Solar-Cycle Dependence of the Correlation Length for the N-Component of the Magnetic Field From IMP and ACE Observations From 1973 to 2016

Any self-consistent model for the solar-cycle dependence of cosmic ray intensity in the heliosphere, requires information about turbulence quantities (e.g. Engelbrecht and Burger 2013, ApJ). We report on an analysis of 43 years of 1-minute resolution data for the N-component of the magnetic field to study the solar-cycle dependence of the correlation length. Similar previous studies by Wicks et al. (2010, Solar Phys) and Zhao et al. (2018, ApJ), did not find any clear sensitivity to solar activity.

We calculate the second-order structure function from OMNI data, averaged over approximately six-month intervals. The correlation function derived from the second-order structure function is then fitted with an exponential function to find the correlation length. We find an average value of 1.3 hours for the correlation time, well within the nominal range of 0.7 - 4 hours (Borovsky 2012, JGR), or 2.0 Mkm (0.013 AU) for the correlation length. There is a clear positive correlation with solar activity, with an increase of more than a factor of two from solar minimum to solar maximum. A Lomb periodogram shows a peak at 11.5 years, with a false-alarm probability of 0.00066. We note that a similar periodogram for (digitized) data from Wicks et al. (2010, Solar Phys), actually shows a significant peak at 10.3 years, with p = 0.00037. Moreover, Matthaeus et al. (1986, JGR) report a broad but discernible positive correlation between variance and the correlation length. Since it is well-established that magnetic variance is positively correlated with solar activity (e.g. Bieber et al. 1993, JGR; Smith et al. 2006, ApJ), the possibility that the magnetic correlation length has a solar-cycle dependence, cannot be ruled out. This should have a significant effect when modelling cosmic-ray modulation over a solar activity cycle.

This work is based on research supported wholly by the National Research Foundation of South Africa. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the NRF.