Open Solar Flux Research Articles

Solar Forcing of Climate

Solar activity is evident both in the equatorial activity centres and in the polar magnetic field variations. The total solar irradiance variation is due to the former component. During the extraordinarily long minimum of activity between sunspot cycles 23 and 24, the variations related to the equatorial field components reached their minimum values in the first half of 2008, while those related to the polar field variations had their extreme values rather at the end of 2009 and the first half of 2010. The explanation of this delay is another challenge for dynamo theories. The role of the open solar flux has so far been grossly underestimated in discussions of Sun-climate relations. The gradual increase in the average terrestrial ground temperature since 1610 is related both to the equatorial and polar field variations. The main component (0.077 K/century) is due to the variation of the total solar irradiance. The second component (0.040 K/century) waits for an explanation. The smoothed residual increase, presumably antropogenic, obtained after subtraction of the known components from the total increase was 0.31 K in 1999.

Cyclic loss of open solar flux since 1868: The link to heliospheric current sheet tilt and implications for the Maunder Minimum

Open solar flux (OSF) variations can be described by the imbalance between source and loss terms. We use spacecraft and geomagnetic observations of OSF from 1868 to present and assume the OSF source, S, varies with the observed sunspot number, R. Computing the required fractional OSF loss, χ, reveals a clear solar cycle variation, in approximate phase with R. While peak R varies significantly from cycle to cycle, χ is surprisingly constant in both amplitude and waveform. Comparisons of χ with measures of heliospheric current sheet (HCS) orientation reveal a strong correlation. The cyclic nature of χ is exploited to reconstruct OSF back to the start of sunspot records in 1610. This agrees well with the available spacecraft, geomagnetic, and cosmogenic isotope observations. Assuming S is proportional to R yields near‐zero OSF throughout the Maunder Minimum. However, χ becomes negative during periods of low R, particularly the most recent solar minimum, meaning OSF production is underestimated. This is related to continued coronal mass ejection (CME) activity, and therefore OSF production, throughout solar minimum, despite R falling to zero. Correcting S for this produces a better match to the recent solar minimum OSF observations. It also results in a cycling, nonzero OSF during the Maunder Minimum, in agreement with cosmogenic isotope observations. These results suggest that during the Maunder Minimum, HCS tilt cycled as over recent solar cycles, and the CME rate was roughly constant at the levels measured during the most recent two solar minima.

How is open solar magnetic flux lost over the solar cycle?

[1] The Sun's open magnetic field, magnetic flux dragged out into the heliosphere by the solar wind, varies by approximately a factor of 2 over the solar cycle. We consider the evolution of open solar flux in terms of a source and loss term. Open solar flux creation is likely to proceed at a rate dependent on the rate of photospheric flux emergence, which can be roughly parameterized by sunspot number or coronal mass ejection rate, when available. The open solar flux loss term is more difficult to relate to an observable parameter. The supersonic nature of the solar wind means open solar flux can only be removed by near-Sun magnetic reconnection between open solar magnetic field lines, be they open or closed heliospheric field lines. In this study we reconstruct open solar flux over the last three solar cycles and demonstrate that the loss term may be related to the degree to which the heliospheric current sheet (HCS) is warped, i.e., locally tilted from the solar rotation direction. This can account for both the large dip in open solar flux at the time of sunspot maximum as well as the asymmetry in open solar flux during the rising and declining phases of the solar cycle. The observed cycle-to-cycle variability is also well matched. Following Sheeley et al. (2001), we attribute modulation of open solar flux by the degree of warp of the HCS to the rate at which opposite polarity open solar flux is brought together by differential rotation.

Centennial changes in the heliospheric magnetic field and open solar flux: The consensus view from geomagnetic data and cosmogenic isotopes and its implications

