# Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature

Daniele Telloni, Vincenzo Andretta, Ester Antonucci, Alessandro Bemporad, Giuseppe Capuano, Silvano Fineschi, Silvio Giordano, Shadia Habbal, Denise Perrone, Rui Pinto, et al.

► To cite this version:

Daniele Telloni, Vincenzo Andretta, Ester Antonucci, Alessandro Bemporad, Giuseppe Capuano, et al.: Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature. The Astrophysical Journal Letters, 2021, 920 (1), pp.L14. 10.3847/2041-8213/ac282f. insu-03440357

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# Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature

Daniele Telloni¹, Vincenzo Andretta², Ester Antonucci¹, Alessandro Bemporad¹, Giuseppe E. Capuano³,⁴,
Silvano Fineschi¹, Silvio Giordano¹, Shadia Habbal⁵, Denise Perrone⁶, Rui F. Pinto⁷,⁸, Luca Sorriso-Valvo⁹,¹⁰,
Daniele Spadaro³, Roberto Susino¹, Lloyd D. Woodham¹¹, Gary P. Zank¹²,¹³, Marco Romoli¹⁴, Stuart D. Bale¹⁵,¹⁶,
Justin C. Kasper¹⁷,¹⁸, Frédéric Auchère¹⁹, Roberto Bruno²⁰, Gerardo Capobianco¹, Anthony W. Case²¹,
Chiara Casini²²,²³, Marta Casti²⁴, Paolo Chioetto²², Alain J. Corso²², Vania Da Deppo²², Yara De Leo⁴,²⁵,
Thierry Dudok de Wit²⁶, Federica Frassati¹, Fabio Frassetto²², Keith Goetz²⁷, Salvo L. Guglielmino³,
Peter R. Harvey¹⁵, Petr Heinzel²⁸, Giovanna Jerse²⁹, Kelly E. Korreck²¹, Federico Landini¹, Davin Larson¹⁵,
Alessandro Liberatore¹, Roberto Livi¹⁵, Robert J. MacDowall³⁰, Enrico Magli³¹, David M. Malaspina³²,³³,
Giuseppe Massone¹, Mauro Messerotti²⁹,³⁴, John D. Moses³⁵, Giampiero Naletto³⁶, Gianalfredo Nicolini¹,
Giuseppe Nisticò³⁷, Olga Panasenco³⁸, Maurizio Pancrazzi¹, Maria G. Pelizzo³⁹, Marc Pulupa¹⁵, Fabio Reale⁴⁰,⁴¹,
Paolo Romano³, Clementina Sasso², Udo Schühle²⁵, Marco Stangalini⁶, Michael L. Stevens²¹, Leonard Strachan⁴²,
Thomas Straus², Luca Teriaca²⁵, Michela Uslenghi⁴³, Marco Velli⁴⁴, Daniel Verscharen⁴⁵,⁴⁶, Cosimo A. Volpicelli¹,
Phyllis Whittlesey¹⁵, Luca Zangrilli¹, Gaetano Zimbardo³⁷, and Paola Zuppella²²

¹ National Institute for Astrophysics, Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy; daniele.telloni@inaf.it

² National Institute for Astrophysics, Astronomical Observatory of Capodimonte, Salita Moiariello 16, I-80131 Napoli, Italy

³ National Institute for Astrophysics, Astrophysical Observatory of Catania, Via Santa Sofia 78, I-95123 Catania, Italy

⁴ University of Catania, Department of Physics and Astronomy, Via Santa Sofia 64, I-95123 Catania, Italy

⁵ Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, USA

⁶ Italian Space Agency, Via del Politecnico snc, I-00133 Roma, Italy

⁷ Département d'Astrophysique, Astrophysique Instrumentation Modélisation, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Institut de Recherche sur les lois Fondamentales de l'Univers, Centre National de la Recherche Scientifique, Institut National des Sciences de l'Univers, Université Paris-Saclay, Université de Paris, Orme des Merisiers Bât 709, F-91191 Gif-sur-Yvette, France

⁸ Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, Université fe Paul Sabatier, Midi-Pyrénées Observatory, Centre National de la Recherche Scientifique, 9 Avenue du Colonel Roche, F-31028 Toulouse, France

⁹ Swedish Institute of Space Physics, Ångström Laboratory, Lägerhyddsvägen 1, SE-751 21 Uppsala, Sweden

¹⁰ National Research Council, Institute for the Science and Technology of Plasmas, Via Amendola 122/D, I-70126 Bari, Italy

¹¹ Department of Physics, Imperial College London, London SW7 2AZ, UK

¹² Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35805, USA

¹³ Department of Space Science, University of Alabama in Huntsville, Huntsville, AL 35805, USA

¹⁴ University of Florence, Department of Physics and Astronomy, Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy

