Long Term Evolution of Solar Meridional Circulation and Phase Synchronization Viewed Through a Symmetrical Kuramoto Model

The solar-cycle oscillations of the toroidal and poloidal components of the solar magnetic field in the northern solar hemisphere have a persistent phase difference of about \(\pi \). We propose a symmetrical Kuramoto model with three coupled oscillators as a simple way to understand this anti-synchronization. We solve an inverse problem and reconstruct natural frequencies of the top and bottom oscillators under the conditions of a constant coupling strength and a non-delayed coupling. These natural frequencies are associated with angular velocities of the meridional flow circulation near the solar surface and in the deep layer of the solar convection zone. A relationship between our reconstructions of the shallow and the deep meridional flow speed during recent Solar Cycles 21?–?23 is in agreement with estimates obtained in helioseismology and flux-transport dynamo modeling. The reconstructed top oscillator speed presents significant solar-cycle like variations that agree with recent helioseismical reconstructions. The evolution of reconstructed natural frequencies strongly depends on the coupling strength. We find two stable regimes in the case of strong coupling with a change of regime during anomalous solar cycles. We see the onset of a new transition in Solar Cycle 24. We estimate the admitted range of coupling values and find evidence of cross-equatorial coupling between solar hemispheres not accounted for by the model.     

New paleomagnetic result from the Ethiopian flood basalts in the Abbay (Blue Nile) and Kessem gorges

New paleomagnetic investigations on the Ethiopian trap series have been undertaken at the Abbay and Kessem gorges in an attempt to better constrain the 30 Ma paleomagnetic pole of Africa. We sampled six thick massive basaltic lava flows, totaling 230 m, from Abbay Gorge and 10 lava flows, 180 m in thickness, from Kessem Gorge. Detailed paleomagnetic analyses disclosed that the carriers of the characteristic remanent magnetization (ChRM) are different in different lava flows. These are mostly titanomagnetites, titanomaghemites, and magnetite minerals with a broad range of coercive force and blocking temperatures. The heating and cooling susceptibility vs. temperature curves, many of which are irreversible, may indicate chemical remagnetization, notably low temperature maghemitization. Only one flow (KS04) with a clear 580°C Curie temperature was apparently unaffected by chemical remagnetization. The ChRM direction of this flow is identical to that in other flows, which suggests that if and when remagnetization occurred, this was shortly after emplacement of the lava flows. All of the flows sampled have normal polarity. However, a reversed component of low to medium coercive force and low to medium unblocking temperature occurs in flow KS01 at Kessem Gorge. The ChRM directions for the 16 sites are D=3.1°, I=5.8° (α₉₅=12.7°). The paleomagnetic pole obtained from these is at λ=83.0°N, φ=193.3°E (A₉₅=9.0°). Comparison with three previous studies of the traps shows remarkable consistency and a number of means are derived and discussed. Two final preferred poles for the traps are at λ=79.0°N, φ=196.9°E (A₉₅=2.8°) when all 112 published flows are used, and λ=78.7°N, φ=209.4°E (A₉₅=3.4°) when only the 76 flows from the four more recently analyzed sections are included. Both are compatible with the recent reference synthetic pole for Africa of Courtillot and Besse [J. Geophys. Res. (2002) in press]. In that sense, the Ethiopian trap pole is not anomalous and does not require more of a non-dipolar contribution than indicated by analyses of the global paleomagnetic data base covering the last few million years.     

Propagation of an accreting plate boundary: a discussion of new aeromagnetic data in the Gulf of Tadjurah and southern Afar

A detailed aeromagnetic survey of the Republic of Djibouti and immediate surroundings was performed in 1977. This paper summarizes the reduction techniques which are used in order to produce a magnetic anomaly map and discusses the accuracy of this map, which is presented as an insert at a scale of 1/250,000. Two distinct magnetic styles are recognized: linear anomalies with both large amplitude and short wavelength, considered to be typical of oceanic lithosphere, contrast with areas of lower-amplitude longer-wavelength anomalies, which are found mostly in the northern part of the survey. This quiet zone of subdued magnetic style is thought to have undergone major tectonic deformation in the last millions of years. The general morphology of magnetic anomalies is interpreted in terms of a propagating crack model, as proposed by Courtillot [23]. The crack propagates westwards at approximately 3 cm/yr and the crack tip is thought to lie close to Lake Asal, both on the basis of the magnetic data and of other geophysical evidence. The land section of the survey is a central topic of this paper and is interpreted in terms of the crack propagation model in the light of other available geological, geochemical and geophysical data.     

