∎

11institutetext: H. Peter, L.P. Chitta, A. Feller, D. Przybylski, L. Teriaca
22institutetext: Max Planck Institute for Solar System Research, Göttingen,
Germany 33institutetext: E. Alsina Ballester 44institutetext: Istituto
Ricerche Solari Locarno, Locarno-Monti, Switzerland 55institutetext: L.
Belluzzi 66institutetext: Istituto Ricerche Solari Locarno, Locarno-Monti,
Switzerland and Leibniz-Institut für Sonnenphysik, Freiburg, Germany
77institutetext: V. Andretta 88institutetext: INAF Osservatorio Astronomico di
Capodimonte, Napoli, Italy 99institutetext: F. Auchère, E. Buchlin, M. Janvier
1010institutetext: Université Paris-Saclay, CNRS, Institut d’Astrophysique
Spatiale, 91405 Orsay, France 1111institutetext: A. Bemporad
1212institutetext: INAF Osservatorio Astrofisico di Torino, Italy
1313institutetext: D. Berghmans 1414institutetext: Royal Observatory of
Belgium, Brussels, Belgium 1515institutetext: A. Calcines 1616institutetext:
Centre for Advanced Instrumentation, Durham University, UK 1717institutetext:
K. Dalmasse 1818institutetext: IRAP, Université de Toulouse, CNRS, CNES, UPS,
Toulouse, France 1919institutetext: T. del Pino Alemán, J. Trujillo-Bueno
2020institutetext: Instituto de Astrofísica de Canarias, Tenerife, Spain
2121institutetext: C. Froment 2222institutetext: LPC2E, CNRS/University of
Orléans/CNES, Orléans, France and Institute of Theoretical Astrophysics,
University of Oslo, Norway 2323institutetext: R. Harrison 2424institutetext:
RAL Space, STFC Rutherford Appleton Laboratory, Oxfordshire, UK
2525institutetext: S. Matthews 2626institutetext: UCL Mullard Space Science
Laboratory, Surrey, UK 2727institutetext: S. Parenti 2828institutetext:
Institut d’Astrophysique Spatiale, Orsay, France and Département
d’Astrophysique/AIM, CEA/IRFU, CNRS/INSU, Université Paris-Saclay, Université
de Paris, 91191 Gif-sur-Yvette, France 2929institutetext: S.K. Solanki
3030institutetext: Max Planck Institute for Solar System Research, Göttingen,
Germany and School of Space Research, Kyung Hee University, Yongin, Republic
of Korea 3131institutetext: J. Štěpán 3232institutetext: Astronomical
Institute ASCR, Ondřejov, Czech Republic

# Magnetic Imaging of the Outer Solar Atmosphere (MImOSA)

Unlocking the driver of the dynamics in the upper solar atmosphere

H. Peter E. Alsina Ballester V. Andretta F. Auchère L. Belluzzi A. Bemporad D.
Berghmans E. Buchlin A. Calcines L.P. Chitta K. Dalmasse T. del Pino Alemán A.
Feller C. Froment R. Harrison M. Janvier S. Matthews S. Parenti D. Przybylski
S.K. Solanki J. Štěpán L. Teriaca J. Trujillo Bueno

(draft version: )

###### Abstract

The magnetic activity of the Sun directly impacts the Earth and human life.
Likewise, other stars will have an impact on the habitability of planets
orbiting these host stars. Although the magnetic field at the surface of the
Sun is reasonably well characterised by observations, the information on the
magnetic field in the higher atmospheric layers is mainly indirect. This lack
of information hampers our progress in understanding solar magnetic activity.
Overcoming this limitation would allow us to address four paramount long-
standing questions: (1) How does the magnetic field couple the different
layers of the atmosphere, and how does it transport energy? (2) How does the
magnetic field structure, drive and interact with the plasma in the
chromosphere and upper atmosphere? (3) How does the magnetic field destabilise
the outer solar atmosphere and thus affect the interplanetary environment? (4)
How do magnetic processes accelerate particles to high energies? New ground-
breaking observations are needed to address these science questions. We
suggest a suite of three instruments that far exceed current capabilities in
terms of spatial resolution, light-gathering power, and polarimetric
performance: (a) A large-aperture UV-to-IR telescope of the 1-3 m class aimed
mainly to measure the magnetic field in the chromosphere by combining high
spatial resolution and high sensitivity. (b) An extreme-UV-to-IR coronagraph
that is designed to measure the large-scale magnetic field in the corona with
an aperture of about 40 cm. (c) An extreme-UV imaging polarimeter based on a
30 cm telescope that combines high throughput in the extreme UV with
polarimetry to connect the magnetic measurements of the other two instruments.
Placed in a near-Earth orbit, the data downlink would be maximised, while a
location at L4 or L5 would provide stereoscopic observations of the Sun in
combination with Earth-based observatories. This mission to measure the
magnetic field will finally unlock the driver of the dynamics in the outer
solar atmosphere and thereby will greatly advance our understanding of the Sun
and the heliosphere.

###### Keywords:

Sun: magnetic fields Sun: atmosphere Space vehicles: instruments Techniques:
polarimetic ESA Voyage 2050

††journal: Experimental Astronomy

##  1 Introduction

The magnetic field plays a central role in many if not most of the processes
we observe in our universe. It governs complex plasma processes from the
formation of structures in the early universe to the interplanetary space that
connects planets to their host stars. Although we know the magnetic field at
the solar surface reasonably well, our information on it in the higher layers
is mainly indirect. This state of knowledge is highly unsatisfactory because
the field carries most of the energy in these layers and is the dominant
driver of most of the phenomena that are observed there (e.g. heating of the
gas to millions of degrees, coronal shape and brightness, magnetic
reconnection and its effects, and large-scale ejection of parts of the solar
atmosphere). The lack of direct measurements of coronal magnetic fields is
similar to being blind to the main driver of solar activity. We contend that
this is one of the major hindrances to our understanding of coronal physics.
Obtaining these measurements would help to explain a very wide variety of
phenomena.

We can follow the interaction of the magnetic field and plasma on our central
star in detail and may essentially use the Sun as a laboratory for uncovering
key magnetic and plasma processes that act throughout the universe. In the
coming decades, we expect that answering the following overarching questions
will lead to a giant leap in understanding the Sun:

  * 1.

How does the magnetic field couple the different layers of the atmosphere, and
how does it transport energy?

  * 2.

How does the magnetic field structure, drive and interact with the plasma in
the chromosphere and upper atmosphere?

  * 3.

How does the magnetic field destabilise the outer solar atmosphere and thus
affect the interplanetary environment?

  * 4.

How do magnetic processes accelerate particles to high energies?

Answers to these questions will be relevant not only to solar research alone,
but will affect a broad range of current and upcoming topics in astrophysics.
The Sun is a template for other stars. This makes it a key to understanding
the host stars of other planets and how these host stars might affect the
formation and evolution of life on their planets. For the reliable detection
of Earth-sized planets around other stars and in particular for their
habitability, we have to understand stellar variability. The magnetic field is
also responsible for the UV emission from planet-hosting stars, which is
central for the chemistry in the planetary atmosphere, for instance. If the
magnetic field destabilises parts of the stellar atmosphere, which results in
the ejection of plasma and magnetic field into interplanetary space, this can
also strongly affect planets around the host star. Finally, high-energy
particles generated by magnetic and plasma processes in the stellar atmosphere
can have severe impacts on life. In the case of the the solar system, this
includes space technology.

The Solar and Heliospheric Observatory (SOHO) was launched in 1995
1995SoPh..162….1D . The intensive research in the two decades since then has
enabled us now to define the questions we outlined above with high precision.
Observational work together with progress in theoretical understanding and
numerical modelling shows clear paths to solving these questions in the coming
decades if the observational tools can be made adequately available.

In this paper we describe the key measurements that give direct access to the
magnetic fields in the solar chromosphere and upper atmosphere. These
measurements will have to exceed what is currently available. This will enable
us to address the overarching questions when we combine it with the
(simultaneous) measurements of the dynamic response of the plasma to changes
that are induced by the evolving magnetic field.

Figure 1: Hot plasma loops on the Sun outlining the magnetic field in an
active region. This multi-color image is a composite of AIA 171 Å (ca. 1 MK;
green), AIA 193 Å (ca. 1.5 MK; blue) and AIA 94 Å (ca. 7 MK; red). An image of
Earth to scale is overlaid at the bottom right corner. The image is processed
using a Multi-Scale Gaussian Normalization technique 2014SoPh..289.2945M .
Data courtesy of NASA/SDO and AIA science team.

##  2 Overarching science questions

The focus of this paper is on measuring the magnetic field in the outer solar
atmosphere, i.e. in the upper chromosphere, transition region, and corona.
This information is currently not directly available on a routine basis.
Extrapolations together with extreme UV imaging can give an instructive
overview of the large-scale structure of the magnetic field in the outer solar
atmosphere, where the relevant physical processes occur (see Fig. 1). Our
understanding of the solar atmosphere is drastically limited by such indirect
estimations of the magnetic field, however. We have to rely on the theory of
extrapolations of the magnetic field that is measured in the photosphere, i.e.
the visible surface of the Sun. These extrapolations have to apply several
assumptions, e.g. that the solar atmosphere is a vacuum or that the Lorentz
force is the only relevant force and that the inertia of the plasma is
completely negligible. Observations of the dynamic solar atmosphere clearly
show that assumptions like this are not appropriate. The actual measurement of
the changing magnetic configuration is a key part in solving the puzzle of how
the magnetic field interacts with the plasma, in particular when fast-changing
processes are followed that are driven by magnetic reconnection, for instance.

With direct measurements of the magnetic field throughout the solar
atmosphere, we will be able to locate sites of transient energy release
(through magnetic reconnection), analyse the formation and disruption of
current sheets where plasma is heated, study the transport of energy through
different modes of magnetohydrodynamic waves (or through energetic particles),
and investigate the helicity of erupting structures, all by unveiling how the
magnetic field connects the different parts of the atmosphere. These
measurements together will provide us with an understanding of solar magnetic
activity: how does the magnetic field govern the energetic radiation from the
Sun and how does it drive space weather effects? These two questions have
implications for Earth, and likewise for planets of other host stars.