¹⁵ Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA

¹⁶ Physics Department, University of California, Berkeley, CA 94720, USA

¹⁷ BWX Technologies, Inc., Washington, DC 20002, USA

¹⁸ Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA

¹⁹ Université Paris-Saclay, Centre National de la Recherche Scientifique, Institut d'Astrophysique Spatiale, Rue Jean-Dominique Cassini, F-91440 Bures-sur-Yvette, France

²⁰ National Institute for Astrophysics, Institute for Space Astrophysics and Planetology, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy

²¹ Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA

²² National Research Council, Institute for Photonics and Nanotechnologies, Via Trasea 7, I-35131 Padova, Italy

²³ Centre of Studies and Activities for Space “Giuseppe Colombo”, Via Venezia 15, I-35131 Padova, Italy

²⁴ The Catholic University of America at the National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, MD 20771, USA

²⁵ Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany

²⁶ Laboratoire de Physique et de Chimie de l'Environnement et de l'Espace, Center National de la Recherche Scientifique, 3A Avenue de la Recherche Scientifique, F-45071 Orléans, France

²⁷ School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

²⁸ Czech Academy of Sciences, Astronomical Institute, Fríčova 298, CZ-25165 Ondřejov, Czech Republic

²⁹ National Institute for Astrophysics, Astronomical Observatory of Trieste, Località Basovizza 302, I-34149 Trieste, Italy

³⁰ National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, MD 20771, USA

³¹ Politecnico of Turin, Department of Electronics and Telecommunications, Corso Duca degli Abruzzi 24, I-90129 Torino, Italy

³² Astrophysical and Planetary Sciences Department, University of Colorado, Boulder, CO 80309, USA

³³ Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA

³⁴ University of Trieste, Department of Physics, Via Alfonso Valerio 2, I-34127 Trieste, Italy

³⁵ National Aeronautics and Space Administration, Headquarters, Washington, DC 20546, USA

³⁶ University of Padua, Department of Physics and Astronomy, Via Francesco Marzolo 8, I-35131 Padova, Italy

³⁷ University of Calabria, Department of Physics, Ponte Pietro Bucci Cubo 31C, I-87036 Rende, Italy

³⁸ Advanced Heliophysics, Pasadena, CA 91106, USA

³⁹ National Research Council, Institute of Electronics, Information Engineering and Telecommunications, Via Gradenigo 6/B, I-35131 Padova, Italy

⁴⁰ University of Palermo, Department of Physics and Chemistry—Emilio Segrè, Piazza del Parlamento 1, I-90134 Palermo, Italy

⁴¹ National Institute for Astrophysics, Astronomical Observatory of Palermo, Piazza del Parlamento 1, I-90134 Palermo, Italy

⁴² Naval Research Laboratory, Space Science Division, Washington, DC 20375, USA

⁴³ National Institute for Astrophysics, Institute of Space Astrophysics and Cosmic Physics of Milan, Via Alfonso Corti 12, I-20133 Milano, Italy

⁴⁴ Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095, USA

⁴⁵ Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking RH5 6NT, UK

⁴⁶ Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH 03824, USA
Received 2021 August 15; revised 2021 September 15; accepted 2021 September 17; published 2021 October 7
Abstract

This Letter addresses the first Solar Orbiter (SO)-Parker Solar Probe (PSP) quadrature, occurring on 2021 January 18 to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in the corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic field and the bulk kinetic energy flux density can be empirically inferred along the coronal current sheet with an unprecedented accuracy, allowing in particular estimation of the Alfvén radius at 8.7 solar radii during the time of this event. This is thus the very first study of the same solar wind plasma as it expands from the sub-Alfvénic solar corona to just above the Alfvén surface.

*Unified Astronomy Thesaurus concepts: Magnetohydrodynamics (1964); Space plasmas (1544); Interplanetary turbulence (830); Solar corona (1483); Heliosphere (711); Solar wind (1534)*

1. Introduction

Remote sensing observations are essential to study the global
magnetic configuration of the solar corona and to explore the
acceleration regions of the solar wind (Antonucci et al. 2020a).
However, complications in integrating along the line of sight
(LOS; e.g., Dolei et al. 2018) over an extended region of the
corona (an optically thin plasma; e.g., Bradshaw & Ray-
mond 2013) and the low cadence measurements of corona-
graphs make it difficult to investigate in detail local coronal
heating, identify high-frequency waves of different kinds, or
study turbulent properties of the coronal plasma as a
magnetohydrodynamic fluid. On the other hand, in situ
measurements provide direct physical parameters of the plasma
at a single point in space and time, enabling the examination of
the local mechanisms that control, e.g., energy dissipation in
the solar wind (Bruno & Carbone 2013; Verscharen et al.
2019). However, single-spacecraft in situ measurements alone
cannot provide topological information about the magnetic
field, and thus a three-dimensional view of the plasma
surrounding the spacecraft. Therefore, the combination of
remote sensing observations and in situ measurements provides
an unequaled opportunity to connect solar wind source regions
to the local properties of plasma and electromagnetic fields.
This link works best for in situ measurements close to the Sun,
where solar plasma is not yet fully reprocessed by stream-
stream interactions.

