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New mathematical formula sheds light on solar activity past and future

2nd July 2019

A new mathematical formula has been discovered which allows researchers to accurately plot the Sun’s activity cycles over hundreds of thousands of years.

As well as giving an insight into the Sun’s past activity, the formula also allows scientists to predict future patterns, giving a clearer picture of how conditions might change here on Earth as a result.

The new research, by Professor Valentina Zharkova, of Northumbria University, and academic colleagues from Bradford University, Hull University and Moscow Research University, has now been published in the online journal Scientific Reports.

In their paper, Oscillations of the baseline of solar magnetic field and solar irradiance on a millennial timescale, the authors state that over a period of 2000 years the Sun’s magnetic field, as measured from the Earth, fluctuates from its baseline, both increasing and decreasing in strength.

This is due to the process known as solar inertial motion (SIM), whereby the Sun does not simply rotate on the spot around its own axis, but instead slowly moves around a small almost-circular area at the barycentre of the solar system.

This movement is caused in part by the positions of the larger planets within the solar system, such as Jupiter, Saturn, Uranus and Neptune. Because all planets orbit around the Sun in an elliptical, or oval orbit, their position can vary depending on the stage of their orbit.

In its current cycle of movement, the Sun is slowly moving towards the aphelion of the Earth’s orbit – the point of the orbit furthest away from the Sun.

This will result in the Earth’s orbit becoming more circular, increasing the amount of solar energy to hit the surface of the Earth. This movement will occur over the next 600 years and will slowly lead to an increase in the average terrestrial temperature by around 2.5°C.

During a cycle lasting around 2,000 years, the Sun slowly moves slightly closer (0.02% of the distance from the Earth to the Sun, known as an astronomical unit) to the Earth’s aphelion, the point of the orbit furthest away from the Sun, and further away from its perihelion, the point of the orbit closest to the Sun. This small difference in the solar position can have an impact on the temperature here on Earth.

Through statistical analysis of data gathered during the author’s previous research, as published in Scientific Reports in 2015, Professor Zharkova and her colleagues identified that this cycle of movement, known as a super-grand cycle, takes approximately 2,000 years to complete. They have therefore been able to recreate almost 60 such super-grand cycles, going back 120,000 years.

Their research has established that the current super-grand cycle began sometime between 1645 and 1715, during a period known as the Maunder Minimum during, which the Sun was experiencing far fewer sunspots, and the temperature here on Earth decreased as a result.

The authors state that we are now in the growing, or ‘warming’ phase of the current cycle, which is expected to reach its peak by the year 2600. By this time the temperature on Earth is expected to have increased by between 2.5°C and 3°C.This rise is due to happen in addition to any rise related to man-made activity such as carbon emissions.

The cycle will then enter the ‘cooling’ phase, during which the Sun will move slightly further away from the Earth. This is expected to last until the year 3700.

However, within this current super-grand cycle there will be further variations of solar activity due to the double dynamo effect within the Sun, leading to either an increase or decrease in the frequency and amount of sunspots, as reported in their 2015 paper.

In this earlier research, Professor Zharkova predicts that over the next 33 years the Sun will enter a period of decreased sunspot activity, or grand solar minimum (GSM), leading to a decrease in temperature of between 0.5°C and 1°C.

A second GSM is expected between the years 2370 and 2415. These periods of decreased sunspot activity during grand solar minima (GSMs) will offset the rise of the terrestrial temperatures in the current super-grand cycle imposed by SIM.

Professor Zharkova will present her research at the National Astronomy Meeting 2019 at Lancaster University at 10.16 am on Thursday 4 July.

Her co-authors on this latest paper are S. J. Shepherd of the University of Bradford, School of Engineering; S. I. Zharkov of the University of Hull, Department of Physics and Mathematics;  S.I.3, and E. Popova of Nasir al-Din al-Tusi Shamakhi Astrophysical Observatory in Azerbaijan and the National Research University, Higher School of Economics, in Moscow, Russia.


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