Multiple-coordinate mutual signals of planetary orbits, as dimensionally-compacted estimators, are gravitationally-correlated to sunspot cycle length and variation through magnetohydrodynamic tidal forces and nonlinear coronal feedbacks with solar magnetic field, with respect to the nonstationary distribution of solar wind stream and shock interaction regions.
A series of plots of conventional analyses of time series and Fourier analysis of sunspot and radio flux cyclicity are included below.
Charge potential modulation of electromagnetic field boundary density and coupling relations at vacuum gaps may result from bifurcations and shocks in solar-interplanetary stream interaction regions, intimately related both to the formation and stability of coronal holes, cyclical behavior of ICMEs, and to the triggering of sawtooth trans-magnetospheric mode propgating between Earth, and the interplanetary magnetic field [Cai and Clauer 2013]; deterministic aspects of metastable vacuua in co-rotating interaction regions [Cairns 1999] are expressed in the eigenmodes and eigenphases of sawtooth events. Solstice-Equinox clustering is significant for LIGO events and Sawtooth events, with effective geomagnetic maxima and minima often preceding or following seasonal boundaries with intervals of 3,5,7, and 21 days (consistent with LIGO trigger days) [Cai and Clauer 2013]. Magnetic outflow, mirroring the dynamics of coronal holes, may drive sawtooth events, which may produce transients due to plasma instability at bifurcating vacuum gaps with enhanced solar wind pressure.
Here, the 12-year Jupiter orbit seems to control the Schwabe cycle reciprocally with Earth's orbital perturbation, resulting [with perturbative power from multiple-bodied planetary gravitational harmonics] in strong 8-year sub-cycles. The 6 to 8-year component is strongly-resolved, paired with the 10 to 12-year component in PSDs (with integer z-scores as powers of 2) of solar radio flux and sunspots (SSN). Just as compelling, the165 year orbit of Neptune is also a strong mode in the PSD of solar radio flux. When applied to the available extended sunspot count model after 11-year trend smoothed and with respect to harmonic conjugation, these partitions can be integrated directly (see PSD and DCT analysis below). Mercury and Uranus in relation to the gravitational interplay between the sun and Earth-Moon explain the data better than the norms of consecutive planetary vectors, the orbital paths of intervening planets omitted. These 3-bodied systems are indicated M-E-J and E-J-U. The entire eight-planet system follows the same consecutive rule: M-V-E-M-J-S-U-N.
Examples of event embeddings into extended time domain superpositions I have performed toward the elimination of correlations between LIGO event timing and various geomagnetic, ionospheric, magnetospheric, interplanetary magnetic field, and solar coronal data: time domain histograms (superposed epoch analyses) and statistical functions for solar, IMF/solar wind, magnetosphere, and ionosphere records
These are some admittedly strange (but formally correct) results demonstrating that particular anomalous space weather intervals are also correlated with sawtooth oscillations and magnetospheric proton injection events through LIGO triggers.
[this post is under construction, and additional data sources and references are coming]
The Saturn orbit-asynchronous great storm of 2010-11 is a strong peak in the RMS signal of the mutual orbits of M-V-E-M-J-S-U-N, with respect to body-specific variations in solar distance around barycenter [Sánchez-Lavega et al. 2016]
sunspots, zero daily counts/yr; LIGO GW events, day/yr, luminosity distance
sunspots, zero and all Fibonacci number daily counts/yr; LIGO GW events, day/yr, luminosity distance
Sunspots, January 1749-Feb. 2009, y/x=count/mo.
There should be no multiple-correlations to exact changes in broad, coupled planetary orbit and interplanetary-solar magnetic field change with the timing, distance, energy, and magnitudes of gravitational wave events; this ensemble covariance appears throughout the analysis. Revision of LIGO GW event parameter estimation is now unavoidable, unless coincident sawtooth events are found to be causally independent from LIGO noise floor (which shares power with "signal" during LIGO events and cannot be merely symmetrically subtracted)
A public, exhaustively-controlled, multiply-falsifiable, and analytically/mathematically-rigorous program that applies the most stable numerical methods equally and exhaustively onto all available datasets for any time scale possibly comparable to any possible domain of LIGO GW stochastic-transient density has been lacking. LIGO magnetometer data are not available for O1 or O2, nor data completion/coverage intervals and quality flag times available for O2, which are necessary for calculating the extended joint probability for coincident sampling periods with paired detection.
LIGO has failed to express their concern for checking the complementary fitness of statistical-numerical NR models with the evolution of phase behavior in strain noise surrounding putative GW transients, exceeding GW signal amplitude by an order or magnitude.