Photospheric Magnetic Field Research Articles

Formation and Evolutionary Changes of Coronal Holes in the Growth Phase of Cycle 23

Regularities of formation of coronal holes (CH) at the rising phase of cycle 23 are investigated. The period from 01.01.1997 to 01.03.2000 (Carrington rotations (CRs) 1918-2059) is considered in detail. The evolution of the global magnetic field (GMF) of the Sun from the zonal to the sectorial structure is analyzed. It is shown that the zonal structure is quasi-stable. The sum of zonal harmonics dominated up to CR 1941, although a stable four-sector structure of GMF was formed in 1932. In CRs 1941-1950 the contribution of the zonal and sectorial components becomes approximately equal and from CR 1950 the sectorial structure of GMF was dominated. Sectorial structure of GMF undergoing sharp changes from four-sector, at the beginning of growth of the sectorial harmonics (CR 1926), to the two-sector structure, then back to four-sector and then again to the two-sector structure. CHs clearly trace all evolutionary changes in the GMF. The structure of the polarity of the GMF uniquely determines the zones of photospheric magnetic fields where the CHs are formed.

On the Lorentz Force and Torque of Solar Photospheric Emerging Magnetic Fields

Abstract Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR’s size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.

A statistical study of the long-term evolution of coronal hole properties as observed by SDO

Context.Understanding the evolution of coronal holes is especially important when studying the high-speed solar wind streams that emanate from them. Slow- and high-speed stream interaction regions may deliver large amounts of energy into the Earth’s magnetosphere-ionosphere system, cause geomagnetic storms, and shape interplanetary space.Aims.By statistically investigating the long-term evolution of well-observed coronal holes we aim to reveal processes that drive the observed changes in the coronal hole parameters. By analyzing 16 long-living coronal holes observed by the Solar Dynamic Observatory, we focus on coronal, morphological, and underlying photospheric magnetic field characteristics, and investigate the evolution of the associated high-speed streams.Methods.We use the Collection of Analysis Tools for Coronal Holes to extract and analyze coronal holes using 193 Å EUV observations taken by the Atmospheric Imaging Assembly as well as line–of–sight magnetograms observed by the Helioseismic and Magnetic Imager. We derive changes in the coronal hole properties and look for correlations with coronal hole evolution. Further, we analyze the properties of the high–speed stream signatures near 1AU from OMNI data by manually extracting the peak bulk velocity of the solar wind plasma.Results.We find that the area evolution of coronal holes shows a general trend of growing to a maximum followed by a decay. We did not find any correlation between the area evolution and the evolution of the signed magnetic flux or signed magnetic flux density enclosed in the projected coronal hole area. From this we conclude that the magnetic flux within the extracted coronal hole boundaries is not the main cause for its area evolution. We derive coronal hole area change rates (growth and decay) of (14.2 ± 15.0)×108km2per day showing a reasonable anti-correlation (ccPearson = −0.48) to the solar activity, approximated by the sunspot number. The change rates of the signed mean magnetic flux density (27.3 ± 32.2 mG day−1) and the signed magnetic flux (30.3 ± 31.5 1018Mx day−1) were also found to be dependent on solar activity (ccPearson = 0.50 andccPearson = 0.69 respectively) rather than on the individual coronal hole evolutions. Further we find that the relation between coronal hole area and high-speed stream peak velocity is valid for each coronal hole over its evolution, but we see significant variations in the slopes of the regression lines.

Concept of the solar ring mission: An overview

The concept of the Solar Ring mission was gradually formed from L5/L4 mission concept, and the proposal of its pre-phase study was funded by the National Natural Science Foundation of China in November 2018 and then by the Strategic Priority Program of Chinese Academy of Sciences in space sciences in May 2019. Solar Ring mission will be the first attempt to routinely monitor and study the Sun and inner heliosphere from a full 360-degree perspective in the ecliptic plane. The current preliminary design of the Solar Ring mission is to deploy six spacecraft, grouped in three pairs, on a sub-AU orbit around the Sun. The two spacecraft in each group are separated by about 30 degrees and every two groups by about 120 degrees. This configuration with necessary science payloads will allow us to establish three unprecedented capabilities: (1) determine the photospheric vector magnetic field with unambiguity, (2) provide 360-degree maps of the Sun and the inner heliosphere routinely, and (3) resolve the solar wind structures at multiple scales and multiple longitudes. With these capabilities, the Solar Ring mission aims to address the origin of solar cycle, the origin of solar eruptions, the origin of solar wind structures and the origin of severe space weather events. The successful accomplishment of the mission will advance our understanding of the star and the space environment that hold our life and enhance our capability of expanding the next new territory of human.