Received 17 October 2010; revised 12 January 2011; accepted 21 January 2011; published 21 April 2011. [1] Svalgaard and Cliver (2010) recently reported a consensus between the various reconstructions of the heliospheric field over recent centuries. This is a significant development because, individually, each has uncertainties introduced by instrument calibration drifts, limited numbers of observatories, and the strength of the correlations employed. However, taken collectively, a consistent picture is emerging. We here show that this consensus extends to more data sets and methods than reported by Svalgaard and Cliver,includingthatusedbyLockwoodetal.(1999),whentheiralgorithmisusedtopredict theheliosphericfieldratherthantheopensolarflux.Oneareawherethereisstillsomedebate relates to the existence and meaning of a floor value to the heliospheric field. From cosmogenic isotope abundances, Steinhilber et al. (2010) have recently deduced that the near‐Earth IMF at the end of the Maunder minimum was 1.80 ± 0.59 nT which is considerably lower than the revised floor of 4nT proposed by Svalgaard and Cliver. We here combine cosmogenic and geomagnetic reconstructions and modern observations (with allowance for the effect of solar wind speed and structure on the near‐Earth data) to derive an estimate for the open solar flux of (0.48 ± 0.29) × 10 14 Wb at the end of the Maunder minimum. By way of comparison, the largest and smallest annual means recorded by instruments in space between 1965 and 2010 are 5.75 × 10 14 Wb and 1.37 × 10 14 Wb, respectively, set in 1982 and 2009, and the maximum of the 11 year running means was 4.38 × 10 14 Wb in 1986. Hence the average open solar flux during the Maunder minimum is found to have been 11% of its peak value during the recent grand solar maximum.

In Situ Signatures of Interchange Reconnection between Magnetic Clouds and Open Magnetic Fields: A Mechanism for the Erosion of Polar Coronal Holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995 – 2007), we show that the time of disappearance of the northern polar coronal hole (1998 – 1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.

The Floor in the Solar Wind Magnetic Field Revisited

Svalgaard and Cliver (Astrophys. J. Lett.661, L203, 2007) proposed that the solar-wind magnetic-field strength [B] at Earth has a “floor” value of ≈4.6 nT in yearly averages, which is approached but not broached at solar minima. They attributed the floor to a constant baseline solar open flux. In both 2008 and 2009, the notion of such a floor was undercut by annual B averages of ≈4 nT. Here we present a revised view of both the level and the concept of the floor. Two independent correlations indicate that B has a floor of ≈2.8 nT in yearly averages. These are i) a relationship between solar polar-field strength and yearly averages of B for the last four 11-year minima (BMIN), and ii) a precursor relationship between peak sunspot number for cycles 14 – 23 and BMIN at their preceding minima. These correlations suggest that at 11-year minima, B consists of i) a floor of ≈2.8 nT, and ii) a component primarily due to the solar polar fields that varies from ≈0 nT to ≈3 nT. The solar polar fields provide the “seed” for the subsequent sunspot maximum. Removing the ≈2.8 nT floor from BMIN brings the percentage decrease in B between the 1996 and 2009 minima into agreement with the corresponding decrease in solar polar-field strength. Based on a decomposition of the solar wind (from 1972 – 2009) into high-speed streams, coronal mass ejections, and slow solar wind, we suggest that the source of the floor in B is the slow solar wind. During 2009, Earth was in slow solar-wind flows ≈70% of the time. We propose that the floor corresponds to a baseline (non-cyclic or ground state) open solar flux of ≈8×1013 Wb, which originates in persistent small-scale (supergranular and granular) field.

Enhanced signature of solar variability in Eurasian winter climate

We demonstrate that open solar flux (Fs, derivable from geomagnetic data) exhibits stronger correlations with atmospheric circulation variations than conventionally‐used measures of solar activity. The circulation anomalies are particularly enhanced over the North Atlantic/Eurasian sector, where there are large changes in the occurrence of blocking and the winter mean surface temperature differs by several degrees between high‐ and low‐solar terciles. The relationship is stronger and simpler for Fs, being more linear between high‐ and low‐solar winters. While the circulation anomalies strongly resemble the North Atlantic Oscillation they also extend deeper into Eurasia, especially in high‐solar conditions. This distinct signature may be useful for the detection and attribution of observed changes and also the identification of dynamical mechanisms.

On the long-term variability of the heliosphere–magnetosphere environment

Annual means of measured and reconstructed solar, heliospheric, and magnetospheric parameters are used to infer solar activity signatures at the Hale and Gleissberg cycles timescales. Available open solar flux, modulation strength, cosmic ray flux, total solar irradiance data, reconstructed back to 1700, solar wind parameters (speed and density) and the magnitude of the heliospheric magnetic field at 1 AU, reconstructed back to 1870, as well as the time series of geomagnetic activity indices ( aa, IDV, IHV), going back to 1870, have been considered. Simple filtering procedures (successive 11-, 22-, and 88-year running averages and differences between them) and scaling by the standard deviation from the average value for the common interval covered by the data show that the long-discussed variation in the 20th century (a pronounced increase since ∼1900, followed by a depression in the ‘60s and a new, slower, increase) seen in the 11-year averages of parameters such as geomagnetic activity indices and reconstructed heliospheric magnetic field strength, solar wind speed, open solar flux, is a result of the superposition in data of solar activity signatures at Hale and Gleissberg cycles timescales. The Hale and Gleissberg signals were characterized and similarities and differences in the temporal behavior of the analyzed parameters at these timescales are discussed. The similarities in the studied parameters point to a common pacing source, the solar dynamo.

