Solar Photospheric Magnetic Field Research Articles

Inner-heliospheric Signatures of Steadily Declining Solar Magnetic Fields and Their Possible Implications

Abstract We examined solar photospheric magnetic fields for the solar cycles 21–25, covering the period 1975–2024. The unsigned photospheric magnetic fields at low latitudes (0°–45°), known as solar toroidal fields, showed a solar cycle variation with the total field strength being stronger during the maximum of cycle 25 than the maximum of cycle 24. However, the unsigned field strength of photospheric magnetic fields at high latitudes (45°–78°), known as solar polar fields, has shown a significant steady decline since around the mid-1990s. The unsigned field strength of solar polar fields, after an increase during 2015–2020, has declined again until 2024, continuing the declining trend for a long 30 yr. Also, we examined the solar wind microturbulence levels in the inner heliosphere (0.2–0.8 au), using interplanetary scintillation observations at 327 MHz, covering the period 1983–2022, that steadily declined since the mid-1990s and continued until 2022, synchronously with the solar polar fields. We found that the floor level in both solar toroidal fields and solar wind magnetic fields was reduced during the minimum of cycle 23 and recovered back during the minimum of cycle 24. In addition, a hemispherically asymmetric solar polar reversal was evident in the signed (axial) solar polar fields during cycles 21–25, with the reversal in cycle 25 for the northern hemisphere already completed but the same for the southern hemisphere yet to be completed. We discuss the implications of the long declining trend and other anomalies in solar cycle activity.

Prediction of Solar Coronal Structures Using Fourier Neural Operators Based on the Solar Photospheric Magnetic Field Observation

AbstractThis paper constructs the structures of the solar corona (SC) using Fourier neural operators (FNO) based on solar photospheric magnetic field observation. The purpose is to learn the mapping between two infinite‐dimensional function spaces, which takes the photospheric magnetic field as input and the magnetohydrodynamic (MHD) solar wind plasma parameters as output, from a finite collection of input‐output pairs. The FNO‐SC model is established using MHD simulated results of 36 Carrington rotations (CRs) from 2008, 2009, and 2020. The performance of the FNO‐SC model is tested for 6 CRs during various phases of the solar activity such as descending, minimum, and ascending phases to generate the 3D structures of the SC. With the MHD simulations as references, the average structure similarity index measure (SSIM) value for the magnetic field topology from 1 to 3Rs is around 0.88. From 1 to 20Rs, the SSIM values for the number density and radial speed surpass 0.9. Relative to OMNI observations, the mean absolute percentage error for the radial speed generated from the FNO‐SC model does not exceed 0.25. These results indicate that the FNO‐SC model effectively captures the solar coronal structures typical of the periods investigated, by recovering the MHD simulations as well as the observations. The FNO‐SC model is further trained with enriched data from the maximum phase to assess the capability of modeling such a situation. The FNO‐SC model costs 48.7 s for a single CR prediction, and thus facilitates real‐time space weather forecasting.

Nowcasting Solar EUV Irradiance With Photospheric Magnetic Fields and the Mg II Index

AbstractA new method to nowcast spectral irradiance in extreme ultraviolet (EUV) and far ultraviolet (FUV) bands is presented here, utilizing only solar photospheric magnetograms and the Mg II index (i.e., the core‐to‐wing ratio). The EUV and FUV modeling outlined here is a direct extension of the SIFT (Solar Indices Forecasting Tool) model, based on Henney et al. (2015, https://doi.org/10.1002/2014sw001118). SIFT estimates solar activity indices using the earth‐side solar photospheric magnetic field sums from global magnetic maps generated by the ADAPT (Air Force Data Assimilative Photospheric Flux Transport) model. Utilizing strong and weak magnetic field sums from ADAPT maps, Henney et al. (2015, https://doi.org/10.1002/2014sw001118) showed that EUV & FUV observations can also be well modeled using this technique. However, the original forecasting method required a recent observation of each SIFT model output to determine and apply a 0‐day offset. The new method described here expands the SIFT and ADAPT modeling to nowcast the observed Mg II index with a Pearson correlation coefficient of 0.982. By correlating the Mg II model‐observation difference with the model‐observation difference in the EUV & FUV channels, Mg II can be used to apply the 0‐day offset correction yielding improvements in modeling each of the 37 studied EUV & FUV bands. With daily global photospheric magnetic maps and Mg II index observations, this study provides an improved method of nowcasting EUV & FUV bands used to drive thermospheric and ionospheric modeling.

