Estimating the Open Solar Flux from In-Situ Measurements

Abstract

A fraction of the magnetic flux threading the solar photosphere extends to sufficient heliocentric distances that it is dragged out by the solar wind. Understanding this open solar flux (OSF) is central to space weather, as the OSF forms the heliosphere, magnetically connects the Sun to the planets, and dominates the motion of energetic particles. Quantification of OSF is also a key means of verifying global coronal models. However, OSF estimates derived from extrapolating the magnetic field from photospheric observations are consistently smaller than those based on heliospheric magnetic field (HMF) measurements, by around a factor two. It is therefore important to understand the uncertainties in estimating OSF from in-situ HMF measurements. This requires both an assumption of latitudinal invariance in the radial component of the HMF in the heliosphere, and that structures without an immediate connection to the Sun, such as local magnetic field inversions (or ‘switchbacks’), can be correctly accounted for. In this study, we investigate the second assumption. Following an established methodology, we use in-situ electron and magnetic data to determine the global topology of the HMF and correct for inversions that would otherwise lead to an overestimation of the OSF. The OSF estimation is applied to the interval 1994 – 2021 and combines measurements from the Wind and ACE spacecraft. This extends the time range over which this methodology has previously been applied from 13 years (1998 – 2011) to 27 years. We find that inversions cannot fully explain the discrepancy between heliospheric and photospheric OSF estimations, with the best heliospheric estimate of OSF still, on average, a factor 1.6 higher than the values extrapolated from photospheric observations.

Application of historic datasets to understanding open solar flux and the 20th-century grand solar maximum. 1. Geomagnetic, ionospheric, and sunspot observations

“…This has resulted in the best estimate of the percentage rise in OSF over the first half of the 20th century changing from 100% in the study by Lockwood et al (2014b) to the 67% found here. The use of strahl electrons is by far the best method devised (Owens et al, 2017b;Frost et al, 2022), and it generates slightly lower excess flux values than the kinematic correction employed by Lockwood et al (2014b). This raises all OSF estimates, and a small rise in OSF estimates for early in the 20th century explains the change in the percent rise estimate.…”

“…Note that the excess flux Δ is accounted for by the intercept of the regression, c and the slope s allows for the mean fractional error μ ϵ introduced by using the Parker spiral theory for annual means (see Figure 11). Table 2 presents the coefficients s and c for the OSF values F S ′ of Frost et al (2022), available for 1995-2020, and the values of F SG from individual geomagnetic index pairs. It should be noted that the correction for excess flux from strahl electrons by Frost et al (2022) provides a slightly larger OSF than the kinematic correction, which was used in past reconstructions by Lockwood et al (2014b).…”

“…Table 2 presents the coefficients s and c for the OSF values F S ′ of Frost et al (2022), available for 1995-2020, and the values of F SG from individual geomagnetic index pairs. It should be noted that the correction for excess flux from strahl electrons by Frost et al (2022) provides a slightly larger OSF than the kinematic correction, which was used in past reconstructions by Lockwood et al (2014b). On the other hand, Figure 11 shows that proper allowance for Parker spiral means we need to reduce OSF by a factor of (1 + μ ϵ ) ≈ 1.2.…”

“…The signed OSF derived this way is presented in Figure 12 and compared with the values of Frost et al (2022) indicated by the blue dots after 1995 in Part A. Before 1995, no suitable strahl data are available, and the blue dots for 1964-1994 are the kinematically corrected values of Lockwood et al (2009a) that have been adjusted using the best-fit linear regression of the excess flux estimates with the Frost et al (2022) values for 1995-2020. This composite of satellite OSF values, corrected for excess flux, F S ′ are plotted along the x-axis in Part B.…”

“…The blue dots in part (A) and x-axis in part (B) are the values from satellite observations that have been corrected using the excess flux. For 1995-2020, excess flux has been derived using strahl electrons by Frost et al (2022Frost et al ( ), but for 1966Frost et al ( -1994 suitable strahl data are available, and the values are kinematically corrected using the method of Lockwood et al (2009a), with values adjusted using the linear regression with the strahl-corrected values for 1995-2020.…”