Interplanetary magnetic field during the past 9300 years inferred from cosmogenic radionuclides

We have reconstructed the interplanetary magnetic field (IMF), its radial component, and the open solar magnetic flux using the solar modulation potential derived from cosmogenic 10Be radionuclide data for a period covering the past 9300 years. Reconstructions using the assumption of both constant and variable solar wind speeds yielded closely similar results. During the Maunder Minimum, the strength of the IMF was approximately 2 nT compared to a mean value of 6.6 nT for the past 40 years, corresponding to an increase of the open solar magnetic flux of about 350%. We examine four cycles of the Hallstatt periodicity in the IMF with a mean period of ∼2250 years and an amplitude of ∼0.75 nT. Grand solar minima have largely occurred in clusters during the Hallstatt cycle minima around the years −5300, −3400, −1100, and +1500 A.D. The last cluster includes the Dalton, Maunder, and Spörer minima. We predict that the next such cluster will occur in about 1500 years. The long‐term IMF has varied between ∼2 nT and ∼8 nT and does not confirm a proposed floor (lower limit). There is a slowly changing long‐term trend of amplitude 1.5 nT, with a minimum around the year −4600 and a maximum around 0 A.D. that may be of solar origin but which also may be due to unknown long‐term changes in the atmospheric effects or geomagnetic field intensity.

Climate proxies for recent fjord sediments in the inner Sognefjord region, western Norway

Abstract Three high-resolution sediment cores from the periodically anoxic Inner Barsnesfjord and the oxic Outer Barsnesfjord and Sogndalsfjord, Western Norway, are analysed for signals of climate variation. Sedimentation rates are 0.85, 0.75 and 0.45 cm a −1 , respectively. Sediment slices are taken of 0.3–0.5 cm thickness revealing annual resolution. Corresponding peaks of mineral clay particles, total organic matter and freshwater diatoms correlate well with maxima in regional precipitation, temperature and cloud cover over the last 20 years. This regional climate record is also correlated to the wider NAO (North Atlantic Oscillation) winter index, northern hemisphere temperature and solar activity (cosmic rays and open solar flux) based on 60 years of continuous observation. There is a strong indication that the fjord sediment record contains a climate archive spanning the last 20–100 a; it is suggested that these proxies might also work on longer timescales. A simple box model is presented describing the use of the sediment record for the interpretation of climate variability on a regional scale and at a longer timescale on a millennium scale. It is predicted that this model can be transferred to sediment settings of similar regional climate influence.

Excess open solar magnetic flux from satellite data: 2. A survey of kinematic effects

We investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the kinematic effect on these open solar flux estimates of large‐scale longitudinal structure in the solar wind flow, with particular emphasis on correcting estimates made using data from near‐Earth satellites. We show that scatter, but no net bias, is introduced by the kinematic “bunching effect” on sampling and that this is true for both compression and rarefaction regions. The observed flux excesses, as a function of heliocentric distance, are shown to be consistent with open solar flux estimates from solar magnetograms made using the potential field source surface method and are well explained by the kinematic effect of solar wind speed variations on the frozen‐in heliospheric field. Applying this kinematic correction to the Omni‐2 interplanetary data set shows that the open solar flux at solar minimum fell from an annual mean of 3.82 × 1016 Wb in 1987 to close to half that value (1.98 × 1016 Wb) in 2007, making the fall in the minimum value over the last two solar cycles considerably faster than the rise inferred from geomagnetic activity observations over four solar cycles in the first half of the 20th century.

