) of the
Extreme Ultraviolet Imager (EUI) telescopes on board Solar Orbiter (Rochus et
al., 2020), corresponding to the first close perihelion, which happened
between March and April 2022 (Berghmans et al., 2023). The HRIEUV is an EUV
imaging instrument in the 174 Å passband, which is dominated by the Fe ix (at
171.1 Å ) and Fe x (at 174.5 Å and 177.2 Å ) emission forming at $\approx
10^{6}\leavevmode\nobreak\ $K (Chen et al., 2021). The importance of the high
resolution achieved by this instrument was already evident in HRIEUV data from
May 2020, when the spacecraft was at 0.556 au, which revealed small EUV
brightenings at spatial and temporal resolutions that could be barely detected
by SDO/AIA observations (known as ‘campfires’; Berghmans et al., 2021).

EUI also includes a high-resolution imager HRILya, whose bandpass is centered
at 121.6 nm and is dominated by the Lyman-$\alpha$ line of hydrogen. We do not
useHRILya in this work due to the degradation issues the telescope suffered
during the perihelion approach (see Berghmans et al., 2023, for details).

In this work we analyse HRIEUV data and identify several coronal rain events
at unprecedented spatial resolution of $\approx 240$ km in the EUV that allow
us to clearly identify the EUV variability and morphology associated with
coronal rain. The paper is organised as follows. The HRIEUV observations are
presented in Section 2. The methods are presented in Section 3. Results can be
found in Section 4, and discussion and conclusions in Section 5.

##  2 Observations

The observations analysed in this work belong to the first perihelion passage
of Solar Orbiter in March and April 2022. Specifically, we analyse two
datasets of HRIEUV at 174 Å, one of NOAA 12974 on 2022 March 30, and the other
of ARs NOAA 12975 and 12796 on 2022 April 1, both on-disk (Mampaey et al.,
2022). At this time, Solar Orbiter was near quadrature with Earth (with
separation angles between Solar Orbiter and the Sun-Earth line of
$91.88^{\circ}$ and $102.02^{\circ}$ for March 30 and April 1, respectively).

On March 30 and April 1, Solar Orbiter was at 0.33 au and 0.34 au,
respectively. With an HRIEUV plate scale of 0.492″, the spatial resolution of
these observations is estimated to be close to the Nyquist limit of $2\times
0.492\arcsec$ (Berghmans et al., 2023), corresponding to 237 km and 247 km,
approximately. HRI images have $2048\times 2048$ pixels, leading to a
$17^{\prime}\times 17^{\prime}$ field-of-view (FOV). The full FOV for each
date can be seen in Figure 1. The observations on March 30 and April 1 are
part of the R_BOTH_HRES_HCAD_Nanoflares and R_SMALL_MRES_MCAD_AR-Long-Term
SOOPs (Zouganelis et al., 2020), respectively, which operated the HRIEUV
camera at a cadence of 3 s over a duration of 45 min (UT 00:03 – 00:48) on
March 30, and at a cadence of 10 s over a duration of $\approx
75\leavevmode\nobreak\ $min (UT 09:19 – 10:34) on April 1.

EUI is equipped with software controlled onboard calibration electronics to
correct the images pixel-wise for offset and flat field before compression.
The images are then prepped with the euiprep routine to level 2, which reduces
the jitter and pointing error. However, significant jitter still remains that
needs to be removed. To this end, we apply a cross-correlation technique to
align the images as described in Chitta et al. (2022).

For better visualisation of the fine structure in the HRIEUV images, we have
applied the wavelets-optimised whitening (WOW) enhancement technique described
in Auchère et al. (2023). This method works by equalizing the variance at all
scales and locations in the image, thereby reducing the large scale gradients
and conversely enhancing the small scale structures.

We have also checked HRILya for the presence of rain in the Lyman-$\alpha$
line. However, none could be detected probably due to the problem affecting
the resolution of the instrument, as discussed in Berghmans et al. (2023).

Solar Orbiter also carries the Spectral Imaging of the Coronal Environement
(SPICE, SPICE Consortium et al., 2020), as part of the remote sensing payload.
For March 30, the SPICE data analyzed (data release
3.0111https://doi.org/10.48326/idoc.medoc.spice.3.0), is the 96-step raster
starting at 00:00:32 UTC with a field of view of $384^{\prime\prime}\times
914^{\prime\prime}$. It has a duration of 16 min 24 s and an exposure time of
10 s. The selected slit is 4″wide, while the data spatial pixel size is
1.098″along the slit. The temperature coverage of the spectral windows was
from the chromosphere to the corona through the observation of the following
spectral lines: H I Ly$\beta$ 1025.72 Å (Log $T_{e}$ = 4.0 K); C III 977.03 Å
(Log $T_{e}$ = 4.8 K); S V 786.47 Å (log $T_{e}$ = 5.2 K); O IV 787.72 Å (log
$T_{e}$ = 5.2 K); O VI 1031.93 Å (log $T_{e}$ = 5.5 K); Ne VIII 770.42 Å (log
$T_{e}$ = 5.8 K ); Mg IX 706.02 Å (log $T_{e}$ = 6.0 K). For April 1st, we
analysed five 160-step rasters which use the 4′′ slit each producing a field
of view of $640^{\prime\prime}\times 911^{\prime\prime}$. They run from
09:15:36 to 10:15:37 UTC. The rasters duration is 14 min with the exposure
time of 5 s. The spectral windows of April 1st study covered similar lines as
the March 30 raster, with the exception of the S V and O IV lines. These two
lines were replaced by N IV 765.15 Å (Log $T_{e}$ = 5.2 K). For both datasets
we used L2 data which are original data corrected for dark current, flat-
field, geometrical distortion. An additional step in the data processing was
the application of the radiometric calibration.

The pointing information in SPICE L2 headers is not accurate and the SPICE
rasters need to be co-aligned with the HRIEUV sequence. We started by binning
the HRIEUV images to the same pixel size of SPICE. We then built a HRIEUV
synthetic raster by selecting, from the HRIEUV time sequence, the image
closest in time to each SPICE exposure making the raster. For each SPICE
exposure, the SPICE pixel positions along the slit make an irregular grid in
Helioprojective coordinates. The HRIEUV image closest in time to this exposure
is reprojected into this grid. We then made SPICE images in Ne VIII intensity
by spectrally summing over the 32 pixels window. The Ne VIII and HRIEUV images
are, in fact, comparable in terms of plasma temperature coverage. Finally, the
SPICE images are co-aligned with the HRIEUV synthetic raster using a cross-
correlation technique. The SPICE FOV for March 30 and April 1 in the Ne VIII
line co-aligned with HRIEUV can be seen in Figure 2. Snapshots of each FOV in
all the other spectral lines are shown in Figure 25 for March 30 and Figure 24
for April 1.

In addition to EUI images we also briefly analyse images from the Atmospheric
Imaging Assembly (AIA; Lemen et al., 2012) on board the Solar Dynamics
Observatory (SDO; Pesnell et al., 2012) to locate, if possible, the coronal
rain events observed with HRIEUV. The AIA data correspond to level 2 data,
processed through the standard SolarSoft packages. Since strict AIA-EUI co-
alignment at a pixel scale is not needed for our purpose (we do not need to
identify specific rain trajectories across different viewpoints), we rely on
co-alignment using header information through the JHelioviewer software
(Müller et al., 2009), which is sufficient to identify the large-scale
structure common to both FOVs (such as loops, rain showers, prominences etc.).

##  3 Methodology

Figure 3: Time-distance diagram along the white dashed curve in Figure 1
(right panel) for the April 1 HRIEUV observation, with distance ‘0’
corresponding to the western end of the curve. The curve crosses a loop bundle
at the apex, which is seen to undergo a large-scale reconfiguration (radially
inward corresponding to shrinkage), as pointed by the arrows. This time-
distance diagram is made from images that have been processed with the
wavelet-optimised whitening enhancement technique of Auchère et al. (2023).
Figure 4: Close-up on the footpoint of the loop bundle where coronal rain is
seen on March 30. The FOV corresponds to the white rectangle shown in Fig. 1
(left), rotated by 90∘ so that the loop is orientated with the height of the
page. The red and labelled curves vertically oriented denote several rain
clump trajectories. The black arrows point to some of the clumps. The image
corresponds to the average over 3 consecutive frames. The cyan rectangle in
the figure corresponds to the FOV shown in Figure 7. Path 11 is a transverse
cut across the loop bundle. The accompanying animation runs from UT 00:23 to
UT 00:37 and shows several coronal rain clumps in absorption falling towards
the chromosphere (dark structure at bottom). Note the strong EUV variation
associated with this event. The images composoing the movie are processed with
the wavelet-optimized whitening enhancement technique of Auchère et al.
(2023). The movie first runs without and then with the rain paths overlaid.
Figure 5: SPICE multi-wavelength view on the loop bundle with rain seen on
March 30. The FOV corresponds to the red rectangle shown in Figure 2 (top) and
the overlaid red curves mostly denote the rain paths seen with HRIEUV (see
Figure 4). The HRIEUV panel corresponds to a synthetic raster matching the
time of the SPICE raster (see text for details) but preserving the HRIEUV
spatial resolution. Each SPICE panel shows the total intensity over a spectral
line indicated in the subtitle, together with its temperature of maximum
formation.

