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Home All issues Volume 669 (January 2023) A&A, 669 (2023) A72 Full HTML
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A&A
Volume 669, January 2023
Solar Orbiter First Results (Nominal Mission Phase)
Article Number A72
Number of page(s) 14
Section The Sun and the Heliosphere
DOI https://doi.org/10.1051/0004-6361/202244248
Published online 11 January 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe-to-Open model. Subscribe to A&A to support open access publication.

1. Introduction

Earth-directed coronal mass ejections (CMEs; magnetized clouds of coronal plasma, and sometimes also cooler and denser material originating from the lower solar atmosphere) from the solar atmosphere that move into the interplanetary space are known to severely impact our space weather (e.g., reviews by Pulkkinen 2007; Koskinen et al. 2017; Temmer 2021). The arrival of CME-driven shocks and their associated material is registered in in situ observations by near-Earth spacecraft in the form of sudden increases in solar wind speed and plasma-β, in combination with enhanced plasma density and temperature, as well as a drastically enhanced magnetic field strength at the shock boundary (e.g., review by van Driel-Gesztelyi & Culhane 2009). The interplanetary manifestations of CMEs are usually referred to as interplanetary CMEs (ICMEs). A particular subset of ICMEs, the so-called magnetic clouds (MCs), adhere to an inherent magnetic field characteristic of a magnetic flux rope, that is, it is twisted around a common axis (e.g., Burlaga et al. 1981). Characteristic in situ signatures of MCs include a smooth rotation of enhanced magnetic field, low proton temperatures, and plasma-β (Zurbuchen & Richardson 2006). MC-like features are present in ≈77% of all ICMEs while the remaining (“nonflux-rope”) events tend to exhibit more internal complexity (e.g., Nieves-Chinchilla et al. 2019).

When traveling through interplanetary space, ICMEs expand in a manner determined by the interaction of their inherent magnetic field and that of the ambient solar wind (e.g., Démoulin & Dasso 2009). In general, ICMEs tend to expand self-similarly in the radial direction (e.g., Vršnak et al. 2019). Therefore, the increase in their size as well as the corresponding decrease in the magnetic field strength can be described by a power-law function (Bothmer & Schwenn 1998; Leitner et al. 2007; Démoulin et al. 2008; Gulisano et al. 2010; Good et al. 2019; Salman et al. 2020; Davies et al. 2022). Observational studies constrain the size and magnetic field power-law indices to 0.45 < na < 1.14 and −1.89 < nB < −0.88, respectively (e.g., Gulisano et al. 2012). More specifically, a study by Patsourakos & Georgoulis (2016) showed that the best-fit power-law index describing the decrease in the ICME magnetic field magnitude up to 1 AU is nB = −1.6. Regardless of the expansion, the magnetic flux of the MC will be conserved under ideal MHD conditions, whereas it may not be conserved in the case of magnetic reconnection between the MC structure and the ambient solar wind (Manchester et al. 2017).

The rotational profile of the magnetic field of an MC indicates its handedness (geometrical sense; Bothmer & Schwenn 1998; Palmerio et al. 2018), and is therefore indicative of its magnetic helicity. The property of magnetic helicity to be quasi-conserved even in the case of high Reynolds numbers (Berger 1984) implies that a consistency regarding the magnetic helicity budget (both in sign and magnitude) should be revealed when tracing knowingly associated features in the solar atmosphere and in interplanetary space. In other words, the helicity budget from a (pre-eruptive) solar source region has to roughly match that of an associated ICME/MC measured near Earth. In a pioneering study of 46 solar eruptions associated with sigmoidal structures observed in soft X-rays (SXRs), Leamon et al. (2002) found an overall positive correlation between the shape of coronal sigmoids and the handedness of the associated MCs. In the systematic study of helicity in MCs and their associated solar source regions for 12 events, Leamon et al. (2004) found the helicity of MCs to be typically an order of magnitude greater than that of the corresponding host active region (AR; estimates based on linear force-free models of the coronal magnetic field) and no systematic sign or amplitude relationship between them. This led these authors to conclude that the eruptive process must involve reconnection between the magnetic field of the solar source region and that of its surroundings.

Also, the magnetic flux of an MC can be set in relation to the magnetic flux involved in the magnetic reconnection process that caused the expulsion of the coronal plasma from a solar source region. During a large eruptive flare, the outward erupting CME leaves behind a growing magnetic field arcade (emitting in SXRs and at extreme ultra-violet (EUV) wavelengths) that is anchored at chromospheric locations of enhanced Hα and UV emission. These enhanced emissions, which separate from each other and the polarity inversion line (PIL) as time progresses, are caused by the deposition of energy from interaction with the ambient chromospheric plasma by particles accelerated toward the solar surface along newly reconnected field (for reviews see Fletcher et al. 2011; Benz 2017; Green et al. 2018). As it is generally accepted that the flare-induced acceleration can only stem from magnetic reconnection, flare ribbons can be used to trace the local reconnection rate (and therefore the flare reconnection flux; Priest & Forbes 2002). Similarly, coronal dimmings (Thompson et al. 1998, 2000; Qiu et al. 2007; Dissauer et al. 2018a, 2019) can be used to estimate the global reconnection rate as they reflect plasma evacuation in the low corona along field lines of an arcade initially overlying a pre-existing flux rope and closed down by magnetic reconnection in the wake of a CME. In that case, coronal dimming develops ahead in time of magnetic reconnection. Furthermore, when magnetic reconnection happens at large coronal altitudes and is not energetic enough to produce visible radiation signatures in near-surface layers of the solar atmosphere, the magnetic flux encompassed by dimming areas has been suggested to represent a better estimate of the reconnected flux than that encompassed by flare ribbons (e.g., Forbes & Lin 2000; Lin et al. 2004; Qiu et al. 2007).

Qiu et al. (2007) systematically summarized how the low-corona reconnection flux may be related to the magnetic flux of ICMEs/MCs. When magnetic reconnection takes place below a pre-existing magnetic flux rope as in the 2.5D standard flare model (see, e.g., Lin et al. 2004, for details), it contributes solely to the poloidal (azimuthal) component of the ejected flux rope. Here, the poloidal flux refers to the integration of the magnetic field projected to a plane that is perpendicular to the flux-rope axis, and is therefore related to the amount of twist along the axis of the flux rope. In that case, the poloidal flux of an associated MC should exceed the (dimming) reconnection flux. In the scenario of “in situ-formed” flux ropes, where twisted magnetic flux ropes form from sheared arcades and then erupt, the entirety of their flux is anchored to the solar surface. In that case, the poloidal flux should be close to the flare reconnection flux.

The study of Leamon et al. (2004) revealed a close correspondence between the axial magnetic fluxes of MCs (approximated using a linear force-free field solution in cylindrical geometry) and their host AR (estimated by spatial integration of the vertical magnetic field magnitude), with their ratio tending to be of order unity. Qiu et al. (2007) obtained that the poloidal (toroidal) magnetic flux budget of MCs is comparable to (a fraction of) the reconnection flux (measured based on areas in optical, UV, and EUV observations swept by flare ribbons). This is frequently interpreted as evidence of the formation of the helical structure of a magnetic flux rope by reconnection, over the course of which magnetic flux and helicity are added (for individual case studies, see e.g., Attrill et al. 2006; Longcope et al. 2007; Möstl et al. 2008, 2009; Temmer et al. 2017). Depending on the relative magnitude of the magnetic flux and helicity estimates, different conclusions may be drawn regarding the ICME passage in interplanetary space. Reduced magnetic fluxes and helicities recovered from MC analysis might indicate an erosion while the ICME propagates through interplanetary space (e.g., Dasso et al. 2006; Möstl et al. 2008; Ruffenach et al. 2015; Temmer et al. 2017). However, corresponding interpretations should be considered with care due to the significant uncertainties in the underlying estimates.