Excess open solar magnetic flux from satellite data: 1. Analysis of the third perihelion Ulysses pass

We use the third perihelion pass by the Ulysses spacecraft to illustrate and investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the potential effects of small‐scale structure in the heliospheric field (giving fluctuations in the radial component on timescales smaller than 1 h) and kinematic time‐of‐flight effects of longitudinal structure in the solar wind flow. We show that the flux excess is explained by neither very small‐scale structure (timescales < 1 h) nor by the kinematic “bunching effect” on spacecraft sampling. The observed flux excesses is, however, well explained by the kinematic effect of larger‐scale (>1 day) solar wind speed variations on the frozen‐in heliospheric field. We show that averaging over an interval T (that is long enough to eliminate structure originating in the heliosphere yet small enough to avoid cancelling opposite polarity radial field that originates from genuine sector structure in the coronal source field) is only an approximately valid way of allowing for these effects and does not adequately explain or account for differences between the streamer belt and the polar coronal holes.

THE ACCURACY OF USING THEULYSSESRESULT OF THE SPATIAL INVARIANCE OF THE RADIAL HELIOSPHERIC FIELD TO COMPUTE THE OPEN SOLAR FLUX

We survey observations of the radial magnetic field in the heliosphere as a function of position, sunspot number, and sunspot cycle phase. We show that most of the differences between pairs of simultaneous observations, normalized using the square of the heliocentric distance and averaged over solar rotations, are consistent with the kinematic effect whereby the radial component of the frozen-in heliospheric field is increased by longitudinal solar wind speed structure. In particular, the survey shows that, as expected, the flux excess effect at high latitudes is almost completely absent during sunspot minimum but is almost the same as within the streamer belt at sunspot maximum. We study the uncertainty inherent in the use of the Ulysses result that the radial field is independent of heliographic latitude in the computation of the total open solar flux: we show that after the kinematic correction for the excess flux effect has been made it causes errors that are smaller than 4.5%, with a most likely value of 2.5%. The importance of this result for understanding temporal evolution of the open solar flux is reviewed.

THE RISE AND FALL OF OPEN SOLAR FLUX DURING THE CURRENT GRAND SOLAR MAXIMUM

We use geomagnetic activity data to study the rise and fall over the past century of the solar wind flow speed V SW, the interplanetary magnetic field strength B, and the open solar flux F S. Our estimates include allowance for the kinematic effect of longitudinal structure in the solar wind flow speed. As well as solar cycle variations, all three parameters show a long-term rise during the first half of the 20th century followed by peaks around 1955 and 1986 and then a recent decline. Cosmogenic isotope data reveal that this constitutes a grand maximum of solar activity which began in 1920, using the definition that such grand maxima are when 25-year averages of the heliospheric modulation potential exceeds 600 MV. Extrapolating the linear declines seen in all three parameters since 1985, yields predictions that the grand maximum will end in the years 2013, 2014, or 2027 using V SW, F S, or B, respectively. These estimates are consistent with predictions based on the probability distribution of the durations of past grand solar maxima seen in cosmogenic isotope data. The data contradict any suggestions of a floor to the open solar flux: we show that the solar minimum open solar flux, kinematically corrected to allow for the excess flux effect, has halved over the past two solar cycles.

A potential lag between the open solar magnetic source flux and solar EUV and X-ray emissions as measured by the Earth's ionosphere during total solar eclipses

Abstract. Measurements of the ionospheric E-region during total solar eclipses have been used to provide information about the evolution of the solar magnetic field and EUV and X-ray emissions from the solar corona and chromosphere. By measuring levels of ionisation during an eclipse and comparing these measurements with an estimate of the unperturbed ionisation levels (such as those made during a control day, where available) it is possible to estimate the percentage of ionising radiation being emitted by the solar corona and chromosphere. Previously unpublished data from the two eclipses presented here are particularly valuable as they provide information that supplements the data published to date. The eclipse of 23 October 1976 over Australia provides information in a data gap that would otherwise have spanned the years 1966 to 1991. The eclipse of 4 December 2002 over Southern Africa is important as it extends the published sequence of measurements. Comparing measurements from eclipses between 1932 and 2002 with the solar magnetic source flux reveals that changes in the solar EUV and X-ray flux lag the open source flux measurements by approximately 1.5 years. We suggest that this unexpected result comes about from changes to the relative size of the limb corona between eclipses, with the lag representing the time taken to populate the coronal field with plasma hot enough to emit the EUV and X-rays ionising our atmosphere.

