Open Solar Flux Research Articles

Reconstruction of Carrington Rotation Means of Open Solar Flux over the Past 154 Years

We generate reconstructions of signed open solar flux (OSF) for the past 154 years using observations of geomagnetic activity. Previous reconstructions have been limited to annual resolution, but this is here increased by a factor of more than 13 by using averages over Carrington rotation (CR) intervals. We use two indices of geomagnetic activity, the homogeneous aa index, aaH, and the IDV(1d) index; a combination of the two is fitted to OSF estimates from near-Earth interplanetary satellite data. For 1995 – 2022, these are corrected for excess flux (i.e. orthogardenhose flux and switchbacks) using strahl electrons. For 1970 – 2022, we also use the absolute values of the radial component of the near-Earth interplanetary magnetic field 〈|〈Br〉τ|〉CR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\langle }|{\\langle }B_{r}{\\rangle }_{\ au }|{\\rangle }_{CR}$\\end{document}, where the excess flux is allowed for by adopting the optimum averaging interval τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\ au }$\\end{document} of 20 h. However, in the interval 1970 – 1995, data gaps in the interplanetary data are a serious problem. The errors that these missing data cause in CR averages of OSF are evaluated by synthetically masking data for CRs that have a full complement, using the same number and time series of data gaps as for the CR in question. Given the potential for missing data to generate large errors, we use the near-continuous 1995 – 2022 data to derive the best-fit combination of the geomagnetic data and employ the 1970 – 1995 data for testing in which we can readily allow for the errors caused by data gaps. Errors caused by inaccuracies in the geomagnetic data are shown to be considerably smaller than the uncertainties due to the polynomial fitting. It is shown that the new reconstructions are consistent with the previous annual estimates and that there is considerable variability in the OSF values from one CR to the next; in particular, in high-activity solar cycles, there can be individual CRs in which the OSF exceeds that for adjacent CRs by a factor as large as two.

Spatial resolution effects on the solar open flux estimates

Context. Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. Aims. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. Methods. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630 nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. Results. The results show a significant decrease in the mean magnetic flux density – related to the open flux observed at the disk center – with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20 cm aperture telescope yields a 30% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Conclusions. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle.

Reconstructing Sunspot Number by Forward-Modelling Open Solar Flux

The open solar flux (OSF) is the integrated unsigned magnetic flux leaving the top of the solar atmosphere to form the heliospheric magnetic field. As the OSF modulates the intensity of galactic cosmic rays at Earth, the production rate of cosmogenic isotopes – such as 14C and 10Be stored in tree rings and ice sheets – is closely related to the OSF. Thus on the basis of cosmogenic isotope data, OSF can be reconstructed over millennia. As sunspots are related to the production of OSF, this provides the possibility of reconstructing sunspot number (SSN) and hence properties of the solar cycles prior to the first sunspot telescopic observations in 1610. However, while models exist for estimating OSF on the basis of SSN, the hysteresis present in OSF and the lack of a priori knowledge of the start/end dates of individual solar cycles means that directly inverting these models is not possible. We here describe a new method that uses a forward model of OSF to estimate SSN and solar cycle start/end dates through a Monte Carlo approach. The method is tested by application to geomagnetic reconstructions of OSF over the period 1845-present, and compared to the known SSN record for this period. There is a substantial improvement in reconstruction of both the SSN time series and the solar cycle start/end dates compared with existing OSF-SSN regression methods. This suggests that more accurate solar-cycle information can be extracted from cosmogenic isotope records by forward modelling, and also provides a means to assess the level of agreement between independent SSN and OSF reconstructions. We find the geomagnetic OSF and observed SSN agree very well after 1875, but do differ during the early part of the geomagnetic record, though still agree within the larger observational uncertainties.