Active region 12891 was the first geo-effective AR of the current solar cycle 25 when it produced a long-duration M-class flare (SOL-2021-11-02T01:20M1.7; peak time ∼03:01 UT; heliographic position ∼N16W09) preceded by a smaller C-class flare (SOL-2021-11-01T23:35C4.5; peak time ∼23:40 UT; heliographic position ∼N17E04). An extended filament partially erupted during successive activity and gave rise to a CME and associated MC arrival at Earth. The ICME was clearly captured by the Solar and Heliospheric Observatory Large Angle and Spectrometric Coronagraph Experiment and Solar Terrestrial Relations Observatory Ahead imagery, separated by −34.3° from the Sun–Earth line. The MC caused clearly identifiable in situ signatures measured near Earth by the almost aligned Solar Orbiter spacecraft (located 3° east in longitude from Earth at a distance of ∼0.84 AU from the Sun) and the Advanced Composition Explorer and Wind satellites located at L1 (at a distance of ∼0.98 AU). This setting allows us to trace physical parameters from the Sun to Solar Orbiter and further to Earth-orbit, including magnetic fluxes and helicities, under the assumption that the ejected flux rope did not change its magnetic morphology during the transit through interplanetary space. Our aims in this paper are twofold. First, we apply state-of-the-art modeling in order to retrieve the structure of the (pre-)eruptive active-region coronal magnetic field by means of stereoscopy and nonlinear force-free magnetic field modeling. Second, we estimate the flare reconnection flux and magnetic helicity in the solar source region based on remote-sensing imagery and compare these to corresponding estimates of the associated MC based on in situ measurements in order to allow interpretation of the Sun–Earth connection and ICME evolution.

2. Data and methods

2.1. Coronal aspects

2.1.1. Structural properties

Multi-point observations from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) and Solar Terrestrial Relations Observatory-Ahead (STEREO-A; Kaiser et al. 2008) Extreme-Ultraviolet Imaging Telescope (EUVI; Wuelser et al. 2004) allow us to use stereoscopy for 3D reconstructions of the extended filament and to estimate its height using tie-pointing and triangulation techniques (Inhester 2006; Liewer et al. 2009). Figure 1a shows the triangulation scheme applied to a theoretical filament (indicated by the red curve) above the solar surface. Points A and B schematically indicate the locations of the SDO and STEREO-A spacecraft, respectively. The elevation of a certain point along of the filament (indicated by “C”) is defined by the distance CP, where P is the orthogonal projection of C onto the solar sphere. C is observed by both spacecraft and is located at the intersection of the respective view directions. The line of sight (LOS) from SDO (at position “A”) directed to point C intersects the solar surface at point “M”. Similarly, the LOS of STEREO-A (at position “B”) directed to point C intersects the solar surface at point “N”. To construct the paths AM and BN in 3D and to define their point of intersection (C), identical features along the filament as observed from SDO (blue dots in Fig. 1b) and from STEREO-A (blue dots in Fig. 1c) are matched using epipolar geometry (for further details, we refer to Podladchikova et al. 2019).

thumbnail Fig. 1.

Three-dimensional reconstruction of the extended filament. (a) Schematic illustration of triangulation and a filament (red) above the solar surface. Points A and B show schematic locations of the SDO and STEREO-A spacecraft, respectively. C is the highest point of the filament. Point P shows the orthogonal projection of C onto the sphere. Points M and N are the projections of point C on the sphere along the LOS of SDO (AC) and STEREO-A (BC). (b) Selected points M (blue) in the AIA 304 Å image along the filament axis are used for the 3D reconstructions. (c) STEREO-A image showing the points N (blue) matching the same features observed in the SDO image.

Being tightly related to the observed structure of the solar corona, the magnetic field in and around a solar AR can be indirectly inferred from extrapolation of magnetic field measurements at a photospheric level to the coronal volume. To do so, we use cylindrical equal-area (CEA) projected photospheric magnetic field vector data with the azimuthal component of the vector magnetic field being disambiguated (Metcalf 1994; Leka et al. 2009) and binned to a plate scale of 720 km as an input to a nonlinear force-free (NLFF) model (Wiegelmann et al. 2012). Having the modeled 3D magnetic field structure at hand, we are able to retrieve structural properties associated to the observed filament channel, such as the coronal altitude of the flux rope axis and arcade field which can be compared to the stereoscopy-based estimates. Also, magnetic-field-related properties, such as the axial magnetic flux, average magnetic field, and so on, can be estimated from the NLFF modeling, and compared to corresponding estimates for the in situ measured MC properties and parameters deduced from those (see Sect. 2.3).

In order to gain information on the time evolution of the nonpotential coronal magnetic field in and around AR 12891, we constructed several time series of NLFF models using time series of vector magnetograms at 12-minute time cadence around the time of the M-class flares and a 1-hour cadence otherwise. From those models and the corresponding potential (current-free) model fields, the free magnetic energy (EF) can be readily estimated. These NLFF model time series are force- and divergence-free (solenoidal) to a different level based on different combinations of free model parameters (for a dedicated in-depth study, see Thalmann et al. 2020). With the level of solenoidality of the NLFF solutions being of utmost importance for the reliability of the subsequent computation of magnetic helicity (Valori et al. 2013, 2016; Thalmann et al. 2019), we select the NLFF time series of highest solenoidal quality (with nonsolenoidal errors of less than 30% of the free magnetic energy; for a dedicated study see Thalmann et al. 2019) for subsequent analyses and apply the Coulomb-gauge finite-volume helicity method of Thalmann et al. (2011) to compute a physically meaningful magnetic helicity of the coronal volume (the “relative” helicity; Berger & Field 1984; Finn & Antonsen 1984). In particular, we compute the relative helicity of the current-carrying field (HJ; Berger 1999, 2003), presumably being mostly determined by the magnetic structure hosting the observed filament.

2.1.2. Flare, CME, and dimming analysis

2.1.3. Thermal and nonthermal flare emission

We analyze the thermal and nonthermal X-ray emissions using the X-ray sensor (XRS) of the Geostationary Operational Environmental Satellites (GOES) and the Spectrometer Telescope for Imaging X-rays (STIX; Krucker et al. 2020) on board Solar Orbiter (Müller 2020) to derive the characteristics of the flare-accelerated electron beams and to study the response of the ambient plasma to that energy input.

STIX level-1 compressed pixel science data and level-4 spectrogram science data were used to generate light curves, spectra, and images (for a description of the STIX data compression levels, we refer to Krucker et al. 2020). The STIX data are observed in 32 science energy channels from 4−150 keV, with a spectral resolution of 1 keV up to 16 keV. For the present study, 17 channels up to 28 keV showed significant signal above background and were used for analysis. The spectrogram data are binned over all pixels and detectors on board. Therefore, it has a much lower telemetry requirement and can be downloaded at the full observed time cadence which is as high as 0.5 s during a flare. The pixel data on the other hand are needed to produce images. As each pixel is downloaded separately, it has less uncertainty due to statistics and compression but is only available at a reduced time cadence.

2.1.4. Flare ribbons

Flare ribbons are best observed in AIA filters capturing emission from the low solar atmosphere, like 1700 Å (photospheric), 1600 Å (upper photosphere and transition region), and 304 Å (chromosphere and transition region). They can be also observed in images produced from the coronal AIA filters, although when using such images their identification is more difficult and ambiguous because flare loops and arcades also appear brightened in these filters (partly also in the 304 Å channel). Therefore, to identify the flare ribbons we use sequences of AIA 1600 Å maps corrected for differential rotation to a reference time of 1 November 23:05 UT.