Coronal rain clumps and showers can be seen with a sharp eye without any image
enhancement technique such as ‘WOW’, but certainly become more discernible in
the processed images. To analyse the morphology and dynamics of several of
these events we start by tracking several rain clumps manually in the image
sequences, with the help of CRISPEX (CRisp SPectral EXplorer), a widget-based
tool programmed in the Interactive Data Language (IDL), which enables the easy
browsing of the data, the determination of loop paths, extraction, and further
analysis of space-time diagrams (Vissers & Rouppe van der Voort, 2012).

Figure 6: Sequence of 8 snapshots separated by 15 s showing the pre- (top) and
post-impact (bottom) phases of a coronal rain shower from the event of March
30. The black arrows on the top panels show the head of a rain clump as it
falls (note the bright tip indicated by red arrows, followed by a dark
elongated structure). For reference, path 5 is shown in the Figure with a
cyan-black dashed curve (same labelling as in Fig. 4). The lower panel shows a
bright upward propagating feature that we interpret as a combination of a
rebound shock and flow produced by the impact of the rain shower. These images
have been processed with the wavelet-optimized whitening enhancement technique
of Auchère et al. (2023).

The determination of projected velocities in the plane-of-the-sky (POS) is
done by calculating slopes in resulting rain clump tracks in the time-distance
diagrams obtained from CRISPEX. These tracks define $(x,y,t)$ positions of the
rain. The errors incurred in this process depend on the length of the tracks
in the time-distance diagrams. By varying slightly the spatial and temporal
end points of the tracks it is possible to estimate the errors in each
calculation. The availability of AIA in quadrature would allow to estimate the
total speed of a rain event through 3D stereoscopy. However, this is beyond
the scope of the present manuscript.

No rain is detected in the time-distance diagrams (through dark or bright
propagating features) without prior check with the image sequences. This is
necessary since several effects (such as lateral motions of loops) can produce
apparent dark or bright propagating features in time-distance diagrams.

Regarding the morphology of the rain, we are primarily interested in the
observed widths. For this purpose, we apply the same semi-automatic routine as
in previous work (for more details see Antolin et al., 2015). For a given
clump path and a given track in the time-distance diagram corresponding to
this path, the routine takes a cut perpendicular to the trajectory at every
$(x,y,t)$ location defined by the track and fits a single Gaussian over the
interpolated profile. The Full-Width at Half-Maximum (FWHM) is then taken as
the width of the clump at that location. Several checks are performed to
reduce errors in the fitting. We first calculate the average intensity profile
of a feature for the time range in which it is seen (as defined by a slope in
the time-distance diagram) and require a difference of at least 100 DN s-1
between its intensity (which can be in emission or absorption) and the
background (which is also calculated over the same path but at times without
rain, immediately before or after the rain episode). We then require the
contrast between the feature’s average intensity and the background to be at
least 10 %. Lastly, we also require that the Gaussian fit of the rain feature
is good enough. The latter is ensured by requiring that the $\sigma-$error
resulting from the fit is below 0.4 and that the total of the residuals fromt
he fit is low, that is
$\sum|I_{x,y}(x_{\perp},y_{\perp},t)-f(x_{\perp},y_{\perp},t)|<0.75$, where
$(x_{\perp},y_{\perp})$ denotes the transverse cut to the path at point
$(x,y)$, $I$ is the intensity along this cut, and $f$ denotes the Gaussian fit
to $I$. Visual inspection of the fittings indicate that these values ensure an
accurate calculation of the rain width while avoiding artefacts due to cosmic
rays or other features. The width of a clump corresponds to the average over
all measurements performed for the track in the time-distance diagram
corresponding to that clump. A measure of the error in the width calculation
is given by the standard deviation over all the measurements for a given
track.

##  4 Results

###  4.1 Coronal loop bundles

We analyse several coronal rain events observed with HRIEUV. On March 30, the
event occurs in a coronal loop bundle belonging to AR NOAA 12974 in the
southern hemisphere, which is on-disk but near the limb as seen in Figure 1
(left panel). The rain is seen to fall onto the leading polarity, onto a
region with abundance of dark jet-like structures fanning outwards. No sunspot
is seen in the vicinity, suggesting that this corresponds to a decaying AR.
Several rain clumps were followed, whose trajectories can be seen in the
figure.

On April 1, HRIEUV observed a wide region of activity composed of 2 ARs, NOAA
12975 and 12976, in the northern hemisphere, also not far from the limb as
seen in Figure 1 (right panel). Coronal rain is seen much more pervasively
compared to the other HRIEUV observation. In particular, we analysed four
different regions, labelled in the panel, where several coronal rain events
can be seen, as indicated in the figure.

Region 1 focuses on the West footpoint of a very large coronal loop bundle
that is seen to undergo a wide-scale reconfiguration. Some of this
reconfiguration is also associated with a bundle of loops that are rooted
closer to the lower-right corner of box-2 in the right panel of Figure1. To
see this more clearly we take a transverse cut at the apex of the loop bundle,
as shown by the dashed curve in the right panel, and plot the time-distance
diagram in Figure 3 (distance ‘0’ in the diagram denotes the western end of
the dashed curve, as seen in Figure 1). In the diagram we indicate with arrows
several instances of large-scale motions of individual coronal strands
directed radially inwards, suggesting a shrinkage. This process is also
accompanied by large-amplitude transverse oscillations that can also be
identified in the figure. At the same time, large amounts of coronal rain are
observed to fall along the leg captured by Region 1.

Region 2 on April 1 focuses on a region with different polarity compared to
Region 1, where the other footpoint of the loop bundle appears to be rooted.
Region 2 shows stronger activity (pores, moss, light-walls and jets) and a
more complex magnetic topology as discussed in the accompanying paper
(Berghmans et al., 2023). Between regions 1 and 2, a highly twisted filament
is seen, whose eruption was observed by EUI and SPICE on the following day,
and is discussed in (Berghmans et al., 2023).

Region 3 on April 1 is located at the North-West of the AR. A different bundle
of loops is seen, with footpoints close to those in Region 2, and therefore
also in a high-activity region.

Region 4 on April 1 is located on the East limb and captures part of a long
loop that is rooted in the trailing AR (NOAA 12976).

###  4.2 March 30 loop bundle as seen with SPICE

Figure 7: Close-up of the sub-FOV indicated by the white rectangle in Figure
4. The dark feature indicated by the arrows corresponds to the EUV absorption
produced by a rain clump. We interpret the bright feature below (downstream
of) the rain clump indicated by the red arrow as compression and heating
produced by the rain clump as it falls.  Figure 8: Time-distance diagrams
along paths 1 and 3 indicated in Figure 4. Distance increases with height
along the paths. The dark tracks traced by cyan-black dashed lines correspond
to EUV absorption from falling rain clumps. The dashed lines are offset by a
fraction of a minute in order to better see the rain features. An estimate of
the projected velocity is given for the closest slope to each value. Note the
bright tracks indicated by the red arrows immediately beneath the first dark
tracks in each diagram. We interpret this feature as compression and heating
from the clump. We interpret the upward bright and diffuse slope at the end of
the time sequence ($t\approx 30-32\leavevmode\nobreak\ $min) in Path 3 as a
combination of a rebound shock and flow produced by the rain impact on the
chromosphere.

Several of the loop bundles seen in HRIEUV can also be seen in SPICE in the Ne
VIII line, as expected from the similar formation temperature. In particular,
the loop bundle where rain is observed with HRIEUV can be seen with SPICE. In
Figure 5 we show a close-up on the loop bundle, which includes the FOV shown
in Figure 4. The raster through this region occurred at UT00:08:44, which is
roughly $20-25$ min prior to the main rain shower. The loop can be seen in the
Mg IX coronal line and in the upper transition region lines (Ne VIII and O
VI), suggesting that it is in a state of cooling. However, emission in the
lower temperature lines seems to be dominated by the background and we cannot
detect any clear chromospheric emission from coronal rain. This could also be
due to timing, since the main rain shower happens after the raster.