Data Assimilative Optimization of WSA Source Surface and Interface Radii using Particle Filtering

AbstractThe Wang‐Sheeley‐Arge (WSA) model estimates solar wind speed and interplanetary magnetic field polarity in the inner heliosphere using global photospheric magnetic field maps. WSA employs the Potential Field Source Surface (PFSS) and Schatten Current Sheet (SCS) models to determine the Sun's global coronal magnetic field. The PFSS and SCS models are connected through two radial parameters, the source surface and interface radii, which specify the overlap region between the inner SCS and outer PFSS models. Though both radii values are adjustable, they have typically been fixed to 2.5 solar radii. Our work highlights how solar wind predictions improve when the radii are allowed to vary over time. Data assimilation using particle filtering (sequential Monte Carlo) is used to infer optimal values over a fixed time window. Solar wind model predictions and satellite observations are compared with a newly developed quality‐of‐agreement prediction metric. The agreement metric between the model and observations is assumed to correspond to the probability of the two key WSA model parameters, the source surface and interface radii, where the highest metric value implies the optimal radii. We find that the optimal particle filter values of solar radii can perform twice as well as standard values for an exploratory period during Carrington Rotation 1901, with these values also reducing nonphysical kinking effects seen in solar magnetic field lines. Data assimilation choices of input realization and time frame have implications for variation in the solar wind over time. We present this work's theoretical context and practical applications for prediction accuracy.

A New Parameter of the Photospheric Magnetic Field to Distinguish Eruptive-flare Producing Solar Active Regions

Abstract Solar flares and coronal mass ejections (CMEs) are eruptive phenomena caused by coronal magnetic fields. In particular, large eruptive events originate in active regions (AR) with strong surface magnetic fields. However, it is still unclear what determines the capability of an AR to specifically produce eruptive flares and CMEs, and this hinders our knowledge of the initiation mechanism for the eruptive component of these phenomena. In this study, we propose a new parameter r m to measure the possibility that a flare that occurs in an AR can be eruptive and produce a CME. The parameter r m is defined by the ratio of the magnetic flux of twist higher than a threshold T c to the surrounding—and specifically, the overlying—magnetic flux. The value of r m for each AR can be estimated using nonlinear force-free field extrapolation models of the coronal magnetic field. Based on the data obtained by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, we calculated the values of r m for 29 ARs at 51 times prior to flares larger than M5.0 class. We find that the footpoints of field lines with twist higher than 0.2 can represent the subsequent flare ribbons well, and field lines that overlie and “fence in” the highly twisted region will work to confine the eruption, generating confined flares. Discriminant function analysis is used to show that r m is moderately well able to distinguish ARs that have the capability of producing eruptive flares.

A Magnetic Snapshot Survey of F-Type Stars

Abstract We present a spectropolarimetric magnetic snapshot survey of 55 stars which includes 53 F-type stars ranging from spectral types F0 to F9 plus 2 chemically peculiar stars β CrB, and δ Cap. We look for magnetic fields in stars spanning a range of effective temperatures where the transition from fossil to dynamo magnetic fields is believed to occur. High-resolution spectropolarimetry using circularly polarized spectra is used to look for a magnetic detection in the Stokes V profile, determine the mean longitudinal magnetic field (Bl), and to look for correlations with stellar parameters. Surface magnetic fields are detected on 14 F-stars, and present in every spectral class from F3V-F9V ranging in strength from 0.3 ± 0.1 G (36 UMa, F8V) to 8.3 ± 0.9 G (h Dra, F8V). Thus we find photospheric magnetic fields are present in stars as early as spectral type F3V with an outer convection zone thickness less than a few per cent of the stellar radius.