Global solar photospheric and coronal magnetic field over activity cycles 21–25

The evolution of the global solar magnetic field from the beginning of cycle 21 (mid-1970s) until the currently-ascending cycle 25 is described using photospheric full-disk and synoptic magnetograms from NSO Kitt Peak Vacuum Telescope (KPVT) 512-channel and Spectromagnetograph (SPMG) and the Synoptic Optical Long-term Investigation of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) and Global Oscillations Network Group (GONG), and Stanford University’s Wilcox Solar Observatory (WSO). The evolving strength and symmetry of the global coronal field are described by potential-field source-surface models decomposed into axisymmetric and non-axisymmetric, and even- and odd-ordered magnetic multipoles. The overall weakness of the global solar magnetic field since cycle 23 splits the 50-year observing window into the stronger, simpler, more hemispherically symmetric cycles 21 and 22 and the weaker, more complex cycles 23 and 24. An anomalously large decrease in the global solar field strength occurred during cycles 23, and an anomalously weak axial/polar field resulted from that cycle, accompanied by an anomalously weak radial interplanetary magnetic field (IMF) during cycle 23 activity minimum and a weakened radial IMF overall since cycle 23. The general long-term decline in solar field strength and the development during cycle 24 of strong swings of hemispheric and polar asymmetry are analyzed in detail, including their transfer through global coronal structural changes to dominate mean in situ interplanetary field measurements for several years. Although more symmetric than cycle 24, the rise phase of cycle 25 began with the southern leading the northern hemisphere, but the north has recovered to lead this cycle’s polar field reversal. The mean polar flux (poleward of ±60°) has reversed at each pole, so far more symmetrically than the cycle 23 and 24 polar reversals.

Solar Radio Spectro-polarimeter (50–500 MHz). I. Design, Development, and Characterization of a Cross-polarized, Log-periodic Dipole Antenna

The Zeeman effect has been routinely used to image and quantify the solar photospheric magnetic field (B). Such a direct measuring technique is not yet available for the corona (Lin et al. 2004). Since almost all transient nonthermal radio emissions from the corona are either partially or fully circularly polarized, observing their polarization signatures over broad frequency ranges would be of help to estimate B as a function of heliocentric height. This article aims to describe the design and development of a Cross-polarized Log-Periodic Dipole Antenna (CLPDA), an integral part of a radio spectro-polarimeter, which works in the 50–500 MHz frequency-range and to explain the tests that were carried out to characterize it. The above frequency range corresponds to a heliocentric height range ≈1.03 < r < 2.5 R ⊙ (R ⊙ = photospheric radius), wherein the numerous coronal nonthermal transients associated with space-weather effects are observed to originate. The CLPDA is used to determine the strength and sense of polarization of the received radio signal. The uncertainty involved in the determination depends on the polarization-isolation (PI) between the two orthogonal components of a CLPDA. Some of the recent advancements made in the antenna design concepts at high frequencies (∼GHz) were adopted to reduce the PI at low frequencies (∼MHz). Throughout the above frequency range, the CLPDA has a gain, return loss, and PI of ≈6.6 dBi, ≲−10 dB, and ≲−27 dB, respectively. The average PI of the CLPDA varies from −30 to −24 dB over an azimuthal angle range 0° to ±45° within which the observations are performed regularly.

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

Evolution of coronal magnetic field parameters during X5.4 solar flare

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz|≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface |B| ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with |B| ≥ 1000 G and |Tw|≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt.