Opening of the Gulf of Aden and Afar by progressive tearing

A new detailed aeromagnetic survey of the Republic of Djibouti and surrounding area reveals a wealth of new information which can be correlated with other data, in particular geologic and tectonic maps. Oceanic magnetic anomalies are identified from the Gulf of Aden westward to the Ghoubbet-Asal rift in Afar. Identification of the anomalies, together with a reinterpretation of earlier magnetic profiles, indicates that rifting started earlier in the east and provides clear evidence for the westward propagation of a crack through the lithosphere at an approximate velocity of 3 cm y^?1. The crack tip is now thought to lie somewhere close to lake Asal and should continue its motion further to the northwest. Some first consequences of this non-rigid model of plate opening are discussed and independent support from a number of sources is obtained.     

Reconstruction of the North–South Solar Asymmetry with a Kuramoto Model

This paper applies a Kuramoto model of coupled oscillators to investigate the north–south (N–S) solar asymmetry and properties of meridional circulation. We focus our study on the asymmetry of the 11-year phase, which is slight but persistent: only two changes of sign (around 1928 and 1968) are observed in the past century. We present a model of two non-linear coupled oscillators that links the hemispheric phase asymmetry of sunspots with the asymmetry of the meridional flow. We use a Kuramoto model with evolving frequencies and constant symmetric coupling to show how asymmetry in meridional circulation could produce a persistent phase lead of one solar hemisphere over the other. We associate the natural frequencies of the two oscillators with the velocities of the meridional flow cells in the northern and southern hemispheres. We assume the respective circulations to be independent and estimate the value of the relevant cross-equatorial coupling by the coupling coefficient in the Kuramoto model. We find that a persistent N–S asymmetry of sunspots and the change of the leading hemisphere could indeed both be the result of the evolving frequencies of meridional circulation; the necessary asymmetry of the meridional flow may be small; and the cross-equatorial coupling has an intermediate range value. Possible applications of these results in solar dynamo models are discussed.     

Identification of Gleissberg Cycles and a Rising Trend in a 315-Year-Long Series of Sunspot Numbers

We show in this short note that the method of singular spectrum analysis (SSA) is able to clearly extract a strong, clean, and clear component from the longest available sunspot (International Sunspot Number, ISN) time series (1700?–?2015) that cannot be an artifact of the method and that can be safely identified as the Gleissberg cycle. This is not a small component, as it accounts for 13% of the total variance of the total original signal. Almost three and a half clear Gleissberg cycles are identified in the sunspot number series. Four extended solar minima (XSM) are determined by SSA, the latest around 2000 (Cycle 23/24 minimum). Several authors have argued in favor of a double-peaked structure for the Gleissberg cycle, with one peak between 55 and 59 years and another between 88 and 97 years. We find no evidence of the former: solar activity contains an important component that has undergone clear oscillations of \(\approx90\) years over the past three centuries, with some small but systematic longer-term evolution of “instantaneous” period and amplitude. Half of the variance of solar activity on these time scales can be satisfactorily reproduced as the sum of a monotonous multi-secular increase, a \(\approx90\)-year Gleissberg cycle, and a double-peaked (\(\approx10.0\) and 11.0 years) Schwabe cycle (the sum amounts to 46% of the total variance of the signal). The Gleissberg-cycle component definitely needs to be addressed when attempting to build dynamo models of solar activity. The first SSA component offers evidence of an increasing long-term trend in sunspot numbers, which is compatible with the existence of the modern grand maximum.     

Kuramoto Model of Nonlinear Coupled Oscillators as a Way for Understanding Phase Synchronization: Application to Solar and Geomagnetic Indices

We apply a Kuramoto model of nonlinear coupled oscillators to the simulation of slow variations of the phase difference between sunspot number [R _I ] and geomagnetic indices [aa and ζ]. The Kuramoto model is described for the particular case of two oscillators connected by symmetric coupling with quasi-stationary behavior, and its properties are investigated. By solving an inverse problem, we reconstruct the evolution of the couplings between pairs of indices [R _I and aa, R _I and ζ, aa and ζ], and interpret these in terms of the physics of the solar dynamo. The de-correlation between R _I and geomagnetic indices found in Solar Cycle 20 by Le Mouël et al. (J. Geophys. Res. 117, A09103, 2012) is successfully reproduced by the Kuramoto model and corresponds to the alternation of the leading oscillator. Application of the Kuramoto model to the cross-correlations [C(R _I ,ζ) and C(aa,ζ)] for ζ-indices computed in eight geomagnetic stations shows the latitudinal dependence of the mean phase difference. We discuss these results in terms of the solar-wind contribution to local geomagnetic indices [ζ].     

On the existence of lateral relative motions on Mars

A preliminary study of photomosaic maps of Mars suggests that large lateral relative motions of a relatively thick lithosphere may have occurred. Transform faults (at two different stages of their evolution) are described, together with a possible triple junction. Diffuse diverging plate boundaries can be found, whereas converging ones remain a problem.