Irradiation study of liquid crystal variable retarder for Full-disk Magneto-Graph payload onboard ASO-S mission**Project supported by the Strategic Pioneer Program on Space Science, Chinese Academy of Sciences (Grant Nos. XDA15010800 and XDA15320102) and the National Natural Science Foundation of China (Grant Nos. 11427901, 11773040, 11403047, and 11427803).

The Advanced Space-based Solar Observatory (ASO-S) is a mission proposed by the Chinese Solar Physics Community. As one of the three payloads of ASO-S, the Full-disc Magneto-Graph (FMG) will measure the photospheric magnetic fields of the entire solar disk with high spatial and temporal resolution, and high magnetic sensitivity, where liquid crystal variable retarder (LCVR) is the key to whether FMG can achieve its scientific goal. So far, there is no space flight experience for LCVR. Therefore, irradiation study for LCVRs becomes more important and urgent in order to make sure their safety and reliability in space application. In this paper, λ irradiation, proton irradiation, and ultra-violet (UV) irradiation are tested for LCVRs respectively. The optical and chemical properties during irradiation tests are measured and analyzed. For optical properties, there is no significant change in those parameters FMG payload concerned except the retardation. Although there is no drastic degradation in the retardation versus voltage during irradiations, the amount of retardation variation is much higher than the instrument requirements. Thus, an in-flight retardation versus voltage should be added in FMG payload, reducing or even avoiding the impact of retardation change. For chemical properties, the clearing point and birefringence of the LC materials almost have no change; the ion density dose not change below 60 krad[Si], but begin to increase dramatically above 60 krad[Si].

Chirality and magnetic configuration associated with two-ribbon solar flares: AR 10930 versus AR 11158

The structural property of the magnetic field in flare-bearing solar active regions (ARs) is one of the key aspects for understanding and forecasting solar flares. In this paper, we make a comparative analysis on the chirality and magnetic configurations associated with two X-class two-ribbon flares happening in AR 10930 and AR 11158. The photospheric magnetic fields of the two ARs were observed by space-based instruments, and the corresponding coronal magnetic fields were calculated based on the nonlinear force-free field model. The analysis shows that the electric current in the two ARs was distributed mostly around the main polarity inversion lines (PILs) where the flares happened, and the magnetic chirality (indicated by the signs of force-free factor α) along the main PILs is opposite for the two ARs, i.e., left-handed (α<0) for AR 10930 and right-handed (α>0) for AR 11158. It is found that, for both the flare events, a prominent magnetic connectivity (featured by co-localized strong α and strong current density distributions) was formed along the main PIL before flare and was totally broken after flare eruption. The two branches of the broken magnetic connectivity, combined with the prominent magnetic connectivity before flare, compose the opposite magnetic configurations in the two ARs owing to their opposite chirality, i.e., Z-shaped configuration in AR 10930 with left-handed chirality and inverse Z-shaped configuration in AR 11158 with right-handed chirality. It is speculated that two-ribbon flares can be generally classified to these two magnetic configurations by chirality in the flare source regions of ARs.

Photospheric magnetic field properties of active region 12740

Active regions, which are mainly responsible for the energetic blast from the Sun so-called flare, have a highly concentrated magnetic field. Almost all flares have been attributed to the dynamics of its magnetic field on the photosphere. One method to know the changings is through studying their properties using magnetogram data. The data that are obtained from Helioseismic Magnetic Imager (HMI) instruments onboard Solar Dynamics Observatory (SDO) have a good temporal resolution which can make a better analysis. We analyze three properties of photospheric magnetic field namely total photospheric magnetic free energy (TOTPOT), total unsigned vertical current (TOTUSJZ) and total unsigned current helicity (TOTUSJH) of the active region (AR) 12740 which produced almost M-class flare at the very minimum phase of solar cycle 24. Then, we compared their values to the average values of all the corresponding parameters for almost one solar cycle. The results showed that the values of each parameter in AR 12740 was below the average values of C-flare-productive ARs. The TOTPOT was half of the average while TOTUSJH and TOTUSJZ were around one-third of the average.