SPICE also executed high cadence 3-step rasters at various times during the
HRIEUV observing window, including the rain shower time. However, the slit
crosses higher up along the loop at $X\approx-2500\arcsec$ (barely crossing a
few of the longer rain paths), coinciding with a strong background emission.
We could not find any clear rain signatures in these fast rasters.

###  4.3 Two-pixel wide coronal rain clumps in absorption, and downstream
compression and heating

In Figure 4 we show several coronal rain paths identified for the event of
March 30. The coronal rain clumps can be seen in the figure and corresponding
animation as dark features, produced by EUV absorption from neutral hydrogen,
neutral and singly ionised helium (Anzer & Heinzel, 2005). In Figure 6 (top
panel) we show several snapshots separated by 15 s each, where large and small
absorption features can be seen falling.

For better visualisation of the fine-scale structure we show in Figure 7 a
sub-FOV of only $2\text{\leavevmode\nobreak\ Mm}\times 3$ Mm centred on a dark
absorption feature produced by a clump (white rectangle in Figure 4). Note
that it is barely 2 pixels wide (i.e. $\approx 240$ km), and is therefore the
highest resolution of a rain clump in EUV absorption to date. Another
interesting feature is the bright region downstream of the clump. The
animation shows that this bright feature is always beneath the dark absorption
feature from the clump. Similar features can be seen for other clumps, some
appearing only moments prior to impact in the chromosphere. We interpret this
feature as compression and heating produced by falling individual clumps.

To see the EUV variation produced by the rain more clearly, we plot in Figure
8 the time-distance diagrams corresponding to paths 2 and 3, shown in Figure
4. The dark tracks in this figure correspond to the EUV absorption produced by
the rain as it falls. The observed slopes indicate average speeds of
$70-80\leavevmode\nobreak\ $km s-1. Immediately below the first dark track, a
parallel bright slanted track can be seen, corresponding to the compression
and heating downstream of the rain clump. Note that several such bright tracks
can be seen, but are all very small with lengths under 1 Mm (vertical axis in
time-distance diagram).

Although we do not calculate accurately the lengths of the clumps in this
work, a rough estimate is given by the size of the dark tracks (vertical
distance) in the time-distance diagrams of Figure 8, which can be seen to have
$1-5\leavevmode\nobreak\ $Mm lengths.

Figure 9: Time-distance diagrams for all coronal rain paths shown in the left
panel of Figure 1. The cyan-black dashed lines with negative slopes show some
of the tracks produced by the rain clumps as they fall. The lines are offset
in time by 1 minute to better see the rain features. Note the extent of the
rain shower across all paths. Upward propagating features (positive slopes)
can also be seen, particularly at the end of the rain shower ($t\approx
30\leavevmode\nobreak\ $min). Zero distance corresponds to the footpoint of
the loop (seen in Figure 4).

###  4.4 Rebound shock and flow

Figure 6 (lower panel) shows another interesting feature of the event from
March 30, also seen in the animation of Figure 4. Following the impact on the
chromosphere of the rain shower a bright upward propagating feature can be
seen. We interpret this as a rebound shock and flow produced by the rain
impact. To the best of our knowledge, this is the first time that such feature
is observed, despite being predicted by every numerical simulation of coronal
rain (e.g. Müller et al., 2003; Fang et al., 2015). This feature can also be
seen in each time-distance diagram of Figure 8 as a bright upward slope just
after the end of the rain shower. The slope indicates speeds between $50-130$
km s-1. The lower end of this velocity range matches the expected value for
upward flows, while the upper end matches the tube speed for a plasma
temperature of $10^{5.8}$ K, which is close to the temperature at the peak of
the Fe X 174 Å formation. This is also supported by numerical simulations
(Antolin et al., 2022).

###  4.5 Extent of the rain shower

To examine the extent of the rain shower we plot in Figure 9 the time-distance
diagrams corresponding to all the paths shown in Figure 4. Several clump
tracks are shown by dashed lines. We can see that the main rain shower occurs
in the time range $t=20-30$ min. Although it can best be seen in paths 2 to 5
we can still traces of it across all the paths. This indicates that the extent
of the rain shower across the loop bundle is at least 15 Mm in the POS, and
possibly larger given the observed expansion of the loop bundle seen in Figure
1 (left panel). This is supported by the SPICE observations in Figure 5, which
show cool transition region emission over a width larger than that set by the
rain clumps detected by HRIEUV. Along the loop, the clumps can be tracked for
up to 25 Mm. Note that many clumps are only clearly visible in the last 10 Mm,
suggesting that the catastrophic cooling is non-uniform, with accelerated
cooling rates down to chromospheric temperatures being more confined in the
transverse direction. This effect may also be due to the line-of-sight, as
shown in section 4.13.

Figure 9 also shows that the rebound shock and flow occurs across a wide
expanse, but appears more concentrated than the rain shower and can only be
clearly seen in paths $1-6$.

###  4.6 Region 1 of April 1 - a large coronal rain event

Figure 10: Close-up on the footpoint of a large coronal loop bundle observed
on 2022 April 1 by HRIEUV. The FOV corresponds to that of Region 1 indicated
by the white rectangle in Figure 1, right panel. Except for path 8 (which
crosses the loop bundle), the red paths denote several rain paths. An
animation of this figure is available, whose images have been processed with
the wavelet-optimized whitening enhancement technique of Auchère et al.
(2023). It runs from UT09:19 to UT10:34 and shows several rain clumps falling
towards the chromosphere. The movie first runs without and then with the rain
paths overlaid.

We now turn our attention to some of the coronal rain events seen on the April
1 dataset (see Figure 1, right panel).

In Figure 10 we show the close-up on the footpoint of the large coronal loop
bundle undergoing a global change (akin to shrinkage), denoted as Region 1 in
Figure 1 (right). We follow several rain clumps and plot in Figure 36 the
corresponding time-distance diagrams. A main shower event is seen in the time
range $t=40-70$ min particularly along paths $2-4$, but signatures of another
rain shower are also seen at the beginning ($t<20$ min), particularly along
paths $6-7$. Also in this case, a combination of neighboring dark and bright
paths can be seen. Although not as clear as for the March 30 event, some of
the bright tracks may correspond to the downstream compression and heating,
especially those that immediately precede the absorption feature. Note that
some of these tracks only appear bright, for example the last track of Path 6.
Furthermore, upward propagating features can also be observed, some of which
do seem to appear just after rain impact. The observed morphology and speeds
are similar to those seen for the March 30 event, all of which are calculated
and presented in Section 4.11.

The rain shower seen in Region 1 appears to be far wider in extent than that
of March 30. As seen in Figure 10, the transverse length across which the
clumps are seen is at least 20 Mm, but certainly greater given the observed
expansion. Furthermore, the clumps can be followed for longer lengths along
the loop, with some being tracked for over 40 Mm. This suggests catastrophic
cooling down to chromospheric temperatures over a larger coronal volume, which
is supported by SPICE observations.

Figure 11: FOV corresponding to Region 2, shown in Figure 1 (right panel). The
red curves correspond to paths of some of the observed coronal rain clumps.
Note that intensities are scaled with a power of 0.1 to see a larger range of
variations. An animation of this figure is available, whose images have been
processed with the wavelet-optimized whitening enhancement technique of
Auchère et al. (2023). It runs from UT09:19 to UT10:34 and shows several rain
clumps falling towards the chromosphere. The movie first runs without and then
with the rain paths overlaid. Figure 12: FOV of Region 3 shown in Figure 1
(right panel). The red curves correspond to paths of some of the observed
coronal rain clumps. Paths 1 to 6 belong to the bright loop in the lower half
of the image, while paths 7 to 10 belong to a very long loop going towards the
top right corner of the image. Paths 9 and 10 are very short and parallel to
each other. Note that intensities are scaled with a power of 0.1 to see a
larger range of variations. An animation of this figure is available, whose
images have been processed with the wavelet-optimized whitening enhancement
technique of Auchère et al. (2023). It runs from UT09:19 to UT10:34 and shows
several brightenings followed by mostly bright rain clumps falling towards the
chromosphere. The movie first runs without and then with the rain paths
overlaid.

###  4.7 Region 2 of April 1 - null-point topology at footpoint

Region 2 on April 1 shows several coronal rain events belonging to different
regions in the AR. In Figure 11 we show the FOV corresponding to Region 2, as
shown in the full FOV of Figure 1 (right panel), with several rain clump paths
overlaid. The corresponding time-distance diagrams for these paths are shown
in Figure 37.