There are several possible orbital configurations between
two or more spacecraft relative to the Sun that allow the study
of the connection of the plasma observed in situ to its solar
source. One interesting case is provided by “quadratures,” i.e.,
when the angular separation of two spacecraft with the Sun as
reference point is 90°. Important examples of this kind of
quadrature are given by the SOlar and Heliospheric Observa-
tory (SOHO; Domingo et al. 1995)–Sun–Ulysses (Wenzel et al.
1992) campaigns, when the same plasma remotely observed
with SOHO was sampled in situ when it left the coronal source
in the direction of Ulysses (Suess et al. 2000; Suess &
Poletto 2001; Poletto et al. 2002). The comparison of plasma
properties in the corona and heliosphere was made possible
thanks to the combined use of the Large Angle Spectroscopic
CORonagraph (LASCO; Brueckner et al. 1995) to understand
the overall coronal configuration at the time of quadratures, and
the UltraViolet Coronographic Spectrometer (UVCS; Kohl
et al. 1995) to derive its physical characteristics, on SOHO, and
the Solar Wind Ion Composition Spectrometer (SWICS;
Gloeckler et al. 1992) to provide interplanetary data, on

Ulysses. Multiple quadratures (twice a year) during the SOHO–
Ulysses era allowed the study of solar wind parameters, such as
density, speed and temperature, and their evolution from the
Sun to the heliosphere. Other quantities, such as ion
abundances or the ionization state, which instead remain
almost unchanged during solar wind expansion, have been used
to conclusively link a plasma stream measured in situ with the
coronal source as identified in coronagraphic images (Bem-
porad et al. 2003).

The launch of Parker Solar Probe (PSP; Fox et al. 2016) in 2018 August and Solar Orbiter (SO; Müller et al. 2020) in 2020 February, offers an exciting new era to explore the connection between the Sun and the heliosphere. On the one hand, PSP will be the first spacecraft to fly into the extended solar corona, a yet unexplored environment with in situ experiments. On the other hand, SO is the first spacecraft to carry both remote sensing and in situ instruments at distances as close as 0.28 au. It will leave the ecliptic plane, allowing for the first time observation of the solar poles, the regions where the fast solar wind originates (during solar minimum) and where magnetic fields cyclically reverse (Zouganelis et al. 2020). The importance of this new era for solar physics also lies in the synergy between these two missions (Velli et al. 2020), which will allow the tracing of the magnetic connectivity of transient outflows and the continuous solar wind to their solar sources. Particular attention has been paid to radial alignments between the two probes. Indeed, the first PSP–SO line-up occurred in 2020 September, allowing the radial evolution of solar wind turbulence between 0.1 and 1 au to be studied, i.e., from a highly Alfvénic and less developed turbulence state near the Sun to a fully developed and intermittent turbulence state close to the Earth (Telloni et al. 2021).

As far as it concerns quadrature configurations between the
two spacecraft, with SO remotely observing the source region
of the solar wind that is measured in situ with PSP, the first
SO–Sun–PSP quadrature occurred on 2021 January 18. At that
time, when traveling along its orbit very close to the Sun, PSP
crossed the very inner heliosphere at a heliocentric distance just
above 20 solar radii (R), while the coronagraph Metis
(Antonucci et al. 2020b) on SO was observing the solar
atmosphere in an annular field of view (FOV) extending from
3.5 to 6.3 R above the solar limb. It is thus the first time that
an expanding coronal plasma, observed remotely with Metis, is
almost immediately measured as it propagates outward with a
suite of in situ instruments.

This Letter presents joint SO–PSP observations that describe
the evolution of the pristine solar wind, not yet reprocessed by
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Top panel: cartoon showing how the same plasma volume observed remotely with SO/Metis can be measured locally with PSP during their quadrature. Bottom panels: SO (blue) and PSP (red) positions relative to the Sun (yellow star), in side (a) and top (b) views of the ecliptic plane in the HGI coordinate system, at the times (reported in the legends) of the observation of the same solar wind stream. The corresponding heliocentric distances (r), and heliographic latitudes (φ) and longitudes (λ) are also reported. The spacecraft trajectories from 2021 January 14–21, and their longitudinal separation of 90° in the XY plane are shown as color-coded solid and black dotted lines, respectively.</figcaption></figure>

nonlinear interactions, from the corona into the very inner heliosphere, aiming to link the local properties of the plasma stream measured in situ with PSP with the coronal source from where it originated imaged by the SO/Metis coronagraph.

