The 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

Solar cycle variation of the microwave spectrum and total irradiance

We have extended the proxy relationship between irradiance and microwaves by using the daily solar fluxes from Toyokawa Observatory at 1000, 2000, 3750 and 9400 MHz in addition to the Ottawa 2800 MHz flux for the years 1980–1989. It turns out that the flux at 1000 MHz is better correlated with irradiance than the flux at higher frequencies-an unexpected result. We have also found that the spectrum of the flux shows shape changes that are related to the number and type of active regions. Because of this the five-frequency spectral measurements of microwave flux allow one to separate the sunspot and coronal features, providing an improved proxy of solar variability.     

The influence of solar system oscillation on the variability of the total solar irradiance

Total solar irradiance (TSI) is the primary quantity of energy that is provided to the Earth. The properties of the TSI variability are critical for understanding the cause of the irradiation variability and its expected influence on climate variations. A deterministic property of TSI variability can provide information about future irradiation variability and expected long-term climate variation, whereas a non-deterministic variability can only explain the past.This study of solar variability is based on an analysis of two TSI data series, one since 1700 A.D. and one since 1000 A.D.; a sunspot data series since 1610 A.D.; and a solar orbit data series from 1000 A.D. The study is based on a wavelet spectrum analysis. First, the TSI data series are transformed into a wavelet spectrum. Then, the wavelet spectrum is transformed into an autocorrelation spectrum to identify stationary, subharmonic and coincidence periods in the TSI variability.The results indicate that the TSI and sunspot data series have periodic cycles that are correlated with the oscillations of the solar position relative to the barycenter of the solar system, which is controlled by gravity force variations from the large planets Jupiter, Saturn, Uranus and Neptune. A possible explanation for solar activity variations is forced oscillations between the large planets and the solar dynamo.We find that a stationary component of the solar variability is controlled by the 12-year Jupiter period and the 84-year Uranus period with subharmonics. For TSI and sunspot variations, we find stationary periods related to the 84-year Uranus period. Deterministic models based on the stationary periods confirm the results through a close relation to known long solar minima since 1000 A.D. and suggest a modern maximum period from 1940 to 2015. The model computes a new Dalton-type sunspot minimum from approximately 2025 to 2050 and a new Dalton-type period TSI minimum from approximately 2040 to 2065.     

Essential features of the 11-year solar cycle

Investigation of sunspots, coronal lines intensity, flares and other solar and geophysical data have confirmed the fact that the 11-year cycle consists of two events (maxima) having different features.During the first maximum (it coincides in time with the maximum of the Wolf numbers) the solar activity increases in all heliographic latitudes but it is maximal in latitude 25° in each hemisphere. The far UV radiation and number of small spots, flares and geomagnetic disturbances with sudden commencements and without 27-day recurrences are maximum at this time.During the second maximum, which appears 2–3 years after the first one, the activity is maximal in latitudes ± 10°. At this time the biggest spots, big flares, aurora and geomagnetic disturbances with the gradual commencements and long series of 27-day recurrences appear.The variations of averaged 5303 and 6374 Å coronal line intensities may be interpreted as an increase of coronal density and temperature during the first maximum and a sharp decrease of density and temperature rise during the second one. The temperature during the second maximum is higher than that during the first one.The distribution of activity on time-latitude diagrams (so-called butterflies) is a result of superposition of two random distributions corresponding to the two maxima mentioned above.     

Solar neutrino data and the 11-year solar activity cycle

Recent data on solar neutrino flux have been analysed and it is shown that there is a statistically significant variation of solar neutrino flux data with the solar activity cycle. Thus the observation suggests that the solar activity cycle is due to the pulsating characters of the nuclear energy generation in the interior of the Sun.     