The most interesting rain shower is tracked by paths $1-5$ in these figures.
First, a loop bundle appears, with the intensity all along the loop increasing
in a uniform manner (but particularly at the apex) around UT 09:30 (about 10
min from the start of the observation). This brightening can be best seen
along path 5 (white arrows in Figure 37). The intensity uniformly decreases
along the loop over the next 10 min, after which, the first rain clumps
appear, with the bulk of the rain seen after 20 min from the first intensity
increase. Following the rain shower impact, the intensity increases strongly
at the footpoint with some signatures of upward propagating features (red
arrow in Figure 37)). As the rain falls, it is observed to strongly deviate
from its path and spread in different directions, reminiscent of a null-point
topology structure at the footpoint.

Figure 13: SPICE rasters in the N IV line ($\log T=5.2$ K) over a region that
overlaps with Regions 1 and 2 on April 1. The FOV corresponds to the red
rectangle to the East shown in Figure 2 (bottom) and the overlaid red curves
denote some of the rain paths seen with HRIEUV (see Figures 10 and 11). The
HRIEUV panel corresponds to a synthetic raster matching the time of the first
SPICE raster (see text for details) but preserving the HRIEUV spatial
resolution. The SPICE panels show the total intensity integrated over the N IV
spectral line for each raster (time shown in subtitle). The brightening
indicated by the red arrow in the UT09:52:36 panel corresponds to cooling
through the passband.

The paths $6-7$ and possibly path 8 seem to correspond to another loop bundle
that also experiences a similar uniform and global loop brightening as
described above. In this case, the loop bundle brightens at the very start of
the observation, and disappears after almost 1 hr. The rain is seen roughly 50
min after the start of the brightening, but is much fainter in terms of EUV
absorption than for the previous case. This loop is rooted close to a pore,
and periodic upward/downward ballistic motion is seen (particularly for paths
7 and 8), characteristic of Type 1 spicules (Beckers, 1964) or the EUV
counterparts of AR dynamic fibrils (Mandal et al., 2022).

Path $9$ (and possibly path 8 as well) may correspond to the other footpoint
of the large loop bundle of Region 1. However, contrary to the other
footpoint, the amount of rain that can be observed falling into this footpoint
is minimal and is further very faint.

The last path 10 may also belong to the large loop bundle of Region 1, and the
location of its footpoint is uncertain. Instead of the region where the
previous paths are rooted, path 10 appears to be rooted in a moss. Minimal
rain events are seen in this case.

All rain tracks observed in Region 2 show mostly EUV absorption, with little
EUV emission of the kind described earlier associated with compression. Also,
most tracks are relatively short ($10-20\leavevmode\nobreak\ $Mm) when
compared to Region 1, which may be due to the different inclination of the
loops relative to the LOS.

Figure 14: Top: Loop brightening prior to a coronal rain event. This time-
distance diagram (close up on the time range $t=[5,25]\leavevmode\nobreak\
$min) corresponds to path 3 in Region 3 on April 1 shown in Figure 38. Note
that the intensities have been scaled to the power of 0.1 to better see the
large intensity variation. Bottom: Time-distance along path 2 in the same lop
bundle. The white dashed lines correspond to dark and bright tracks from
coronal rain. Figure 15: Close-up on the time range
$t=[25,45]\leavevmode\nobreak\ $min in the time-distance diagram of paths 7
(top) and 10 (bottom) shown in Figure 38. Note that the beginning of the
brightening at $t\approx 33$ min starts essentially at the same time along the
path. The cyan-black dashed lines trace the outer envelope of the brightening
indicating a speed of $\approx 150\leavevmode\nobreak\ $km s-1.

###  4.8 SPICE view on Regions 1 and 2

The SPICE rasters managed to capture part of the regions of interest observed
with HRIEUV on April 1. This includes the top part of Region 1 and most of
Region 2 (see Figure 2, bottom), which mostly correspond to the apexes of the
loops with coronal rain. These loops are barely visible in the Mg IX coronal
line (Figure 26) but their filamentary structure are well seen in the upper
transition region lines (Ne VIII, O VI in Figures 27 and 28). Furthermore,
emission similar in morphology and strong variability can also be seen in the
lower transition region N IV line (Figure 13). For instance, the large-scale
brightening in the loop that corresponds to paths 1 to 5 in Region 2
(described in section 4.7) can be seen to peak in Mg IX at UT09:36 (red arrow
in the corresponding Figure), while in Ne VIII, O VI and N IV the brightening
peaks at UT09:52, and in C III the peak is sseen at UT10:06 (with some hints
of increased brightness in Lyman-$\beta$ as well but inconclusive due to the
strong background). This strongly supports our interpretation of cooling
through the passbands of HRIEUV and SPICE and subsequent appearance of rain in
EUV absorption.

###  4.9 Region 3 of April 1 - Localised and large-scale flash-like EUV
emission from rain

Figure 12 shows Region 3, as denoted in the full FOV of Figure 1 (right
panel), with several rain paths overlaid. Most of the loops analysed in Region
3 show a very different inclination with respect to the LOS when compared to
the previous cases. In this case, the LOS appears much less inclined with the
loop plane, leading to a top view of the loop rather than a sideways view.
Consequently, while the footpoint legs appear very short, the apexes appear
long in the projected view.

Paths $1-6$ appear to correspond to the same loop bundle, although paths $4-5$
show slightly different trajectories relative to paths $1-3$, which may be
indicative of braiding. This is further supported by the AIA observations of
the same event, as discussed in Section 4.13. As for the loops in Region 2, a
strong EUV enhancement uniformly along several coronal strands composing the
loop bundle are seen roughly 10 min from the start of the observation. The
coronal strands appear extremely thin, with sub-arcsecond widths (see section
4.12). This brightening can be clearly seen in the time-distance diagrams
shown in Figure 38. Most of the coronal strands disappear 20 min later. Both
dark and bright tracks can be seen in most time-distance diagrams, indicative
of flows in both directions (towards both footpoints). Some appear at the
start of the global intensity enhancement and others appear $20-60$ min after.
Note that despite the very close proximity of paths 1 and 2 and paths 4 and 5,
they show different (dim) features in their evolution. AIA 304 confirms the
presence of rain along this loop bundle (Section 4.13).

Path 3 corresponds to one of the best visible coronal strands. As shown in the
time-distance diagram, no clear bright or dark track can be seen. We select
this path to more accurately investigate the uniform global intensity
enhancement common to many of the strands in the loop bundle. In Figure 14
(top) we show the part of the time-distance diagram corresponding to the
intensity enhancement for path 3. Compared to the background, the enhancement
appears diffuse and seems to start close to the apex and propagates towards
both footpoints in a couple of minutes. Overall, this global intensity
enhancement over the strand lasts $\approx 8\leavevmode\nobreak\ $min. In
Figure 14 (bottom) we show a similar case for path 2. However, in this case
about 4 intensity enhancements are observed and almost all are accompanied by
dark or bright propagating features.

Although many of the features in paths $1-6$ do not show the EUV absorption,
but rather emission, we still associate them with coronal rain. Besides
similar velocities (see Section 4.11), the AIA observations of the same event
provide conclusive proof (Section 4.13).

The last set of paths we analyse are paths $7-10$, which correspond to a
different loop, apparently much larger in size. We were able to track a bright
clumpy feature over 40 Mm, leading to path 7. The clump falls at speeds of
$\approx$150 km s-1 in the POS, which, to our knowledge, is the fastest ever
recorded speed for a falling clump with imaging devices (besides erupting
fall-back). Just prior to impact, over the last $5-15$ Mm, several other
clumps are seen along parallel paths (tracks in paths 8, 9 and 10), suggesting
that the catastrophic cooling into chromospheric temperatures takes longer for
these neighboring strands.

In Figure 15 we show a close-up of the time-distance diagram corresponding to
paths 7 (top) and 10 (bottom) over the time where the falling clump is
observed. The bottom panel in the figure shows a very interesting pattern.
While the outer envelope (traced by the cyan-black dashed line in the figure)
corresponds to the same speed as observed in the longer time-distance path of
path 7 (top panel), there is an almost instantaneous intensity increase all
along the path at time $t\approx 33$ min. We believe that this feature is due
to the compression of the rain downstream, that is, physically similar to the
small brightening observed for the March 30 rain clumps. However, while the
brightening for the latter is always immediately below the rain’s head, for
the present case it occupies a much larger longitudinal extent. This is
probably due to a much stronger compression, which is able to increase the
temperature of the entire region below the rain to a temperature close to the
emissivity peak of HRIEUV ($\log T=5.8-6$), thereby generating a flash-effect.