The polarisation of spectral lines encodes the information on the magnetic
field of the outer solar atmosphere (i.e. the chromosphere and beyond). This
encoded information has not been accessible to current space instruments. Sub-
orbital rocket flights of about a few minutes each have provided the only
glimpse into this domain. Because the level of polarisation is generally low,
the required noise level has to be as low as a few times 10-4 in terms of the
intensity for some polarimetric measurements. In order to achieve this signal-
to-noise ratio at high spatial resolution, the required instrumentation has to
combine large aperture and high throughput. This is as yet unavailable in
space.

In the following we describe how the direct measurement of the magnetic field
in the outer solar atmosphere (from the upper chromosphere into the corona)
will provide the crucial information we need to answer the general four
questions we listed above. We first concentrate on the implications for solar
research and then address how this will contribute to a better understanding
in other fields of astrophysics.

###  2.1 Interaction of magnetic field and plasma

The interaction of magnetic field and plasma includes a diversity of processes
that are currently poorly understood. Of particular interest are the role of
the magnetic field in the coupling of the different layers of solar and
stellar atmospheres, and the conversion and transport of energy. The most
complex mixture of physics on the Sun is found in the chromosphere. In a
simple one-dimensional picture, this is the layer above the surface, where the
temperature starts to rise outwards. This layer is sandwiched between the
photosphere, where most photons originate, and the corona, where the
temperature reaches several million Kelvin.

The chromosphere is a highly complex region. The magnetic field energy there
is comparable to the internal energy of the gas. This causes an intense
turbulent interaction between the two, in particular when the velocities reach
the sound speed. To add to the complexity, the radiation processes and line
formation are far away from local thermodynamic equilibrium (LTE), and the
ionisation is only partial. A model that describes this requires an extended
Ohm’s law and the consideration of multi-fluid effects.

The hot part of the outer atmosphere, the corona, is magnetically rooted in
the chromosphere. To answer fundamental questions on the dynamics and
energisation of the corona, we have to understand how the magnetic field
couples the corona to the chromosphere. This is essential for describing the
internal magnetic state of coronal loops. They are the basic building blocks
of the corona. Understanding the magnetic structure of coronal features on the
Sun is a stepping stone to the unsolved problem of the heating of hot plasma
that is observed throughout the universe.

The large magnetic Reynolds numbers in the chromosphere and corona mean that
we can expect magnetic turbulence. The chromosphere and corona are
additionally filled with different wave modes that range from acoustic waves
to Alfvén waves, including all mixed forms. To unravel the magnetic effects on
the plasma, we have to decompose these wave modes into their respective parts
and relate them to the (slower) build-up of currents that are then dissipated
to energise the plasma. The key for this is a continuous knowledge of the
magnetic field throughout the atmosphere. Only then can we understand the
coupling and the transport of energy by the magnetic field.

Figure 2: Coupling from the photosphere to the corona. The right panel (b)
shows 10 6 K hot plasma loops in the corona in a small active region
(150′′$\times$150′′) seen by AIA/SDO. The left panel (a) shows the magnetic
field on the surface in the center part of the active region
(50′′$\times$50′′). Black and white are opposite magnetic polarities. Small
regions with opposite magnetic polarities are found at the footpoints of
coronal loops, as marked by circles. Based on 2017ApJS..229….4C .

New observations will have to provide reliable information on the magnetic
structure of the upper atmosphere that is not available today and will not be
available in the coming years with current instrumentation. We need direct
access to the magnetic field through remote-sensing observations to detect the
magnetic current sheets that cover a range of spatial and temporal scales
2003Natur.425..692S . In coronal loops as in chromospheric features, we see
fine structure down to the resolution limit of current instruments. Imaging
and spectroscopic observations indicate thin structures at scales down to 50
km 2017ApJS..229….1S .

The requirements on spatial resolution for magnetic structure measurements are
slightly more relaxed: the magnetic field starts to dominate the plasma in
terms of (internal) energy in the upper chromosphere (and beyond). Thus the
spatial variations of the magnetic field can be expected to be smaller than
those of the plasma in responding to the magnetic driving. To achieve magnetic
field measurements, the light needs to be decomposed into its polarisation
states. This increases the requirements on the noise level, i.e. the collected
number of photons. This means that a large aperture is also required for the
magnetic measurements.

###  2.2 Magnetic coupling in the atmosphere

To understand the magnetic activity of the Sun, we have to follow the magnetic
connections that channel the energy transport throughout the atmosphere. This
is a multi-scale problem because large-scale magnetic features, such as long
coronal loops or helmet streamers, are rooted in small magnetic patches in the
low atmosphere. Recent observations demonstrated the key role of small-scale
magnetic patches in the photosphere for large coronal structures
2017ApJS..229….4C , see Fig. 2. Even compact flaring loops show small-scale
flux cancellation at their foot points 2018A&A…615L…9C . Only by tracing and
quantifying the energy flux deep in the chromosphere can we build a physical
connection between the small-scale processes in the photosphere and the large-
scale coronal features. The prime requirement to achieve this is to measure
the magnetic field in all layers of the solar atmosphere in order to gain
insight into the magnetic coupling.

Here we describe with one example how we investigate the magnetic coupling
from the chromosphere to the large-scale corona. High-resolution observations
enable us to characterise the magnetic field close to the limb. Very stable
observing conditions such as are found on a space-based platform are crucial
for observations like this. For example, the modest 50 cm telescope on Hinode
was able measure the magnetic field up to heliocentric angles of about 80∘,
and the polar magnetic field could be characterised based on this
2008ApJ…688.1374T . With higher resolution and sufficient sensitivity, an
investigation even closer to the limb would be possible and the magnetic field
in the chromosphere could be measured. This could then be directly connected
to coronagraphic observations above the limb. When observations in the extreme
UV are added to this, structures can be followed continuously from the
chromosphere into the corona, i.e. from small to large scales. With this full
magnetic field information, magnetic disturbances such as Alfvénic
perturbations could be traced, and the energy flow from the chromosphere into
the corona could be followed.

Another prime target for the study of magnetic connectivity is the
destabilisation of the upper solar atmosphere (discussed in more detail in the
next subsection). Magnetic structures in the corona can become unstable in a
very short time (compared to their overall lifetime) and then erupt. The
actual triggers of this process are still elusive. Only a full
characterisation of the connectivity of the magnetic field before the onset of
the destabilisation can provide the necessary information for understanding
the magnetic configuration that later erupts. Here again the coupling of the
magnetic field across scales plays a significant role: at least in some
scenarios, small-scale processes cut the tethers of the magnetic field that
holds the magnetic structure down that later erupts 2001ApJ…552..833M .

###  2.3 Destabilising the outer solar atmosphere

During large disruptions of the upper solar atmosphere, huge amounts of
magnetic energy are converted into thermal energy and kinetic energy, and
accelerate energetic particles. The associated heating and acceleration
processes through magnetic reconnection are still poorly understood, and even
the change in magnetic structures in the course of an eruption is not well
constrained. Extrapolations of the magnetic field from the surface are
currently used to constrain the change in free energy of the magnetic field.
Before and during dynamic events, however, the assumptions that underlie these
extrapolations break down. It is therefore mandatory to actually measure the
coronal magnetic field before, during, and after the disruption to fully
characterise this process. This destabilisation is the origin of coronal mass
ejections (CMEs). Once initiated, CMEs can dominate the inner heliosphere, and
stellar CMEs are likely to be a major influence on exoplanetary atmospheres.

A CME expands when it lifts off. In this process, some CMEs reveal their
complex internal structure (e.g. Fig. 3). Our current information is based on
intensity images, therefore no direct information on the magnetic field is
available. Only direct measurements of the magnetic field will allow us to
distinguish between the very different physical mechanisms that have been
proposed for the initiation of CMEs 2011LRSP….8….1C . This knowledge is needed
not only to strongly improve the predictability of CMEs and their space
weather effects, but also to predict what the CMEs on other stars could look
like (e.g. 2018ApJ…862…93A, ; 2019NatAs.tmp..328A, ). Coronagraphic direct
measurements of the magnetic field in the corona will close this gap in our
knowledge.

Many erupting features show a high degree of magnetic twist and writhe.
Magnetic helicity quantifies how elementary magnetic flux tubes are wound
around each other in a defined volume. In a closed system, magnetic helicity
is almost conserved in resistive magnetohydrodynamics (MHD) on timescales
shorter than the global diffusion timescale Matthaeus1982 ; Berger1984 .
Magnetic helicity can be used to quantitatively link flux ropes that are
observed in situ in the solar wind to their sources in the solar atmosphere.
Magnetic helicity also constrains the dynamical evolution of the ejected
magnetic field in the solar wind (e.g. 2009JGRA..114.2109D, ). Determining the
magnetic helicity carried by a CME requires measuring the magnetic field and
is therefore fundamental to understanding the evolution of CMEs.

The magnetic field is reconfigured on large scales in the course of large-
scale disruptions. This magnetic reconfiguration requires that the connection
to the small-scale magnetic features in the lower atmosphere changes as well.
This is illustrated by the emergence and submergence of magnetic flux on the
solar surface and the tether-cutting mechanism for CME eruption. Information
on the magnetic field beyond what extrapolations can provide is required to
understand the physics of eruptions. Extrapolations of the magnetic field from
the surface level are currently used to investigate the change in free energy
of the magnetic field. However, as mentioned above, before and during dynamic
events the assumptions of these extrapolations break down, . and it is
mandatory to directly measure the coronal magnetic field. This underlines the
need for direct coronagraphic measurements of the magnetic field during
eruptions.

The most spectacular events on the Sun are flares and CMEs. They govern the
space weather. During such events, particles are accelerated to high energies
and can leave the Sun. If they hit Earth, they cause a wide range of effects,
including damage to satellites and harm to astronauts. With an understanding
of the magnetic processes before and during the initiation of flares and CMEs,
we will finally be able to understand the roots of space weather.