Analyses for graphical records for a total solar eclipse in May 1230: a possible reference for the “Medieval Grand Maximum”

Abstract Datable graphical records of total solar eclipses allow us to assess contemporaneous variability of Earth's rotation speed, solar coronal structure, and solar-wind conditions. Such records are known back to the early 18th century. Here, we examine Matthew Paris’ medieval manuscript, an eyewitness account of a total solar eclipse just after local sunrise, and analyse his eclipse drawings on 14 May 1230. We philologically identify his observational site as St. Albans and compute local eclipse visibility. To locate St. Albans in the totality path, our analysis requires ΔT in 555 s < ΔT < 923 s (loose scenario), consistent with the latest published ΔT spline curve, which indicates that only the upper part of the eclipsed Sun should have been visible in this case. The eclipsed Sun sould have been entirely visible over the local horizon if we set the ΔT margins to 555 s < ΔT < 571 s (strict scenario), which requires slightly modifying the latest ΔT spline curve. Matthew Paris’ drawing of the total solar eclipse showed streamer-like structures similar to solar-minimum-type coronal streamers, consistent with the local tilt of the apparent solar equator. This is morphologically consistent with the minimum-type solar coronal streamers predicted from the open solar flux reconstructed from the 14C dataset. This record potentially demonstrates a similarity in solar cycles between the ‘Medieval Grand Maximum’ and modern solar cycles. Collectively, historical eclipse records could be used to assess Earth's rotation speed, solar coronal dynamics, and background solar dynamo activity on a millennial timescale.

Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism

ABSTRACT Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.

Evidence of persistence of weak magnetic cycles driven by meridional plasma flows during solar grand minima phases

ABSTRACT Long-term sunspot observations and solar activity reconstructions reveal that the Sun occasionally slips into quiescent phases known as solar grand minima, the dynamics during which is not well understood. We use a flux transport dynamo model with stochastic fluctuations in the mean-field and Babcock–Leighton poloidal field source terms to simulate solar cycle variability. Our long-term simulations detect a gradual decay of the polar field during solar grand minima episodes. Although regular active region emergence stops, compromising the Babcock–Leighton mechanism, weak magnetic activity continues during minima phases sustained by a mean-field α-effect; surprisingly, periodic polar field amplitude modulation persists during these phases. A spectral analysis of the simulated polar flux time series shows that the 11-yr cycle becomes less prominent while high frequency periods and periods around 22 yr manifest during grand minima episodes. Analysis of long-term solar open flux observations appears to be consistent with this finding. Through numerical experimentation, we demonstrate that the persistence of periodic amplitude modulation in the polar field and the dominant frequencies during grand minima episodes are governed by the speed of the meridional plasma flow – which appears to act as a clock.

Application of historic datasets to understanding open solar flux and the 20th-century grand solar maximum. 2. Solar observations

We study historic observations of solar activity from the 20th-century rise towards the peak of the Modern Grand Solar Maximum (MGSM) and compare with observations of the decline that has occurred since. The major difference in available solar observations of the rise and of the fall are accurate magnetograms from solar magnetographs: we here use synthetic magnetograms to interpret the rise and employ historic observations of Polar Crown Filaments to test them and verify their use. We show that eclipse images at sunspot minimum reveal the long-term variation of open flux deduced from geomagnetic observations in Paper 1 (Lockwood et al., 2022). We also make use of polar coronal hole fluxes derived from historic white light images of polar faculae, but have to consider the implications of the fact that these facular images do not tell us the polarity of the field. Given this caveat, the agreement between the polar coronal hole fluxes and the values derived from open flux continuity modelling based on sunspot numbers is extremely good. This comparison indicates that one possible solution to the “open flux problem” is open flux within the streamer belt that potential-based modelling of coronal fields from photospheric fields is not capturing. We take a detailed look at the solar cycle at the peak of the MGSM, cycle 19, and show the variation of the polar coronal hole fluxes and the inferred poleward flux surges are predictable from the asymmetries in flux emergence in the two hemispheres with implied transequatorial flux transfer and/or “anti-Hale” (or more general “rogue” active region flux) emergence late in the sunspot cycle.