###  4.10 Region 4 - Off-limb coronal rain

On April 1 HRIEUV captures various long loops rooted in the trailing AR closer
to the limb. Small EUV absorption features falling towards the surface can be
seen in one such loop, which we follow and show in red within Region 4 shown
in Figure 1. The time-distance diagram along this path is shown in Figure 16,
where various characteristic dark and bright tracks of coronal rain can be
seen falling at projected speeds of $50-90$ km s-1. This loop is also partly
visible in the SPICE rasters of April 1. In Figures 31 to 35 we show the
evolution through the SPICE rasters of the emission in this region. In
particular we notice strong variability in the upper and lower transition
region (Ne VIII, O VI, N IV) and chromospheric emission (C III and
Lyman-$\beta$) as shown in Figure 17. Therefore, SPICE confirms the presence
of coronal rain emitting at transition region and chromospheric temperatures
in this loop.

Figure 16: Time-distance diagram along a loop observed partly off-limb by
HRIEUV on April 1. The path corresponds to red curve in Region 4 shown in
Figure 1. The cyan and black dashed lines correspond to dark and bright tracks
from coronal rain (offset in time by 1 min in the figure for better
visualisation). Figure 17: SPICE rasters in the C III line ($\log T=4.8$ K)
over a region that overlaps with Region 4 on April 1. The FOV corresponds to
the red rectangle to the East shown in Figure 2 (bottom) and the overlaid red
curves denote some of the rain paths seen with HRIEUV (see Figures 10 and 11).
The HRIEUV panel corresponds to a synthetic raster (SR) matching the time of
the first SPICE raster (see text for details) but preserving the HRIEUV
spatial resolution. The SPICE panels show the total intensity integrated over
the C III spectral line for each raster (time shown in subtitle).

###  4.11 Statistics

Figure 18: Projected velocities (top) and widths (bottom) and associated
standard deviation (corresponding right panels) for all rain clumps tracked in
this work. The colours include transparency and denote different dates (see
legends).

In this section we provide statistics of all the velocity and width
measurements on the coronal rain clumps (both in absorption and in emission).
Please see Section 3 for the methods on how these quantities were calculated.

In Figure 18 we show a histogram of all the measured projected velocities for
both datasets. We note that the peak of the distribution is between $40-60$ km
s-1, with speeds as low as 10 km s-1 and as high as 150 km s-1. The latter
high projected velocities are not common for coronal rain, and may well
constitute the highest projected velocities to date (note that eruptive
prominence fallback is not coronal rain). No major differences exist between
both dates, except that April 1 presents a bigger spread, which is normal
given the higher number of rain events analysed for that date. The bulk of the
distribution matches well with previously reported speeds (Antolin & Rouppe
van der Voort, 2012; Schad, 2017; Antolin & Froment, 2022), as well as those
obtained in numerical simulations (Fang et al., 2015; Li et al., 2022). As
shown in the figure, the errors in the velocity measurements are generally
small (on the order of 5 km s-1 for most).

Similarly, in Figure 18 we show a histogram of all measured rain clump widths.
The distribution peaks between $400-600$ km, but goes as low as 260 km and as
high as 890 km. Both dates present small differences in terms of distribution
shape. While both datasets have relatively small pools, the dataset of Aptil 1
presents a broader distribution with values about 100 km larger. The standard
deviation figure indicates that there is a relatively large variation or error
in the width measurement. This is not unexpected, since along a given track
the rain clump’s background varies significantly, leading to differences in
the results of the Gaussian fits (despite efforts in reducing the background
influence, see Section 3).

Figure 19: Time-distance diagram along paths that cross several loop bundles:
path 11 in Figure 4 (top), path 8 in Figure 10 (second panel from top), path
11 in Figure 11 (third panel from top) and path 11 in Figure 12 (bottom). The
red lines between crosses denote times and location at which rain clumps are
observed. The vertical black arrow in the top panel indicates an example of an
EUV absorption feature produced by a rain clump. Note that the intensities in
the bottom panel have been scaled to the power of 0.1 to better see the large
intensity variation.

###  4.12 Coronal strands associated with coronal rain

To investigate more carefully a possible relation between the filamentary
coronal structure (coronal strands) within loop bundles and the coronal rain
they host, we take cuts across several of the analysed loop bundles, as shown
in Figures 4 (path 11), 10 (path 8), 11 (path 11) and 12 (path 11). We show
the resulting time-distance diagrams along these cross-cuts in Figure 19.

Several coronal strands can be seen in each Figure, some of which very likely
belong to the loop bundle hosting the rain event. In many instances, as the
rain crosses the transverse cuts it produces a small absorption feature (whose
time duration depends on the clump’s length as speed). One example of such a
feature is shown by an arow in Figure 19. Note that it is preceded and
followed by a bright EUV feature of roughly the same width as the rain clump.
A large group of rain clumps is seen around $t=22-32$ min, followed by a
bright feature at $t=32-40$ min. This bright feature corresponds to the
rebound shock and upward flow produced by the rain shower impact.

In Figure 19 a group of strands can be seen appearing after
$t=30\leavevmode\nobreak\ $min between distance 5 and 8 Mm across the
transverse cut, which seems to coincide with the location in time and space of
a group of rain clumps. Similarly, in the other panels in the Figure the rain
clumps appear to be preferentially located in regions where coronal strands
are observed. While sometimes a 1-to-1 association between a coronal strand
and a rain clump can be made (particularly for the latter), it is not the
general case. However, we can notice that the widths of coronal strands
(around 500 km) are on average similar to rain clump widths.

###  4.13 SDO/AIA observations at different line-of-sight and resolution

Our investigation on the coronal rain events with HRIEUV is complemented by
co-temporal SDO/AIA observations. On these dates, Solar Orbiter was in
quadrature with SDO, thereby offering a different view on the same ARs. In
Figures 20 and 22 we show snapshots for March 30 and April 1, respectively,
with a FOV centred on the regions of interest. The same large-scale coronal
structures can be identified across both instruments.

Despite the similarity between AIA 171 and HRIEUV in terms of the emission,
and the large-scale nature of the event (occurring across at least 15 Mm in
HRIEUV), no clear downflow can be observed in absorption or emission with AIA
171 on March 30 over the same time period. Sections of the loop bundle appear
and disappear over the same duration, which likely correspond to the EUV
variation associated with coronal rain observed with HRIEUV. Some upward
flows, bright in EUV, are observed, which could correspond to the rebound
shock and flow observed with HRIEUV. To check this we have identified and
tracked a few large rain clumps in AIA 304, whose paths are shown in Figure
20. The time-distance diagrams along these paths are shown in Figure 21 and we
can easily identify the characteristic rain slopes in AIA 304 (tracks in the
time-distance diagrams). Note the brightenings at the times the rain impacts
the chromosphere. With the help of AIA 304 we are able to recognise the rain
features in AIA 171, such as EUV absorption and in particular a rebound shock
and flow feature following the rain impact. The strong EUV variation that is
seen in the image sequence is therefore attributable to the rain episode.

On April 1, only region 1 shows clear coronal rain in the image sequence of
AIA 171, with the characteristic EUV absorption features downflowing along the
loop. Regions 2 and 3 show very similar EUV variation as observed with HRIEUV,
but as for March 30, we were unable to directly identify coronal rain
downflows only based on EUV absorption features in the image sequences.
However, the expected coronal rain is revealed in the 304 channel and we were
able to roughly identify the large-scale coronal rain events for each of the
loops. As for March 30, we track several large rain clumps in each region
(shown in Figure 22) and plot the time-distance diagrams in Figure 23. Path 1
tracks a rain clump belonging to Region 1’s loop, paths 2 and 3 belong to
Region 2 and may correspond to the loops outlined by paths 8 and 9 in Figure
11, and paths 4 and 5 follow clumps in the loop bundle outlined by paths 1 to
6 in Figure 12. We are able to detect several rain tracks in the time-distance
diagrams of AIA 304 and a very clear EUV absorption profile in AIA 171 for
path 1. However, the signatures in AIA 171 are much harder to detect. In paths
2 and 4 we do not see any features of the rain falling in AIA 171, but a
bright feature can be seen near the footpoint of path 4 that may correspond to
the impact and rebound shock and flow from a rain shower. In paths 3 and 5 we
are able to recognise a few EUV absorption and emission tracks co-temporal and
co-spatial to the rain tracks in AIA 304. The bright EUV emission in 171 is
similar to that seen in HRIEUV in paths 1 or 6 of Figure 38, in that a large-
scale emission is seen simultaneously all along the path that precedes the
bright downflowing feature from the rain.