Flare Energy Release at the Magnetic Field Polarity Inversion Line during the M1.2 Solar Flare of 2015 March 15. II. Investigation of Photospheric Electric Current and Magnetic Field Variations Using HMI 135 s Vector Magnetograms

Abstract This work is a continuation of Paper I and is devoted to the analysis of nonthermal electron dynamics and plasma heating in the confined M1.2 class solar flare SOL2015-03-15T22:43, revealing energy release in the highly sheared interacting magnetic loops in the low corona, above the polarity inversion line (PIL). The aim of the present work is to perform the first extensive quantitative analysis of the photospheric magnetic field and photospheric vertical electric current (PVEC) dynamics in the confined flare region near the PIL using new vector magnetograms obtained with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory with a high temporal resolution of 135 s. Data analysis reveals sharp changes of the magnetic structure and PVEC associated with flare onset near the PIL. It is found that the strongest plasma heating and electron acceleration are associated with the largest increase in the magnetic reconnection rate, total PVEC, and effective PVEC density in the flare ribbons. Observations and nonlinear force-free field extrapolations show that the magnetic field structure around the PIL is consistent with a tether-cutting magnetic reconnection (TCMR) geometry. We give a qualitative interpretation of the observed dynamics of the flare ribbons, magnetic field, PVEC, and electron acceleration within the TCMR scenario.

Temporal Evolution of the Inverse Evershed Flow

Abstract The inverse Evershed flow (IEF) is an inflow of material into the penumbra of sunspots in the solar chromosphere that occurs along dark, elongated super-penumbral fibrils extending from about the outer edge of the moat cell to the sunspot. The IEF channels exhibit brightenings in the penumbra, where the supersonic IEF descends to the photosphere causing shock fronts with localized heating. We used an 1 hr time series of spectroscopic observations of the chromospheric spectral lines of Ca ii IR at 854 nm and Hα at 656 nm taken with the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope to investigate the temporal evolution of IEF channels. Complementary information on the photospheric magnetic field was obtained from observations with the Facility Infrared Spectropolarimeter at 1083 nm and the Helioseismic and Magnetic Imager. We find that individual IEF channels are long-lived (10–60 minutes) and only show minor changes in position and flow speed during their lifetime. Initiation and termination of IEF channels takes several minutes. The IEF channels with line-of-sight velocities of about 10 km s−1 show no lasting impact from transient or oscillatory phenomena with maximal velocity amplitudes of only about 1 km s−1 that run along them. We could not detect any clear correlation of the location and evolution of IEF channels to local magnetic field properties in the photosphere in the penumbra or moving magnetic features in the sunspot moat. Our results support a picture of the IEF as a field-aligned siphon flow along arched loops. From our data we cannot determine if their evolution is controlled by events at the outer end in the moat or at the inner end in the penumbra.

The Trigger Mechanism of Recurrent Solar Active Region Jets Revealed by the Magnetic Properties of a Coronal Geyser Site

Abstract Solar active region jets are small-scale collimated plasma eruptions that are triggered from magnetic sites embedded in sunspot penumbral regions. Multiple trigger mechanisms for recurrent jets are under debate. Vector magnetic field data from Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI) observations are used to analyze a prolific photospheric configuration, identified in extreme ultraviolet observations as a “coronal geyser,” that triggered a set of at least 10 recurrent solar active region jets. We focus on interpreting the magnetic fields of small-scale flaring sites aiming to understand the processes that govern recurrent jet eruptions. We perform a custom reprocessing of the SDO-HMI products, including disambiguation and uncertainty estimation. We scrutinized the configuration and dynamics of the photospheric magnetic structures. The magnetic configuration is described, via the analysis of the photospheric magnetic vertical fields, to identify the process that is responsible for driving the jet eruptions. We report that the two widely debated magnetic trigger processes, namely magnetic flux cancellation and magnetic flux emergence, appear to be responsible on a case by case basis for generating each eruption in our set. We find that 4 out of 10 jets were due to flux cancellation, while the rest were clearly not and were more likely due to flux emergence.