Figure 3: Erupting prominence on the Sun on 31. 8. 2012 at 19:49 UT. This
shows a composite of plasma at 10 5 K (red) and 10 6 K (yellow) erupting into
interplanetary space. The complex internal structure is either a remnant of
the precursor structure in the low corona or forms during the eruption. Direct
measurements of the magnetic field are essential to distinguish between these
and other scenarios. Image credit: NASA’s GSFC and SDO/AIA Team
(https://apod.nasa.gov/apod/ap180916.html)

###  2.4 High-energy processes in the atmosphere

Particles are accelerated to high energies during flares and CMEs. Energetic
processes are not limited to large scales, however. They essentially occur on
all scales, including those we cannot currently resolve. For example, it has
been proposed that particles are also accelerated during unresolved energy
release events (nanoflares), but we have only indirect evidence for this
2014Sci…346B.315T . These nanoflares are associated with magnetic
reconnection. Measuring the magnetic configuration and its change during such
events will greatly advance our understanding of the basic plasma physics
process of reconnection and particle acceleration.

Our diagnostics for reconnection in the upper solar atmosphere are currently
restricted to imaging the thermal response of the plasma that is associated
with the heating during such events, in particular through extreme-UV imaging
(e.g. 2014ApJ…787L..27S, ; 2018ApJ…868L..33L, ). The presence of current
sheets is often indirectly derived from thin threads that are visible in
extreme-UV images. For a few cases, however, observations have revealed
current sheets through direct measurements of the magnetic field. They were
all very low in the atmosphere 2003Natur.425..692S ; 2004A&A…414.1109L .

Measuring the change in the magnetic field in space and time around the
reconnection site is very important to understand the heating and particle
acceleration at a reconnection site. This alone gives access to the structure
of the current sheets that form during the event and to the location and
manner in which particles are accelerated. Imaging observations in the extreme
UV and X-rays can show the changing structure of the magnetic field (assuming
that the emission indeed outlines the magnetic field). We can quantify how
much magnetic energy is converted into other forms of energy only through
directly measuring the magnetic field because some of that energy is in forms
that are hard to detect (e.g. in the form of energetic particles, or in small
brightenings in the visible and IR wavelength ranges). Measuring the magnetic
field will therefore be essential to derive the energy that is available for
particle acceleration and for the generation of (hard) X-ray emission during
the flare events.

###  2.5 Relation to other science fields

The upper solar atmosphere is the source region of the radiation in the UV.
This radiation is of paramount importance for Earth’s atmosphere. It controls
the chemistry and heating in the stratosphere and in higher layers of the
atmosphere of our home planet, and thereby may significantly affect the long-
term climate evolution. The extreme-UV radiation from the corona is important
for the upper atmosphere of Earth, and the near-UV radiation affects the
stratosphere. The near-UV originates from the solar photosphere and
chromosphere. To date, the relative variability in the UV radiation and its
contribution to solar variability is not fully understood, although it is
clear that it is driven by magnetic field variations. When we understand why
the outer atmosphere becomes unstable, we can scientifically define the
ingredients of space weather, which through energetic particles and CMEs
impacts the terrestrial environment.

The science proposed here is also relevant for host stars of other planets.
Far more violent disruptions than on the Sun have been observed in the outer
atmospheres of other stars. For example, super-flares have been found on sun-
like stars (e.g. 2000ApJ…529.1026S, ; 2012Natur.485..478M, ). The energy
released by these flares exceeds the energy released by the largest flares on
our Sun by 1000 times. Stars that are more active than the Sun can produce
CMEs that then propagate into the astrosphere of the star (e.g.
2019NatAs.tmp..328A, ). It is clear that this will affect the exoplanets of
these stars in terms of their (magnetic) environment and possible
habitability.

Understanding the magnetic processes in the outer solar atmosphere will also
greatly enhance our understanding of accretion disc coronae and winds. We can
expect the same processes to operate in these magnetically dominated
environments as in the solar corona. As in many other cases, the Sun can serve
here as a template and laboratory for other astrophysical objects.

The science we propose will also contribute to basic space plasma physics
(e.g. current sheets, reconnection, and instabilities). By imaging the
magnetic field in the outer solar atmosphere, we can characterise the large-
and small-scale structure. This is otherwise only possible through in situ
measurements in planetary magnetospheres (and possibly the heliosphere) with
large swarms of probes. We can study the cross-scale coupling through one
single solar observatory as proposed here.

##  3 Measuring magnetic fields by remote-sensing methods

Almost all the information on the magnetic field is contained in the
polarisation profiles of solar spectral lines. In other words, it is contained
in the wavelength variation of the Stokes parameters $Q$ and $U$ (which
quantify the linear polarisation) and of the Stokes parameter $V$ (which
quantifies the circular polarisation). Together with the Stokes parameter $I$
(i.e. the intensity), these Stokes parameters fully characterise any beam of
electromagnetic radiation. In order to carry out quantitative investigations
of the magnetic fields in the solar atmosphere, we therefore require
telescopes that are equipped with instruments capable of measuring the four
Stokes parameters in suitable lines of the solar electromagnetic spectrum. The
relevant physical mechanisms that produce polarisation in solar spectral lines
are described next.

###  3.1 The Zeeman effect

In the presence of a magnetic field, the spectral lines split into various
components with specific polarisation properties that depend on the angle
between the line of sight and the magnetic field vector. While the circular
polarisation signal (caused by the longitudinal component of the magnetic
field) scales with the ratio ${\cal R}$ between the Zeeman splitting and the
Doppler width, the linear polarisation signal (caused by the transverse
component of the magnetic field) scales as ${\cal R}^{2}$. The Zeeman effect
is therefore more prominent in circular polarisation than in linear
polarisation. Moreover, because $\mathcal{R}$ increases with the spectral line
wavelength, the Zeeman effect is much more effective in the IR than in the UV.
This makes it a valuable tool for coronagraphic observations above the limb in
IR lines of highly ionised species, such as Fe xiii at 1074 nm
2000ApJ…541L..83L . The circular polarisation can also be measured in some UV
lines from the upper solar chromosphere. This has been demonstrated by the
CLASP-2 suborbital rocket experiment. With a telescope with an aperture of
only 27 cm, it could measure the circular polarisation produced by the Zeeman
effect in the Mg ii h & k resonance lines in a plage region.

###  3.2 Linear polarisation by scattering processes

The scattering of anisotropic radiation produces linear polarisation in a
multitude of solar spectral lines, without the need of any magnetic field.
This especially occurs in many of the spectral lines that originate in the
outer solar atmosphere, where the anisotropy of the radiation field coming
from the underlying solar disc is higher than in the photosphere. The physical
origin of this resonance-line polarisation lies in the fact that the radiative
transitions induced by the incident anisotropic radiation produces atomic
level polarisation, that is, population imbalances and quantum coherence among
the magnetic sublevels of degenerate atomic energy levels. This in turn
produces polarisation in the radiation that is re-emitted in the scattering
process.

###  3.3 The Hanle effect

The atomic level polarisation is induced by radiation. This polarisation is
modified through the magnetic field; this is called the Hanle effect.
Therefore, the Hanle effect also modifies the linear polarisation that is
produced by the scattering of anisotropic radiation. For the Hanle effect, the
degeneracy of the levels is lifted in the presence of a magnetic field, and
the radiation-induced atomic polarisation is modified. The characteristic
magnetic field dependence of the linear polarisation of the scattered spectral
line radiation that is caused thereby is suitable for exploring the outer
solar atmosphere. Importantly, the Hanle effect is sensitive even for magnetic
fields that are tangled at sub-resolution scales (e.g. 2004Natur.430..326T, ).

There is a critical magnetic field strength ($B_{H}$) for the onset of the
Hanle effect. This is independent of the plasma temperature and of the
wavelength of the considered spectral line. Typically, measurements through
the Hanle effect are sensitive in a range of $0.1\,B_{H}$ to $10\,B_{H}$ of
the critical value. For magnetic fields that are significantly above the
critical value $B\,{>}10\,B_{H}$, the line is saturated. Then the linear
polarisation of the emerging spectral line radiation is sensitive only to the
orientation of the magnetic field. The expected magnetic field in the source
region of the observation thus determines the choice of lines with different
critical strengths $B_{H}$.

Figure 4: Expected magnetic field strength $B$ in the outer solar atmosphere.
This represents the average drop of the magnetic field from the surface (at
one solar radius) out into the corona. Large spatial variations are expected.
Compiled from different sources (based on 2012ExA….33..271P, ).

The magnetic field on the Sun drops dramatically from the surface to the outer
atmosphere. The field at the surface reaches several 1000 G, in the
chromosphere we expect a few 100 G, and the field in the corona drops to 1 G
and below (see Fig. 4). The Ly-$\alpha$ line of H I at 121 nm is ideally
suited for diagnostics of the chromosphere on the disc and for coronagraphic
observations of the corona above the limb. Its critical Hanle value is
$B_{H}=53$ G. The Mg II line at 280 nm ($B_{H}=22$ G) is also well suited, but
it is only visible on the disc. The critical values of IR lines for
coronagraphic observations (e.g. Fe XIII at 1075 nm) are well below 1 G. This
means that they will be in saturation and can only provide the field
orientation. Extreme UV permitted lines for off-limb and on-disk observations
(e.g. Fe X at 17.4 nm) will only provide information on the field orientation
(apart from the electron density) because their critical magnetic field for
the onset of the Hanle effect is much larger than the magnetic strength
expected for the solar coronal plasma 2009ASPC..405..423M .

###  3.4 Magneto-optical effects in strong resonance lines

In strong resonance lines such as H I Ly-$\alpha$ and Mg ii h & k, the joint
action of quantum interference between the sub-levels pertaining to the upper
$J$ levels of these lines and the correlation effects between the incoming and
outgoing photons in the scattering events (partial frequency redistribution)
produce very strong $Q/I$ signals in the wings of these lines (see
2012ApJ…750L..11B, ; 2012ApJ…755L…2B, ).

Without the need of any magnetic field the value of $Q/I$ can be very large in
the wings of strong resonance lines. The magneto-optical terms of the Stokes-
vector transfer equation then introduce magnetic sensitivity in the wings of
$Q/I$ and $U/I$. This happens already for magnetic fields with strengths
similar to those needed for the onset of the Hanle effect. Such magneto-
optical effects are expected to produce measurable magnetic sensitivity in the
wings of the Mg ii h & k lines (2016ApJ…831L..15A, ; 2016ApJ…830L..24D, ) and
in the wings of the H I Ly-$\alpha$ line (2019ApJ…880…85A, ).