Figure 20: SDO/AIA observation in the 171 (left) and 304 (right) channels of
the March 30 coronal rain event. AIA was roughly in quadrature with Solar
Orbiter on this date. The large loop bundle observed in the AIA 171 map
corresponds to the same loop bundle observed by HRIEUV in Figure 4. The white-
black dashed paths follow some rain clumps observed in AIA 304. An animation
corresponding to this figure is available. The animation shows several rain
clumps in AIA 304 but no clear counterpart is seen in AIA 171, although strong
intensity variations are observed at the same locations. The animation runs
from UT00:02 to UT00:49 and comprises the time where coronal rain is observed
with HRIEUV. It first runs without and then with the rain paths overlaid.
Figure 21: Time distance diagrams along paths 1 and 2 shown in Figure 20 on
March 30, with AIA 171 (top) and AIA 304 (bottom). Dark and bright paths from
coronal rain are highlighted with white-black dashed lines, which are offset
by a fraction of a minute to better see the rain features. Zero distance
corresponds to the footpoints of the loops. Note that the AIA 171 intensities
have been scaled to the power of 0.1 to better see the large intensity
variation.

It is interesting to note that, as shown by the AIA 304 animation, there is
widespread coronal rain over the AR over the same FOV as HRIEUV and including
loops for which it is not observed with HRIEUV. A large amount of coronal
emission ahead of the rain along the LOS can easily decrease the contrast
produced by EUV absorption or emission from the rain in the 171 or 174
channels, thereby making it undetectable. As we show here, high spatial
resolution can help retaining this contrast, which is why we observe far more
in HRIEUV than AIA 171. On the other hand, AIA 304 shows the
emission/absorption from the rain more directly since no further emission is
present ahead of the rain along the LOS. Nevertheless the rain can be hard to
discern due to the very bright TR background in AIA 304.

The larger FOV provided by SDO/AIA sheds more light into the large-scale
magnetic structure of Region 1 on April 1. AIA 171 reveals a topology akin to
null-point topology, with open field lines (or much larger loops) above, with
the loop arcade below the null-point. This provides an explanation to both the
large-scale reconfiguration and the observed large-scale coronal rain event in
the loop, with continuous coronal rain over a very wide loop cross-section
observed for the entirety of the HRIEUV observation. Indeed, as discussed in
Li et al. (2018); Mason et al. (2019), magnetic dips are often observed above
null-point topologies, which act as mass reservoirs where large amounts of
material can catastrophically cool down. The cool and dense material can then
either spill sideways from the magnetic dip or flow through the null-point,
facilitated by the reconnection process, downward into the newly formed
reconnected loops. This process can be very long-lived (Chitta, L. P. et al.,
2016; Chen et al., 2022) and can be accompanied by a reconfiguration of the
loop, similar to shrinkage (as in the standard flare model).

Figure 22: SDO/AIA observation in the 171 (left) and 304 (right) channels of
the April 1 coronal rain events. AIA was roughly in quadrature with Solar
Orbiter on this date. Some of the large loop bundles observed by HRIEUV can be
easily identified. The white-black dashed paths follow some rain clumps
belonging to these loop bundles, observed in AIA 304. Path 1 follows the same
loop bundle seen in Region 1 of Figure 10. Paths 2 and 3 may correspond to the
same rain events shown in paths 8 or 9 in Region 2 of Figure 11. Paths 4 and 5
follow the same loop bundle shown in the lower part of Figure 12 (paths 1 to 6
in that Figure). An animation corresponding to this figure is available. The
animation shows widespread rain in AIA 304 but the counterparts in AIA 171 can
only clearly be seen for the loop around path 1, although strong intensity
variations are observed at the same locations. The animation runs from UT09:20
to UT10:32 and comprises the time where coronal rain is observed with HRIEUV.
It first runs without and then with the rain paths overlaid. Figure 23: Time
distance diagrams along paths 1 to 5 shown in Figure 22 on April 1, with AIA
171 (top) and AIA 304 (bottom). Dark and bright paths from coronal rain are
highlighted with white-black dashed lines, which are offset in time by 1 min
to better see the rain features. Zero distance corresponds to the footpoints
of the loops. Note that the intensities have been scaled to the power of 0.1
to better see the large intensity variation.

###  4.14 Widespread coronal rain as suggested by SPICE

All the loops with coronal rain captured with HRIEUV show clear counterparts
in SPICE in the upper and lower transition region lines. For the off-limb loop
of Region 4 we were also able to capture clear emission in the chromospheric
lines of SPICE, thanks to the lower background emission. In Figure 24 we show
a multi-wavelength view of the full FOV of SPICE for 1 raster. What is
striking of this figure is that cool loops emitting in the upper and lower
transition region lines, with similar features (morphology, variability) as
those where we have detected coronal rain, are widespread in the FOV. Indeed,
all the 5 rasters of this region show strong variability in these loops. This
strongly suggests that at least for this AR coronal rain is widespread and
that only a fraction of it is observed in EUV absorption with HRIEUV. This
matches also the picture obtained with AIA 304.

Figure 24: SPICE multi-wavelength full FOV on April 1. The SPICE FOV is the
same as that shown in Figure 2 (bottom), co-aligned with HRIEUV. The overlaid
red curves denote some of the rain paths seen with HRIEUV (see Figures 10 and
11). Each SPICE panel shows the total intensity over a spectral line indicated
in the subtitle, together with its temperature of maximum formation.

##  5 Discussion and Conclusions

In this work we analysed coronal rain at unprecedented spatial resolution in
the EUV, provided by Solar Orbiter observations with HRIEUV during the 2022
spring perihelion. Observations were complemented with SPICE and AIA,
providing a multi-wavelength picture of the phenomenon in various active
regions. The resolution achieved is $\approx 240\leavevmode\nobreak\ $km,
which is only about two times lower than previous H$\alpha$ observations of
the phenomenon with the SST (Antolin & Rouppe van der Voort, 2012). The strong
correlation between EUV absorption and H$\alpha$ emission, expected from
radiative transfer theory (Anzer & Heinzel, 2005), is here confirmed down to
the smallest resolved scales ever achieved, with clump FWHM widths as small as
260 km. This fine-scale structure is also reflected in the fact that many
clumps only produce very faint EUV absorption features, thereby requiring
high-resolution and sensitivity to detect them.

We selected 2 dates on which Solar Orbiter observed several ARs on-disk and
partly off-limb. On March 30 we focused our attention on one coronal loop
bundle and discovered new features of coronal rain dynamics. As the rain
falls, the region immediately beneath the clump (downstream) is observed to
brighten, leading to very fine light streaks in time-distance diagrams. We
interpret this phenomenon as being the result of compression and heating due
to the relatively large momentum of the condensation. Fang et al. (2015)
report the formation of rebound shocks when coronal rain forms, produced by
the localised loss of pressure driving strong flows that lead to the
condensation. These rebound shocks may be thought as the source of the
brightening that we see. However, the rebound shocks are then seen to
propagate away at the sound speed from both sides of a condensation, much
faster than the condensation’s falling speeds. There is no reason why these
rebound shocks should propagate at the same speed. Therefore these rebound
shocks cannot explain our observations. On the other hand, our interpretation
as commpression and heating is supported by 2.5-D MHD simulations of coronal
rain by Li et al. (2022, see their Figure 4) and Antolin et al. (2022). This
phenomenon is therefore similar to the fireball phenomenon on Earth linked to
meteoric ablation, with the region below the clump being compressed and heated
as it falls. We do not observe this phenomenon for all coronal rain events,
which suggests that not only a high spatial resolution is needed but also
favorable line-of-sight relative to the rain trajectory. It is also possible
that the compressed material exists in all cases but emits at different
temperatures not sampled by HRIEUV.

EUV enhancement associated with coronal rain is also observed during the fall
ahead and at the wake of rain clumps. The latter can be seen in the time-
distance diagrams along or across rain clump trajectories as an increase of
the EUV intensity that follows the EUV absorption feature. This may correspond
to a coronal strand and is likely due to the CCTR, which extends from the
clump far into the wake, as shown by numerical simulations (Antolin et al.,
2022; Li et al., 2022). Observations with SPICE show the filamentary structure
in the upper and lower transition region lines, thereby supporting this
interpretation. Ahead of the clump, besides the fireball feature, a second,
more elusive kind of brightening is observed just prior to the rain impact
(with the brightening spreading over $\approx 6$ Mm), and manifests as a
flash-like simultaneous intensity enhancement of the entire space between the
clump and the chromosphere. We suspect that this is also due to the
compression of the plasma ahead of the clump, as suggested by the same
numerical simulations cited previously, with a compression strong enough as to
increase the temperature of the entire region below the rain close to the
emissivity peak of HRIEUV ($\log T=5.8-6$), thereby generating a flash-effect.
However, we only found one clear occurrence of this larger-scale compression,
for which the rain is extremely fast (with projected speeds of 150 km s-1).
Such speeds may be supersonic, in which case the compression argument may not
fully explain it. Indeed, if produced by compression, it means that sound
waves are produced ahead of the clump and travel fast enough to compress the
entire region donwstream (leading to the ‘flash-like’ character of the
brightening). However, this is not possible if the clumps are supersonic.