To identify and segment the flare ribbon pixels, we apply a threshold-based method, following Veronig & Polanec (2015) and Tschernitz et al. (2018). More precisely, we determine the lowest intensity maximum Im across the entire set of AIA maps, which usually corresponds to a time of low solar activity. Empirically, we find a scale factor 1.2 Im as a threshold level suitable to extract both ribbons associated to the C4.5 as well as to the M-class flares. To minimize artifacts due to saturated pixels and blooming around the flare peak, a requirement for a flare pixel to be identified is to be detected as such in at least five consecutive images (cf. Thalmann et al. 2015). Using co-registered Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) LOS magnetic field maps, we derive the total magnetic reconnection flux from the derived flare ribbon masks. To estimate the uncertainty of the reconnection flux due to the specific threshold used, we apply a ±5% change to the threshold level, and compute the mean values and corresponding standard deviation of the reconnection flux for further analysis.

2.1.5. Coronal dimmings

For the analysis of coronal dimmings, we use sequences of AIA 211 Å maps corrected for differential rotation with respect to the same reference time as for the flare ribbon analysis (1 November 23:05 UT). This choice is based on the systematic study performed by Dissauer et al. (2018a) who revealed that 211 Å and 193 Å are optimal for the observation and extraction of coronal dimmings, as they capture the “quiet” as well as AR coronal plasma that is ejected with the CME. As solar flare emission – which might hamper the identification of coronal dimmings – is more pronounced in 193 Å, we use the 211 Å filter for the coronal dimming analysis.

Using logarithmic base-ratio images constructed by dividing each image in the time series under study by a set of pre-event “base images”, we track coronal dimmings using the threshold-based method of Dissauer et al. (2018a,b), which was further developed for the application to dimmings observed off-limb by Chikunova et al. (2020). The cumulative dimming area at time t, A(t), is defined by the sum of all pixels that have been flagged as dimming pixels up to time t. Its derivative, dA/dt, represents the dimming area growth rate, and therefore shows how fast the dimming is growing over time. We estimate the total cumulative dimming flux using HMI LOS magnetograms within the “magnetic dimming region”, which is defined as the region where the flux density exceeds 10 G (cf. Dissauer et al. 2018b). Analogously to the flare ribbon analysis, we apply a ±5% change to the threshold level, and compute the mean values and corresponding standard deviation of the reconnection flux for further analysis.

2.2. (I)CME reconstruction

The CME related to the flaring region is well observed by SOHO/LASCO (Brueckner et al. 1995) and STEREO-A Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al. 2008) in the white-light coronagraph data (see Sect. 3.3 for a visualization of the relative positions of the operating satellites). Having two vantage points on the well-developed CME, we apply the graduated cylindrical shell model (GCS; Thernisien et al. 2006, 2009). GCS is a 3D reconstruction technique to derive the CME geometry, propagation direction, and 3D (de-projected bulk) speed by fitting a projection of a 3D croissant geometry on 2D images from at least two different vantage points simultaneously. To follow the CME evolution through interplanetary space and to clearly link it to the in situ measurements, the GCS results (propagation direction, speed, half-angle, and tilt with respect to ecliptic) are fed into the drag-based ensemble model (DBEM; see Vršnak et al. 2013; Dumbović et al. 2018a; Čalogović et al. 2021). DBEM is a CME propagation tool and gives probabilistic predictions of the CME arrival time and speed at a given target in the Solar System. The model results are used to compare with in situ observations in order to unambiguously link between CME signatures observed close to the Sun and in interplanetary space. The https://swe.ssa.esa.int/graz-dbem-federated is available as ESA (European Space Agency) space weather service from the Heliospheric Weather Expert Service Centre (H-ESC).

2.3. In situ analysis

We analyze in situ signatures of the ICME at Solar Orbiter (Müller 2020) and near-Earth using data from the https://omniweb.gsfc.nasa.gov/html/owdata.htmlnormpla database (King & Papitashvili 2005). To analyze magnetic field properties at Solar Orbiter we use one-minute averaged level-2 data in RTN (Radial-Tangential-Normal; a spacecraft centered coordinate system) coordinates from the magnetometer (MAG; Horbury et al. 2020), whereas for plasma properties we use level-2 data with moments computed from the proton part of the ion distribution function measured by the Solar Wind Analyser (SWA; Owen et al. 2020) Proton and Alpha particle Sensor (PAS) and taken from the Solar Orbiter archive (http://soar.esac.esa.int/soar/). SWA-PAS data were further processed in order to obtain one-minute averages. For the analysis of near-Earth magnetic and plasma properties, we use one-minute-averaged OMNI magnetic field and plasma data in GSE (Geocentric Solar Ecliptic) coordinates, which are time-shifted to Earth’s bow shock. In order to compare the orientation of the magnetic field near Earth and at Solar Orbiter, we convert Solar Orbiter RTN coordinates to GSE-aligned coordinates using the following substitutions: Br = −Bx and Bt = −By. In the RTN system, the radial component is aligned with the Sun-spacecraft line and the tangential direction is defined through the projection of the solar rotational axis to the plane perpendicular to the radial component. In the GSE system, the x-component is aligned with the Earth-Sun line and the z direction points towards the ecliptic north pole (for overview of coordinate systems see e.g., Fränz & Harper 2002). Therefore, for a spacecraft aligned perfectly radially with Earth and lying in the ecliptic plane, Br = −Bx and Bt = −By are exact coordinate transformations. Given the position of Solar Orbiter at the considered time this substitution is a solid approximation for this event.

Uncertainties of the in situ-based quantities are approximated based on the respective scales used for their visualization and subsequent analysis (Fig. 9 in Sect. 3.3). Therefore, we assume a quarter of the timescale (0.025 DOY) for the uncertainty in arrival times, 1 nT for the uncertainty of the magnetic field, and 10 km s−1 for that of the flow speed. The uncertainties of other parameters are derived using rules of error propagation.

3. Results

3.1. Pre-flare corona

The main polarity inversion line (PIL) that separates the two major polarities of AR 12891 is oriented roughly along of the solar north–south direction (black dotted curve in Fig. 2a). ARs with such a basic morphology (dubbed “spot-spot” type by Toriumi et al. 2017, see their Fig. 6) may be created by many episodes of flux emergence and may produce flares with long elongated ribbons. The AR hosted a total unsigned magnetic flux of a few 1021 Mx, placing it at the lower end of corresponding distributions (e.g., Figs. 8 and 9 of Kazachenko et al. 2017). Spatially associated with the main PIL, a pronounced filament is observed in the form of a dark elongated structure in AIA 304 Å images (Fig. 2b). We apply stereoscopic means to provide a purely observation-based estimate of the coronal height of the filament, where we find heights of ≲10 Mm (Fig. 2d). At higher temperatures, bright emission in the form of inverse-S-shaped coronal loops is observed, indicating a left-handed underlying magnetic field (Fig. 2c). The stereoscopic estimates for three time instances for which data were available for analysis (1 November 23:05 UT, 2 November 00:05 UT and 01:05 UT; not shown explicitly) indicate that the height of the filament channel remained more or less constant.

thumbnail Fig. 2.

Observations and stereoscopic reconstruction of AR 12891 on 2021 November 2 at 00:59 UT. (a) Vertical photospheric magnetic field saturated at ±1 kG. Contours are drawn at ±0.75 kG. The main PIL is indicated by a black dotted curve. (b) Nearest-in-time AIA 304 Å unsharp-mask image. The path along which stereoscopic reconstruction of the height of the filament is performed is indicated by gray crosses (differentially rotated from the time of stereoscopic reconstruction at 2 November 01:05 UT). (c) Nearest-in-time AIA 94 Å image. (d) Stereoscopy-based estimate of the height of the filament (black diamonds) and associated uncertainty (gray-shaded area).

NLFF modeling of the coronal magnetic field in and around AR 12891 at 2 November 00:59 UT (Fig. 3a) reveals a pronounced coronal arcade extending up to ≳60 Mm (blueish color), overlying strongly twisted field (reddish color), the latter being spatially associated to the main PIL (Fig. 3b) as well as to the filament observed in AIA 304 Å (see Fig. 2b). The strongly twisted model magnetic field exhibits a rotational pattern around a common axis and is therefore referred to as a flux rope in the following. When viewed along of the solar south–north direction (i.e., along of the field starting from the positive-polarity area in the southwest of the AR), this flux rope exhibits a left-handed rotation, indicative of a dominant left-handed helicity of the AR coronal field.

thumbnail Fig. 3.