To summarise, the polarisation signals in UV and IR spectral lines are
sensitive to the presence of magnetic fields throughout the whole outer
atmosphere. The Hanle effect is sensitive to the (weak) magnetic fields
expected for the upper chromosphere and transition region because it operates
at the line centre where the opacity is high. The magneto-optical effects that
operate in the wings of strong resonance lines are sensitive to the presence
of similarly weak magnetic fields in the underlying chromospheric and
photospheric layers because the opacity in the line wings is lower. The
circular polarisation produced by the Zeeman effect in some UV lines (e.g. Mg
ii at 280 nm) is sensitive to the longitudinal component of the magnetic field
in the solar chromosphere. The linear polarisation produced by scattering in
UV lines has been successfully exploited to investigate the solar coronal
magnetic field (e.g. 2002A&A…390..691R, ; 2002A&A…396.1019R, ). From the upper
chromosphere and transition region into the corona, the two sub-orbital rocket
flights of CLASP obtained and exploited spectropolarimetric data in the
Ly-$\alpha$ line at 121 nm 2017ApJ…839L..10K ; 2018ApJ…866L..15T  and Mg II
near 280 nm. In permitted (electric dipole) UV lines and in forbidden
(magnetic dipole) IR lines, measurements of the polarisation produced by atoms
in the solar coronal plasma can probe the magnetism of solar coronal
structures, and the solar wind velocity (e.g. 2017SSRv..210..145C, ;
2017SSRv..210..183T, ).

When spectropolarimetric measurements in the UV are complemented by IR
observations, new discoveries in solar and stellar physics are facilitated:
through the Hanle and Zeeman effects, the He I triplet at 1083 nm is sensitive
to the magnetic field of plasma structures in the chromosphere and corona. UV
lines such as Ly-$\alpha$ at 121 nm and the resonance and subordinate lines of
Mg ii (all around 280 nm) are suitable for probing the upper chromosphere.

A space telescope that is equipped with instruments that are designed to
measure the four Stokes parameters in suitably chosen UV and IR spectral lines
will be able to achieve a true revolution in our empirical understanding of
solar magnetism.

##  4 Integral role of realistic atmospheric models

The polarisation measurements need to be inverted to derive the magnetic field
from observations. More than a century ago, magnetic fields on the Sun were
discovered through the Zeeman splitting of spectral lines in the strong
magnetic field of a sunspot 1908ApJ….28..315H . This was possible even without
analysing the polarisation state of the light. When the geometry of the
magnetic field or the thermal structure of the atmosphere is more complex, the
full information of the polarisation has to be taken into account to
reconstruct the full 3D vector of the magnetic field, i.e. its strength and
direction. Not only the Zeeman effect, but also the Hanle effect has to be
considered for the weaker magnetic fields in the outer atmosphere. This
requires an inversion of the observed polarisation data.

Several inversion codes are available for the chromosphere that include the
Zeeman effect 2000ApJ…530..977S ; 2019A&A…623A..74D . In the next few years,
they will be extended to also cover the Hanle effect, so that all available
types of data can then in principle be invertible. Initially, these inversions
will be made in 1D, but will include non-LTE effects (i.e. departures from
local thermodynamic equilibrium). Ultimately, 3D versions will be required,
and first steps in this direction have been taken. Inversion codes have been
developed and implemented that take into account the coupling of neighbouring
pixels in the observation 2012A&A…548A…5V ; 2013A&A…557A..24V . This coupling
is introduced by the point spread function of the instrument.

A very important role will be played by realistic models of the outer solar
atmosphere. Here a numerical simulation that includes all relevant physical
processes provides the evolution of the plasma and the magnetic field in a 3D
volume. A forward-modelling code is then used to calculate the emission,
including the state of polarisation, from the simulation results (see Fig. 5
for an example). The numerical simulations are currently mostly run by solving
the 3D MHD equations (with extensions). Examples are MURaM 2017ApJ…834…10R
and Bifrost 2016A&A…585A…4C , both including the radiative transfer problem,
or Pencil that allows to model a data-driven corona 2019A&A…624L..12W .
Several 3D non-LTE codes also exist for the forward modelling of the radiation
in spectral lines, e.g. Multi-3D 2009ASPC..415…87L  for the intensity and
PORTA 2013A&A…557A.143S  for all Stokes parameters. This shows that the basic
tools are available even now so that numerical models can be used to evaluate
and improve inversion techniques with which the magnetic field can be derived
from observations.

Numerical simulations of the outer solar atmosphere are computationally
demanding. They can be included in inversions of spectropolarimetric
observations within a few years, however, and first steps have already been
taken 2017ApJS..229…16R . For example, forward-modelling calculations today
provide an essential reference to identify and distinguish the impact of
various physical processes that affect scattering polarisation. This approach
is necessarily model dependent, but the availability of increasingly realistic
MHD simulations make it the most reliable approach to infer information about
the magnetism of the outer solar atmosphere.

Realistic atmospheric models allow us to investigate the parameter space of
possible polarisation signals and thus can show new paths for interpreting the
data. In the recent IRIS mission 2014SoPh..289.2733D , for instance, numerical
models have been an integral part of the data analysis. By exploring the
spectral line profiles that were found in the forward models, the profiles
could be classified and were used to derive physical quantities from features
in the Mg II h and k line profiles (e.g. 2013ApJ…778..143P, ). Future
realistic 3D models will play the same role for interpreting polarisation data
from the outer solar atmosphere. Models like this will in particular be
essential for understanding how the different spectral lines form in different
regions (heights) of the outer atmosphere and how the different lines can be
best combined for a reliable inversion of the magnetic field.

We proceed with a brief overview of models for the chromosphere and (large-
scale) corona. We also consider future developments.

Figure 5: Snapshot from a data-driven 3D MHD model of an active region. The
model uses the evolving observed photospheric magnetic field to drive the
evolution of the solar atmosphere from the photosphere all the way into the
corona. The left panel shows the vertical magnetic field in the photosphere
(in the range of $\pm$500 G) and the right panel the coronal emission as it
would be observed by the 171 Å channel of AIA showing ca. 106 K hot plasma
when looking from straight above, i.e. close to disk center. The panels show a
375$\times$300 Mm2 part of the computational domain. The model captures the
large-scale structure of the corona above the modelled active region (AR 12139
from 16. Aug. 2014) quite well. Based on 2019A&A…624L..12W .

###  4.1 Chromospheric models

Simulations of the solar chromosphere require challenging theory: the energy
densities of magnetic field, plasma, and waves are all of a similar magnitude,
which provides a wealth of dynamics. Radiation cannot be treated as optically
thin as in the case of the corona, nor can the atoms be assumed to be in local
thermodynamic equilibrium (LTE) as in the photosphere. The gas in the
chromosphere is dynamic and only partially ionised, so that additional effects
have to be taken into account, such as ambipolar diffusion and time-dependent
partial ionisation.

The past decade saw a very fast evolution of chromosphere modelling, and
different models can now account for a range of the required physics,
including non-equilibrium populations (2007A&A…473..625L, ; 2016ApJ…817..125G,
), non-LTE radiation transfer (2012A&A…539A..39C, ), two-fluid MHD
(2019A&A…627A..25P, ), and non-ideal MHD (2012ApJ…753..161M, ;
2018A&A…618A..87K, ). With further progress at this pace, we can expect to
have reasonably realistic 3D numerical experiments of the solar chromosphere
in another decade. In other words, the required models will be available when
they are needed to develop and evaluate improved inversions to retrieve the
chromospheric magnetic field.

###  4.2 Coronal models

Numerical models for the large-scale corona potentially involve fewer physical
processes than are required in the chromosphere. The coupling across scales
and the loss of collisional coupling between particles adds to the problem,
however. The former requires high spatial resolution or adaptive grids, the
latter means that kinetic models or particle-in-cell simulations are
necessary. These effects have been considered, but are still far from being
realistic in the sense of reproducing actual coronal structures. Still,
significant progress has been achieved, e.g. in modelling the dynamics of
flares 2019NatAs…3..160C .

Another complication in the large-scale corona is the integration along the
line of sight of the optically thin emission that prevents simple direct
inversions of the magnetic field (Kramar2006, ; Kramar2013, ). Recent forward
models show paths to interpreting coronagraphic measurements by minimising the
difference between synthesised coronal observables and real coronal data (e.g.
Dalmasse2019, ). In the same way as for the chromospheric models, we can
expect (global) coronal models to be ready within a decade to assist in the
inversion of the polarimetric measurements of the global corona.

###  4.3 Outlook

When realistic 3D models of the chromosphere and the corona become available,
the assimilation of data into the models will be a powerful tool to better
understand the structure of the outer solar atmosphere and its evolution. The
experience of data assimilation in weather forecasting shows the enormous
potential of this technique. Continuously assimilating the acquired data into
the model provides a way to iterate from the measured polarisation maps
towards a correct solution of the magnetic field structure and its evolution.
These are ensemble models, therefore the computations require two orders of
magnitude more computational power than current models. With more efficient
codes and the expected progress of computational resources in the next decade,
however, this will become feasible. This would then provide an advanced tool
for analysing the polarimetric measurements of the outer solar atmosphere.

##  5 Scientific requirements for measuring the magnetic field in the upper
solar atmosphere

###  5.1 Limitations in current approaches

Measurements of the magnetic field at the surface of the Sun (the photosphere)
are currently routinely performed at high spatial resolution in smaller
regions, and with moderate resolution when they cover the whole Sun. This is
achieved by remote-sensing observations, mainly through the Zeeman effect (see
Sect. 3). However, the magnetic field at only about 1000 km above the surface
dominates the gas in terms of energy, i.e. plasma-$\beta$ becomes smaller than
unity. To understand how the magnetic field governs solar activity above the
surface (in the chromosphere and corona), we require reliable and routine
measurements there as well.

To estimate the magnetic field in the outer solar atmosphere, we currently
mostly have to take recourse to extrapolations of the magnetic field based on
observations of the solar surface. While this has reached a considerable
degree of sophistication, these methods are not satisfactory because there are
limitations in principle (e.g. 2009ApJ…696.1780D, ). Also, it is not possible
to capture the temporal evolution of dynamic phenomena from the chromosphere
to the atmosphere at large with extrapolation methods that assume a static or
stationary situation. This prevents further progress in solar atmospheric
research because the magnetic field structures and drives the dynamics in the
solar atmosphere, from the chromosphere to the outer corona. Therefore we need
direct observations of the magnetic field not only in the photosphere, but
throughout the whole outer solar atmosphere.

