Reconstruction of Carrington Rotation Means of Open Solar Flux over the Past 154 Years

Abstract

We generate reconstructions of signed open solar flux (OSF) for the past 154 years using observations of geomagnetic activity. Previous reconstructions have been limited to annual resolution, but this is here increased by a factor of more than 13 by using averages over Carrington rotation (CR) intervals. We use two indices of geomagnetic activity, the homogeneous aa index, aaH, and the IDV(1d) index; a combination of the two is fitted to OSF estimates from near-Earth interplanetary satellite data. For 1995 – 2022, these are corrected for excess flux (i.e. orthogardenhose flux and switchbacks) using strahl electrons. For 1970 – 2022, we also use the absolute values of the radial component of the near-Earth interplanetary magnetic field 〈|〈Br〉τ|〉CR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\langle }|{\\langle }B_{r}{\\rangle }_{\ au }|{\\rangle }_{CR}$\\end{document}, where the excess flux is allowed for by adopting the optimum averaging interval τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\ au }$\\end{document} of 20 h. However, in the interval 1970 – 1995, data gaps in the interplanetary data are a serious problem. The errors that these missing data cause in CR averages of OSF are evaluated by synthetically masking data for CRs that have a full complement, using the same number and time series of data gaps as for the CR in question. Given the potential for missing data to generate large errors, we use the near-continuous 1995 – 2022 data to derive the best-fit combination of the geomagnetic data and employ the 1970 – 1995 data for testing in which we can readily allow for the errors caused by data gaps. Errors caused by inaccuracies in the geomagnetic data are shown to be considerably smaller than the uncertainties due to the polynomial fitting. It is shown that the new reconstructions are consistent with the previous annual estimates and that there is considerable variability in the OSF values from one CR to the next; in particular, in high-activity solar cycles, there can be individual CRs in which the OSF exceeds that for adjacent CRs by a factor as large as two.