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Toshifumi Shimizu

Publications and source records attributed to Toshifumi Shimizu.

At least 19 recordsLinked to original sources
arXiv2026

Measuring the Expansion of Solar Magnetic Fields with Multiline Inversions from Sunrise III

Magnetic fields in the solar atmosphere are expected to expand with height, forming magnetic canopies that couple the photosphere and chromosphere. Except for sunspots, direct measurements of this expansion remain scarce because they require simultaneous magnetic diagnostics over a broad range of atmospheric heights. We analyze four consecutive high-resolution spectropolarimetric raster scans of an emerging flux region observed with the Sunrise III/SCIP instrument. Simultaneous inversions of five photospheric Fe I lines and two chromospheric Ca II lines provide a quasi-continuous reconstruction of the magnetic field from the deep photosphere to the lower chromosphere. We apply a constant-flux method that follows the same magnetic flux through different atmospheric layers to quantify magnetic expansion. All three pores analyzed exhibit an overall increase in magnetic area with height, approximately doubling their cross section between the lower photosphere and the highest atmospheric layers sampled by the inversions. The expansion remains broadly stable throughout the 48-minute observing sequence. We further characterize the expansion with a quadratic parameterization and investigate its relation to pore properties. The three pores exhibit similar core magnetic field strengths but different expansion behaviors, indicating that the magnetic core strength alone does not determine the expansion. However, the present sample is too small to establish whether these differences are related to the thermodynamic or magnetic properties of the pores and their surroundings. These results demonstrate the potential of simultaneous multiline inversions for investigating the three dimensional magnetic topology of solar magnetic structures and provide the first direct measurements of the height-dependent magnetic expansion of solar pores.

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arXiv2026

Cause of chromospheric opposite polarity intrusions discovered in Sunrise III/SCIP data: MURaM-ChE simulations point to twisted flux ropes

The Sunrise Chromospheric Infrared spectroPolarimeter (SCIP) instrument onboard the balloon-borne Sunrise III observatory provided new high-resolution observations of the solar chromosphere in the Ca II 854.2 nm line. The Stokes-V signal in magnetic network regions was found to show fine-structured details, which suggests the magnetic field above the network elements does not simply expand as a unipolar feature but displays opposite-polarity-intrusions (OPIs). These features appear as elongated structures in Stokes-V observations. In this work, we demonstrate that such features appear ubiquitously in a numerical simulation of the solar chromosphere. We use a simulation that is computed with the recently developed chromospheric extension of MURaM (MURaM-ChE) and resembles an enhanced network region. We find that OPIs appear ubiquitously in the vertical component of the magnetic field at around 1 Mm above the surface and are visible in the synthetic Stokes-V signal of the Ca II 854.2 nm line. The structures have lengths of 2 Mm to 7 Mm and widths of approximately 1 Mm. The magnetic field configurations associated with the OPI features appear to belong to twisted flux ropes (TFRs) and are visible for most of the time in the presented 21 min time series. Our results show that the magnetic structure of the chromosphere is more complex than previously thought, with even seemingly simple flux tubes showing embedded twisted fields pointing in the opposite direction. This may help in explaining new high-resolution observations from the Sunrise III mission.

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arXiv2026

Science operation, data handling, and ground support system of the SOLAR-C mission

SOLAR-C is an international solar-observing satellite mission led by Japan Aerospace Exploration Agency (JAXA). It aims to elucidate mass and energy transport in solar atmospheres through extreme ultraviolet (EUV) spectroscopy. The mission carries the EUV High-throughput Spectroscopic Telescope (EUVST) and the Solar Spectral Irradiance Monitor (SoSpIM), enabling comprehensive observations across a wide temperature range (10^4 K to 10^7 K) with minimum temperature gaps and high spatial and temporal resolution. To achieve its science objectives regarding atmospheric heating and solar flare eruptions, SOLAR-C implements a flexible and responsive operational procedure and a data processing system, while building on the heritage of the Hinode and IRIS satellites. The Chief Observer creates observation timelines that include core observation plans and approved proposed plans while taking into account the solar activity levels. A SpaceWire communication architecture is employed onboard the spacecraft, and a method is implemented in which the mission instrument temporarily acts as the network master during data transfer to support the high data rate requirements. Telemetry is downlinked at ground stations worldwide and gathered at the Institute of Space and Astronautical Science, JAXA. The EUVST data are calibrated at the SOLAR-C Science Center at Nagoya University, while the SoSpIM data are calibrated at the Processing and Archiving Facility before being integrated into the science data products. The data will be made publicly available immediately. The integrated operational scheme for this mission is expected to advance our understanding of solar atmospheric heating and flare processes.