**2. Analysis and Results**

The SO-PSP orbital configuration offers the opportunity to track the same plasma volume as it expands from the extended corona to the inner heliosphere. Indeed, thanks to the continuous expansion of the solar corona, the two probes will at some point be located such that the plasma crossed by PSP, which is moving outward at a speed around 100–200 km s⁻¹ on the solar equatorial plane, is the same plasma observed with Metis just a few hours earlier at a distance of 3.5–6.3 R⊙. From the cartoon of Figure 1 (top panel), this condition requires that during Metis observations, PSP is not yet on the instantaneous plane of the sky (POS) of the coronagraph, so that PSP and the Metis-observed volume of plasma reach the same location at the same time.

On the basis of the spacecraft's ephemerides and (as shown below) of the solar wind speed at both coronal and heliospheric heights, this particular condition occurred when Metis was observing the solar corona on 2021 January 17 at 16:30 UT ($t_0$

in the cartoon of Figure 1). At that time PSP was about 30° behind the instantaneous POS of Metis and it took ~16.2 hr to travel that longitudinal separation, thus reaching the Metis POS on 2021 January 18 at 08:44 UT ($t_2$ in the cartoon of Figure 1). This occurred when PSP was approaching perihelion at 0.1 au from the Sun and at a latitude of 3°8 below the ecliptic plane (i.e., 93°8 counterclockwise from the North Pole). As shown below (based on the expansion velocity inferred from Metis observations), the plasma observed (at $t_0$) with Metis at a distance of 3.5–6.3 R⊙ took 16.3 ± 1.1 hr to travel the distance from PSP thus encountering it on its way outward. The corresponding SO and PSP locations are shown along their orbits in the XZ and XY planes of the HelioGraphic Inertial (HGI) coordinate frame of Figures 1(a) and (b), respectively.

A time interval of about 2.5 hr centered on $t_2$, comparable to the coronal plasma transit time through the Metis FOV (according to the speed of the outflowing plasma shown below) and resulting in a slight off-quadrature of ±2° longitude relative to the Metis POS, is thus identified in PSP data as corresponding to the same plasma volume observed remotely with Metis 16.3 hr earlier. Some relevant parameters during this time period are displayed between the vertical dotted lines in Figure 2, which overall spans a time interval of 3.5 days.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** PSP solar wind parameters over the 3.5 day window centered on the ~2.5 hr long selected time interval (delimited by vertical dotted lines) around $t_2$: solar wind radial speed $V_R$ and Alfvén speed $V_A$ (a), magnetic field vector **B** (b), angles $\theta_{RB}$ and $\theta_{VB}$ of **B** with the radial and velocity directions (c), proton number density $n_p$ (d), temperature $T_p$ (e), temperature anisotropy $T_{\perp,p}/T_{\parallel,p}$ (f), and parallel plasma beta $\beta_{\parallel}$ (g), and radial distance $r$ (h). The average values reported within each panel refer to the identified period.</figcaption></figure>

Specifically, magnetic field and plasma measurements were acquired with the fluxgate magnetometer of the FIELDS suite (Bale et al. 2016) and with the SPAN-Ai top-hat electrostatic analyzer of the Solar Wind Electrons Alphas & Protons suite (SWEAP; Kasper et al. 2016), respectively, and then merged at 1 minute resolution. As described by Woodham et al. (2021), the core proton velocity distributions have been fitted to a bi-Maxwellian function to obtain plasma moments (i.e., proton density, velocity, and temperature).

The solar wind radial speed $V_R$ and the Alfvén speed $V_A$ are displayed in Figure 2(a), showing that the plasma flow, despite being slow, is largely super-Alfvénic. Several spikes indicate bursts of accelerated wind. The magnetic field **B**, in the inertial

Radial Tangential Normal (RTN) frame, and its angles with the radial ($\theta_{RB}$) and solar wind ($\theta_{VB}$) directions are shown in Figures 2(b) and (c), respectively. While the large-scale time profile of the magnetic field radial component is attributed to the expected $1/r^2$ scaling, with $r$ the radial distance displayed in Figure 2(h), two sharp magnetic field ~180° rotations clearly indicate crossings of the heliospheric current sheet (HCS), so that during the interval under study the magnetic field is directed sunward. Several sharp rotations are present, coinciding with wind accelerations, although these do not reverse the field direction. In particular, there are no switch-backs (Bale et al. 2019) during the selected interval. The very small difference between $\theta_{RB}$ and $\theta_{VB}$ indicates that the solar
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Metis images of the pB (a) and UV H I Lyα (b) emission of the solar corona observed on 2021 January 17 at 16:30 UT ($t_0$) within the 3.5–6.3 R⊙ FOV. Data corresponding to the 93°8 ± 2°5 coronal sector in the PSP direction (delimited by dotted lines) are shown as black dots in panels (c) and (f) for pB and UV, respectively, where green triangles denote averaged values along the radial profile (corresponding standard deviation error bars are smaller than symbols size). A van de Hulst (1950) fit (red line), used to infer electron density, is applied to pB averages in panel (c). NRGF-processed pB and UV images in the angle sector ranging from 60° to 120° (indicated by dashed lines) are displayed in panels (b) and (e), respectively, to enhance coronal structures near the region under study.</figcaption></figure>

