Is the solar cycle timed by a clock?

Dicke (1978) has argued that the phase of the solar cycle appears to be coupled to an internal clock: shorter cycles are usually followed by longer ones, as if the Sun remembers the correct phase. The data set is really too short to demonstrate the presence of a phase memory, but phase and amplitude of the cycle are strongly correlated for 300 yr or more. It is shown that this memory effect can be explained by mean field theory in terms of fluctuations in , which induce coherent changes in the frequency and amplitude of a dynamo wave. It is concluded that there is neither a strong observational indication nor a theoretical need for an extra timing device, in addition to the one provided by dynamo wave physics.Dedicated to Cornelis de Jager     

On ‘bimodality of the solar cycle’ and the duration of cycle 21

The period-growth dichotomy of the solar cycle predicts that cycle 21, the present solar cycle, will be of long duration (>133 mo), ending after July 1987. Bimodality of the solar cycle (i.e., cycles being distributed into two groups according to cycle length, based on a comparison to the mean cycle period) is clearly seen in a scatter diagram of descent versus ascent durations. Based on the well-observed cycles 8–20, a linear fit for long-period cycles (being a relatively strong inverse relationship that is significant at the 5% level and having a coefficient of determination r ² 0.66) suggests that cycle 21, having an ascent of 42 mo, will have a descent near 99 mo; thus, cycle duration of about 141 mo is expected. Like cycle 11, cycle 21 occurs on the downward envelope of the sunspot number curve, yet is associated with an upward first difference in amplitude. A comparison of individual cycle, smoothed sunspot number curves for cycles 21 and 11 reveals striking similarity, which suggests that if, indeed, cycle 21 is a long-period cycle, then it too may have an extended tail of sustained, low, smoothed sunspot number, with cycle 22 minimum occurring either in late 1987 or early 1988.     

Influence of the moon on the earth’s magnetosphere at various phases of a solar activity cycle

We studied the dependence of the A _p -index describing the geomagnetic disturbance on the Moon’s phase. We processed available data for cycles 20–23 of the solar activity by the epoch super-position method. We discovered that, in the declining branch of the solar cycle, the highest values of the A _p -index relative to an average value are observed near new moon. The difference of the A _p -index values for new moon and full moon is approximately 18%. In the branch of increase and maximum of the solar cycle, we observed minimum values of the A _p -index during several days before full moon, and maximum values of the A _p -index take place during several days after full moon. The conclusion follows from this that the mechanism of the Moon’s effect on the earth’s magnetosphere is different essentially for intervals near new moon and full moon.     

Does the tachocline show solar cycle related changes?

The tachocline at the base of the convection zone is generally believed to be the seat of the solar dynamo. Here we investigate whether the tachocline shows any detectable change using several 72 day time-series of the Michelson Doppler Imager (MDI) Medium-l data. We do not find any clear evidence of change with time.     

Date of minimum of the “protracted” solar cycle 23

We offer an interpretation of the now widely discussed protracted onset of the epoch of solar activity minimum after cycle 23. The interpretation appeals to the Gnevyshev-Ohl rule, but in the context of a new statistical quantity-the product of the cycle amplitude by its duration. Considering this quantity, which has the same physical meaning as that of the integrated characteristic used by Gnevyshev and Ohl, yields a probable estimate for the onset of the minimum of the current cycle in the interval 2009.0–2012.4.     

Prediction verification of solar cycles 18–24 and a preliminary prediction of the maximum amplitude of solar cycle 25 based on the Precursor Method

Predictions of the strength of solar cycles are important and are necessary for planning long-term missions.A new solar cycle 25 is coming soon,and the amplitude is needed for space weather operators.Some predictions have been made using different methods and the values are drastically different.However,since 2015 July 1,the original sunspot number data have been entirely replaced by the Version 2.0 data series,and the sunspot number values have changed greatly.In this paper,using Version 2 smoothed sunspot numbers and aa indices,we verify the predictions for cycles 18–24 based on Ohl’s Precursor Method.Then a similar-cycles method is used to evaluate the aa minimum of 9.7(±1.1)near the start of cycle 25 and based on the linear regression relationship between sunspot maxima and aa minima,our predicted Version 2maximum sunspot number for cycle 25 is 121.5(±32.9).     

Solar magnetic cycle dependence in corotating modulation of galactic cosmic rays

We study the temporal evolution of cosmic ray intensity during ～27-day Carrington rotation periods applying the method of superposed epoch analysis. We discuss about the average oscillations in the galactic cosmic ray intensity, as observed by ground based neutron monitors, during the course of Carrington rotation in low solar activity conditions and in different polarity states of the heliosphere (A<0 and A>0). During minimum and decreasing phases in low solar activity conditions, we compare the oscillation in one polarity state with that observed in other polarity state in similar phases of solar activity. We find difference in the evolution and amplitude of ～27-day variation during A<0 and A>0 epoch. We also compare the average variations in cosmic ray intensity with the simultaneous variations of solar wind parameters such as solar wind speed and interplanetary magnetic field strength. From the correlation analysis between the cosmic ray intensity and the solar wind speed during the course of Carrington rotation, we find that the correlation is stronger for A>0 than A<0.     