Real-time Flare Prediction Based on Distinctions between Flaring and Non-flaring Active Region Spectra

Abstract With machine learning entering into the awareness of the heliophysics community, solar flare prediction has become a topic of increased interest. Although machine-learning models have advanced with each successive publication, the input data has remained largely fixed on magnetic features. Despite this increased model complexity, results seem to indicate that photospheric magnetic field data alone may not be a wholly sufficient source of data for flare prediction. For the first time, we have extended the study of flare prediction to spectral data. In this work, we use Deep Neural Networks to monitor the changes of several features derived from the strong resonant Mg II h and k lines observed by the Interface Region Imaging Spectrograph. The features in descending order of predictive capability are: the triplet emission at 2798.77 Å, line core intensity, total continuum emission between the h and k line cores, the k/h ratio, line width, followed by several other line features such as asymmetry and line center. Regions that are about to flare generate spectra that are distinguishable from non-flaring active region spectra. Our algorithm can correctly identify pre-flare spectra approximately 35 minutes before the start of the flare, with an AUC of 86% and an accuracy, precision, and recall of 80%. The accuracy and AUC monotonically increase to 90% and 97%, respectively, as we move closer in time to the start of the flare. Our study indicates that spectral data alone can lead to good predictive models and should be considered an additional source of information alongside photospheric magnetograms.

A Magnetohydrodynamic Relaxation Method for Non-force-free Magnetic Field in Magnetohydrostatic Equilibrium

A nonlinear force-free field (NLFFF) extrapolation is widely used to reconstruct the three-dimensional magnetic field in the solar corona from the observed photospheric magnetic field. However, the pressure gradient and gravitational forces are ignored in the NLFFF model, even though the photospheric and chromospheric magnetic fields are not in general force-free. Here we develop a magnetohydrodynamic (MHD) relaxation method that reconstructs the solar atmospheric (chromospheric and coronal) magnetic field as a non-force-free magnetic field (NFFF) in magnetohydrostatic equilibrium where the Lorentz, pressure gradient, and gravitational forces are balanced. The system of basic equations for the MHD relaxation method is derived, and mathematical properties of the system are investigated. A robust numerical solver for the system is constructed based on the modern high-order shock capturing scheme. Two-dimensional numerical experiments that include the pressure gradient and gravitational forces are also demonstrated.

Comparative Study of Data-driven Solar Coronal Field Models Using a Flux Emergence Simulation as a Ground-truth Data Set

Abstract For a better understanding of the magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-driven models using a magnetic flux emergence simulation as a ground-truth (GT) data set. We compare the GT field with those reconstructed from the GT photospheric field by four data-driven algorithms. It is found that, at minimum, the flux rope structure is reproduced in all coronal field models. Quantitatively, however, the results show a certain degree of model dependence. In most cases, the magnetic energies and relative magnetic helicity are comparable to or at most twice of the GT values. The reproduced flux ropes have a sigmoidal shape (consistent with GT) of various sizes, a vertically standing magnetic torus, or a packed structure. The observed discrepancies can be attributed to the highly non-force-free input photospheric field, from which the coronal field is reconstructed, and to the modeling constraints such as the treatment of background atmosphere, the bottom boundary setting, and the spatial resolution.

Predicting Coronal Mass Ejections Using SDO/HMI Vector Magnetic Data Products and Recurrent Neural Networks

