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

Abstract

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 regeression 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.

A history of solar activity over millennia

“…Some models, mostly based on precursor method, succeed in reasonable predictions of a forthcoming solar cycle (i.e., several years ahead), but they do not pretend to extend further in time. On the other hand, many claims of the solar activity forecast for 40-50 years ahead and even beyond that, even millennia ahead (Zharkova et al 2015), have been made recently, often without sensible argumentation. However, so far there is no evidence of any method giving a reasonable prediction of solar activity beyond the solar-cycle scale (see, e.g., Sect.…”

“…Indeed, numerous attempts of this kind have been made even recently (e.g., Nagovitsyn 1997;de Meyer 1998;Rigozo et al 2001;Zharkova et al 2015). Such models aim to find the main feature of the actually-observed sunspot series, e.g., a modulated carrier frequency or a multi-harmonic representation, which is then extrapolated backwards in time.…”

Book of Proceedings: Ninth Workshop, Sunny Beach, Bulgaria, May 30 - June 3, 2017

“…This reasoning confirm the finding of PCA [Zharkova et al, 2012] reporting the secondary latitudinal magnetic field components caused by quadruple sources [Popova et. al., 2013] to have the amplitudes ranging from 0.2 to 0.7 of the dipole one.Extending these model simulations of the joint dipole and quadruple waves to the simulations of the summary curve for the 2000 years, similar to that presented by Fig.6 in [Zharkova et al, 2015] we can obtain the summary curves ( Fig.1) with a quadruple wave with the amplitude a factor 0.3 of the dipole wave amplitude is presented in the top tree plots and the original summary curve derived for dipole waves from observations [Zharkova et al, 2015] in the bottom plot. Fig.1a is obtained for 80 year Gleissberg cycle, Fig1.b for 90 year Gleissberg cycle, and Fig1.c for 100 year Gleissberg cycle.…”

“…If in each layer meridional flows have different amplitudes and tree waves interfere with each other, then we can obtain double beating effect of these waves. Such double beating effect can lead to simultaneous presence of global minima similar to the Maunder minimum and the Gleisberg cycle against the background of 22-year oscillations of the magnetic field.Following the technique presented by [Zharkova et al, 2015] (their formula (1) in section on beating effects) we can estimate periods of waves for obtaining double beating effect. Any two interfering waves with the close cyclic frequencies ω 1 and ω 2 can produce a beating effect with their upper frequency, ω u being the average of these two, ω u = 1/2(ω 1 +ω 2 ) and the lower frequency, ω l , being their difference, ω l = 1/2(ω 1 -ω 2 ).…”

“…We used a simple scheme for the stabilization of the magnetic field growth, namely, the algebraic quenching of the helicity. This scheme assumes Proceedings of Ninth Workshop "Solar Influences on the Magnetosphere, Ionosphere and Atmosphere" Sunny Beach, Bulgaria, May 30 -June 3, 2016 Topic: Sun and Solar Activity), where α 0 (θ) = cosθ is the helicity in the unmagnetized medium and B 0 = ξ --1 is the magnetic field for which the α-effect is considerably suppressed.For two layers consider the latitude distribution of the magnetic field for dipole magnetic sources in the form [Zharkova et al, 2015]:By substituting the chosen set of components of magnetic field into the dynamo equations and collecting the coefficients of the sines with similar arguments, one can obtain a dynamical system of six equations containing the two dipole and one quadruple modes.Suppose that in the third layer a wave is generated from the quadruple source, then we have to consider the latitude distribution of the magnetic field in such form [Popova, 2013]:A dynamical system for quadruple source can be obtained in the similar way as for dipole sources, but expanding the terms to include the quadruple source contributions.In [Popova et. al., 2008] it was shown that periods of dynamo waves are regulated by the amplitude of a meridional flow.…”