Is the Suess cycle present in historical naked-eye observations of sunspots?

Sunspot numbers are available for the past four centuries. However, solar activity indices with a longer time span are required by geophysicists and solar physicists. The yearly naked-eye sunspot number in the past is reconstructed using observations recorded in historical documents. Some studies from different solar proxies (including radiocarbon and aurora records) show the presence of the so-called Suess cycle (around 200 years) in solar variability. In this work, a modified Lomb–Scargle periodogram analysis is used to investigate the Suess cycle in naked-eye observations of sunspots during 200 BC–1918 AD. The most relevant characteristic of the periodogram is a cycle with a frequency very close to the Suess cycle, though this cycle is not significant statistically.     

Evidence for a 17-year cycle in the IMF directions at 1 AU, in solar coronal hole variations, and in planetary magnetospheric modulations

A dominant 16–17 yr cycle was observed in the net exposure times of the Earth to Toward and Away field directions of the interplanetary magnetic field (IMF). A cycle of the same frequency and phase was observed in the polarity of the long-term hemispheric differences in coronal hole distributions. This was determined from north/south differences in average Fexiv green line quiet regions at high- and mid-latitudes. It is argued that the 17-yr cycle is a fundamental oscillation of coronal hole topology, which is transferred to Earth via variations in the neutral sheet. A comparison of the 17-yr cycle to the 22-yr Hale cycle indicated that they are not identical, but rather, can mix to form a 75-yr cycle plus a 9-yr cycle. Evidence for the 75-yr cycle existed in the Earth's net exposure times to fields from the solar North and South, and in the long-term imbalance of solar quiet regions between the northern and southern hemispheres. The 9-yr cycle was manifested in the mid- to low- latitude Fexiv modulations and in solar wind velocity variations in the ecliptic. At Earth, evidence for a similar 17-yr cycle was observed in the horizontal magnetic field observations in a multitude of surface magnetic recording stations. In addition, the detection of a 17-yr cycle in the Huancayo neutron monitor cosmic ray series suggests that the effects of this cycle extend to the heliospheric boundaries. It is concluded that sufficient preliminary evidence exists to consider the hypothesis that the Sun contains a magnetic moment with an oscillatory cycle of 17 years.     

North–south asymmetry of different solar activity features during solar cycle 23

A study on north–south (N–S) asymmetry of different solar activity features (DSAF) such as solar proton events, solar active prominences [total, low (?40°) and high (?50°) latitudes], Hα flare indices, soft X-ray flares, monthly mean sunspot areas and monthly mean sunspot numbers carried out from May 1996 to October 2008. Study shows a southern dominance of DSAF during this period. During the rising phase of the cycle 23 the number of DSAF approximately equals on both, the northern and the southern hemispheres. But these activities tend to shift from northern to southern hemisphere during the period 1998–1999. The statistical significance of the asymmetry time series using a χ²-test of goodness of fit indicates that in most of the cases the asymmetry is highly significant, meaning thereby that the asymmetry is a real feature in the N–S distribution of DSAF.     

Photon in a cavity – a Gedankenexperiment

The inertial and gravitational mass of electromagnetic radiation (i.e., a photon distribution) in a cavity with reflecting walls has been treated by many authors for over a century. After many contending discussions, a consensus has emerged that the mass of such a photon distribution is equal to its total energy divided by the square of the speed of light. Nevertheless, questions remain unsettled on the interaction of the photons with the walls of the box. In order to understand some of the details of this interaction, a simple case of a single photon with an energy $E_{\nu }=h\nu$ bouncing up and down in a static cavity with perfectly reflecting walls in a constant gravitational field $\mathit{g}$, constant in space and time, is studied and its contribution to the weight of the box is determined as a temporal average.     

Evaluation of the intermediate-term periodicities in solar and cosmic ray activities during cycle 23

In this paper we investigate the presence and temporal evolution of galactic cosmic rays (GCRs) time-series and three solar parameters, namely the daily sunspot number, the coronal green line and the 10.7 cm solar radio flux over the period 1996–2003 by the wavelet technique. A number of short- and intermediate-term quasi-periodicities were also detected in both GCR and solar parameters. For the short-term range, we have identified quasi-periods of 16–30 days, 40–55 days, 60–70 days, 80–90 days and 80–100 days. In the case of intermediate range, the significant periods were 120–140 days, 150–170 days, 190–210 days, 240–260 days, ≈1.09 yr. and ≈1.23 yr. The wavelet power spectra show that all the above-mentioned periods are intermittent in nature and occurred in different time-series in different intervals. The result exhibits that the well-known “Rieger period” of (150–160 days) was prominent in both GCR and solar data sets during the ascending phase of cycle 23. Possible reasons behind the observed periods were discussed with the help of previous results and existing numerical models.     