Coronal magnetic field modeling of AR 12891 on 2021 November 2 at 00:59 UT. (a) Field line connectivity. Model field lines are drawn from randomly selected footpoints and are color coded according to the magnitude of the local electric current density. The grayscale background resembles the vertical photospheric magnetic field component, saturated at ±1 kG. (b) Vertical component of photospheric magnetic field saturated at ±1 kG. Black and white contours are drawn at ±0.75 kG. The main PIL is indicated by the green curve. Red straight lines resemble the footprints of selected vertical slices, labeled C1–C3, for which the spatial distribution of the azimuthal magnetic field (arrows) and unsigned axial electric current density (color-coded background) are shown in panels (c)–(e), respectively. Estimates of the average height of the center of the flux rope and arcade field within the selected slices are indicated as crosses and diamonds, respectively. Dashed lines indicate corresponding uncertainties. (f) Estimate of the altitude of the flux rope center (plus signs) and envelope (diamonds) along the main PIL based on 40 vertical slices distributed at regular intervals along the PIL.

From projection of the 3D NLFF magnetic field into vertical planes oriented locally perpendicular to the main PIL (see Figs. 3c–e for a visualization and their footprints labeled C1–C3 in Fig. 3b, respectively) we approximate the height of the flux rope along the PIL (green line in Fig. 3b). More precisely, we use the unsigned axial current density (Jaxi; see color-coded background in Figs. 3c–e) to estimate the average height of the flux rope center (indicated by crosses) and of the associated arcade field (indicated by triangles). The averages are computed using selected thresholds in the regimes > 0.75 × Jaxi, max (assuming that the strongest currents are located near the central axis) and < 0.25 × Jaxi, max (assuming a rapid decay of Jaxi toward the arcade field). We find from the NLFF-model based estimate that the center of the flux rope (where the strongest electric currents reside) is located at altitudes of ≲5 Mm above the NLFF model’s lower boundary (represented by crosses in Fig. 3f). The associated arcade field extends up to altitudes in the approximate range of 5−10 Mm (represented by diamonds), in close agreement with the stereoscopic estimate.

From the 22 NLFF models employed for the considered time interval, we estimate the mean axial flux along of the flux rope as ≈2.9±1.7 × 1020 Mx and the average magnetic field as ≈262±126 G. Furthermore, from the NLFF model at 2 November 00:59 UT, we estimate a free magnetic energy of ≃5.7 × 1032 erg and a current-carrying helicity of ≃−3.2 × 1041 Mx2, the latter being consistent with the left-handed sense of the model flux rope. The time evolution of the coronal magnetic energies and helicities is analyzed in detail in Sect. 3.2 and interpreted in context with observations of flare-related emission as well as measures deduced from those.

3.2. Eruptive activity

Figure 4 shows the EUV emission of the AR under study between 1 November ∼23:46 UT and 2 November ∼04:00 UT, at selected time instances representative for the main eruptive activity: a C4.5 flare that peaked at 1 November ∼23:40 UT, a partial filament eruption timely centered around 2 November ∼00:30 UT, and the M1.7 flare that peaked at 2 November ∼03:01 UT. In the following, these observations (see corresponding https://www.aanda.org/10.1051/0004-6361/202244248/olm for clarity) are interpreted in context with spatial and temporal aspects of simultaneously detected coronal dimmings, the latter interpreted as to represent signatures that stem from the evacuation of plasma material when a CME expands outwards.

thumbnail Fig. 4.

EUV images showing the main features of activity in AR 12891 between late November 1 and early November 2: A C4.5 flare (top row), a subsequent partial filament eruption (second row), the early stages of a double-peak M-class flare (third row), as well as its aftermath (bottom row). From left to right, AIA 1600 Å, 304 Å, and 94 Å filtergrams are shown. A https://www.aanda.org/10.1051/0004-6361/202244248/olm accompanying the figure is available in the electronic material (flare.mp4).

During the C4.5 flare late on November 1, part of the observed filament erupted (Fig. 4b). Correspondingly, distinct flare kernels appear to the east of the leading sunspot (Fig. 4a) that developed into short northward-progressing flare ribbons, along with the appearance of pronounced intermediate and nonthermal X-ray sources (Fig. 5a). Simultaneous EUV observations reveal enhanced emission along loop-like structures connecting to the northern parts of the AR (Fig. 4c) yet without signatures characteristic of the successful expulsion of coronal plasma in the form of a nonzero dimming growth rate (green curve in Fig. 6e). Later, around 2 November ∼00:35 UT, the northernmost segments of the filament channel erupted (visible as outward-moving dark features in AIA 304 Å maps; indicated by the white arrow in Fig. 4e; see also accompanying https://www.aanda.org/10.1051/0004-6361/202244248/olm for clarity) and accompanied by the first appearance of spatially pronounced dimming features (see nonzero dimming area and growth rate in Figs. 6a and e, respectively).

thumbnail Fig. 5.

STIX images showing 4−1 keV (thermal; purple), 11−16 keV (intermediate; blue), and 16−28 keV (nonthermal; green) contours at the 50%, 70%, and 90% levels, each integrated over a two-minute period centered around a peak in the STIX 16−28 keV energy band (cf. Fig. 7b). The STIX images were generated using the maximum entropy method MEM_GE (Massa et al. 2020) with an AIA 171 Å base selected from around the mean time of the image. Units are arcseconds within the Solar Orbiter view. The AIA images have been rotated to the Solar Orbiter viewpoint.

thumbnail Fig. 6.

Spatial and temporal evolution of coronal dimmings and flare ribbons. Top: area newly occupied by coronal dimmings (color coded according to time) during individual episodes: (a) the C4.5 flare and a subsequent (flare-less) partial filament eruption (1 November 23:05–2 November 1:20 UT), (b) the early phase of the M1.6 flare (01:20–02:05 UT), (c) the impulsive phase of the M1.6 flare (02:05–02:40 UT), and (d) the early decay phase of the M1.7 flare (02:40–05:48 UT). The corresponding total area occupied by flare ribbons is outlined as a black contour. Bottom: cumulative dimming area (black) and instantaneous growth rate (green) as a function of time. The width of the time windows covered in (a)–(d) is indicated by dotted horizontal lines at the top axis in (e). Gray-shaded vertical bands mark the impulsive phases of flares.

During the early phase of the M1.6 flare, extended flare ribbons developed after ∼02:14 UT (Figs. 4g and h) yet lacked the signatures of an obviously erupting structure. The latter appeared only after ∼02:20 UT and was directed toward solar south (see accompanying https://www.aanda.org/10.1051/0004-6361/202244248/olm). At that time, pronounced X-ray sources also developed (Figs. 5b and c) and the maximum growth rate in dimming area was reached (≈4 × 107 km2 s−1; see vertical dotted line in Fig. 6e), the latter associated to the growth of dimming areas both toward the solar north and south direction (Fig. 6c). A broad bright post-flare arcade spanning the whole underlying filament channel appears in EUV after ∼03:00 UT (Figs. 4k and l), along with mainly thermal X-ray sources (Fig. 5d) and along with pronounced dimmings mainly toward the solar south direction (Fig. 6d).

The temporal profiles of the full-disk GOES 1−8 Å and 0.5−4 Å SXR flux (Fig. 7a) show a short-lived enhanced emission associated to the C4.5 flare late on November 1 as well as a long-duration enhanced emission associated to the M-class flaring early on November 2. Closer inspection of the temporal profile reveals that the latter actually consisted of two main episodes: a preceding prolonged one which started at ∼01:20 UT and peaked around ∼02:51 UT (an M1.6-class flare) as well as a subsequent narrow peak at M1.7 level at ∼03:01 UT. For completeness, we note that the C-flare activity before the C4.5 flare was related to other sources on the solar disk.

thumbnail Fig. 7.