Sunspot photometry and the total solar irradiance deficit measured in 1980 by ACRIM

Until now a simple Photometric Sunspot Index (PSI) model was used (e.g. Willsonet al., 1981) to describe the contribution of sunspots to the solar irradiance deficit measurement by ACRIM. In this work we replace this model by a photometry of sunspot pictures for the period of 19 August to 4 September, 1980 taking into account the individual features, like lightbridges or umbral dots, of each spot. The main results of this preliminary analysis are: (1) theA _u/A _p ratios and alsos the values vary in a wide range and are by no means constant as in the PSI model; (2) the general trend of the irradiance deficit from our analysis agrees well with the ACRIM measurements; (3) on some days there are differences of more than 50% between the deficits derived from our measurements and from the PSI model.Paper presented at the 11th Eurpean Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

Configurations of dynamo waves in a two-layer medium and the 11-year solar cycle

The behavior of dynamo waves in a two-layer medium is investigated in terms of the Parker dynamo model. The solar cycle duration is shown to depend on the ratio of turbulent diffusivities in the layers. Meridional circulation has been incorporated into the Parker system. An increase in the intensity of meridional flows is shown to decelerate the propagation of dynamo waves. The minimum of solar magnetic activity can occur not only in the case of intense meridional circulation in both layers but also when a difference in physical characteristics arises between the layers and the meridional flows are moderate.     

Empirical estimate of p-mode frequency shift for solar cycle 23

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed frequency shifts for the ascending phase of cycle 23, indicates that the derived relations are independent of epoch and do not change significantly from cycle to cycle. We propose that these relations could be used to estimate the shift in p-mode frequencies for past, present and future solar activity cycles, if the solar activity index is known. The maximum frequency shift for cycle 23 is estimated to be 265±90 nHz, corresponding to a predicted maximum smoothed sunspot number 118.1±35.     

On possible cosmic origin of the 11-year solar cycle

In order to test Dicke??s idea of a clock hidden inside the Sun and determine the initial phase of the solar cycle, the epochs of the extrema of the Wolf numbers observed over the past 400 years are examined. It is shown that extrema that obey the period P _W equaled 11.07(4) years retain the initial phase, which cannot be explained in terms of local physics and concepts of the past century regarding the mechanism of the solar cycle based on the theory of a magnetic dynamo and the phenomenological model of the Babcock-Leighton cycle. It is suggested that the cycle has a cosmic (cosmological) origin. This is clearly indicated by the correlation of the cycle period with a holographic time-scale of the Universe, (a ₀ R ³)^1/4/c ?? 11.0(4) years, where a ₀ and R are the radii of the first Bohr orbit of a hydrogen atom and the observable Universe, respectively, and c is the speed of light. It is noted that there are other strict holographic relations that include a ₀, R, P _W , the wavelength of the microwave background radiation (with a temperature of 2.7 K), and a period of the global solar pulsations equal to 9600.6 s. The true physical nature of the governing mechanism for the 11-year cycle can perhaps only be understood based on modern concepts about the nonlocality of our world, which follows from Bell??s theorem, which is grounded on the achievements of quantum mechanics at the turn of the 20th and 21st centuries, as well as using a model of a holographic Universe free of c.     

Modulations of the surface magnetic field on the intra-cycle variability of total solar irradiance

Solar photospheric magnetic field plays a dominant role in the variability of total solar irradiance (TSI). The modulation of magnetic flux at six specific ranges on TSI is characterized for the first time. The daily flux values of magnetic field at four ranges are extracted from MDI/SOHO, together with daily flux of active regions (MF\(_{\text{ar}}\)) and quiet regions (MF\(_{\text{qr}}\)); the first four ranges (MF\(_{1\mbox{--}4}\)) are: 1.5–2.9, 2.9–32.0, 32.0–42.7, and 42.7–380.1 (\(\times 10^{18}\) Mx per element), respectively. Cross-correlograms show that MF₄, MF\(_{\text{qr}}\), and MF\(_{ \text{ar}}\) are positively correlated with TSI, while MF₂ is negatively correlated with TSI; the correlations between MF₁, MF₃ and TSI are insignificant. The bootstrapping tests confirm that the impact of MF₄ on TSI is more significant than that of MF\(_{\text{ar}}\) and MF\(_{\text{qr}}\), and MF\(_{\text{ar}}\) leads TSI by one rotational period. By extracting the rotational variations in the MFs and TSI, the modulations of the former on the latter at the solar rotational timescale are clearly illustrated and compared during solar maximum and minimum times, respectively. Comparison of the relative amplitudes of the long-term variation show that TSI is in good agreement with the variation of MF₄ and MF\(_{\text{ar}}\); besides, MF₂ is in antiphase with TSI, and it lags the latter by about 1.5 years.     

