Solar Dipole Moment Research Articles

Algebraic quantification of an active region contribution to the solar cycle

Context. The solar dipole moment at cycle minimum is considered to be the most reliable precursor with which to determine the amplitude of the subsequent cycle. Numerical simulations of the surface flux transport (SFT) model are widely used to effectively predict the dipole moment at cycle minimum. An algebraic method was recently proposed to quickly predict the contribution of an active region (AR) to the axial dipole moment at cycle minimum instead of SFT simulations. The method assumes a bipolar magnetic region (BMR) configuration of ARs, however most ARs are asymmetric in configuration of opposite polarities, or have more complex configurations. Such ARs evolve significantly differently from those of BMR approximations. Aims. We propose a generalized algebraic method to describe the axial dipole contribution of an AR with an arbitrary configuration, and evaluate its effectiveness compared to the BMR-based method. Methods. We employ mathematical deductions to obtain the generalized method. We compare the results of the generalized method with SFT simulations of observed ARs, artificially created BMRs, and ARs with more complex configurations. We also compare the results with those from the BMR-based method. Results. The generalized method is equivalent to the SFT model, and precisely predicts the contributions of ARs to the dipole moment, but has a much higher computational efficiency. Although the BMR-based method has similar computational efficiency to the generalized method, it is only accurate for symmetric bipolar ARs. The BMR-based method systematically overestimates the dipole contributions of asymmetric bipolar ARs, and randomly miscalculates the contributions of more complex ARs. Conclusions. The generalized method provides a quick and precise quantification of the contribution of an AR to solar cycle evolution, which paves the way for application in physics-based solar cycle predictions.

Towards an algebraic method of solar cycle prediction

An algebraic method for the reconstruction and potentially prediction of the solar dipole moment value at sunspot minimum (known to be a good predictor of the amplitude of the next solar cycle) was suggested in the first paper in this series. The method sums up the ultimate dipole moment contributions of individual active regions in a solar cycle: for this, detailed and reliable input data would in principle be needed for thousands of active regions in a solar cycle. To reduce the need for detailed input data, here we propose a new active region descriptor called ARDoR (Active Region Degree of Rogueness). In a detailed statistical analysis of a large number of activity cycles simulated with the 2 × 2D dynamo model we demonstrate that ranking active regions by decreasing ARDoR, for a good reproduction of the solar dipole moment at the end of the cycle it is sufficient to consider the top N regions on this list explicitly, where N is a relatively low number, while for the other regions the ARDoR value may be set to zero. For example, with N = 5 the fraction of cycles where the dipole moment is reproduced with an error exceeding ±30% is only 12%, significantly reduced with respect to the case N = 0, i.e. ARDoR set to zero for all active regions, where this fraction is 26%. This indicates that stochastic effects on the intercycle variations of solar activity are dominated by the effect of a low number of large “rogue” active regions, rather than the combined effect of numerous small ARs. The method has a potential for future use in solar cycle prediction.

Impact of rogue active regions on hemispheric asymmetry

The solar dipole moment at activity minimum is a good predictor of the strength of the subsequent solar cycle. Through a systematic analysis using a state-of-the-art 2×2D solar dynamo model, we found that bipolar magnetic regions (BMR) with atypical characteristics can modify the strength of the next cycle via their impact on the buildup of the dipole moment as a sunspot cycle unfolds. In addition to summarizing these results, we present further effects of such “rogue” BMRs. These have the ability to generate hemispheric asymmetry in the subsequent sunspot cycle, since they modify the polar cap flux asymmetry of the ongoing cycle. We found strong correlation between the polar cap flux asymmetry of cycle i and the total pseudo sunspot number asymmetry of cycle i+1. Good correlation also appears in the case of the time lag of the hemispheres of cycle i+1.

How Many Active Regions Are Necessary to Predict the Solar Dipole Moment?