A magnetic cycle of τ Bootis? The coronal and chromospheric view

τ Bootis is a late F‐type main sequence star orbited by a Hot Jupiter. During the last years spectropolarimetric observations led to the hypothesis that this star may host a global magnetic field that switches its polarity once per year, indicating a very short activity cycle of only one year duration. In our ongoing observational campaign, we have collected several X‐ray observations with XMM‐Newton and optical spectra with TRES/FLWO in Arizona to characterize τ Boo's corona and chromosphere over the course of the supposed one‐year cycle. Contrary to the spectropolarimetric reconstructions, our observations do not show indications for a short activity cycle (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global solar cycle in the distribution of the green coronal emission period: 1940–1989

We have studied the latitude-time distribution of the green (5303 Å) coronal line emission for 1940–1989 from observations by Waldmeier (1957), Kislovodsk, Lomnický tít, Norikura, and Pic-du-Midi - Q.B.S.A. (1955–1987). We have compared these data with the distributions of the weak magnetic field (Stenflo, 1988), of polar faculae and sunspots, and have given our interpretation of the results. We have found that a new cycle of coronal activity commences after the polar field reversal in the form of two components in each hemisphere. We identify the first component with the polar faculae that appear at latitude 40° and migrate polewards. The second component representing sunspots shows up at 40° latitude 5–6 years after and drifts equatorward. Thus the global coronal activity cycle has a duration of 16–17 years and is described by two components that reflect the activity of polar faculae and sunspots.     

Predicting monthly sunspot numbers of solar cycle 23 by the method of “similar cycles”

We briefly describe the concept and method of “similar cycles” to be used in sunspot prediction. We have checked on the reliability of this method and made the comparison of the predictions and observations for the 23rd solar activity cycle.     

Estimates of the number of sunspot groups: Application to the activity cycle 1960–1970

It was verified that the total number of sunspot groups at certain region on the solar surface for a certain activity cycle can be estimated quite accurately by using the Markov chain approximation method on the total number of spot groups observed on the same region at an earlier activity cycle. Application has been carried out on the observed sunspots on three northern longitude intervals (40–50, 80–90, and 130–140) during the activity cycle 1950–1960 and 1960–1970. The total number of spot groups in these regions for the activity cycle 1960–1970 has been estimated from the observational data of the cycle 1950–1960. A good correlation between the observed and estimated number of spot groups for the activity cycle 1960–1970 has been noted.     

Did predictions of the maximum sunspot number for solar cycle No. 22 come true?

Solar cycle No. 22 which started in 1986 seems to have already passed through a maximum. The maximum annual mean sunspot number was 157 for 1989. The maximum twelve-month running average was 159, centered on July 1989. For cycle 21, the similar value was 165 centered at December 1979. Thus, cycle 22 is slightly weaker than cycle 21. Schatten and Sofia (1987) had predicted a stronger cycle 22 (170 ± 25) as compared to cycle 21 (140 ± 20). Predictions based on single variable analysis, viz., R _z (max) versus aa(min) were 165 and came true. Predictions based on a bivariate analysis, viz., R _z (max) versus aa(min) and R _z (min) were 130 and proved to be underestimates. Other techniques gave over- or underestimates.     

Dynamics of a triaxial gyrostat at a Lagrangian equilibrium of a binary asteroid

The non-canonical Hamiltonian dynamics of a triaxial gyrostat in Newtonian interaction with two punctual masses is considered. This serves as a model for the study of the attitude dynamics of a spacecraft located at a Lagrangian equilibrium point of the system formed by a binary asteroid and a spacecraft. Using geometric-mechanics methods, the approximated dynamics that arises when developing the potential in series of Legendre functions and truncating the series to the second harmonics is studied. Working in the reduced problem, the existence of equilibria in Lagrangian form are studied, in analogy with classic results on the topic. In this way, the classical results on equilibria of the three-body problem, as well as other results by different authors that use more conventional techniques for the case of rigid bodies, are generalized. The rotational Poisson dynamics of a spacecraft located at a Lagrangian equilibrium and the study of the nonlinear stability of some important equilibria are considered. The analysis is done in vectorial form avoiding the use of canonical variables and the tedious expressions associated with them.     

An apparent ‘even-odd’ cycle distribution in Mt. Wilson ‘numbers of spots’ data

Mt. Wilson numbers of spots data (as defined in Howard et al., 1984) appear to be distributed according to even-odd cycle numbering. Linear fits of annual numbers of spots versus annual sunspot number for even- and odd-numbered cycles have slopes which are statistically different at the 5% level of significance. The existence of an even-odd split in Mt. Wilson numbers of spots data may be due either to a real difference in even- and odd-numbered cycles on the Sun or to a difference in weather at Mt. Wilson (perhaps, related to the 22-yr rhythm of drought in the western United States) during even- and odd-numbered cycles, or both. For cycle 22, an even-numbered cycle, the peak numbers of spots is estimated to be near 2600.