• SOLAR CYCLES

The Sun knows four types of activities that are more or less significant depending on the duration of this activity. The variations in solar activity have been studied according to the analysis of C₁₄ (carbone 14). This isotope is formed by the action of cosmic rays on atmospheric nitrogen. The more the Sun is active the more the solar wind prevents these cosmic rays to enter the Earth's atmosphere. Therefore less C₁₄ is formed.

• SCHWABE CYCLE

This solar cycle lasting from 8 to 13 years for an average of 11 years is the best known of the four variations of solar activity. The amateur, Heinrich Schwabe (1789-1875) discovered this cycle by observing the appearance of sunspots. With satellites astronomers were able to directly measure the flow of energy emitted by the Sun during the most recent cycles. The flux decreases to 0,10.% between the maximum and minimum of this cycle. But this solar activity is more or less significant depending on the three other solar cycles.

As shown in the diagram below the temperature evolution follows the evolution of the solar constant. From 1645 to 1715, during the Maunder minimum, both the solar constant as the temperature was low. The solar constant had dropped by 0,25.%. This it is reproduced from 1795 to 1830 during the Dalton minimum.

The evolution from 1611 to 1980 of the solar constant and the temperature of the
northern hemisphere according to the average of 1960-1990 average. NOAA data.

We find the same result with the number of sunspots which is a good indicator for this solar cycle as you can see by comparing the above diagram with that of below.

This graph was created and updated according to the NOAA data
Click here for to enlarge

• GLEISSBERG CYCLE

This cycle with a duration of 80 to 90 years was discovered by Gleissberg in 1958. It has effects on the amplitude of the 11-years schwabe solar cycle. However, the ten-year cycles only being identified over a period of three centuries by using the sunspots, accurate extraction of this period presents some difficulties. This is why other data are used (carbone 14). This period was also found in the secular variation of the solar diameter. Evaluating minimums and maximums eras per Gleissberg was based on data of auroral activity (Schove, 1955). The Gleissberg maximum around 1984 is the first in a long sequence of maximum associated with zero phase in the cycle of 166 years. Next Gleissberg the maximums should occur around 2069, 2159 and 2235.

• SUESS OR VRIES CYCLE

The data of the carbon 14 concentration also indicate a period of about 150-200 years.

MINIMUM	BEGINNING	END
OORT	1010	1050
WOLF	1281	1347
SPORER	1411	1524
MAUNDER	1645	1715
DALTON	1795	1830

Date of beginning and end of Oort, Wolf, Spörer, Maunder and Dalton minimums

The dates of Oort, Wolf, Spörer, Maunder and Dalton Minimum, presented in the table above, suggest a periodicity of the order of about one to two centuries.. It leads to variability in the amplitude of the cycle of Schawbe, for example when comparing the solar cycle of 1715 with that of 1958.

The red curve represents the evolution of the temperature according to the
average of 1960-1990 and the blue curve the solar constant from 843 to 1980

This must have links with the rotation of the gaseous planets which have an effect on the variation of the speed of the momentum of the Sun around the barycenter of the solar system as explained further in THE CAUSE OF LONG CYCLES.

• HALLSTATTZEIT CYCLE

The Sun has an oscillation of the diameter of amplitude of 0,5 arc second with a period of about 900 days or 27 months of the same phase.

But following solar activity this oscillation is more or less important. When solar activity is at its maximum the oscillation of its diameter is less significant than whether solar activity is at a minimum. What makes the variation of the diameter of the Sun varies opposite to the variation of solar activity as shown in the diagram below.

Variation of the solar diameter and solar activity from 1978 to 1998. Solar activity
is represented by the number of sunspots (in red). The variation of the semi-diameter
of the sun in arc second is represented by the blue circles. The oscillation of
diameter has a anti-correlation with the 11-years cycle. (F. Laclare, 1999)

Mouton (1659-1661), Picard and Richer (1666-1672) and La Hire (1683-1718) and his son (1719) were among the first to measure the diameter of the sun depending on the day of the year and also according to solar eclipses. Ribes et al. (1987) examined again in 1987 the data with the withdrawal of the variation of the solar diameter depending on the Earth-Sun distance according to the seasons and they concluded that measures of Picard and La Hire are similar. By comparing the values achieved from 1666 to 1719 we find that during the Maunder Minimum the semi-diameter of the Sun was bigger approximately 0,5 arcsecond compared to the end of the Maunder Minimum. Because during the Maunder Minimum (1683) the Sun had a semi-diameter of 962,5 arcseconds against a semi-diameter of 961,78 arcseconds at the end of Maunder Minimum in 1715. And according to the data recorded by the European satellite Picard during his mission from 06/15/2010 until 04/04/2014, now that the Sun has an even stronger activity, his semi-diameter is smaller as it oscillates between 959,2 and 959,8 arcseconds during the 11-years cycle (150 km). A difference of about 3 arcseconds compared to the Maunder Minimum, representing 2,000.km more than the current value of the average diameter.

Variation of the solar diameter, 1860-1940. Arrows indicate
maximum of sunspots. (From ASO-X6 in The Sun and Solar System Debris).

The variation in the diameter of the Sun causes the variation of the solar constant. That is what exactly has an effect on the climate as it affects the thermal and dynamic structure of the stratosphere that after causes changes in the troposphere and thus a slight variation of the temperature of the Earth. According to the equation W=(DR/R)/(DS/S) where there is the solar radius (R) and the solar constant (S) can be calculated relative change ratio of R and S. Following that W=0,2. According to measurements of the solar diameter during the Maunder Minimum, which had varied about 1 arcsecond it can be inferred that the solar constant the solar constant was lower of 3,5W/m2. And this is the reason why there is a variation in contrast between the temperature and the diameter of the Sun as shown in the diagram to the right.

Temperature anomalies and evolution of the solar radius from 1650 to 1990 (data of Jones and al., 1999) as a function of time. Over 300 years, the climate trend correlates with the evolution of the solar ray.

In addition to this variation, the differential rotation of the Sun on itself follows the evolution of the oscillation of the diameter of the Sun. The observation of the movement of sunspots since the early 17^th centuries allowed to follow the evolution of its diameter during the last four centuries.

During the Maunder minimum either when solar activity was very low and the Sun's diameter was bigger that currently, the speed of rotation was 3% lower than the current speed. Furthermore, the observation of sunspots during the last centuries was used to assess the differential rotation. It observed around the Maunder minimum, when there were sunspots, was more pronounced that currently due to a latitudinal gradient of speed greater than now.

In addition to changing the diameter and differential rotation of the Sun on itself according to solar activity, the luminosity also varies. During the low active period of the Sun therefore to the Maunder Minimum it is estimated that its luminosity had declined between 0,2 and 0,3%.