Abstract

A Hale cycle, one complete magnetic cycle of the Sun, spans two complete Schwabe cycles (also referred to as sunspot and, more generally, solar cycles). The approximately 22-year Hale cycle is seen in magnetic polarities of both sunspots and polar fields, as well as in the intensity of galactic cosmic rays reaching Earth, with odd- and even-numbered solar cycles displaying qualitatively different waveforms. Correct numbering of solar cycles also underpins empirical cycle-to-cycle relations which are used as first-order tests of stellar dynamo models. There has been much debate about whether the unusually long solar cycle 4 (SC4), spanning 1784–1799, was actually two shorter solar cycles combined as a result of poor data coverage in the original Wolf sunspot number record. Indeed, the group sunspot number does show a small increase around 1794–1799 and there is evidence of an increase in the mean latitude of sunspots at this time, suggesting the existence of a cycle “4b”. In this study, we use cosmogenic radionuclide data and associated reconstructions of the heliospheric magnetic field (HMF) to show that the Hale cycle has persisted over the last 300 years and that data prior to 1800 are more consistent with cycle 4 being a single long cycle (the “no SC4b” scenario). We also investigate the effect of cycle 4b on the HMF using an open solar flux (OSF) continuity model, in which the OSF source term is related to sunspot number and the OSF loss term is determined by the heliospheric current sheet tilt, assumed to be a simple function of solar cycle phase. The results are surprising; Without SC4b, the HMF shows two distinct peaks in the 1784–1799 interval, while the addition of SC4b removes the secondary peak, as the OSF loss term acts in opposition to the later rise in sunspot number. The timing and magnitude of the main SC4 HMF peak is also significantly changed by the addition of SC4b. These results are compared with the cosmogenic isotope reconstructions of HMF and historical aurora records. These data marginally favour the existence of SC4b (the “SC4b” scenario), though the result is less certain than that based on the persistence of the Hale cycle. Thus while the current uncertainties in the observations preclude any definitive conclusions, the data favour the “no SC4b” scenario. Future improvements to cosmogenic isotope reconstructions of the HMF, through either improved modelling or additional ice cores from well-separated geographic locations, may enable questions of the existence of SC4b and the phase of Hale cycle prior to the Maunder minimum to be settled conclusively.

Highlights

  • Solar magnetic activity varies over a huge range of time scales, from seconds to millennia

  • We investigate the effect of cycle 4b on the heliospheric magnetic field (HMF) using an open solar flux (OSF) continuity model, in which the OSF source term is related to sunspot number and the OSF loss term is determined by the heliospheric current sheet tilt, assumed to be a simple function of solar cycle phase

  • That the relation between galactic cosmic rays (GCRs) intensity at Earth and sunspot number is not a direct one: GCRs are modulated by the total open solar flux (OSF) and structure within heliospheric magnetic field (HMF) (Usoskin 2013), which is related to sunspot number in a non-linear manner

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Summary

Introduction

Solar magnetic activity varies over a huge range of time scales, from seconds to millennia. Isotope abundance is consistent (or at least, not inconsistent) with the existence of SC4b (Usoskin et al 2001, 2002; Karoff et al 2014) It should be noted, that the relation between GCR intensity at Earth and sunspot number is not a direct one: GCRs are modulated by the total open solar flux (OSF) and structure within heliospheric magnetic field (HMF) (Usoskin 2013), which is related to sunspot number in a non-linear manner. The GCR intensity immediately prior to solar minimum at the end of odd-numbered solar cycles displays ‘‘peaked’’ temporal variations, while it is ‘‘domed’’ prior to even-numbered cycles (Potgieter & Moraal 1985) This behaviour is primarily attributed to differing GCR drift patterns (Jokipii et al 1977), though 22-year variations in the heliospheric magnetic field may have an effect (Cliver & Ling 2001; Rouillard & Lockwood 2004; Thomas et al 2013). The addition of solar cycle 4b has an effect on the HMF through the OSF loss rate, even though the sunspot number is unchanged

Heliospheric Hale cycle variations
Reconstructing the heliospheric magnetic field
Summary and discussion
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