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arXiv2026

High-order Paschen emission from the quiet-Sun off-limb chromosphere

We report the detection of high-order hydrogen Paschen emission lines (Pa~15, Pa~16, and Pa~17) in the quiet-Sun chromosphere off the solar limb using the Chromospheric Infrared SpectroPolarimeter (SCIP) on board the {\sc Sunrise~iii} balloon telescope. These lines reveal thread-like structures resembling spicules and exhibit systematically smaller Doppler velocities than Ca~II~854.2~nm, suggesting that they are optically thinner and more affected by line-of-sight averaging, especially near the limb. Non-LTE radiative transfer synthesis using the spherically symmetric one-dimensional code \texttt{rhsphere} reproduces the overall spectral properties. The observed ratios among three Paschen lines show systematic deviations from synthetic and theoretical results, suggesting that additional physical effects may influence the formation of high-order Paschen lines. The study demonstrates the potential of high-order Paschen lines as a new diagnostic of optically thin plasma in the off-limb chromosphere.

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arXiv2026

Magnetoacoustic Portals in Quiet-Sun Fluxtubes Revealed by Chromospheric Spectropolarimetry with SUNRISE III/SCIP

Acoustic waves propagate into the chromosphere, contributing to energy transport and their dynamics. Their upward propagation is restricted to frequencies above the acoustic cutoff frequency. The magnetic field configuration plays a key role in determining whether acoustic waves can propagate upward because the cutoff frequency is reduced in regions where the field is inclined with respect to gravity, forming so-called magnetoacoustic portals. Previous studies linked magnetic fields and oscillations in quiet regions, but these analyses were based on photospheric magnetic field information, leaving chromospheric structure unconstrained. This study investigates the coupling between acoustic waves and magnetic topology using photospheric and, for the first time, chromospheric spectropolarimetry in a quiet region, obtained with the Sunrise Chromospheric Infrared SpectroPolarimeter (SCIP) aboard the Sunrise iii balloon-borne solar observatory launched in 2024. The SCIP sit-and-stare observations sampled magnetic features in which the line-of-sight field strength exhibits multiple sharp spatial peaks in the photosphere while becoming broader and weaker at two heights in the chromosphere, indicating expanding fluxtubes. The chromospheric velocity field in these fluxtubes exhibits strong 5-minute oscillations, while the surrounding regions show weak 3-minute oscillations. In these fluxtubes, sawtooth temporal velocity variations are associated with intensity enhancements, suggesting steepened shocks. Fluxtubes with low-frequency oscillations are identified not only in network regions but also in weak internetwork regions. These results provide observational evidence that fluxtubes expanding into the chromosphere act as magnetoacoustic portals, in both network and internetwork regions, allowing low-frequency waves to propagate upward and driving chromospheric dynamics via shocks.

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arXiv2026

Chromospheric Dynamics of an Umbral Flare Kernel - Based on Coordinated SUNRISE III SCIP and Domeless Solar Telescope Observations

We report imaging spectroscopic observations of an M1.4 solar flare obtained during a coordinated observation between the infrared spectropolarimeter SCIP onboard the SUNRISE-III balloon mission and Domeless Solar Telescope (DST) at Hida Observatory, Kyoto University. The flare that occurred on 2024 July 13 in NOAA Active Region 13738 exhibited a compact flare kernel located within a sunspot umbra. SCIP performed rapid slit-scan observations over a field of view of 58" x 58" around the umbra with a cadence of 40 s, covering infrared chromospheric and upper-photospheric lines including Ca II 8498/8542 A and K I D1. At the same time, DST observed a wider surrounding region with a cadence of 25 s in H-alpha, Ca II 8542 A, and Na I D1/D2. Clear flare-related brightenings are detected in all chromospheric lines observed by SCIP and DST, while no significant enhancement is found in photospheric lines. The high spatial resolution of SCIP reveals fine substructures within the kernel on spatial scales of order 1000 km, which appear smeared in ground-based observations. The spectral profiles exhibit temporally and spatially varying Doppler shifts and line broadenings, indicating complex, fine-scale plasma motions in the chromosphere. These results suggest that the observed red asymmetry arises from the temporal succession of multiple fine-scale kernels, as revealed by SCIP, rather than from a single continuous process.