Abstract We test recent claims that the polar field at the end of Cycle 23 was weakened by a small number of large, abnormally oriented regions, and investigate what this means for solar cycle prediction. We isolate the contribution of individual regions from magnetograms for Cycles 21, 22, and 23 using a 2D surface flux transport model, and find that although the top ∼10% of contributors tend to define sudden large variations in the axial dipole moment, the cumulative contribution of many weaker regions cannot be ignored. To recreate the axial dipole moment to a reasonable degree, many more regions are required in Cycle 23 than in Cycles 21 and 22 when ordered by contribution. We suggest that the negative contribution of the most significant regions of Cycle 23 could indeed be a cause of the weak polar field at the following cycle minimum and the low-amplitude Cycle 24. We also examine the relationship between a region’s axial dipole moment contribution and its emergence latitude, flux, and initial axial dipole moment. We find that once the initial dipole moment of a given region has been measured, we can predict the long-term dipole moment contribution using emergence latitude alone.

Long‐term neutron monitor observations and the 2009 cosmic ray maximum

The solar minimum of 2009 was characterized by a prolonged increase toward the maximum cosmic ray intensity, which was higher than it was during the maxima of 22 and 44 years ago. In the previous two so‐called qA <0 (solar dipole moment facing South) magnetic cycles, these increases were more sharply peaked than in 2009. The observations of the Sanae, Hermanus, Potchefstroom, and Tsumeb neutron monitors are used to investigate this behavior in terms of propagation conditions due to solar activity, the heliospheric magnetic field, and the profile of the wavy current sheet in the field. This 2009 cosmic ray maximum can only be understood after an investigation of the long‐term cosmic ray record. This study is augmented by observations of eight other neutron monitors. During 2009, solar activity parameters were significantly different from previous solar minima: The sun was much quieter, and the the heliospheric magnetic field was more than 20% weaker than during other recent minima. Both of these parameters imply a higher cosmic ray diffusion coefficient, which provides a natural explanation for both the higher galactic cosmic ray intensities that were observed and the absence of such an effect for anomalous cosmic rays.

Changes in the Low-Energy Particle Cutoff and Primary Spectrum of Cosmic Radiation

The low-rigidity cutoff for particles in the primary cosmic-ray spectrum has decreased within the period 1948 through 1951. This decrease corresponds to a 3\ifmmode^\circ\else\textdegree\fi{} change (northward) in the "knee" position of the geomagnetic latitude curve for the nucleonic component. The phenomenon is accompanied by both a change in the primary spectrum for particle rigidities less than approximately 4 Bv and by an increase in total primary intensity. The spectral change is such that if the differential primary intensity, $j$, at low rigidities in 1948 was $j=C{(\frac{p}{z})}^{\ensuremath{-}2}$; then the new spectrum for 1951 through 1954 is approximately $j\ensuremath{\approx}{C}^{\ensuremath{'}}{(\frac{p}{z})}^{\ensuremath{-}2.7}$. The total change of intensity arising from the changes in spectrum and low-rigidity cutoff is more than 13%.The measurements were obtained in 1948 and 1951, and have been confirmed and extended in November, 1954 using nucleonic component detectors. The vertical charged particle intensity was also measured and displays changes equivalent to those reported for the nucleonic component.Three regions of space are considered for the location of the mechanism producing the low energy cutoff; namely, the vicinity of the earth, the region of the solar system, and regions of the galaxy outside our solar system. Although the general solar dipole moment is at least an order of magnitude too small to account for the observations, it is concluded that the mechanism is operative within the solar system and is not a terrestrial phenomenon.

Solar Magnetic Moment and Cosmic-Ray Effects Associated with Solar Flares

A close correlation between solar flares and small cosmic-ray intensity increases has recently been established by the Climax, Colorado, neutron monitor data. The correlation, however, is restricted only to those flares which occur when the station lies within a certain interval of local solar time. This has been explained by supposing that the new cosmic-ray particles approach the earth preferentially along the earth-sun line, before deflection in the terrestrial magnetic field takes place. In the present paper, this evidence is used to establish an upper limit to a possible solar magnetic dipole field. Allowance is made for the fact that the dipole field may be seriously perturbed by local fields near the sun; but on the assumption that the dipole field predominates far from the sun (at distances greater than one-fifth the earth-sun distance), the upper limit on the solar dipole moment is 5\ifmmode\times\else\texttimes\fi{}${10}^{32}$ gauss-${\mathrm{cm}}^{3}$.