Time evolution of (a) GOES 1−8 Å (black) and 0.5−4 Å (gray) SXR flux. (b) STIX count rates at 4−11 keV (purple), 11−16 keV (blue), and 16−28 keV (green) energies together with the GOES 1−8 Å SXR flux (black). (c) Free magnetic energy. (d) Reconnection flux change rate (solid) and cumulative reconnection flux (dashed) in flare ribbons. (e) Magnitude of the helicity of the current-carrying field (|HJ|). (f) Reconnection flux change rate (solid) and cumulative reconnection flux (dashed) in dimmings. Gray-shaded vertical bands mark the impulsive phases of flares. The panels in the right column cover the time around the eruptive activity (1 November 23:00 UT–2 November 04:00 UT) while the panels in the left column cover an extended time range (1 November 20:00 UT–2 November 09:00 UT).

The time evolution of the coronal free energy, EF, during that period of enhanced flare activity of AR 12891 was characterized by an overall decrease from values of ≳7 × 1031 erg late on November 1 to ≲6 × 1031 erg prior to the M-class flaring early on November 2, followed by an increase back to a nearly pre-C-flare level in its aftermath (Fig. 7c). In a similar manner, the magnitude of the helicity of the current-carrying field, HJ, decreases from values ≳4.5 × 1041 Mx2 prior to the C-class flare to values of ≲3.5 × 1041 Mx2 prior to the M-class flaring and is replenished back to an approximate pre-C-flare level quickly afterwards (within ∼two hours; Fig. 7e). Notably, pronounced decreases of the coronal free energy and current-carrying helicity occur before 2 November ≈02:40 UT, the time when the dimming area growth rate peaked (compare Fig. 6e). Considering the mean “pre-flare” (in the time range 1 November 22:00−23:00 UT) and post-flare (in the time range 2 November 03:00−04:00 UT) values, the notable decreases in the coronal budgets amount to ΔEF ≈ 1.4±0.4 × 1031 erg and Δ|HJ| ≈ 1.5±0.4 × 1041 Mx2, supporting the scenario of a successful ejection of left-handed (negative-helicity) magnetic field.

Inspection of eruptivity-related emission allows us to establish a link to the magnetic flux involved, more precisely to that portion of magnetic flux which was processed by means of magnetic reconnection. On the one hand, flare ribbons stem from the energy deposition of flare-accelerated electrons precipitating downward along newly reconnected field. The electron beams also cause the nonthermal hard X-ray emission spatially associated to the low atmosphere where the newly reconnected field is anchored (see Fig. 5). On the other hand, coronal dimmings reflect plasma evacuation in the low corona. The time evolution of the mean magnetic flux change rates associated to flare ribbons and dimmings (both on the order of 1018 Mx s−1 during the times of eruptive activity) are shown in Figs. 7d and f, respectively, and are summarized below in context with the observed X-ray emission.

The temporal profile of the STIX 4−11 keV (thermal) and 11−16 keV (intermediate) X-ray emission appears similar to that of the GOES SXR flux, yet exhibits much more detail. In addition to the enhanced emission co-temporal with the GOES SXR peak times of the C4.5 (at 1 November 23:40 UT), M1.6 (at 2 November 02:51 UT), and M1.7 (at 2 November 03:01 UT) flares, two additional peaks are noticed in the intermediate and nonthermal (16−28 keV) energy bands centered around ∼02:20 UT and ∼02:40 UT (see red and green curves in Fig. 7b). Noteworthy, the latter two are observed to be co-temporal with peaks in the dimming growth rate (compare green curve in Fig. 6e) and to two pronounced peaks in the mean flare ribbon flux change rate (compare black solid curve in Fig. 7d). The latter also exhibits a strongest peak co-temporal with the impulsive phase of the C4.5-class flare. In comparison, the mean magnetic flux change rate in coronal dimmings (black solid curve in Fig. 7f) exhibits no obvious response to the C4.5-class flare and strongest responses occur during the early impulsive phase of the M1.6 flare, that is before notable ribbon-associated fluxes are detected. From the mean cumulative flare ribbon flux (black dashed curve in Fig. 7d), we estimate that a total of ≈1.5 ± 0.1 × 1021 Mx was liberated between 1 November 23:40 UT and 2 November 04:00 UT during the course of the C4.5 and M-class flares. Similarly, from the cumulative dimming flux (black dashed curve in Fig. 7f), we estimate a total of ≈9.7 ± 0.5 × 1021 Mx.

3.3. Upper corona and interplanetary space

In LASCO imagery, the CME appears as a halo event directed to the northeast (Fig. 8a). STEREO-A, located at ∼34° east of the Sun–Earth line, observes the CME from a side view as it propagates away from the northwest and southwest quadrants (Fig. 8c). In the coronagraph data, a CME appears first in LASCO/C2 at 1 November ∼02:00 UT, in STEREO-A/COR1 at ∼01:31 UT, and in STEREO-A/COR2 at ∼01:53 UT. From visual inspection of images at later times, when the CME has developed further into interplanetary space, we identify multiple fronts (see red arrows in Fig. 8c), hinting at multiple (at least two) eruptions: an earlier eruption oriented toward the northwest and a subsequent one heading toward the southwest.

thumbnail Fig. 8.

Observations and modeling of the (I)CME. Observations of the CME as seen from (a) LASCO/C2 and (c) STEREO-A. Bright emission fronts seen in STEREO-A are indicated exemplary by red arrows. GCS-reconstructed CME fronts are shown as green mesh in (b) and (d), respectively, on the respective white-light coronagraph data. (e) DBEM-based CME propagation direction (red dashed line) and width (red-shaded area) in context with the interplanetary position of operating spacecrafts (triangles) and planets (bullets).

We reconstruct the flux rope geometry of the ICME using the GCS method applied to the coronagraph white-light image data from LASCO/C2 on 2 November 03:12 UT and from STEREO-A/COR2 on 2 November 03:23 UT (see green meshes in Figs. 8b and d, respectively). The GCS parameters are derived as longitude E10, latitude N20, half-width α = 25° (calculated using the relation given in Dumbović et al. 2019), aspect ratio κ = 0.35 rad, and tilt angle as −75°. To calculate the 3D speed, we derive the CME height from subsequent STEREO-A/COR2 and LASCO/C3 images, covering the time period up to 04:23 UT, and assuming a self-similar expansion. For that purpose, we keep constant the GCS-based parameters α, κ, longitude, latitude, and tilt angle, and only vary the height. As a result, we find that on 2 November at 04:23 UT, the CME apex reached a height of 17.5 solar radii (Rs) with an average speed of 1600 km s−1.

The GCS-derived CME parameters (speed and angular half width at a certain time and distance, as well as the longitude of the solar source region) and their default uncertainty ranges (time ±30 min; angular half width ±15°; speed ±200 km s−1; longitude ±30°) together with the a priori unknown values of the drag parameter (γ) and ambient solar wind speed (u) are used as input for the DBEM in order to connect the ICME signatures as observed close to the Sun to those measured in situ. The unknown values of γ and u are chosen such that the modeled ICME mean arrival time and speed for Solar Orbiter and Earth matches well with the observed arrival times and speeds at the targets (we allowed for a maximum difference in the arrival times of 2 h and a maximum speed of 50 km s−1). Varying values as γ = (0.25±0.1) × 10−7 km s−1 and u = (500±50) km s−1, the best agreement with the observed ICME arrival time and speed is found for Earth (with a difference of only a few minutes between the modeled and observed values; see Table 1). For Solar Orbiter, the estimated arrival time of the ICME is ≈1.5 h too early with a difference in speed of about 25 km s−1. However, these values are clearly within the statistical uncertainties (see Vršnak et al. 2013), and therefore support the connection between CME structures observed close to the Sun and the signals measured in situ. With the same input parameters, we also run DBEM for the target STEREO-A and compare the results to the in situ measurements. For STEREO-A, the ICME is predicted to arrive about 3.5 h too early with a difference between modeled and observed speed of about 120 km s−1. Figure 8e illustrates the results from the DBEM simulation, showing the CME propagation direction (red dashed line) and width (red-shaded area) together with the constellation of planets and spacecraft in operation. The DBEM result reveals that Solar Orbiter and near-Earth spacecraft are located close to the ICME apex while STEREO-A is hit by its flank only, the latter explaining the larger differences between modeled and observed arrival time and speed. The spatial information derived from DBEM supports our analysis and interpretation of the in situ measurements by Solar Orbiter and the ACE/Wind satellites in the following.