wind velocity is nearly radial, thus supporting the assumption of a radially expanding coronal plasma underlying the ballistic assumption used in this work. Finally, Figures 2(d)—(g) show the proton density $n_p$, temperature $T_p$, temperature anisotropy $T_{\perp,p}/T_{\parallel,p}$, and parallel plasma beta $\beta_{\parallel} = v_{th,\parallel}^2/V_A^2$ ($v_{th,\parallel}$ is the proton parallel thermal speed, where the suffix p has been dropped for simplicity), all of which are relatively smooth during the selected interval (between the vertical dotted lines).

The temperature anisotropy $T_{\perp,p}/T_{\parallel,p} = 1.72$ observed at PSP suggests a preferential plasma heating perpendicular to the magnetic field (presumably through dissipation of low-frequency magnetohydrodynamic turbulence; see Zank et al. 2021, for a comprehensive review of theoretical turbulence models and their convergence with PSP and SO observations). At the observed parallel plasma beta $\beta_{\parallel} = 0.66$ (i.e., the plasma is magnetically dominated), such an anisotropy is above the theoretical threshold for proton cyclotron instability (see, e.g., Hellinger et al. 2006; Telloni et al. 2019), which is therefore at work generating ion-cyclotron waves, as confirmed by wind-owed Fourier transforms of PSP magnetometer data in the 3–8 Hz range (not shown).

The plasma stream detected with PSP originated from the equatorial region of the east limb solar corona imaged by Metis<fnref n="47" /> on 2021 January 17 at 16:30 UT simultaneously in polarized brightness (pB) and in H I Lyα ultraviolet (UV) light (Figures 3(a) and (d), respectively). This displays a typical solar minimum configuration with enhanced emission in the equatorial plane.

Two structures can be identified within the region of enhanced emission in both pB and UV. They are better distinguished by applying a normalizing-radial-graded filter

(NRGF; Morgan et al. 2006) to both images in an angle sector (delimited by dashed lines) ±30° wide centered on the equator (Figures 3(b) and (e), respectively). The double equatorial structure is easily interpreted in light of the Wilcox Solar Observatory synoptic charts of the coronal magnetic field at the source surface.<fnref n="48" /> In the Metis POS the coronal current sheet was intersecting the equator. However, at about ±30° in longitude from it were two small sheet warps, with maximum latitude extension to about ±10°, that might explain the double equatorial structure around the equator. This interpretation is also supported by the double HCS crossing experienced by PSP during its approach to the Sun (approximately on 2021 January 17 at 13:30 UT and on 2021 January 19 at 21:00 UT; see Figure 2(c)).

The solar wind plasma crossing PSP came from the coronal sector ±2.5° wide centered at 93°8, which is the latitude reached by PSP on the POS of Metis during the observation time (Figure 1(a)). This sector is delimited by dotted lines in Figures 3(a), (b), (d), and (e). Black dots in Figures 3(c) and (f) refer to pB and UV data in the selected coronal region, while green triangles denote the averaged values in steps of 0.1 R⊙, from 3.5 to 6.3 R⊙. The pB and UV radial profiles are then used to infer the electron density $n_e$ and the radial outflow velocity $V_R$ of the coronal plasma that is later impinging on the PSP in situ instruments.

Specifically, the electron density is derived by applying the inversion technique developed by van de Hulst (1950) and based on fitting pB data with a polynomial function (red line in Figure 3(c)). These values are reported in Figure 4(a) (black diamonds) along with a polynomial fit (red line) extrapolated to the PSP location: the very good agreement with the PSP

<footnote n="47">⁴⁷ The images were processed and calibrated according to the procedures adopted in Romoli et al. (2021).</footnote>

<footnote n="48">⁴⁸ http://wso.stanford.edu/synoptic/WSO-S.2240.gif</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Radial evolution of electron density $n_e$ (a), radial component of the magnetic field $B_R$ (b), radial coronal outflow $V_R$ and Alfvén speed $V_A$ (c), and bulk kinetic energy flux density of the solar wind $F_w$ (d), at coronal (black signs) and PSP (green sign, pointed by an arrow) heights. Diamonds denote direct Metis/PSP observations, while triangles mark extrapolated values based on conservation laws and PSP data as described in the text. Red solid or dashed curves denote corresponding fit and/or extrapolated empirical functions. The vertical dashed line and the blue solid curve in (c) indicate the inferred Alfvén radius $r_A = 8.7 \pm 1.2 R_⊙$ (compared with the result by Verscharen et al. 2021, black full circle) and the Parker model for an isothermal corona with $T = 1.2 \times 10^6$ K, respectively. As shown in the legend, empirical profiles previously reported in the literature are shown in (b) and (d) for comparison. Uncertainties of the derived quantities are drawn as error bars.</figcaption></figure>