Reconstructing solar magnetic fields from historical observations

Context. We apply our recently developed method to reconstruct synoptic maps of the photospheric magnetic field from observations of chromospheric plages and the magnetic polarity of sunspots. Here, we apply the method to an extended time interval from 1915 to 1985. Aims. Systematic magnetographic observations of the solar photospheric magnetic field were initiated as recently as the 1970s and the lack of earlier observations limits our ability to study and understand the long-term evolution of the Solar global field. This study is aimed at creating synoptic maps of magnetic fields for the pre-magnetograph era and using these maps as input for modern simulation models to investigate the long-term (centennial) evolution of the Sun’s global magnetic fields. Methods. We reconstructed active Solar regions by identifying chromospheric plages from Ca II K line synoptic maps and assigning magnetic polarities based on the observed polarity of sunspots. We used a surface flux transport (SFT) model to simulate the evolution of the photospheric magnetic field from the reconstructed active regions. We used the potential field source surface (PFSS) model to determine the amount of open magnetic flux from the reconstruction and from magnetographic observations. We also reconstructed the coronal field during two eclipses and compared the result with eclipse drawings. Results. We successfully reconstructed the photospheric magnetic field from 1915 to 1985. The number and total magnetic flux of the reconstructed active regions shows a realistic cyclic behavior that mostly follows the evolution of the sunspot number, even on relatively short timescales. The polar field strengths of cycles 19 and 20 do not reflect the evolution of the sunspot number very accurately, which may be related to problems related to the calcium data during cycle 19 and the long data gap during cycle 20. The polarity of polar fields and the amount of open field both at high and low latitudes all demonstrate the expected cyclic behavior. The agreement of the modeled coronal structure with eclipse drawings in 1922 and 1923 is fair.

Solar Photospheric Magnetic Fields, Coronal Mass Ejections, and Type II Radio Bursts in Cycles 23 and 24

Solar Photospheric Magnetic Fields, Coronal Mass Ejections, and Type II Radio Bursts in Cycles 23 and 24

A Study on Correcting the Effect of Polarization Crosstalk in Full-Disk Solar Photospheric Magnetic Field Observations

Magnetography using magnetic sensitive lines is regarded traditionally as the main instrument for measuring the magnetic field of the whole Sun. Full polarized Stokes parameters (\(I\), \(Q\), \(U\), \(V\)) can be used to deduce the magnetic field under specific theoretical models or inversion algorithms. Due to various reasons, there are often cross-talk effects among Stokes signals observed directly by magnetographs. Especially, the circularly polarized signal \(V\) usually seriously affects the linearly polarized \(Q\) and \(U\) signals, which is one of the main errors in the value of the transverse magnetic field (parallel to the solar surface) that is related to \(Q\) and \(U\). The full-disk magnetograph onboard the Advanced Space based Solar Observatory (ASO-S/FMG) is designed to observe Stokes parameters and deduce the magnetic-field vector. In this article, the methods for correcting the effects of cross-talk \(V\) on \(Q\) and \(U\) based on the assumption of perfectly symmetric \(Q\) and \(U\) and anti-symmetric Stokes \(V\) profiles and a new method for reducing the crosstalk effect under observation mode of the FMG are developed. Through the test, it is found that the two methods are effective in cross-talk removal in the sunspot region and have better consistency. Additionally, the developed method can be applied to remove the cross-talk effect by using only one group of \(Q\), \(U\) and \(V\) images observed at one wavelength position.

Data-driven MHD Simulation of Successive Solar Plasma Eruptions

Abstract Solar flares and plasma eruptions are sudden releases of magnetic energy stored in the plasma atmosphere. To understand the physical mechanisms governing their occurrences, three-dimensional magnetic fields from the photosphere up to the corona must be studied. The solar photospheric magnetic fields are observable, whereas the coronal magnetic fields cannot be measured. One method for inferring coronal magnetic fields is performing data-driven simulations, which involves time-series observational data of the photospheric magnetic fields with the bottom boundary of magnetohydrodynamic simulations. We developed a data-driven method in which temporal evolutions of the observational vector magnetic field can be reproduced at the bottom boundary in the simulation by introducing an inverted velocity field. This velocity field is obtained by inversely solving the induction equation and applying an appropriate gauge transformation. Using this method, we performed a data-driven simulation of successive small eruptions observed by the Solar Dynamics Observatory and the Solar Magnetic Activity Telescope in 2017 November. The simulation well reproduced the converging motion between opposite-polarity magnetic patches, demonstrating successive formation and eruptions of helical flux ropes.

Understanding the origins of the heliosphere: integrating observations and measurements from Parker Solar Probe, Solar Orbiter, and other space- and ground-based observatories