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arXiv2026

Horizontal Magnetic Fields Dominate the Quiet Sun Internetwork in Sunrise III Observations. Evidence from Traditional and Transformer-Based Inversions

The relative prevalence of horizontal and vertical magnetic fields in the quiet-Sun internetwork remains debated, owing to the weak linear polarisation signals that make the inferred magnetic inclination distributions sensitive to observational quality and inversion methodology. We investigate the magnetic topology of the quiet-Sun internetwork in {\sc Sunrise~iii} observations by independently applying transformer-based and traditional inversion techniques to the same spectropolarimetric dataset. We analyse observations obtained with the Sunrise Chromospheric Infrared spectroPolarimeter (SCIP). Transformer-based inversions (SINN), trained exclusively on synthetic Stokes profiles generated from a large radiative magnetohydrodynamic simulation, are compared with independent inversions performed using the \textsc{DeSIRe} code. Both inversion methods recover a quiet-Sun magnetic topology in which internetwork fields are strongly dominated by the horizontal component, whereas network fields exhibit a substantially more balanced topology. At $\logτ=-1.2$, the median horizontal and unsigned line-of-sight field components in the internetwork are 64 and 7G with \textsc{DeSIRe}, and 71 and 8G with SINN, respectively, corresponding to a horizontal-to-line-of-sight ratio of approximately nine for both methods. The agreement between the two fundamentally different inversion methodologies indicates that the quiet-Sun internetwork is characterised by a substantially stronger horizontal than vertical magnetic field component. These results demonstrate that transformer-based inversions can be successfully transferred from synthetic training data to real spectropolarimetric observations, while providing inference orders of magnitude faster than traditional inversion techniques.

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arXiv2026

Expanding magnetic canopy structure and parasitic polarities in a quiet-Sun network element observed by Sunrise III/SCIP

We present high-resolution multi-line spectropolarimetric observations of a quiet-Sun network element obtained with the {\sc Sunrise~iii} Chromospheric Infrared SpectroPolarimeter. The observations combine photospheric, upper-photospheric, and chromospheric diagnostics at a spatial resolution and polarimetric sensitivity that allow the transverse magnetic structure of the network boundary to be examined directly. We find that the strongest linear polarisation is concentrated in a narrow ridge around the edge of the magnetic element, co-spatial with enhanced transverse magnetic field inferred from multiline inversions. The magnetic azimuth exhibits a coherent, predominantly radial organisation around a more vertical core, consistent with an expanding magnetic canopy. An azimuth proxy derived directly from the observed Fe~\textsc{i} and K~\textsc{i} linear polarisation reproduces the same large-scale organisation, showing that this structure is encoded in the Stokes profiles rather than imposed by the inversion. Response functions and a MURaM-based forward-synthesis test indicate that the Fe~\textsc{i}~8468~Å linear polarisation is sensitive to magnetic azimuth in the upper photosphere, with the closest proxy agreement occurring near $\logτ\approx-3$. We find no evidence for strong azimuthal shear between the Fe- and K-sensitive diagnostics. At the network boundary, we also identify localised parasitic-polarity patches associated with complex, multi-lobed Stokes $V$ profiles, and one case in which the Stokes $V$ polarity reverses between photospheric Fe~\textsc{i} and chromospheric Ca~\textsc{ii} lines. These results demonstrate that quiet-Sun network boundaries contain organised upper-photospheric canopy fields together with small-scale mixed-polarity structure, providing new constraints on the three-dimensional magnetic structure of network elements.

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arXiv2026

Three-dimensional Magnetic Field Structure of a Quiet-Sun Region Revealed by Sunrise III/SCIP