Conservation of open solar magnetic flux and the floor in the heliospheric magnetic field

The near‐Earth heliospheric magnetic field intensity, |B|, exhibits a strong solar cycle variation, but returns to the same “floor” value each solar minimum. The current minimum, however, has seen |B| drop below previous minima, bringing in to question the existence of a floor, or at the very least requiring a re‐assessment of its value. In this study we assume heliospheric flux consists of a constant open flux component and a time‐varying contribution from CMEs. In this scenario, the true floor is |B| with zero CME contribution. Using observed CME rates over the solar cycle, we estimate the “no‐CME” |B| floor at ∼4.0 ± 0.3 nT, lower than previous floor estimates and below |B| observed this solar minimum. We speculate that the drop in |B| observed this minimum may be due to a persistently lower CME rate than the previous minimum, though there are large uncertainties in the supporting observational data.

An Alternative Interpretation of the Relationship between the Inferred Open Solar Flux and the Interplanetary Magnetic Field

Photospheric observations at the Wilcox Solar Observatory (WSO) represent an uninterrupted data set of 32 years and are therefore unique for modeling variations in the magnetic structure of the corona and inner heliosphere over three solar cycles. For many years, modelers have applied a latitudinal correction factor to these data, believing that it provided a better estimate of the line-of-sight magnetic field. Its application was defended by arguing that the computed open flux matched observations of the interplanetary magnetic field (IMF) significantly better than the original WSO correction factor. However, no physically based argument could be made for its use. In this Letter we explore the implications of using the constant correction factor on the value and variation of the computed open solar flux and its relationship to the measured IMF. We find that it does not match the measured IMF at 1 AU except at and surrounding solar minimum. However, we argue that interplanetary coronal mass ejections (ICMEs) may provide sufficient additional magnetic flux to the extent that a remarkably good match is found between the sum of the computed open flux and inferred ICME flux and the measured flux at 1 AU. If further substantiated, the implications of this interpretation may be significant, including a better understanding of the structure and strength of the coronal field and I N providing constraints for theories of field line transport in the corona, the modulation of galactic cosmic rays, and even possibly terrestrial climate effects.

Centennial changes in the solar wind speed and in the open solar flux

We use combinations of geomagnetic indices, based on both variation range and hourly means, to derive the solar wind flow speed, the interplanetary magnetic field strength at 1 AU and the total open solar flux between 1895 and the present. We analyze the effects of the regression procedure and geomagnetic indices used by adopting four analysis methods. These give a mean interplanetary magnetic field strength increase of 45.1 ± 4.5% between 1903 and 1956, associated with a 14.4 ± 0.7% rise in the solar wind speed. We use averaging timescales of 1 and 2 days to allow for the difference between the magnetic fluxes threading the coronal source surface and the heliocentric sphere at 1 AU. The largest uncertainties originate from the choice of regression procedure: the average of all eight estimates of the rise in open solar flux is 73.0 ± 5.0%, but the best procedure, giving the narrowest and most symmetric distribution of fit residuals, yields 87.3 ± 3.9%.

Role of coronal mass ejections in the heliospheric Hale cycle

The 11‐year solar cycle variation in the heliospheric magnetic field strength can be explained by the temporary buildup of closed flux released by coronal mass ejections (CMEs). If this explanation is correct, and the total open magnetic flux is conserved, then the interplanetary‐CME closed flux must eventually open via reconnection with open flux close to the Sun. In this case each CME will move the reconnected open flux by at least the CME footpoint separation distance. Since the polarity of CME footpoints tends to follow a pattern similar to the Hale cycle of sunspot polarity, repeated CME eruption and subsequent reconnection will naturally result in latitudinal transport of open solar flux. We demonstrate how this process can reverse the coronal and heliospheric fields, and we calculate that the amount of flux involved is sufficient to accomplish the reversal within the 11 years of the solar cycle.

Centennial changes in solar activity and the response of galactic cosmic rays

There is a growing consensus that the eleven year-modulation of galactic cosmic rays (GCRs) resulting from solar activity is related to interplanetary propagating diffusive barriers (PDBs). The source of these PDBs is not well understood and numerical models describing GCR modulation simulate their effect by scaling the diffusion tensor to the interplanetary magnetic field strength (IMF). The implications of a century-scale change in solar wind speed and open solar flux, for numerical modelling of GCR modulation and the reconstruction of GCR variations over the last hundred years are discussed. The dominant role of the solar non-axisymmetric magnetic field in both forcing longitudinal solar wind speed fluctuations at solar maximum and in increasing the IMF is discussed in the context of a long-term rise in the open solar magnetic flux.