Context.The launch of Parker Solar Probe (PSP) in 2018, followed by Solar Orbiter (SO) in February 2020, has opened a new window in the exploration of solar magnetic activity and the origin of the heliosphere. These missions, together with other space observatories dedicated to solar observations, such as the Solar Dynamics Observatory, Hinode, IRIS, STEREO, and SOHO, with complementary in situ observations from WIND and ACE, and ground based multi-wavelength observations including the DKIST observatory that has just seen first light, promise to revolutionize our understanding of the solar atmosphere and of solar activity, from the generation and emergence of the Sun’s magnetic field to the creation of the solar wind and the acceleration of solar energetic particles.Aims.Here we describe the scientific objectives of the PSP and SO missions, and highlight the potential for discovery arising from synergistic observations. Here we put particular emphasis on how the combined remote sensing and in situ observations of SO, that bracket the outer coronal and inner heliospheric observations by PSP, may provide a reconstruction of the solar wind and magnetic field expansion from the Sun out to beyond the orbit of Mercury in the first phases of the mission. In the later, out-of-ecliptic portions of the SO mission, the solar surface magnetic field measurements from SO and the multi-point white-light observations from both PSP and SO will shed light on the dynamic, intermittent solar wind escaping from helmet streamers, pseudo-streamers, and the confined coronal plasma, and on solar energetic particle transport.Methods.Joint measurements during PSP–SO alignments, and magnetic connections along the same flux tube complemented by alignments with Earth, dual PSP–Earth, and SO-Earth, as well as with STEREO-A, SOHO, and BepiColumbo will allow a better understanding of the in situ evolution of solar-wind plasma flows and the full three-dimensional distribution of the solar wind from a purely observational point of view. Spectroscopic observations of the corona, and optical and radio observations, combined with direct in situ observations of the accelerating solar wind will provide a new foundation for understanding the fundamental physical processes leading to the energy transformations from solar photospheric flows and magnetic fields into the hot coronal plasma and magnetic fields and finally into the bulk kinetic energy of the solar wind and solar energetic particles.Results.We discuss the initial PSP observations, which already provide a compelling rationale for new measurement campaigns by SO, along with ground- and space-based assets within the synergistic context described above.

Using the Stokes V widths of Fe I lines for diagnostics of the intrinsic solar photospheric magnetic field

Aims. The goal of this study is to explore a novel method for the solar photospheric magnetic field diagnostics using Stokes V widths of different magnetosensitive Fe I spectral lines. Methods. We calculate Stokes I and V profiles of several Fe I lines based on a one-dimensional photospheric model VAL C using the NICOLE radiative transfer code. These profiles are used to produce calibration curves linking the intrinsic magnetic field values with the widths of blue peaks of Stokes V profiles. The obtained calibration curves are then tested using the Stokes profiles calculated for more realistic photospheric models based on magnetohydrodynamic of magneto-convection. Results. It is shown that the developed Stokes V widths method can be used with various optical and near-infrared lines. Out of six lines considered in this study, Fe I 6301 line appears to be the most effective: it is sensitive to fields over ∼200 G and does not show any saturation up to ∼2 kG. Other lines considered can also be used for the photospheric field diagnostics with this method, however, only in narrower field value ranges, typically from about 100 G to 700–1000 G. Conclusions. The developed method can be a useful alternative to the classical magnetic line ratio method, particularly when the choice of lines is limited.

Height variation of magnetic field and plasma flows in isolated bright points

Aims. The expansion with height of the solar photospheric magnetic field and the plasma flows is investigated for three isolated bright points (BPs). Methods. The BPs were observed simultaneously with three different instruments attached to the 1.5 m GREGOR telescope: (1) filtergrams of Ca II H and blue continuum (4505 Å) with the HiFI, (2) imaging spectroscopy of the Na I D2 line at 5890 Å with the GFPI, and (3) slit spectropolarimetry in the 1 μm spectral range with the GRIS. Spectral-line inversions were carried out for the Si I 10827 Å Stokes profiles. Results. Bright points are identified in the Ca II H and blue continuum filtergrams. Moreover, they are also detected in the blue wing of the Na I D2 and Si I 10827 Å lines, as well as in the Ca I 10839 Å line-core images. We carried out two studies to validate the expansion of the magnetic field with height. On the one hand, we compare the photospheric Stokes V signals of two different spectral lines that are sensitive to different optical depths (Ca I vs. Si I). The area at which the Stokes V signal is significantly large is almost three times larger for the Si I line – sensitive to higher layers – than for the Ca I one. On the other hand, the inferred line-of-sight (LOS) magnetic fields at two optical depths (log τ = −1.0 vs. −2.5) from the Si I line reveal spatially broader fields in the higher layer, up to 51% more extensive in one of the BPs. The dynamics of BPs are tracked along the Na I D2 and Si I lines. The inferred flows from Na I D2 Doppler shifts are rather slow in BPs (≲1 km s−1). However, the Si I line shows intriguing Stokes profiles with important asymmetries. The analysis of these profiles unveils the presence of two components, a fast and a slow one, within the same resolution element. The faster one, with a smaller filling factor of ∼0.3, exhibits LOS velocities of about 6 km s−1. The slower component is slightly blueshifted. Conclusions. The present work provides observational evidence for the expansion of the magnetic field with height. Moreover, fast flows are likely present in BPs but are sometimes hidden because of observational limitations.