The balloon-borne stratospheric solar observatory Sunrise III successfully completed 6.5 days of observations in July 2024. One of its focal-plane instruments, the Sunrise Chromospheric Infrared spectroPolarimeter (SCIP), is a slit-scanning spectropolarimeter that simultaneously measures full Stokes profiles of multiple spectral lines in the 850 nm and 770 nm bands. SCIP obtained an unprecedented data set of a quiet-sun region near disk center, covering a $58'' \times 58''$ field of view. With an integration time of 10 s per slit position, the scan was completed in 107 minutes without interruption, achieving remarkably stable polarimetric precision of 0.03-0.04% (1$σ$) of the continuum level. The multi-wavelength SCIP observations reveal that the chromospheric line-of-sight (LOS) magnetic field exhibits thread-like, elongated structures over the internetwork regions, with no obvious photospheric counterpart directly below. These threads are typically narrower than $1''$ and are embedded within the canopy fields extending from the network regions. Their LOS field strengths derived from the weak-field approximation are typically 10-20 G weaker than the surrounding canopy. In particularly clear cases, the magnetic polarity of the threads is opposite to that of the adjacent canopy. These findings suggest that the canopy field is not simply an expanding structure originating from network regions, but instead has a complex three-dimensional configuration containing numerous localized substructures. These observations provide new constraints on the quiet-sun magnetic topology from the photosphere to the chromosphere.

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arXiv2026

Three-dimensional Magnetic Structures of Ellerman Bombs revealed by SUNRISE III/SCIP

Ellerman bombs (EBs) are widely recognized as photospheric and chromospheric signatures of magnetic reconnection. However, the three-dimensional (3D) magnetic topology has remained elusive due to the lack of seamless height coverage in observations. Here, we present initial results from the SUNRISE III/SCIP (Sunrise Chromospheric Infrared spectroPolarimeter) observations of an emerging flux region. Exploiting the seeing-free, high-spatial-resolution observations provided by the 1-meter balloon-borne telescope, SCIP achieved seamless multi-line spectropolarimetry from the photosphere to the lower chromosphere. We analyzed the multi-line Stokes profiles of the photospheric Fe I and K I lines and the chromospheric Ca II lines, and applied the Weak Field Approximation to the K I and Ca II lines to reconstruct the 3D magnetic field structure. The blue- and red-wing brightenings of the Ca II 8542 Å line appear at spatially offset locations, indicating bi-directional reconnection flows. The reconstructed 3D magnetic field reveals that the opposite-polarity field structure reaches different heights in the two events analyzed. In one event, it is confined to the lower layers and is absent at the formation height of Ca II 8542 Å core, which shows no intensity enhancement, whereas in the other event it extends up to the Ca II 8542 Å core formation height, where enhanced line-core intensity is also observed. We interpret this as the reconnection current sheet reaching different altitudes. These results demonstrate that SCIP has successfully resolved the 3D structure of EBs, distinguishing magnetic reconnection events occurring at different atmospheric heights.

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arXiv2026

Pre-flare and active region plasma flows and structure seen by the short wavelength camera on SOLAR-C/EUVST

The mechanisms triggering solar flares and driving coronal heating occur across wide temperature ranges on small spatial scales and short timescales, making them difficult to observe with current instrumentation. The upcoming SOLAR-C mission, launching in the late 2020s, will provide unprecedented plasma diagnostic capability with its high-throughput extreme-ultraviolet (EUV) spectroscopic telescope (EUVST), capable of ~0.2 arcsec/pix spatial sampling (~0.4 arcsec resolution), continuous temperature coverage from 0.02-15 MK, and exposure times down to 0.5 seconds. We present forward modelling of the spectrograph's short wavelength camera (170-210 Å; SOLAR-C/EUVST-SW) and its response to log T~6.2 coronal plasma in a three-dimensional MHD-simulated pre-flare active region. We compare this performance to that of the previous-generation EUV Imaging Spectrometer (EIS) on Hinode (SOLAR-B). Our results demonstrate that SOLAR-C/EUVST can distinguish individual flux tubes in simulated active region loops which Hinode/EIS cannot resolve. In simulated pre-flare plasma, SOLAR-C/EUVST captures sharp velocity gradients between adjacent upflowing and downflowing plasma which Hinode/EIS is unable to resolve. Doppler velocity measurement accuracy will reach better than 1 km/s in active regions. We show that this next-generation spectrograph can be expected to directly observe processes potentially related to flare triggering, such as plasma flows from low-altitude reconnection linked to emerging flux, and determine whether active region loops consist of a small number of strands or the hundreds predicted by magnetic reconnection-induced nanoflare heating models.