Application of historic datasets to understanding open solar flux and the 20th-century grand solar maximum. 1. Geomagnetic, ionospheric, and sunspot observations

We updated annual mean reconstructions of near-Earth interplanetary conditions and (signed) open solar flux FS for the past 186 years. Furthermore, we added observations for solar cycle 24 to refine regressions and improved allowance for orthogardenhose and folded (a.k.a., switchback) heliospheric flux from studies using strahl electrons. We also improved the allowance made for the annual mean gardenhose angle of the interplanetary magnetic field. We used both multiple regression with interplanetary magnetic field B and solar wind speed VSW and linear regression with the function BVSWn and demonstrated that the latter gives correlations that are not significantly lower than those given by the former. We conducted a number of tests of the geomagnetic indices used, of which by far the most important is that all four usable pairings of indices produce almost identical results for B, VSW, and FS. All reconstructions were given full 2σ uncertainties using a Monte Carlo technique that generates an ensemble of 1 million members for each pairing of indices. The long-term variations of near-Earth interplanetary field B and open solar flux FS were found to closely match those of the international sunspot numbers but VSW show a significantly different variation. This result explains why of the two peaks of 20th-century grand solar maximum, the range geomagnetic indices give a larger second peak, whereas the diurnal variation indices give a first peak that is larger, as it is for sunspots. We found that the increase in solar cycle averages of FS was between 2.46 × 1014 Wb in 1906 and 4.10 × 1014 Wb in 1949, the peak of the grand maximum, and hence, the rise in open flux was by a factor of 67%.

Estimating the Open Solar Flux from In-Situ Measurements

A fraction of the magnetic flux threading the solar photosphere extends to sufficient heliocentric distances that it is dragged out by the solar wind. Understanding this open solar flux (OSF) is central to space weather, as the OSF forms the heliosphere, magnetically connects the Sun to the planets, and dominates the motion of energetic particles. Quantification of OSF is also a key means of verifying global coronal models. However, OSF estimates derived from extrapolating the magnetic field from photospheric observations are consistently smaller than those based on heliospheric magnetic field (HMF) measurements, by around a factor two. It is therefore important to understand the uncertainties in estimating OSF from in-situ HMF measurements. This requires both an assumption of latitudinal invariance in the radial component of the HMF in the heliosphere, and that structures without an immediate connection to the Sun, such as local magnetic field inversions (or ‘switchbacks’), can be correctly accounted for. In this study, we investigate the second assumption. Following an established methodology, we use in-situ electron and magnetic data to determine the global topology of the HMF and correct for inversions that would otherwise lead to an overestimation of the OSF. The OSF estimation is applied to the interval 1994 – 2021 and combines measurements from the Wind and ACE spacecraft. This extends the time range over which this methodology has previously been applied from 13 years (1998 – 2011) to 27 years. We find that inversions cannot fully explain the discrepancy between heliospheric and photospheric OSF estimations, with the best heliospheric estimate of OSF still, on average, a factor 1.6 higher than the values extrapolated from photospheric observations.

Time Lag Between Cosmic-Ray and Solar Variability: Sunspot Numbers and Open Solar Magnetic Flux

Solar magnetic activity drives the dominant 11-year cyclic variability of different space environmental indices, but they can be delayed with respect to the original variations due to the different physical processes involved. Here, we analyzed the pairwise time lags between three global solar and heliospheric indices: sunspot numbers (SSN), representing the solar surface magnetic activity, the open solar flux (OSF), representing the heliospheric magnetic variability, and the galactic cosmic-ray (GCR) intensity near Earth, using the standard cross-correlation and the more detailed wavelet-coherence methods. All the three indices appear highly coherent at a timescale longer than a few years with persistent high coherence at the timescale of the 11-year solar cycle. The GCR variability is delayed with respect to the inverted SSN by about eight 27-day Bartels rotations on average, but the delay varies greatly with the 22-year cycle, being shorter or longer around positive A+ or negative A- solar polarity epochs, respectively. The 22-year cyclicity of the time lag is determined by the global heliospheric drift effects, in agreement with theoretical models. The OSF lags by about one year behind SSN, and is likely determined by a combination of the short lifetime of active regions and a longer (≈3 years) transport time of the surface magnetic field to the poles. GCRs covary nearly in antiphase with the OSF, also depicting a strong 22-year cycle in the delay, confirming that the OSF is a good index of the heliospheric modulation of GCRs. This provides an important observational constraint for solar and heliospheric physics.

