Retraction Note: Oscillations of the baseline of solar magnetic field and solar irradiance on a millennial timescale.

This article has been retracted.

Oscillations of the baseline of solar magnetic field and solar irradiance on a millennial timescale.

Recently discovered long-term oscillations of the solar background magnetic field associated with double dynamo waves generated in inner and outer layers of the Sun indicate that the solar activity is heading in the next three decades (2019-2055) to a Modern grand minimum similar to Maunder one. On the other hand, a reconstruction of solar total irradiance suggests that since the Maunder minimum there is an increase in the cycle-averaged total solar irradiance (TSI) by a value of about 1-1.5 Wm-2 closely correlated with an increase of the baseline (average) terrestrial temperature. In order to understand these two opposite trends, we calculated the double dynamo summary curve of magnetic field variations backward one hundred thousand years allowing us to confirm strong oscillations of solar activity in regular (11 year) and recently reported grand (350-400 year) solar cycles caused by actions of the double solar dynamo. In addition, oscillations of the baseline (zero-line) of magnetic field with a period of 1950 ± 95 years (a super-grand cycle) are discovered by applying a running averaging filter to suppress large-scale oscillations of 11 year cycles. Latest minimum of the baseline oscillations is found to coincide with the grand solar minimum (the Maunder minimum) occurred before the current super-grand cycle start. Since then the baseline magnitude became slowly increasing towards its maximum at 2600 to be followed by its decrease and minimum at ~3700. These oscillations of the baseline solar magnetic field are found associated with a long-term solar inertial motion about the barycenter of the solar system and closely linked to an increase of solar irradiance and terrestrial temperature in the past two centuries. This trend is anticipated to continue in the next six centuries that can lead to a further natural increase of the terrestrial temperature by more than 2.5 °C by 2600.

Heartbeat of the Sun from Principal Component Analysis and prediction of solar activity on a millenium timescale.

We derive two principal components (PCs) of temporal magnetic field variations over the solar cycles 21-24 from full disk magnetograms covering about 39% of data variance, with σ = 0.67. These PCs are attributed to two main magnetic waves travelling from the opposite hemispheres with close frequencies and increasing phase shift. Using symbolic regression analysis we also derive mathematical formulae for these waves and calculate their summary curve which we show is linked to solar activity index. Extrapolation of the PCs backward for 800 years reveals the two 350-year grand cycles superimposed on 22 year-cycles with the features showing a remarkable resemblance to sunspot activity reported in the past including the Maunder and Dalton minimum. The summary curve calculated for the next millennium predicts further three grand cycles with the closest grand minimum occurring in the forthcoming cycles 26-27 with the two magnetic field waves separating into the opposite hemispheres leading to strongly reduced solar activity. These grand cycle variations are probed by α - Ω dynamo model with meridional circulation. Dynamo waves are found generated with close frequencies whose interaction leads to beating effects responsible for the grand cycles (350-400 years) superimposed on a standard 22 year cycle. This approach opens a new era in investigation and confident prediction of solar activity on a millenium timescale.