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arXiv2026

Vector Magnetic Field associated with an Active Region Filament Observed by SUNRISE III/SCIP in the Ca II 8542 Å Line

We report high-spatial-resolution spectropolarimetric observations spatially associated with a solar filament, obtained with the SUNRISE Chromospheric Infrared spectro-Polarimeter (SCIP) onboard the SUNRISE III balloon-borne solar observatory on 15 July 2024. The observed filament was located near the solar disk center, adjacent to an active region, and remained quiescent for at least two hours during the observing period. SCIP recorded full Stokes profiles in the Ca II 8542 Å line, revealing clear signatures of linear polarization produced by the transverse Zeeman effect. The detected linear polarization signals within the filament region exceeded the 2$σ$ noise level and exhibited a characteristic Zeeman double-lobe spectral shape that distinguishes them from polarization due to scattering. The magnetic field strength derived using the weak field approximation is approximately -80 G along the line of sight and 300-500 G in the transverse direction. These values likely reflect the magnetic properties of the filament and its supporting chromospheric environment. The orientation of the magnetic field vector is nearly parallel to the filament axis in its northeastern portion, while the southeastern part of the filament extends outside the field of view. To our knowledge, this is the first unambiguous detection of linear polarization associated with a solar filament with the Ca II 8542 Å line. Our results open a new diagnostic window on the vector magnetic structure of solar filaments in the lower chromosphere, complementing existing He I based diagnostics that probe the upper chromosphere.

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arXiv2026

Sunrise III: Instrument, mission, data, and first results

Sunrise III is a stratospheric balloon-borne solar observatory with a 1-m diameter telescope and three post-focus instruments, along with an image stabilisation system, all within a protective gondola. It samples the lower solar atmosphere, from the solar surface to the middle chromosphere, at a resolution approaching 50~km on the Sun. Sunrise III flew successfully for 6.5 days suspended from a zero-pressure stratospheric balloon from northern Sweden to north-western Canada in July 2024, gathering around 200 TB of data. The present issue of ApJL focuses on the first scientific results from the data collected during that flight. This paper introduces this Focus Issue, providing a very brief overview of the capabilities of the instrumentation, the flight and of the gathered data. Challenges for the measurements, data reduction and interpretation are also briefly touched upon. The paper ends with an overview of the first set of science results obtained from these data, as presented in the current Focus Issue.

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arXiv2026

Temporal Evolution of Sunspot Groups and Increase in the Open flux During Solar Maximum in Cycle 24

The evolution of the global solar magnetic field directly impacts the interplanetary magnetic field (IMF). During the solar maximum of Cycle 24, the monthly averaged IMF strength doubled over five Carrington rotations in late 2014. To understand the physical origin of this increase, we investigate the temporal evolution of open magnetic flux resulting from the emergence and decay of bipolar magnetic regions (BMRs). Using surface flux transport and potential field source surface models, we simulated how BMR characteristics, spatial distributions, and interaction with background magnetic fields affect open flux evolution. Our simulation confirmed that the relative configuration of BMRs can either inhibit open flux expansion via closed loops or promote it through favorable connections. The increase in open flux is primarily driven by the equatorial dipole component, which is enhanced by differential rotation acting on tilted BMRs. These behaviors suggest that large open field structures develop from equatorial dipole components formed by these stretched BMRs. We attribute the rapid IMF increase in 2014 (Carrington rotations 2152-2157) to the combination of the following three factors: (1) a specific sunspot configuration that facilitated the expansion of the southern coronal hole; (2) the emergence of a giant sunspot group (active region 12192) with high magnetic intensity; and (3) the diffusion of these regions, which reinforced the global magnetic field. These results imply that rapid open flux variations during solar maximum are governed not only by the characteristics of emerging BMRs but also by their interaction with pre-existing large coronal holes.

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arXiv2025

Observational Comparison Between Confined and Eruptive Flares: Magnetohydrodynamics Instability Parameters in a Similar Magnetic Configuration

Unstable states of the solar coronal magnetic field structure result in various flare behaviors. In this study, we compared the confined and eruptive flares that occurred under similar magnetic circumstances in the active region 12673, on 2017 September 6, using the twist number, decay index, and height of magnetic field lines to identify observational behaviors of the flare eruption. We investigated the parameters from the magnetic field lines involved in an initial energy release, which were identified from the positions of the core of flare ribbons, i.e., flare kernels. The magnetic field lines were derived by nonlinear force-free field modeling calculated from the photospheric vector magnetic field obtained by the Solar Dynamics Observatory SDO/Helioseismic and Magnetic Imager, and flare kernels were identified from the 1600 angstrom data obtained by the SDO/Atmospheric Imaging Assembly. The twist number of all the magnetic field lines in the confined flare was below 0.6; however, the twist number in seven out of twenty-four magnetic field lines in the eruptive flare was greater than 0.6. These lines were tall. It is found that the decay index is not a clear discriminator of the confined and eruptive flares. Our study suggests that some magnetic field lines in the kink instability state may be important for eruptive flares, and that taller magnetic field lines may promote flare eruption.