With the instrumentation we have so far, attempts to measure the magnetic
field in the corona have been more a proof of concept than regular
observations. The first of such observations above the limb using a
coronagraphic technique in the IR had very low spatial resolution and required
very long exposure times 2000ApJ…541L..83L ; 2004ApJ…613L.177L . While the
field progressed, observations are still sparse and limited to a few sample
structures on the Sun. For example, a post-flare-loop system above the limb
has recently been observed in some detail in the IR 2019ApJ…874..126K  and in
radio wavelengths 2018ApJ…863…83G . This gave consistent results.

Observations of the magnetic field in the chromosphere have been obtained in a
more regular fashion, but are mostly limited to the diagnostics in the lines
of He I at 1083 nm and the triplet of Ca II around 854 nm. Observations in
these lines are limited in that they do not provide information on the upper
chromosphere, where the magnetic field energetically dominates the plasma.
Observations in the UV part of the spectrum are required to reach the upper
chromosphere and even higher layers.

Previous observations on sub-orbital rockets showed the potential of the
polarisation that is measured in the UV in Ly-$\alpha$ and Mg II for the
magnetic field measurements in the chromosphere (see Sect. 3). Polarisation
measurements have also been performed for C IV by UVSP on SMM from space
1982SoPh…81..231H ; 1983SoPh…84…13H  for the hotter layer of the transition
region to the corona. The short rocket observation in Ly-$\alpha$ and Mg II
only provided a glimpse of polarisation measurements in the UV, however, and
the existing measurements in C IV are not reliable 2001ASPC..248..553L .

Upcoming and planned space-based solar observatories will not provide
polarimetric information in the UV. They will therefore not provide
measurements of the magnetic field in the uppermost layers of the
chromosphere. We propose to close this observational gap in this paper.

###  5.2 Scientific requirements

To measure the magnetic field in the upper atmosphere, we distinguish (a)
measurements in front of the solar disc and (b) measurements above the limb.
Observations on the disc will give access to the small-scale structures in the
chromosphere that form the base of the outer atmosphere and thereby shape the
magnetic connection throughout the whole atmosphere (see Sect. 5.2.1). The
off-disc measurements will provide information on the large-scale structure of
the magnetic field, giving a view of the corona similar to what is seen during
a solar eclipse (see Sect. 5.2.2). Finally, the small-scale chromospheric
features have to be connected to the global corona, for which observations in
the extreme UV are crucial because they can also give access to coronal
structures when observations are made on the solar disc (see Sect. 5.2.3). To
describe the respective requirements, we restrict the discussion to one
example for each case. More than one process that constrains each requirement
in most cases. The scientific requirements for the respective observations are
summarised in Table 1.

Table 1: Overview of scientific requirements.

| chromospheric |  | extreme UV
---|---|---|---
| telescope | coronagraph | coronal imager
| (Sect. 5.2.1) | (Sect. 5.2.2) | (Sect. 5.2.3)
Spatial resolution | 0.1′′ | 2 – 10′′ (b) | 1.2′′
Temporal resolution | 1 s | 5 – 100 s (b) | 3 – 60 s (e)
Field of view | 300′′$\times$300′′ | 1.1 – 3.0 $R_{\odot}$ (c) | 0.8∘$\times$0.8∘
Spectral resolution or band width |  $\lambda/\Delta\lambda$: 30 000 |  $\Delta\lambda$: 5 nm (UV); 0.1 nm (IR) |  $\Delta\lambda$: 0.35 nm
Signal-to-noise ratio (a) | $3\times 10^{3}$ | $10^{2}$ | $10^{3}$
Key spectral lines/ranges | Mg II (280 nm) | VL (pB) (d) | Fe X (17.4 nm)
(small selection only) | C IV (155 nm) | Ly-$\alpha$ (121 nm) |
| H I Ly-$\alpha$ (121 nm) | Fe XIII (1075 nm) |
| Ca II IR (854 nm) | He I (1083 nm) |
| He I (1083 nm) |  |

Notes:  |  (a) Ratio of the signal in the line compared to the noise.
---|---
|  (b) Depending on observation mode: polarised brightness, intensity only, or
polarisation.
|  (c) Radial distance from disc centre, i.e. from 0.1 – 2.0 $R_{\odot}$ above
the limb.
|  (d) Visible light (polarised brightness), broad-band observation in the
visible.
|  (e) Faster cadence for imaging-only mode, slower cadence for polarimetric
observations.

####  5.2.1 Magnetic field in the chromosphere

The chromosphere is a highly structured and very dynamic part of the solar
atmosphere. Current 1m class ground-based and balloon-borne solar telescopes
show features down to scales smaller than 100 km. The Sunrise telescope, for
example, revealed fibrils (Fig. 6) with widths ranging from 100 to 270 km
2017ApJS..229….6G . These fibrils are generally thought to map the magnetic
field 2017ApJS..229…11J  and are heated when magnetic flux emerges
2018A&A…612A..28L . Current instruments do not allow us to directly measure
the magnetic field in these fibrils, and similar conclusions apply to other
key chromospheric features. This leads to the requirement for an angular
resolution of 0.1′′ for chromospheric magnetic measurements, which corresponds
to about 70 km. Only by achieving this resolution will we be able to reveal
the formation and evolution physics of these chromospheric structures.

The required temporal resolution is closely linked to the spatial resolution.
Essentially, the time resolution should be equivalent to the time it takes for
a perturbation to cross the resolution element. The relevant speed for
magnetic changes is the Alfvén velocity, which is of the order of 10 to 100
km/s in the chromosphere. Consequently, the observations have to allow for a
temporal resolution of about 1 s.

Because of the cross-scale coupling, the field of view of the chromospheric
observations has to encompass a whole active region on the Sun. This applies
to the observations of the chromosphere for its own sake and for the magnetic
connection through the atmospheric layers. For example, magnetic flux often
emerges and cancels on small scales 2017ApJS..229….4C , but it might still
govern the formation and evolution of hot structures in the core of an active
region 2018A&A…615L…9C . The required field of view is therefore
300′′$\times$300′′ to fully cover an active region. This corresponds to 3% of
the visible solar disc.

The spectral resolution for spectroscopic and spectropolarimetric observations
is set by the expected velocity (dispersion) seen in the spectral lines and by
the need to resolve the polarisation signals, which are often narrower than
the intensity profiles of the spectral lines. The expected velocities in the
chromosphere are of the order of 1 km/s and higher, as we know from existing
spectroscopic observations. A spectral resolution corresponding to 10 km/s is
sufficient to determine the shift of an optically thin line (through
centroiding). This corresponds to a spectral resolving power
$\lambda/\Delta\lambda$ of 30 000. To resolve features in optically thick
chromospheric lines, such as self-absorption in Mg II, an equivalent spectral
resolution is required, as we know from observations with IRIS
2014SoPh..289.2733D .

Figure 6: Fibrils seen in the solar chromosphere in Ca II K. The field of view
is only 34′′$\times$14′′ and thus tiny compared to the solar diameter of about
0.5${}^{\,\circ}$ (based on 2017ApJS..229…11J, ).

Line selection is a fundamental question for a spectropolarimetric instrument.
Chromospheric lines investigated from the ground for magnetic measurements are
mostly from Ca II and He I. The IR triplet of Ca II 854 nm has been used for
quiet Sun and active regions (e.g. 2019A&A…621A…1R, ), while no robust routine
observations have been possible in the H and K lines of Ca II so far. The He I
line at 1083 nm has been widely used for magnetic diagnostics (e.g.
2003Natur.425..692S, ), even though it is mostly limited to active regions.
The He I D3 line at 588 nm has also recently been evaluated during a flare
2019A&A…621A..35L . To interpret the observations, it is important to perform
multi-line inversions. This has been amply demonstrated for photospheric
observations 2019A&A…622A..36R . To apply such techniques to the chromosphere,
two of the most prominent and important lines must be added to the
observations set: the Ly-$\alpha$ line of H I at 121 nm and the Mg II h and k
lines near 280 nm. These two lines have proven their potential during rocket
flights of the CLASP instrument (see Sect. 3) and are well studied
theoretically. A line from the transition region into the corona, such as C IV
near 155 nm, would also add valuable information on the connection of the
chromosphere to the corona (e.g. 2013SoPh..288..531P, ). To maximise the
scientific return of the multi-line inversions, the observations must also
include visible and IR lines from the chromosphere, e.g. of Ca II, He I, and
visible lines from the photosphere. A gap-less coverage of the atmosphere is
possible only then. This is necessary to fully characterise the magnetic field
in the chromosphere.

Fluctuations of the polarization signal have to be measured with a
polarimetric signal-to-noise ratio of 3$\times$103 to exploit the Hanle and
magneto-optical effects in Ly-$\alpha$ and Mg ii. This is based on experience
with the CLASP experiment 2017ApJ…839L..10K  and consistent with theoretical
predictions (e.g. 2015ApJ…803…65S, ).

####  5.2.2 Global magnetic field in the corona

The structures in the global corona are dominated by the streamer structures,
coronal holes, cavities, and, if present, CMEs and their precursors. The main
factor in measuring the magnetic field in the global corona is the field of
view of the coronagraphic instrument. From the ground (except for rare
eclipses) this is rather limited because the light that is scattered in the
Earth’s atmosphere limits the distance from the Sun at which coronagraphic
observations can be carried out. For current ground-based coronagraphs this is
less than 0.5 solar radii ($R_{\odot}$) above the limb (COMP,
2008SoPh..247..411T, ). Most of the large-scale coronal features extend
farther out, however. A larger and more adequate field of view for a
coronagraph can only be achieved by a space-based instrument. The current
sheets at the top of the streamers typically start at below 1 to 2 $R_{\odot}$
above the limb. The initial acceleration of a CME is also essentially achieved
at these heights. The inner edge of the field of view should cover the low-
lying concentrated current-carrying systems from coronal cavities and active
regions. These are usually found within the first one or two pressure scale
heights, the latter being about one tenth of the solar radius (for a corona at
about 1 MK). Consequently, the field of view should cover 1.1 – 3 $R_{\odot}$
from disc centre.