Table 1.

In situ measured or observed (O) CME arrival time and arrival speed at several targets (Solar Orbiter, Earth, and STEREO-A) compared to the DBEM propagation model results (M).

Solar Orbiter and OMNI in situ data show great similarity (Fig. 9). In both, we clearly observe a shock arrival followed by characteristic sheath properties (green-shaded area), the disturbed frontal region of a flux rope (olive-shaded), and MC signatures (red-shaded). We observe the shock arrival at Solar Orbiter at DOY 307.6 (1 November 14:30 UT) and at Earth at DOY 307.9 (3 November 21:30 UT), followed by a region of increased density and temperature, with high plasma beta and fluctuating magnetic field indicative of the arrival of the ICME body. Especially the magnetic field components at Solar Orbiter and Earth show a striking resemblance: starting at DOY 308.3 at Solar Orbiter (4 November 07:00 UT) and DOY 308.55 at Earth (4 November 13:00 UT) clear MC signatures are recorded (for an overview on MC properties see, e.g., Klein & Burlaga 1982; Zurbuchen & Richardson 2006; Kilpua et al. 2017). These include enhanced magnetic field (top panels in Fig. 9), low proton temperatures (red curve in third row of Fig. 9), and low plasma-β (gray curve in bottom panels of Fig. 9). Notably, throughout the MC, the By component of the magnetic field is rotating from positive to negative values, while the Bz component remains positive. This is indicative of a left-handed flux rope that is highly inclined with respect to the ecliptic. According to the classification by Bothmer & Schwenn (1998), this is an east-northwest(ENW)-type flux rope. Though not shown explicitly, from both Solar Orbiter and OMNI data, the polar angle of the magnetic field is positive (indicating north), whereas the azimuthal angle of the magnetic field rotates by roughly 140° from the eastern direction to the western direction. More precisely, at Solar Orbiter we observe a rotation from ∼125 to ∼265°, and in OMNI data from roughly 135 to 273°. This, according to the classification by Nieves-Chinchilla et al. (2019), corresponds to a flux rope with a single rotation in the range 90−180° (“F_r”) at both spacecraft.

thumbnail Fig. 9.

In situ measurements given in day-of-year (DOY) time series around 2021 November 4 (DOY 308) from Solar Orbiter (left panels) and OMNI (right panels). Top row: magnetic field strength. Second row: x-, y-, and z-component (red, blue and green, respectively) of the magnetic field in the Geocentric solar ecliptic (GSE). Third row: plasma density (black), plasma temperature (red), and expected temperature (blue). Bottom row: plasma flow speed (black) and plasma-β (gray). Observed features corresponding to the sheath region, frontal region of the interplanetary flux rope, and magnetic cloud are indicated by green-, olive-, and red-shaded areas, respectively.

We performed measurements of basic properties of the sheath, frontal region, and MC at Solar Orbiter and Earth (see Table 2), and focus on the MC properties, as they can be compared to corresponding estimates from the solar source region. The MC shows a clear and symmetric profile, which can be approximated by a linear fit, indicating that a simple circular-cross-section Lundquist-type model is applicable (see e.g., Démoulin et al. 2019). In particular, we are interested in the size, average magnetic field strength, axial magnetic flux, and helicity at Solar Orbiter and Earth. We assume that the ICME expands self-similarly in the radial direction from Solar Orbiter to Earth. We base this assumption on the fact that the flow speed exhibits a globally monotonically decreasing profile at both Solar Orbiter and Earth. This assumption is further supported by the visual similarity of the magnetic field configuration at two spacecraft. For self-similarly expanding ICMEs, the expansion in size can be written as a power law with an expansion factor na, observationally constrained to 0.45 < na < 1.14 (see e.g., Bothmer & Schwenn 1998; Leitner et al. 2007; Démoulin et al. 2008; Gulisano et al. 2012; Vršnak et al. 2019). Accordingly, the falloff of the magnetic field magnitude is assumed to follow a power law with an expansion factor nB, observationally constrained to 0.88 < na < 1.89. The size of the MC was estimated assuming that the flux rope has a circular cross section and that the detector passes through the center of the flux rope. The “size” of the MC therefore represents the diameter of the flux rope. Assuming a Lundquist-type flux rope, the axial and poloidal flux of the MC were calculated using Eq. (52) in DeVore & Antiochos (2000) and Eq. (3) in Qiu et al. (2007). The length of the flux rope at Earth was estimated according to DeVore & Antiochos (2000), whereas the length at Solar Orbiter was estimated assuming the flux rope length expanded self-similarly according to the same power law as the radial expansion.

Table 2.

In situ measurements of the sheath, frontal region, and MC at Solar Orbiter and Earth, as well as properties deduced for the ICME.

From Table 2, it can be seen that both power-law expansion factors na and nB for the size and magnetic field magnitude, respectively, reside at larger values of the observational constraint interval, indicating a substantial expansion. The corresponding values of axial magnetic flux and helicity indicate that both magnetic flux and helicity are roughly conserved from Solar Orbiter to Earth, though uncertainties are rather large. Based on the assumption of self-similarity and using the estimated power-law index nB, the average magnetic field magnitude of the flux rope at 10 Mm above the solar surface can be estimated as B0 = 200±300 G (see, e.g., Eq. (14) in Dumbović et al. 2018b). We note that the large uncertainty is due to error propagation of relatively large errors in the estimation of expansion factors na and nB, which are directly related to the uncertainty of estimation of the MC signature borders in the in situ measurements.

4. Summary and discussion

In this paper, we connect coronal observations and magnetic field-related properties of solar eruptivity to observations and modeling of the interplanetary consequences. A MC hit Earth on 2021 November 4 that was initiated by a sequence of solar eruptions hosted by AR 12891 on late November 1 and early November 2: a C-class flare (SOL-2021-11-01T23:35C4.5) followed by a flare-less filament eruption and a double-peak M-class flare (SOL-2021-11-02T01:20M1.6 and SOL-2021-11-02T02:50M1.7). For an unambiguous ICME-MC association, we made use of the GCS reconstruction technique (based on simultaneous observations by SOHO/LASCO and STEREO-A coronagraphy, separated by ∼34° with respect to the Sun–Earth line and at the time of arrival of the ICME at Earth) and by feeding the GCS-derived geometry (propagation direction and de-projected speed of the ICME) into DBEM. For the analysis of the MC, we took particular advantage of multi-spacecraft observations of the almost perfectly radially aligned Solar Orbiter and ACE/Wind satellites (separated by only 3° in longitude). This setting allowed us to trace magnetic-field-related physical parameters (average field strength, magnetic flux, and magnetic helicity) from the solar source region (approximated based on a time series of NLFF models) to a distance of 0.84 AU (Solar Orbiter MAG and SWA) and further to 0.98 AU (ACE/Wind), assuming that the ejected magnetic field structure did not change its magnetic topology during the transit through interplanetary space. The latter is supported by the fact that the corona and interplanetary space represent a frozen-in environment. Our main findings are summarized in Table 3 and discussed hereafter.

Table 3.

Properties of the left-handed magnetic flux rope expelled from the solar source region (AR 12891) during an extended period of activity (a C4.5-class flare, a flare-less filament eruption, and a double-peak M-class flare) in comparison to that of the associated MC detected near Earth.