Coronal Hole Detection and Open Magnetic Flux

Abstract Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 2010 September 19, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH ≈ 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in situ measurements (by 2.2–4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it.

Active Region Contributions to the Solar Wind over Multiple Solar Cycles

Both coronal holes and active regions are source regions of the solar wind. The distribution of these coronal structures across both space and time is well known, but it is unclear how much each source contributes to the solar wind. In this study we use photospheric magnetic field maps observed over the past four solar cycles to estimate what fraction of magnetic open solar flux is rooted in active regions, a proxy for the fraction of all solar wind originating in active regions. We find that the fractional contribution of active regions to the solar wind varies between 30% to 80% at any one time during solar maximum and is negligible at solar minimum, showing a strong correlation with sunspot number. While active regions are typically confined to latitudes ±30∘ in the corona, the solar wind they produce can reach latitudes up to ±60∘. Their fractional contribution to the solar wind also correlates with coronal mass ejection rate, and is highly variable, changing by ±20% on monthly timescales within individual solar maxima. We speculate that these variations could be driven by coronal mass ejections causing reconfigurations of the coronal magnetic field on sub-monthly timescales.

Solar cyclic activity over the last millennium reconstructed from annual 14C data

Aims. The 11-year solar cycle (Schwabe cycle) is the dominant pattern of solar magnetic activity reflecting the oscillatory dynamo mechanism in the Sun’s convection zone. Solar cycles have been directly observed since 1700, while indirect proxy data suggest their existence over a much longer period of time, but generally without resolving individual cycles and their continuity. Here we reconstruct individual solar cycles for the last millennium using recently obtained 14C data and state-of-the-art models. Methods. Starting with the 14C production rate determined from the so far most precise measurements of radiocarbon content in tree rings, solar activity was reconstructed in the following three physics-based steps: (1) correction of the 14C production rate for the changing geomagnetic field; (2) computation of the open solar magnetic flux; and (3) conversion into sunspot numbers outside of grand minima. All known uncertainties, including both measurement and model uncertainties, were straightforwardly accounted for by a Monte-Carlo method. Results. Cyclic solar activity is reconstructed for the period 971–1900 (85 individual cycles) along with its uncertainties. This more than doubles the number of solar cycles known from direct solar observations. We found that the lengths and strengths of well-defined cycles outside grand minima are consistent with those obtained from the direct sunspot observations after 1750. The validity of the Waldmeier rule (cycles with fast-rising phase tend to be stronger) is confirmed at a highly significant level. Solar activity is found to be in a deep grand minimum when the activity is mostly below the sunspot formation threshold for about 250 years. Therefore, although considerable cyclic variability in 14C is seen even during grand minima, individual solar cycles can hardly be reliably resolved therein. Three potential solar particle events, ca. 994, 1052, and 1279 AD, are shown to occur around the maximum phases of solar cycles. Conclusions. A new approximately 1000-year-long solar activity reconstruction, in the form of annual (pseudo) sunspot numbers with the full assessment of all known uncertainties, is presented based on new high-precision Δ14C measurements and state-of-the-art models, more than doubling the number of individually resolved solar cycles. This forms a solid basis for new, more detailed studies of solar variability.

The Solar Corona during the Total Eclipse on 1806 June 16: Graphical Evidence of the Coronal Structure during the Dalton Minimum

Abstract Visible coronal structure, in particular the spatial evolution of coronal streamers, provides indirect information about solar magnetic activity and the underlying solar dynamo. Their apparent absence of structure observed during the total eclipses throughout the Maunder minimum has been interpreted as evidence of a significant change in the solar magnetic field from that during modern solar cycles. Eclipse observations available from the more recent Dalton minimum may be able to provide further information, with sunspot activity being between the levels seen during recent solar cycles and in the Maunder minimum. Here, we show and examine two graphical records of the total solar eclipse on 1806 June 16, during the Dalton minimum. These records show significant rays and streamers around an inner ring. The ring is estimated to be ≈0.44 R ⊙ in width and the streamers in excess of 11.88 R ⊙ in length. In combination with records of spicules or prominences, these eclipse records visually contrast the Dalton minimum with the Maunder minimum in terms of their coronal structure and support the existing discussions based on the sunspot observations. These eclipse records are broadly consistent with the solar cycle phase in the modeled open solar flux and the reconstructed slow solar wind at most latitudes.