On the cause of total irradiance variations observed by the CCD solar surface photometer

Spatially-resolved precise photometric observations of the whole Sun at wavelengths of 545nm (FWHM 40nm) were carried out by using the CCD solar surface photometer. Bright parts of photospheric network have contrast of several tenths of percent, and their contribution to the total irradiance is approximately half that of active region faculae. The solar irradiance variations estimated from sunspots, faculae and active network (contrast>0.3%) agreed with the ACRIM data. The quiet Sun irradiance used in the present results was different from the total irradiance at the solar minimum observed by the ACRIM, which indicates unmeasured components (contrast>0.1%) cause the 11-year cycle irradiance variation.     

Effects of activity complexes and active longitudes on variations in total solar irradiance

A numerical technique of time-longitude analysis has been developed by studying the fine structure of temporal variations in total solar irradiance (TSI). This analysis produces maps of large-scale thermal inhomogeneities on the Sun and reveals corresponding patterns of radiative excess and deficit relative to the unperturbed solar photosphere. These patterns are organized in two-and four-sector structures and exhibit the effects of both activity complexes and the active longitudes. Large-scale patterns with radiative excess show a facular macrostructure caused by the relaxation of large-scale thermo-magnetic perturbations and/or energy output due to very large-scale solar convection. These thermal patterns are related to long-lived magnetic fields that are characterized by rigid rotation. The patterns with radiative excess tend to concentrate around the active longitudes and are centered at 103° and 277° in the Carrington system when averaged over the time-longitude distribution of thermal inhomogeneities during activity cycles 21–23.     

Period and phase of the 88-year solar cycle and the Maunder minimum: Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic and auroral activity cycles. We find sub-harmonics of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder type minima reoccur irregularly for millennia, it appears that the Sun remains close to this transition to and from chaos. We postulate this as a universal characteristic of solar type stars caused by feedback in the dynamo number.     

On the stability of the 11-year solar cycle period (and a few others)

The existence of an 11.1-yr periodic variation in the sunspot number record has been recognized for many years; however, periodicities other than this remain questionable. Power spectral analysis of the International sunspot number is performed and the results are compared with those for the same period using values that were taken randomly inside the error bars. The findings are that only a few periodicities show noticeable peaks. These include periodicities of 8.49, 10.01, 10.58, 11.10, 12.50, 58.50, and 97.20 yr. On the basis of these seven periodicities, one can loosely simulate the observable sunspot record (r = 0.75). We find that discrepancies in number and value of periodicities with other authors appear to be related to the length of the sunspot record used in the analysis and to the occurrence of 0.3-yr windows around the inferred periodicities.     

Changes in solar irradiance and atmospheric turbidity in Costa Rica during the total solar eclipse of July 11, 1991

Solar global radiation was measured in several places in Costa Rica during the total solar eclipse that occurred on July 11, 1991. In two of these places, Puntarenas and Santa Cruz, measurements in the ultraviolet range (295–385 nm) were also taken. In Santa Cruz, a normal incidence pyrheliometer with Schott filters OG530 and RG630 was used to measure direct solar radiation in its whole range, and in the 530–2800 nm and 630–2800 wavebands respectively. Global radiation, and consequently direct, diffuse and irradiance in any of the wavebands considered, decreased gradually as the sun was being eclipsed and reached zero during the totality, then increased to their normal values. Data registered in Santa Cruz were used to determine Ångstrom's atmospheric turbidity parameters and. Computations show that between 13:00 and 14:30 LT (local time), decreased and increased significantly. This indicates that atmospheric turbidity was high and large particles were more abundant than small ones. The size of hygroscopic particles increased during the eclipse when temperature decreased and relative humidity increased in a comparatively short time.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

Dependence of stratospheric temperature on the 11-year solar activity cycle?

An investigation has been undertaken as to whether the 11-year activity cycle of the Sun can affect the temperature of the stratosphere at heights between 11 km (tropopause) and 36 km. An extended, and more sophisticated analysis of diurnal temperature data, available from radio-sonde measurements made at Berlin during the period 1958–1982, revealed, in contrast to an earlier result, that during both the summer and autumn seasons, when the radiative balance is dominant in determining the temperature profiles, and also during the winter and spring, when warming and cooling effects are present respectively, no clear dependence on the solar cycle was found to exist. Furthermore warming effects observed in winter show no dependence on solar activity.