Another new phenomenon is the rebound shock and upflow that follows the rain
impact onto the chromosphere. The feature is detected best after the end of
rain showers rather than individual rain clumps, and is characterised by a
bright and diffuse propagating EUV feature roughly along the same paths over
which the cool downflows occur. The propagating speeds are between $50-130$ km
s-1, depending on the selected path for the time-distance diagram. Based on
multi-dimensional simulations of this phenomenon (Antolin et al., 2022), we
suspect that this difference is due to the combination of the rebound shock,
which propagates at the tube speed of $\approx 130\leavevmode\nobreak\ $km s-1
(for temperatures corresponding to the Fe X 174 Å formation temperature of
$10^{5.98}$ K), and an upward flow produced by the impact (which are bound by
gravity and thus slower). To the best of our knowledge, this is the first
report of this effect, despite being predicted by numerical simulations for
decades (Müller et al., 2003; Mendoza-Briceño et al., 2002; Antolin et al.,
2010; Fang et al., 2015; Li et al., 2022). Indeed, we expect a response from
the lower atmosphere in the form of an upflow or upward propagating wave along
every magnetic field line and probably even over a wider region compared to
that affected by the rain impact, due to the high-$\beta$ conditions and
strong gas pressure increase at the chromospheric heights of rain impact
(Antolin et al., 2022). For the March 30 event, this upward propagating
feature is seen to reheat the loop bundle and may correspond to the start of a
new TNE cycle. Simulations indicate that efficient refilling and reheating of
the loop is only obtained in the case that the stratified heating is still on-
going. In other words, if there is no continuous heating at the loop
footpoint, the simple rebound shock and flow obtained from a rain shower is
insufficient to bring the density and temperature back to usual coronal
values. The rebound shock and upflow can be seen mainly after rain showers
rather than individual rain clumps, suggesting an additional feedback effect
from the large rain shower momentum. Only a subset of rain showers show these
features, despite their relatively large-scale nature, indicating that the
conditions to observe this atmospheric response to the rain impact are
stringent. This is further supported by the AIA 171 co-temporal observations
on March 30 in quadrature with HRIEUV, where some hints of an upward
propagating disturbance are observed but remain much dimmer and elusive.

As shown by Şahin & Antolin (2022), rain showers can help identify coronal
loop entities (defined as a coronal volume evolving in similar way and
therefore subject to similar heating conditions). This is particularly
important given the optically thin nature of the corona, leading to great LOS
superposition (also referred to as ‘the coronal veil’; Malanushenko et al.,
2022). Furthermore, the occurrence of coronal rain points to a state of TNE,
for which stringent coronal heating conditions are needed. This is
particularly the case of quiescent coronal rain, which occurs in usual coronal
loops and is accompanied by long-period intensity pulsations for long-duration
heating (Froment et al., 2020). It is still unclear whether the TNE-TI
scenario still applies to prominence-coronal rain hybrid structures (although
initial results indicate quasi-periodic occurrence that may correspond to
long-period intensity pulsations Li et al., 2019) or even to flare-driven
rain.

Klimchuk & Luna (2019) have quantified the conditions for TNE, which include a
strong heating stratification (ratio of apex-to-footpoint volumetric heating
rate below 0.1) and not too high heating asymmetry between footpoints (below
3, to prevent siphon flows that effectively reduce the lifetime of the
condensations in the corona relative to their falling time). Johnston et al.
(2019) further show that a high frequency rate for the heating events (with
repeating time less than the radiative cooling time of the loop) is needed.
Several of the observed rain showers in this work occur following a global
brightening of the loop. This is expected from the TNE-TI cycle, in which the
loops start at a hot, indeterminate temperature and radiatively cool down.
What is observed then corresponds to the loop’s temperature going through the
temperature response range of the HRIEUV channel, which peaks at $\approx
10^{6}$ K (Rochus et al., 2020). Usual draining and cooling of loops would
explain this global brightening feature, but would fail to explain the
appearance of the clumpy downflows in EUV absorption or emission that follow
the global brightening events (Peter et al., 2012). This is also the case in
post-flare cooling, where simple draining and global cooling of loops is
unable to explain flare-driven rain (Reep et al., 2020). Our cooling
interpretation is further supported by the SPICE observations, which show that
the brightening is delayed for cooler spectral lines at transition region and
chromospheric temperatures.

It is interesting to note that the observed global brightening occurs fairly
uniformly and symmetrically along the loop, with the apex brightening a few
minutes prior to the rest of the loop. To our knowledge, very few works
investigate in detail (including the necessary forward modelling into e.g. AIA
171) the spatial distribution of the cooling during TNE cycles. The published
literature indicate that we should expect symmetric global brightening in a
channel such as AIA 171 during the cooling stage of TNE cycles when the
heating is symmetric across both footpoints (Müller et al., 2003; Peter et
al., 2012; Winebarger et al., 2018; Johnston et al., 2019), while asymmetric
heating or loop geometry may tend to produce asymmetric global brightening,
with significant brightening only along one loop leg (Mikić et al., 2013;
Froment et al., 2018; Pelouze et al., 2022). This would suggest that both the
heating along the observed loops with rain and the geometry of such loops are
symmetric rather than asymmetric.

In our observations, the rain is observed to occur in some cases right after
the loop global brightening (within 10 min or so), while other cases show
longer waiting time (over 40 min), which indicates different average loop
densities. While some clumps are seen to fall over large distances over 40 Mm,
most only appear in the last $10-20$ Mm. This spatial occurrence of coronal
rain is often the case when the heating or loop geometry is asymmetric since
such configurations generate siphon flows that reduce the lifetime of the
cooling plasma in the loop, also leading to what is known as incomplete
condensations that do not appear in chromospheric lines (Mikić et al., 2013;
Froment et al., 2018; Pelouze et al., 2022). Hence, contrary to the argument
in the previous paragraph, this would suggest asymmetric heating or loop
geometries. This contradiction suggests another possibility. For instance, it
is also possible that better visibility of the condensations with decreasing
height is due to a simple LOS effect, since we expect a larger column mass of
cool material along the LOS (and therefore stronger EUV absorption) closer to
the footpoints. This is supported by the SPICE observations, which show cool
emission down to low transition region temperatures or less along the loops
with rain.

Another interesting point is that the height at which the condensations occur
seems to decrease the farther away we are from the largest/clearest clumps
(those producing the clearest EUV absorption features). This behaviour
suggests progressive and non-uniform cooling across the loop, which may
reflect slightly different conditions, such as field line length and
differences in the heating that ultimately affect the character of the thermal
instability (as seen in numerical simulations, e.g. Froment et al., 2018;
Pelouze et al., 2022).

We observe some showers that occur over a very wide volume, over $15-20$ Mm in
the POS. This is a lower estimate, given that the loops are observed to expand
and most rain clumps appear closer to the footpoint, over the last $10-20$ Mm
lengths prior to impact. The SPICE observations confirm this, since the loops
appear wider in the cool transition region lines. The footpoint of these loop
bundles is relatively wide ($4-10\leavevmode\nobreak\ $Mm, as seen in Figures
4, 10, 11, and 12). This suggests similar heating conditions over a relatively
wide region (several times the granular scale) and probably a locking /
synchronising mechanism that can act over wide distances across the magnetic
field. Thermal instability has been suggested for this synchronising role
(Antolin & Froment, 2022).