measurement (green diamond: $n_{e,\text{PSP}} = n_{p,\text{PSP}}/0.95$, assuming a fully ionized plasma with 2.5% helium, according to Moses et al. 2020) corroborates the fact that the same element of plasma is indeed followed from the coronal region, where it is undergoing acceleration during its outward propagation, to the PSP position in the very inner heliosphere. The radial component of the coronal wind velocity on the POS is obtained by the Doppler dimming technique applied to a 3D solar coronal modeled on the basis of the so-inferred electron density and the measured UV H I Lyα intensity (the reader is referred to Antonucci et al. 2020b; Romoli et al. 2021, for an exhaustive review on how to infer outflow velocities from UV radiative lines observed in the expanding corona and for the Metis first light observations of the coronal solar wind, respectively), under the following assumptions: (i) a hydrogen temperature $T_p = 1.6 \times 10^6$ K (Antonucci et al. 2005); (ii) a helium abundance of 2.5% (Moses et al. 2020); (iii) a temperature anisotropy $T_{\perp,p}/T_{\parallel,p} = 1.72$ as constrained by PSP observations; (iv) the electron temperature derived by Gibson et al. (1999); (v) the chromospheric H I Lyα profile given by Auchère (2005), scaled to the irradiance on 2021 January 17 ($5.42 \times 10^{15}$ photons cm$^2$ s$^{-1}$ sr$^{-1}$), as provided by the LASP Interactive Solar Irradiance Data Center.<fnref n="49" /> The resulting coronal $V_R$ values are displayed as black diamonds in Figure 4(c), where they are compared with the Parker outflow solution for an isothermal solar corona with $T = 1.2 \times 10^6$ K (Parker 1958, blue solid line).

The coronal solar wind velocity undergoes a rapid increase with heliocentric distance, from ~80 to ~150 km s⁻¹, in the range from 3.5 to 4.5 $R_⊙$. Above this height, the acceleration

slows down and a velocity of ~180 km s⁻¹ is reached at 6.3 $R_⊙$. Some residual acceleration persists up to the PSP location, where a solar wind speed of 247 km s⁻¹ is measured locally (green diamond). Despite the overall good agreement with the purely hydrodynamic Parker model, in order to estimate as accurately as possible the transit time of the plasma volume from the Metis FOV ($r_1 = 3.5 R_⊙$) to the PSP location ($r_2 = 0.1$ au = $21.4 R_⊙$), Metis and PSP results were fitted to a parametric curve (solid red line: sum of a log-normal distribution and logarithmic quadratic function), which has no interpretative ambition, but aims only at defining an analytical profile. The transit time results in $t = \frac{1}{r_2-r_1} \int_{r_1}^{r_2} V(r)dr = 16.3 \pm 1.1$ hr, thus confirming, as mentioned above, that PSP was measuring the same plasma observed with Metis during its propagation across the coronal region.

The simultaneous Metis and PSP observation of the same solar wind plasma is a noticeable step forward allowing the estimation of the coronal magnetic field beyond a few solar radii (not directly measurable in the corona nowadays). This is achieved by applying the conservation of mass and magnetic flux (assuming flux-freezing) to Metis measurements of density and velocity (black diamonds in Figures 4(a) and (c)) and using the plasma and magnetic field data obtained at PSP, according to, e.g., Wang (1995). The so-extrapolated coronal magnetic field along the plasma flow $B_R$, in the equatorial region close to the coronal current sheet, is displayed in Figure 4(b) (black triangles): it varies from ~10⁴ to ~2×10³ nT from 3.5 to 6.3 $R_⊙$. These values are somewhat lower than those previously reported in the literature (Dulk & McLean 1978; Pätzold et al. 1987; Vršnak et al. 2004; Gopalswamy & Yashiro 2011;

<footnote n="49">⁴⁹ https://lasp.colorado.edu/lisird/data/composite lyman alpha/</footnote>
Poomvises et al. 2012; Mancuso & Garzelli 2013; shown in Figure 4(b) with different colors and line styles) based solely on remote sensing observations (and thus suffering from LOS integration effects) and/or in situ measurements very far from the Sun (thus not allowing a clear connection to the coronal source regions). In the present case, however, the accuracy of the values inferred for the coronal magnetic field is much higher due to the proximity of PSP, whose local measurements of the same plasma observed with Metis act as a constraint for extrapolations into the extended corona. Similarly, but considering $n_e$ and $V_R$ fits, an empirical function for $B_R$ (red line) can be extrapolated using the aforementioned conservation laws and PSP data.