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arXiv2024

Solar chromospheric heating by magnetohydrodynamic waves: dependence on magnetic field inclination

A proposed mechanism for solar chromospheric heating is that magnetohydrodynamic waves propagate upward along magnetic field lines and dissipate their energy in the chromosphere. In particular, compressible magneto-acoustic waves may contribute to the heating. Theoretically, the components below the cutoff frequency cannot propagate into the chromosphere; however, the cutoff frequency depends on the inclination of the magnetic field lines. In this study, using high temporal cadence spectral data of IRIS and Hinode SOT spectropolarimeter (SP) in plages, we investigated the dependence of the low-frequency waves on magnetic-field properties and quantitatively estimated the amount of energy dissipation in the chromosphere. The following results were obtained: (a) The amount of energy dissipated by the low-frequency component (3--6 mHz) increases with the field inclination below 40 degrees, whereas it is decreased as a function of the field inclination above 40 degrees. (b) The amount of the energy is enhanced toward $10^4 W/m^2$, which is the energy required for heating in the chromospheric plage regions, when the magnetic field is higher than 600 G and inclined more than 40 degree. (c) In the photosphere, the low-frequency component has much more power in the magnetic field inclined more and weaker than 400 G. The results suggest that the observed low-frequency components can bring the energy along the magnetic field lines and that only a specific range of the field inclination angles and field strength may allow the low-frequency component to bring the sufficient amount of the energy into the chromosphere.

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arXiv2023

High-speed data processing onboard sunrise chromospheric infrared spectropolarimeter for the SUNRISE III balloon telescope

The Sunrise Chromospheric Infrared spectroPolarimeter (SCIP) has been developed for the third flight of the SUNRISE balloon-borne stratospheric solar observatory. The aim of SCIP is to reveal the evolution of three-dimensional magnetic fields in the solar photosphere and chromosphere using spectropolarimetric measurements with a polarimetric precision of 0.03\% (1$σ$). Multiple lines in the 770 and 850 nm wavelength bands are simultaneously observed with two 2k$\times$2k CMOS cameras at a frame rate of 31.25 Hz. Stokes profiles are calculated onboard by accumulating the images modulated by a polarization modulation unit, and then compression processes are applied to the two-dimensional maps of the Stokes profiles. This onboard data processing effectively reduces the data rate. SCIP electronics can handle large data formats at high speed. Before the implementation into the flight SCIP electronics, a performance verification of the onboard data processing was performed with synthetic SCIP data that were produced with a numerical simulation modeling the solar atmospheres. Finally, we verified that the high-speed onboard data processing was realized on ground with the flight hardware by using images illuminated by natural sunlight or an LED.

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arXiv2023

Which Component of Solar Magnetic Field Drives the Evolution of Interplanetary Magnetic Field over Solar Cycle?

The solar magnetic structure changes over the solar cycle. It has a dipole structure during solar minimum, where the open flux extends mainly from the polar regions into the interplanetary space. During maximum, a complex structure is formed with low-latitude active regions and weakened polar fields, resulting in spread open field regions. However, the components of the solar magnetic field that is responsible for long-term variations in the interplanetary magnetic field (IMF) are not clear, and the IMF strength estimated based on the solar magnetic field is known to be underestimated by a factor of 3 to 4 against the actual in-situ observations (the open flux problem). To this end, we decomposed the coronal magnetic field into the components of the spherical harmonic function of degree and order $(\ell, m)$ using the potential field source surface model with synoptic maps from SDO/HMI for 2010 to 2021. As a result, we found that the IMF rapidly increased in December 2014 (seven months after the solar maximum), which coincided with the increase in the equatorial dipole, $(\ell, m)=(1, \pm1)$, corresponding to the diffusion of active regions toward the poles and in the longitudinal direction. The IMF gradually decreased until December 2019 (solar minimum) and its variation corresponded to that of the non-dipole component $\ell\geq2$. Our results suggest that the understanding of the open flux problem may be improved by focusing on the equatorial dipole and the non-dipole component and that the influence of the polar magnetic field is less significant.

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