The shape of the sunspot cycle

Hathaway, David H.; Wilson, Robert M.; Reichmann, E. J.

doi:10.1007/bf00654090

Cited by 256 publications

(213 citation statements)

References 9 publications

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“…f min , which was not present in the Du model, is an offset which sets the value of cycle minimum. We also tried the quasi-Planck function of Hathaway et al (1994) for this purpose and obtained similar results, however we prefer the above function due to the simplicity of interpreting its parameters and developing heuristics to guide the fit. We fit the model to the data using the Python scipy library curve fit routine with bounds.…”

Section: Cycle Shape Model Fit For Cycle 23mentioning

confidence: 93%

The Mount Wilson Observatory S-Index of the Sun

Egeland

Soon

Baliunas³

et al. 2017

ApJ

108

118

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The most commonly used index of stellar magnetic activity is the instrumental flux scale of singlyionized calcium H & K line core emission, S, developed by the Mount Wilson Observatory (MWO) HK Project, or the derivative index R HK . Accurately placing the Sun on the S scale is important for comparing solar activity to that of the Sun-like stars. We present previously unpublished measurements of the reflected sunlight from the Moon using the second-generation MWO HK photometer during solar cycle 23 and determine cycle minimum S 23,min = 0.1634 ± 0.0008, amplitude ∆S 23 = 0.0143 ± 0.0012, and mean S 23 = 0.1701 ± 0.0005. By establishing a proxy relationship with the closely related National Solar Observatory Sacramento Peak calcium K emission index, itself well-correlated with the Kodaikanal Observatory plage index, we extend the MWO S time series to cover cycles 15-24 and find on average S min = 0.1621 ± 0.0008, ∆S cyc = 0.0145 ± 0.0012, S cyc = 0.1694 ± 0.0005. Our measurements represent an improvement over previous estimates which relied on stellar measurements or solar proxies with non-overlapping time series. We find good agreement from these results with measurements by the Solar-Stellar Spectrograph at Lowell Observatory, an independently calibrated instrument, which gives us additional confidence that we have accurately placed the Sun on the S-index flux scale.

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Section: Cycle Shape Model Fit For Cycle 23mentioning

confidence: 93%

The Mount Wilson Observatory S-Index of the Sun

Egeland

Soon

Baliunas³

et al. 2017

ApJ

108

118

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“…In general, there is good agreement between the two methods. This is because, while solar cycle length can vary considerably, it tends to be a result of short or long declining phases, with rise phases showing much less variability in length (Waldmeier, 1935;Hathaway, Wilson, and Reichmann, 1994;.…”

Section: The 22-year Solar Cycle Variationsmentioning

confidence: 99%

The 22-Year Hale Cycle in Cosmic Ray Flux – Evidence for Direct Heliospheric Modulation

2013

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The ability to predict times of greater galactic cosmic ray (GCR) fluxes is important for reducing the hazards caused by these particles to satellite communications, aviation, or astronauts. The 11-year solar cycle variation in cosmic rays is highly correlated with the strength of the heliospheric magnetic field. Differences in GCR flux during alternate solar cycles yield a 22-year cycle, known as the Hale Cycle, which is thought to be due to different particle drift patterns when the northern solar pole has predominantly positive (denoted a qA>0 cycle) or negative (qA<0) polarities. This results in the onset of the peak cosmic ray flux at Earth occurring earlier during qA>0 cycles than for qA<0 cycles and hence the peak being more domed for qA>0 and more sharply peaked for qA<0. In this study, we demonstrate that properties of the large-scale heliospheric magnetic field are different during the declining phase of the qA<0 and qA>0 solar cycles, when the difference in GCR flux is most apparent. This suggests that particle drifts may not be the sole mechanism responsible for the Hale Cycle in GCR flux at Earth. However, it is also demonstrated that these polarity-dependent heliospheric differences are evident during the space-age but much less clear in earlier data: using geomagnetic reconstructions, it is shown that for the period of 1905 -1965, alternate polarities do not give as significant a difference during the declining phase of the solar cycle. Thus we suggest that the 22-year cycle in cosmic ray flux is at least partly the result of direct modulation by the heliospheric magnetic field and that this effect may be primarily limited to the grand solar maximum of the space-age.

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“…We propose that it is indeed the case, in spite of some other opinions. For instance, Hathaway et al (1994) claimed that such an asymmetry is not only not very important, but also that its variation from cycle to cycle is small and not indicative of solar maxima. In the present analysis we present evidence for an opposite conclusion.…”

Section: Summary Discussion and Conclusionmentioning

confidence: 99%

On solar cycle predictions and reconstructions

Brajša

Wöhl

Hanslmeier

et al. 2009

A&A

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Context. Generally, there are two procedures for solar cycle predictions: the empirical methods -statistical methods based on extrapolations and precursor methods -and methods based on dynamo models. Aims. The goal of the present analysis is to forecast the strength and epochs of the next solar cycle, to investigate proxies for grand solar minima and to reconstruct the relative sunspot number in the Maunder minimum. Methods. We calculate the asymmetry of the ascending and descending solar cycle phases (Method 1) and use this parameter as a proxy for solar activity on longer time scales. Further, we correlate the relative sunspot numbers in the epochs of solar activity minima and maxima (Method 2) and estimate the parameters of an autoregressive moving average model (ARMA, Method 3). Finally, the power spectrum of data obtained with the Method 1 is analysed and the Methods 1 and 3 are combined. Results. Signatures of the Maunder, Dalton and Gleissberg minima were found with Method 1. A period of about 70 years, somewhat shorter than the Gleissberg period was identified in the asymmetry data. The maximal smoothed monthly sunspot number during the Maunder minimum was reconstructed and found to be in the range 0-35 (Method 1). The estimated Wolf number (also called the relative sunspot number) of the next solar maximum is in the range 88-102 (Method 2). Method 3 predicts the next solar maximum between 2011 and 2012 and the next solar minimum for 2017. Also, it forecasts the relative sunspot number in the next maximum to be 90 ± 27. A combination of the Methods 1 and 3 gives for the next solar maximum relative sunspot numbers between 78 and 99. Conclusions. The asymmetry parameter provided by Method 1 is a good proxy for solar activity in the past, also in the periods for which no relative sunspot numbers are available. Our prediction for the next solar cycle No. 24 is that it will be weaker than the last cycle, No. 23. This prediction is based on various independent methods.

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The shape of the sunspot cycle

Cited by 256 publications

References 9 publications

The Mount Wilson Observatory S-Index of the Sun

The Mount Wilson Observatory S-Index of the Sun

The 22-Year Hale Cycle in Cosmic Ray Flux – Evidence for Direct Heliospheric Modulation

On solar cycle predictions and reconstructions

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