Given the estimate of the coronal magnetic field, it is then also possible to extrapolate the Alfvén speed $V_A$ and, in turn, the Alfvén radius $r_A$ along the coronal current sheet, as done for $B_R$. Similarly, the solar wind bulk kinetic energy flux density $F_w$ can be obtained considering the conservation of total energy along the stream line (see, e.g., Wang 1995 for details). The corresponding empirical trends are also deduced. The extrapolated values for $V_A$ and $F_w$ are shown as black triangles in Figures 4(c) and (d), respectively. Specifically, $F_w$ varies from $\sim 2 \times 10^3$ to $\sim 4 \times 10^2$ erg cm$^{-2}$ s$^{-1}$ from 3.5 to 6.3 $R_⊙$ and is in fair agreement with the empirical profile deduced by Verscharen et al. (2021) on the basis of a two-fluid magnetohydrodynamics framework and Ulysses observations, when neglecting enthalpy, magnetic stresses, and nonradial components of the solar wind flow velocity (blue solid line in Figure 4(d)). Additionally, taking advantage of the $V_A$ empirical function (red dashed curve in Figure 4(c), deduced in the same way as that relative to $B_R$), the Alfvén radius $r_A$ can be estimated to be $8.7 \pm 1.2$ $R_⊙$ (in agreement, within uncertainties, with the value of $9.5 \pm 0.2$ $R_⊙$ found by Verscharen et al. 2021). This result is extremely interesting since, during the upcoming SO-PSP quadrature on 2022 June 1, PSP will skim the Metis FOV that will extend from 5.6 to 11.9 $R_⊙$, thus likely allowing for the very first time the study of the transition of the coronal plasma from a sub-Alfvénic to a super-Alfvénic regime. Interestingly, the initial increase of $B_R$ (and, in turn, $V_A$ and $F_w$) up to about 3.8 $R_⊙$ might depend on residual convergence of the magnetic field lines along the coronal current sheet before starting to diverge (see discussion in, e.g., Schatten et al. 1969; Pinto & Rouillard 2017).

It is worth noting that the above estimates have been inferred assuming a helium abundance of 2.5% (Moses et al. 2020). This value can be considered a lower limit (in fact, it refers to a particularly weak solar minimum). For the sake of completeness, it is therefore of interest to report how much the estimates of outflow velocity, magnetic field, kinetic energy flux, and Alfvén point vary assuming an upper limit of helium abundance of, say, 10%. The velocity and kinetic energy flux would be reduced on average by 5.7%, while the average reduction in the magnetic field and Alfvén speed would be 17.6% and 11.8%, respectively. Finally, the Alfvén radius would approach the Sun by 0.5 $R_⊙$, i.e., it would be 8.2 $R_⊙$.

This is the first time that crucial quantities such as the radial magnetic field in the outer corona, the Alfvén radius, and the bulk kinetic energy flux density of the solar wind have been extrapolated in the wind acceleration region with such an accuracy due to the opportunity offered by the first SO-PSP quadrature. Moreover, it is worth noting that, as PSP approaches the solar corona more and more closely and finally

enters it (crossing the Alfvén surface), the accuracy in deriving such quantities will further improve, providing a powerful tool to characterize, thanks to Metis observations, the corona in its expansion.

Solar Orbiter is a space mission of international collaboration between ESA and NASA, operated by ESA. D.T. was partially supported by the Italian Space Agency (ASI) under contract 2018-30-HH.0. L.S.V. was funded by the Swedish Contingency Agency, grant 2016-2102, and by SNSA, grant 86/20. L. D.W. is supported by the STFC consolidated grant ST/S000364/1. G.P.Z. acknowledges the partial support of a NASA PSP contract SV4-84017, an NSF EPSCoR RII-Track-1 Cooperative Agreement OIA-1655280, and a NASA IMAP grant through SUB000313/80GSFC19C0027. O.P. was supported by the NASA grant 80NSSC 20K1829. L.S. was supported by a grant from the NASA Heliophysics Technology and Instrument Development for Science Program, NNH15ZDA001N-HTIDS, and also by the basic Research Funds of the Office of Naval Research. D.V. is supported by STFC Ernest Rutherford Fellowship ST/P003826/1 and STFC Consolidated Grant ST/S000240/1. The Metis program is supported by ASI under contracts to the National Institute for Astrophysics and industrial partners. Metis was built with hardware contributions from Germany (Bundesministerium für Wirtschaft und Energie through the Deutsches Zentrum für Luft- und Raumfahrt e.V.), the Czech Republic (PRODEX) and ESA. The FIELDS and SWEAP teams acknowledge support from NASA contract NNN06AA01C. PSP data were downloaded from the NASA's Space Physics Data Facility (https://pdf.gsfc.nasa.gov). D.T. wishes to thank Masaru Nakanotani for his help in sketching the cartoon of Figure 1.