Flux Erosion of Magnetic Clouds by Reconnection With the Sun's Open Flux

AbstractMagnetic clouds (MCs) are flux rope magnetic structures forming a subset of solar coronal mass ejections, which have significant space weather impacts. The geoeffectiveness of MCs depends on their properties, which evolve during their interplanetary passage. Based on an analysis of observations spanning two solar cycles, we establish that MCs interacting with the ambient solar wind magnetic field (i.e., heliospheric open flux) lose a substantial amount of their initial magnetic flux via magnetic reconnection, which, in some cases, reduce their geoeffectiveness. We find a linear correlation between the eroded flux of MCs and solar open flux which is consistent with the scenario that MC erosion is mediated via the local heliospheric magnetic field draping around an MC during its interplanetary propagation. The solar open flux is governed by the sunspot cycle. This work therefore uncovers a hitherto unknown pathway for solar cycle modulation of the properties of MCs.

Signatures of Coronal Loop Opening via Interchange Reconnection in the Slow Solar Wind at 1 AU

The opening of closed magnetic loops via reconnection with open solar flux, so called “interchange reconnection”, is invoked in a number of models of slow solar wind release. In the heliosphere, this is expected to result in local switchbacks or inversions in heliospheric magnetic flux (HMF). When observed at 1 AU, inverted HMF has previously been shown to exhibit high ion charge states, suggestive of hot coronal loops, and to map to the locations of coronal magnetic separatrices. However, simulations show that inverted HMF produced directly by reconnection in the low corona is unlikely to survive to 1 AU without the amplification by solar wind speed shear. By considering the surrounding solar wind, we show that inverted HMF is preferably associated with regions of solar wind shear at 1 AU. Compared with the surrounding solar wind, inverted HMF intervals have lower magnetic field intensity and show intermediate speed and density values between the faster, more tenuous wind ahead and the slower, denser wind behind. There is no coherent signature in iron charge states, but oxygen and carbon charge states within the inverted HMF are in agreement with the higher values in the slow wind behind. Conversely, the iron-to-oxygen abundance ratio is in better agreement with the lower values in the solar wind ahead, while the alpha-to-proton abundance ratio shows no variation. One possible explanation for these observations is that the interchange reconnection (and subsequent solar wind shear) that is responsible for generation of inverted HMF involves very small, quiet-Sun loops of approximately photospheric composition, which are impulsively heated in the low corona, rather than large-scale active region loops with enhanced first-ionisation potential elements. Whether signatures of such small loops could be detected in situ at 1 AU still remains to be determined.

On Solutions of the PFSS Model With GONG Synoptic Maps for 2006–2018

AbstractThe potential field source surface (PFSS) model is widely used to derive the magnetic field of the solar corona. The only free parameter in the PFSS model is the radius of the so‐called source surface, where magnetic field lines are forced to open. The radius of this surface is typically set to 2.5 solar radii in research and operational PFSS numerical models. Here, using Global Oscillation Network Group (GONG) synoptic maps of the photospheric field, solutions of the PFSS model for various heights of the source surface are investigated for 2006–2018. In particular, numerically derived open solar magnetic flux and coronal holes are examined. Solutions of the PFSS model based on GONG synoptic maps are particularly important since they are often used to drive operational space weather forecast models. Comparisons between observations and numerical results in this paper suggest that the radius of the source surface is significantly lower than 2.5 solar radii during the active phase of solar cycle 24. The fact that the source surface location depends on the solar activity suggests that relations which associate solar wind properties with the coronal magnetic field in the PFSS‐based solar wind modes should be revisited. Furthermore, although the correction of the polar magnetic field is part of GONG synoptic map production pipeline, the results suggest that better treatment of polar fields is needed to cover observational gaps. The issue with the polar fields in GONG maps is particularly pronounced in recent years.

