Topological diagnostics of the cyclic component of the time series associated with helium

Detection of the deterministic component from noised time series is a common procedure in the solar–terrestrial coupling problem when climate is modeled, solar activity is analyzed, or a signal associated with helium is extracted. Such series are mostly generated by the superposition of different processes for which the concept of a noise component cannot be determined formally. A method based on the combination of time-series topological embedding in Euclidean space and the identification of a persistent cycle by homology theory methods is proposed. The method application is demonstrated based on actual data.     

Solar Activity from the Mid-Second Millennium B.C. to the First Millennium A.D. Based on Radiocarbon Data

Geomagnetism and Aeronomy - The paper reports the results of reconstruction of the heliospheric modulation potential from radiocarbon data for the time interval from the mid-second millennium B.C....     

The Waldmeier rule and early diagnostics of the maximum of the current solar cycle

The well known Waldmeier rule and its modifications applied to forecasting of the solar activity are discussed. The maximum annual mean rate of the increase in the magnetic flux observed on the growth branch of the cycle is proposed as a predicting (diagnosing) parameter for the amplitude of the cycle currently in progress. The maximum Wolf number of the current (24th) cycle is estimated to reach 104 (±12) or more, and to occur in 2013 or later. The yearly average Wolf numbers observed during the 24th cycle are presented.     

Influence of climatic factors on the past atmospheric content of the C-14 isotope

Reconstructions of solar activity in the past epochs based on information on the past atmospheric content of the cosmogenic ¹⁴C isotope are nowadays actively discussed. The ¹⁴C isotope is generated in the atmosphere of the Earth under the influence of cosmic rays, and its concentration in annual tree rings carries information on the past solar activity. However, the concentration of this isotope in annual tree rings may also be influenced by climatic factors. In the present work, the possible correlation between variations in the ¹⁴C atmospheric content and in the Earth’s global temperature from the late 14th century to the middle of the 19th century is studied. It is shown that variations in global temperature may produce changes in the ¹⁴C atmospheric content and consequently have to be taken into account in reconstructions of the past solar activity.     

Solar Activity in the Past: From Different Proxies to Combined Reconstruction

Using proxy series that includes ancient observations of sunspots and auroras, concentrations of cosmogenic isotopes ¹⁴C and ¹⁰Be, we reconstruct sunspot activity level since 850 AD to the present. As a main reference index of solar activity we use the Wolf sunspot numbers, which, as we demonstrate, reflect true levels of the activity in the 18th and 19th centuries better than the Group sunspot numbers. We construct a set of linear and nonlinear inductive models, which are in a good agreement with each other and reproduce the known global solar activity extrema. According to our results, amplitudes of the global maxima are in intermediate positions in respect to estimations of other authors. It follows from our reconstructions that the global maximum of the 20th century is not much higher, if at all, than others.     

Long-Period Cycles of the Sun's Activity Recorded in Direct Solar Data and Proxies

Different records of solar activity (Wolf and group sunspot number, data on cosmogenic isotopes, historic data) were analyzed by means of modern statistical methods, including one especially developed for this purpose. It was confirmed that two long-term variations in solar activity – the cycles of Gleissberg and Suess – can be distinguished at least during the last millennium. The results also show that the century-type cycle of Gleissberg has a wide frequency band with a double structure consisting of 50–80 years and 90–140 year periodicities. The structure of the Suess cycle is less complex showing a variation with a period of 170–260 years. Strong variability in Gleissberg and Suess frequency bands was found in northern hemisphere temperature multiproxy that confirms the existence of a long-term relationship between solar activity and terrestial climate.     

Solar cyclicity during the Maunder minimum

A multifaceted statistical study of all available data on solar activity during the Maunder minimum (1645–1715) is presented. The data include European telescope observations, Asian sunspot observations using the unaided eye, concentrations of cosmogeneous isotopes, and catalogues of polar aurorae. Joint analyses of data on the cosmogeneous isotopes ¹⁰Be and ¹⁴C are a promising source of information on solar activity in the past. The dates of relative sunspot maxima during the Maunder minimum are consistent with the idea that there were chaotic bursts of solar activity randomly distributed in time during this interval. The available evidence that the 11-year cyclicity was preserved in 1645–1715 are worthy of attention but require additional deep study and verification. No convincing evidence for a 22-year periodicity of the occurrence of sunspots during the Maunder minimum has been found.     

Long-period variations in the magnetic field of small-scale solar structures

Thirty small-scale structures in the solar atmosphere, i.e., facula nodes at ±(20°–46°) latitudes, have been studied in order to analyze quasi-periodic variations in the magnetic field. SDO/HMI magnetograms have been used for this purpose. Long-period variations in the magnetic field strength of the considered objects in the 60–280 min range have been revealed as a result of data processing. It has been shown that there are no dependences between the magnetic field and period, nor between the magnetic field and object area. It has been assumed that the discovered variations are not natural oscillations of the magnetic field strength.     

The properties of long-term sunspot oscillations

It is shown that neglecting the motion of sunspots in the plane of the sky in pixels of SOHO MDI magnetograms obtained for the vertical direction results in false periods of 700–1300 min in the long-term oscillations of the magnetic fields of sunspots observed near the central meridian (the Y artefact). The oscillation mode proposed by Efremov, Parfinenko, and Solov’ev in 2012 to be the lowest-frequency sunspot mode is an artefact. A proposed technique for monitoring this artefact using wavelet transforms can be used to study oscillation periods in the range 15 min < T < 500 min. The observational dependence of the oscillation frequency of the sunspot magnetic field on the field strength is constructed using observations of 45 sunspots. This dependence shows a multimode behavior that is consistent with earlier ground observations. One interpretation of this dependence based on the existence of four geometrical oscillation modes detected earlier is proposed.