Figure 7: Composite image of the Sun during the eclipse on 20 March 2015. The
inner part exhibits a quadrant of the solar disk showing the corona in the
extreme UV by AIA/SDO (multi-colour representation of AIA channels; blue/cyan:
211 Å, red: 171 Å; green: 193 Å). The outer part shows the corona as seen
during totality from the ground. The loops from the extreme UV image are seen
to extend into the outer corona. Bright radial structures might represent
current sheets created by magnetic field gradients. Image credit: N. Alzate.
For details on image processing see 2017ApJ…848…84A . AIA Data courtesy of
NASA/SDO and AIA science team. Eclipse image by Druckmüller, Habbal & The
Solar Wind Sherpas.

The requirements for spatial resolution are not as strict for the global
corona as they are for the chromospheric observations. The magnetic field
expands towards the outer corona, so that the spatial scales in the outer
parts are much larger than near the chromosphere. In the photosphere magnetic
concentrations with a diameter of a few 100 km have magnetic field strengths
of more than 1 kG 2010ApJ…723L.164L . Coronal loops with lengths of 100 Mm
have field strengths of still more than 5 to 10 G 2004ApJ…613L.177L . A 100 Mm
long semi-circular loop will reach only 30 Mm height, which is less than 0.05
$R_{\odot}$. In the field of view of the coronagraph we therefore expect no
more than 1 G to a few 10 G 2016NatPh..12..179J . Conservation of magnetic
flux implies that a photospheric flux tube with a diameter of 200 km would
then expand to a cross section of some 2 to 6 Mm, corresponding to up to 8′′.
A spatial resolution of about 10′′ might be sufficient to characterise the
magnetic field in these elementary flux tubes, but finer threads will be seen
in emission, even though the magnetic field structure is significantly
smoother. This is well known for structures in the lower atmosphere and is
found in models (e.g. 2013SoPh..288..531P, ). The spatial resolution to be
achieved in the intensity mapping should therefore be higher. Thin threads
seen in eclipse observations, for instance, show that a resolution of at least
2′′ is required. In addition, recent imaging observations have revealed
plasmoids of $\sim$2′′ that form and coalesce into larger plasmoids that
expand into a CME bubble 2019SciA….5.7004G . Investigating the dynamics of
these plasmoids using coronagraphic observations up to 3 $R_{\odot}$ will
provide inestimable information on the initial acceleration of CMEs. Combining
this, the coronagraphic observations have to provide an angular resolution of
2 to 10′′, depending on whether the observations are in intensity only, or if
they are used to measure the state of polarisation to derive the magnetic
field.

The cadence for the coronagraphic observations is governed by dynamic
phenomena. A CME can reach 1000 km/s or even more when it is accelerated from
the low corona to about 1 to 2 $R_{\odot}$ above the limb. Such a transient
can cross the field of view of the coronagraph in about 600 s. In order to
capture the acceleration phase, the observational cadence for the magnetic
field measurements should be at least 100 s. The intensity-only observations
should be acquired faster, so that we can follow the disturbances that cross
the resolution element. This means that the temporal resolution should be in
the range of 5 to 100 s, again depending on the observation mode.

To derive the magnetic field in coronagraphic observations, ground-based
observations have shown the high potential of IR lines such as Fe XIII near
1075 nm. He I at 1083 nm is also sensitive to the weak coronal magnetic field
2010ApJ…722.1411M . When the Hanle effect is used, UV lines have very high
potential, in particular Ly-$\alpha$. So far, they have been used successfully
with SOHO/UVCS (1995SoPh..162..313K, ), but without the polarisation
capability required to derive the coronal magnetic field. Density information
crucial for interpreting the extreme-UV data, which calls for the additional
capability of polarised brightness observations in the visible light, VL (pB).
A coronagraph should therefore cover a wide range of wavelengths from the
extreme UV to the IR.

The required spectral resolution (or bandwidth) of the instruments can be
estimated based on current instruments for coronagraphic observations in the
UV (METIS; Antonucci-etal:2019, ) and IR (COMP; 2008SoPh..247..411T, ). These
give an requirement for the bandwidth of the narrow-band imaging of 5 nm in
the UV and of 0.1 nm in the IR. A signal-to-noise ratio of 100 is required to
measure the coronal magnetic field in the UV 1992SPIE.1546..402F ;
1999SPIE.3764..147F  and IR.

####  5.2.3 Connecting local and global

Observations at medium resolution are required to understand the cross-scale
coupling between the small-scale features of the chromosphere to the large-
scale magnetic features. These observations also have to show the corona in
front of the solar disc in order to connect them to the on-disc chromospheric
observations. This can be achieved by imaging in the extreme UV. Because the
(black-body) radiation from the surface is negligible in the extreme UV, these
images will show the corona in front of the disc and above the limb. One
example would be on-disc observations that are performed near the limb. The
chromospheric observations (Sect. 5.2.1) would then show the roots of the
global coronal magnetic structure (Sect. 5.2.2), and an extreme-UV observation
would show the essential connection between the two (see Fig. 7).

Coronal observations in the extreme UV are routinely performed by AIA on SDO
2012SoPh..275…17L . SWAP on Proba 2 showed that imaging in the extreme UV can
also record the corona out to 2 $R_{\odot}$ 2013SoPh..286…43S . To ensure
sufficient overlap with the coronagraphic observations (Sect. 5.2.2), the
imaging in the extreme UV should cover the corona across the whole disc out to
1.5 $R_{\odot}$ (see Fig. 8). This corresponds to a field of view of
0.8∘$\times$0.8∘.

Figure 8: Sample image of the corona in the extreme UV as seen by SWAP/Proba 2
(inverse colour scale). The field of view is cropped to ca. 0.8∘$\times$0.8∘
(see Sect. 5.2.3). The inner box shows the coverage of AIA, and the dotted
lines in the corners mark a distance of 2 $R_{\odot}$ from disc centre (Image
credit: ROB; see instrument description in 2013SoPh..286…43S, ).

Coronal features seen in the extreme UV have a distribution of widths, with a
peak around 550 km and a tail to broader features 2017ApJ…840….4A . A spatial
resolution of 1′′ should therefore be achieved; this is slightly better than
that of AIA.

With the same arguments as above, the cadence of the observations should reach
3 s to follow changes in intensity. Polarimetric observations of the magnetic
field can have a lower cadence of 60 s because the magnetic field evolves
slower than the thermal properties of the corona. The temporal resolution
therefore must be in the range of 3 to 60 s.

A very good choice for the observations is the coronal line of Fe X at 17.4
nm. To isolate the line, the width of the band has to be 0.35 nm. The emission
from this ion shows high contrast in coronal structures, as is well know from
AIA and SWAP. Because the line lies in the saturated Hanle regime, it will
allow determining the direction of the magnetic field through an analysis of
the linear polarisation. Based on an earlier study, the required signal-to-
noise ration is $10^{3}$ 2012ExA….33..271P .

###  5.3 Instrumentation required to perform measurements of the magnetic
field in the upper atmosphere

The two quite distinct measurements requirements are to record the small-scale
magnetic fields that are observed in the chromosphere and the large-scale
magnetic field in the solar corona. They necessitate quite different
techniques: the former needs observations on the disc at high resolution, and
the latter coronagraphic observations by occulting the solar disc. These tasks
require two separate instruments. A third instrument is needed to connect the
measurements of these first two instruments. More details and a possible
mission scenario are discussed in Sect. 6.

1) UV-to-IR telescope with a large aperture. A UV-to-IR telescope with an
aperture of about 3 m is required to achieve the necessary signal-to-noise
ratios to derive the magnetic field in the solar chromosphere from the
polarisation measurements. The required spectral lines in the UV can be
recorded only in space, and only the stable space environment will allow the
high-performance observations required in the IR. Equally important, the high
spatial resolution over a large field of view is only possible from a space-
based platform that is not affected by the Earth’s atmosphere.

2) Extreme UV-to-IR coronagraph. A coronagraph is required to study the large-
scale magnetic field out to 3 $R_{\odot}$ from disc centre. The large field of
view can only be achieved from space, even for observations in the IR. UV
observations in Ly-$\alpha$ provide high sensitivity to the magnetic field by
use of the Hanle effect. An aperture of 40 cm is required to achieve the
necessary signal-to-noise ratio.

3) Extreme UV imaging polarimeter. An instrument is required to observe the
corona in front of the disc and above the limb to connect the observations of
the other two instruments. This requires an aperture of about 30 cm to achieve
the signal-to-noise ratio that is necessary to also derive the magnetic field
direction from polarimetric observations.

##  6 Mission scenario for measuring magnetic fields throughout the solar
atmosphere

One notable constraint for a possible mission scenario is the size of the
telescope for chromospheric observations. Our considerations in Sects. 6.1 and
6.4 will show that this should have an aperture of 1 to 3 m, which means that
this instrument would dominate the configuration of the space observatory.
Because of its size, it will have to be part of the spacecraft and thus be
under ESA responsibility. Post-focus instrumentation such as a
spectropolarimeter and an imager can then be considered as payload provided by
institutions throughout ESA member states. The other two telescopes, the
coronagraph and the EUV polarimetric imager (Sects. 6.2 and 6.3), can be
mounted on the sides of the main telescope. This ensures that the coronagraph
aperture has an unobstructed view over 2$\pi$ steradians to fulfil the
stringent stray-light requirements of this instrument.

We assume that a near-Earth orbit would be adequate for such a mission, even
though a position at L1 would provide a continuous coverage of the Sun and a
very stable environment. Observations from L4 or L5 would provide the highly
interesting possibility of conducting coordinated observations with Earth-
based facilities: viewing the Sun at the same time from two different angles
would enable stereoscopic observations. Determining the orbit that is best
suited for the mission will require a careful trade-off study based on the
available technology in data transmission, spacecraft pointing stability,
thermal environment control, and science goals.

In Sects. 6.1 to 6.3 we provide details of straw-man instruments (cf. Sect.
5.3). In Sect. 6.4 we discuss options for a possible M-class mission scenario.