A Method to Correct the Intensity to Polarization Crosstalk in Measuring Full-Disk Solar Photospheric Vector Magnetic Fields

Precise polarimetry is very important for studying the characteristics and evolution of solar magnetic fields. We focus on the intensity to linear and circular polarization crosstalk that affect polarimetric accuracy of full-disk vector magnetic-field measurements. An attempt is made to correct such crosstalk and to reconstruct full-disk vector magnetic fields from polarization data. By analyzing the data taken at 31 filter positions from −0.3 A to 0.3 A off the spectral line Fe i $\lambda $ 5324.19 A spaced by 0.02 A, we estimate that the intensity to linear and circular polarization crosstalks are less than 0.1% (≈ 10 G) of the quiet-Sun intensity. The method, which uses background maps obtained by averaging over many Stokes -Q, -U, and -V images to correct the crosstalks of I-to-Q, -U, and -V, is proved to be effective.

Photospheric and coronal magnetic fields in six magnetographs

Context. Solar photospheric magnetic fields have been observed since the 1950s and calibrated digital data are available from the 1970s onwards. Synoptic maps of the photospheric magnetic field are widely used in solar research, especially in the modeling of the solar corona and solar wind, and in studies of space weather and space climate. Magnetic flux density of the solar corona is a key parameter for heliospheric physics. Aims. The observed photospheric magnetic flux depends on the instrument and data processing used, which is a major problem for long-term studies. Here we scale the different observations of the photospheric field to the same absolute level and form a uniform record of coronal magnetic flux since the 1970s. Methods. We use a recently suggested method of harmonic scaling, which scales any pair of synoptic observations of any resolution to the same level. After scaling, we use the Potential Field Source Surface (PFSS) model to calculate the scaled magnetic field at various altitudes from photosphere to coronal source surface. Results. Harmonic scaling gives effective, latitudinally dependent scaling factors, which vary over the solar cycle. When scaling low-resolution data to high-resolution data, effective scaling factors are typically largest at low latitudes in the ascending phase of solar cycle and smallest for unipolar polar fields around solar minima. The harmonic scaling method used here allows for the observations of the different data sets to be scaled to the same level and the scaled unsigned coronal flux densities agree very well with each other. We also find that scaled coronal magnetic fields show a slightly different solar cycle variation from that of the nonscaled fields.

Evidence of Twisting and Mixed-polarity Solar Photospheric Magnetic Field in Large Penumbral Jets: IRIS and Hinode Observations

Abstract A recent study using Hinode (Solar Optical Telescope/Filtergraph [SOT/FG]) data of a sunspot revealed some unusually large penumbral jets that often repeatedly occurred at the same locations in the penumbra, namely, at the tail of a penumbral filament or where the tails of multiple penumbral filaments converged. These locations had obvious photospheric mixed-polarity magnetic flux in Na i 5896 Stokes-V images obtained with SOT/FG. Several other recent investigations have found that extreme-ultraviolet (EUV)/X-ray coronal jets in quiet-Sun regions (QRs), in coronal holes (CHs), and near active regions (ARs) have obvious mixed-polarity fluxes at their base, and that magnetic flux cancellation prepares and triggers a minifilament flux-rope eruption that drives the jet. Typical QR, CH, and AR coronal jets are up to 100 times bigger than large penumbral jets, and in EUV/X-ray images they show a clear twisting motion in their spires. Here, using Interface Region Imaging Spectrograph (IRIS) Mg ii k λ2796 SJ images and spectra in the penumbrae of two sunspots, we characterize large penumbral jets. We find redshift and blueshift next to each other across several large penumbral jets, and we interpret these as untwisting of the magnetic field in the jet spire. Using Hinode/SOT (FG and SP) data, we also find mixed-polarity magnetic flux at the base of these jets. Because large penumbral jets have a mixed-polarity field at their base and have a twisting motion in their spires, they might be driven the same way as QR, CH, and AR coronal jets.