Cosmic Radiation in the Trapped Orbits of a Solar Magnetic Dipole Field

One of the well-known consequences which would follow from the existence of an appreciable solar magnetic dipole field is a diurnal variation in cosmic-ray intensity at intermediate latitudes on the earth. For the purpose of calculating the expected diurnal effect, it is first necessary to determine the extent to which the bounded orbits of the solar field are filled by the mechanism which has been discussed by Kane, Shanley, and Wheeler: namely, the scattering of cosmic-ray particles into bounded orbits as a result of magnetic deflection in the earth's field. A calculation of this effect is carried out here along the lines indicated by Kane, Shanley, and Wheeler but with several modifications. A solar dipole moment of 6.5\ifmmode\times\else\texttimes\fi{}${10}^{33}$ gauss-${\mathrm{cm}}^{3}$, which is implied by the latitude cutoff at the earth, is adopted for the calculations. The cosmic-ray intensity in the trapped orbits is found to be appreciably smaller than indicated in the earlier calculations. Correspondingly, it is expected that the diurnal effect at the earth will be larger than the currently accepted theoretical values. The apparent experimental absence of the effect, although not conclusive, casts doubt on the existence of a solar dipole field as large as 6.5\ifmmode\times\else\texttimes\fi{}${10}^{33}$ gauss-${\mathrm{cm}}^{3}$. The present work also provides an estimate of the average time which a cosmic-ray particle would spend in the trapping region. The value 5000 years, previously given, is revised downward by an order of magnitude.

The cosmic ray intensity above the atmosphere near the geomagnetic pole

With the help of new high altitude intensity measurements of Meredith, Van Allen and Gottlieb with single Geiger counters near the north geomagnetic pole, an assessment of existing knowledge of the low rigidity end of the primary cosmic ray spectrum is presented. The new Iowa rocket experiments fully confirm and substantially extend previous evidence for the marked flattening of the integral primary cosmic ray spectrum below a magnetic rigidity of about 1.5–109 volts. In particular, they indicate a complete or nearly complete absence of the major components (H, He) of the primary radiation in the following spectral regions: (a) For hydrogen, the magnetic rigidity range 1.2–109 volts to 0.18-109 volts (kinetic energy range 590 MeV to 18 MeV). (b) For helium, the magnetic rigidity range 1.2 · 109 volts to 0.37·109 volts (kinetic energy range 700 MeV to 72 MeV). The low end of these ranges is far below that attainable by any means except rocket-borne apparatus. This observed absence of low rigidity primaries is not inconsistent with a solar dipole moment as large as 0.6–1034 gauss-cm3. But there may be an entirely different physical cause. Due to the low relative abundance of primary nuclei ofZ > 2, the present data are not of sufficient accuracy to conclusively exclude their presence in the low rigidity region of the spectrum. A crucial test of the solar cut-off hypothesis is available in this connection. Preliminary roeket flights of pulse ionization chambers have been made with the intention of investigating the intensities of low rigidity heavy nuclei.

The sun’s magnetic field and the diurnal and seasonal variations in cosmic ray intensity

The diurnal and seasonal variations in the vertical cosmic ray intensity, produced by a solar magnetic dipole field, are calculated at latitudes 0 and 45°, and compared with ‘observed’ data. It appears that the diurnal variation at latitude 45° can be largely accounted for by assuming the existence of a solar dipole of moment 1.1 x 10 34 gauss cm. 3 , a value which is consistent with observational evidence. The diurnal variation at the equator, however, cannot be explained by the hypothesis of a solar magnetic dipole field. The seasonal variation in intensity inferred by the above value for the solar dipole moment is of the same order of magnitude as the observational variation, but shows a phase discrepancy of two months.