Figure 9: Spectropolarimetric measurements with CLASP from its first sub-
orbital flight on 3 Sept. 2015. The background image shows the chromosphere of
the Sun, and the inset displays the slit-jaw filtergram acquired by CLASP in
the Ly-$\alpha$ line at 121 nm. Panels (a) to (e) show the spectrum along the
slit in Ly-$\alpha$ in total intensity (left) and in different orientations of
the linear polarization (image credit NAOJ, JAXA, NASA/MSFC, IAC, IAS; taken
from https://www.nao.ac.jp/en/news/science/2017/20170518-clasp.html; based on
2017ApJ…839L..10K, ).

###  6.1 Measuring the magnetic field in the chromosphere

The primary requirement for spectropolarimetric observations is the signal-to-
noise ratio at the spatial and temporal scales to be resolved. Following the
arguments presented in the previous sections, true advances in the study of
the magnetic field throughout the solar chromosphere will be obtained with
spectropolarimetric measurements in the key lines Mg h & k near 280 nm and
Ly-$\alpha$ at 121 nm at spatial scales of the order of 0.1′′ (about 70 km)
and temporal scales of the order 1 to10 s. Accurate measurements of the
magnetic field at these scales will be obtained with a signal-to-noise ratio
in the Stokes parameters of the order of $2\times 10^{3}$. Finally, another
important requirement is the ability to map the magnetic field structure over
areas that are comparable to typical large-scale magnetic structures, e.g.
active regions (about 300$\times$300′′). A spatial resolution of 0.1′′
requires a spatial sampling of 0.05′′ per pixel. Thus a field of view of
300$\times$300′′ requires a 6k$\times$6k sensor. This is only marginally
larger than the 4k$\times$4k sensors that are used by SDO and are expected to
be easily available in the next decade.

Our estimates for the chromospheric telescope are based on the performances of
current and near-future facilities that are designed to measure the solar
magnetic field at high resolution. The suborbital rocket flights of CLASP
(2017ApJ…839L..10K, ) in particular can be regarded as the true pathfinders
for this mission (see Fig. 9). CLASP included spectropolarimetric and imaging
capabilities (i.e. slit-jaw imagers) to analyse Ly-$\alpha$ and Mg II. The two
CLASP flights demonstrated that the required polarimetric accuracy at the 1′′
spatial and 1 s temporal resolution can be reached with an aperture of about
30 cm. When we scale this to the 0.1′′ spatial resolution required here, this
calls for an effective area that is 100 times larger. When we assume no
(significant) increase in throughput for the whole instrument, this would
require a 3 m class telescope. In the IR, e.g. for observing He I at 1083 nm,
the diffraction limit of such an instrument is about the required spatial
resolution of 0.1′′. At the wavelength of Ly-$\alpha$, the required resolution
of 0.1′′ is less stringent than the theoretical diffraction limit, so that the
design of the telescope will be challenging but possible within the envelope
of an L-class mission. Moreover, the required resolution of 0.1′′ can be
maintained over the required large field of view.

The science requirements for an instrument like this demand
spectropolarimetric observations at the Ly-$\alpha$ and the Mg II h & k lines,
but also in the visible and IR (see Table 1). Currently available Al-based
coatings with high reflectivity in the visible (also required for the thermal
control of the instrument) easily allow observing lines from the IR down to
the UV at about 110 nm. At the required resolving power of $\sim 3\times
10^{4}$ (over two pixels) at 120 nm, and with a 6k$\times$6k detector, the
Ly-$\alpha$ line can be observed simultaneously with several very important
lines such as the Si III and 120.6 nm and the N V lines at 123.8 and 124 nm.
The resolving power at the Mg II h & k doublet, on the other hand, would be of
the order of $6\times 10^{4}$.

A separate post-focus instrument would be required to cover the visible and IR
lines to be observed. Here, well-known concepts from existing and upcoming
ground-based facilities can be used to reach the required specification. We do
not discuss these further.

###  6.2 Measuring the magnetic field in the off-limb corona

The instrument for on-disc spectropolarimetry described above should be paired
with a coronagraph capable of observing the large-scale corona. Again, the
Ly-$\alpha$ line should be observed together with IR lines (see Table 1), now
in narrow-band polarimetric imaging. Broad-band measurements of visible-light
polarised brightness, called pB, are also essential for the coronagraph. They
will provide the coronal electron density, a basic ingredient for an analysis
based on which the coronagraphic spectropolarimetric observations are
interpreted.

The primary requirements on the instrument design are again the signal-to-
noise ratio in polarimetric measurements and the field of view. The latter
should have an inner edge as low as 1.1 $R_{\odot}$ to have a significant
overlap with the on-disc polarimetric imager (Sect. 6.3) and an outer edge out
to 3 $R_{\odot}$ to capture the large-scale corona that is not visible from
the ground. The spatial, temporal, and spectral resolution requirements are
less stringent than those for the chromospheric telescope (see Table 1). In
terms of coronagraphic performances, any residual stray light should be lower
than the disc brightness by a factor $10^{-9}$ in the visible and IR and
$10^{-7}$ in Ly-$\alpha$.

The baseline for such an instrument would be a dual-band coronagraph capable
of obtaining large field-of-view narrow-band polarimetric images in the UV
(Ly-$\alpha$) and in the visible and IR ranges. The set of visible and IR
lines to be considered for would include Fe XIV at 530.3 nm (“green line”), Fe
X at 637.6 nm (“red line”), Fe XI at 789.2 nm, and the Fe XIII doublet and He
I lines around 1080 nm, for instance.

An instrument such as this has a strong archetype in the Metis coronagraph
(Antonucci-etal:2019, ), which is now flying on Solar Orbiter. With respect to
Metis, the proposed instrument will have polarimetric capabilities in
Ly-$\alpha$ and in a selection of visible and IR lines, a field of view
extending down to 1.1 solar radii instead of 1.6, and higher spatial
resolution (especially at Ly-$\alpha$). Scaling the Metis instrument to the
requirements outlined here in Table 1 results in a coronagraph with an
aperture of about 40 cm.

###  6.3 Measuring the magnetic field in the on-disc corona

This instrument is mainly required to characterise the magnetic field in the
million Kelvin corona and to provide context and connection information for
the chromospheric telescope (Sect. 6.1) and the coronagraph (Sect. 6.2). This
is essentially an improved development of imagers that were used for SDO/AIA
or Proba 2/SWAP, for example, but now with the capability of recording the
polarisation signal.

The field of view and resolution requirements (Table 1) call for a
6k$\times$6k detector and a focal length of 4.4 m with 12 $\mu$m pixels. With
currently available 4k$\times$4k detectors, we can expect the required
detectors to become available in the coming years. A single on-axis parabolic
mirror would meet the resolution requirement, but over a limited field of
view, and would be overly bulky. Even though it adds one reflection, the
preferred option is therefore a Ritchey-Chretien telescope. The linear
polariser is a 45∘ folding mirror that is located before the detector.

The 45∘ polariser is located close to the detector (about 10 mm), and the
whole assembly is rotated to provide the necessary measurements of linear
polarisation. A single-mirror polarising system is required to maximise the
photon count in a given exposure time. This is achieved by a rotating focal
plane assembly, which implies that any connectors follow the movements of the
detector. A two-mirror polariser would not require a rotating focal plane
assembly, but would reduce the flux at the focal plane by a factor two.

To select the main target line of Fe X at 17.4 nm, multi-layer coatings can be
optimised for maximum throughput at 17.4 nm and maximum rejection of other
nearby emission lines, some of which are predicted to show zero or opposite
polarisation compared to Fe X. It is important to reject these lines because
they constitute stray light in the polarisation measurement and degrade the
measurement signal-to-noise ratio. Such coatings have already been developed
for EUI/Solar Orbiter. Using new techniques for the multi-layer mirror
coatings, we can reach a width of the transmitted band of only 0.35 nm, which
is twice as narrow as bands on current instruments.

###  6.4 Mission scenario in case of an M-class mission opportunity

What we outlined so far in this paper calls for an L-class mission. We
consider that the chromospheric telescope with an aperture of up to 3 m is the
main cost driver in our mission profile. When we downsize our mission scenario
for an M-class mission, the 3 m telescope is therefore the first item to
consider. Other mission options can also open up when a smaller main telescope
is considered.

The effect of reducing the size of the chromospheric telescope from a 3 m
class to a 1 m class instrument means cuts in the science return. In addition
to a reduced spatial resolution, the main downgrade would be the sensitivity
to the magnetic field, and here in particular in the UV, where the aperture is
essential for reaching the required signal-to-noise ratio. The smaller
telescope will reduce the spatial resolution by more than what is suggested by
the reduction of the aperture (to collect the same number of photons per
resolution element), or the sensitivity to the magnetic field will be reduced,
or both. A trade-off study will have to show possible paths when the aperture
needs to be reduced and what effects these would have for the science goals.

Even a 1 m class telescope would outperform any currently operational or
planned solar space observatory. We can still expect significant advances. The
scientific return would be downgraded from a full characterisation of the
magnetic field in the outer atmosphere, however. We would mostly be able to
investigate only bright structures on the Sun, while the faint features are
often essential to understanding the global large-scale connection. This would
affect all of the science goals outlined in Sect. 2 because the magnetic field
is present not only in the bright features, but is volume filling. It would
mean that we could only investigate a fraction of the outer solar atmosphere.

Downgrading the chromospheric telescope from a 3 m to a 1 m class instrument
might also open new opportunities. For example, one could place a smaller
observatory at either L4 or L5 instead of in Earth orbit (or at L1). In
combination with a facility either in Earth orbit or on the ground, this would
give the possibility for stereoscopic observations.

##  7 Technological challenges

###  7.1 Main telescope: Thermal control and optical performance over the
field of view

Relatively large telescopes that cover the visible to UV range have previously
been flown into space or near-space (stratospheric) environments, for example
the 0.5 m telescope on the Hinode telescope 2008SoPh..249..197S  or the
Sunrise balloon-borne 1 m telescope 2011SoPh..268….1B . These two instruments
have proven that it is possible to build a UV-to-visible light solar telescope
that manages the solar flux while keeping performances up to the tight
requirements (e.g. the Sunrise telescope is diffraction limited in the
visible). In the case of the 3 m telescope discussed here, a Gregory design
with a heat rejection field stop will also have to be used. The telescope can
be seen as a scaled-up version of the telescope on board Sunrise. Because of
the size, it will be challenging but possible, especially when we consider
that it does not have to be diffraction limited.