We observe a width distribution for rain clumps peaking at $\approx 500\pm
200$ km. At the smaller range of this distribution we have the widths observed
in H$\alpha$ with the SST or GST (Froment et al., 2020; Jing et al., 2016),
while the larger range is common for the widths observed in chromospheric and
TR lines with IRIS (Antolin et al., 2015; Sahin et al., 2023). Not much
variation is observed across different regions. This little variation has been
reported in Sahin et al. (2023) and suggests a more fundamental nature of
plasma morphology in MHD. These widths could be governed by the underlying
magnetic topology and/or by the length scales of the heating (Antolin et al.,
2022). However, they can also be associated with thermal instabilities
(Antolin et al., 2015; Claes, N. & Keppens, R., 2019; Claes, N. et al., 2020).
We have shown that very sharp bright coronal strands appear co-located with
the rain clumps within the loop bundle and exhibit very similar widths of
$\approx 500$ km, consistent with the widths of coronal sub-structure found
with Hi-C (Brooks et al., 2013; Peter et al., 2013; Aschwanden & Peter, 2017;
Williams et al., 2020). This similarity suggests that, (a) the sub-structure
is similar for TNE and non-TNE loops (assuming that at least part of the
investigated loops by Hi-C are not under TNE) and, (b) such morphology does
not directly depend on the spatial scales of the heating in the lower
atmosphere. For instance, we know that the latter determines the spatial
distribution of the rain showers (Şahin & Antolin, 2022), but clearly the rain
showers do not have the same widths as rain clumps (differing by an order of
magnitude). Hence, a different mechanism may be responsible for the fine-scale
structure for both the rain and the coronal strands. This mechanism may be the
same in the case of TNE loops and may correspond to the CCTR produced by
thermal instability, as shown in Antolin et al. (2022).

The observed speeds for the coronal rain clumps exhibit a wide projected
velocity distribution, as reported in the past (e.g. Antolin & Rouppe van der
Voort, 2012; Kohutova & Verwichte, 2016; Verwichte et al., 2017; Schad, 2017).
The peak of the observed distribution is below 50 km s-1, with minima and
maxima of $10-150$ km s-1. This peak contrasts with previously observed peaks
of $80-100$ km s-1 (Antolin, 2020). This may be explained by the fact that
previous reports focus on off-limb coronal rain for which the FOV is small and
only captures a small region around the footpoint (a constraint of current
ground-based instrumentation that depends on AO locking). Here, we are able to
detect the rain closer to its formation time higher up along the loop, where
the speeds are naturally lower. This is in agreement with a recent AR-scale
study of coronal rain with IRIS by Sahin et al. (2023) and with 2.5-D MHD
numerical simulations (Li et al., 2022).

Most of the rain events we observe are rooted in moss, with strong jet
activity at the footpoints. Previous studies have indicated that strong
heating may occur in such regions (Testa et al., 2014; Chitta, L. P. et al.,
2018; Tiwari et al., 2019; Nived et al., 2021), favorable for the onset of
TNE-TI. In addition, we also observed a structure undergoing a large-scale
reconfiguration on April 1 (Region 1). This topological change may play a
major role in triggering TI due to the expected long-wavelength perturbations
(through magnetic pressure for example). Through coronal rain tracking we were
able to detect a null-point topology at the footpoint of one of the loops.
Such structures are preferential locations for magnetic reconnection and
therefore heating (Chitta et al., 2017; Priest et al., 2018; Syntelis et al.,
2019).

The availability of two co-temporal observations in similar TR lines but with
very different LOS, provided by SDO and Solar Orbiter in quadrature, allows to
disentangle to some extent the effect of LOS superposition and spatial
resolution. Large-scale events such as those of March 30 and most of April 1
were not detected in AIA 171, suggesting a major role of LOS superposition. On
the other hand, the various events observed on April 1 with HRIEUV pale in
comparison to the spatial extent seen in AIA 304 for that day, also indicated
by the SPICE observations. This suggests that although HRIEUV is a game
changer for observing coronal rain on-disk (in terms of its fine-structure and
the associated EUV changes) it is not the ideal channel for detecting how
pervasive the phenomenon is in the solar atmosphere. Still, the HRIEUV
observations show for the first time the extent of the EUV variation
associated with coronal rain events. We see EUV variation from the small
scales of rain clumps and fireballs to the large loop scales of CCTR-induced
coronal strands and rebound shocks and flows that partly reheat the loop
bundles. This supports previous suggestions based on numerical simulations
(Antolin et al., 2022) that the TNE-TI scenario plays a major role in the
observed filamentary morphology and high variability of the corona in TR and
low coronal spectral lines (Kjeldseth-Moe & Brekke, 1998; Ugarte-Urra et al.,
2009; Hinode Review Team et al., 2019).

###### Acknowledgements.

Solar Orbiter is a space mission of international collaboration between ESA
and NASA, operated by ESA. The EUI instrument was built by CSL, IAS, MPS,
MSSL/UCL, PMOD/WRC, ROB, LCF/IO with funding from the Belgian Federal Science
Policy Office (BELPSO); Centre National d’Études Spatiales (CNES); the UK
Space Agency (UKSA); the Deutsche Zentrum für Luft- und Raumfahrt e.V. (DLR);
and the Swiss Space Office (SSO). The building of EUI was the work of more
than 150 individuals during more than 10 years. We gratefully acknowledge all
the efforts that have led to a successfully operating instrument. The
development of SPICE has been funded by ESA member states and ESA. It was
built and is operated by a multi-national consortium of research institutes
supported by their respective funding agencies: STFC RAL (UKSA, hardware
lead), IAS (CNES, operations lead), GSFC (NASA), MPS (DLR), PMOD/WRC (Swiss
Space Office), SwRI (NASA), UiO (Norwegian Space Agency). SDO is a mission for
NASA’s Living With a Star (LWS) program. The ROB co-authors thank the Belgian
Federal Science Policy Office (BELSPO) for the provision of financial support
in the framework of the PRODEX Programme of the European Space Agency (ESA)
under contract numbers 4000112292, 4000134088, 4000134474, and 4000136424.
P.A. and D.M.L. acknowledge funding from STFC Ernest Rutherford Fellowships
No. ST/R004285/2 and ST/R003246/1, respectively. S.P. acknowledges the funding
by CNES through the MEDOC data and operations center. L.P.C. gratefully
acknowledges funding by the European Union (ERC, ORIGIN, 101039844). Views and
opinions expressed are however those of the author(s) only and do not
necessarily reflect those of the European Union or the European Research
Council. Neither the European Union nor the granting authority can be held
responsible for them. This research was supported by the International Space
Science Institute (ISSI) in Bern, through ISSI International Team project #545
(‘Observe Local Think Global: What Solar Observations can Teach us about
Multiphase Plasmas across Physical Scales’).

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##  Appendix A Multi-wavelength views with SPICE on March 30 and April 1.

Figure 25: SPICE multi-wavelength full FOV on March 30. The SPICE FOV is the
same as that shown in Figure 2 (top). The HRIEUV panel corresponds to a
synthetic raster matching the time of the SPICE raster (see text for details)
including spatial binning to match the SPICE platescale. Each SPICE panel
shows the total intensity over the indicated spectral line, together with its
temperature of maximum formation. The overlaid red curves denote the rain
paths seen with HRIEUV (see Figure 4). Figure 26: Same as in Figure 13 but for
the Mg IX line. Figure 27: Same as in Figure 13 but for the Ne VIII line.
Figure 28: Same as in Figure 13 but for the O VI line. Figure 29: Same as in
Figure 13 but for the C III line. Figure 30: Same as in Figure 13 but for the
Lyman-$\beta$ line. Figure 31: Same as in Figure 17 but for the Mg IX line.
Figure 32: Same as in Figure 17 but for the Ne VIII line. Figure 33: Same as
in Figure 17 but for the O VI line. Figure 34: Same as in Figure 17 but for
the N IV line. Figure 35: Same as in Figure 17 but for the Lyman-$\beta$ line.

##  Appendix B Time-distance diagrams with HRIEUV on April 1

Figure 36: Time-distance diagram for the rain paths tracked in Region 1 shown
in Figure 10. The cyan-black dashed lines with negative slopes track the
dark/bright absorption/emission features produced by several rain clumps
falling into the chromosphere. A few bright upward propagating features can
also be seen (positive slopes). Zero distance corresponds to the footpoint of
the loop (top-right of Figure 10). Figure 37: Time-distance diagrams for the
paths of the rain clumps shown in Figure 11. The cyan-black dashed lines
correspond to coronal rain tracks along the paths, with zero distance
corresponding to the loop footpoints on the right side in Figure 11. The lines
are offset in time by 1 min to better see the rain features.The white arrows
in the time-distance diagrams for path 5 indicate the times when the loop
brightens prior to the appearance of the rain.  Figure 38: Time-distance
diagrams for the paths of the rain clumps shown in Figure 12. The cyan dashed
lines correspond to coronal rain tracks along the paths, with zero distance
corresponding to the loop footpoints (left in Figure 12). The lines are offset
in time by 1 min to better see the rain features. Note the loop brightening
seen clearly in Paths 3 and 6 at time $t=15\leavevmode\nobreak\ min$.