Variation of solar irradiance and mode frequencies during Maunder minimum

Using the sunspot numbers reported during the Maunder minimum and the empirical relations between the mode frequencies and solar activity indices, the variations in the total solar irradiance and 10.7 cm radio flux for the period 1645 to 1715 is estimated. We find that the total solar irradiance and radio flux during the Maunder minimum decreased by 0.19% and 52% respectively, as compared to the values for solar cycle 22. This revised version was published online in July 2006 with corrections to the Cover Date.     

The 22-year cycle of the sun

The 22-yr solar cycle is being explained as due to a spin-aligned magnetic quadrupole frozen into the (radiative) core. Differential rotation of the poorly conducting convection zone gives rise to flux winding and to an alternating dominance, near the surface, of one of the two constituent dipoles. Equatorial superrotation and polar subrotation are stabilized by the same magnetic flux that transfers angular momentum from the (radiative) core to the (escaping) solar wind. The time- and radius-dependent magnetic torque is also responsible for the rigid and twisting oscillations of a thin surface layer, and for the relative velocities of different tracers.     

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.     

The revival of solar activity after Maunder minimum in reports and observations of E. Manfredi

We present information, published here for the first time, concerning observations of sunspots made at the beginning of the XVIIIth century. The information has been taken from specola's archives in Bologna. It concerns the years just after the end of the Maunder minimum. The data confirms the presence of a double maximum in 1704–1707, and shows a high asymmetry in sunspots latitude distribution, possibly related to the abnormal Sun activity in the second half of XVIIth century.     

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.     

The phase variations of the solar cycle

It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219 ± 0.032 yr. It is shown that the great solar anomaly of 1760–1800 is most likely real and not due to poor data.     

Prediction for the amplitude of solar cycle 24 from the pattern of activity near the cycle minimum

Correlations are investigated between the pattern of solar activity described by the smoothed monthly relative sunspot numbers (Wolf numbers) near the minimum of a solar cycle and the cycle amplitude. The closest correlation is found between the amplitude of a solar cycle and the sum of the decrease in activity over two years prior to the cycle minimum and the increase in activity over two years after the minimum; the correlation coefficient between these parameters is 0.92. This parameter is used as a precursor to predict the amplitude of solar cycle 24, which is expected to reach its maximum amplitude (85 ± 12) in February 2014. Based on the correlations between the mean parameters of solar cycles, cycle 24 is expected to last for approximately 11.3 years and the minimum of the next cycle 25 is predicted for May 2020.     

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.     

Evidence for a long-term variation of the dynamo action responsible for the solar magnetic cycle

By using the sunspot time series as a proxy, we have made a detailed analysis of the mean solar magnetic field over the last two and half centuries, by means of a reconstruction of its phase space. We find evidence of a long-term trend variation of some of the solar physical processes (over a few decades) that might be responsible for the apparent erratic behaviour of the solar magnetic cycle. The analysis is done by means of a careful study of the axisymmetric dynamo model equations, where we show that the temporal counterpart of the magnetic field can be described by a self-regulated two-dimensional dynamic system, usually known as a Van der Pol–Duffing oscillator. Our results suggest that during the last two and half centuries, the velocity of the meridional flow, v _p, and the efficiency of the α mechanism responsible for the conversion of toroidal magnetic field into poloidal magnetic field might have suffered variations that can explain the observed variability in the solar cycle.     

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

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.     

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.     

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.     

Evidence for a poleward meridional flow on the sun

We define for observational study two subsets of all polar zone filaments, which we call polemost filaments and polar filament bands. The behavior of the mean latitude of both the polemost filaments and the polar filament bands is examined and compared with the evolution of the polar magnetic field over an activity cycle as recently distilled by Howard and LaBonte (1981) from the past 13 years of Mt. Wilson full-disk magnetograms. The magnetic data reveal that the polar magnetic fields are built up and maintained by the episodic arrival of discrete f-polarity regions that originate in active region latitudes and subsequently drift to the poles. After leaving the active-region latitudes, these unipolar f-polarity regions do not spread equatorward even though there is less net flux equatorward; this indicates that the f-polarity regions are carried poleward by a meridional flow, rather than by diffusion. The polar zone filaments are an independent tracer which confirms both the episodic polar field formation and the meridional flow. We find:

1. The mean latitude of the polemost filaments tracks the boundary of the polar field cap and undergoes an equatorward dip during each arrival of additional polar field.
2. Polar filament bands track the boundary latitudes of the unipolar regions, drifting poleward with the regions at about 10 m s^-1.
3. The Mt. Wilson magnetic data, combined with a simple model calculation, show that the filament drift expected from diffusion alone would be slower than observed, and in some cases would be equatorward rather than poleward.
4. The observation that filaments drift poleward along with the magnetic regions shows that fields of both polarities are carried by the meridional flow, as would be expected, rather than only the f-polarity flux which dominates the strength. This leads to the prediction that in the mid-latitudes during intervals between the passage of f-polarity regions, both polarities are present in nearly equal amounts. This prediction is confirmed by the magnetic data.

     

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.     

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.     

Asymmetries during the maximum phase of solar cycle 22

This paper presents the results of studies of the asymmetries (N-S and E-W) for different manifestations of solar activity events (sunspot groups, H flares and active prominences/filaments) during the maximum-phase (1989–1991) of solar cycle 22. During the period considered, the results obtained show the existence of a real N-S asymmetry, whereas the E-W asymmetry may exist only for H flares. There is no definite relationship between the asymmetries and the occurrence of events; however, around low activity sometimes we find enhanced asymmetry, and low asymmetry around high activity. Our study suggests a good agreement with similar studies made by others.