## ORCID iDs

Daniele Telloni https://orcid.org/0000-0002-6710-8142
Vincenzo Andretta https://orcid.org/0000-0003-1962-9741
Ester Antonucci https://orcid.org/0000-0003-4155-6542
Alessandro Bemporad https://orcid.org/0000-0001-5796-5653
Giuseppe E. Capuano https://orcid.org/0000-0002-8430-8218
Silvano Fineschi https://orcid.org/0000-0002-2789-816X
Silvio Giordano https://orcid.org/0000-0002-3468-8566
Shadia Habbal https://orcid.org/0000-0003-4089-9316
Denise Perrone https://orcid.org/0000-0003-1059-4853
Rui F. Pinto https://orcid.org/0000-0001-8247-7168
Luca Sorriso-Valvo https://orcid.org/0000-0002-5981-7758
Daniele Spadaro https://orcid.org/0000-0003-3517-8688
Roberto Susino https://orcid.org/0000-0002-1017-7163
Lloyd D. Woodham https://orcid.org/0000-0003-2845-4250
Gary P. Zank https://orcid.org/0000-0002-4642-6192
Marco Romoli https://orcid.org/0000-0001-9921-1198
Stuart D. Bale https://orcid.org/0000-0002-1989-3596
Justin C. Kasper https://orcid.org/0000-0002-7077-930X
Frédéric Auchère https://orcid.org/0000-0003-0972-7022
Roberto Bruno https://orcid.org/0000-0002-2152-0115
Gerardo Capobianco https://orcid.org/0000-0003-0520-2528
Anthony W. Case https://orcid.org/0000-0002-3520-4041
Chiara Casini https://orcid.org/0000-0001-8783-0047
Marta Casti https://orcid.org/0000-0002-9716-3820
Paolo Chioetto https://orcid.org/0000-0002-3379-2142

Alain J. Corso https://orcid.org/0000-0003-0378-9249

Vania Da Deppo https://orcid.org/0000-0001-6273-8738

Yara De Leo https://orcid.org/0000-0003-2426-2112

Thierry Dudok de Wit https://orcid.org/0000-0002-4401-0943

Federica Frassati https://orcid.org/0000-0001-9014-614X

Fabio Frassetto https://orcid.org/0000-0001-5528-1995

Keith Goetz https://orcid.org/0000-0003-0420-3633

Salvo L. Guglielmino https://orcid.org/0000-0002-1837-2262

Peter R. Harvey https://orcid.org/0000-0002-6938-0166

Petr Heinzel https://orcid.org/0000-0002-5778-2600

Giovanna Jerse https://orcid.org/0000-0002-0764-7929

Kelly E. Korreck https://orcid.org/0000-0001-6095-2490

Federico Landini https://orcid.org/0000-0001-8244-9749

Davin Larson https://orcid.org/0000-0001-5030-6030

Alessandro Liberatore https://orcid.org/0000-0002-0016-7594

Roberto Livi https://orcid.org/0000-0002-0396-0547

Robert J. MacDowall https://orcid.org/0000-0003-3112-4201

Enrico Magli https://orcid.org/0000-0002-0901-0251

David M. Malaspina https://orcid.org/0000-0003-1191-1558

Giuseppe Massone https://orcid.org/0000-0002-2656-1557

Mauro Messerotti https://orcid.org/0000-0002-5422-1963

John D. Moses https://orcid.org/0000-0001-9670-2063

Giampiero Naletto https://orcid.org/0000-0003-2007-3138

Gianalfredo Nicolini https://orcid.org/0000-0002-9459-3841

Giuseppe Nisticò https://orcid.org/0000-0003-2566-2820

Olga Panasenco https://orcid.org/0000-0002-4440-7166

Maurizio Pancrazzi https://orcid.org/0000-0002-3789-2482

Maria G. Pelizzo https://orcid.org/0000-0002-1383-6750

Marc Pulupa https://orcid.org/0000-0002-1573-7457

Fabio Reale https://orcid.org/0000-0002-1820-4824

Paolo Romano https://orcid.org/0000-0001-7066-6674

Clementina Sasso https://orcid.org/0000-0002-5163-5837

Udo Schühle https://orcid.org/0000-0001-6060-9078

Marco Stangalini https://orcid.org/0000-0002-5365-7546

Michael L. Stevens https://orcid.org/0000-0002-7728-0085

Leonard Strachan https://orcid.org/0000-0002-5425-7122

Thomas Straus https://orcid.org/0000-0002-6280-806X

Luca Teriaca https://orcid.org/0000-0001-7298-2320

Michela Uslenghi https://orcid.org/0000-0002-7585-8605

Marco Velli https://orcid.org/0000-0002-2381-3106

Daniel Verscharen https://orcid.org/0000-0002-0497-1096

Cosimo A. Volpicelli https://orcid.org/0000-0002-4997-1460

Phyllis Whittlesey https://orcid.org/0000-0002-7287-5098

Luca Zangrilli https://orcid.org/0000-0002-4184-2031

Gaetano Zimbardo https://orcid.org/0000-0002-9207-2647

Paola Zuppella https://orcid.org/0000-0003-0290-3193

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