Modulations of the surface magnetic field on the intra-cycle variability of total solar irradiance

Solar photospheric magnetic field plays a dominant role in the variability of total solar irradiance (TSI). The modulation of magnetic flux at six specific ranges on TSI is characterized for the first time. The daily flux values of magnetic field at four ranges are extracted from MDI/{\sl SOHO}, together with daily flux of active regions (MF$_{\text{ar}}$) and quiet regions (MF$_{\text{qr}}$); the first four ranges (MF$_{1-4}$) are: 1.5--2.9, 2.9--32.0, 32.0--42.7, and 42.7--380.1 ($\times 10^{18}$ Mx per element), respectively. Cross-correlograms show that MF$_4$, MF$_{\text{qr}}$, and MF$_{\text{ar}}$ are positively correlated with TSI, while MF$_2$ is negatively correlated with TSI; the correlations between MF$_1$, MF$_3$ and TSI are insignificant. The bootstrapping tests confirm that the impact of MF$_4$ on TSI is more significant than that of MF$_{\text{ar}}$ and MF$_{\text{qr}}$, and MF$_{\text{ar}}$ leads TSI by one rotational period. By extracting the rotational variations in the MFs and TSI, the modulations of the former on the latter at the solar rotational timescale are clearly illustrated and compared during solar maximum and minimum times, respectively. Comparison of the relative amplitudes of the long-term variation show that TSI is in good agreement with the variation of MF$_4$ and MF$_{\text{ar}}$; besides, MF$_2$ is in antiphase with TSI, and it lags the latter by about 1.5 years.

Investigating the Magnetic Imprints of Major Solar Eruptions with SDO/HMI High-cadence Vector Magnetograms

Abstract The solar active region photospheric magnetic field evolves rapidly during major eruptive events, suggesting appreciable feedback from the corona. Previous studies of these “magnetic imprints” are mostly based on line of sight only or lower-cadence vector observations; a temporally resolved depiction of the vector field evolution is hitherto lacking. Here, we introduce the high-cadence (90 s or 135 s) vector magnetogram data set from the Helioseismic and Magnetic Imager, which is well suited for investigating the phenomenon. These observations allow quantitative characterization of the permanent, step-like changes that are most pronounced in the horizontal field component (B h ). A highly structured pattern emerges from analysis of an archetypical event, SOL2011-02-15T01:56, where B h near the main polarity inversion line increases significantly during the earlier phase of the associated flare with a timescale of several minutes, while B h in the periphery decreases at later times with smaller magnitudes and a slightly longer timescale. The data set also allows effective identification of the “magnetic transient” artifact, where enhanced flare emission alters the Stokes profiles and the inferred magnetic field becomes unreliable. Our results provide insights on the momentum processes in solar eruptions. The data set may also be useful to the study of sunquakes and data-driven modeling of the corona.

THE ROTATION OF THE SOLAR PHOTOSPHERIC MAGNETIC FIELD

ABSTRACT The rotational characteristics of the solar photospheric magnetic field at four flux ranges are investigated together with the total flux of active regions (MFar) and quiet regions (MFqr). The first four ranges (MF1–4) are (1.5–2.9) × 1018, (2.9–32.0) × 1018, (3.20–4.27) × 1019, and (4.27–38.01) × 1019, respectively (the unit is Mx per element). Daily values of the flux data are extracted from magnetograms of the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. Lomb–Scargle periodograms show that only MF2, MF4, MFqr, and MFar exhibit rotational periods. The periods of the first three types of flux are very similar, i.e., 26.20, 26.23, and 26.24 days, respectively, while that of MFar is longer, 26.66 days. This indicates that active regions rotate more slowly than quiet regions on average, and strong magnetic fields tend to repress the surface rotation. Sinusoidal function fittings and cross-correlation analyses reveal that MFar leads MF2 and MF4 by 5 and 1 days, respectively. This is speculated to be related with the decaying of active regions. MF2 and MFar are negatively correlated, while both MF4 and MFqr are positively correlated with MFar. At the timescale of the solar activity cycle, MFar leads (negatively) MF2 by around one year (350 days), and leads MF4 by about 3 rotation periods (82 days). The relation between MF2 and MFar may be explained by the possibility that the former mainly comes from a higher latitude, or emerges from the subsurface shear layer. We conjecture that MF4 may partly come from the magnetic flux of active regions; this verifies previous results that were obtained with indirect solar magnetic indices.