Our results suggest that the coronal magnetic field that later became involved in eruptive activity was structured in the form of a sheared arcade (flux rope) oriented along the northern (southern) portion of the flare-relevant PIL (Figs. 3a and b). This is supported by the spatial association to an observed filament and a sigmoid seen in EUV observations (Figs. 2b and c). The NLFF modeling suggests that a left-handed (negative-helicity) flux rope existed with the central axis and arcade field residing at a coronal altitudes of ≲5 Mm and 8−10 Mm above a photospheric level, respectively (Figs. 3c and e). The estimate of the vertical extent of the arcade field is in close agreement with a stereoscopic estimate of the height of the observed filament (Fig. 2d). The stereoscopic estimates for different time instances moreover suggest that the filamentary material traced was quickly replenished, allowing us to conclude that the overall (supporting) magnetic field configuration of the filament must have survived the repeated eruptive activity. The observed coronal EUV emission (Fig. 4 and accompanying https://www.aanda.org/10.1051/0004-6361/202244248/olm) as well as the time evolution of the coronal free energy and current-carrying helicity (Figs. 7c and d, respectively) suggest that the different eruptive phenomena represent different episodes of a single yet spatially and temporally extended eruptive coronal process. Over the course of that process, as estimated from a time series of NLFF models, a total of ≈1.4±0.4 × 1031 erg in free magnetic energy and a total of ≈1.5±0.4 × 1041 Mx2 in current-carrying helicity was released from the corresponding coronal budgets, supporting the scenario of a successful ejection of left-handed (negative-helicity) magnetic field.

An important question pertains to the formation process of the magnetic structure that reaches 1 AU. The relative contribution from the existing (pre-eruptive) coronal structure and that resulting from magnetic reconnection during the eruption process remains to be determined. In the case of a stronger importance of the eruptive process, one would expect the magnetic flux of the MC to clearly exceed that of the (pre-)eruptive solar structure (e.g., Lin et al. 2004). This scenario is supported by our finding of an axial magnetic flux in the MC being approximately twice that of the solar source region (filament/flux rope), as is the case if we assume the cross section of the flux rope to span roughly 17 Mm across the flare-relevant PIL (Figs. 3b–e). The validity of the assumed cross-sectional area is supported by the spatial distribution of intense axial electric current. This overall scenario – of a considerable contribution of the eruptive process to the structural properties of the ejected flux rope – is also supported by our finding that the helicity of the MC (approximated by a cylindrical LFF model) exceeds that of the solar flux rope (approximated by the change to the current-carrying helicity due to the repeated eruptive activity). This is in line with the suggestion of Leamon et al. (2004) that helical field is added to that of the pre-eruptive structure in the course of the reconnection process. In contrast to their overall conclusion of the magnetic reconnection in the eruptive process being capable of explaining the MC helicity (see also, e.g., Longcope et al. 2007; Qiu et al. 2007), our results – notwithstanding the rather large uncertainty ranges – indicate that the helicity budget of the pre-eruptive structure may need to be considered as essential contribution as well.

From flare ribbon and coronal dimming emission, we obtain the magnetic flux injected to the CME flux rope (Figs. 7d and f, respectively). The reconnection processes started with the observed C4.5 flare – spatially concentrated in the center of AR 12891 – well before the flare-less filament eruption and M-class flaring. In comparison, the dimming-associated reconnection flux covering remote areas in the outskirts of the AR shows regions involved in the reconnection process – first in the direction of the observed flare-less filament eruption (in the northern parts of the AR) and later, at the time when the CME fully erupted, toward solar south (Figs. 6a–d). Comparison of the relative timing of the cumulative reconnection fluxes reveals a period of significant contribution from dimmings without a simultaneous significant contribution from flare ribbons. This suggests that during the flare-less filament eruption and the early phase of the double-peak M-class flare, between 2 November ∼01:00 and 2:00 UT, magnetic reconnection was taking place high in the solar corona, but was too weak to produce a measurable imprint onto the low solar atmosphere where the flare ribbons have been tracked (using AIA 1600 Å images). This is also supported by the fact that the flare ribbons were much more pronounced and exhibited larger spatial extents when observed in AIA 304 Å (compare left and middle columns in Fig. 4). Therefore, the ribbon-based cumulative estimate likely represents a lower limit of the total reconnection flux.

During the series of eruptive events that originated from AR 12891, given the estimated uncertainties, a total magnetic flux was accumulated in flare ribbons comparable to the poloidal flux estimated for the associated MC, in line with the findings in other case studies (e.g., Leamon et al. 2004; Attrill et al. 2006; Möstl et al. 2008; Temmer et al. 2017) as well as the statistical study of Qiu et al. (2007). However, in sharp contrast to those is our finding that the dimming reconnection flux exceeds the poloidal flux of the associated MC by a factor of ∼10. This difference can be partly explained by the fact that the reconnection flux faces the problem of projection effects when estimated from dimming regions (due to the nature of EUV emission being LOS-integrated). Therefore, corresponding estimates likely represent an upper limit for the actual flux processed through magnetic reconnection. Another partial explanation might be related to the fact that only the in situ measured well-defined (“inner”) structure of the MC was used for considerations, while the (distorted) frontal region was disregarded (see Fig. 9). Including the frontal region in the calculations (i.e., considering a larger size and magnetic field magnitude because the magnetic field there is compressed), would lead to a larger estimate of the magnetic fluxes. However, in that case the assumption of a symmetric flux rope with a circular cross section would no longer be justified, and therefore the Lundquist solution would not be applicable.

We do not have information on how the flux rope evolved between the Sun and Solar Orbiter. However, back-extrapolation of specific magnetic-field-related properties of the ICME/MC to the solar source region, under the assumption that the structure evolved in the same manner as it did between Solar Orbiter and Earth, allows a comparison to the remote solar observations and modeling. For instance, back-extrapolation of the average magnetic field strength of the MC at Solar Orbiter and Earth ((1.8±0.1) × 10−4 G and (1.4±0.1) × 10−4 G, respectively) suggests that the corresponding solar source-region value is ≃200±300 G. The overall agreement with the respective estimate from NLFF modeling (≃262±126 G) serves as a strong indication that the CME indeed evolved self-similarly between the Sun and Solar Orbiter. Along the same lines, very well-matching in situ signatures of the magnetic structure in Solar Orbiter and ACE/Wind, with the corresponding spacecraft separated in longitude by less than 3°, suggest an expansion of the ICME/MC structure with a power-law index of 1.1±0.6. DBEM shows that Solar Orbiter and ACE/Wind probed the CME close to its apex (Fig. 8e). Hence, the interpretation of our results holds for the CME nose but might be different for flank regions. Nevertheless, the findings are in line with the known self-similar manner of expansion (e.g., Vršnak et al. 2019) and the coherency in structure over longitudinal ranges of ≳10° (Lugaz et al. 2018).

5. Conclusion

Combining sophisticated numerical (NLFF) and geometrical reconstruction techniques (stereoscopy) with remote-sensing data at various distances from the Sun allowed us to gain insight into the structural characteristics of the (pre-)eruptive solar source region and fluxes and helicities processed by means of magnetic reconnection (the latter estimated from flare ribbon and coronal dimming signatures). The spatial and propagation characteristics of the associated (I)CME can be reliably estimated from geometric fitting techniques (GCS) and interplanetary propagation models (DBEM). From the presented application, it is evident that the in situ plasma and field measurements of the well-established ACE/Wind satellites in combination with those provided by the recently launched Solar Orbiter mission serve as an eligible combination with which to pursue in-depth studies of the ICME/MC characteristics between Solar Orbiter and Earth. However, the uncertainties, especially in the derived magnetic-field-related parameters, leave many questions open and prevent us from transposing the obtained results into unique interpretations, particularly in light of the lack of in situ data at closer proximity to the Sun. These missing data will be partially compensated for by measurements of Solar Orbiter at later stages of the mission or with co-aligned measurements from Parker Solar Probe.