Abstract We present two recurrent neural networks (RNNs), one based on gated recurrent units and the other based on long short-term memory, for predicting whether an active region (AR) that produces an M- or X-class flare will also produce a coronal mass ejection (CME). We model data samples in an AR as time series and use the RNNs to capture temporal information on the data samples. Each data sample has 18 physical parameters, or features, derived from photospheric vector magnetic field data taken by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. We survey M- and X-class flares that occurred from 2010 to 2019 May using the Geostationary Operational Environmental Satellite's X-ray flare catalogs provided by the National Centers for Environmental Information (NCEI), and select those flares with identified ARs in the NCEI catalogs. In addition, we extract the associations of flares and CMEs from the Space Weather Database of Notifications, Knowledge, Information. We use the information gathered above to build the labels (positive versus negative) of the data samples at hand. Experimental results demonstrate the superiority of our RNNs over closely related machine learning methods in predicting the labels of the data samples. We also discuss an extension of our approach to predict a probabilistic estimate of how likely an M- or X-class flare is to initiate a CME, with good performance results. To our knowledge this is the first time that RNNs have been used for CME prediction.

Abrupt Shrinking of Solar Corona in the Late 1990s

Abstract We derive the longest uniform record of rotational intensities solar coronal magnetic field since 1968 and compare it with the heliospheric magnetic field (HMF) observed at the Earth. We scale the Mount Wilson Observatory and Wilcox Solar Observatory observations of the photospheric magnetic field to the level of the Synoptic Optical Long-term Investigations of the Sun/Vector Spectro Magnetograph and apply the potential field source surface model to calculate the coronal magnetic field. We find that the evolution of the coronal magnetic field during the last 50 yr agrees with the HMF observed at the Earth only if the effective coronal size, the distance of the coronal source surface of the HMF, is allowed to change in time. We calculate the optimum source surface distance for each rotation and find that it experienced an abrupt decrease in the late 1990s. The effective volume of the solar corona shrunk to less than one half during a short period of only a few years. We note that this abrupt shrinking coincides with other changes in solar magnetic fields that are likely related to the decrease of the overall solar activity, i.e., the demise of the Grand Modern Maximum.

Relations between Coronal Mass Ejections and the Photospheric Magnetic Field in Cycles 23 and 24

Abstract The number of coronal mass ejections (CMEs) and their parameters and cycle variations were investigated and compared to the photospheric magnetic field evolution in cycles 23 and 24. The Coordinated Data Analysis Workshops (CDAW) catalog of white-light CMEs detected by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph coronagraphs and the data on the photospheric magnetic fields from the Kitt Peak Vacuum Telescope Spectromagnetograph (KPVT/Spectromagnetograph) and the Synoptic Optical Long-term Investigations of the Sun Vector-Spectromagnetograph (SOLIS/VSM) were used. The results suggest that not only did the number of CMEs increase in cycle 24, but that their parameters, cycle variations, distributions, and dependencies on the photospheric magnetic fields were also different. Various CME categories behave in different ways during solar cycles. The differences in the number and parameters of CMEs and their cycle variations may be related to the differences in the photospheric magnetic fields during the cycles. The strong photospheric magnetic fields maintained approximately the same strength from cycle 23 to cycle 24, whereas the weak fields became weaker and the area they occupied increased. Taking into account that the global magnetic field diminished from cycle 23 to cycle 24, the increase in the number of CMEs in cycle 24 can be understood. A detailed analysis of the similarities and differences in CME parameters and their cycle evolution indicates that, along with the influence of changes in the CME detection mode in 2004 and 2010, the changes in CME rate and parameters were also associated with real differences in the behavior of strong and weak photospheric magnetic fields in cycles 23 and 24.

Two-dipole model of the asymmetric Sun

The large-scale photospheric magnetic field is commonly thought to be mainly dipolar during sunspot minima, when magnetic fields of opposite polarity cover the solar poles. However, recent studies show that the octupole harmonics contribute comparably to the spatial power of the photospheric field at these times. Also, the even harmonics are non-zero, indicating that the Sun is hemispherically asymmetric with systematically stronger fields in the south during solar minima. We present here an analytical model of two eccentric axial dipoles of different strength, which is physically motivated by the dipole moments produced by decaying active regions. With only four parameters, this model closely reproduces the observed large-scale photospheric field and all significant coefficients of its spherical harmonics expansion, including the even harmonics responsible for the solar hemispheric asymmetry. This two-dipole model of the photospheric magnetic field also explains the southward shift of the heliospheric current sheet observed during recent solar minima.