The requirement of maintaining the image quality over the large
(300′′$\times$300′′) field of view needs some consideration, however. A simple
Gregory design with two powered mirrors cannot maintain the required 0.1′′
resolution (two pixels) over the full field of view. A corrective optical
element or a curved focal plane assembly will have to be considered.

###  7.2 Data transmission, handling, and storage

The number of large-format cameras will be significant: at least three for the
chromospheric telescope, two for the coronagraph, and one for the EUV
polarimetric imager. They have to operate simultaneously with a cadence of
down to 1 s, so that even with some loss-less data compression, this leads to
a data rate of the order of 1 Gbit/s (see Fig. 10). A data rate like this is
certainly challenging and will require the use of high-capacity transmission
systems such as the laser communication systems currently under development
and testing. It is likely that such systems are available in one or two
decades.

Large on-board storage units are required that have a capacity to temporarily
save 50 TB or more. This is the equivalent of continuously observing for 8
hours. Such a storage unit requires an improvement in capacity by a factor of
10 compared to PHI/Solar Orbiter, for instance, which might be feasible in a
decade from now.

The continuous stream of data at a high rate requires re-thinking the
techniques for processing and archiving data. While the storage of this amount
of data might not pose a significant challenge in a decade, the processing
will need significant improvements. Here machine-learning techniques to be
developed in the framework of big-data strategies will help with the efficient
and automated standard processing steps, and may even provide a (preliminary)
data selection.

Figure 10: Multi-wavelength observation of the solar photosphere and
chromosphere. From left to right the maps recorded by the Sunrise balloon
telescope show: UV at 300 nm, Ca II K at 397 nm, Fe I at 525 nm and the
photospheric magnetic field (red and blue are opposite magnetic polarities).
The field of view is very small, ca. 13′′$\times$38′′. We propose to acquire
data in multiple lines in a much larger field of view with a continuous high
data rate. This would produce more than 50 TB within 8 hours. Image based on
2010ApJ…723L.127S .

##  8 Relation to other space- and ground-based observations

Synoptic observations of the whole solar disc and the corona (at moderate
resolution) are important to place high-resolution data acquisition as
proposed in this paper into context. Synoptic observations are currently
available through a range of space- and ground-based facilities, for example
by SOHO/LASCO, SDO, Proba2, STEREO, Hinode, or GONG+. Because of the relevance
for operational space weather services, it can be assumed that (similar)
global monitoring observations will remain continuously present in the future
(GOES, SWFO, ESA Lagrange). This will guarantee that the high-resolution data
we propose in this paper for the time frame of 2035 to 2050 will be
supplemented by proper context information.

The near future will see a significant shift in ground-based solar telescopes
from the 1 m class to the 4 m class. Current high-resolution ground-based
solar observations (GREGOR, SST, GST, NVST, ONSET) are complemented by unique
high-resolution data from occasional balloon flights (Sunrise), all with
apertures from 1 m to 1.5 m. The Daniel K. Inoue Solar Telescope (DKIST) with
4 m aperture has just seen first light. DKIST observes the solar disc, and has
a coronagraphic mode for the innermost part of the corona. Using lines such as
Ca II near 394 nm and 854 nm and He I near 1083 nm, it will explore the
magnetic field in the low chromosphere through on-disc measurements.
Observations in Fe XIII at 1075 nm above the limb will give access to the
magnetic field in the very low corona, at only a few 100′′ (less than 0.5
$R_{\odot}$) above the limb. A telescope with comparable specifications is
proposed by the European solar community (European Solar Telescope, EST), for
which first light is scheduled for the mid- to end-2020s.

The 3 m class telescope we propose here for a space-based platform will
provide a great leap in scientific exploitation compared to the upcoming 4 m
class ground-based telescopes. The wavelength range can be extended farther
into the UV, which is not accessible from the ground. This is indispensable to
obtain access to lines such as Ly-$\alpha$ at 121 nm or Mg II near 280 nm and
thus measure the magnetic field in the uppermost parts of the chromosphere. A
complete coverage and a holistic view of the whole outer solar atmosphere
becomes available only then. The high-resolution field of view of ground-based
observations will always be limited by seeing effects that are introduced by
the Earth’s atmosphere. With adaptive optics systems, the corrected high-
resolution region is roughly 10′′ across, multi-conjugate adoptive optics,
might extend this to some 50′′. Only a seeing-free space-based platform can
provide the required large field of view of 300′′ across at constant high
resolution, however. Furthermore, only a space platform can provide stable
observing conditions to follow structures over hours and to minimise the
cross-talk between the different polarisation states.

Coronagraphic measurements from the ground are marred by the inevitable stray
light in the Earth’s atmosphere. Among other effects, this limits the coverage
of the field of view to a maximum of 0.5 solar radii (optimistic estimate)
above the limb for DKIST. While DKIST can observe the coronal magnetic field
at a high spatial resolution of about 0.1′′, it will not be able to
investigate the large-scale magnetic field. To reach significantly farther
out, we have to enter space.

The next important step for the solar community in space is provided by the
Solar Orbiter mission that was launched in February 2020. This mission will
address many of the fundamental questions in solar physics, in particular
those concerning the connection from the Sun to the heliosphere. However, it
will not directly measure the magnetic field in the outer solar atmosphere.
The science questions outlined in this paper in Sect. 2 will remain largely
open after Solar Orbiter. EUVST, a Japan-led high-resolution extreme-UV
spectrometer, is planned to be launched in the late 2020s. This will also lack
the capability of investigating polarisation and thus the magnetic field in
the outer solar atmosphere.

In this paper we suggest to measure the magnetic field to determine what
drives the dynamics in the outer solar atmosphere. The full science return can
only be achieved by an L-class mission. With a downgrade to an M-class mission
(see Sect. 6.4), other scenarios with a broader scope might become possible.
One option that could be instigated would be an L-class mission in the context
of Voyage2050 that would combine our suggestion (downgraded to M-class) with
one or more missions in the fields of solar, heliospheric, magnetospheric, and
ionospheric physics as described in other papers in this volume. This would
provide a Grand European Heliospheric Observatory and ensure scientific
advances in the coming decades in a broad scientific context.

##  9 Conclusions

The Sun is the star closest to Earth. It is the only star for which we can
resolve details on its surface and in its atmosphere. The outer solar
atmosphere from the cool chromosphere to the hot corona is permeated by a
magnetic field that energetically dominates the gas. The magnetic field
controls the level of solar activity. It thus modulates the radiative output
of the Sun throughout the activity cycle, largely governs the emission from
the UV to X-ray radiation, ejects particles and fields from the corona, and
drives space weather effects. Through these magnetic activity effects, the Sun
directly impacts the Earth and human life. Likewise, the magnetic activity of
other stars will have an impact on the planets orbiting these host stars, and
it will govern the habitability on these planets.

Although we can observationally characterise the magnetic field on the solar
surface (the photosphere) reasonably well, we fail to do so for the higher
layers. In the overlying chromosphere and in the corona that stretches
essentially into interplanetary space, our information on the magnetic field
is mainly indirect. This state of knowledge is highly unsatisfactory because
the magnetic field energetically dominates the plasma in this outer solar
atmosphere and thus largely controls the phenomena that are observed there.
Only by knowing the magnetic field and its evolution can we unlock the source
of heating of the gas to millions of degrees, understand the shape and
brightness of the corona, learn about magnetic reconnection and its effects
such as flares and the associated energetic particles and radiation, and
unravel the initiation of large-scale ejections of parts of the solar
atmosphere.

The lack of direct measurements of the magnetic field in the outer solar
atmosphere is a major hindrance to our understanding of the physics of the
outer solar atmosphere. If we could remedy this, we would be able to explain a
very wide variety of phenomena. In essence, we are blind to the main driver of
solar activity in the critical layers of the solar atmosphere.

By directly measuring the magnetic field in the outer atmosphere of the Sun,
we will be able to address four paramount long-standing questions of solar
physics:

  * 1.

How does the magnetic field couple the different layers of the atmosphere, and
how does it transport energy?

  * 2.

How does the magnetic field structure, drive and interact with the plasma in
the chromosphere and upper atmosphere?

  * 3.

How does the magnetic field destabilise the outer solar atmosphere and thus
affect the interplanetary environment?

  * 4.

How do magnetic processes accelerate particles to high energies?

To address these science questions, we have to perform new ground-breaking
observations with a suite of space-based solar telescopes that far exceed
current capabilities in terms of spatial resolution, light-gathering power,
and polarimetric performance. This requires instruments for different parts of
the outer solar atmosphere with sufficiently large apertures.

  * a.

Large-aperture UV-to-IR telescope. Depending on the mission scenario (M or L),
this telescope of the 1-3 m class is aimed mainly to measure the magnetic
field in the chromosphere by combining high spatial resolution and high
sensitivity.

  * b.

Extreme-UV-to-IR coronagraph. A coronagraph that is designed to measure the
large-scale magnetic field in the corona. The required aperture is about 40
cm.

  * c.

Extreme-UV imaging polarimeter. A 30 cm telescope that combines high
throughput in the extreme UV with polarimetry to connect the magnetic
measurements of the other two instruments.

All three instruments will perform novel measurements of the magnetic field in
the outer atmosphere that currently cannot be achieved. This solar observatory
could be placed in a near-Earth orbit to maximise the data downlink, or at L4
or L5 to provide stereoscopic observations of the Sun in combination with
Earth-based observatories.

This mission to measure the magnetic field will unlock the driver of the
dynamics in the outer solar atmosphere. Through this it will greatly advance
our understanding of the Sun and the heliosphere.

###### Acknowledgements.

E.A.B. and L.B. gratefully acknowledge financial support from the Swiss
National Science Foundation (SNSF) through Grant 200021_175997 S.P.
acknowledges the funding by CNES through the MEDOC data and operations center,
and the funding by ESA through the Virtual Space Weather Modelling Centre -
Part III. J.T.B. acknowledges the funding received from the European Research
Council (ERC) under the European Union?s Horizon 2020 research and innovative
programme (Advanced Grant agreement No. 742265).

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