Evolution of Large‐Scale Magnetic Fields From Near‐Earth Space During the Last 11 Solar Cycles

AbstractWe use hourly mean magnetic field measurements from 34 midlatitude geomagnetic observatories between 1900 and 2015 to investigate the long‐term evolution and driving mechanism of the large‐scale external magnetic field at ground. The Hourly Magnetospheric Currents index (HMC) is derived as a refinement of the Annual Magnetospheric Currents index (HMC, Pick & Korte, 2017, https://doi.org/10.1093/gji/ggx367). HMC requires an extensive revision of the observatory hourly means. It depends on three third party geomagnetic field models used to eliminate the core, the crustal, and the ionospheric solar‐quiet field contributions. We mitigate the dependency of HMC on the core field model by subtracting only nondipolar components of the model from the data. The separation of the residual (dipolar) signal into internal and external (HMC) parts is the main methodological challenge. Observatory crustal biases are updated with respect to AMC, and the solar‐quiet field estimation is extended to the past based on a reconstruction of solar radio flux (F10.7). We find that HMC has more power at low frequencies (periods ≥ 1 year) than the Dcx index, especially at periods relevant to the solar cycle. Most of the slow variations in HMC can be explained by the open solar magnetic flux. There is a weakly decreasing linear trend in absolute HMC from 1900 to present, which depends sensitively on the data rejection criteria at early years. HMC is well suited for studying long‐term variations of the geomagnetic field.

Sunward Strahl: A Method to Unambiguously Determine Open Solar Flux from In Situ Spacecraft Measurements Using Suprathermal Electron Data

AbstractA fraction of the magnetic flux which threads the photosphere reaches sufficient coronal altitude to be dragged out by the solar wind and form the heliospheric magnetic field (HMF). Directly measuring this “open solar flux” (OSF) component, however, is difficult. While OSF can be extrapolated from photospheric magnetic field measurements, the most direct method is from in situ spacecraft measurements of the HMF. The difficultly is unambiguously distinguishing between HMF which connects directly back to the Sun (the OSF) and that which is locally distorted by waves, turbulence, and near‐Sun reconnection. Suitable temporal filtering of the data can remove such “noise,” but the level of filtering cannot be known a priori and varies with solar cycle, solar wind types, etc. Here we use the suprathermal electron beam, or “strahl,” to distinguish between different HMF topologies. As strahl moves antisunward on global scales, times when strahl is observed to be moving sunward indicate that the HMF is locally inverted. By subtracting the inverted HMF, we compute the OSF without need for arbitrary filtering of the data. We find that the OSF obtained in this manner is slightly larger than the proposed “kinematic correction” based on observed solar wind velocity structure, though in general agreement. Our new OSF estimate agrees with methods based wholly on HMF data, if the data are first used to compute approximately 1 day averages during solar minimum and approximately 3 day averages during solar maximum, stressing the point that the filter method is unreliable because the required characteristics vary.

Coronal and heliospheric magnetic flux circulation and its relation to open solar flux evolution.

Solar cycle 24 is notable for three features that can be found in previous cycles but which have been unusually prominent: (1) sunspot activity was considerably greater in the northern/southern hemisphere during the rising/declining phase; (2) accumulation of open solar flux (OSF) during the rising phase was modest, but rapid in the early declining phase; (3) the heliospheric current sheet (HCS) tilt showed large fluctuations. We show that these features had a major influence on the progression of the cycle. All flux emergence causes a rise then a fall in OSF, but only OSF with foot points in opposing hemispheres progresses the solar cycle via the evolution of the polar fields. Emergence in one hemisphere, or symmetric emergence without some form of foot point exchange across the heliographic equator, causes poleward migrating fields of both polarities in one or both (respectively) hemispheres which temporarily enhance OSF but do not advance the polar field cycle. The heliospheric field observed near Mercury and Earth reflects the asymmetries in emergence. Using magnetograms, we find evidence that the poleward magnetic flux transport (of both polarities) is modulated by the HCS tilt, revealing an effect on OSF loss rate. The declining phase rise in OSF was caused by strong emergence in the southern hemisphere with an anomalously low HCS tilt. This implies the recent fall in the southern polar field will be sustained and that the peak OSF has limited implications for the polar field at the next sunspot minimum and hence for the amplitude of cycle 25.