Movie

Movie 1 associated with Fig. 4 (flare) Access here

Acknowledgments

We thank the referee for the positive evaluation of our manuscript and for the suggestions to optimize it. J.K.T. acknowledges the Austrian Science Fund (FWF): P31413-N27. M.D. acknowledges support by the Croatian Science Foundation under the project IP-2020-02-9893 (ICOHOSS). K.D. acknowledges support from NASA under award No. 80NSSC21K0738 and the NSF under AGS-ST Grant 2154653. M.T. gratefully acknowledges the Austrian Science Fund (FWF): P 33285. A.M.V. and E.D. acknowledge the Austrian Science Fund (FWF): I4555. S.D.O. data are courtesy of the NASA/SDO AIA and HMI science teams. We acknowledge and thank the ACE SWEPAM and MAG instrument teams and the ACE Science Center for providing the ACE data. Solar Orbiter is a mission of international cooperation between ESA and NASA, operated by ESA.

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All Tables

Table 1.

In situ measured or observed (O) CME arrival time and arrival speed at several targets (Solar Orbiter, Earth, and STEREO-A) compared to the DBEM propagation model results (M).

In the text
Table 2.

In situ measurements of the sheath, frontal region, and MC at Solar Orbiter and Earth, as well as properties deduced for the ICME.

In the text
Table 3.

Properties of the left-handed magnetic flux rope expelled from the solar source region (AR 12891) during an extended period of activity (a C4.5-class flare, a flare-less filament eruption, and a double-peak M-class flare) in comparison to that of the associated MC detected near Earth.

In the text

All Figures

thumbnail Fig. 1.

Three-dimensional reconstruction of the extended filament. (a) Schematic illustration of triangulation and a filament (red) above the solar surface. Points A and B show schematic locations of the SDO and STEREO-A spacecraft, respectively. C is the highest point of the filament. Point P shows the orthogonal projection of C onto the sphere. Points M and N are the projections of point C on the sphere along the LOS of SDO (AC) and STEREO-A (BC). (b) Selected points M (blue) in the AIA 304 Å image along the filament axis are used for the 3D reconstructions. (c) STEREO-A image showing the points N (blue) matching the same features observed in the SDO image.
In the text
thumbnail Fig. 2.

Observations and stereoscopic reconstruction of AR 12891 on 2021 November 2 at 00:59 UT. (a) Vertical photospheric magnetic field saturated at ±1 kG. Contours are drawn at ±0.75 kG. The main PIL is indicated by a black dotted curve. (b) Nearest-in-time AIA 304 Å unsharp-mask image. The path along which stereoscopic reconstruction of the height of the filament is performed is indicated by gray crosses (differentially rotated from the time of stereoscopic reconstruction at 2 November 01:05 UT). (c) Nearest-in-time AIA 94 Å image. (d) Stereoscopy-based estimate of the height of the filament (black diamonds) and associated uncertainty (gray-shaded area).
In the text
thumbnail Fig. 3.

Coronal magnetic field modeling of AR 12891 on 2021 November 2 at 00:59 UT. (a) Field line connectivity. Model field lines are drawn from randomly selected footpoints and are color coded according to the magnitude of the local electric current density. The grayscale background resembles the vertical photospheric magnetic field component, saturated at ±1 kG. (b) Vertical component of photospheric magnetic field saturated at ±1 kG. Black and white contours are drawn at ±0.75 kG. The main PIL is indicated by the green curve. Red straight lines resemble the footprints of selected vertical slices, labeled C1–C3, for which the spatial distribution of the azimuthal magnetic field (arrows) and unsigned axial electric current density (color-coded background) are shown in panels (c)–(e), respectively. Estimates of the average height of the center of the flux rope and arcade field within the selected slices are indicated as crosses and diamonds, respectively. Dashed lines indicate corresponding uncertainties. (f) Estimate of the altitude of the flux rope center (plus signs) and envelope (diamonds) along the main PIL based on 40 vertical slices distributed at regular intervals along the PIL.
In the text
thumbnail Fig. 4.

EUV images showing the main features of activity in AR 12891 between late November 1 and early November 2: A C4.5 flare (top row), a subsequent partial filament eruption (second row), the early stages of a double-peak M-class flare (third row), as well as its aftermath (bottom row). From left to right, AIA 1600 Å, 304 Å, and 94 Å filtergrams are shown. A https://www.aanda.org/10.1051/0004-6361/202244248/olm accompanying the figure is available in the electronic material (flare.mp4).
In the text
thumbnail Fig. 5.

STIX images showing 4−1 keV (thermal; purple), 11−16 keV (intermediate; blue), and 16−28 keV (nonthermal; green) contours at the 50%, 70%, and 90% levels, each integrated over a two-minute period centered around a peak in the STIX 16−28 keV energy band (cf. Fig. 7b). The STIX images were generated using the maximum entropy method MEM_GE (Massa et al. 2020) with an AIA 171 Å base selected from around the mean time of the image. Units are arcseconds within the Solar Orbiter view. The AIA images have been rotated to the Solar Orbiter viewpoint.
In the text
thumbnail Fig. 6.

Spatial and temporal evolution of coronal dimmings and flare ribbons. Top: area newly occupied by coronal dimmings (color coded according to time) during individual episodes: (a) the C4.5 flare and a subsequent (flare-less) partial filament eruption (1 November 23:05–2 November 1:20 UT), (b) the early phase of the M1.6 flare (01:20–02:05 UT), (c) the impulsive phase of the M1.6 flare (02:05–02:40 UT), and (d) the early decay phase of the M1.7 flare (02:40–05:48 UT). The corresponding total area occupied by flare ribbons is outlined as a black contour. Bottom: cumulative dimming area (black) and instantaneous growth rate (green) as a function of time. The width of the time windows covered in (a)–(d) is indicated by dotted horizontal lines at the top axis in (e). Gray-shaded vertical bands mark the impulsive phases of flares.
In the text
thumbnail Fig. 7.

Time evolution of (a) GOES 1−8 Å (black) and 0.5−4 Å (gray) SXR flux. (b) STIX count rates at 4−11 keV (purple), 11−16 keV (blue), and 16−28 keV (green) energies together with the GOES 1−8 Å SXR flux (black). (c) Free magnetic energy. (d) Reconnection flux change rate (solid) and cumulative reconnection flux (dashed) in flare ribbons. (e) Magnitude of the helicity of the current-carrying field (|HJ|). (f) Reconnection flux change rate (solid) and cumulative reconnection flux (dashed) in dimmings. Gray-shaded vertical bands mark the impulsive phases of flares. The panels in the right column cover the time around the eruptive activity (1 November 23:00 UT–2 November 04:00 UT) while the panels in the left column cover an extended time range (1 November 20:00 UT–2 November 09:00 UT).
In the text
thumbnail Fig. 8.

Observations and modeling of the (I)CME. Observations of the CME as seen from (a) LASCO/C2 and (c) STEREO-A. Bright emission fronts seen in STEREO-A are indicated exemplary by red arrows. GCS-reconstructed CME fronts are shown as green mesh in (b) and (d), respectively, on the respective white-light coronagraph data. (e) DBEM-based CME propagation direction (red dashed line) and width (red-shaded area) in context with the interplanetary position of operating spacecrafts (triangles) and planets (bullets).
In the text
thumbnail Fig. 9.

In situ measurements given in day-of-year (DOY) time series around 2021 November 4 (DOY 308) from Solar Orbiter (left panels) and OMNI (right panels). Top row: magnetic field strength. Second row: x-, y-, and z-component (red, blue and green, respectively) of the magnetic field in the Geocentric solar ecliptic (GSE). Third row: plasma density (black), plasma temperature (red), and expected temperature (blue). Bottom row: plasma flow speed (black) and plasma-β (gray). Observed features corresponding to the sheath region, frontal region of the interplanetary flux rope, and magnetic cloud are indicated by green-, olive-, and red-shaded areas, respectively.
In the text

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